If a*b means 2a + b , then what is 2*5 ?

If the campers at Camp Grilled Meat prefer hot dogs to hamburgers by a ratio of 4:3, and they need 500 hot dogs, how many hambur

Morgarella [4.7K]

Answer:

375

Step-by-step explanation:500 equals 100% divide by 4 its 125 times 3 equals 375, your welcome

7 0

3 years ago

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What is the area of the trapezoid shown below?

denis-greek [22]

Hello there!

Your answer is 180 units²

Step-by-step explanation:

$\large \boxed{ \mathsf{ \frac{1}{2} \times sum \: of \: two \: parallel \: \times height}}$

The formula in the box is an area of trapezoid formula. We know the sum of two parallel lines which is 15 because 7+4 = 11 + 4 = 15

another 4 comes from parallel side. If both sides are parallel, they have same length.

The only thing that is missing is the height. The height can be found by using Pythagorean Theorem as you notice a right-angle triangle when splitting in half.

$\large \boxed{ {a}^{2} + {b}^{2} = {c}^{2} }$

The formula in the box is Pythagorean Theorem for finding a length of right-angle triangle.

Given where a is opposite, b is adjacent and c is hypotenuse. (Note that c must be hypotenuse.)

Our a is missing

Our b is 7

Our c is 25.

From the formula and given lengths:

$\large{ {a}^{2} + {7}^{2} = {25}^{2} } \\ \large{ {a}^{2} + 49 = 625} \\ \large{ {a}^{2} = 625 - 49} \\ \large{ {a}^{2} = 576} \\ \large{a = 24}$

Therefore, our opposite is 24. Since our opposite equals the height of a trapezoid. We can proceed with the trapezoid formula.

$\large{ \frac{1}{2} \times 15 \times 24 = 15 \times 12 = 180 } \\ \large{180}$

Therefore, the area of trapezoid is 180 units²

We can also use another method to find the area by adding up between area of triangle and area of Rectangle.

Our rectangle formula is length × width. We know width which is 4 and our length is 24 from opposite side of triangle which equal to the length of rectangle.

Length × Width = 24 × 4 = 96

Hence, the area of Rectangle is 96.

Next, we find the area of triangle which is 1/2 × base × height.

Our base is 7 and height is the opposite side of triangle which is 24.

Therefore, the area of triangle is 1/2 × 7 × 24 = 7 × 12 = 84

If we add the area of triangle and rectangle up each other, we will get the area of trapezoid for this problem which is 96 from rectangle and 84 from triangle. Therefore, 96+84 = 180 units²

4 0

3 years ago

7

trasher [3.6K]

Answer:

we have to use the formula of simple interest, which is

I = P r t

Where I is the interest earned, P is the amount invested, r is the rate of interest and t is the time duration .

In the given question, I = $4840 , r =11% or 0.11, t=11, P is unknown .

Substituting the values in the formula, we will get

4840=0.11*11*P4840=0.11∗11∗P

4840=1.21 P4840=1.21P

P=4000

So she invested $4000

5 0

2 years ago

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Maria has decided to invest to help with her retirement savings. How much would she have to invest to have $113,400 after 20 yea

Ipatiy [6.2K]

Answer:

$56,226

Step-by-step explanation:

x = investment

Earning interest of 3.57% is the equivalent of multiplying the initial balance (investment) by 1.0357;

Over 20 years, the new balance can be found by multiplying the initial balance by (1.0357)²⁰;

We can formulate an equation to solve to get the initial investment:

x(1.0357)²⁰ = 113400

(2.01687752)x = 113400

x = ¹¹³⁴⁰⁰/₍₂.₀₁₆...₎

x = 56225.5263 → 56226

5 0

3 years ago

Janelys leans a 16-foot ladder against a wall so that it forms an angle of 61^{\circ} ∘ with the ground. How high up the wall do

Lilit [14]

The height the ladder reaches up the wall is $13.99ft$

The ladder, the wall, and the ground form a right-angled triangle.

The ladder is the hypotenuse, or the longest side, of the triangle. The wall is opposite of the angle, $61^{\circ}$ , that the ladder makes with the ground.

The formula relating the angle the ladder makes with the ground, the ladder, and the wall is the trigonometric ratio

$sin 61^{\circ}=\dfrac{\text{wall height}}{\text{ladder length}}$

substituting the values for the ladder length, and $sin61^{\circ}$ , and solving, we get

$0.8746=\dfrac{\text{wall height}}{16}\\\\\text{wall height}=0.8746\times16\approx13.99ft\text{ (to the nearest hundredth)}$

Learn more about trigonometry here brainly.com/question/10726141

5 0

2 years ago