Abdul is making a smoothie of 10 veggies. He has 12 to choose from. How many different smoothies can Abdul make?

A reflecting pool is shaped like a right triangle with one leg along the wall of a building. the hypotenuse is 9 feet longer tha

morpeh [17]

Answer:

Leg side along the wall = x ft = 8 ft

The other leg side = 7+x ft = 7+8=15 ft

The Hypotenuse =9+x ft = 9+8 = 17 ft

Step-by-step explanation:

In the question, the shape of the pool is right triangle.

Let the leg side along the wall to be the x ft

Let the other leg side to be 7+x ft

Let the longest side/hypotenuse to be x+9 ft

Apply the Pythagorean relationship where the sum of squares of the legs equals the square of the hypotenuse

This means;

$x^2 +(x+7)^2=(x+9)^2\\\\$

Expand the terms in brackets

$x^2+(x+7)^2=(x+9)^2\\\\\\x^2+x^2+14x+49=x^2+18x+81$

collect like terms

$x^2+x^2-x^2=18x-14x+81-49\\\\\\x^2=4x+32\\\\\\x^2-4x-32=0$

solve for x in the quadratic equation by factorization

$x^2-4x-32=0\\\\\\x^2-8x+4x-32=0\\\\\\x(x-8)+4(x-8)=0\\\\\\(x+4)(x-8)=0\\\\\\x+4=0,x=-4\\\\x-8=0,x=8$

Taking the positive value of x;

x=8ft

Finding the lengths

Leg side along the wall = x ft = 8 ft

The other leg side = 7+x ft = 7+8=15 ft

The Hypotenuse =9+x ft = 9+8 = 17 ft

6 0

3 years ago

The linear equation was solved using these steps. Linear equation: 1 3 (12x + 15) = 7 Step 1: 4x + 5 = 7 Step 2: 4x = 2 Step 3:

bagirrra123 [75]

Answer:

The property that was used in step 1 was the distributive property.

The property that was used in step 2 was the subtraction property of equality.

The property that was used in step 3 was the division property of equality.

Step-by-step explanation:

5 0

3 years ago

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Ratio and proportion. if 2:x=5:8. Find x

Ksju [112]

analyze problem

5/2=3.5

8/3.5=

16/7=

2 2/7

6 0

2 years ago

L<br> 1) Factor the rational function.<br> 22-4<br> 22-50-14<br> X intercept

Afina-wow [57]

Answer: i dont know

Step-by-step explanation:

3 0

2 years ago

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Please help

harkovskaia [24]

Answer:

Sergio's strategy was to multiply the sum of the length and width of the rectangle by 2. This was one correct way to find the perimeter of the rectangle.

Jamie's strategy was to add the given measurements of the length and width of the rectangle together. This was another correct way to find the perimeter of the rectangle.

Karina's strategy was to multiply the given length of the rectangle by 2 and add this product to the width of the rectangle. This was NOT a correct way to find the perimeter of the rectangle, as it did not follow the formulas to finding the perimeter of a rectangle: l + w + l + w, or 2(l + w) and furthermore formulas that explain the same thing. Karina only multiplied the length by 2 and did not account for the width of the retangle which she should have done as well.

Ethan's strategy was to multiply the width by 2, multiply the length by 2, and add these two products together to find the perimenter. This final strategy was correct, and can be used to find the perimeter of the rectangle.

Hope this helps you! I love doing math, so enjoy!

3 0

2 years ago

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