a line in the standard (x,y) coordinate plane contains the points M(-2,4) and N(8,10) What is the midpoint of MN

The formula:

[tex]\theta=\dfrac{\theta\pi}{180}[/tex]

We have

[tex]\theta=453[/tex]

Substitute:

[tex]453^o=\dfrac{453\pi}{180}=\dfrac{453\pi:3}{180:3}=\dfrac{151\pi}{60}\to\boxed{B)}[/tex]

The conversion of 453° into radians is 151π/60.

The angle made by taking the radius and wrapping it round the circle.

Given that, 453°

To convert any degree into radians, we multiply by π/180

453*π/180 = 151π/60

Hence, The conversion of 453° into radians is 151π/60.

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The equation of the line parallel to the graph of 14x - 7y = 1 that passes through the point at (-2, 4) is y = 2x + 8. The correct option is C.

To find the equation of the line parallel to the graph of 14x - 7y = 1 that passes through the point at (-2, 4), we first need to determine the slope of the given line. We can write the given equation in slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept.

Starting with 14x - 7y = 1, we solve for y:

The slope of the original line is 2, so a line parallel to it will also have a slope of 2. Using the point-slope form of a line equation, y - [tex]y_1[/tex] = m(x - [tex]x_1[/tex]), and the point (-2, 4), we get:

Therefore, the equation of the line parallel to 14x - 7y = 1 and passing through (-2, 4) is y = 2x + 8.

Complete Question:

Find the equation of the line parallel to the graph of 14x-7y=1 that passes through the point at (-2,4).

Select the correct response:

[tex]\begin{aligned}A) \:& y=2 x+3 \\B)\: & y=\frac{1}{2} x+3 \\C) \:& y=2 x+8 \\D) \:& y=-\frac{1}{2} x-3\end{aligned}[/tex]

The formula of a volume of a rectangle prism:

[tex]V=lwh[/tex]

l - length

w - width

h - height

We have

[tex]l=n^2+2;\ w = 10,\ h=n+5[/tex]

Substitute:

[tex]V=(n^2+2)(10)(n+5)=(10n^2+20)(n+5)\\\\=(10n^2)(n)+(10n^2)(5)+(20)(n)+(20)(5)\\\\=10n^3+50n^2+20n+100[/tex]

The volume of the aquarium in terms of n is calculated by multiplying its length (n2 +2 inches), width (10 inches), and height (n + 5 inches) giving the formula V = (n2 + 2)  imes (n + 5)  imes 10, which expands to V = 10n3 + 60n2 + 20n + 100 cubic inches.

We use the formula V = length  times width  times height, where the volume V is the space inside the aquarium. The question provides the dimensions of the aquarium in terms of n: the length (n2 +2 inches), height (n + 5 inches), and width (10 inches).

To calculate the volume, simply multiply the dimensions together:

Volume, V = (n2 + 2)  imes (n + 5)  imes 10

Expanding the expression gives us the volume V in cubic inches as a function of n:

V = 10n3 + 60n2 + 20n + 100 cubic inches

Answer:

2.4 hours Electrician works.

Step-by-step explanation:

Let us assume that the number of hours  Electrician works be x.

As given

An Electrician charges $30 for a service call plus $75 per hour of service.

If Electrician  charged $210.

Than the equation becomes

30 + 75x = 210

75x = 210 - 30

75x = 180

[tex]x =\frac{180}{75}[/tex]

x =2.4 hours

Therefore 2.4 hours Electrician works.

Answer:

(-10, 0) , (-4, 0)

Step-by-step explanation:

[tex]\text{We know that the parabola is given by the quadratic equation.}\\\text{let the general equation of the parabola is}\\\\y=a(x-h)^2+k, \text{ where (h, k) is the vertex of the parabola.}\\\\\text{here we have given that vertex, }(h,k)=(-7,45), \text{ so above equation gives}\\\\y=a(x-(-7))^2+(45)\\\\y=a(x+7)^2+45\\\\\text{now this parabola has y-intercept at }(0,-200), \text{ so with this point}\\\text{above equation gives}[/tex]

[tex]-200=a(0+7)^2+45\\\\\Rightarrow -200=49a+45\\\\\Rightarrow 49a=-245\\\\\Rightarrow a=-\frac{245}{49}=-5\\\\\text{so the equation of the parabola is}\\\\y=-5(x+7)^2+45[/tex]

[tex]\\\text{Now to find the x-intercepts, we set }y=0, \text{ so we get}\\\\-5(x+7)^2+45=0\\\\\Rightarrow -5(x+7)^2=-45\\\\\Rightarrow (x+7)^2=\frac{-45}{-5}\\\\\Rightarrow (x+7)^2=9\\\\\Rightarrow (x+7)=\pm \sqrt{9}\\\\\Rightarrow x+7=\pm 3\\\\\Rightarrow x=-7\pm 3\\\\\Rightarrow x=-7-3, \text{ and } x=-7+3\\\\\Rightarrow x=-10, \text{ and } x=-4\\\\\text{so x-intercepts of parabola occur at: }(-10,0), \text{ and }(-4,0)[/tex]

Answer:

We are given that there are total 170 toy robots

Number of defective robots out of total 170 toy robots [tex]=20[/tex]

We have to find the percentage of toy robots that are disaffected.

The percentage of toy robots that are disaffected is given below:

[tex]\frac{20}{170} \times 100[/tex]

[tex]0.1176 \times 100[/tex]

[tex]11.76[/tex]

Therefore, the percent of toy robots that are disaffected is [tex]\bold{11.76\%}[/tex]

Answer:

1 foot = 0.305 meters.

Convert 1 meter to feet:

1 meter = 1/0.305 = 3.28 feet

Find the weight in pounds per meter:

5 pounds x 3.28 feet = 16.4 pounds per meter.

Convert pounds per meter to kilograms per meter:

16.4 pounds x 0.454 kilograms per pound = 7.44 kg/m

Answer: D

Step-by-step explanation:

An on-line electronics store must sell at least $5000 worth of computers and printers per day.

Each printer costs $350 and each computer costs $750.

This equation is: 350p + 750c ≥ 5000

The store can ship a maximum of 20 items per day

This equation is: c + p ≤ 20

Final answer:

Billie has $2.02 left after buying fabric, craft glue, and craft paper, which in total cost her $14.93 from her initial $16.95.

Explanation:

To find out how much money Billie has left after purchasing her items, we need to calculate the total cost of the items and subtract it from the amount she had initially.

Fabric cost: $8.69

Craft glue cost: $1.95

Craft paper cost: $4.29

We add these amounts together to find the total cost of the items:

$8.69 (fabric) + $1.95 (glue) + $4.29 (paper) = $14.93.

Now, we subtract the total cost of items from the amount she had to start with:

$16.95 - $14.93 = $2.02.

Therefore, Billie has $2.02 left after her purchases.

Answer:

B

Step-by-step explanation:

The expected value of profit margin is the sum of the product of profit margin and probability.

Wrench A:

... 10×.05 +20×.6 +30×.2 +40×.15 = 0.5 +12 +6 +6 = 24.5

Wrench B:

... (20+40)×.3 +(30+50)×.2 = 18 +16 = 34

Wrench C:

... 15×.4 +30×.5 +(45+60)×.05 = 6 +15 +5.25 = 26.25

Wrench D:

... 5×.2 +10×.4 +15×.15 +20×.25 = 1 +4 +2.25 +5 = 12.25

___

Clearly, Wrench B has the greatest expected profit margin. That would be the one Jose should order if he's trying to maximize his profit.

Answer:

I'm not sure if it is correct but i hope it helps you

Step-by-step explanation:

So you subtract 25 and 15 and you will get 10

then you add 65 and 5 and you will get 70

you add 45 and 20 and you will get 65

Answer: 15

from what i believe

Step-by-step explanation: i did the math that i thought it was and i did 240 divided by 16 and i got 15 hope this helps.

3. Answer: y = 4

Step-by-step explanation:

Need to find the slope (m):

  [tex]\dfrac{y_2-y_1}{x_2-x_1}[/tex]

  [tex]\dfrac{4 - 4}{-3-1}[/tex]

= [tex]\dfrac{0}{-4}[/tex]

= 0

Now input ONE of the points (1, 4) and the slope (m = 0) into the Point-Slope formula:

y - y₁ = m(x - x₁)

y - 4 = 0(x - 1)

y - 4 = 0

y      = 4

********************************************************************

4. Answer: [tex]\bold{y = \dfrac{2}{3}x + 3}[/tex]

Step-by-step explanation:

 [tex]y - y_1 = m(x - x_1)[/tex]

 [tex]y - 1 = \dfrac{2}{3}(x - (-3))[/tex]

 [tex]y - 1 = \dfrac{2}{3}(x + 3)[/tex]

 [tex]y - 1 = \dfrac{2}{3}x + 2[/tex]

 [tex]y = \dfrac{2}{3}x + 3[/tex]

Answer:

Max for g(x) is 3

Max for f(x) is 2

Step-by-step explanation:

The maximum value of a function is the highest value on the graph of the function. It is the greatest value of the function and is always a y value. We can see on the graph that the blue function peaks at 3. The max is 3.

A normal sine or cosine without any transformations has the max of 1. We can see in the equation for f(x) that there is a vertical stretch of 2. So the max here is 2(1)=2.

Answer:

The answer is C

Step-by-step explanation:

I just answered it on edg

The second step is

2.5 (42 ÷ 3.2 – 2 + 3) - 5.2

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

Step 1:

2.5 (42 ÷ 3.2 – 10(0.2) + 3) - 5.2

Step 2:

2.5 (42 ÷ 3.2 – 2 + 3) - 5.2

Step 3:

2.5 (13.125 + 1) - 5.2

Step 4:

2.5 (14.125) - 5.2

Step 5:

35.3125 - 5.2

Step 6:

30.1125

Thus,

The value of the expression is 30.1125.

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Answer:

Step-by-step explanation:

a) When will the height be 307 feet?

h = − 16t^2 + 171t + 17

307 = − 16t^2 + 171t + 17

Solving the quadratic equation by the general formula (find the plot attached). It reaches 307' twice as it is a parabolic shot.

t=2.1141s

t=8,5734s

b) When will the object reach the ground?

h = − 16t^2 + 171t + 17

0 = − 16t^2 + 171t + 17

t=-0.0985s (not real as there exists no negative time)

t=10.786s

The object will be at a height of 307 feet approximately 9.54 seconds after it was thrown. The object will reach the ground approximately 0.21 seconds after it was thrown.

To find when the height will be 307 feet, you can set the equation for the height h to 307 and solve for t:

h = -16t² + 171t + 17

307 = -16t² + 171t + 17

Now, let's rearrange the equation and set it equal to zero:

-16t² + 171t + 17 - 307 = 0

Combine like terms:

-16t² + 171t - 290 = 0

Now, you can solve this quadratic equation for t. You can use the quadratic formula:

t = (-b ± √(b² - 4ac)) / (2a)

In this case, a = -16, b = 171, and c = -290. Plug these values into the quadratic formula:

t = (-171 ± √(171² - 4 * (-16) * (-290))) / (2 * (-16))

Now, calculate the values for t:

t₁ = (-171 + √(171² - 4 * (-16) * (-290))) / (2 * (-16))

t₂ = (-171 - √(171² - 4 * (-16) * (-290))) / (2 * (-16))

Calculate t₁ and t₂ separately:

t₁ ≈ 9.54 seconds

t₂ ≈ -9.69 seconds

Since time cannot be negative in this context, we discard the negative solution. Therefore, the object will be at a height of 307 feet approximately 9.54 seconds after it was thrown.

To find when the object will reach the ground, you can set h equal to 0 and solve for t:

h = -16t² + 171t + 17

0 = -16t² + 171t + 17

Rearrange the equation:

-16t² + 171t + 17 = 0

Now, solve for t using the quadratic formula as we did before:

t = (-171 ± √(171² - 4 * (-16) * 17)) / (2 * (-16))

Calculate t₁ and t₂:

t₁ ≈ 0.21 seconds

t₂ ≈ 10.30 seconds

Again, you discard the negative solution. So, the object will reach the ground approximately 0.21 seconds after it was thrown.

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Answer:

It should be A, $12.75

Step-by-step explanation: Add 10.5+10.5+10.5+4.5+4.5+6.75= $47.25, subtract 60-47.25= $12.75

11(.25)= 2.75

Cryus should order 3 pizzas.

Answer:

The hyperbolas which open horizontally are:

(x+2)^2/3^2-(2y-10)^2/8^2=1

(x-1)^2/6^2-(2y+6)^2/5^2=1

Step-by-step explanation:

A hyperbola with equation of the form:

(x-h)^2/a^2-(y-k)^2/b^2)=1 opens horizontally

Then, the hyperbolas which open horizontally are:

(x+2)^2/3^2-(2y-10)^2/8^2=1

(x-1)^2/6^2-(2y+6)^2/5^2=1

Answer:

[tex]\frac{(x-2)^2}{3^2}-\frac{(2y-10)^2}{8^2}=1[/tex]

and

[tex]\frac{(x-1)^2}{6^2}-\frac{(2y+6)^2}{5^2}=1[/tex]

Step-by-step explanation:

There are 2 types of hyperbolas:

Horizontal:

[tex]\frac{(x-h)^2}{a^2}-\frac{(y-k)^2}{b^2}=1[/tex]

Vertical:

[tex]\frac{(y-k)^2}{a^2}-\frac{(x-h)^2}{b^2}=1[/tex]

If the x term is positive then parabola is horizontal.

If the y term is positive then parabola is vertical.

so, only first two equations are in which x term is positive.

hence, equations are

[tex]\frac{(x-2)^2}{3^2}-\frac{(2y-10)^2}{8^2}=1[/tex]

and

[tex]\frac{(x-1)^2}{6^2}-\frac{(2y+6)^2}{5^2}=1[/tex]

Answer:

11 feet wood will tenly use to make the frame.

Step-by-step explanation:

As given

Tey is making a square frame for her painting.

She is using 4 pieces of wood that are each 2.75 feet long.

Tenly uses wood to make the frame = Number of pieces of wood × Length of each pieces

Here

Number of pieces of wood = 4

Length of each pieces = 2.75 feet

Put in the above

Tenly uses wood to make the frame = 4 × 2.75

                                                             = 11 feet

Therefore 11 feet wood will tenly use to make the frame.

w - width

2w - length (l)

30 cm - perimeter

w + w + 2w + 2w = 6w - perimeter

The equation:

6w = 30    divide both sides by 6

w = 5 cm

2w = 2(5) = 10

l = 10 cm

The area of a rectangle: A = lw.

Substitute:

A = (5)(10) = 50

In the equation 2.5x + 2y = 225, the term 2.5x represents the cost of dried fruit, with 2.5 being the cost per pound.

In the provided equation 2.5x + 2y = 225, where x stands for the pounds of dried fruit and y represents the pounds of nuts, the term 2.5x signifies the cost associated with the dried fruit in making the trail mix.

The coefficient 2.5 represents the cost per pound of dried fruit, which is $2.50. Therefore, multiplying the pounds of dried fruit (x) by the cost per pound (2.5) gives the total cost of the dried fruit in the trail mix. In essence, 2.5x calculates the financial contribution of the dried fruit to the overall cost of producing the trail mix.

For example, if there are 10 pounds of dried fruit (x = 10), then 2.5 times 10 equals 25, representing the cost, in dollars, of the dried fruit in the trail mix. This interpretation extends to any quantity of dried fruit used in the trail mix.

In summary, the term 2.5x in the equation 2.5x + 2y = 225 specifically denotes the cost associated with the pounds of dried fruit (x) used in producing the trail mix.

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Answer:

D.

Step-by-step explanation:

Add the x values and divide by the amount of x's and same with the y's

Answer:

missing data for the following exponential function is 27

Step-by-step explanation:

To find out missing data , we use the given f(x) equation

Given f(x) = 3^x

WE need to find the missing number f(x) when x=3

To find f(x) we plug in 3 for x  in f(x) = 3^x

[tex]f(x) = 3^3= 3*3*3= 27[/tex]

So missing number is 27

Answer:

B. 27

Step-by-step explanation:

Answer:

option A  and E

Step-by-step explanation:

Arithmetic sequence converge,  only  in the case only when r=0

otherwise , arithmetic sequence goes increasing or decreasing at a constant rate.

So we ignore second and fourth option

If |r|<1 then geometric sequence converge

if |r|>1 then geometric sequence diverge

In option A, r= 1/5  that is less than 1  so it converge

In option C, r= -2 , |r| > 1 so geometric sequence diverge

In option E, r= 2/3 that is less than 1  so it  converges

Answer is option A  and E

If you mean the y coordinate of that line, then it would be negative because it goes through -4 on the y axis.