This graph shows the solutions to the inequalities y> 3x + 14 and y< 3x + 2.
Does the system of inequalities have solutions? If so, which region contains
the solutions?
A
-10 -8
10
-10
A. There is a solution, and it is shown by region B.
B. There is a solution, and it is shown by region C.
C. There is a solution, and it is shown by region A.
D. There is no solution.
B2
4
FO
C
00

Answer:

5ft

Step-by-step explanation:

8/10=0.8

4/0.8=5

[tex](\stackrel{x_1}{4}~,~\stackrel{y_1}{1})\qquad (\stackrel{x_2}{7}~,~\stackrel{y_2}{10}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{10}-\stackrel{y1}{1}}}{\underset{run} {\underset{x_2}{7}-\underset{x_1}{4}}}\implies \cfrac{9}{3}\implies 3 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{1}=\stackrel{m}{3}(x-\stackrel{x_1}{4}) \\\\\\ y-1=3x-12\implies y=3x-11[/tex]

The solution range of the given inequality is  (-∞, -4.121) and (0.121,∞)

Here we want to solve:

[tex]2x - 1/(x + 4) \geq 0[/tex]

To solve this, we multiply both sides by (x + 4) so we get:

[tex]2x*(x + 4) - 1 \geq 0\\\\2x^2 + 8x - 1 \geq 0[/tex]

Now we can solve it graphically, below we have:

There we can see that the solution range is (-∞, -4.121) and (0.121,∞), the regions where the graph is equal or above the horizontal axis.

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The area of the reflective material is:  284 square yards.

A rectangle is a quadrilateral with four sides and four right-angles.

it has two lines of symmetry.

Analysis:

To find the area of the reflecting material we find the area of the following shapes: trapezium + rectangle + triangle

bigger base of trapezium = 2 + 6 + 2 = 10 yard

smaller base of trapezium = 6

length of rectangle = 18 yard

width of rectangle : 2+6+2 = 10 yard

base of triangle is =  10 yard

Area of reflective material = 1/2(6+10) + 18x10 + 1/2(10)(8) = 284 square yards

In conclusion, the area of reflective material is : 284 square yards.

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Answer:

5 / 16

Step-by-step explanation:

For a question such as this, we most often simply use a calculator. However, I suppose that to do this by hand you would do as follows:

0.025 / 0.080

= 0.005  / 0.016

= 100 * (0.005 / 0.016)

= 5 / 16

The first step is a simplification. Both the numerator and denominator are divisible by 0.005.  In the next step, we can multiply the numerator and denominator both by 100 to get whole numbers. Because we multiply each by the same number, we have not changed the value of the original fraction. This leaves us with 5 / 16.

Done

Given that the first term of the sequence is –1.5, the next term of the sequence would be 3

The recursive function is given as:

f(n + 1) = -2f(n)

Substitute 1 for n

f(1 + 1) = -2f(1)

Evaluate

f(2) = -2f(1)

Given that the first term is -1.5, the equation becomes

f(2) = -2 * -1.5

Evaluate

f(2) = 3

Hence, the next term of the sequence is 3

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Answer:

(D) 3

Step-by-step explanation:

The y-intercept of the correct graph is 185 and  y-intercept of the incorrect graph is 195. The value of average change in distance is -10 for each increase of 1 iron number.

The x-intercept is the point on the coordinate at which a line, curve or plane intersect with the y-axis.

In the graph it can be seen that the correct graph is intersect y-axis at the value 185. Thus, the y-intercept of the correct graph is 185.

c=185

For the incorrect graph this value is 195. Thus, the y-intercept of the incorrect graph is 195.

b=195

Here, the values of y-intercepts are not the same-

c≠b

185≠195

The average change in distance for each increase of 1 iron number is,

[tex]r=\dfrac{155-145}{3-4}\\r=-10[/tex]

Thus, the y-intercept of the correct graph is 185 and  y-intercept of the incorrect graph is 195. The value of average change in distance is -10 for each increase of 1 iron number.

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Based on the calculation below, the amount that can be withdrawn each month for 10 years is a. $769.27.

First, we calculate the future value (FV) of the amount after 20 years using the formula for calculating the Future Value (FV) of an Ordinary Annuity as follows:

FV = A * (((1 + r)^n – 1) / r) ................................. (1)

Where,

FV = Future value of the amount after 20 years =?

A = Monthly deposit = $235.15

r = Monthly interest rate = 3.2% / 12 = 0.00266666666666667

n = number of months = 20 * 12 = 240

Substituting the values into equation (1), we have:

FV = $235.15 * (((1 + 0.00266666666666667)^240 – 1) / 0.00266666666666667) = $78,910.41

The amount planned to be withdrawn on monthly basis can be calculated using the formula for calculating the present value (PV) of an ordinary annuity as follows:

P = PV / ((1 - (1 / (1 + r))^n) / r) …………………………………. (2)

Where;

P = Monthly withdrawal or payment = ?

PV = Present value = FV calculated above = $78,910.41

r = Monthly interest rate = 3.2% / 12 = 0.00266666666666667

n = number of months = 10 * 12 = 120

Substitute the values into equation (2), we have:

P = $78,910.41PV / ((1 - (1 / (1 + 0.00266666666666667))^120) / 0.00266666666666667) = $769.27

Therefore, the amount that can be withdrawn each month for 10 years is $769.27.

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The answer is A: $769.27

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Have a great day and God bless! :D

Answer:

[tex] |x|1 | \: 2 | \: 3 | \: 4 | \: 5 | \\ |y| 5| \: 4 \: | 3 \: | 2 | 1| [/tex]

Step-by-step explaination:

We were told that:

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

therefore to see if it is correct you can just input the values for x and y and see if they add up to 6 (add the vertical values). For example;when x = 1, y = 5 or when x = 2, y = 4

Answer:

1. You can solve this problem by applying the Tangent Secant Theorem. Then, you have:

YX²=(YZ)(YV)

YX=√(YZ)(YV)

YZ=9+19

YV=9

2. When you substitute the values of YZ and YV into YX=√(YZ)(YV), you obtain:

YX=√(YZ)(YV)

YX=√(9+19)(9)

YX=√(28)(9)

YX=√252

YX=15.87

What is the length of YX?

The answer is: The lenght of YX is 15.87

Answer:

∠N = 21

Step-by-step explanation:

Sum of all angles of triangle = 180°

   4x - 13 + 2x - 13 + 5x + 19 = 180

    4x + 2x + 5x  -13 - 13 + 19 = 180

Combine like terms

                       11x  - 7  = 180

                               11x = 180 + 7

                                11x = 187

                                  x = 187/11

x = 17

m∠N = 2x - 13

           = 2*17 - 13

           = 34 - 13

          = 21

Answer: Second statement is false

Step-by-step explanation: You cannot subtract 89 from 500 and get 500. You get 411.

in an exponential expression, the rate of change is usually the parenthesized expression, namely on y = a(b)ˣ, the rate will be "b", so in this case the rate is just ∛24

[tex]\sqrt[3]{24} ~~ \begin{cases} 24=2\cdot 2\cdot 2\cdot 3\\ \qquad 2^3\cdot 3 \end{cases}\implies \sqrt[3]{2^3 \cdot 3}\implies 2\sqrt[3]{3}[/tex]

Answer:

[tex]t^{3}[/tex]

Step-by-step explanation:

cubed means to the power of 3

Answer:

Since there isn't any of the following attached, I made my wn attached below

Step-by-step explanation:

Population size: 12

Median: 28.5

Minimum: 23

Maximum: 37

First quartile: 25.5

Third quartile: 30.75

Interquartile Range: 5.25

Outliers: none

Hope this helps you a little more for your last day of finishing hmw :)

Let me know if you need anymore help !

OR have questions

Answer:

[tex]f(2)=\frac{7}{4}[/tex]

Step-by-step explanation:

Step 1:  Input 2 for x and solve

[tex]f(x) = \frac{2x + 7 - x^2}{4}[/tex]

[tex]f(2) = \frac{2(2) + 7 - (2)^2}{4}[/tex]

[tex]f(2)=\frac{4+7-4}{4}[/tex]

[tex]f(2)=\frac{7}{4}[/tex]

Answer: [tex]f(2)=\frac{7}{4}[/tex]

Answer:

8x4-2x2+7

Step-by-step explanation:

it's 100 percent right trust me

The mean of the data set is 22.1

The sample proportion of numbers less than the mean is %53

To find the mean,

We would sum the numbers and then divide them by the number of data.

25.5 + 26 + 18.2 + 15.3 + 28.5 + 27 + 20.7 + 20.2 + 26.1 + 18.2 + 21.4 + 17.9 + 24.3 + 22.6 + 19.6

= 331.5

331.5/15= 22.10.

To find the proportion of numbers, we would order them:

15.3

17.9

18.2

18.2

19.6

20.2

20.7

21.4

---------

22.6

24.3

25.5

26

26.1

27

28.5

The discontinuous line shows the split of the data that are less than the mean.

Those data are 8 in number and their proportion is:

8 / 15

= 0.53

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Answer:

28 m

Step-by-step explanation:

full roll length: r

Ryan bought: r/4

He trimmed 2 m: r/4 - 2

Length left: 5

r/4 - 2 = 5

r/4 = 7

r = 28

Answer: 28 m

Answer:

[tex]y=\sqrt{\frac{x^{2}}{2} +34}[/tex]

Step-by-step explanation:

[tex]2y\left( x\right) y^{\prime }\left( x\right) =x[/tex]

[tex]\Longrightarrow \int 2y\left( x\right) y^{\prime }\left( x\right) dx=\int x\ dx[/tex]

[tex]\Longrightarrow y^{2}\left( x\right) =\frac{x^{2}}{2} +c\ \text{(c is a constant)}[/tex]

[tex]y\left( 2\right) =6\Longleftrightarrow y^{2}\left( 2\right) =36[/tex]

[tex]y^{2}\left( 2\right) =36\Longleftrightarrow \frac{\left( 2\right)^{2} }{2} +c=36\ \Longleftrightarrow c=34[/tex]

[tex]\Longrightarrow y\left( x\right) =\pm\sqrt{\frac{x^{2}}{2} +34}[/tex]

Answer:

Step-by-step explanation:

-u-5+10u-25=9u-30

it was easy.

Answer:

=170/3 or (decimal 56.67)

Step-by-step explanation:

Steps

∫⁵ x²+3dx

⁰

Apply the Sum Rule: ∫fx) + gx) dx = ∫f(x)dx +-∫ g(x)

dx

∫⁵ x² dx +∫⁵ 3dx

⁰ ⁰

∫⁵ x² dx=125/3

⁰

∫⁵ 3dx=15

⁰

125/3+15

=170/3

Answer:

Could you possible line the numbers up a little bit, it'd be better to understand that way.

Answer:

A) 5

Explanation:

[tex]\sf Distance \ between \ two \ points = \sqrt{(x_2 - x_1)^2 - (y_2 - y_1)^2}[/tex]

Here given points:

Distance:

[tex]\rightarrow \sf \sqrt{(6 - 3)^2 - (8 - 4)^2}[/tex]

[tex]\rightarrow \sf \sqrt{9 +16}[/tex]

[tex]\rightarrow \sf \sqrt{25}[/tex]

[tex]\rightarrow \sf 5[/tex]

Answer:

D

Step-by-step explanation:

the number of days for 80 - 82 is 7 and the number of days for 82-84 is 9. Those are the only temperatures below 84 degrees, so you add them and get 16 :)

The radius and the height of the dimension that will minimize the amount of material used in the construction are [tex]\mathbf{r = \sqrt[3]{\dfrac{1500}{\pi}} }[/tex] and [tex]\mathbf{h = \dfrac{3000}{\pi ({\dfrac{1500}{\pi}} )^{2/3}}}[/tex] respectively.

The dimension that minimizes the surface area of a cylinder can be determined by:

Given that:

The area of the cylinder = (2 πr)h + 2(πr²)

The volume of the cylinder

Let's identify the constraint equation and Optimization equation:

To minimize the surface area of the can, we have:

The constraint equation is the equation that limits us:

So, Let's solve for h in our volume equation, we have:

3000 = πr² h

h = 3000/πr²

Now, from the Area equation

[tex]\mathbf{A = 2 \pi r(\dfrac{3000}{\pi r^2}) + 2\pi r^2}[/tex]

Taking the derivate and setting it to zero, we have;

Derivative:

[tex]\mathbf{A = \dfrac{6000}{ r}+ 2\pi r^2}[/tex]

[tex]\mathbf{A = 6000 r^{-1} + 2\pi r^2}[/tex]

[tex]\mathbf{A' = -6000 r^{-2} + 4\pi r}[/tex]

[tex]\mathbf{A' = 4\pi r-\dfrac{6000}{ r^{2} }}[/tex]

Setting it to zero, we  have:

[tex]\mathbf{0=\dfrac{ 4 \pi r^3 - 6000}{r^2}}[/tex]

Factor out 4

0 = 4(πr³ - 1500)

1500 = πr³

r³ = 1500/π

[tex]\mathbf{r = \sqrt[3]{\dfrac{1500}{\pi}} }[/tex]

The above is the radius that minimizes the surface area of the cylinder;

From [tex]\mathbf{h = \dfrac{3000}{\pi r^2}}[/tex]

[tex]\mathbf{h = \dfrac{3000}{\pi ( \sqrt[3]{\dfrac{1500}{\pi}} )^2}}[/tex]

[tex]\mathbf{h = \dfrac{3000}{\pi ({\dfrac{1500}{\pi}} )^{2/3}}}[/tex]

Thus, the radius and height that minimize the amount of material to be used in its construction are [tex]\mathbf{r = \sqrt[3]{\dfrac{1500}{\pi}} }[/tex] and [tex]\mathbf{h = \dfrac{3000}{\pi ({\dfrac{1500}{\pi}} )^{2/3}}}[/tex] respectively.

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Answer:

Option 4

Step-by-step explanation:

Equating given length and width to the area :

Finding the dimensions :

Answer:

the answer will be

K' = -9, 5

L' = 0,5

M' = -8,3

Step-by-step explanation:

the x axis is written first and the y axis is written after that.

hope it helps!!

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Answer:

K': (9,5)

L': (0,5)

M': (8,3)

Step-by-step explanation:

Tell me if im wrong!

Answer:

  800 ft²

Step-by-step explanation:

The total surface area of a square-base pyramid is given by the formula ...

  A = s(s +2h) . . . . . . where s is the side length, h is the face slant height

In this problem, we need to find the slant height of a face in order to use this formula.

__

The distance from the middle of one edge of the base to the peak of the pyramid is the slant height of a face of the pyramid. It is the hypotenuse of a right triangle whose legs are the pyramid height, and half the width of the base. For this pyramid, that is a right triangle with legs 15 and 8.

The Pythagorean theorem is used to find the hypotenuse of that triangle:

  c² = a² +b² . . . . square of hypotenuse = sum of squares of legs

  c² = 15² +8² = 225 +64 = 289

  c = √289 = 17

The slant height of a face of the pyramid is 17 ft.

The area formula tells us the total surface area is ...

  A = s(s +2h)

  A = (16 ft)(16 ft + 2×17 ft) = (16 ft)(50 ft)

  A = 800 ft²

The total surface area is 800 square feet.