Answers
Answer:
See below
Step-by-step explanation:
GivenR is the midpoint of SQ and PTTo proveΔPQR ≅ ΔTSRSolutionR is the midpoint of SQ
SR = 1/2SQ and RQ = 1/2SQ ⇒ SR ≅ RQR is the midpoint of PT
PR = 1/2PT and RT = 1/2PT ⇒ PR ≅ RTSQ and PT intersect at point R ⇒
∠PRQ ≅ ∠TRS as vertical anglesTriangles PQR and TSR have two sides and the included angle congruent, therefore:
ΔPQR ≅ ΔTSR,as per SAS congruence postulate
If two sides and the included angle in one triangle are congruent to two sides and the included angle in another triangle, then the two triangles are congruentRelated Questions
A tree planted today has a height of 5 feet and grows one foot each month.
Is the height of the tree a function of the number of months? If so, is it a linear or a nonlinear function?
A. Yes, it's a linear function
B. Yes, it's a nonlinear function
C. No
Answers
Answer:
Liner function
x = 5 + n
Step-by-step explanation:
Given:
Height of tree = 5 ft
Grow per month = 1 ft
Find:
Equation:
Computation:
Assume;
New height of tree x
Number of month = n
x = 5 + 1(n)
x = 5 + n
Triangle 1 and triangle 2 are similar right triangles formed from a ladder leaning against a building.
Determine the distance from the bottom of the building to the point where the ladder is touching the building for triangle 2.
4 feet
7 feet
9 feet
14 feet
Answers
The distance from the bottom of the building to the point where the ladder is touching the building for Triangle 2 is 14 feet.
What is triangle?
A triangle is a polygon with three sides and three angles. It is one of the most basic geometric shapes and is often used in geometry, trigonometry, and other branches of mathematics.
Since Triangle 1 and Triangle 2 are similar right triangles formed from the same ladder leaning against the same building, their corresponding sides are proportional to each other.
Let's use the concept of similarity and proportions to solve for the unknown distance in Triangle 2. We can set up the following proportion based on the corresponding sides of the two triangles:
(vertical leg of Triangle 1) : (horizontal leg of Triangle 1) = (vertical leg of Triangle 2) : (horizontal leg of Triangle 2)
We know that in Triangle 1:
the length of the hypotenuse (the ladder) is 16 feet
the length of the horizontal leg (the distance along the ground) is 8 feet
the length of the vertical leg (the distance from the bottom of the building to the point where the ladder is touching the building) is 16 feet
Using the Pythagorean Theorem, we can solve for the length of the vertical leg of Triangle 2:
(vertical leg of Triangle 1) : (horizontal leg of Triangle 1) = (vertical leg of Triangle 2) : (horizontal leg of Triangle 2)
16 : 8 = (vertical leg of Triangle 2) : 7
Simplifying the proportion, we get:
2 : 1 = (vertical leg of Triangle 2) : 7
To solve for the vertical leg of Triangle 2, we can multiply both sides of the proportion by 7:
2 * 7 : 1 * 7 = (vertical leg of Triangle 2)
14 : 1 = (vertical leg of Triangle 2)
Therefore, the distance from the bottom of the building to the point where the ladder is touching the building for Triangle 2 is 14 feet.
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Match the name with the correct figure help please!!!
Answers
Answer:
B Is the right one that the answer
Determine, to the nearest tenth, the perimeter of the triangle shown in the accompanying diagram.
This is a diagram of triangle ABC. Point A is located at (-9,6). Point B is located at (-3,10). Point C is located at (-2,2).
Answers
Answer:
23.3
Step-by-step explanation:
if y varies direckly as x and y =12 when x = 4, find y when x = 12.
Answers
SOMEONE ANSWER THIS REALLY QUICK
Answers
Answer:
jk= 10 units
kl= 5 units
Step-by-step explanation:
just trust me lol
Answer:
JK = 10 units
KL = 5 units
Step-by-step explanation:
JK + KL = JL
When doing these types of problems, always try to solve the unknown variable before you solve the equations.
Solve for x:
-x + 15 + 2x - 5 = 15
x + 10 = 15
x = 5
Now plug in the x into the 2 equations,
JK = - (5) + 15
JK = 10 units
KL = 2(5) -5
KL = 10 - 5
KL - 5 units
i hope this helps you! :D
A rectangular storage container without a lid is to have a volume of 10 m3. the length of its base is twice the width. material for the base costs $15 per square meter. material for the sides costs $9 per square meter. let w denote the width of the base. Find a function in the variable w giving the cost C in dollars) of constructing the box.
Answers
The function in variable w giving the cost C (in dollars) of constructing the box is C(w) = 30w² + 270/w. The result is obtained by using the formula of volume and area of the box.
How to determine the function?We have a rectangular storage container without a lid.
Volume, V = 10 m³Length, l = 2wWidth, w = wBase costs $15/m²Sides costs $9/m²The formula of volume of the box is
V = l × w × h
Where
l = lengthw = widthh = heightSo, the height is
10 = 2w × w × h
10 = 2w² × h
h = 10/2w²
h = 5/w²
To find the total cost, calculate the area of base and sides of the box!
See the picture in the attachment!
The base area is
A₁ = 2w × w = 2w² m²
The sides area is
A₂ = 2(2wh + wh)
A₂ = 2(3wh)
A₂ = 6wh
A₂ = 6w(5/w²)
A₂ = 30/w m²
The total cost is
C = $15(2w²) + $9(30/w)
C = $30w² + $270/w
The function of the total cost is
C(w) = 30w² + 270/w
Hence, the function of constructing the box is C(w) = 30w² + 270/w.
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Hi! I hope u can help but I least quickly if possible :D
Answers
find the area (in cm2) of the largest rectangle that can be inscribed in a right triangle with legs of lengths 3 cm and 8 cm if two sides of the rectangle lie along the legs.
Answers
The area of the largest rectangle that can be inscribed in the right triangle is calculated to be 6 cm^2
As we know that for a rectangle of width W and length L the area is given as;
A = L × W
Now let's say that L is along the 8 cm side and W is along the 3 cm side, let's find a relation between these two.
When we inscribe the rectangle in the larger triangle the quotient between the catheti of the right triangle must be equal to the quotient of the catheti of the right triangle that is generated.
Therefore that new triangle will have legs equal to the;
8cm - L and W.
Then we have that:
8cm - L / W = 8 cm / 3 cm
L = 8 cm - 8/3 × W
Now we can write L in terms of W so that we can replace that in the area equation to get
A = (8cm - (8/3)×W)×W = 8cm×W - (8/3)×W^2
This is the equation we have to maximize, also this is a quadratic polynomial of negative leading coefficient, which means that the maximum is at the vertex.
As we know the vertex of the general quadratic polynomial;
a × x^2 + b × x + c
is at:
x = -b / 2a
Then, in this scenario, the vertex is at;
W = (-8 cm) / (2 × 8/3) = 1.5 cm
Then the length is given by:
L = 8cm - (8/3) × 1.5cm = 4 cm
Therefore the area of the largest rectangle that can be inscribed in the given right triangle is;
A = 1.5 cm × 4 cm = 6 cm^2
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What type of variable is the number of auto accidents reported in a given month q?
Answers
Answer:
Discrete
Step-by-step explanation:
Discrete is the type of variable in which the number of auto accidents reported in a given month q
Discrete data is a count that uses integers and has a finite number of potential values. This sort of information can't be broken down into smaller chunks. Discrete data consists of finite, numeric, countable, and non-negative integers with discrete variables.
As we know that the number of auto accidents that can be reported in a month will be always a whole number, therefore, the number of accidents can be represented as 0, 1, 2,..., 1000, etc.
Thus, the type of variable is the number of auto accidents reported in a given month is Discrete.
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14137.17 in terms of pi
Answers
Answer:64π cm2
Step-by-step explanation:your welcome
What is the value of x in the matrix equation below?
3
8
х
10
Х
-2
3
5
-1
6
-7 -4
0 -1
ОО
1
Answers
Answer:
The horizontal value in a pair of coordinates: how far along the point is. The X Coordinate is always written first in an ordered pair of coordinates (x,y), such as (12,5). In this example, the value "12" is the X Coordinate. Also called "Abscissa" See: Coordinates.
Step-by-step explanation:
The value of x in the matrix is 1.
Option D is the correct answer.
What is a matrix?Matrix is a form of writing items in rows and columns.
We have,
From the matrix addition, we can write as,
-2x + 3 = x
Now,
Combining the like terms.
-2x - x + 3 = 0
-3x = -3
Dividing 3 into both sides.
-x = -1
x = 1
Thus,
The value of x in the matrix is 1.
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A square tile mesures 20 cm by 20cm a rectangular tile is 3 cm longer and 2 cm narrower. What is the different in area between the two tiles?
Answers
Answer:
Rectangular tile has 14 cm² larger area-----------------
Find each area and then find their difference.
A(square) = 20² = 400 cm²A(rectangle) = (20 + 3)(20 - 2) = 23*18 = 414 cm²The difference is:
414 - 400 = 14 cm²What is (528^5 x 2419^9)^6 - 328?
Also don’t answer unless your fine with getting hundreds of notifications.
Answers
Answer:
Exact Form:
(41036433850368 ^6 x 2419 ^54 )− 328
Decimal Form:
2.48516121 x 10 ^264
Answer:
Heyyy T-T
Step-by-step explanation:
Allison works in a department store selling clothing. She makes a guaranteed salary of $350 per week, but is paid a commision on top of her base salary equal to 15% of her total sales for the week. How much would Allison make in a week in which she made $300 in sales? How much would Allison make in a week if she made x dollars in sales?
Answers
Answer: 395
0.15x+350
Step-by-step explanation:
(01.05 LC)
What is the equation in point-slope form of the line passing through (1, 2) and
(2,5)? (5 points)
A) (y - 2) = 3(x - 1)
B) (y + 2) = 3(x + 1)
C) (y - 1) = -3(x - 2)
D) (y - 2) = -3(x - 1)
Answers
Please help.
1) LaTeX: m\angle1=\:\:\:\:\:\:\:\:^\circm ∠ 1 = ∘
2) LaTeX: m\angle2=\:\:\:\:\:^\circm ∠ 2 = ∘
3) LaTeX: x\:=\:\:\:\:m\:\left(exterior\:angle\right)\:=x = m ( e x t e r i o r a n g l e ) =
Answers
9514 1404 393
Answer:
Angle 1 = 139°Angle 2 = 41°x = 29; exterior angle = 131°Step-by-step explanation:
These problems let you make use of the fact that the sum of the remote interior angles is equal to the exterior angle.
__
1. 53° +86° = ∠1
139° = ∠1
__
2. ∠2 +92° = 133°
∠2 = 133° -92°
∠2 = 41°
__
3. (x +9)° +93° = (4x+15)°
87 = 3x . . . . . . . . . . . . . . . . subtract x+15°
29 = x . . . . . . . divide by 3
The exterior angle is ...
(4x +15)° = (4·29 +15)° = 131° . . . exterior angle
Point A is at (2,-8) and point is at (-4.7).
Find the coordinates of point B on AC such that the ratio of AB to BC is 2:1
B=0
Answers
Answer:
bro use gauth mathhhhhhh
what expresses the specific number of instances in an entity
Answers
The specific number of instances in an entity is typically expressed using the term "count" or "quantity."
It represents the numerical value that indicates how many individual instances or objects are present within a given entity or set.
For example, if you are referring to the number of students in a classroom, you might say, "The count of students in the classroom is 25." Here, "25" represents the specific number of instances (students) within the entity (classroom).
Similarly, if you are discussing the quantity of apples in a basket, you might say, "The quantity of apples in the basket is 10." In this case, "10" represents the specific number of instances (apples) within the entity (basket).
So, "count" or "quantity" are the terms commonly used to express the specific number of instances in an entity.
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How do u check your answer for 4x+12-2x=26
Answers
Answer:
7
Step-by-step explanation:
4x+12-2x=26
Or, 2x=26-12
Or, 2x=14
Or, x=7
will mark brainliest need help
simplify 4a^3b^2 x 3a^6b^5
Answers
Answer:
12a^9b^7
Step-by-step explanation:
Multiply all like terms together.
4 times 3 = 12
a^3(a^6) = a^9
b^2(b^5) = b^7
Combine all together
Answer:2160a2b2
Step-by-step explanation:
Help. Ill give 20 points and brainliest
Answers
Answer:
EF = 10
Step-by-step explanation:
DE + EF = DF
So, x + 22 + x + 23 = 21
2x + 47 = 21
2x = -26
x = -13
EF = x + 23
EF = 10
A kitten and a puppy noticed each other and started to run in opposite directions .How far from each other will they be in 15 seconds, If the puppy with the speed of 6 meters per second, and then the kitten runs 2/3 as fast as puppy?
Answers
In 15 seconds, the puppy, running at a speed of 6 meters per second, will be 90 meters away from the starting point. The kitten, running at 2/3 of the puppy's speed, will be 60 meters away from the starting point. Therefore, they will be 150 meters away from each other.
Given that the puppy has a speed of 6 meters per second, we can calculate the distance it covers in 15 seconds by multiplying the speed by the time:
Distance covered by the puppy = 6 meters/second * 15 seconds = 90 meters.
Next, we need to calculate the speed of the kitten. It is stated that the kitten runs 2/3 as fast as the puppy. Therefore, the speed of the kitten can be calculated as:
Speed of the kitten = 2/3 * 6 meters/second = 4 meters/second.
Using the speed of the kitten, we can calculate the distance it covers in 15 seconds:
Distance covered by the kitten = 4 meters/second * 15 seconds = 60 meters.
Finally, to find the distance between them, we add the distances covered by the puppy and the kitten:
Distance between the puppy and the kitten = 90 meters + 60 meters = 150 meters.
Therefore, after 15 seconds, the puppy and the kitten will be approximately 150 meters away from each other.
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Faizah is paid $11 per hour for her work at a factory. She works 9 hours a day and 24 days a month. She saves $594 a month. Express the amount she saves as a percentage of her income.
Answers
Answer:
The amount she saves is 25% of her income
Step-by-step explanation:
She is paid $11 per hour
She works 9 hours per day
and for 24 days per month
So, she works 9(24) hours per month
= 216 hours per month
Now, she is paid $11 hourly, so for 216 hours,
she will have 11(216) = $2376
Total income = $2376 per month
Saving = $594 per month
As a percentage, we divide the savings by the total income,
savings/(total income) = 594/2376 = 1/4 = 0.25
Hence we get 25%
Please help me on this and explain it.
Answers
Answer:
no solutions
Step-by-step explanation:
if u divide the second equation by -2 u get
-4x+5y= 7.5
and -4x+5y can’t equal 7 and 7.5
(2+2+2+2+2) 90^5 x 50 divided by 100 ..
Answers
Answer: 5000000000..........
The soccer field at a park is 9,000 square yards. The soccer field takes up 6 2/5 square inches on the map of the park. How many square yards does 1 square inch on the map represent? Show your work. Help me pls
Answers
Answer: 1406.25
Step-by-step explanation:
The soccer field at a park is 9,000 square yards. The soccer field takes up 6 2/5 square inches on the map of the park. How many square yards does 1 square inch on the map represent? Show your work. Help me pls
Given that:
Area of soccer field = 9000 sq yards
Soccer field takes up 6 2/5 square inches on the map of park
Hence,
9000 yd² = 6 2/5 in²
Let 1 in² on map = m
9000 yd² = 32/5 in² - - - (1)
m = 1 in² - - - (2)
Cross multiply ;
6.4 * m = 9000
m = 9000/6.4
m = 1406.25
Hence,
1 in² on map = 1406.25 feet²
900
The mean of 11 numbers is 7 one of the numbers, 13, is deleted. What is the mean of the remaining 10 numbers?.
Answers
If mean of 11 numbers is 7 one of the numbers, 13, is deleted then the mean of remaining 10 numbers is 6.4
The mean of 7 numbers = 11
We know,
Mean = Sum of the terms / Number of terms
Substitute the values in the equation
11 = Sum of the terms / 7
The sum of the terms = 11 × 7
= 77
Number 13 is deleted
Sum of the terms = 77 - 13
= 64
Number of terms = 11 - 1
= 10
The mean = Sum of the terms / Number of terms
Substitute the values in the equation
= 64 / 10
= 6.4
Hence, the mean of the remaining 10 numbers is 6.4
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Exercise 2. Geneticist Seymour Blooms has been performing a plant breeding experiment in which the four possible types of plants that may bloom will occur, according to Bloom's model, with probabilitiies shown in the table below.
Plant type (i) 1 2 3 4
Probability (p₁)0 , 0/2 ,0/2 ,1-20
Dr. Bloom bred n = 80 plants and observed the following frequencies for the four plant types.
Plant type (i) 1 2 3 4
Frequencies (Oi) 28 7 5 40
Test, at level a = .05, the null hypothesis that Dr. Bloom's model fits the data.
Answers
The hypothesis test aims to determine if Dr. Seymour Bloom's plant breeding model fits the observed frequencies of plant types. The null hypothesis assumes that the model is a good fit, while the alternative hypothesis suggests otherwise.
To test the hypothesis, we can utilize a chi-square goodness-of-fit test. The test compares the observed frequencies (Oi) with the expected frequencies (Ei) based on Dr. Bloom's model. The expected frequencies can be calculated by multiplying the total number of plants (n = 80) by the respective probabilities (p₁) for each plant type.
Using the given probabilities for plant types, we can calculate the expected frequencies as follows: E₁ = 0 × 80 = 0, E₂ = 0.5 × 80 = 40, E₃ = 0.5 × 80 = 40, E₄ = 1 - 0.2 × 80 = 64.
Next, we calculate the chi-square statistic by summing up the squared differences between observed and expected frequencies divided by the expected frequencies: χ² = Σ[(Oᵢ - Eᵢ)²/Eᵢ]. For our data, this yields χ² = [(28-0)²/0 + (7-40)²/40 + (5-40)²/40 + (40-64)²/64] ≈ 97.63.
To determine the critical chi-square value at a significance level of 0.05 with 3 degrees of freedom (4 plant types - 1), we consult the chi-square distribution table or use statistical software. The critical value is approximately 7.815.
Since our calculated χ² (97.63) is greater than the critical value (7.815), we have sufficient evidence to reject the null hypothesis. Thus, we conclude that Dr. Bloom's model does not fit the observed frequencies of plant types.
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determine the rate of change for the graph from 2014 to 2015:____ students per year
Answers
Answer:
The answer would be 9
Step-by-step explanation: