Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar. Subtracting 3x2 + 4x – 5 from 7x2 + x + 9 results in a polynomial. After subtracting 4x2 – 3x from this polynomial, the difference is ____________.

The measure of the angle formed with the positive x-axis and the equation of the given line is 51° to the nearest degree

Step-by-step explanation:

The formula to find the angle between the positive part of x-axis and a line y = m x + b is tan(Ф) = m, where

∵ The equation of the line is [tex]y=\frac{5}{4}x[/tex]

∵ The form of the equation of a line is y = m x + b

∴ m = [tex]\frac{5}{4}[/tex] and b = 0

∵ Ф is the angle between the line and the positive part of x-axis

∵ tan(Ф) = m

∴ tan(Ф) = [tex]\frac{5}{4}[/tex]

- To find Ф use the inverse function of tan ( [tex]tan^{-1}[/tex]

∵ Ф = [tex]tan^{-1}(\frac{5}{4})[/tex]

∴ Ф = 51.34°

- Round it to the nearest degree

∴ Ф = 51°

The measure of the angle formed with the positive x-axis and the equation of the given line is 51° to the nearest degree

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Answer:

The graph is attached below.

Step-by-step explanation:

Given:

Zahra runs a 800-meter race at a constant speed.

Race starts from the finish line.

Finish line is at a distance of 800 m from the starting point.

Time is plotted on the x axis and Distance is plotted on the y axis.

So, the graph must start from the [tex]800^{th}[/tex] mark on the y axis when time is 0.

Now, the speed is constant which means that the slope of the line of distance versus time is a straight line because,

Speed [tex]=\frac{Distance}{TIme}[/tex].

Now, the graph should have the following properties:

1. Starting point of the graph should be (0, 800).

2. Final point of the graph should be (t, 0).

3. Slope should be constant everywhere. So, the graph must be a straight line.

Thus, the graph is a line joining the points (0, 800) and (t, 0) as shown below.

Answer:

bottom left

Step-by-step explanation:

Answer:

-13

Step-by-step explanation:

We are given:

[tex]\frac{x}{a}=4[/tex]

[tex]\frac{a}{y}=6[/tex]

[tex]a^2=9[/tex]

[tex]ab^2=-8[/tex]

Since [tex]ab^2=-8[/tex] then [tex]a[/tex] has to be negative.

Solving [tex]a^2=9[/tex] therefore gives [tex]a=-3[/tex].

(Note: [tex](-3)^2=(-3)(-3)=9[/tex].)

[tex]\frac{x}{a}=4[/tex] and [tex]a=-3[/tex] gives us:

[tex]\frac{x}{-3}=4[/tex].

Multiplying both sides by -3 gives: [tex]x=-12[/tex].

[tex]\frac{a}{y}=6[/tex] and [tex]a=-3[/tex] gives us:

[tex]\frac{-3}{y}=6[/tex].

Multiplying both sides by [tex]y[/tex] gives: [tex]-3=6y[/tex].

Divide both sides by 6 gives: [tex]\frac{-3}{6}=y[/tex].

Simplifying this gives us [tex]\frac{-1}{2}=y[/tex].

Now we are asked to find the numerical value for [tex]x+2y[/tex].

[tex]-12+2(\frac{-1}{2})[/tex]

[tex]-12+-1[/tex]

[tex]-13[/tex]

D.

Answer:

The diameter of the sphere is 6 centimeters

Step-by-step explanation:

we know that

The surface area of a sphere is

[tex]SA=4\pi r^{2}[/tex]

The volume of the sphere is

[tex]V=\frac{4}{3}\pi r^{3}[/tex]

Equate both formulas

[tex]\frac{4}{3}\pi r^{3}=4\pi r^{2}[/tex]

Simplify

[tex]\frac{1}{3}r^{3}=r^{2}[/tex]

[tex]\frac{r^3}{r^2}=3[/tex]

[tex]r=3\ cm[/tex]

Remember that the diameter is two times the radius

so

[tex]D=2r=2(3)=6\ cm[/tex]

therefore

The diameter of the sphere is 6 centimeters

Final answer:

The diameter of a sphere where the surface area equals the volume is 1.5 cm.

Explanation:

To find the diameter of a sphere where the surface area in square centimeters is equal to the volume in cubic centimeters, we use the formulae for the surface area and volume of a sphere:

Since the surface area is equal to the volume (SA = V), we can set the equations equal to each other and solve for the radius (r):

Now that we have the radius, we can find the diameter, which is twice the radius:

Diameter (d) = 2r = 2 × (3/4) = 3/2 cm or 1.5 cm

The actual distance from Los Angeles to San Diego is 130 miles.

Step-by-step explanation:

Given,

Distance from Los Angeles to San Diego on map = 6.35 cm

The given scale is;

1 cm = 20 miles

For measuring the actual distance we will multiply the distance on map with 20.

Actual distance = 6.5*20 = 130 miles

The actual distance from Los Angeles to San Diego is 130 miles.

Keywords: distance, multiplication

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Final answer:

To find the actual distance from Los Angeles to San Diego, multiply the map distance (6.35 cm) by the scale conversion factor (20 miles per cm), resulting in an actual distance of 127 miles.

Explanation:

The question deals with calculating the actual distance between Los Angeles and San Diego, given the scale on the map and the measured distance. To find the actual distance, you multiply the distance on the map by the conversion factor provided by the scale. In this case, the scale is 1 cm for every 20 miles. The measured distance on the map is 6.35 cm.

Therefore, the actual distance between Los Angeles and San Diego is calculated as follows:

Actual distance = Map distance × Scale conversion factor

Actual distance = 6.35 cm × 20 miles/cm

Actual distance = 127 miles

The actual distance from Los Angeles to San Diego is 127 miles.

Answer: the bakery will need about 70 trays

Step-by-step explanation:

718 can be rounded to 700

9 can be rounded to 10

700/10 = 70

Answer:

80 trays

Step-by-step explanation:

   718

÷     9

_________

    79.78 ≈ 80 trays

Answer:

The required equation of line is 3x + 2y =13

Step-by-step explanation:

Here we are given two points are we are supposed to find the line passing through the two points.

The given points are (3,2) and (5,-1).

There is only one line passing through these two points.

The slope of the given line = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1}}[/tex]

                                              = [tex]\frac{-3}{2}[/tex]

y - [tex]y_{1} = m(x - x_{1})[/tex]  

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

2y - 4 = - 3x + 9

3x + 2y = 13

The required line is 3x + 2y = 13

Answer: A = 1350.61

Step-by-step explanation:

Using the formula for calculating amount, which is given as

A = P [tex](1 + r)^{n}[/tex]

A = amount

P = Principal

r = rate

n = number of years

substituting the values given into the formula , we have

A = 1200 ([tex](1 + 0.03)^{4}[/tex]

A = 1200 ([tex](1.03)^{4}[/tex]

A = 1350.61

Therefore , the amount after four years is 1350.61

Answer:

23400

Step-by-step explanation:

Answer:

$23,400

Step-by-step explanation:

19500*0.2=3900

19500+3900=23400

Answer:

-4, 3.

Step-by-step explanation:

x^2 + x - 12 = 0

(x + 4)(x - 3) = 0

x = -4, 3.

Answer:

Step-by-step explanation:

As per the given question, [tex]u(x) = -2x^{2}[/tex] and [tex]v(x) = \frac{1}{x}[/tex].

Hence,  (u circle v) (x) = u{v(x)} = [tex]\frac{-2}{x^{2} }[/tex]

The range of the function, (u circle v) (x) means the set of the values of x so that we will be able to get a proper finite, countable and exact value of the function.

For the above function, (u circle v) (x) we can not get a proper value of the function for x = 0.

Hence, the options A, C, D can not be the range of the function, since it contains 0.

The range of the given function will be the option B, since it does not contain the value 0.

Answer: C (pictured below)

This is the answer I selected on e2020 and got it correct.

Answer:

7x15+40=145

9.5x15=142.5

Step-by-step explanation:

To ensure Jackie barely wins the race with a 40m headstart against Marion, who runs at 9.5 m/s, we can calculate the distance of the race to be 112 meters, which Jackie will cover in 16 seconds at her speed of 7 m/s.

To determine how long the race should be so that Jackie barely wins over Marion Jones, we can utilize the concept of relative motion in physics. Given Marion's speed is 9.5 m/s and Jackie's speed is 7 m/s, and Jackie gets a 40m headstart, we can set up an equation to find the time it takes for Marion to catch up to Jackie.

We know the distance covered is speed times time, so for Marion: distance = 9.5 m/s time, and for Jackie: distance = 40m (headstart) + 7 m/s time. Since we are looking for the point where they are at the same distance we can set the equations equal to each other: 9.5 time = 40 + 7 time. Solving for time gives us:

9.5t = 40 + 7t
=> 2.5t = 40
=> t = 40 / 2.5
=> t = 16 seconds

Jackie will win the race if the race ends exactly when Marion catches up to her, so the race should be:

distance = 7m/s
16s = 112 meters

Therefore, the race needs to be 112 meters long for Jackie to barely win with a 40m headstart against Marion.

Answer:

No solution

Step-by-step explanation:

There is no way we can find the value of y, if x eliminates itself. Therefore, there is no solution.

Answer:

option 3 ⇒ f⁻¹(x) =  [tex]\frac{x^{2} -2 }{3} [/tex]

Step-by-step explanation:

Given F(x) = [tex]\sqrt{3x+2}[/tex]

let y = f(x)

y = [tex]\sqrt{3x+2}[/tex]   ⇒ squaring the both sides

y² = 3x + 2  ⇒ subtract 2 from both sides

y² - 2 = 3x ⇒ divide both sides by 3

[tex]\frac{y^{2} -2 }{3} = x[/tex]

replace the location of x and y

∴ y = [tex]\frac{x^{2} -2 }{3} [/tex]

So, y will be f⁻¹(x)

∴ f⁻¹(x) =  [tex]\frac{x^{2} -2 }{3} [/tex]

The diary farmer should use 1000 pounds of 85 % protien and 55 % of 200 pounds to make 1200 pounds of a high-grade 80% protein ration

Solution:

Let the amount of 85 % protien supplement be "x"

Then amount of 55 % protien be (1200 - x)

According to given question,

85 % of "x" protien supplement + 55 % of 1200 - x protien used to get 80 % of 1200 pounds

85 % of x + 55 % of (1200 - x) = 80 % of 1200

[tex]\frac{85}{100} \times x + \frac{55}{100} \times (1200 - x) = \frac{80}{100} \times 1200\\\\0.85x + 0.55(1200 - x) = 960\\\\0.85x + 660 - 0.55x = 960\\\\0.3x = 960 - 660\\\\0.3x = 300\\\\x = 1000[/tex]

Pounds of 85 % protien used = 1000 pounds

Then pounds of 55 % protien used = 1200 - 1000 = 200 pounds

Thus he should use 1000 pounds of 85 % protien and 200 pounds of 55 % protien to get 1200 pounds of a high-grade 80% protein ration

If Greg saves $20 per week from his paycheck, by the end of the year he would have saved $1,040, which is less than his goal of $1,500. Thus, he cannot reach his goal with this savings plan.

The question asks if Greg can save $1,500 in a year by putting away $20 from his weekly paycheck into a savings account. If we multiply $20 (the amount he saves each week) by 52 (the number of weeks in a year), we get $1,040. So, Greg will have saved $1,040 in a year, which is less than his goal of $1,500. Therefore, saving $20 from each weekly paycheck will not allow Greg to reach his goal of $1,500 in a year.

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Answer:

  31. D: {8, 4, 0, -4}; R: {2, -1}; yes

  32. D: {-1, 2, 7}; R: {-4, -3, -2, 0}; no

  33. D: {-4, -3, -1, 2, 3, 5}; R: {-3, -2, 0, 3, 5}; yes

  34. D: (-∞, ∞); R: (-∞, 4]; yes

  35. D: [0, 5]; R: [-2, 3]; no

Step-by-step explanation:

In this context, D means "domain" and R means "range." The domain of a function is the list of input values for which the function is defined. For ordered pairs, it is the first number of the pair. For an x-y table, it is the list of x-values. For a graph, it is the possible values of x.

A relation is a function only if there are no repeated values in the domain (2 or more outputs for the same input.)

The range of a function is the list of output values produced by the function. For ordered pairs, it is the second number of the pair. For an x-y table, it is the list of y-values. For a graph, it is the possible values of y.

__

31. D: {8, 4, 0, -4}

    R: {2, -1}

Function: yes

Domain and range values don't need to be repeated. Often, they're listed in order from lowest to highest. Here, we have listed them in order of occurrence in the function definition.

__

32. D: {-1, 2, 7}

      R: {-4, -3, -2, 0}

Function: no

__

33. D: {-4, -3, -1, 2, 3, 5}

     R: {-3, -2, 0, 3, 5}

Function: yes

__

34. D: (-∞, ∞)

     R: (-∞, 4]

Function: yes

__

35. D: [0, 5]

     R: [-2, 3]

Function: no . . . . . . there are 2 y-values for most x-values

Answer:

Step-by-step explanation:

[tex]\bold{METHOD\ 1:}\\\\\begin{array}{ccc}34,000&-&100\%\\\\x&-&20\%\end{array}\qquad\text{cross multiply}\\\\100x=(34,000)(20)\\\\100x=680,000\qquad\text{divide both sides by 100}\\\\x=\dfrac{680,000}{100}\\\\x=6,800\\\\34,000+6,800=40,800[/tex]

[tex]\bold{METHOD\ 2:}\\\\p\%=\dfrac{p}{100}\\\\\text{The price has increased by 20}\%\\\\100\%+20\%=120\%\\\\120\%=\dfrac{120}{100}=1.2\\\\120\%\ of\ 34,000\to1.2\cdot34,000=40,800[/tex]

Answer: x1=5/2

               x2=1/3

Step-by-step explanation:

Eqation

(2x - 5)(3x – 1) = 0

has two options when 2x-5= 0 or 3x-1=0

2x-5=0

2x=5

X1=5/2

3x-1=0

3x=1

x2=1/3

Answer:

[tex]\sqrt[7]{x^{4}}[/tex]

[tex](x^{\frac{1}{7}})^{4}[/tex]

[tex](\sqrt[7]{x})^{4}[/tex]

Step-by-step explanation:

we have

[tex]x^{\frac{4}{7}}[/tex]

Remember the properties

[tex]\sqrt[n]{a^{m}}=a^{\frac{m}{n}}[/tex]

[tex](a^m)^{n}=a^{m*n}[/tex]

so

Verify each case

Part 1) we have

[tex]\sqrt[4]{x^{7}}[/tex]

we know that

[tex]\sqrt[4]{x^{7}}=x^{\frac{7}{4}}[/tex]

Compare with the given expression

[tex]x^{\frac{7}{4}} \neq x^{\frac{4}{7}}[/tex]

Part 2) we have

[tex]\sqrt[7]{x^{4}}[/tex]

we know that

[tex]\sqrt[7]{x^{4}}=x^{\frac{4}{7}}[/tex]

Compare with the given expression

[tex]x^{\frac{4}{7}} = x^{\frac{4}{7}}[/tex]

therefore

Is equivalent to the given expression

Part 3) we have

[tex](x^{\frac{1}{7}})^{4}[/tex]

we know that

[tex](x^{\frac{1}{7}})^{4}=x^{\frac{4}{7}}[/tex]

Compare with the given expression

[tex]x^{\frac{4}{7}} = x^{\frac{4}{7}}[/tex]

therefore

Is equivalent to the given expression

Part 4) we have

[tex](x^{\frac{1}{4}})^{7}[/tex]                      

we know that

[tex](x^{\frac{1}{4}})^{7}=x^{\frac{7}{4}}[/tex]

Compare with the given expression

[tex]x^{\frac{7}{4}} \neq x^{\frac{4}{7}}[/tex]

Part 5) we have

[tex](\sqrt[4]{x})^{7}[/tex]

we know that

[tex](\sqrt[4]{x})^{7}=(x^{\frac{1}{4}})^{7}=x^{\frac{7}{4}}[/tex]

Compare with the given expression

[tex]x^{\frac{7}{4}} \neq x^{\frac{4}{7}}[/tex]

Part 6) we have

[tex](\sqrt[7]{x})^{4}[/tex]

we know that

[tex](\sqrt[7]{x})^{4}=(x^{\frac{1}{7}})^{4}=x^{\frac{4}{7}}[/tex]

Compare with the given expression

[tex]x^{\frac{4}{7}} = x^{\frac{4}{7}}[/tex]

therefore

Is equivalent to the given expression

Complete Question:

4 friends evenly divided up a n-slice pizza. One of the friends,Harris, ate 1 fewer slice than he received. How many slices of pizza did Harrison eat?

Answer:

Harrison ate [tex]\frac{n}{4}-1[/tex] slices of pizza.

Step-by-step explanation:

Given data, 4 friends evenly divided up a ‘n’ slice pizza.

Thereby, the number of slices that each friend get =  [tex]\frac{n}{4}[/tex]

Now, given Harrison ate 1 fewer slice than he received. As he received  [tex]\frac{n}{4}[/tex] slices, so 1 fewer than [tex]\frac{n}{4}[/tex] means [tex]\frac{n}{4}-1[/tex]

Thus, Harrison ate [tex]\frac{n}{4}-1[/tex] slices of pizza.

Answer:

n/4 - 1

Step-by-step explanation:

Hope this helps!

This is the remainder when 64 oz is divided by 6 oz,

64 = 6 × 10 + 4

That's a remainder of 4.

Answer: 4 ounces

Answer:

Step-by-step explanation:

64 = 60 + 4 = 6*10 +4

Left over   =4 ounce

Sharon will drink 4 ounces of juice

Answer:

8 ft²

Step-by-step explanation:

Since ΔEFG ~ ΔABC, they are proportionately related. Each of the corresponding sides differ by the scale factor, which shows how much bigger or smaller the new triangle is from the original triangle.

Purple = original triangle, triangle 1

Pink = new triangle, triangle 2

Find the scale factor, "k". It will be a fraction because the triangle gets smaller.

k = FG/BC = 2/3

The scale factor can be used to find a side, the height or the area of the new triangle.

Use the scale factor squared to find the area.

A₂ = (A₁)(k²)

= (18 ft²)(2/3)²

= 7.999...ft²

= 8 ft²

Answer:

Number of games won = 110

Step-by-step explanation:

Given:

Total games played = 154

The ratio of number of games won to number of games lost = [tex]\frac{5}{2}[/tex]

Solution:

Let the number of games won be = [tex]5x[/tex]

Thus, number of games lost = [tex]2x[/tex]

The total games played can be given as = [tex]5x+2x=7x[/tex]

Thus, we have:

[tex]7x=154[/tex]

Dividing both sides by 7.

[tex]\frac{7x}{7}=\frac{154}{7}[/tex]

∴ [tex]x=22[/tex]

So, number of games won  = [tex]5\times 22 = 110[/tex]

Answer:

D

Step-by-step explanation:

Answer:

A) The repair bill would be at least $320 after 8 hours

B) The repairman would have worked for 5 hours

Step-by-step explanation:

A) Set up your equation with x equaling hours

30x + 80 = 320

subtract 80 to the opposite side of the equation

30x = 240

divide by 30

30x/30 = 240/30

x = 8

B) Set up your equation with x equaling hours

30x + 80 = 230

subtract 80 to the opposite side of the equation

30x = 150

divide by 30

30x/30 = 150/30

x = 5

After setting up inequalities for each scenario, we find that for the cost of the repair to be at least $320, at least 8 hours of work are required. When the total bill is $230, the repair person worked for 5 hours.

To answer question (a) on how many hours the repair would need to be at least $320 given an initial fee of $80 and an hourly rate of $30, we set up the inequality:

80 + 30h ≥ 320

Subtract 80 from both sides to isolate the hourly term:

30h ≥ 240

Divide both sides by 30 to solve for h:

h ≥ 8

So, the repair would need to be at least 8 hours to cost $320.

To answer question (b) on how many hours the repair person worked for a total bill of $230, we use the equation:

80 + 30h = 230

Subtract 80 from both sides:

30h = 150

Divide both sides by 30:

h = 5

The repair person worked for 5 hours.

Answer:

Step-by-step explanation:

What's the question?

Answer:

5 children

Step-by-step explanation:

7 adults = $70

5 children = $25

total= 12 people

○○○○○○○○○○○○○○○

therefore 5 children went

○○○○○○○○○○○○○○○

Step-by-step nvm............

Answer:

[tex]sin \theta =\frac{-8}{10} =-\frac{4}{5}[/tex]

Step-by-step explanation:

For this case we have a point given (-6,-8) and we know that this point is terminal side of 0​

We can assume that the length of th opposite side is given by:

b=-8 and the length for the adjacent side would be a=-6

And we can find the hypothenuse on this way:

[tex] c= \sqrt{a^2 +b^2}=\sqrt{(-6)^2 +(-8)^2}=10[/tex]

From the definition of sin we know this:

[tex]sin O =\frac{opposite}{hypothenuse}[/tex]

And if we replace we got this:

[tex]sin \theta =\frac{-8}{10} =-\frac{4}{5}[/tex]

We can aslo find the cos with the following identity:

[tex]cos^2 \theta + sin^2 \theta = 1[/tex]

And then:

[tex]cos \theta = \pm \sqrt{1-sin^2 \theta}=\pm \sqrt{1- (-4/5)^2}=\pm \frac{3}{5}[/tex]

But since both corrdinates are negative we are on the 3 quadrant and then [tex]cos \theta= -\frac{3}{5}[/tex]

Answer:

y-2=1/3(x-3)

Step-by-step explanation:

y-y1=m(x-x1)

y-2=1/3(x-3)