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3 years ago

The value of x must be greater than

Mathematics

1 answer:

frozen [14]3 years ago

4 0

Using the Pythagorean theorem:

12^2 + x^2 = 15^2

144 + x^2 = 225

x^2 = 225 - 144

x^2 = 81

x = sqrt(81)

x = 9

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What is the side length, in inches, of the pets

tatiyna

Candy draws a square design with a side length of x inches for the window at the pet shop. She takes the design to the printer and asks for a sign that has an area of 16x2 – 40x + 25 square inches. What is the side length, in inches, of the pet shop sign?

Answer:

the length of the sign is $4x-5$ inches

Step-by-step explanation:

Given

Area of the square of design = $16x^{2} -40x+25$

First we find the roots of equation $16x^{2} -40x+25=0$

The roots of the quadratic equation $ax^{2} +bx^{2} +c=0$ are given by

$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

where $a=16, b=-40, c=25$

$x=\frac{40\pm\sqrt{(-40)^2-4\times 16\times 25}}{2\times 16}$

$x=\frac{40\pm\sqrt{1600-1600}}{32}$

$x=\frac{40\pm\sqrt{0}}{32}$

$x=\frac{40}{32}$

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

$4x=5\\4x-5=0$

That is, the factors of the polynomial $16x^{2} -40x+25$ are $4x-5$ and $4x-5$ .

So, Area of the square design = $16x^{2} -40x+25$ = $(4x-5)^{2}$

Area of a square = Length^2

Thus, the length of the sign is $4x-5$ inches

7 0

2 years ago

You're ordering a sandwich at the local deli, below is a tree diagram of the possible orders. What is the probability that your

dusya [7]

Answer:

Step-by-step explanation:

1. So there is two bread options but let's ignore that due every option being the same for both bread options.

2. So if you look there are three meat options meaning there is a one in three chance logical chance someone picks turkey (note when I say logical I mean that doesn't mean that this will be true in real life) and there is a one in two logical chance someone picks Swiss cheese.

3. So with a one in three chance logical meat option and a one two chance cheese option and.

4. Now knowing this it is simple math at this point as simple as $\frac{1}{3}$ x $\frac{1}{2}$

5. 1 x 1 = 1 and 3 x 2 = 6

6. leading to $\frac{1}{6}$

4 0

2 years ago

An actor invests some money at 7%, and $48000 and more than twotimes the amount of 9%. The total annual interest earned from the

forsale [732]

Answer:

At 7% $54,000

At 9% $156,000

Step-by-step explanation:

Let x be the amount invested at 7%, Then 2x + 48000 will be the amount invested at 9%

We know that:

7% = 0.07 & 9% = 0.09

So we can write the interest equation as follows:

0.07x + 0.09 (2x + 48000) = 17820

0.07x + 0.18x + 4320 = 17820

0.25x + 4320 = 17820

Subtracting 4320 from both sides of the equation we get:

0.25x = 17820 - 4320

0.25x = 13500

Dividing both sides of the equation by 0.25 we get:

x = 13500 / 0.25

x = $54,000 invested at 7%

2 x 54000 + 48000

= $156,000 invested at 9%

Hence the amount invested at 7% is $54,000.

& the amount invested at 9% is $156,000.

5 0

3 years ago

What are the zeros of this graph

kotegsom [21]

The zeroes ( where the graph cuts the x axis) ar (-2,0) AND (2,0)

tHE FACTOrIAL FORM IS (x - 2)(x + 2)

Its B

3 0

3 years ago

Help please!!

Free_Kalibri [48]

Tan²( θ ) - (1 + √3) tan (θ) + √3 = 0

tan²( θ ) - (tan (θ) + √3 tan (θ)) + √3 = 0

tan²( θ ) - tan (θ) - √3 tan (θ) + √3 = 0

tan( θ ) ( tan (θ) - 1) - √3 ( tan (θ) - 1 ) = 0

( tan( θ ) - 1 ) ( tan( θ ) - √3 ) = 0

tan( θ ) - 1 = 0

θ = π/₄

tan( θ ) - √3 = 0

θ = π/₃

so θ = π/₄ and θ = π/₃

7 0

2 years ago

Read 2 more answers