1. (07.02)

What is the value of x in the equation 2x + 9 = 21?

2
6
9
15

From the information given, in order to find who hikes faster, we need to determine the speed of John and Sara. The person with the greater speed hikes faster.

John's speed is determined by:

Sara's speed is determined by:

Since Sara's speed is greater than John's speed

Therefore, Sara hikes faster than John

============================================================

Explanation:

The distance traveled is d = 80 miles.

When going to work, her speed is r = 60 mph. She takes t = d/r = 80/60 = 4/3 hours which converts to 80 minutes. Multiply by 60 to go from hours to minutes.

Notice how the '80' shows up twice (in "80 miles" and "80 minutes"). This is because traveling 60 mph is the same as traveling 1 mile per minute.

-----------------

Now as she's coming home, her speed becomes r = 40 and she takes t = d/r = 80/40 = 2 hours = 120 minutes.

The difference in time values is 120 - 80 = 40 minutes.

Her commute back home takes 40 more minutes compared to the morning drive to work.

Hey!

For any graphing calculator problems I would recommend using desmos if your teacher allows it or getting a graphing calculator such as a ti-nspire :)

This way, it will be able to graph and get the answers quicker!

The answers to this question is (37.5,15) and (0,60). To find your answers when you graph always look for where the lines intersect. If the lines do not intersect then it is not one of your answer choices. (examples are below).

The probability of landing on the dark blue target is 2/5.

Probability is the ratio of required to the total possible outcomes of an event.

P(dark blue ) = 40/100

divide through by 20

P(dark blue ) = 2/5

Therefore, the probability of landing on target is 2/5

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Answer:

Step-by-step explanation:

To graph the equation y-2=2/3(x+4), you can follow these steps:

Begin by isolating the y term on one side of the equation. To do this, you can add 2 to both sides of the equation:

y-2+2=2/3(x+4)+2

y=2/3(x+4)+2

Next, you can simplify the right side of the equation by multiplying 2/3 by (x+4):

y=2/3(x+4)+2

y=(2/3)x+(2/3)4+2

y=(2/3)x+8/3+2

y=(2/3)x+14/3

This is the standard form of the equation y=mx+b, where m is the slope and b is the y-intercept. In this case, the slope is m=2/3 and the y-intercept is b=14/3.

To graph the equation, you can use the slope and y-intercept to plot the first point on the graph. The y-intercept is the point where the graph crosses the y-axis, so you can plot the point (0,14/3) on the graph.

From this point, you can use the slope to find the next point on the graph. The slope is the change in y over the change in x, so you can use the slope to find the change in y and the change in x between two points on the graph. For example, you could choose a point that is 1 unit to the right of the y-intercept, or (1,0). The change in y between these two points is (14/3)-0=14/3 and the change in x is 1-0=1. Using the slope, you can find the y-coordinate of the next point on the graph:

y2=y1+m(x2-x1)

y2=14/3+2/3(1-0)

y2=14/3+2/3

y2=20/3

You can repeat this process to plot additional points on the graph. For example, you could choose a point that is 2 units to the right of the y-intercept

Slope of the point is 11/8.

here we use the slope equation so -1-10 would be -11, Then 1-9 is -8 and then -11 divided by -8 is a positive 11/8.

given;

x1=9

x2=1

y1=10

y2=-1

slope=y2-y1/x2-x1

        =-1-10/1-9

        = 11/8

therefore, the slope of the line that passes through the points ; 11/8.

The slope of a line is a measure of its steepness. Mathematically, slope is calculated as "rise over run"

there are 4 types of slope,

negative, positive, zero, and undefined. as x increases

Whenever the equation of a line is written in the form y = mx + b, it is called the slope-intercept form of the equation. The m is the slope of the line. And b is the b in the point that is the y-intercept (0, b)..

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There will be no change in the price of the car.

A number line is a representation of a graduated straight line used to abstract real numbers in elementary mathematics. Its points are considered to correspond to real numbers and vice versa.

Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Let the sticker price = x, Price reduced by $300

Hence the new price is,

N= x-$300

The cost of additional features = $900

Hence the new price for selling will be.

=x-$300+$900

=x+$600

Dealer also provides a discount of $600

Hence Final  selling price will be

=x+$600-$600

Hence there seems to be no change in the sticker price as the sticker price and the final selling price are the same.

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To complete the job in 12 days, they need 100 workers.

We know that 30 workes can complete 1 job in 40 days, then if each worker works at a rate R, then we can write:

30*R*40 days = 1 job

R = (1/1200) job/day

Then if they need to complete the job in 12 days, the number N of workers needed is:

N*(1/1200)*12 = 1

N = (1200/12) = 100

100 workers are needed.

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The approach for solving for incenter.

Incenter:

The incenter of a triangle is the intersection point of all the three interior angle bisectors of the triangle.

It can also be defined as the point where the internal angle bisectors of the triangle cross. This point will be equidistant from the sides of a triangle, as the central axis’s junction point is the center point of the triangle’s inscribed circle.

Formula for solving incenter:

Let (x1,y1) , (x2,y2) and (x3,y3) are three points of triangle.

and a,b,c are lengths of sides.

I = ((ax1+bx2+x3 / a+b+c  ,  ay1+by2+cy3 / a+b+c))

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The Operating income is $172,500.

To calculate the margin of safety, contribution margin ratio, and operating income, we need to use the given information.

a. Margin of Safety:

Margin of Safety = Actual Sales - Break-even Sales

Given that the break-even point is at $750,000 in sales revenue and actual sales are $1,100,000, we can calculate the margin of safety:

Margin of Safety = $1,100,000 - $750,000 = $350,000

Therefore, the margin of safety is $350,000.

b. Margin of Safety as a Percentage of Sales:

Margin of Safety Percentage = (Margin of Safety / Actual Sales) * 100

Using the values from the previous calculations:

Margin of Safety Percentage = ($350,000 / $1,100,000) * 100 = 31.82%

Therefore, the margin of safety expressed as a percentage of sales is approximately 31.82%.

c. Contribution Margin Ratio:

Contribution Margin Ratio = (Contribution Margin / Sales) * 100

To calculate the contribution margin, we need to subtract variable costs from sales:

Contribution Margin = Sales - Variable Costs = $1,100,000 - $645,000 = $455,000

Using the values, we can calculate the contribution margin ratio:

Contribution Margin Ratio = ($455,000 / $1,100,000) * 100 = 41.36%

Therefore, the contribution margin ratio is approximately 41.36%.

d. Operating Income:

Operating Income = Sales - Variable Costs - Fixed Costs

Using the values provided:

Operating Income = $1,100,000 - $645,000 - $282,500 = $172,500

Therefore, the operating income is $172,500.

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Answer:

The probability of getting one ten from the deck of 52 cards is 4/52, since there are four tens in the deck. After one ten is drawn, there are only 51 cards remaining in the deck.

Step-by-step explanation:

The probability of getting four kings from the remaining 51 cards is (4/51) * (3/50) * (2/49) * (1/48), since there are four kings left in the deck after the ten is drawn, and the probability of drawing a king decreases with each card drawn.

Therefore, the probability of getting one ten and four kings is:

(4/52) * (4/51) * (3/50) * (2/49) * (1/48)

= 0.0000026

This is an extremely low probability, since the chances of getting this specific combination of cards is very low.

Answer:

Step-by-step explanation:

The measure of the interior angle of a triangle is 180 degrees

therefore 3x + 2x + 90 = 180

5x + 90 = 180

5x = 90

x = 18

3x = 3(18)  = 54 degrees

2x = 2(18) = 36 degrees

To check:

54 + 36 + 90 = 180

Answer: A≈78.54

Step-by-step explanation:  A=πr2=π·52≈78.53982

Applying logarithms, it is found that the earthquake in LA was 251.19 times more intense, and the correct option is A.

The logarithm of the ratio of intensity of two earthquakes of magnitudes \(M_1\) and \(M_2\) is given by:

\(\log{\frac{I_1}{I_2}} = M_1 - M_2\)

In this problem, \(M_1 = 6.2, M_2 = 3.8\), then:

\(\log{\frac{I_1}{I_2}} = M_1 - M_2\)

\(\log{\frac{I_1}{I_2}} = 6.2 - 3.8\)

\(\log{\frac{I_1}{I_2}} = 2.4\)

\(10^{\log{\frac{I_1}{I_2}}} = 10^{2.4}\)

\(\frac{I_1}{I_2} = 251.19\)

Hence, the earthquake in LA was 251.19 times more intense, and the correct option is A.

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The United States' decision to remain neutral was motivated by its over $1 billion in annual trade with Europe.

Early 20th-century American trade with Europe helped the US remain neutral by enabling it to maintain business ties with both the Allied and Central Powers.

The US was able to avoid taking a political stance and maintain its neutral status by supplying goods to both sides of the conflict. Additionally, trade helped the US maintain its economic stability because it would have been detrimental to the nation's economy to break off trade with one party.

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Answer:

Step-by-step explanation:

Plot the given points and connect in pairs to get a triangle.

Visually we can say it is a right triangle as legs TD and ED seem perpendicular.

Let's confirm this by finding the slopes.

Slope of TD:

Slope of ED:

Product of the slopes is:

This confirms DT⊥ED

Correct choice is B

Answer:

D

Step-by-step explanation:

The selling price after adding the profit to the dealer’s cost is $17628

The dealership averages 13% profit on new car sales

If the dealership pays $15,600 for a Rancho Turbo,

The profit is 13% of the dealership

profit =(13/100) 15600

profit = 2028

Selling proce =  cost price + profit

= 15600 + 2028

= 17628

Therefore, the selling price after adding the profit to the dealer’s cost is $17628

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A regression through the origin is a linear regression model where the intercept time period is assumed to be 0, meaning the regression line passes through the starting place.

This version is also referred to as zero-intercept regression or homogeneous regression.

It's far frequently used whilst there's a theoretical foundation to agree with that the relationship among the dependent and unbiased variable passes via the foundation or whilst the information propose that the intercept ought to be 0.

The slope coefficient represents the change within the structured variable for a one-unit increase inside the unbiased variable.

However, this kind of regression may not be appropriate in all cases, and a general linear regression version with an intercept term can be greater suitable.

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Answer:

\(\huge \boxed{6x^2 }\)

Step-by-step explanation:

6 times a number squared.

Let the number be \(x\).

6 is multiplied to \(x\) squared.

\(6 \times x^2\)

Answer:

-46

Step-by-step explanation:

5 (x - 2) - 14x.   x=4

5 (4 - 2) - 14(4)  (distribute)

20 - 10 - 14(4)   (multiply)

20 - 10 - 56    (subtract and solve.)

10 - 56 = -46 - solution

hope this helps (:

The percent error in Guido's estimate is 40%.

From the question, we have the following parameters that can be used in our computation:

Estimate = 3 hours

Actual = 5 hours

To find the percent error, we can use the formula:

Percent error = (|estimated value - actual value| / actual value) x 100%

Substitute the known values in the above equation, so, we have the following representation

|estimated value - actual value| = |3 - 5| = 2

So, we have

Percent error = (2 / 5) x 100%

Percent error = 40%

hence, the error is 40%

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Answer:

<AFB

Step-by-step explanation:

First you must know the two adjacent angles are placed side ways in a diagram. Most of this angles are supplementary i.e their sum is 180 degrees. From the diagram shown, you can see that the two angles that are supplementary are <BFD and <AFB. Hence we can conclude that <AFB is adjacent to <BFD

The value of tan 2π/3 without calculator is -√3.

The value of tan 2π/3 without calculator is calculated by applying trig identities as follows;

the value of π = 180 degrees

So we can replace the value of π in the function with 180 degrees as follows;

tan ( 2π / 3) = tan (2 x 180 / 3)

tan (2 x 180 / 3) = tan (2 x 60)

tan (2 x 60) = tan (120)

tan (120) if found in the second quadrant, and the value will be negative since only sine is positive in the second quadrant.

tan (120) = - tan (180 - 120)

= - tan (60)

= -√3

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Answer:

\((\frac{1}{2}+\frac{\sqrt{3}}{2}i)^5=\frac{1}{2}-\frac{\sqrt{3}}{2}i\)

Step-by-step explanation:

Convert 1/2 + i√3/2 to rectangular form

\(\displaystyle z=a+bi=\frac{1}{2}+\frac{\sqrt{3}}{2}i\\\\r=\sqrt{a^2+b^2}=\sqrt{\biggr(\frac{1}{2}\biggr)^2+\biggr(\frac{\sqrt{3}}{2}\biggr)^2}=\sqrt{\frac{1}{4}+\frac{3}{4}}=\sqrt{1}=1\\\\\theta=\tan^{-1}\biggr(\frac{b}{a}\biggr)=\tan^{-1}\biggr(\frac{\frac{\sqrt{3}}{2}}{\frac{1}{2}}\biggr)=\tan^{-1}(\sqrt{3})=\frac{\pi}{3}\\\\z=\cos\frac{\pi}{3}+i\sin\frac{\pi}{3}\)

Use DeMoivre's Theorem

\(\displaystyle z^n=r^n(\cos(n\theta)+i\sin(n\theta))\\\\z^5=1^5\biggr(\cos\biggr(\frac{5\pi}{3}\biggr)+i\sin\biggr(\frac{5\pi}{3}\biggr)\biggr)\\\\z^5=\frac{1}{2}-\frac{\sqrt{3}}{2}i\)

Answer:

Step-by-step explanation:

Let x be the length of the shortest section of the pipe.

Then, according to the problem:

The longest section is 5 times as long as the shortest, so its length is 5x.

The middle-sized section is 9 feet longer than the shortest, so its length is x + 9.

The sum of the lengths of the three sections must equal the length of the original 72-foot pipe:

x + 5x + (x + 9) = 72

Simplifying the left-hand side, we get:

7x + 9 = 72

Subtracting 9 from both sides, we get:

7x = 63

Dividing by 7, we get:

x = 9

Therefore:

The length of the shortest section is x = 9 feet.

The length of the longest section is 5x = 45 feet.

The length of the middle-sized section is x + 9 = 18 feet.

To complete the diagram, we can label the sections as follows:

Shortest section: |---a---|

Middle-sized section: |-----b-----|

Longest section: |----------5a----------|

where a = 9 and b = a + 9. Therefore:

a = 9 feet

b = a + 9 = 18 feet

The amount of mulch that he put on each vegetable bed will be 1/9.

A fraction simply means a piece of a whole. In this situation, the number is represented as a quotient such that the numerator and denominator are split.

In this situation, the gardener spread 1/3 of a bag of mulch evenly over his 3 equal-sized vegetable beds.

The amount of mulch that he put on each vegetable bed will be:

= 1/3 ÷ 3

= 1/3 × 1/3

= 1/9

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Amplitude is the maximum displacement of a function on a graph.

Amplitude is the maximum displacement of a function on a graph. It refers to the maximum height or distance from the baseline of a wave or oscillation.

It is often used in physics and engineering to describe the strength or size of a signal, vibration, or wave. In simple terms, it can be thought of as the "peak-to-peak" distance of a waveform, or the height of the waveform above and below the baseline.

But the minimum displacement of a function on a graph would typically be referred to as the minimum value or the "valley" of the function.

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