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2 years ago

Find the value of 5w+1 given that 7w-7=7.

Mathematics

1 answer:

Katyanochek1 [597]2 years ago

4 0

Answer:

lets find the exact value of w

7w - 7 = 7

+7 +7

7w = 14

/7 /7

w = 2

Now let's replace w with 2

5(2) + 1 = 11

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How can I find the exact distance between the points(√7,-√2)and (4√7,5√2)

chubhunter [2.5K]

$\bf \textit{distance between 2 points}\\ \quad \\
\begin{array}{lllll}
&x_1&y_1&x_2&y_2\\
% (a,b)
&({{ \sqrt{7}}}\quad ,&{{ -\sqrt{2}}})\quad 
% (c,d)
&({{4\sqrt{7}}}\quad ,&{{ 5\sqrt{2}}})
\end{array}~~~
% distance value
d = \sqrt{({{ x_2}}-{{ x_1}})^2 + ({{ y_2}}-{{ y_1}})^2}
\\\\\\
$

$\bf d=\sqrt{[4\sqrt{7}-\sqrt{7}]^2~+~[5\sqrt{2}-(-\sqrt{2})]^2}
\\\\\\
d=\sqrt{(4\sqrt{7}-\sqrt{7})^2~+~(5\sqrt{2}+\sqrt{2})^2}\implies d=\sqrt{(3\sqrt{7})^2~+~(6\sqrt{2})^2}
\\\\\\
d=\sqrt{3^2\cdot 7~~+~~6^2\cdot 2}\implies d=\sqrt{63+72}\implies d=\sqrt{135}
\\\\\\
\begin{cases}
135=5\cdot 3\cdot 3\cdot 3\\
\qquad 5\cdot 3^2\cdot 3\\
\qquad 15\cdot 3^2
\end{cases}\implies d=\sqrt{15\cdot 3^2}\implies d=3\sqrt{15}$

8 0

3 years ago

The right isosceles triangle shown is rotated about line k with the base forming perpendicular to k. The perimeter of the triang

kipiarov [429]

Answer:

The new shape will be cone with a radius of 17 units, tilt height 24 and units of height k.

Step-by-step explanation:

The image related to the exercise is necessary, to be able to solve therefore the attached one.

We have the following information:

Perimeter of the triangle = 58 units

Hypotenuse = 24 units

We have that the other two sides are equal and have x units, therefore we have the following:

x + x + 24 = 58

2 * x = 58-24

2 * x = 34

x = 34/2

x = 17

Now the triangle rotates around line k , and then it will result in a cone, which is a three-dimensional shape.

Therefore, the new shape will be cone with a radius of 17 units, tilt height 24 and units of height k.

4 0

3 years ago

A mailbox that is 36 inches tall is beside a tree.The length of the mailboxes shadow is 28 inches.The length of the trees shadow

mixer [17]

Answer:

10.5 feet

Step-by-step explanation:

In this problem, we have two similar triangles:

- One consists of the mailbox, its shadow and the hypothenuse

- The other one consists of the tree, its shadow and the hypothenuse

The two triangles are similar, so they have same proportions between their sides: therefore, we can apply the rule of three:

$\frac{m}{s_m}=\frac{t}{s_t}$

where

m = 36 in is the height of the mailbox

$s_m=28 in$ is the shadow of the mailbox

t is the height of the tree

$s_t=98 in$ is the length of the shadow of the tree

Solving for t, we find the height of the tree:

$t=\frac{m\cdot s_t}{s_m}=\frac{(36)(98)}{28}=126 in$

And since

1 feet = 12 inches

The height of the tree in feet is

$t=\frac{126}{12}=10.5 ft$

3 0

3 years ago

1. Given ΔQRS (is congruent to) ΔTUV, QS = 3v + 2 and TV = 7v - 6, find the length of QS and TV. Provide a detailed response bel

Morgarella [4.7K]

Because ΔQRS is congruent to ΔTUV, the the segments GS and TV are also congruent due to the letter order (Q and T are first and S and V are 3rd.) Since they are congruent QS=TV. So 3v + 2 = 7v - 6

Work:
3v + 2 = 7v - 6
+6 +6
3v + 8=7v
-3v -3v
8 = 4v
4 4
2 = v

3(2) + 2 = GS
6+2 = GS
8 = GS

7(2) - 6 = TV
14-6=TV
8 = TV

Final Answer: 8=QS and 8=TV

3 0

3 years ago

Read 2 more answers

Prove that in each triangle the total angles are 180 degrees

dmitriy555 [2]

This is a proof that the angles in a triangle equal 180°:

The top line (that touches the top of the triangle) is
running parallel to the base of the triangle.

So:

angles A are the same angles B are the same

And you can easily see that A + C + B does a complete rotation from one side of the straight line to the other, or 180°

8 0

3 years ago

Read 2 more answers