John measures the angle of elevation to the top of a cliff to be 23 degrees. He walks 720 metres horizontally towards the cliff and finds the angle of elevation has doubled. What is the height of the cliff to the nearest metre ?

Answer:

She is not correct

x = -9

Step-by-step explanation:

The sum of interior angles in a triangle is equal to 180° therefore if you add all three angles in this triangle it must add up to 180°

50 - 5x + 5 - 4x + 17 - 3x = 180 add/subtract the like terms

72 - 12x = 180

- 12x = 108 divide both sides by 12

-x = 9

x = -9

Answer:

The system has no solution

Step-by-step explanation:

we have

[tex]y=\frac{2}{3}x+7[/tex] ----> equation A

[tex]3y=2x-3[/tex]

Isolate the variable y

Divide by 3 both sides

[tex]y=\frac{2}{3}x-1[/tex] ------> equation B

Compare equation A and equation B

Both lines have the same slope and different y-intercept

so

Line A and Line B are parallel lines

The lines do not intersect

therefore

The system has no solution, because both lines are parallel

see the attached figure to better understand the problem

Answer:

31 deaths per month

Step-by-step explanation:

12 months in a year

372 / 12 = 31

Answer:185,422.61

Step-by-step explanation:8.25%/100=0.0825 but since it a sale tax you add a 1 so it would be 1.0825•35=37.88•89= 337.32•55=185,422.61

Answer:

NO

Step-by-step explanation:

84*84=7056

62*62= 3844

58*58=3364

3844+3364=7208

7208 is not equal to 7056

Madison purchased 5 cans of soup and 7 frozen dinners.

Step-by-step explanation:

Given,

Quantity of sodium in each soup can = 500 mg

Quantity of sodium in each frozen dinner = 700 mg

Total quantity = 7400

Let,

Number of soup cans purchased = x

Number of frozen dinners purchased = y

According to given statement;

500x+700y=7400        Eqn 1

y = x+2        Eqn 2

Putting value of y from Eqn 2 in Eqn 1

[tex]500x+700(x+2)=7400\\500x+700x+1400=7400\\1200x=7400-1400\\1200x=6000[/tex]

Dividing both sides by 1200

[tex]\frac{1200x}{1200}=\frac{6000}{1200}\\x=5[/tex]

Putting x=5 in Eqn 2

[tex]y=5+2\\y=7[/tex]

Madison purchased 5 cans of soup and 7 frozen dinners.

Keywords: linear equation, substitution method

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Answer:

Madison purchased 5 cans of soup and 7 frozen dinners

Step-by-step explanation:

Answer:

[tex]\displaystyle \frac{1-x}{(5-x)(-x)} =-\frac{x-1 }{ x(x-5)}[/tex]

[tex]\displaystyle \frac{5}{s}\times \frac{2}{5} =\frac{2}{s}[/tex]

Step-by-step explanation:

Errors in Algebraic Operations

It's usual that students make mistakes when misunderstanding the application of algebra's basic rules. Here we have two of them

The first expression is

[tex]1-x / (5-x)(-x)=x-1 / x(x-5)[/tex]

Let's arrange into format:

[tex]\displaystyle \frac{1-x}{(5-x)(-x)} =\frac{x-1 }{ x(x-5)}[/tex]

We can clearly see in all of the factors in the expression the signs were changed correctly, but the result should have been preceeded with a negative sign, because it makes 3 (odd number) negatives, resulting in a negative expression. The correct form is

[tex]\displaystyle \frac{1-x}{(5-x)(-x)} =-\frac{x-1 }{ x(x-5)}[/tex]

Now for the second expression

[tex]5/s+2/5=2/s[/tex]

Let's arrange into format

[tex]\displaystyle \frac{5}{s}+\frac{2}{5} =\frac{2}{s}[/tex]

It's a clear mistake because it was asssumed a product of fractions instead of a SUM of fractions. If the result was correct, then the expression should have been

[tex]\displaystyle \frac{5}{s}\times \frac{2}{5} =\frac{2}{s}[/tex]

Answer:

The annual interest rate is 5.247%.

Step-by-step explanation:

Question

Claire deposited $2,500 into an account that accrues interest monthly. She made no additional deposits or withdrawals. After 2 years, Claire had $2,762.35 in the account. what is the annual interest rate of the account?

Subtract $2,500.00 from $2,762.35 and you get 262.35- the 2-year interest. To get the annual interest, divide 262.35 by 2, which equals 131.75. Then, divide 131.75 by 2,500 (original amount) and you get 0.05247. Lastly, multiply 0.05247 by 100 to get the answer (5.247%).

To find the annual interest rate, use the compound interest formula and set it equal to the final amount in the account. After performing the necessary computations, 'r' comes out to approximately 5%.

To find the annual interest rate of Claire's account, you'll need to use the compound interest formula: v(t) = p * (1 + r/n)^(nt), where:

Claire's account had $2,762.35 in it after 2 years. Therefore, you would set $2,762.35 equal to the formula and solve for 'r'.

Doing so yields $2,762.35 = $2,500 * (1 + r/12)^(12*2) which simplifies, after some mathematical computations, to an annual interest rate (r) of roughly 5%.

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Answer:

raymond has about 38 cars left

Step-by-step explanation:

Because raymond started off with 57 cars and he got rid of( take away) 19 you must use subtraction. 57 - 19 =38

Answer:

if Jara has [tex]\$4[/tex] and she wants to buy pen the Prince of each pen is [tex]\$\frac{1}{2}[/tex].

How many pens she can buy.

Step-by-step explanation:

If Jara has [tex]\$4[/tex] and she wants to buy pen the wants to buy pen the Prince of each pen is [tex]\$\frac{1}{2}[/tex] .

How many pen she can buy.

[tex]Let\ Jara\ can\ buy=x\ pens\\\\each\ pen\ cost=\$\frac{1}{2}\\\\Then\ Jara\ can\ buy\ pens=\$\frac{1}{2}x\\\\\frac{1}{2}x=4\\x=8\\Jara\ can\ buy\ =8\ pens[/tex]

Answer:

10

Step-by-step explanation:

5(3x-5)=20

3x-5=20/5

3x-5=4

3x=4+5

3x=9

x=9/3

x=3

6x-8=6(3)-8=18-8=10

Answer:

C. 8,624

Step-by-step explanation:

recall that the formula for circumference is

Circumference = 2πr  ( = given as 85 meters)

hence,

85 = 2πr

r = 85/(2π)

given h = 15m

volume of cylinder

= πr²h

= π (85/2π)² 15  (using calculator and assuming π = 3.14)

= 8628.58

Comparing with the choices, the closest choice (within rounding error) is C. 8,624

Answer:

Marcos had 6 nickel coins and 9 quarter coins.

Step-by-step explanation:

We are given the following in the question:

Let x be the number of nickel coins and y be the number of quarter coins.

Marcos had 15 coins in nickels and quarters.

Thus, we can write the equation:

[tex]x + y =15[/tex]

He had 3 more quarters than nickels. We can write he equation,

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

Solving the two equations, we get,

[tex]2y = 18\\y = 9\\x + 9 = 15\\x = 6[/tex]

Thus, Marcos had 6 nickel coins and 9 quarter coins.

The solution to the system of equations representing Marcos's coins is x = 6 and y = 9. Hence, Marcos had 6 nickels and 9 quarters.

This question pertains to creating and solving a system of equations in mathematics. Given Marcos had 15 coins in nickels and quarters and considering the information that he had 3 more quarters than nickels, two equations can be formed from this. The first equation sets up the total number of coins: x + y = 15. The second equation sets ups the difference in quantity of each coin: y = x + 3.

To find the solution, substitute the second equation in for y in the first equation. This gives: x + (x + 3) = 15. Solve the equation and find x = 6. Furthermore, using x in our second equation, we get y = 6 + 3 = 9. Therefore, Marcos had 6 nickels and 9 quarters.

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Answer:

110°

Step-by-step explanation:

the supplement of an angle is 30 degrees less than twice the measure of the angle itself. find the angle and its supplement.

Let the angle be A, then its supplement = (180 - A)

Now, since the supplement is 30 degrees less than twice the measure of the angle itself, then we'll have:

180 - A = 2A - 30

-3A = - 210

A, or the angle = [tex]\frac{-210}{-3}[/tex]= 70 °

Its supplement, (180 - A) = 180 - 70 = 110°

Final answer:

To determine the maximum number of adults and children that can attend the play without exceeding the bus capacity of 40 people and the $400 budget, set up and solve a system of equations representing the capacity and budget constraints. The solution is 8 adults and 32 children.

Explanation:

We are given a situation where a company charges $18 for each adult (a) and $8 for each child (c) for a bus trip to an upcoming play, with the constraints that the bus holds a maximum of 40 people and the available budget is $400. To find the maximum number of adults and children that can attend under these constraints, we need to set up a system of equations:

For the capacity constraint: a + c = 40

For the budget constraint: 18a + 8c = 400

We can solve this system using substitution or elimination. Let's use elimination. Multiply the first equation by -8 and add it to the second equation to eliminate c:

-8a - 8c = -320

18a + 8c = 400

Adding these two equations together gives us:

10a = 80

Thus, a = 8. Plugging a = 8 back into the first equation, we get c = 32.

The maximum number of adults and children that can attend the play is 8 adults and 32 children.

Answer: for the third one you use x= 55

so angle = 110

for the fourth one x= 102

angle = 100

Step-by-step explanation:

Option C:

Surface area of the three dimensional figure is 166 unit².

Solution:

Let us find the area of the net of the figure.

Length = 7, Width = 5, Height = 4

Area of the bottom = length × width

                                = 7 × 5

                                = 35 unit²

Area of the Top =  length × width

                          = 7 × 5

                          = 35 unit²

Area of the left = width × height

                         = 5 × 4

                         = 20 unit²

Area of the right = width × height

                         = 5 × 4

                         = 20 unit²

Area of the front = length × height

                            = 7 × 4

                            = 28 unit²

Area of the back = length × height

                            = 7 × 4

                            = 28 unit²

Surface area = 35 + 35 + 20 + 20 + 28 + 28

                     = 166 unit²

Surface area of the three dimensional figure is 166 unit².

Final answer:

In the equation f(-11)=5x+1, solving for x yields x = -2.4.

Explanation:

To find what x equals in the function f(-11)=5x+1, we start by understanding that the function f(x) identifies the relation between x and f(x). In this case, f(-11) has been given the value of 5x+1. Therefore, we solve for x by setting the expression equal to f(-11).

We have the equation 5x + 1 = f(-11). Since f(-11) is given as a constant, we substitute and solve for x:

5x = -12

x = -2.4

Hence, x equals -2.4 in the function f(-11)=5x+1.

Answer:

156

Step-by-step explanation:

13 × 12

13

×

12

=

26

130

=

156

Answer:

Step-by-step explanation:

m*n

m=13

n=12

13 * 12

156

Answer:

47.314

Step-by-step explanation:

We want find the results of the multiplication,

[tex]4.7314 \times 10[/tex]

When we multiply by 10, we move the decimal point forward once.

When we divide by 10, we move the decimal point backwards once.

In this case, we are multiplying, so

[tex]4.7314 \times 10 = 47.314[/tex]

Answer:

16 feet.

Step-by-step explanation:

Given:

Ben’s living room is a rectangle measuring 10 yards x 168.

Question asked:

How many feet does the legs of the room exceed the width ?

Solution:

By applying unitary method:

Length of rectangle = 10 yards = 30 feet (1 yard = 3 feet)

                                                                    (10 yard = [tex]3\times10 = 30)[/tex]

Breadth of  rectangle = 168 inch = 14 feet   (12 inch = 1 feet)

                                                                       (1 inch = [tex]\frac{1}{12}[/tex])

                                                                       ( 168 inch = [tex]\frac{1}{12}[/tex][tex]\times168 = 14 feet)[/tex]

By subtracting the breadth from the length of rectangle,

30 feet - 14 feet = 16 feet

Therefore,  by 16 feet, length of the room exceed the width.

Answer:

no6666//7

Step-by-step explanation:

88../6

Answer:

x = 25

Step-by-step explanation:

You would need to start by creating an equation.  X would represent the numbers of weeks.

500 + 30x = 750 + 20x

Now get the numbers on one side.  To do this subtract 500 form each side.

30x = 250 + 20x

Next, get the variables to one side.  This can be done by subtracting 20x from each side.

10x = 250

Finally divide by 10 to get the variable by its self.

x = 25

Hope this helps.

After 25 weeks, Collin and Kamryn have the same amount of

money in their accounts.

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

Let's suppose the after x weeks, Collin and Kamryn have the same amount of money in their accounts:

Then we can frame a linear equation as per the problem:

Collin's amount of money  = 500 + 30x

Kamryn amount of money = 750 + 20x

500 + 30x = 750 + 20x

10x = 250

x = 25

Thus, after 25 weeks Collin and Kamryn have the same amount of

money in their accounts.

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Answer:

4.875

Step-by-step explanation:

Answer:

a. Number of people surveyed were 900.

b. 360 people preferred running.

Step-by-step explanation:

Given:

On a recent survey, 60% of those surveyed indicated that they preferred walking to running.

If 540 people preferred walking.

Now, to find a. number of people were surveyed. b. number of people preferred running.

a.

Number of people preferred walking = 540.

Percentage of people preferred walking = 60%.

Let the total number of people surveyed be [tex]x.[/tex]

Now, to get the number of people surveyed:

60% of x = 540.

[tex]\frac{60}{100} \times x=540[/tex]

[tex]0.60\times x=540[/tex]

[tex]0.60x=540[/tex]

Dividing both sides by 0.60 we get:

[tex]x=900.[/tex]

Thus, number of people surveyed = 900.

b.

Total number of people surveyed = 900.

People preferred walking = 540.

Now, to get the people preferred running we subtract people preferred walking from total number of people surveyed:

[tex]900-540[/tex]

[tex]=360.[/tex]

Thus, people preferred running = 360.

Therefore, a. Number of people surveyed were 900.

b. 360 people preferred running.

Answer: 9

Step-by-step explanation:

2x + 3 when x = 3

2(3) + 3

2 * 3 = 6

6 + 3 = 9

To evaluate the mathematical expression 2x + 3 for x = 3, substitute x = 3 into the equation to get 2(3) + 3 = 6 + 3, and then add the numbers to get 9.

To evaluate the expression 2x + 3 for x = 3, you would replace x with 3 in the expression, then follow the order of operations (PEMDAS/BODMAS) to solve the expression.

Here is the step-by-step breakdown:

So, when x = 3, the value of the expression 2x + 3 is 9.

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The sum of the 3 angles needs to be 180.

To find the third angle subtract to the known angles from 180.

180 - 48 - 71 = 61

The third angle is 61 degrees.

Answer:

7 cabins

Step-by-step explanation:

So with division, we can find out

49 campers / 7 per cabin = 7

14 counselors / 2 per cabin = 7

As we can see, both problems equal 7, which lets us see that the camp needs 7 cabins to hold all the campers and counselors