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11 months ago

Which ordered pair would be the solution to the system ofequations?1.) -22.) 13.) (1, 2)4.) (1, -1)

Mathematics

1 answer:

Norma-Jean [14]11 months ago

7 0

Explanation

when you have two lines in a graph, the solution is the point where the line intersect each other, so to solve this we need to find that point

so, the answer is

$(1,-1)$

I hope this helps you

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Line segment GT contains the point G(−3, 5) and a midpoint at A(1, −4). What is the location of endpoint T?

algol [13]

Imagine you're moving along the segment. Since the midpoint is in the middle of the segment (obviously), it means that when you've traveled from G to A, you're halfway through your journey, along both x and y directions. So, let's break the problem in two and analyze both directions.

Along the x axis, you've moved from -3 to 1, so you moved 4 units forward. This means that you have 4 units still to go, and your journey will end at coordinate 5.

Similarly, along the y axis, you've moved from 5 to -4, so you moved 9 units downward. This means that you have 9 units still to go, and your journey will end at coordinate -13.

So, the coordinates of the endpoint are $T = (5,-13)$

If you prefer a more analyitical approach, simply write the definition of the midpoint and solve it for the coordinates of T.

We have $G = (-3, 5)$ and $T = (x_T,y_T)$ . The midpoint is computed as

$A = \left( \frac{-3+x_T}{2},\frac{5+y_T}{2} \right) = (1, -4)$

So, you have the equations

$\frac{-3+x_T}{2} = 1,\qquad \frac{5+y_T}{2} = -4$

Multply both equations by 2 to get

$-3+x_T = 2,\qquad 5+y_T = -8$

Move the constants to the right hand sides to get

$x_T = 5,\qquad y_T = -13$

8 0

3 years ago

In the figures below, the cube-shaped box is 6 inches wide and the rectangular box is 10 inches long, 4 inches wide, and 4 inche

11111nata11111 [884]

The difference in volume= $v^{3} -V*L*H$
= $6^{3}-(10*4*4)$
=216-160
= 56 cubic inches

4 0

3 years ago

Arrange the equations in the correct sequence to rewrite the formula for displacement, , to find a. In this formula, d is displa

valina [46]

Answer:

$a=2[d-V_0t]/t^2=2d/t^2-2v_0/t$

Explanation:

Since, you have not included the formula, I will work here with the formula for constant accelaration motion that relates the four variables: displacement (d), Vo (initial velocity), a (acceleration) and t (time).

1) displacement formula:

$d= V_0t+\frac{1}{2} at^2$

2) Subtract the term Vot from both sides:

$d-V_0t= \frac{1}{2} at^2$

3) Multiply both sides by 2:

$2d -2V_0t=at^2$

4) Divide both sides by t²

$2[d-V_0t]/t^2=a$

So, you have obtainded:

a = 2[d - Vo×t] / t²

Yet, you can arrange it in different ways. For example, you might separate into two terms:

$a = \frac{2d}{t^2} - \frac{2V_0}{t}$

8 0

2 years ago

I need all the answers

MA_775_DIABLO [31]

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6 0

3 years ago

In 2012, about 24% of high-school seniors reported binge drinking (defined as five or more drinks in a row in the past two weeks

Artist 52 [7]

Answer: (0.24 - 1.96*0.019, 0.24 + 1.96*0.019)

Step-by-step explanation:

We know that the confidence interval population proportion (p) is given by :-

$\hat{p}\pm z*\cdot SE$

, where $\hat{p}$ = sample proportion.

z* = Critical value (Two -tailed)

SE = standard error

Given : In 2012, about 24% of high-school seniors reported binge drinking (defined as five or more drinks in a row in the past two weeks), a substantial drop since the late 1990s.

$\hat{p}=0.24$

SE = 0.019

Significance level = $\alpha=1-0.95=0.05$

Two-tailed value corresponds for $\alpha=0.05$ :

z*=1.96 [Using z-table]

Now, the 95% confidence interval for the proportion of high-school seniors in the sample who would report binge drinking will be :-

$0.24\pm (1.96)\cdot (0.019)=(0.24-1.96\times 0.019,\ 0.24+1.96\times 0.019)$

Hence, the correct answer = (0.24 - 1.96*0.019, 0.24 + 1.96*0.019)

8 0

3 years ago