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2 years ago

The two triangles shown are congruent. Find the value of x

Mathematics

1 answer:

shusha [124]2 years ago

4 0

Answer:

x = 11

Step-by-step explanation:

right triangle ABC

using Pythagoras' identity

BC² = 7² + 24² = 49 + 576 = 625 ( take square root of both sides )

BC = $\sqrt{625}$ = 25

Since the triangles are congruent then corresponding sides are congruent.

ST = BC , that is

3x - 8 = 25 ( add 8 to both sides )

3x = 33 ( divide both sides by 3 )

x = 11

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Identify the values that should be written to complete the X diagram.

cestrela7 [59]

Answer:

See the attachment for what goes on your X diagram.

Rewrite: x² -7x +4x -28

Grouping: (x² -7x) +(4x -28) = x(x -7) +4(x -7) = (x +4)(x -7)

Step-by-step explanation:

The given quadratic is ...

... x² -3x -28 . . . . . a=1, b=-3, c=-28

a) The value at the top of the X diagram is the product a·c = 1·(-28) = -28.

The value at the bottom of the X diagram is the coefficient b = -3.

The values on the sides of the diagram are the factors of -28 that add up to make -3. These are -7 and 4. That is, ...

(-7)·(4) = -28

(-7)+(4) = -3

b) Since the two values on the sides of the diagram add up to give "b", the value of "b" in the equation can be rewritten as the sum of these two numbers. Doing that, we have ...

... x² -3x -28

... = x² +(-7+4)x -28

... = x² -7x +4x -28 . . . . . . order does not matter. It could also be x² +4x -7x -28

c) We can group pairs of terms in the rewritten expression and factor each pair.

... = (x² -7x) +(4x -28) . . . . . first pair has a common factor of x; second pair, 4

... = x(x -7) +4(x -7) . . . . . . . these terms now have a common factor: (x -7)

... = (x +4)(x -7) . . . . . . . . . . the complete factorization of x² -3x -28

3 0

3 years ago

The first term of an arithmetic sequence is -5, and the tenth term is 13. Find the common difference.

zzz [600]

Hello,

$u_{1} =-5\\
 u_{2} =-5+d\\
 u_{3} =-5+2d\\
 u_{4} =-5+3d\\
...\\
 u_{10} =-5+9d=13\\
==\ \textgreater \ 9d=18 \\
==\ \textgreater \ d=2

$

6 0

3 years ago

Jake charges $50 plus $2 per window. Hannah charges $20 plus $5 per window. For how many windows washed do they charge the same

tester [92]

Answer:

Step-by-step explanation:

50 plus 10 windows by 2 dollars will give you 70 dollars.

20 plus 10 Windows by 5 dollars give you 70 dollars

6 0

2 years ago

Read 2 more answers

Choose the equation that represents the graph below: (1 point) Graph of a line passing through points 0 comma 6 and 9 comma 0 y

aleksklad [387]

Answer:

Option C is correct.

Equation of a line $y=\frac{-2}{3}x+6$ passing through (0,6) and (9,0).

Explanation:

Given the two points (0, 6) and (9 ,0).

To find the equation for the given two points $(x_{1},y_{1})$ and $(x_{2},y_{2})$ is,

$y-y_{1}=m(x-x_{1})$ ; where m is the slope and is given by:

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

First find the slope m:

$m=\frac{0-6}{9-0} =\frac{-6}{9} =\frac{-2}{3}$

Substitute this value in equation of line:

$y-6=\frac{-2}{3} (x-0)$ or

$y-6=\frac{-2}{3} x$

⇒ $y=\frac{-2}{3}x+6$

Therefore, the equation for the given point is: $y=\frac{-2}{3}x+6$

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2 years ago

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tangare [24]

Answer:

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3 years ago