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2 years ago

I need help please with this math problem

Mathematics

1 answer:

Arada [10]2 years ago

8 0

When the dilation is centered on the origin, you can multiply each of the individual coordinates by the scale factor.

All the coordinates are ±5 and the scale factor is 1/5. Multiplying those gives ±1. The only selection with all coordinates being ±1 is
.. Selection A.

You can check to see if the signs agree in detail. (They do.)

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Patrick has just finished building a pen for his new dog. The pen is 3 feet wider than it is long. He also built a doghouse to p

zalisa [80]

General Idea:

(i) Assign variable for the unknown that we need to find

(ii) Sketch a diagram to help us visualize the problem

(iii) Write the mathematical equation representing the description given.

(iv) Solve the equation by substitution method. Solving means finding the values of the variables which will make both the equation TRUE

Applying the concept:

Given: x represents the length of the pen and y represents the area of the doghouse

Statement 1: "The pen is 3 feet wider than it is long"

$Length \; of\; the \; pen = x\\ Width \; of\; the\; pen=x+3$

------

Statement 2: "He also built a doghouse to put in the pen which has a perimeter that is equal to the area of its base"

$Area \; of\; the\; Dog \; house=y\\ Perimeter \; of\; Dog\; house=y$

------

Statement 3: "After putting the doghouse in the pen, he calculates that the dog will have 178 square feet of space to run around inside the pen."

$Area \; of \; the\; Pen - Area \;of \;the\;Dog \;House=\;Space\;inside\;Pen\\ \\ x \cdot (x+3)-y=178\\ Distributing \;x\;in\;the\;left\;side\;of\;the\;equation\\ \\ x^2+3x-y=178\Rightarrow\; 1^{st}\; Equation\\$

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Statement 4: "The perimeter of the pen is 3 times greater than the perimeter of the doghouse."

$Perimeter\; of\; the\; Pen=3\; \cdot \; Perimeter\; of\; the\; Dog\; House\\ \\ 2(x \; + \; x+3)=3 \cdot y\\ Combine\; like\; terms\; inside\; the\; parenthesis\\ \\ 2(2x+3)=3y\\ Distribute\; 2\; in\; the\; left\; side\; of\; the\; equation\\ \\ 4x+6=3y\\ Subtract \; 6\; and \; 3y\; on\; both\; sides\; of\; the\; equation\\ \\ 4x+6-3y-6=3y-3y-6\\ Combine\; like\; terms\\ \\ 4x-3y=-6 \Rightarrow \; \; 2^{nd}\; Equation\\$

Conclusion:

The systems of equations that can be used to determine the length and width of the pen and the area of the doghouse is given in Option B.

$178=x^2+3x-y\\ \\ -6=4x-3y$

8 0

3 years ago

Read 2 more answers

Suppose the average price for new cars in 2012 has a mean of $30,100 and a standard deviation of $5,600. Based on this informati

KatRina [158]

Answer:

($13,300,$46,900)

Step-by-step explanation:

We are given the following in he question:

Mean, μ = $30,100

Standard Deviation, σ = $5,600

Chebyshev's Theorem:

According to theorem atleast $1 - \dfrac{1}{k^2}$ percent of data lies within 2 standard deviations of mean.
For k = 3,

$1 -\dfrac{1}{(3)^2} = 0.889 \approx 89\%$

Thus, 89% of data lies within three standard deviation of mean.

$\mu - 3(\sigma) = 30100 - 3(5600) = 13300\\\mu + 3(\sigma) = 30100 + 3(5600) = 46900$

Thus, we expect at least 89% of new car prices to fall within ($13,300,$46,900)

3 0

2 years ago

How do i find the average speed for his question: "A bicycle racer rides from a starting marker at 10m/s. She then rides back al

padilas [110]

To find the average speed for the whole race, you just have to add the speed from a starting marker and the speed from the turnaround marker going back and divide it by 2 since there are only two speeds involved.

10 m/s + 16m/s = 26 m/s / 2 = 13 m/s

Therefore, the average speed for the whole race is 13 m/s.

7 0

3 years ago

Read 2 more answers

A line includes the point (7,5)has a slope of 1.What is its equation in slope intercept form?

Lina20 [59]

Given:

Point( 7, 5)

x = 7 and y=5

slope(m) = 1

We need to first find the intercept.

Substitute x=7, y=5 and m=1 into y=mx + b and solve for intercept(b)

5 = 1(7) + b

5 = 7 + b

5 - 7 = b

-2 = b

Now, form the equation by substituting the value of the slope and intercept into y=mx + b

y = x - 2

7 0

7 months ago

HELP PLEASEEE, IMAGE IS SHOWN

mojhsa [17]

Answer:

f(x)= (-4)/(5-X)

Step-by-step explanation:

8 0

2 years ago