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2 years ago

10

Write a subtraction sentence that you can use to find the length of the side of the polygon between the vertices located at (3,4

) and (3,1).

1 answer:

max2010maxim [7]2 years ago

8 0

Subtract The x’s and the y’s. 3-3=0, 4-1=3. Thus, the length of this side is 3 units

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Find all points on the x-axis that are 14 units from the point (6,-7) All points on the x-axis that are 14 units from the point

Maksim231197 [3]

Answer: $(6+7\sqrt{3},0)\text{ and }(6-7\sqrt{3},0)$ are the required points.

or (18.124,0) and ( -6.124,0) are the required points.

Step-by-step explanation:

Let (x,0) be the point on x -axis that are 14 units from the point (6,-7) .

Then by distance formula , we have

$\sqrt{(x-6)^2+(0-(-7))^2}=14\ \ \ [\ \because distance=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}]$

Taking square on both the sides , we get

$(x-6)^2+7^2=14^2\\\\\Rightarrow\ x^2+6^2-2(6)x+49=196\\\\\Rightarrow\ x^2+36-12x=147\\\\\Rightarrow\ x^2-12x=111\\\\\Rightarrow\ x^2-12x-111=0$

Using quadratic formula : $x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}$

$x=\dfrac{12\pm\sqrt{(-12)^2-4(1)(-111)}}{2}\\\\\Rightarrow\ x=\dfrac{12\pm\sqrt{144+444}}{2}\\\\\Rightarrow\ x=\dfrac{12\pm\sqrt{588}}{2}\\\\\Rightarrow\ x=\dfrac{12\pm\sqrt{2^2\times7^2\times3}}{2}\\\\\Rightarrow\ x=\dfrac{12\pm14\sqrt{3}}{2}\\\\\Rightarrow\ x=6\pm7\sqrt{3}$

so, $(6+7\sqrt{3},0)\text{ and }(6-7\sqrt{3},0)$ are the required points.

since $\sqrt{3}=1.732$

so, $(6+7(1.732),0)\text{ and }(6-7(1.732),0)$ are the required points.

i.e. (18.124,0) and ( -6.124,0) are the required points.

3 0

3 years ago

A carpenter is framing a window with wood trim where the length of the window is 9 1/3 feet. If the width of the window is 6 3/4

ElenaW [278]

This is not much of a question, because it doesn't take into account the width of the wood trim.

So you are asked to find the perimeter of the window, ignoring the width of the trim.

P = Perimeter = 2L + 2W.

Here, P= 2(9 1/3 feet) + 2(6 3/4 feet) = 2(28/3 feet) + 2(27/4 feet)

So P = 2[28/3 + 27/4] feet. LCD is 3*4 = 12.

Thus, P = 2 [ 28/3 + 27/4 ] feet. Can you finish? Add together the fractions 28/3 and 27/4.

4 0

3 years ago

The junior senator can do a labyrinth in 50 minutes. The senior senator can do a labyrinth in 30 minutes. Working together, how

vladimir2022 [97]

Answer:

$225\:\text{minutes}$

Step-by-step explanation:

To navigate through this problem, start by finding how much each senator can complete in a fixed amount of time. I'll choose 10 as it's the greatest common factor of 30 and 50.

In 10 minutes, the junior senator can complete $\frac{10}{50}=\frac{1}{5}$ of the labyrinth.

In 10 minutes, the senior senator can complete $\frac{10}{30}=\frac{1}{3}$ of the labyrinth.

Therefore, working together, they can complete $\frac{1}{5}+\frac{1}{3}=\frac{8}{15}$ of the labyrinth in 10 minutes. Thus, it will take them $\frac{15}{8}\cdot 10 \text{ minutes}=18.75\:\text{minutes}$ to complete one labyrinth.

The amount of time it take them to complete 12 labyrinths is then $18.75\cdot 12 =\boxed{225\:\text{minutes}}$

5 0

3 years ago

22. y =x-v over b solve for x

GREYUIT [131]

Answer:

See Below

Step-by-step explanation:

y = $\frac{x-v}{b}$

Isolate x

First step, multiply both sides by b to get rid of fraction

y(b) = x - v

+v +v

y(b) +v = x

Hope this helps!=)

8 0

4 years ago

What is 165 in exponents

sasho [114]

165= 5x5x7= 5 to the power of 2 (5^2) x 7
So 165 is 5^2 x 7 in exponents

7 0

3 years ago