Greta and Marge are collecting money for a local charity by taking donations outside of busy
local businesses. Hoping to collect the most money today, Greta gets to her collection spot and
begins collections at 8am. Marge wanted to sleep in so she didn't start collections at her spot
until 11am, by which time Greta had already collected $45.00. If Greta continues to collect
money at a rate of $15 per hour, Marge collects money at a rate of $20 per hour and they each
take a 1 hour break at 2pm, at what time will Greta and Marge have collected the same amount
of money?​

Question:

Set up a right triangle model for this problem and solve by using a calculator. Follow the models above,

A photographer stands 60 yards from the base of a lighthouse and observes that the angle between the  ground and the top of the lighthouse is 41° How tall is the lighthouse?

Answer:

The height of lighthouse is 52.2 yards

Solution:

Given that photographer stands 60 yards from the base of a lighthouse and observes that the angle between the  ground and the top of the lighthouse is 41 degree

The diagram is attached below

Consider a right angled triangle ABC

AB is the height of the lighthouse

BC is the distance between the base of a lighthouse and Photographer

As per given, BC = 60 yards

Angle between the  ground and the top of the lighthouse is 41 degree

Angle ACB = 41 degree

To find: height of lighthouse i.e AB = ?

We know that,

[tex]tan(\angle ACB) = \frac{Perpendicular}{Base}[/tex]

Here Base is BC and perpendicular is AB

[tex]\tan 41^{\circ}=\frac{A B}{B C}[/tex]

Substituting the values,

[tex]\begin{aligned}&\tan 41^{\circ}=\frac{A B}{60}\\\\&0.8692=\frac{A B}{60}\\\\&A B=0.8692 \times 60=52.157 \approx 52.2\end{aligned}[/tex]

Thus the height of lighthouse is 52.2 yards

Answer:

(3x+2)(2x-5)

Step-by-step explanation:

you can use process of elimination on this one just distribute the equations:

3x(2x-5)+2(2x-5)

6x^2-15x+4x-10 <------ Combine like terms

6x^2-11x-10

Final answer:

Factor completely [tex]6x^2[/tex] - 11x - 10 to find the equivalent binomials involves finding two numbers that multiply to -60 and add to -11. In this case, the numbers are -15 and +4, and using factor by grouping, the correct factorization is (3x + 2)(2x - 5).

Explanation:

When asked to factor the expression [tex]6x^2[/tex] − 11x − 10 completely, we're looking for two binomial expressions that multiply together to produce the original quadratic equation. To do this, we seek two numbers that multiply to give [tex]6x^2[/tex] times -10 (which is -[tex]60x^2[/tex]) and add to give -11x. Factoring is a method to express an equation as a product of its factors.

Let's find two such numbers: -15 and +4. These numbers give a product of -60 and a sum of -11, which fits our criteria. Now we replace the middle term (-11x) with -15x+4x to use factor by grouping.

Original equation: [tex]6x^2[/tex] − 11x − 10
Rewritten with new terms: [tex]6x^2[/tex] − 15x + 4x − 10
Factor by grouping: ([tex]6x^2[/tex] − 15x) + (4x − 10)
Factor out common terms: 3x(2x − 5) + 2(2x − 5)
Factor out the common binomial: (2x − 5)(3x + 2)

The completely factored form of the quadratic equation is (3x + 2)(2x − 5).

The sale price of the service is $25.50.

Given that,

We need to find out the sale price

So, the sale price is

= $30 - (15% of $30)

= $30 - $4.50

= $25.50

Therefore we can conclude that the sale price of the service is $25.50.

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The number is -11.

Step-by-step explanation:

Let,

the number be x.

According to given statement;

Sum of a number and five is doubled;

2(x+5)

is equals to one less than the number

= x-1

Combining both the sides and forming an equation

2(x+5)=x-1

[tex]2x+10=x-1\\2x-x=-1-10\\x=-11\\[/tex]

The number is -11.

Keywords: addition, subtraction

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The question asks for equivalent expressions to 3-8/3-4. After clarifying and simplifying the expression, we determined that the equivalent expressions are 3-12 (A) and 13/12 (F).

The question is asking us to determine which expressions are equivalent to 3−83−4. First, let's clarify this expression. The symbols − and − can stand for subtraction or negative signs, making the expression ambiguous. However, we can interpret this as a subtraction problem with mixed numbers, which would be processed as 3 minus 8 thirds minus 4. Converting the mixed numbers to improper fractions, we get: 3−(8/3)−4 which simplifies to (9/3)−(8/3)−(12/3). This simplifies to 1/3−(12/3), or 1/3− 4, which then further simplifies to −(⅔).

When we look for equivalent expressions, we have the following options:

Real word problem ⇒ constant of proportionality

$4.16 for 4 pounds of bananas ⇒ 1.04

$16.48 for 8 pounds of potatoes  ⇒ 2.06

$18.36 for 2 pizzas  ⇒ 9.18

2 cups of flour to make 36 cookies ⇒ 18

Solution:

A proportional relationship is one in which two quantities vary directly with each other.

We say the variable y varies directly as x,

if for x ∝ y

then,  x = y k

Where "k" is called constant of proportionality

[tex]k = \frac{x}{y}[/tex]

$4.16 for 4 pounds of bananas

x = 4.16 and y = 4

[tex]k = \frac{4.16}{4} = 1.04[/tex]

Thus constant of proportionality is 1.04

$16.48 for 8 pounds of potatoes

x = 16.48 and y = 8

[tex]k = \frac{16.48}{8} = 2.06[/tex]

Thus constant of proportionality is 2.06

$18.36 for 2 pizzas

x = 18.36 and y = 2

[tex]k = \frac{18.36}{2} = 9.18[/tex]

Thus constant of proportionality is 9.18

2 cups of flour to make 36 cookies

x = 36 and y = 2

[tex]k = \frac{36}{2} = 18[/tex]

Thus constant of proportionality is 18

Answer:

20,000

Step-by-step explanation:

Answer:

9

Step-by-step explanation:

x= hk/ (k+h)(a-2)

10*15 (15+10) (7/2-2)= 9

Paulo's family has 1 hour and 45 minutes before the trip to Scenic Lake Park after their arrival at the reunion.

The question asks how long Paulo's family has before the trip to Scenic Lake Park if they arrived at a family reunion at 8:30 A.M. and the trip is scheduled to start at 10:15 A.M. To solve this, we need to calculate the time difference between 8:30 A.M. and 10:15 A.M.

Here's how you calculate the time difference:

Answer:

210 people.

Step-by-step explanation:

Here is the correct question: At a school fair, 70% of the people are under 16 years old. One third of the people  remaining are teachers. If there are 21 teachers at the fair, how many people are there at the fair?

Now, solving to find total number people in the fair.

Lets assume total number of people in the fair is "x".

As given, there is 70% of total number of people are under 16 year old.

∴ People under 16 year old= [tex]70\% of x= \frac{7x}{10}[/tex]

Next, finding the number of remaining people.

∴ Number of remaining people= [tex]x-\frac{7x}{10} = x-0.7x[/tex]

Number of remaining people is 0.3x

As given, One third of the people  remaining are teachers.

∴ Number of teachers= [tex]\frac{1}{3} \times 0.3x= 0.1x[/tex]

As given there are 21 teachers at the fair.

⇒ [tex]0.1x= 21\ teachers[/tex]

∴ x= [tex]\frac{21}{0.1} = 210[/tex]

Hence, total number of people in the fair are 210.

Answer:

x = 12

Step-by-step explanation:

both (x+5) and (2x-7) are corresponding angles formed by an intersection between a transversal and 2 parallel lines.

hence they are equal in value

x+5 = 2x-7

x - 2x = -7 - 5

-x = -12

x = 12

Answer: x=12

Step-by-step explanation:

Answer:

49x

Step-by-step explanation:

The equation of line perpendicular to 4y = x-8 passing through (3,-3) is:

[tex]y = -4x+9[/tex]

Step-by-step explanation:

Given equation of line is:

[tex]4y=x-8[/tex]

We have to convert the given line in slope-intercept form to find the slope of the line

So,

Dividing both sides by 4

[tex]\frac{4y}{4} =\frac{x-8}{4}\\y = \frac{1}{4}x-\frac{8}{4}\\y = \frac{1}{4}x-2[/tex]

Let m1 be the slope of given line

Then

[tex]m_1 = \frac{1}{4}\\[/tex]

Let m2 be the slope of line perpendicular to given line

As we know that produt of slopes of two perpendicular lines is -1

[tex]m_1.m_2 = -1\\\frac{1}{4} . m_2 = -1\\m_2 = -1*4\\m_2 = -4[/tex]

The slope intercept form of line is given by:

[tex]y = m_2x+b[/tex]

Putting the value of slope

[tex]y = -4x+b[/tex]

to find the value of b, putting (3,-3) in equation

[tex]-3 = (-4)(3) + b\\-3 = -12 +b\\b = -3+12\\b = 9[/tex]

Putting the value of b in the equation

[tex]y = -4x+9[/tex]

Hence,

The equation of line perpendicular to 4y = x-8 passing through (3,-3) is:

[tex]y = -4x+9[/tex]

Keywords: Equation of line, slope

Learn more about equation of line at:

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Final answer:

The result is the equation f(x) = -4x + 9 in function notation.

Explanation:

To find the equation of a line that is perpendicular to another and passes through a given point, follow these steps:

Therefore, the equation of the line in function notation is f(x) = -4x + 9.

Answer:

Cost of a box of brownies = $5

Cost of a loaf of banana bread = $4

Step-by-step explanation:

Let, x= box of brownies.                                              

y=loaf of banana bread.

Now,

Sarah bought 4 boxes of brownies and 6 loaves of banana at $44, after expressing this in equation form we get:-

[tex]4x+6y=44[/tex] --------------------------(equation 1)

And George bought 5 boxes of brownies and 3 loaves of banana at $37, after expressing this in equation form we get:-

[tex]5x+3y=37[/tex] --------------------------(equation 2)

Now,

[tex]4x+6y=44[/tex]

[tex]4x=44-6y[/tex]

[tex]x=\frac{44-6y}{4}[/tex]

[tex]x=11-\frac{6}{4}y[/tex]

[tex]x=11-\frac{3}{2}y[/tex]------------------(equation 3)

Now substituting equation 3 in equation 2 we get,

[tex]5x+3y=37[/tex]

[tex]5(11-\frac{3}{2}y)+3y=37[/tex]

[tex]55-(\frac{15}{2}\times y) +3y=37[/tex]

[tex]55-37=(\frac{15}{2}\times y)-3y[/tex]

[tex]18=7.5y-3y[/tex]

[tex]18=4.5y[/tex]

[tex]y=4[/tex] ----------------------------------(Equation 4)

Now putting value of y from equation 4 in  equation 3

i.e. [tex]x=11-\frac{3}{2}y[/tex]

[tex]x=11-\frac{3\times 4}{2}[/tex]

[tex]x=11-6[/tex]

[tex]x=5[/tex]

Therefore the cost of a box of brownies = $5

the cost of a loaf of banana bread = $4                                                        

Answer: -47 - 48x

Step-by-step explanation: When you first take a look at this problem, it's tempting to want to subtract -7 - 8 to get -15 and then distribute the -15 through the parentheses.

You wouldn't want to subtract however before you distribute because the distributive property is a form of multiplication and remember from your order of operations that multiplication comes before subtraction.

So the first thing you want to do here is distribute and change the minus sign in front of the -8 to plus a negative 8 so that you know you are distributing a -8 through your parentheses.

So we have -7 + -8 times 6x which is -42x + -8 times 5 which is -40.

Now we have -7 + -48x + -40.

Now just combine your like terms. -7 + -40 is -47 and plus a negative 48x can be written as -48x so we have -47 - 48x.

So your answer is just -47 - 48x.

Step-by-step explanation: Using the diagram shown which I have provided in the image attached, the definition of a midpoint states that M is the midpoint of segment LN, then segment LN ≅ to MN.

The definition of a midpoint can also be stated the other way around. using the diagram shown, if segment LN ≅ to segment MN, then M is the midpoint of segment LN.

We can use hash marks in the figure to show that are 2 segments are congruent.

Answer:

c

Step-by-step explanation:

Answer:

1

Step-by-step explanation:

rise over run 4/4=1

Answer:

m=16/39

Step-by-step explanation:

-5(4m-2)=-2/3+6m

-20m+10=-2/3+6m

-20m-6m=-2/3-10

-26m=-2/3-30/3

-26m=-32/3

26m=32/3

m=(32/3)/26

m=(32/3)(1/26)

m=32/78

m=16/39

Answer:

16 hours and 20 minutes.

Step-by-step explanation:

Please consider the complete question.

Rita's family is moving to Grand Junction to Dallas, which is 980 miles. The moving van averages 60 miles each hour. About how many hours does the van take to reach Dallas?

To find the time taken by van to reach Dallas, we will divide total distance by speed.

[tex]\text{Time}=\frac{\text{Distance}}{\text{Speed}}[/tex]

[tex]\text{Time taken to reach Dallas}=\frac{980\text{ Miles}}{60\frac{\text{ Miles}}{\text{Hour}}}[/tex]

[tex]\text{Time taken to reach Dallas}=\frac{980\text{ Miles}}{60}\times \frac{\text{ Hour}}{\text{Miles}}[/tex]

[tex]\text{Time taken to reach Dallas}=\frac{98}{6}\text{ Hour}[/tex]

[tex]\text{Time taken to reach Dallas}=16.3333\text{ Hour}[/tex]

Let us convert 0.3333 hours into minutes by multiplying 0.3333 by 60.

[tex]0.3333\times 60=19.998\approx 20[/tex]

Therefore, it will take 16 hours and 20 minutes for the van to reach Dallas.

Final answer:

To calculate the time it takes for the van to reach Dallas, divide the distance from Grand Junction to Dallas by the average speed of the van.

Explanation:

To calculate the time it takes for the van to reach Dallas, we need to divide the distance from Grand Junction to Dallas by the average speed of the van.

The distance from Grand Junction to Dallas is not provided in the question, so we cannot calculate the exact time taken. However, if we are given the distance, we can use the formula:

Time = Distance / Speed

For example, if the distance is 300 miles, and the van's average speed is 60 miles per hour, then the time taken would be:

Time = 300 / 60 = 5 hours

8.3524 equals the expression c - 2ab if a = 2.4 b = 0.237 c = 9.49

Step-by-step explanation:

The given is:

We need to find the value of the expression c - 2ab

∵ The expression is c - 2ab

∵ a = 2.4

∵ b = 0.237

∵ c = 9.49

- Substitute the values of a , b and c in the expression to find its value

∴ 9.49 - 2(2.4)(0.237) = 9.49 - 2(0.5688)

∴ 9.49 - 2(2.4)(0.237) = 9.49 - 1.1376

- Subtract the two numbers

∴ 9.49 - 2(2.4)(0.237) = 8.3524

8.3524 equals the expression c - 2ab if a=2.4 b=0.237 c=9.49

Learn more:

You can learn more about the expressions in brainly.com/question/1617787

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Answer:

LA=6 WA=4 LB=6 WB=2

Step-by-step explanation:

Its a square so the sides are 6cm. 2:1 ratio means A is 6*4=24 cm while B is 6*2=12cm.

Answer:

Step-by-step explanation:

CD and AB are parallel; DB transverse

∠D + ∠B = 180     {co interior angles}

112 + 27 + y = 180

139 + y = 180

y = 180 - 139

y = 41

In ΔABC,

49 + x + y = 180   ( sum of all angles of triangle}

49 + x + 41 = 180

90 + x = 180

x = 180 - 90

x = 90

Final answer:

To find the third angle of a triangle, add the two known angles and subtract from 180 degrees. In this case, the third angle measures 90 degrees since the sum of the two given angles is 90 degrees.

Explanation:

When determining the measure of the third angle in a triangle, we utilize the fundamental property that the sum of all angles in a triangle equals to 180 degrees. Given that two of the angles measure 18° and 72°, we can find the third angle by subtracting the sum of these two angles from 180°.

The calculation is as follows:

Therefore, the measure of the third angle in the triangle is 90 degrees.

Answer: Avery's bottle holds 300 milliliters. If Dashawn's container holds 3/4 as much, then his container can hold 225 milliliters. Added together, both containers can hold 525.

Step-by-step explanation: 3/4 of 300 is 225. 300 + 225 = 525.

Answer:

5x + 32 < 50

Step-by-step explanation:

On a particular airline, bags checked in must weigh less than 50 pounds. Betty packed 32 pounds of clothes and five gifts that weigh the same amount.

If each gift weighs w pounds, then the weight of five gifts will be 5w pounds and an additional 32 pounds of clothes will make it total (32 + 5w) pounds.  

Now, this total weight has to be less than 50 pounds.

Therefore, the inequality equation that can be used to find the possible weight of each gift, w is  

5x + 32 < 50 (Answer)

Answer:

G. 17.3

solution:

Answer:

[tex]x \approx 31.8[/tex]

Step-by-step explanation:

[tex]\frac{\sin(75)}{22}=\frac{\sin(x)}{12}[/tex]

Cross multiply:

[tex]\sin(75) \cdot 12=\sin(x)\cdot 22[/tex]

Divide both sides by 22:

[tex]\frac{\sin(75) \cdot 12}{22}=\sin(x)[/tex]

Take [tex]\sin^{-1}( )[/tex] of both sides:

[tex]\sin^{-1}(\frac{\sin(75) \cdot 12}{22}=x[/tex]

Put left hand side into a calculator now:

[tex]31.7941 \approx x[/tex]

To the nearest tenth that is: [tex]x \approx 31.8[/tex]

Step-by-step explanation:

0.2x² − 0.8x = 1.6

Multiply both sides by 5.

x² − 4x = 8

Complete the square by adding 4 to both sides.

x² − 4x + 4 = 12

(x − 2)² = 12

x − 2 = ±√12

x = 2 ± √12

The positive solution is x = 2 + √12 ≈ 5.46.