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3 years ago

The following polygons are similar: True or False

Mathematics

2 answers:

exis [7]3 years ago

8 0

It is true they are not

stellarik [79]3 years ago

7 0

I would have to say false because they do not have the same perimeter and area

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I could use alot of help on this please and thankyouuuu

kicyunya [14]

Answer:

B. Step 4 is incorrect , it should be $\frac{10}{8}$

Step-by-step explanation:

6x-1= -2x+9

Step 1

Collect like terms and change signs if you move anything from one side to the other; 6x+2x = 9+1

Step 2: Add like terms on both sides

8x = 10

Step 3: To remain with just x on one side, divide both sides by 8 and it becomes;

$\frac{8x}{8} = \frac{10}{8}$

The two 8s cancel each other and you remain with $x=\frac{10}{8}$

6 0

4 years ago

Prove that: 7^16+7^ 14 is divisible by 50.

alekssr [168]

Answer:

See Explanation

Answer: $\boxed{ {7}^{14}} .50$

Step-by-step explanation:

${7}^{16} + {7}^{14} \\ \\ = {7}^{14} ( {7}^{2} + 1) \\ \\ = {7}^{14} (49 + 1) \\ \\ = {7}^{14}.50$

Since, one factor of ${7}^{16}+ {7}^{14}$ is 50.

Therefore, ${7}^{16}+ {7}^{14}$ is divisible by 50.

Hence proved.

3 0

3 years ago

Outside of his barn than for the inside. If he uses 107 quarts in all,

Mrac [35]

Answer:

11 gallons of paint Jay needed for the inside .

Step-by-step explanation:

Consider the provided information.

Let x is the quart of paint Jay needed for the outside.

Let y is the quart of paint Jay needed for the inside .

Jay needs 19 quarts more paint for the outside of his barn than for the inside.

$x=y+19$

He uses 107 quarts in all,

$x+y=107$

Substitute the value of x in above equation.

$y+19+y=107$

$2y=107-19$

$2y=88$

$y=44$

Hence, 44 quarts of paint Jay needed for the inside .

But we need to find how many gallons of paint will be used to paint the inside of the barn.

So convert 44 quarts into gallon.

1 quarts = 0.25 gallon

1×44 quarts = 0.25×44 gallon

44 quarts = 11 gallon

Hence, 11 gallons of paint Jay needed for the inside .

7 0

3 years ago

If f(x) = 5x + 4, which of the following is the inverse of Ax)?

Levart [38]

Answer:

$f^{-1}$ (x) = $\frac{x-4}{5}$

Step-by-step explanation:

let y = f(x) and rearrange making x the subject, that is

y = 5x + 4 ( subtract 4 from both sides )

y - 4 = 5x ( divide both sides by 5 )

$\frac{y-4}{5}$ = x

change x to $f^{-1}$ (x) and y back to x, thus

$f^{-1}$ (x) = $\frac{x-4}{5}$

6 0

4 years ago

Find the equation of the sphere centered at (-9,9, -9) with radius 5. Normalize your equations so that the coefficient of x2 is

olganol [36]

<h2>Answer:</h2>

(a) x² + y² + z² + 18(x - y + z) + 218 = 0

(b) (x + 9)² + (y - 9)² + 56 = 0

<h2>Step-by-step explanation:</h2>

The general equation of a sphere of radius r and centered at C = (x₀, y₀, z₀) is given by;

(x - x₀)² + (y - y₀)² + (z - z₀)² = r² ------------------(i)

From the question:

The sphere is centered at C = (x₀, y₀, z₀) = (-9, 9, -9) and has a radius r = 5.

Therefore, to get the equation of the sphere, substitute these values into equation (i) as follows;

(x - (-9))² + (y - 9)² + (z - (-9))² = 5²

(x + 9)² + (y - 9)² + (z + 9)² = 25 ------------------(ii)

Open the brackets and have the following:

(x + 9)² + (y - 9)² + (z + 9)² = 25

(x² + 18x + 81) + (y² - 18y + 81) + (z² + 18z + 81) = 25

x² + 18x + 81 + y² - 18y + 81 + z² + 18z + 81 = 25

x² + y² + z² + 18(x - y + z) + 243 = 25

x² + y² + z² + 18(x - y + z) + 218 = 0 [equation has already been normalized since the coefficient of x² is 1]

Therefore, the equation of the sphere centered at (-9,9, -9) with radius 5 is:

x² + y² + z² + 18(x - y + z) + 218 = 0

(2) To get the equation when the sphere intersects a plane z = 0, we substitute z = 0 in equation (ii) as follows;

(x + 9)² + (y - 9)² + (0 + 9)² = 25

(x + 9)² + (y - 9)² + (9)² = 25

(x + 9)² + (y - 9)² + 81 = 25 [subtract 25 from both sides]

(x + 9)² + (y - 9)² + 81 - 25 = 25 - 25

(x + 9)² + (y - 9)² + 56 = 0

The equation is therefore, (x + 9)² + (y - 9)² + 56 = 0

6 0

4 years ago