An architect builds a scale model of a new house that is being built. The roof line when looking at the front of the house forms an isosceles triangle. In the model, the base of the isosceles triangle is 24 inches and the length of the roof is 15 inches. The base angle that is formed is 37 degrees. In the actual house, the base of the isosceles triangle is 40 feet. What is the length of the roof for the actual house?
and What is the measure of the base angle between the base of the triangle and the roof line of the actual house?

Steven can buy at most 11 packages of balloons and stay within his budget.

Let's use the variable "n" to represent the number of packages of balloons Steven buys. Then the total cost of his purchases can be modeled by the following inequality:

5(1.59) + 3.29n ≤ 45.00

Here, we have multiplied the cost per package of streamers ($1.59) by the number of packages (5), and added the cost of the balloons ($3.29n). The total cost must be less than or equal to Steven's budget of $45.00.

To solve for n, we can first simplify the left side of the inequality:

7.95 + 3.29n ≤ 45.00

Then, we can isolate the variable n by subtracting 7.95 from both sides:

3.29n ≤ 37.05

Finally, we can solve for n by dividing both sides by 3.29:

n ≤ 11.28

Since n represents the number of packages of balloons, we must round down to the nearest whole number.

To know more about inequality here

https://brainly.com/question/28823603

#SPJ4

Answer:

the answer is 13.2

Step-by-step explanation:

Answer:

13.2

Step-by-step explanation:

277.2÷21=13.2 gallons

a. Average sales in the first quarter = (1/(3-0)) * ∫[0,3] (74.4 + 43.08sin(πt/6)) dt

b. Average sales in the second quarter = (1/(6-3)) * ∫[3,6] (74.4 + 43.08sin(πt/6)) dt

c. Average sales for the entire year = (1/(12-0)) * ∫[0,12] (74.4 + 43.08sin(πt/6)) dt

In mathematics, a function is a unique arrangement of the inputs (also referred to as the domain) and their outputs (sometimes referred to as the codomain), where each input has exactly one output and the output can be linked to its input.

To find the average sales for each time period, we need to calculate the average value of the sales function over the given time intervals.

(a) The first quarter (0 ≤ t ≤ 3):

To find the average sales over this time period, we need to calculate the definite integral of the sales function over the interval [0, 3] and divide it by the length of the interval.

Average sales in the first quarter = (1/(3-0)) * ∫[0,3] (74.4 + 43.08sin(πt/6)) dt

(b) The second quarter (3 ≤ t ≤ 6):

To find the average sales over this time period, we need to calculate the definite integral of the sales function over the interval [3, 6] and divide it by the length of the interval.

Average sales in the second quarter = (1/(6-3)) * ∫[3,6] (74.4 + 43.08sin(πt/6)) dt

(c) The entire year (0 ≤ t ≤ 12):

To find the average sales over the entire year, we need to calculate the definite integral of the sales function over the interval [0, 12] and divide it by the length of the interval.

Average sales for the entire year = (1/(12-0)) * ∫[0,12] (74.4 + 43.08sin(πt/6)) dt

Learn more about function on:

https://brainly.com/question/10439235

#SPJ4

Answer:

hope it helps

Answer:

\(x = \frac{z + 11y}{5}\)

Step-by-step explanation:

To solve for x, given the equation: z = 5x - 11y

Add 11y to both sides:

z + 11y = 5x - 11y + 11y

z + 11y = 5x

Divide both sides by 5 to isolate x:

\(\frac{z + 11y}{5} = \frac{5x}{5}\)

\(\frac{z + 11y}{5} = x\)

Using the relation between velocity, distance and time, it is found that the average speed of the record winner of the wheelchair division was of 20.04 miles per hour.

"The record for the Boston Marathon’s wheelchair division is 1 hour,

18 minutes, and 27 seconds.

The Boston Marathon is 26.2 miles long. What was the average speed of the record winner of the wheelchair division?"

Velocity is distance divided by time, that is:

v = d/t.

For this problem, we have that:

Hence the velocity is given by:

v = 26.2/1.3075 = 20.04 miles per hour.

The average speed of the record winner of the wheelchair division was of 20.04 miles per hour.

More can be learned about the relation between velocity, distance and time at https://brainly.com/question/24316569

#SPJ1

Answer:

the answer is c

Step-by-step explanation:

i have spoken that is all im going to do

poe´kmon

The coordinate of the reflection of (8,3) is (8,-3).

In order to find the reflection of the coordinate, one basic rule must be kept in mind that both the original and reflected points are equidistant from their axis or point of reflection.

The given point is (8, 3).

Since the reflection of a point over x-axis means that both the points are equidistant from the x-axis.

Which implies that for a point (x,y), the reflection over x-axis is (x, -y).

Thus, for the point (8, 3), the coordinate of its reflection is (8, -3).

This is shown in the graph given below,

Hence, the coordinate of the reflection of the given point over x-axis is (8 , -3) and its graph has been shown clearly.

To know more about coordinate of reflection of a point click on,

https://brainly.com/question/24215981

#SPJ1

Answer:

$128.10

Step-by-step explanation: (8 * 16.95) - 7.50(135.6) - 7.50128.1

Hopefully this helps you if you don't mind clicking brainliest :)

Answer:

44

Step-by-step explanation:

Step-by-step explanation:

1)  Total rectangle area =  W x H = 12 x 8 = 96 cm^2

 area of triangle (shaded portion) = 1/2 base * height = 1/2 * 7 x 8 = 28 cm^2

              Nonshaded portion = 96 - 28 cm^2 = 68 cm^2

          ratio shaded:nonshaded is then   28 : 68 = 7:17

2)   Look at the two middle triangles :  Height of each = 8 cm

       then reading across the diagram  height + base + height = 21 cm

            so base = 5 cm

   area of ONE triangle = 1/2 * base * height = 1/2 * 5 * 8 = 20 cm^2

        total area for FOUR of them  = 80 cm^2

To prove that triangles AEC and BED are congruent, you can use the ASA (Angle-Side-Angle) congruence criterion.

ASA states that if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent.

In this case, you would need to show that:

If you can prove these three conditions, you can conclude that triangles AEC and BED are congruent by the ASA criterion.

\(\huge{\mathcal{\colorbox{black}{\textcolor{lime}{\textsf{I hope this helps !}}}}}\)

♥️ \(\large{\textcolor{red}{\underline{\texttt{SUMIT ROY (:}}}}\)

Answer:

30

Step-by-step explanation:

Answer:

30

Step-by-step explanation:

your welcome.

Answer:

yes the lines are parralel

Step-by-step explanation:

Answer:

Yes they are. Parallel lines are lines that don't intersect, no matter if they are sideways!

The commutative property of addition is shown here a+bi+c+di = a+c+bi+di which is the correct answer.

The commutative property states that an expression of the form (A + B) can be solved as (B + A) by an addition operation that does not change the result.

This property applies to multiplication also.

We have the given expression:

a+bi+c+di = a+c+bi+di

We have to identify the property of addition in the above expression.

Since we can say here that (bi+c) is expressed as (c+bi).

The commutative property of addition states that the numbers can be added in any order.

Mathematically, it states that a+b = b+a.

Here, (bi+c) can be replaced by (c+bi), whether 'b' is added to 'ci' or 'ci' is added to 'b', the result is always the same.

Therefore, the commutative property of addition is the correct answer

Learn more about the commutative property;

https://brainly.com/question/27325958

Answer:

commutative property

Step-by-step explanation:

edge2020

The antiderivative of the function f(x) = e^(-x) - e^(4x) is given by -e^(-x) - (1/4)e^(4x)/4 + C, where C is the constant of integration. This represents the general solution to the indefinite integral of the function.

In simpler terms, the antiderivative of e^(-x) is -e^(-x), and the antiderivative of e^(4x) is (1/4)e^(4x)/4. By subtracting the antiderivative of e^(4x) from the antiderivative of e^(-x), we obtain the antiderivative of the given function.

To evaluate a definite integral of this function over a specific interval, we need to know the limits of integration. The indefinite integral provides a general formula for finding the antiderivative, but it does not give a specific numerical result without the limits of integration.

To compute the antiderivative of the function f(x) = e^(-x) - e^(4x), we can use basic integration formulas.

∫(e^(-x) - e^(4x))dx

Using the power rule of integration, the antiderivative of e^(-x) with respect to x is -e^(-x). For e^(4x), the antiderivative is (1/4)e^(4x) divided by the derivative of 4x, which is 4.

So, we have:

∫(e^(-x) - e^(4x))dx = -e^(-x) - (1/4)e^(4x) / 4 + C

where C is the constant of integration.

This gives us the indefinite integral of the function f(x) = e^(-x) - e^(4x).

If we want to compute the definite integral of f(x) over a specific interval, we need the limits of integration. Without the limits, we can only find the indefinite integral as shown above.

Learn more about indefinite integral here:

brainly.com/question/28036871

#SPJ11

Step-by-step explanation:

since both points are on the same horizontal line (same y coordinate), we can save the detour via the Pythagoras approach. we only need to look at the difference of the x coordinates to get the distance :

10.8 - -15.6 = 10.8 + 15.6 = 26.4

184,219,440 ways.

What is contestant?

A participant in a contest or competition is known as a contestant. A contestant is someone who challenges election results.

There are 570 contestants, and any one of them can win the first prize.

One of the remaining 569 people can receive the second prize.

Third may be assigned to any of the remaining 568.

We can accomplish this in 570*569*568 ways

= 184,219,440 ways.

To learn more about contestant checkout https://brainly.com/question/27896050

#SPJ4

Answer:

ASA

Step-by-step explanation:

Answer:

Answer:

What is the value of x.

If you know the value of x

then,

perimeter= x+12+7.71

and

if this traingle is an equilateral triangle

then,

area =½×7.71×x

In this all process you need to find x then all will be easy

Hope it helped you

If not then I am sorry for that

Bye

The average Jeremy can create 24 different outfits for school by combining 1 pair of pants, 1 shirt, 1 tie, and 1 jacket.

Jeremy can mix and match his items to create different outfits for school. Since he owns 4 pairs of pants, 3 shirts, 3 ties, and 2 jackets, he can create 24 different outfit combinations. For each outfit, he must wear 1 pair of pants, 1 shirt, 1 tie, and 1 jacket. He can mix and match any of the items he owns to create a variety of looks. For example, he could wear a blue shirt, grey pants, and a striped tie with a black jacket. Or, he could wear a white shirt, black pants, a polka-dotted tie, and a brown jacket. By combining his items in different ways, he can create 24 different outfits for school.

Learn more about average here

https://brainly.com/question/24057012

#SPJ4

We will get  \(61/75\), when 6(1/6) is divided by 7(5/6)

The usually written symbol for division is (÷). The "/" (slash) symbol is used in spreadsheets and other computer applications.

Division is the opposite of multiplication in mathematics.

The division is often considered the most difficult of the four main arithmetic operations. This page explains how to perform division calculations. Once we have a good understanding of the method and rules, we can use the calculator for more complex calculations without making mistakes.

For example, consider how we would find the answer to \(10 / 2\) (ten divided by two). This is the same as "split" \(10\)sweets between \(2\) children. Both children must end up with the same number of candies. In this example, the answer is \(5\).

Hence when \(61/6\) is divided by \(75/6\) it means \((61/6)/(75/6)\)

in which \(6\) cancels the \(6\).

The final answer will be \(61/75\)

Learn more about division here:

https://brainly.com/question/21416852

#SPJ9

The tennis ball has traveled a horizontal distance of 3.717 m, to the nearest tenth of a metre, when it lands on the ground. Hence, the correct option is (A) 3.7.

The given function is h(d) = -0.12d² +0.22d+1.1.

It models the path of a tennis ball hit from a height of 1.1 m above the ground.

Here, d represents the horizontal distance in meters, and h(d) represents the height in meters.

To find how far the tennis ball travelled horizontally when it lands on the ground, we need to find the value of d when h(d) = 0, because the ball will hit the ground when its height is zero.

Substituting h(d) = 0 in the given function, we get:

0 = -0.12d² +0.22d+1.1

Simplifying, we get: 0.12d² - 0.22d - 1.1 = 0

We can solve this quadratic equation using the quadratic formula, which is given by:

-b ± sqrt(b² - 4ac) / 2a, where a, b, and c are the coefficients of the quadratic equation.

Here, a = 0.12, b = -0.22, and c = -1.1.

Substituting the values, we get:

d = [0.22 ± sqrt(0.22² - 4(0.12)(-1.1))] / 2(0.12)

Simplifying,

We get:

d = [0.22 ± sqrt(0.5964 + 0.528)] / 0.24d

= [0.22 ± sqrt(1.1244)] / 0.24d

= [0.22 ± 1.0604] / 0.24

We get two values of d as follows:d = 3.717 m, -1.598 m

Since the ball cannot travel a negative distance, the only possible solution is d = 3.717 m.

For more related questions on horizontal distance:

https://brainly.com/question/11960089

#SPJ8

Answer:

the poet uses unsentimental dialogue to contrast...

explanation:

The poet uses unsentimental dialogue to contrast the father's later concern for the speaker.

Sentiment, better known as emotion, is a broad concept of an experience that is often perceived as positive or negative. Emotions can, for example, include an attempt to communicate something, in which case facial expressions are included as a consequence of the attempt. An emotion can also contain attempts not to show their experience.

Another example is action, where certain emotions only differ in degree of action, where high heart rate and butterflies in the stomach can be experienced as either anxiety or exaltation depending on the degree of action (belief in one's own ability in the situation) and more. Emotions thus often include both own experiences, physiological changes and behavioral tendencies (often facial expressions and body language).

Learn more in https://brainly.com/question/17017484

Answer:

B

Step-by-step explanation:

a fraction is equal to 0 when the numerator is 0

x - 4 = 0

x = 4

The correct answer is x=4.

Step-by-step explanation:

When the numerator is 0, a fraction is equal to 0.

x - 4 = 0

x = 4

Learn more about fractions:

brainly.com/question/10354322

Therefore , the solution of the given problem of area comes out to be

AB/DC =5.

Area is the quantity that describes how much space .A surface or an object's shape occupy. Use a pencil to mark a square on the paper. Specifically, a 2-D figure. A shape's area on paper is referred to as its "Area" in this sentence. Imagine that your square is made out of more compact unit squares.

Here,

Since the heights of both trapezoids are equal, and the area of ABEF is twice the area of FECD,

=> AB+ EF/2 = 2(DC+EF /2)

=> AB + EF / 2= DC + EF,

=> AB + EF = 2DC + 2EF.

EF is exactly halfway between AB and DC, so EF =

AB + (AB+ DC)/2 = 2DC+ AB + DC, so

3/2 AB +  1/2DC = 3DC+AB,

and

=> 1/2AB =5/2DC

=> AB/DC =5

Therefore , the solution of the given problem of area comes out to be

AB/DC =5.

To know more about area , visit

https://brainly.com/question/27683633

#SPJ4

Answer:

y-y1=m(x-x1)

y-4=1/2(x-2)

y=1/2x+3

Answer:

Step-by-step explanation:

m = 1/2

Equation of line: y - y₁ = m(x - x₁)

x₁ = 2  & y₁ = 4

\(y -4 = \dfrac{1}{2}(x - 2)\\\\y - 4 =\dfrac{1}{2}x -2*\dfrac{1}{2}\\\\y-4=\dfrac{1}{2}x -1\\y = \dfrac{1}{2}x -1+4\\\\y=\dfrac{1}{2}x+3\)