The net cash flow from the spreadsheet dataset is $290
What is cash flow?The net cash flow is the difference between the total cash inflow and the total cash outflow.
The given parameters are:
Total cash inflow: $2040Total cash outflow: $1750So, we have:
\(Net = \$2040 - \$1750\)
Calculate the difference
\(Net = \$290\)
Hence, the net cash flow is $290
Read more about cash flows at:
https://brainly.com/question/10295065
for the histogram on the right determine whether the mean is greater​ than, less​ than, or approximately equal to the median. justify your answer.
The median exceeds the mean by more. The histogram is skewed to the right, which shows that lower values are dragging down the mean.
The median of the histogram on the right is higher than the mean. This is evident from the histogram's form, which is tilted to the right. This shows that the lower values tend to drag the mean down. The median is greater than the mean. The right-handed skewness of the histogram indicates that the mean is being pulled down by lesser values and However, because it is the centre number and is only impacted by the higher and lower values equally, the median is unaffected by the lower values. Because of this, the mean in this histogram is less than the median.
Learn more about median here
https://brainly.com/question/28060453
#SPJ4
Help me find the slope using the points on the graph below.
Answer:
3/-4 i think
Step-by-step explanation:
one point is -2/1 and the other 2/-2
1 - -2=3
-2 -2=-4
Determine the intercepts of the line
Answer:
If we look at the graph, we can see that the x-intercept is located at (4, 0) and the y-intercept is located at (0, 2.5)
how many perpendicular bisectors can be constructed for a line segment
Answer:
Infinite
Step-by-step explanation:
ANY line segment can have INFINITE bisectors crossing it
prove that: tan[(π/4)+(x/2)] + tan[(π/4)-(x/2)]= 2secx
we will use the formula of tan(A+B)= (tanA+tanB)/(1-tanAtanB)
and tan(A-B)= (tanA-tanB)/(1+tanAtanB)
tan[(pie/4)+(x/2)]= [1+tan(x/2)]/[1-tan(x/2)] ......(1)
tan[(pie/4)-(x/2)]= [1-tan(x/2)]/[1+tan(x/2)]......(2)
now add the equation (1) and (2) which is LHS of question. So we get:
{[1+tan(x/2)]^2 + [1- tan(x/2)]^2}/1-tan^2(x/2)=2[1+tan^2(x/2)]/1-tan^2(x/2)= 2/cosx = 2secx =RHS
Hence proved.
a man 6 feet tall walks at a rate of 1 o feet per second away from a light that is 15 feet above the ground ( see figure). when he is 13 feet from the base of the light, at what rate is the tip of his shadow moving?
The speed of the man's shadow's tip at a distance of 10 feet from the light's base is given by dy/dt = 10 ft/s.
AB is equal to 15 feet in height.
Man's height in CD is 6 feet.
From the diagram attached, if BE = y, we may use the ratio of related triangles to obtain,
15/y = 6/(y - x) (y - x)
to obtain, cross-multiply;
15(y - x) = 6y
15y - 15x = 6y
15y - 6y = 15x
9y = 15x
To get, multiply both sides by 3.
3y = 5x
separating the two sides according to t provides;
dy = dt + dx = 3.
(5/3)(dx/dt dy/dt)
putting yields for dx/dt at 6 ft/s;
dy/dt = (5/3)(6) (6)
dy/dt equals 10 ft/s
One of the many real-world applications of trigonometry is the study of heights and distance. The terms height and distance are frequently used while discussing the applications of trigonometry.
The following ideas are incorporated in the trigonometry application for height and distance:
determining the heights of large mountains or towerscalculating the distance between the beach and the seaMeasurement of the separation between two heavenly bodies
To learn more about height
brainly.com/question/10726356
#SPJ4
Students were given a sensation-seeking test and then divided into two groups based on their scores. A researcher observed how many times students in each group got out of their seats over the course of 2 hours. The dependent variable is:
The dependent variable in this study is the number of times the students got out of their seats over the course of 2 hours.
The independent variable is the variable that is being manipulated or controlled by the researcher.
It is the variable that is expected to cause a change in the dependent variable which is the variable being measured as the outcome or response to the manipulation of the independent variable.
In the given scenario, the independent variable is the group assignment based on the scores on the sensation-seeking test.
The researcher has divided the students into two groups based on their scores, and this grouping is being used as a way of manipulating or controlling the students' level of sensation-seeking behavior.
The researcher is interested in how this manipulation affects the students' behavior in terms of getting out of their seats.
The dependent variable is the number of times the students got out of their seats over the course of 2 hours.
This variable is expected to vary depending on the level of the independent variable, which is the group assignment based on the sensation-seeking test scores.
The researcher will measure the dependent variable for each group separately and then compare the results to determine if there is a significant difference between the two groups.
In summary,
The independent variable is the grouping of the students based on their scores on the sensation-seeking test and the dependent variable is the number of times the students got out of their seats over the course of 2 hours.
For similar question on dependent variable:
https://brainly.com/question/29430246
#SPJ11
What is the greatest common factor of the terms in the expression StartFraction 7 over 3 EndFraction a b minus StartFraction 7 over 6 EndFraction b? One-third b One-third a b 7 b 7 a b
Answer:
(C)7b
Step-by-step explanation:
Given the expression:
\(\dfrac{7}{3}ab-\dfrac{7}{6}b\)
Let us factor the expression:
\(=\dfrac{7b}{3}\left(a-\dfrac{1}{2}\right)\)
Since we need the greatest common factor, we can rewrite the expression as:
\(7b\left(\dfrac{1}{3}a-\dfrac{1}{6}\right)\)
Therefore, the greatest common factor is 7b.
The correct option is C.
Answer: C. 7 b
Step-by-step explanation:
Got it right on edge
Geometry. Math nation section 3
∠g and ∠h are complementary angles and ∠g and ∠h are acute angles are true statements from the given information
Two angles are given.
∠g = (2x-90)°
∠h = (180-2x)°
We have to find the statement which is true about the angles g and h.
If both angles are greater than zero.
Complementary angles add up to 90 degrees
i.e., ∠g and ∠h are complementary if ∠g + ∠h = 90°.
Substituting the given values:
∠g + ∠h
= (2x-90)° + (180-2x)° = 90°
Thus, ∠g and ∠h are complementary angles.
and both the angles are less than 90 degrees so we can tell that angles ∠g and ∠h are acute.
So the statement ∠g and ∠h are acute angles is also true
Hence, ∠g and ∠h are complementary angles and ∠g and ∠h are acute angles are true statements
To learn more on Angles click:
https://brainly.com/question/28451077
#SPJ1
In the Florida Lottery Cash4Life game a player must select five numbers from 1 to 60 and then one Cash Ball number from 1 to 4. He will win the jackpot of $1000 a day for life if all five numbers and the Cash Ball match the winning numbers drawn on Monday nights. He will win $1000 a week for life if just all 5 numbers match the winning numbers. Assuming that the numbers are equally likely to be
drawn, determine:
(a) (5) The probability that the player will $1000 a day for life;
(b) (5) The probability that the player will $1000 a week for life;
The probability of winning $1000 a day for life is approximately 5.245 x 10^-11 and the probability of winning $1000 a week for life is approximately 1.07 x 10^-8. The probability of winning the jackpot ($1000 a day for life) is 1/(60^5 * 4), while the probability of winning $1000 a week for life is 1/(60^5).
In the Florida Lottery Cash4Life game, a player must select five numbers from 1 to 60 and then one Cash Ball number from 1 to 4. The jackpot prize is $1000 a day for life if all five numbers and the Cash Ball match the winning numbers drawn on Monday nights. If just all five numbers match the winning numbers, the player will win $1000 a week for life.
To determine the probability of winning $1000 a day for life, we can use the formula for the probability of independent events: P(A and B) = P(A) x P(B)
(a) To win the jackpot of $1000 a day for life, the player needs to match all five numbers and the Cash Ball. There are 60 options for each of the five numbers and 4 options for the Cash Ball. The total number of possible outcomes is 60^5 (60 choices for each of the five numbers) times 4 (for the Cash Ball). So the probability of winning the jackpot is 1/(60^5 * 4). (b) To win $1000 a week for life, the player needs to match only the five numbers, without considering the Cash Ball. The total number of possible outcomes for this scenario is 60^5. Therefore, the probability of winning $1000 a week for life is 1/(60^5).
To know more about probability visit:-
https://brainly.com/question/32201909
#SPJ11
Based on Exercise 9, prove that τ and σ are multiplicative. That is, prove that if m and n are relatively prime, then τ(mn)=τ(m)τ(n) and σ(mn)= σ(m)σ(n).
To prove that τ and σ are multiplicative, we need to show that if m and n are relatively prime, then τ(mn) = τ(m)τ(n) and σ(mn) = σ(m)σ(n).
To prove τ(mn) = τ(m)τ(n), we can start by considering the prime factorization of m and n. Let's say m = p₁^a₁ * p₂^a₂ * ... * pₖ^aₖ and n = q₁^b₁ * q₂^b₂ * ... * qₙ^bₙ, where p₁, p₂, ..., pₖ and q₁, q₂, ..., qₙ are distinct prime numbers. Since m and n are relatively prime, none of their prime factors overlap.
Now, the divisors of mn are the numbers of the form p₁^x₁ * p₂^x₂ * ... * pₖ^xₖ * q₁^y₁ * q₂^y₂ * ... * qₙ^yₙ, where 0 ≤ xᵢ ≤ aᵢ and 0 ≤ yⱼ ≤ bⱼ. Thus, the number of divisors of mn, τ(mn), can be calculated by multiplying the number of divisors of m, τ(m), with the number of divisors of n, τ(n). Hence, τ(mn) = τ(m)τ(n).
To prove σ(mn) = σ(m)σ(n), we can again use the prime factorization of m and n. Similar to the previous proof, the sum of divisors of mn, σ(mn), can be calculated by multiplying the sum of divisors of m, σ(m), with the sum of divisors of n, σ(n). Hence, σ(mn) = σ(m)σ(n).
Therefore, we have proved that τ and σ are multiplicative when m and n are relatively prime.
To know more about relatively prime visit:
https://brainly.com/question/4658673
#SPJ11
We have shown that both τ and σ are multiplicative functions, satisfying the properties τ(mn) = τ(m)τ(n) and σ(mn) = σ(m)σ(n) for relatively prime numbers m and n.
To prove that τ (the number of positive divisors) and σ (the sum of positive divisors) are multiplicative functions, we need to show that for any two relatively prime numbers, m and n, the following properties hold:
1. τ(mn) = τ(m)τ(n)
2. σ(mn) = σ(m)σ(n)
Let's start with property 1:
1. τ(mn) = τ(m)τ(n)
If m and n are relatively prime, it means that they do not share any prime factors. Therefore, the divisors of mn are formed by taking a divisor of m and a divisor of n. Each divisor of mn can be uniquely expressed as the product of a divisor of m and a divisor of n.
Since the number of divisors of mn is equal to the product of the number of divisors of m and the number of divisors of n, we can conclude that τ(mn) = τ(m)τ(n).
Now let's move on to property 2:
2. σ(mn) = σ(m)σ(n)
Similar to property 1, we can express the sum of divisors of mn as the sum of products, where each product is formed by taking a divisor of m and a divisor of n. Again, since m and n are relatively prime, their divisors are distinct.
Using the distributive property, we can expand the sum of products as the sum of two separate terms: one involving the divisors of m and another involving the divisors of n. The sum of divisors of mn is therefore equal to the product of the sum of divisors of m and the sum of divisors of n.
Hence, we can conclude that σ(mn) = σ(m)σ(n).
Learn more about multiplicative functions
https://brainly.com/question/5873041
#SPJ11
You are a sales account executive earning $1500 per month plus 6% commission on the amount of sales. Your goal is to earn a minimum of $5100 per month. What amount of sales will enable you to earn $5100 or more per month?
Answer:
$60000.
Step-by-step explanation:
Total income needed is $5,100. Subtract the BASE pay of $1,500 to get the amount of commission needed to earn. This would be $3,600. The equation to solve for is: $3,600 is 6% of X. Take $3,600 and divide by .06 (or 6%). This gives you the answer of $60,000.
To check your work, take $60,000 and multiply by 6%. This will get you back to $3,600. Add back the $1,500 and you have $5,100. If you want to make more than $5,100, then increase your sales above $60,000.
Select the property of equality used to arrive at the conclusion. If x = 4, then 5x = 20 the addition property of equality the multiplication property of equality the subtraction property of equality the division property of equality
Answer:
It’s actually multiplication property of equality
Step-by-step explanation:
I just did an Assignment and someone said it was division, and it was wrong, it says the correct answer is multiplication
Answer:
The correct answer is multiplication.
Step-by-step explanation:
please help
A survey is taken at a movie theater in Winterville. The first 150 people who entered the theater were asked about their favorite type of movie. What is true about this situation?
The population is the first 150 people at the theater, and the sample is the total number of people who go to the movie theater.
The population is the number of people who go to the movie theater, and the sample is the number of people in the town of Winterville.
The population is the total number of people who go to the movie theater, and the sample is the first 150 people at the theater.
The population is the number of people in the town of Winterville, and the sample is the number of people who go to the movie theater.
The population is the total number of people who go to the movie theater, and the sample is the first 150 people at the theater is correct.
In this situation, the population refers to the entire group of individuals that are of interest to the survey. In this case, the population is the total number of people who go to the movie theater. The sample, on the other hand, refers to a subset of the population that is actually observed and surveyed. In this case, the sample is the first 150 people who entered the theater and were asked about their favorite type of movie.
It is important to note that the sample should be representative of the population in order to draw valid conclusions from the survey. This means that the individuals in the sample should be selected in a way that reflects the characteristics of the population as a whole.
In summary, the population in this situation is the total number of people who go to the movie theater, and the sample is the first 150 people at the theater who were asked about their favorite type of movie.
for such more question on population
https://brainly.com/question/13769205
#SPJ11
Let t = 4 and u = 6 + 2i. Find t – u
Step-by-step explanation:
t = 4
u = 6 + 2
Find t - u
solu
t - u
= 4 - ( 6 + 2 ) = 4 - 8
Answer is -4
The value of t-u is -2(1+i).
What is a complex number?
The complex number is basically the combination of a real number and an imaginary number.
How to subtract two complex number?For the subtraction of two complex numbers we subtract real part from the real and imaginary from imaginary.
According to the given question.
We have two complex numbers
t = 4 + 0i and u = 6 + 2i
Therefore,
\(t - u = 4+ 0i - ( 6 + 2i)\)
⇒\(t - u = 4 + 0i - 6 - 2i\)
⇒\(t - u = -2 -2i\)
⇒\(t - u = -2(1+i)\)
Hence, t - u = -2(1 + i).
Find out more information about complex numbers here:
https://brainly.com/question/10251853
#SPJ2
HELP pls will mark you the brainliest
From the given graph solution of lines is (32, 5).
What is a linear system of equations?A system of linear equations consists of two or more equations made up of two or more variables such that all equations in the system are considered simultaneously. The solution to a system of linear equations in two variables is any ordered pair that satisfies each equation independently.
To solve a system of linear equations graphically we graph both equations in the same coordinate system. The solution to the system will be in the point where the two lines intersect.
In the give graph two lines intersect at (32, 6).
Here, 32 represents the number of kites and 6 represents the total cost.
Therefore, from the given graph solution of lines is (32, 5).
To learn more about the linear system of an equations visit:
https://brainly.com/question/27664510.
#SPJ1
Miles makes $14 per hour but has to pay $55 for his cellphone bill.
The number of hours used is 3.93 hours
How to determine the number of hoursFrom the question, we have the following parameters that can be used in our computation:
Rate = $14 per hour
Amount = $55
Using the above as a guide, we have the following:
Time = Amount/Rate
Substitute the known values in the above equation, so, we have the following representation
Time = 55/14
Evaluate
Time = 3.93
Hence, the time is 3.93 hours
Read more about rates at
https://brainly.com/question/26757196
#SPJ1
6
AXYZ will be translated so that the coordinates of X' are (5,11).
y
Y
14
13
12
X
11
10
9
8
N
7
6
5
4
3
2
1
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14
What will be the coordinates of Z' ?
(5,8)
B (6,7)
© (7,6)
D (8,5)
Answer:
Isometry: An isometry is a transformation that maintains congruency. This means that the transformation does not change the figure's size or shape.
Make sure your child is familiar with the Cartesian coordinate system including the horizontal x-axis, the vertical y-axis, and the (x,y) convention used for locating points.
If you have not already done so, you may wish to review this congruency lesson with your child.
Translations
This section will help your child to translate congruent figures on a Cartesian plane. It will also introduce translation vectors which show the distance and direction of the translation.
Translations
Figure J is the pre-image. Figure S is translated.
A figure is a translation if it is moved without rotation.
Translation Vector
A Translation Vector is a vector that gives the length and direction of a particular translation. Vectors in the Cartesian plane can be written (x,y) which means a translation of x units horizontally and y units vertically.
figure being translated
Vectors translations can be written as shown in either of these two ways:
format example for writing vectors
This vector can be said to be ray AB or vector D.
You translate a figure according to the numbers indicated by the vector. So if one point on a figure has coordinates of (-3,3) and the translation vector is (-1,3), the new coordinate is (-4,6). You add or subtract according to the signs in the numbers in the vector.
Work through the two examples below with your child to see how to apply translation vectors.
square translated on cartesian grid
The red square's coordinates are:
(-4,3); (-4,8); (-9,3); (-9,8).
What are the coordinate pairs under a translation vector of (1,-1) as shown by the blue square?
The new coordinates are:
(-3,2); (-3,7); (-8,2); (-8,7).
You can see that the translation did not move the figure far because the vector translation is small.
square translated on cartesian grid
We will try a different vector translation of (3,-9) on the same red square
The new coordinates are:
(-1,-6); (-1,-1); (-6,-6); (-6,-1).
Get you child to try the next example. Do not look at the answer until he or she has tried to work it through the task.
single triangle on cartesian grid
Task: Translate ΔABC with a vector translation of (6,-2)
Steps:
Find the coordinates of Δ ABC.
Add 6 to the X coordinates and subtract 2 (or add -2) from the Y coordinates.
Plot the new coordinates on the grid.
Answer and Explanation
Coordinates of ΔABC are:
(-5,1); (-2.5,7); (0,1)
Add 6 and subtract 2
A1 = (-5 + 6, 1 - 2) = (1,-1)
B1 = (-2.5 + 6, 7 - 2) = (3.5,5)
C1 = (0 + 6, 1 - 2) = (6,-1)
Plot ΔA1B1C1
Rotations
This section will show your child how to rotate a figure about the origin on a Cartesian plane. Work through the two examples below:
Note: Make sure your child knows that the origin is the intersection of the X and Y axes; (0,0) on the Cartesian plane.
Rotation Transformation: Example 1
Look at the four triangles on the Cartesian plane below. Each one is rotated about the origin as shown in the table.
Triangle B Triangle C Triangle D
90° rotation of Triangle A about the origin 90° rotation of Triangle B about the origin 90° rotation of Triangle C about the origin
180° rotation of Triangle A about the origin 180° rotation of Triangle B about the origin
270° rotation of Triangle A about the origin
The coordinates are:
Triangle A (-2,2) (-10,2) (-6,8)
Triangle B (2,2) (2,10) (8,6)
Triangle C (2,-2) (10,-2) (6,-8)
Triangle D (-2,-2) (-2,-10) (-8,-6)
Note the pattern in the coordinates for corresponding vertices on the triangles.
Rotation Transformation: Example 2
The coordinates of Pentagon ABCDE are:
(0,4); (7,4); (9,2); (7,0); (0,0)
Pentagon ABCDE is rotated 180° about
the origin making the coordinates of
Pentagon A1B1C1D1E1:
(0,-4); (-7,-4); (-9,-2); (-7,0); (0,0)
Note how the coordinates of
corresponding vertices are opposite
integers (just the +/- sign is different).
This is always the case with 180°
rotations about the origin.
Reflections
This section will help your child to reflect a figure over an axis on a Cartesian plane
Work through the two reflection examples below.
Reflection Transformation: Example 1
The coordinates of LMNO are:
(-7,5); (0,5); (-2,1); (-5,1)
LMNO is reflected over the X-axis
making the coordinates of
L1M1N1O1:
(-7,-5); (0,-5); (-2,-1); (-5,-1)
Note how the x-coordinates remain the
same but the y-coordinates change to
their opposite integer (i.e. the sign changes).
This is always the case with reflections over the X-axis.
Step-by-step explanation:
The solution is, the coordinates of Z' will be z' = (6,7),
i.e. option B is correct.
What is transformation?A transformation is a dramatic change in form or appearance. An important event like getting your driver's license, going to college, or getting married can cause a transformation in your life. A transformation is an extreme, radical change.
here, we have,
Given that,
X' are (5,11).
now, See attachment
Required that,
The image of Z i.e. z'
From the attachment:
X =(7,11)
This implies that:
X' = ( x- 2, y)
Using the same rule for z;
z=(8,7)
z' = (8-2, 7)
z' = (6,7)
Hence, The solution is, the coordinates of Z' will be z' = (6,7),
i.e. option B is correct.
To learn more on transformation click:
brainly.com/question/20211457
#SPJ7
which of the gollowing cirxles lie completely within the third quadrant? Check all that apply
Option B
Option C
These two circles lie completely within the third quadrant
Answered by GAUTHMATH
A school recorded it's students heights at the begining and end of the year
A school recorded the heights of its students at the beginning and end of the year.
The purpose of this recording is to track the growth and development of the students over the course of the year.
By measuring the heights of the students at the beginning and end of the year, the school can analyze the growth patterns of the students. This data provides valuable insights into the physical development of the students and can be used for various purposes.
It helps monitor the overall health and well-being of the students and can also be used to identify any abnormal growth patterns or potential health issues. Additionally, the recorded heights can be compared to standard growth charts to assess whether the students' growth is within the normal range for their age and gender.
This information is useful for parents, educators, and healthcare professionals in understanding the physical development of the students.
To learn more about data click here:
brainly.com/question/31680501
#SPJ11
How can you determine how many liters of oil the prop maker should purchase for a miniature tank car built with a scale factor of 1 to 24
The prop maker should purchase 3,166.7 liters of oil for the miniature tank car built with a scale factor of 1 to 24.
How to estimate the quantity of oil the prop maker should purchase?To find out how many liters of oil the prop maker should purchase for a miniature tank car built with a scale factor of 1 to 24, we shall use the ratio of the volumes of the actual tank car and the miniature tank car:
Volume ratio = (miniature tank car volume) divided by (actual tank car volume)
Given:
Actual tank car volume = 76,000 L
Scale factor = 1:24
Miniature tank car volume = (1/24) x (actual tank car volume)
= (1/24) x 76,000 L
= 3,166.67 L
Therefore, the prop maker should purchase 3,166.7 liters of oil for the miniature tank car.
Learn more about ratio at brainly.com/question/12024093
#SPJ1
Question completion:
Your Question was incomplete. Find below the full content:
A prop maker is working on a miniature tank car for a train derailment scene in which all the oil spills out of a tank car. The actual tank car can carry up to 76,000 L of oil. How many liters of oil should the prop maker purchase for a miniature tank car built with a scale factor of 1 to 24?
Who prepares the questions for grade 7 math worksheets?
The questions for grade 7 math worksheets are typically prepared by math teachers, curriculum specialists, and educational publishers.
These professionals use their knowledge of math concepts and pedagogy to create questions that are appropriate for the grade level and aligned with educational standards.
Additionally, they may use feedback from students and other teachers to refine the questions and ensure they are effective for teaching and learning. It is important for the questions to be clear, accurate, and challenging in order to help students develop their math skills and prepare for more advanced concepts.
To know more about pedagogy click on below link:
https://brainly.com/question/30400049#
#SPJ11
The high temperature Monday was 4 degrees. The low temperature was -7 degrees. What is the difference between the high and low temperatures?
Answer:
Hey there!
We are trying to find the difference between 4 and -7
We can write -7+x=4, where x is the difference we are trying to find.
Solving for x, we get that the difference is 11.
Let me know if this helps :)
The difference between the high and low temperatures is 11 degrees.
Given :
The high temperature Monday was 4 degrees.
The low temperature was -7 degrees.
We need to find the difference between high and low temperatures .
To find the difference ,we subtract low temperature from high temperature
High temperature - low temperature
\(High - low \; temperature \\4-(-7)\\4+7\\11\)
The difference between the high and low temperatures is 11 degrees.
Learn more : brainly.com/question/4600267
5x - 10 = 0 in division property of equality form
Answer:
x = 2
Step-by-step explanation:
5x = 10
x = 2
a store buys jackets for $49.99 . the markup on the jacket is $18.49.during the sales,the jacketsare sold for 57.99. what is the markup during the sales?
Step-by-step explanation:
$1,999 minds right Jitpur defective defective here note justice Jhapa Jhapa here's
convex quadrilateral has and . diagonals and intersect at , , and triangles and have equal areas. what is ?
Triangle AED and triangle BEC have equal areas. The length of AE can be represented as 14 - x (since AC = 14). AE is equal to 10.
To find the length of AE, we can use the fact that triangle AED and triangle BEC have equal areas. Since the areas of two triangles with the same height are proportional to their base lengths, we can set up the following proportion:
Area of triangle AED / Area of triangle BEC = AE / EC
Let's denote EC as x (the length of EC). Then, the length of AE can be represented as 14 - x (since AC = 14).
Now, let's look at the given information about the lengths of the sides of the quadrilateral:
AB = 9
CD = 12
AC = 14
We can use the given information to find the lengths of the other sides of the quadrilateral:
BC = AC - AB = 14 - 9 = 5
AD = AC - CD = 14 - 12 = 2
Next, we can calculate the areas of triangle AED and triangle BEC using the lengths of their sides:
Area of triangle AED = (1/2) * AD * AE
Area of triangle BEC = (1/2) * BC * EC
Since the areas of the two triangles are equal, we can set up the following equation:
(1/2) * AD * AE = (1/2) * BC * EC
Plugging in the values we know:
(1/2) * 2 * (14 - x) = (1/2) * 5 * x
Simplifying the equation:
14 - x = (5/2) * x
Multiplying both sides by 2 to clear the fraction:
28 - 2x = 5x
Adding 2x to both sides:
28 = 7x
Dividing both sides by 7:
x = 4
Therefore, the length of EC is 4.
Since AE = AC - EC, we can calculate AE:
AE = 14 - EC = 14 - 4 = 10
So, AE is equal to 10.
To learn more about triangles visit:
brainly.com/question/11070154
#SPJ11
The complete question is:<Convex quadrilateral ABCD has AB = 9 and CD = 12. Diagonals AC and BD intersect at E, AC = 14 and triangle AED and triangle BEC have equal areas. What is AE?>
Need help plz ill give brainliest
Answer:
Equation: 145 = 12x + 13
x = 11
FGE = 35
CGE = 110
Step-by-step explanation:
-6
co
3
PLAY
PARTA
In order to isolate z, you need to
both sides by
Answer:
multiply both sides by three
Please can someone answer this
Answer:
Greatest Number of Teams: 8
Number of Girls per Team: 5
Number of Boys per Team: 4
Step-by-step explanation:
32÷8=4
40÷8=5
Sonali purchased some pants and skirts the numbers of skirts is 7 less than eight times the number of pants purchase also number of skirt is four less than five times the number of pants purchased purchased
Sonali purchased some pants and skirts the numbers of skirts is 7 less than eight times the number of pants purchase also number of skirt is four less than five times the number of pants purchased is 1 pant and 1 skirt.
Let's denote the number of pants Sonali purchased as P and the number of skirts as S. We're given two pieces of information:
1. The number of skirts (S) is 7 less than eight times the number of pants (8P). This can be represented as S = 8P - 7.
2. The number of skirts (S) is also 4 less than five times the number of pants (5P). This can be represented as S = 5P - 4.
Now we have a system of two linear equations with two variables, P and S:
S = 8P - 7
S = 5P - 4
To solve the system, we can set the two expressions for S equal to each other:
8P - 7 = 5P - 4
Solving for P, we get:
3P = 3
P = 1
Now that we know P = 1, we can substitute it back into either equation to find S. Let's use the first equation:
S = 8(1) - 7
S = 8 - 7
S = 1
So, Sonali purchased 1 pant and 1 skirt.
Know more about linear equations here:
https://brainly.com/question/26310043
#SPJ11