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3 years ago

Choose the graph that represents the following system of inequalities:

Mathematics

1 answer:

Licemer1 [7]3 years ago

6 0

Answer:

FIRST.

64 square inches matches to a cross section parallel to the base of a right rectangle prism that is 3 inches long, 7 inches wide, and 11 inches tall

This is shown in the first figure below. A right rectangular prism where every edge connecting its base and the opposite face makes right angles with both faces. Since the tall is the side that measures 11 inches, then the base is formed by 3 inches long and 7 inches wide. Therefore, the area of this shape can be found as the area of a rectangle, which is: 21 in squared.

SECOND.

64 square inches matches to a cross section parallel to the base of a cube whose edges are 8 inches long.

This is shown in the second figure below. A cube is a prism whose sides all have the same length and in this case is 8 inches. We name cross section is to the slice that cuts through a solid. If the cross section is parallel to the base of a cube, then it forms a square with length . Therefore, the area of this shape can be found as the area of a square, which is: 64 in squared.

Third.

7 square inches matches to a cross section passing through the diagonal of opposite faces of a cube with edges that are 7 inches long and a diagonal that is approximately 10 inches

This is shown in the third figure below. As you can see, the cross section passes through the diagonals of the base and the top of the cube that are two opposite faces. This form a rectangle having sides where:

So: 70 in squared

FOURTH.

300 square inches matches to a cross section perpendicular to the base and passing through the diagonals of the base and opposite face of a right rectangular prism that is 24 inches wide, 7 inches long, and 12 inches tall and measures 25 inches along the diagonal of the base.

This is shown in the fourth figure below. The cross section passes through the diagonals of the base and the top of the right rectangular prism. They are opposite to each other, so the shape of the cross section is a rectangle whose sides are where:

So: 300 in squared.

Step-by-step explanation:

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Find the least common multiple of 5x cubed times y and 10 x times y squared

Semenov [28]

Answer:

2/5x-3/10x=2

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3 years ago

The weather report gives the temperature as 35 degrees Celsius.

lora16 [44]

$F=\frac{9}{5}C+32 \\ \\ F=\frac{9}{5}(35)+32 \\ \\ =63+32 \\ \\ =\boxed{95^{\circ} \text{F}}$

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2 years ago

1). Write an equation of a line with the given slope and y-intercept.

asambeis [7]

Answers:

1) The Equation of a Line is:

$y=mx+b$ (1)

Where:

$m$ is the slope

$b$ is the y-intercept

For this problem we have a given $m=-2$ and a given $b=4$

So, we only have to substitute this values in the equation (1):

$y=-2x+4$

This is option B

2) Here we have to find the slope $m$ and the y-intercept $b$ of this equation:

$y=\frac{1}{5}x-8$

According to the explanation in the first answer related to the equation (1), the slope of this line is:

$m=\frac{1}{5}$

And its y-intercept is:

$b=-8$

This is option C

3) We have to Equations of the Line, and we are asked if these are parallel:

$y=6x+9$ (a)

$27x-3y=-81$ (b)

Equation (b) has to be written in the same form of (a), in the form $y=mx+b$ in order to be able to compare both:

$-3y=-81-27x$

$y=-\frac{1}{3}(-81-27x)$

$y=\frac{81}{3}+\frac{27}{3}x$

$y=9x+27$ (c)

There is a rule that establishes that Two lines are parallel if they have the same slope. In this case, if we compare equations (a) and (c) we find they don’t have the same slope, then they are not parallel.

4) Here we are asked to write $y=\frac{3}{5}x+4$ in a standard form with integers:

$-\frac{3}{5}x+y=4$

Multiply each side by 5:

$5(-\frac{3}{5}x+y)=5(4)$

$5(-\frac{3}{5}x)+5y=20$

$-3x+5y=20$

In this case none of the options apply, please check if the question was written correctly.

5) In this question we are asked to write an equation parallel to:

$y=2x+7$ (2)

That passes through the given point (3,11). (Notice that in the Cartesian plane the points have an x-component and a y-component)

First, remember that two Equations of the line are parallel when they have the same slope. Now that this is clear, we are going to use the equation of the slope with the given point to find the parallel equation:

Equation of the slope:

$m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$ (3)

From (2) we know the slope is 2, then we only have to substitute this value and the points in (3):

$2=\frac{y-11}{x-3}$

$2(x-3)=y-11$

$2x-6=y-11$

Finally:

$y=2x+5$

This is option B

4 0

3 years ago

Hello today is my birthday please help !!

Ierofanga [76]

Answer:

Happy birthday

Step-by-step explanation:

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3 years ago

A machine is set up to cut metal strips of varying lengths and widths based on the time (t) in minutes. The change in length is

Tcecarenko [31]

If your choices are the following:
a. a(t) = t^4 + 2t
b. a(t) = t^4 + 2t + 3t^(5/2) 
c. a(t) = t^4 - 3t^(5/2) + 2t` 
d. a(t) = t^4 + 2t - 2t^(1/2) + sqrt(t)

The answer is letter c.a(t) = t^4 - 3t^(5/2) + 2t`
Solution:
Area= length times width
Then to get the time, a=a(t), l=l(t), and w=w(t)
So, if Area= l times width
a(t)= l(t) • w(t)
a(t)=[t^2-squrt(t)] • [t^2-2t^1/2]
a(t) = [t^2 - t^(1/2)] • [t^2 - 2t^(1/2)]
=t^4 - 3t^(5/2) + 2t

7 0

3 years ago

Read 2 more answers