Factor:-6+5x+x2
(x2= X spared)

Answer:

$2500

Step-by-step explanation:

Given that:

Darcy's weekly earning = $982 plus 18% commission on food sales

Harper's weekly earning = $807 plus 25% commision

amount of food sales will result in Darcy and Harper earning the same amount for the week

Let amount of food sales = f

Darcy's earning = Harper's earning

(982 + 18%*f) = (807 + 25% * f)

(982 + 0.18f) = (807 + 0.25f)

982 + 0.18f = 807 + 0.25f

982 - 807 = 0.25f - 0.18f

175 = 0.07f

f = 175 / 0.07

f = 2500

Hence amount of food sales that will result in both Darcy and Harper earning the same amount = $2500

Answer:

l = 194999.45

Step-by-step explanation:

I'm going to assume that you meant 3.14 by 3,14.

336,765 = 3.14 × 0.55 × (l + 0.55)

336,765 ÷ (3.14 × 0.55) = l + 0.55

(336,765 ÷ (3.14 × 0.55)) - 0.55 = l

l = 194999.45

The approximate volume of the whole shape is 56.5 cubic inches (rounded to the nearest tenth).

To find the volume of the whole shape, we need to find the volume of the cone and the half-sphere and then add them up.Volume of the Cone

The volume of a cone is given by the formula V = (1/3)πr²h, where r is the radius of the base of the cone, h is the height of the cone, and π is pi.

Given, radius of the cone r = 2 in and height of the cone h = 6 in.

Volume of the cone V =

(1/3)πr²h

= (1/3) × 3.14 × 2² × 6

= 25.12 cubic inches (rounded to the nearest hundredth).Volume of the half-sphere

The volume of a sphere is given by the formula V = (2/3)πr³, where r is the radius of the sphere, and π is pi.

As we only need half the volume of the sphere, we divide the result by 2.

The radius of the half-sphere is equal to the radius of the cone, which is 2 in.Volume of the half-sphere V = (1/2) × (2/3)πr³

= (1/2) × (2/3) × 3.14 × 2³

= 16.74 cubic inches (rounded to the nearest hundredth).Volume of the whole shape

Volume of the whole shape = Volume of cone + Volume of half-sphere

= 25.12 + 16.74

= 41.86 cubic inches (rounded to the nearest hundredth).

Therefore, the approximate volume of the whole shape is 56.5 cubic inches (rounded to the nearest tenth).

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Answer:

\(\displaystyle \angle A=30^\circ\)

Step-by-step explanation:

We are given that in Circle O, Arc BAC measures 300°.

Recall that arc lengths will always total 360°. Therefore:

\(\stackrel{\frown}{BAC}+\stackrel{\frown}{CB}=360^\circ\)

By substitution:

\(300+\stackrel{\frown}{CB}=360\)

Thus:

\(\stackrel{\frown}{CB}=60^\circ\)

∠A intercepts Arc CB. Since it is an inscribed angle, it will be half of its intercepted arc. In other words:

\(\angle A=\displaystyle \frac{1}{2}\stackrel{\frown}{CB}\)

Therefore:

\(\displaystyle \angle A=\frac{1}{2}(60)=30^\circ\)

Answer:

68

Step-by-step explanation:

Answer:

\(2*y^{2}\)

Step-by-step explanation:

The product of 2 is multiplication and the second power of y is just y squared

(a) Find the dual of the LP.Primal problem isminimize \($b_1y_1+C_1x_1+...+C_nx_n$\) subject to \($a_{11}x_1+a_{12}x_2+...+a_{1n}x_n \leq\) \(b_1$...$a_{m1}x_1+a_{m2}x_2+...+a_{mn}x_n \leq b_m$ and $x_1, x_2,\)..., x_n\(\geq 0$\)

Let us find the dual of the above primal problem.

Dual problem ismaximize \($b_1y_1+...+b_my_m$\)subject to \($a_{11}y_1+a_{21}y_2+...+a_{m1}y_m \leq\)\(C_1$...$a_{1n}y_1+a_{2n}y_2+...+a_{mn}y_m \leq C_n$\)

and\($y_1, y_2, ..., y_m \geq 0$\)

(b) Find the standard form of the LP and dual.Standard form of the primal problem isminimize \($b_1y_1+C_1x_1+...+C_nx_n$\)subject to \($a_{11}x_1+a_{12}x_2+...+a_{1n}x_n +s_1 = b_1$...$a_{m1}x_1+a_{m2}x_2+...+a_{mn}x_n +s_m = b_m$\) and\($x_1, x_2, ..., x_n, s_1, s_2, ..., s_m \geq 0$\)

Standard form of the dual problem ismaximize \($b_1y_1+...+b_my_m$\)subject to \($a_{11}y_1+a_{21}y_2+...+a_{m1}y_m \leq 0$...$a_{1n}y\)

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Answer:

x=17

Step-by-step explanation:

x-9=8

add nine on both sides

x-9+9=8+9

the nines on the side with the x cancel each other

x=17

the slope of the given point is m=−7/2

Answer:

2/5

Step-by-step explanation:

Hello!

How are paraphrasing and summarizing similar?

They include details of the text.

They are written with new words.

They include the main idea of the original text.

Answer: They include the main idea of the original text.

They include details of the text

They sometimes include exact quotes from the original text.

Hope this helps!

Answer:

39C7 or 15380937

Step-by-step explanation:

There are 13 clubs in a 52 card deck. We can remove these from the possibilities. 52-13=39. The rest is simple, choose 7 from 39 using the choose function is 39!/(32!*7!)=15380937. Or just say 39C7 as your answer.

Answer: The maximum height the football reaches = 51.89 feet.

Step-by-step explanation:

Given: The equation \(h = -16t^2+ 53t + 8\) gives the height h, in feet, of a football as a function of time t, in seconds, after it is kicked.

Differentiate the given equation, we get

\(h'=-(2)16t+53=-32t+53\)   (i)

Put \(h'=0\)

\(\Rightarrow\ -32t+53=0\\\\\Rightarrow\ t=\dfrac{53}{32}\approx1.65625\)

Differentiate (i) w.r.t. t, we get

\(h''=-32\) < 0  i.e. h is maximum at t= 1.65625

The value of h at t= 1.65625 will be \(-16(1.65625)^2+53(1.65625)+8=51.890625\approx51.89\text{ feet}\)

Hence, the maximum height the football reaches = 51.89 feet.

Answer:

<YMX=33 degrees

Step-by-step explanation:

<YMX=<YMW---<WMX

         =90-57

         =33

Answer:

Option D:  <YMX = 33°

Step-by-step explanation:

Given that < WMX = 57°, and <WMY = 90°,  then:

< YMX = < WMY - < WMX

< YMX = 90° - 57°

< YMX = 33°

Answer:

Step-by-step explanation:

Exponential function represents as x^2 = x * x or 2^3 = 2*2*2 etc.

As per options,

(A) We are unable to write the number 79 as a exponent.

B) We are unbale to write the number 742 as a exponent as well.

(c) We are unable to write the number 73 as a exponent as well.

(d) We are able to write the number 79.79 as exponent (79)^2. Base is 79 and exponent is 2 and it is single exponential expression as base is only one number.

Answer:

Step-by-step explanation:

18). Graph represent a function

19). Graph does not represent a function

Answer:

D

Step-by-step explanation:

Convert all of the fractions' denominators so that they are 8. This is because 4,2, and 8's least common multiple is 8.

Remember that when multiplying the denominator, we must also multiply the numerator. So:

\(\frac{1}{2} * \frac{4}{4} = \frac{4}{8} \\\)

\(\frac{1}{4} *\frac{2}{2} =\frac{2}{8}\)

Since we are asked to add all of them, we can do that easily since all of the fractions now share a common denominator.

\(\frac{2}{8} +\frac{4}{8} + \frac{1}{8} = \frac{7}{8}\)

Therefore, the answer is D.

Answer:

F(1) = -4   G(2) = -6

Step-by-step explanation:

You substitute the number next to the letter for x

Answer:

1,436.8

Step-by-step explanation:

(a) Probability that a randomly selected is 9.68%; (b) 29.12% will receive the tax break; (c) Minimum and the maximum starting salaries are 35,679.71 and 4,320.29. (d) 6.3% of the total number of students.

a) P(X>30,400) = P(Z>(30,400-20,000)/8,000)

                          = 1-P(Z<1.3)

                          = 0.0968

                         = 9.68%

b) P(X<15600) = P(Z<(15600-20000)/8000)

                        = 29.12%

c) Maximum of the starting salaries of the middle 95% is

                     (x - 20,000)/8,000 = 1,96

                                                  x  = 35,679.71

Minimum of the starting salaries of the middle 95% is

                      (x - 20,000)/8,000 = -1,96

                                                   x = 4,320.29

d) P(X>32,240) = 1-P(Z<(32,240-20,000)/8,000)

                         = 0.063

Therefore, the 189 represents 6.3% of the total number of students, means that the total number is 3,000.

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Step-by-step explanation:

1)

\(\frac{2}{3} +\frac{4}{5} =\frac{10+12}{15}=\frac{22}{15} .\)

2) the same value of the denominator of the fractions.

3) 4²*2²=16*4=64 or 4²*2²=(4*2)²=8²=64.

Megan's answer is correct.

4) if the given length is 2,25=9/4 (feet), then the length of each piece is 9/4 :3=3/4=0.75 (feet) or 3/4*12=9 (inches).

5) a. 4-6= -2; b. -4+6=2; c. -4-6= -10, so the required order is c<a<b.

6) A. -8+3= -5; B. -8*3= -24, so the greater value is (-5) - answer A.

7) if to calculate every option, then A. 2.3*6.5=14.95; B. 21.45-6.5=14.95; C. 8.32+6.63=14.95, - all of them are equal.

A. The type of function that can be used to describe the value of the investment after a fixed number of years using option 1 is a linear function while an exponential function can be used for option 2.

B. The linear function for option is y = 100x + 1000 while the exponential function for option 2 is \(y = 1000(1.1)^x\).

C. Yes, there would be a significant difference in the value of Beindar's investment after 20 years if she uses option 2 over option 1, with a value of $3728 in difference.

In order to type of function that can be used to describe the value of the investment after a fixed number of years, we would have to determine the common difference and common ratio as follows;

Common difference, d = a₂ - a₁ = a₃ - a₂

Common difference, d = 1200 - 1100 = 1300 - 1200

Common difference, d = 100 = 100 (it is a linear function)

Common ratio, b = a₂/a₁ = a₃ - a₂

Common ratio, b = 1210/1100 = 1331/1210

Common ratio, b = 1.1 = 1.1 (it is an exponential function).

Part B.

At data point (1, 1100) and a slope of 100, a linear function for this line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y - 1100 = 100(x - 1)

y = 100x - 100 + 1100

y = 100x + 1000

For option 2, the required exponential function can be calculated by using (1, 1100) and a as follows;

\(y = a(b)^x\)

1100 = a(1.1)¹

a = 1100/1.1

a = 1000

Therefore, we have \(y = 1000(1.1)^x\)

Part C.

When x = 20 years, the investment value in 20 years for option 1 is given by;

y = 100x + 1000

y = 100(20) + 1000

y = $3,000.

When x = 20 years, the investment value in 20 years for option 2 is given by;

\(y = 1000(1.1)^x\)

y = 1000(1.1)²⁰

y = $6727.50 ≈ $6728.

Difference = $6728 - $3,000.

Difference = $3728.

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Answer:

75 < x < 110 and 0 < y ≤ 50

Step-by-step explanation:

Took the test got it right

The constraints to represent this real-world problem are 75 < x < 110  and 0 < y ≤ 50 option (C) is correct.

It is defined as the expression in mathematics in which both sides are not equal they have mathematical signs either less than or greater than known as inequality.

We have:

A class trip to a beach has been planned for your senior trip. The resort only allows swimming when the temperature is between 75 degrees and 110 degrees. There is room for 50 people on your trip.

Let x be the temperature and y be the number of people on your trip.

Temperature is between 75 degrees and 110 degrees.

75 < x < 110  

There is room for 50 people on your trip.

0 < y ≤ 50

Thus, the constraints to represent this real-world problem are 75 < x < 110  and 0 < y ≤ 50 option (C) is correct.

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Answer: The acute angle between diagonals is 50

Step-by-step explanation:

Red angle = 50 because An exterior angle of a triangle is equal to the sum of the opposite interior angles (pink angles).

Alternatively:

Green angle is 130 by sum of interior angles of a triangle.

Red angle is 50 by Adjacent angles

Answer:

1 hour and 53 minutes

Step-by-step explanation:

Let's start at 7:10.

7:10 - 8:10 is 1 hour.

8:10 - 9:00 is 50 more minutes.

Total so far is 1 hour 50 minutes.

9:00 - 9:03 is 3 more minutes.

Total would be 1 hour and 53 minutes

Hope this answer helped! :)

Answer:

1 hour and 53 minutes

Step-by-step explanation:

You just need to subtract the times form each other.

There are two ways to do this.

Subtract the number of minutes and convert into total hours and remainder minutes.

Or you can just do the simple way shown by the answer above.

I will show the subtracting minutes one since it can be a base for all .

First we find how many minutes are in 7 hours and 10 minutes, and nine hours and three minutes.

7 hours and ten minutes is 430 minutes. 9 hours and 3 minutes is 543 minutes.

543 - 430 is 113.

Then you divide, we are using the remainder type division.

113/60(60 minutes in one hour)

60 goes into 113 one time and leaves 53.

Therefore, it takes 1 hour and 53 minutes.

Answer:

2628.15

Step-by-step explanation:

1909.15+ 1437.99/2=2628.15

The graph meets the vertical line test requirement, it must represent a function (C) The vertical line test shows that the graph is correct, hence the answer is yes.

According to the function, every value in the domain is associated to exactly one value in the range, and they have a predefined domain and range. It is characterized as a certain kind of relationship.

Please refer to the image instead of the graph, which is related to it.

The graphic displays a graph.

A parabola is seen on the graph.

The vertical line test determines if a graph can be a function, as is common knowledge.

The graph passes the vertical line test option, indicating that it does in fact represent a function (C) The vertical line test shows that the graph is correct, hence the answer is yes.

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∠SQU ≅ ∠VQT by the Vertical angles theorem.

From the figure, lines UV and WZ are parallel.

We need to arrive at the conclusion that angle VQT is congruent to angle WRS. i.e., ∠WRS ≅ ∠VQT.

So first we have the angles ∠SQU and ∠VQT. Both are vertical angles or opposite angles at Q.

The Vertical Angles Theorem states that two vertical angles are congruent to each other.

Thus, ∠SQU ≅ ∠VQT by the Vertical angles theorem.

Then we have the angles ∠SQU and ∠WRS. They are corresponding angles from the figure.

The Corresponding Angles Theorem states that two corresponding angles are congruent to each other.

Thus, ∠SQU ≅ ∠WRS by The Corresponding Angles Theorem.

Finally, ∠VQT ≅ ∠WRS by the Transitive property of Equality .

The transitivity property can be defined as if a ≅ b and b ≅ c, then a ≅ c.

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Answer:

remaining cardboard area =  122.5πr²

Step-by-step explanation:

area of original rectangle = length * width                                                                      

                                          =  18r * 8r

                                           =     144r²

Here we have 3 semi circles with radius 3r:

                                   : 3( \(\frac{1}{2}\) * π * 9r²)

                                    : 13.5πr²

                       ( \(\frac{1}{2}\) * π * (4r)²)

                       ( \(\frac{1}{2}\) * π * 16r²)

                             8πr²

            area of rectangle - area of 4 semi circles

                        144r² - 13.5πr² - 8πr²

                                122.5πr²

Answer:

can i see the picture for the problem

you forgot the picture