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3 years ago

The product of 9 and the quantity 5 more than a number t is less than 5

1 answer:

3 0

$9(t+5) \ \textless \ 5\ \ \ |use\ distributive\ property:a(b+c)=ab+ac\\\\(9)(t)+(9)(5) \ \textless \ 5\\\\9t+45 \ \textless \ 5\ \ \ |subtract\ 45\ from\ bot\ sides\\\\9t \ \textless \ -40\ \ \ \ |divide\ both\ sides\ by\ 9\\\\\huge\boxed{t \ \textless \ -\dfrac{40}{9}\to t \ \textless \ -4\dfrac{4}{9}}$

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Which Rule describes the composition of transformations that maps figure PQRS to figure P”Q’R”S”?

stiv31 [10]

Answer:

I THINK THE SECOND ONE

Step-by-step explanation:

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3 years ago

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(!!15 points!!)<br> Find the measure of arc BDC

Paha777 [63]

Answer:

180°

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The central angle is also 180° and the arc is congruent to the measure of the central angle.

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3 years ago

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What is the equation of the line that is parallel to the given

finlep [7]

Answer

O 4x+3y=-6

Step-by-step explanation:

Hello, I can help you witht this,

to solve this you need

step one

the line we are looking for is paraller to the line in the graph, it means both of then have the same slope.

find the slope of the line in the graph

remember

to find the slope of a line with two known points you can use

Let

$P1(x_{1},y_{1})}\\P1(x_{2},y_{2})\\slope\\s=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

pick two points from he graph

P1(0,3)

P2(3,-1)

put the values into the equation

$slope(m)\\m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\\m=\frac{-1-3}{3-0}\\m= \frac{-4}{3}$

so, the slope of the line we are looking for is m=-4/3 and passes through the point (-3,2)

step 2

use the equation

$y-y_{1}=m(x-x_{1})$

to ding the equation of the line

P1(-3,2)

$y-y_{1}=m(x-x_{1})\\y-2=\frac{-4}{3} (x+3})\\isolate\ y\\y-2=\frac{-4x}{3}-4\\y=\frac{-4x}{3}-4+2\\y+\frac{4x}{3}=-2\\multiply\ each\ side\ by\ 3\\3(y+\frac{4x}{3})=3*-2\\\\3y+4x=-6\\4x+3y=-6\\$

and that's all, that is the equation of the line that is parallel to the given

line and passes through the point (-3, 2).

Have a good day.

7 0

3 years ago

The side of each of the equilateral triangles in the figure is twice the side of the central regular hexagon. What fraction of t

lana [24]

Answer:

The fraction is 1/4

Step-by-step explanation:

we know that

The area of an equilateral triangle, using the law of sines is equal to

$A=\frac{1}{2}x^{2}sin(60^o)$

$A=\frac{1}{2}x^{2}(\frac{\sqrt{3}}{2})$

$A=x^{2}\frac{\sqrt{3}}{4}$

where

x is the length side of the triangle

In this problem

Let

b ----> the length side of the regular hexagon

2b ---> the length side of the equilateral triangle

step 1

Find the area of the six triangles

Multiply the area of one triangle by 6

$A=6[x^{2}\frac{\sqrt{3}}{4}]$

$A=3x^{2}\frac{\sqrt{3}}{2}$

we have

$x=2b\ units$

substitute

$A=3(2b)^{2}\frac{\sqrt{3}}{2}\\\\A=6b^{2}\sqrt{3}\ units^2$

step 2

Find the area of the regular hexagon

Remember that, a regular hexagon can be divided into 6 equilateral triangles

The area of the regular hexagon is the same that the area of 6 equilateral triangles

$A=3x^{2}\frac{\sqrt{3}}{2}$

we have

$x=b\ in$

substitute

$A=3(b)^{2}\frac{\sqrt{3}}{2}$

step 3

To find out what fraction of the total area of the six triangles is the area of the hexagon, divide the area of the hexagon by the total area of the six triangles

$3(b)^{2}\frac{\sqrt{3}}{2}:6b^{2}\sqrt{3}=\frac{3}{2} :6=\frac{3}{12}=\frac{1}{4}$

3 0

4 years ago

Evaluate the following expression 5(1 3)-3(2 -1)

BARSIC [14]

Answer:

Step-by-step explanation:

This problem tests your understanding of order of operations rules.

Here you must do any work inside parentheses first, followed by multiplication, followed by subtraction:

5(13) - 3(2 -1) would be 65 -3(1), or 62.

If you actually meant 5(1 - 3) - 3(2 - 1), then you'd have

5(-2) - 3(1) = -10 - 3 = -13

Please compare the problem you've shared with the original problem, to ensure that these match.

3 0

3 years ago