Answer:
-45/2 - 12/2 = -57/2
Step-by-step explanation:
Substitute 15 for x in the given equation: y = (-3/2)x - 6 becomes
y = (-3/2)(15) - 6 = -45/2 - 6 when x = 15. This is equivalent to -57/2
The points J, K, L and M all lie on the same line segment, in that order, such that the ratio of JK : KL : LM is equal to 2:1:2. If JM=30, find JL.
JKLM forms a line segment. In this, the ratio of JK : KL : LM is equal to 2:1:2. We know that JM = 30 cm.
JK = 2x
KL = x
LM = 2x
JM = JKLM = 30 cm
JL (JK + KL) = 2x + x = 3x
So,
JL + LM = JKLM
3x + 2x = 30
5x = 30
x = 30/5
x = 6.
JL = 3x = 3 × 6 = 18 cm.
=》 JL = 18 cm.
_____
꧁✿ ᴿᴬᴵᴺᴮᴼᵂˢᴬᴸᵀ2222 ✬꧂
What is (I^2)+(I^2)+3x if x=I^2?
Show your work.
Answer:
-5
Step-by-step explanation:
(i^2) = -1 so -1 -1 + 3x = 3x - 2. If x = i^2 = -1, then 3x = -3. -3 - 2 = -5
For triangle ABC (shown here), the value of angle BCD is equal to 30 degrees. If CD is the height of the triangle and is 12 centimeters, then what is the perimeter of triangle ABC?
The perimeter of triangle ABC could be either approximately 27.98 cm or approximately 14.66 cm, depending on the length of AB.
What is the perimeter?
The perimeter is a mathematical term that refers to the total distance around the outside of a two-dimensional shape. It is the length of the boundary or the sum of the lengths of all the sides of a closed figure.
Let's call the length of AB x and the length of BC y.
First, we can use the fact that CD is the height of the triangle to find the area of triangle ABC:
Area of triangle ABC = 1/2 * CD * AB
Substituting the given values, we have:
1/2 * 12 * x = 6x
So the area of triangle ABC is 6x square centimeters.
We can also use the fact that angle BCD is 30 degrees to set up a trigonometric equation involving x and y:
tan(30) = x/y
Simplifying, we get:
y = x/tan(30) = x/(1/√(3)) = √(3) * x
Now we can use the formula for the area of a triangle in terms of its sides:
Area of triangle ABC = 1/2 * AB * BC * sin(B)
where B is the angle between sides AB and BC. In this case, we know that angle BCD is 30 degrees, so angle BCA is 60 degrees, and angle ABC is 90 degrees. Therefore, we have:
Area of triangle ABC = 1/2 * x * √3 * x * sin(60)
Simplifying, we get:
Area of triangle ABC = 1/4 * √3 * x²
Since we already found that the area of triangle ABC is 6x square centimeters, we can set these two expressions equal to each other and solve for x:
6x = 1/4 * √(3) * x²
Multiplying both sides by 4/√3, we get:
24/√(3) * x = x²
Simplifying, we get:
x² - 24/√(3) * x = 0
Using the quadratic formula, we get:
x = (24/√(3) ± √((24/√(3))² - 410)) / 2*1
Simplifying, we get:
x = 16√(3) / 3 or x = 8 √(3) / 3
Since we are looking for the perimeter of triangle ABC, we need to find y as well. Using the equation we derived earlier, we have:
y = √(3) * x
Therefore, we have two possible triangles:
Triangle ABC1: AB = 16 √(3) / 3, BC = 16, and AC = 8 √7 / 3
Triangle ABC2: AB = 8 √3 / 3, BC = 8, and AC = 4 √7 / 3
The perimeter of each triangle is the sum of its side lengths. Therefore:
Perimeter of triangle ABC1 = 16 √3/ 3 + 16 + 8 √7 / 3 ≈ 27.98 cm
Perimeter of triangle ABC2 = 8 √3 / 3 + 8 + 4 √7 / 3 ≈ 14.66 cm
hence, the perimeter of triangle ABC could be either approximately 27.98 cm or approximately 14.66 cm, depending on the length of AB.
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local salesman receives a base salary of $875 monthly. He also receives a commission of 6% on all sales over $1450. How much would he have to sell in a month if he needed to have a monthly income of $2800?
The total sales required to earn the desired income of $2800 is calculated to be $6,375.
What is sale?Sale is a business transaction involving the exchange of goods or services for money. It can refer to the act of selling, or the thing that is sold. Sales are typically the main source of revenue for businesses. The process of selling involves finding potential customers, negotiating a price, and delivering the product or service. The ultimate goal is to make a profit.
In order to earn a monthly income of $2800, a local salesman would need to sell $6,375 worth of goods in a month. This is calculated by subtracting the base salary of $875 from the desired income of $2800, which leaves $2,925. Then, 6% of $1450 is $87, so the remaining $2,838 must be made up of 6% of the sales above $1450. By dividing this amount by 6%, the total sales required to earn the desired income of $2800 is calculated to be $6,375.
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One rectangle is "framed" within another. Find the area of the shaded region if the "frame" is 3 units wide.
The area of the shaded region, with a frame of 3 units wide, is 264 square units. The inner rectangle is 6x4 units, and the outer rectangle is 18x16 units.
To solve the given problem, we have to find the area of the shaded region if the frame is 3 units wide. If the frame is 3 units wide, then the dimensions of the inner rectangle (the shaded region) will be (12 - 6) × (10 - 6) which simplifies to 6 × 4.
Therefore, we can say that the inner rectangle has a length of 6 units and a width of 4 units.The dimensions of the outer rectangle are (12 + 3 + 3) × (10 + 3 + 3) which simplifies to 18 × 16. Therefore, we can say that the outer rectangle has a length of 18 units and a width of 16 units.
The area of the shaded region can be obtained by subtracting the area of the inner rectangle from the area of the outer rectangle. Therefore, the Area of the outer rectangle = length × width= 18 × 16 = 288 square units
Area of the inner rectangle = length × width= 6 × 4 = 24 square units
Area of the shaded region = Area of the outer rectangle - Area of the inner rectangle = 288 - 24= 264 square units
Therefore, the area of the shaded region is 264 square units.
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What is 3/4 plus 2/3
you buy almond milk in 1 gallon containers one portion of waffles requires 2.5 oz of almond milk how many persons can be made with one container?
Answer:
51
Step-by-step explanation:
1 gallon = 128 ounces
128/2.5 = 51.2
51 portions
Yw :D
51 persons can be made with one container.
What is Unitary method?The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.
Given:
1 gallon = 128 ounces
We have 2.5 oz of almond milk.
So, the number of person who can have it
=128/2.5
= 51.2
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can y’all please answer this
Answer: 35 , 14
Step-by-step explanation:
[3(-2)^2-4 ]+[8 (3)-3] [8(3)-3] -[ 3(-1)^2-4]
35 14
Find the missing angle measure. Show work.
17.
7
20
24
Solve the remaining parts of the triangle.
19.
B
38
12.5 C
7
13
17.
18.
19, AC=
AB-
mzB
Need help with all these please. Asap urgent help need this done before Monday
To find the missing angle measure, we need to use the fact that the sum of angles in a triangle is 180 degrees. Let's denote the missing angle as x. We know that one angle is 38 degrees and another angle is 12.5 degrees.Therefore, the missing angle measure is 129.5 degrees.
By subtracting these two angles from 180 degrees, we get:
180 - 38 - 12.5 = 129.5
Without additional information, it is not possible to determine the remaining parts of the triangle. We would need the lengths of at least one side or the measures of other angles to solve for the missing parts.
The given information states that AC is equal to AB minus mzB. Without knowing the values of AB and mzB, we cannot determine the exact length of AC. We would need additional information to solve for the length of AC.Therefore, the missing angle measure is 129.5 degrees.
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Find the rate of change from the table
Answer: 15
Step-by-step explanation:
rate of change = slope
slope = (y2-y1)/(x2-x1) or rise/run
therefore,
50-20/4-2 = 30/2 = 15
find the LCM and solve, it's very very urgent.
Answers:
1. 10502. 12003. 12004. 33605. 10806. 480please see the attached picture for full solution..
Hope it helps....
Good luck on your assignment...
what is 3 x 3 x 9 x 9 x 81 x 81 x 6561 x 6561
Answer:
205891132094649
The volume of this prism is 2 1/2 cubic centimeters.
Its height is 1/3 of a centimeter.
What are possible values for its length and width?
One of the Possible values of length and width of the prism are 15 cm and 0.5 cm
What is the volume of the prism?In geometry, a prism is a polyhedron comprising an n-sided polygon base, a second base which is a translated copy of the first, and n other faces, necessarily all parallelograms, joining corresponding sides of the two bases.
Given here: The volume of the prism is 2¹/₂=2.5 cm³
And the height is 1/3 cm
let the length and breadth of the prism is x and y respectively.
We know the volume of the prism as
1/3 × x×y=2.5
x×y=7.5
Thus possible values of length and breadth are the factors of 7.5
out of which one of the pair whose length is 15 cm and width 0.5 cm
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What factoring method would be the BEST choice
4x² - 121
( 2x + 11 ) ( 2x - 11 ) is factor of linear equation .
What in mathematics is a linear equation?
A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept. Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.
A linear equation with one variable is one that contains just one variable. It has the mathematical formula Ax + B = 0, where A and B can be any two real numbers, and x is an unknowable variable with just one possible value.
= 4x² - 121
= (2x)² - ( 11 )²
= ( 2x + 11 ) ( 2x - 11 )
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write a real-world situation that could be modeled by the equation 8+2x=6x. Then solve the problem.
Answer:
x = 2
Step-by-step explanation:
8 = 6x + -2x
8 = 4x
8 = 4x
4 4
2 = x
The students in Mrs. Barnett's first-grade class sit down in a circle for show-and-tell. The circle they form has a diameter of 4 meters. What is the circle's radius?
Answer:
Step-by-step explanation:
If the diameter is 4 meters, then the radius has to be 2 because the radius is half of the diameter.
The store bought a pair of shoes for $50 and sold them for $80. What percentage was the markup?
Answer: They resold them for $30 more than the original price.
Answer: 37.5%
Step-by-step explanation:
$80 - $50 = $30,
$30/$80 = 0.375 > 37.5%
Suppose that grade point averages of undergraduate students at one university have a bell-shaped distribution with a mean of 2.61 and a standard deviation of 0.4. Using the empirical rule, what percentage of the students have grade point averages that are between 2.21 and 3.01?
Answer:
68%
Step-by-step explanation:
We start by calculating the z-scores of both
z-score = (x-mean)/SD
for 2.21
z-score = (2.21-2.61)/0.4 = -1
For 3.01
z-score = (3.01-2.61)/0.4 = 0.4/0.4 = 1
So what we want to find is the percentage between -1 SD and 1 SD of the mean
This is the percentage corresponding to the probability
P(-1 < x < 1)
According to the empirical rule, this is a value of;
68.269%
When Tyee runs the 400 meter dash, his finishing times are normally distributed with a mean of 61 seconds and a standard deviation of 1.5 seconds. If Tyee were to run 39 practice trials of the 400 meter dash, how many of those trials would be faster than 62 seconds, to the nearest whole number?
To find out how many of the 39 practice trials would be faster than 62 seconds, we need to calculate the proportion of trials that fall within the range of more than 62 seconds.
We can use the z-score formula to standardize the values and then use the standard normal distribution table (also known as the z-table) to find the proportion.
The z-score formula is:
z = (x - μ) / σ
Where:
x = value (62 seconds)
μ = mean (61 seconds)
σ = standard deviation (1.5 seconds)
Calculating the z-score:
z = (62 - 61) / 1.5
z ≈ 0.6667
Now, we need to find the proportion of values greater than 0.6667 in the standard normal distribution table.
Looking up the z-score of 0.6667 in the table, we find the corresponding proportion is approximately 0.7461.
To find the number of trials faster than 62 seconds, we multiply the proportion by the total number of trials:
Number of trials = Proportion * Total number of trials
Number of trials = 0.7461 * 39
Number of trials ≈ 29.08
Rounding to the nearest whole number, approximately 29 of the 39 practice trials would be faster than 62 seconds.
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Use any method to determine whether the series converges or diverges. Give reasons for your answer. sin Choose the correct answer below
A) The series converges because, by the Alternating Series lest, un sin _are nonincreasing for n25 sin
B) The series diverges because, by the Limit Comparison lest, is constant and lim n-70o diverges n 5 Vin O C.
C) The series diverges because, by the Integral Test,sin dx is divergent -- 0 D.
D) The series converges because, by the Ratio Test, lim sin n-oo
Answer:
hello the series to your question is missing attached below in the solution is the missing series
Answer : The series diverges because, by the Limit Comparison lest, is constant and lim n-70o diverges n 5 Vin O C. ( B )
Step-by-step explanation:
Attached below is the detailed solution of the question and the series is divergent because p = 1/5 < 1
Which of the following shows the correct solution steps and solution to 2×+ 7 = -11?
Answer:
x = - 9
Step-by-step explanation:
2x + 7 = - 11 ( subtract 7 from both sides )
2x = - 18 ( divide both sides by 2 )
x = - 9
The answer is:
x = -9
Work/explanation:
The point of equations is to find the variable's value by isolating it step-by-step.
For this equation, the variable is x.
To isolate it, I will perform a few operations.
First, I will subtract 7 from each side:
\(\sf{2x+7=-11}\)
\(\sf{2x=-11-7}\)
\(\sf{2x=-18}\)
Divide each side by 2
\(\sf{x=-9}\)
Hence, x = -9.
\(\rule{350}{4}\)
Can someone help me with this problem please
Answer:
First blank: 11/9
Second blank: 20
Step-by-step explanation:
Hope this helps!
Solve for x: −2(x − 2)2 + 5 = 0 Round your answer to the nearest hundredth.
Answer:
x = 3.25
Step-by-step explanation:
-2(x - 2) * 2 + 5 = 0
Open parathesis
(-2x + 4) * 2 + 5 = 0
Open parenthesis again
-4x + 8 + 5 = 0
-4x + 13 = 0
-4x = -13
Divide -4 on both sides
x = 13/4
x = 3.25
Answer:
-4x+8+5=0
-4x=-13
4x=13
x= 13/4
x=3.25
I need help please.
Answer:
B
Step-by-step explanation:
What are the coordinates of the graphed point? An x y coordinate system. The x axis extends from negative 5 to 5, and y axis extends from negative 5 to 5, with whole numbers marked on the grid. A point is marked 3 units to the left of the y axis and 2.5 units up from the x axis. CLEAR CHECK (2.5, −3) 2.5 , (−3, −2.5) -3 , (3, −2.5) 3 , (−3, 2.5)
The Coordinates of the graphed point are (−3, 2.5).
The coordinates of the graphed point, based on the given description, are (−3, 2.5).
The x-coordinate represents the horizontal position of the point, and it is described as being 3 units to the left of the y-axis. Since the y-axis is the vertical line passing through x = 0, moving 3 units to the left means the x-coordinate is −3.
The y-coordinate represents the vertical position of the point, and it is described as being 2.5 units up from the x-axis. Since the x-axis is the horizontal line passing through y = 0, moving 2.5 units up means the y-coordinate is 2.5.
Therefore, the coordinates of the graphed point are (−3, 2.5).
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Question One:
If a raw score corresponds to a z-score of 1.75, what does that tell you about that score in relation to the mean of the distribution?
Question Two:
What if the raw score corresponds to a z-score of -0.85?
Question One:A positive z-score indicates that the raw score is above the mean, while a negative z-score indicates that the raw score is below the mean.
Question Two: , the raw score is relatively lower than the mean.
If a raw score corresponds to a z-score of 1.75, it tells us that the raw score is 1.75 standard deviations above the mean of the distribution. In other words, the raw score is relatively higher than the mean. The z-score provides a standardized measure of how many standard deviations a particular value is from the mean.
A positive z-score indicates that the raw score is above the mean, while a negative z-score indicates that the raw score is below the mean.
Question Two:
If a raw score corresponds to a z-score of -0.85, it tells us that the raw score is 0.85 standard deviations below the mean of the distribution. In other words, the raw score is relatively lower than the mean. The negative sign indicates that the raw score is below the mean.
To understand the meaning of a z-score, it is helpful to consider the concept of standard deviation. The standard deviation measures the average amount of variability or spread in a distribution. A z-score allows us to compare individual data points to the mean in terms of standard deviations.
In the case of a z-score of -0.85, we can conclude that the raw score is located below the mean and is relatively lower compared to the rest of the distribution. The negative z-score indicates that the raw score is below the mean and is within the lower portion of the distribution. This suggests that the raw score is relatively smaller or less than the average value in the distribution.
By using z-scores, we can standardize and compare values across different distributions, allowing us to understand the position of a raw score relative to the mean and the overall distribution.
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What is the slope of the line represented by the equation f(x)=-3x+7 A. -7 B. -3 c. 3 D. 7
Answer:
B. -3
Step-by-step explanation:
check image for reference. <3
(this is what I am learning so I have some other pictures as well.)
Answer:
Answer B is correct
Step-by-step explanation:
A mover brings a box up the stairs in 10 seconds. If he applied a force of 20 N over a distance 10 m on the box, calculate the power required for him to complete this action
Total work done is calculated as
\(\begin{gathered} \text{work}=\text{force}\times dis\tan ce \\ \text{ =20N}\times10m \\ \text{ =200 J} \end{gathered}\)The power is calculated as ,
\(\begin{gathered} \text{Power}=\frac{work}{\text{time}} \\ \text{ =}\frac{\text{200 J}}{10\text{ sec}} \\ \text{ =20 W} \end{gathered}\)Solve the following system of equations.
y = –5x + 3
y = 2x2 – x – 3
Answer:
Step-by-step explanation:
the first would be _3 ,0
5
and the second would be 0,3
I need help I don’t know how to do these problems
Answer:
It is in fact 113 I'm just here to explain
Step-by-step explanation:
Basically M6 and M7 must make a staright line(180) and since we already know that M6 is 67 we just have to subtract 67 from 180 to get the answer we are looking for. ( it would be the same process if we were looking for M1 (113) and also if you had the measure of M1 you would have had your answer to M7 because they are vertical angles therefore making them congruent