Jerry started his apprenticeship testing day with 72 M&M’s in his pocket. By lunch, he had 45 left. What percent did he have left in his pocket?

a. ΔEGF~ΔGHF~ΔEHG are the similarities between the three right triangles.

b. HF/HG = GH/EH; EF/EG = EG/EH

According to the similar right triangle theorem, if a right triangle's altitude is drawn from its right angle, two similar right triangles are created, and both similar right triangles are identical to the original right triangle. All three right triangles are essentially the same.

Similar triangles contain three pairs of comparable side lengths that are proportionate to one another, or whose ratios are identical.

The corresponding side lengths are taken into account when constructing similarity statements.

A similarity assertion linking the three right triangles is thus: ΔEGF~ΔGHF~ΔEHG.

b. They will have the following side ratios: EF/EG = EG/EH HF/HG = GH/EH

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Hope it helps :)

\(x + 4y = 9 \\

-x - 2y = 3 \\ eliminate \: one \: variable \: by \\ adding \: the \: equations \\ 2y = 12 \\ divide \: both \: sides \\ y = 6 \\ substitute \: the \: value \: of \: y \\ \: into \: equation \: ...2 \\ - x - 2(6) = 3 \\ solve \: the \: equation \\ - x - 12 = 3 \\ - x = 3 + 12 \\ - x = 15 \\ x = - 15 \\ SOLUTION \\ x = - 15 \\ y = 6 \\ Hope \: it \: helps :)\)

Answer:

\(\begin{aligned}SA &= 7.125\pi \text{ in}^2\\& \approx 22.4 \text{ in}^2 \end{aligned}\)

Step-by-step explanation:

We can find the Surface Area of the can by adding the areas of each of its parts:

\(SA = 2( A_{\text{base}}) + A_\text{side}\)

First, we can calculate the area of the circular base:

\(A_{\text{circle}} = \pi r^2\)

\(A_{\text{base}} = \pi (0.75 \text{ in})^2\)

\(A_{\text{base}} = 0.5625\pi \text{ in}^2\)

Next, we can calculate the area of the rectangular side:

\(A_\text{rect} = l \cdot w\)

\(A_\text{side} = (4\text{ in}) \cdot C_\text{base}\)

Since the width of the side is the circumference of the base, we need to calculate that first.

\(C_\text{circle} = 2 \pi r\)

\(C_\text{base} = 2 \pi (0.75 \text{ in})\)

\(C_\text{base} = 1.5 \pi \text{ in}\)

Now, we can plug that back into the equation for the area of the side:

\(A_\text{side} = (4\text{ in}) (1.5\pi \text{ in})\)

\(A_\text{side} = 6\pi \text{ in}^2\)

Finally, we can solve for the surface area of the can by adding the area of each of its parts.

\(SA = 2( A_{\text{base}}) + A_\text{side}\)

\(SA = 2(0.5625\pi \text{ in}^2) + 6\pi \text{ in}^2\)

\(\boxed{SA = 7.125\pi \text{ in}^2}\)

\(\boxed{SA \approx 22.4 \text{ in}^2}\)

Answer:

3x-4=2x+1 the answer is x=5

3x-4-2x=2x+1-2x the answer is x=5

x-4=1 the answer is x=5

x-4+4=1-4 the answer is x=-3

x=-3 is already the answer

Step-by-step explanation:

3x-4=2x+1

=3x-2x=1+4

=1x=5

=1x/1=5/1

=x=5

3x-4-2x=2x+1-2x

=3x-2x-2x+2x=1+4

=1x=5

=1x/1=5/1

=x=5

Answer:

3n + 7.6 = 52.6

Step-by-step explanation:

The corresponding sides of the similar triangles are given as follows:

Similar triangles are triangles that share these two features presented as follows:

The corresponding sides are those that have the proportional side lengths, hence they are those who have the same angle measure in each triangle.

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Answer:

$223,787

Step-by-step explanation:

r = 0.02

C = 191,000

t = 8

S = 191,000 (1 + 0.02)⁸

Follow order of operations (PEMDAS).

S = 191,000 (1.02)⁸

S = 191,000 (1.171659381)

S = 223,786.9

(We want to round to the nearest dollar, which is the ones place, so ignore all digits after the tenths place.)

Rounding, S = 223,787

Answer:

12p=48

Step-by-step explanation:

The equation of the sinusoid function is:

3 Sin πx + 2.

Let's analyze the given options to find the correct equation:

a. 3 Cos πx + 2:

This option is a cosine function with a vertical shift of 2, but it does not have the correct amplitude or period. Therefore, it is not the correct equation.

b. 3 Sin x: This option is a sine function with the correct amplitude, but it does not have the correct vertical shift or period. Therefore, it is not the correct equation.

c. 3 Sin πx + 2: This option is a sine function with the correct amplitude and vertical shift. Let's check if it has the correct period:

To determine if the period is correct, we need to calculate the x-values when the function repeats itself.

In this case, we need to find x-values such that sin(πx) = 0, since the function will reach its maximum and minimum points again at those x-values.

sin(πx) = 0 when πx = 0, π, 2π, 3π, ...

Solving for x, we have:

πx = 0 ⟹ x = 0

πx = π ⟹ x = 1

πx = 2π ⟹ x = 2

πx = 3π ⟹ x = 3

From this, we can see that the function repeats itself every integer value of x, which matches the given information.

Therefore, option (c) is the correct equation: 3 Sin πx + 2.

Option (d) 3 Cos x does not have the correct vertical shift or period, so it is not the correct equation.

Hence, the equation of the sinusoid function is:

3 Sin πx + 2.

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Answer:

4 years and 24% simple interest

Step-by-step explanation:

if 500 make a 6% simple interest then if it asks to get to 2k then it will be like 5x4=20 so 4 years, and it will make 24% vaule of simple interest

The one which not a justification for the higher property taxes in state A would be: Voting day in state A is Tuesday compared to Thursday in state B. The correct answer is D.

Property taxes fund schools, libraries, police and fire departments, along with public works such as roads, parks, and playgrounds. They're essential to our communities, but that doesn't make them any easier to pay. For the appraisal of a taxable property, property tax is determined as a percentage of your home's value, so the more your home increases in value, the higher your property tax bill will increase. And the high property taxes have nothing to do with voting day in any state.

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The expression that could be used to calculate the amount Trina was charged in interest for the billing cycle is  (APR / 365) x 30 days x adjusted balance.

The adjusted balance method is one of the methods for computing the finance charge (interest and other fees) for credit cards.

The adjusted balance is the ending balance determined after adjusting the opening balance with purchases and payments.

Credit card interest method = adjusted balance method

Beginning balance = $780

Purchase = $170

Payment = $210

Adjusted balance, AB = $740 ($780 + $170 - $210)

APR = 17% = 0.17 (17/100)

The interest charged = (APR / 365) x 30 days x adjusted balance

= $10.34 [(0.17/365) x 30 x $740]

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Answer:

D

Step-by-step explanation:

Closed circle is used for inequalities with a line under it.

Open circle is for regular inequalities

Answer:

d

Step-by-step explanation:

closed circle means greater than or equal to and we know its going up from 23

\((\stackrel{x_1}{-3}~,~\stackrel{y_1}{-11})\hspace{10em} \stackrel{slope}{m} ~=~ 4 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-11)}=\stackrel{m}{ 4}(x-\stackrel{x_1}{(-3)}) \implies y +11 = 4 ( x +3) \\\\\\ y+11=4x+12\implies {\Large \begin{array}{llll} y=4x+1 \end{array}}\)

The equation is:

Work/explanation:

Recall that the point slope formula is \(\rm{y-y_1=m(x-x_1)}\),

where m is the slope and (x₁, y₁) is a point on the line.

Plug in the data:

\(\rm{y-(-11)=4(x-(-3)}\)

Simplify.

\(\rm{y+11=4(x+3)}\)

Simplified to slope intercept:

\(\rm{y+11=4x+12}\)

\(\rm{y=4x+1}\) <- this is the simplified slope intercept equation

Answer:

Step-by-step explanation:

Answer:

165

Step-by-step explanation:

The expression that has a value of 26 when a=4 and b=5 is option B: a \((√16+ b) - 10.\)

Let's substitute a=4 and b=5 in each expression and see which one has a value of 26:

An expression is a mathematical phrase that can contain numbers, variables, and mathematical operations such as addition, subtraction, multiplication, and division. Expressions can also include exponents, roots, and other mathematical symbols. The value of an expression can vary depending on the specific values of the variables used in the expression.

A) \(a√16+b-10 = 4√16 + 5 - 10 = 4x4 + 5 - 10 = 9\)(not equal to 26)

B)\(a (√16+ b) - 10 = 4(√16 + 5) - 10 = 4(4 + 5) - 10 = 26\) (equal to 26)

C) \(a√16+ (b-10) = 4√16 + (5-10) = 4x4 - 5 = 11\) (not equal to 26)

D)\((a√16) + b-10 = (4√16) + 5 - 10 = 4x4 + 5 - 10 = 9\)(not equal to 26)

Therefore, the expression that has a value of 26 when a=4 and b=5 is option B: \(a (√16+ b) - 10.\)

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Answer:  if with 3.14 v= 37512.5333

if with pi v= 37531.56

Step-by-step explanation:

the formula is 1/3hπr^2

r= 2d so radius is 32

plus numbers in (square it multiple times pi or 3.14 then multiply times height and divide by 3)

Answer:

First, we need to find the total amount of trail mix that Sarah makes. The total amount of trail mix is the sum of the amount of almonds, dried cherries, walnuts, and raisins.

2 1/2 cups almonds + 3/4 cup dried cherries + 2 1/4 cups walnuts + 3/4 cup raisins = 5 3/4 cups

Next, we need to divide the total amount of trail mix by the amount of trail mix that each bag holds.

5 3/4 cups / 1 1/4 cups per bag = 4.6 bags (rounded down to 4 bags)

Therefore, Sarah fills 4 bags of trail mix.

Answer:

I think A because we can't see the thing

Answer:

x=1

Step-by-step explanation:

Answer:

15m-30

Step-by-step explanation:

\(\huge\fbox{Answer:~~~{\boxed{\bold{15m-30}}}}\)

Step-by-step explanation:

Hi there!

All we should do to simplify this expression is "distribute" 5:

\(\bold{5(3m-6)}\)

Multiply 5 by everything inside the parentheses:

\(\bold{15m-30}\)

Hope it helps! Enjoy your day!

#HaveAnAmazingDay

~Just a teenage girl willing to help

\(\bold{Besties4Ever}\)

Answer:

Step-by-step explanation: [-2.19] = -3

[3.67] = 3

[-0.83] = -1

The domain of this function is a group of real numbers that are divided into intervals such as [-5, 3), [-4, 2), [-3, 1), [-2, 0) and so on. This explains the domain and range relations of a step function.

This can be generalized as given below:

[x] = -2, -2 ≤ x < -1

[x] = -1, -1 ≤ x < 0

[x] = 0, 0 ≤ x < 1

[x] = 1, 1 ≤ x < 2

Answer:

y = - \(\frac{3}{2}\) x

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

with (x₁, y₁ ) = (- 2, 3) and (x₂, y₂ ) = (0, 0) ← 2 points on the line

m = \(\frac{0-3}{0-(-2)}\) = \(\frac{-3}{0+2}\) = - \(\frac{3}{2}\) , then

y = - \(\frac{3}{2}\) x + c ← is the partial equation

to find c substitute either of the 2 points into the partial equation

using (0, 0 )

0 = - \(\frac{3}{2}\) (0) + c = 0 + c , so

c = 0

y = - \(\frac{3}{2}\) x + 0 , that is

y = - \(\frac{3}{2}\) x

Answer:

47.1cm²

Step-by-step explanation:

diameter=15cm

circumference of circle= d×3.14

circumference=15×3.14

circumference=47.1

Answer:

7/6 or 1 1/6

Step-by-step explanation:

2/3 = 4/6

1/2 = 3/6

3/6 + 4/6 = 7/6 = 1 1/6