the range of the function?
1 2
2 4
3 9
4 16

Answer: y = -3

Step-by-step explanation:

The midpoint is [tex]\left(\frac{-2+4}{2}, \frac{2-8}{2} \right)=(1, -3)[/tex].

The line given is a vertical line, so we need a horizontal line.

Thus, the equation is y = -3.

Answer:

the answer is x<9 I found this by simplifying and separating the x

Answer:

y = 2x + 3

Step-by-step explanation:

Hello!

Solve for y by isolating the variable.

The solution is y = 2x + 3.

To Calculate :-

Solution :-

⇒ -20x + 10y = 30

☆ Transposing (-20x) to R.H.S. sign would be changed to positive.

⇒ 10y = 30 + 20x

⇒ y = 30 + 20x / 10

⇒ y = 10 (3 + 2x) / 10

☆ Cancelling 10,

⇒ y = 3 + 2x / 1

⇒ y = 2x + 3

Answer:

6.9

Step-by-step explanation:

If you have a calculator, you can do this easily.

[tex]\sqrt{48}=4\sqrt{3}\quad \left(\mathrm{Decimal:\quad }\:6.92820\dots \right)[/tex]

Round the Decimal to the tenths place, and you get 6.9.

See the graph in the attached image.

The value of sec(V) is 5/3

The tangent is given as:

tan(V) = 4/3

To solve for sec(V), we use the following identity

sec^2(V) = tan^2(V) + 1

So, we have:

sec^2(V) = (4/3)^2 + 1

This gives

sec^2(V) = 16/9 + 1

Evaluate the sum

sec^2(V) = 25/9

Take the square root

sec(V) = 5/3

Hence, the value of sec(V) is 5/3

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The parallel lines cuts the sides in equal proportion to give NP = 0.8

The given diagram consists of a line parallel to one of the sides of the triangle.

According to the triangle proportionality theorem, the parallel line, NQ, proportionally divides the sides MR and MP, such that:

NQ || PR

By triangle proportionality theorem;

[tex]\mathbf{ \frac{ MN }{ NP} } = \frac{ MQ }{ QR } [/tex]

Which gives;

[tex] \mathbf{ \frac{ 5 }{ NP} } = \frac{ 8}{ 2 } [/tex]

2×5 = 8 × NP

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The z-scores of the scores are -1.34, -0.73, 0.48, 0.48 and 1.10

The sample scores are given as:

2, 3, 5, 5, 6.

Calculate the mean and the standard deviation using a statistical calculator.

From the statistical calculator, we have:

[tex]\bar x = 4.2[/tex] --- mean

[tex]\sigma_x = 1.64[/tex] --- standard deviation

The z-score is then calculated using

[tex]z= \frac{x - \bar x}{\sigma}[/tex]

Where:

x = 2, 3, 5, 5, 6.

So, we have:

[tex]z_1= \frac{2 - 4.2}{1.64} = -1.34[/tex]

[tex]z_2= \frac{3 - 4.2}{1.64} = -0.73[/tex]

[tex]z_3= \frac{5 - 4.2}{1.64} = 0.48[/tex]

[tex]z_4= \frac{5 - 4.2}{1.64} = 0.48[/tex]

[tex]z_5= \frac{6 - 4.2}{1.64} = 1.10[/tex]

Hence, the z-scores of the scores are -1.34, -0.73, 0.48, 0.48 and 1.10

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Use desmos graphing calculator, for visuals. It's easy to use as well.

A is 0 (zero)

(1x1 + 2x1 - 3)

B) D ( lies on 1 on our x-axis)

C) This tells you to draw a line at zero on the y-axis, a horizontal line BTW & read off the x values, where the line touches the pink graph/diagram.

y=x^2+2x-3 is the similar to x^2+2x-3=0 because the letter y now represents zero. So, that's why we draw the line y=0 (a horizontal line at zero). Then, use it to find the x values.

Thus, x = - 3 & x = 1

Hope this helps!

Answer:

67.

Step-by-step explanation:

n - m = 66

The 66 includes the number m+1   up to and including n (buy not m).

So the number of integers is 66 +1 = 67

Answer:

hope they do help. in case of any questions feel free to ask.

Using equation, He bought 3 boxes of ballpoint pens and 15  boxes of felt-tip pens

let

x = number of boxes of ballpoint pens

y = number of boxes of felt-tip pens

Therefore, the situation will form an equation.

x = 5y

Hence,

4.33x + 3.42y = 75.21,

4.33(5y) +  3.42y = 75.21

21.65y + 3.42y = 75.21

25.07y = 75.21

y = 75.21 / 25.07

y = 3

x = 5(3) = 15

Hence, he bought 3 boxes of ballpoint pens and 15  boxes of felt-tip pens

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Let, the points be A (8, −4) and B (1, −5). The slope of line AB exists 1/7.

Utilize the slope formula to estimate the slope of a line provided the coordinates of two points on the line.

The slope formula exists [tex]$m = (y_{2} -y_{1})/(x_{2} - x_{1} )[/tex], or the difference in the y values over the difference in the x values. The coordinates of the first point symbolize [tex]$x_{1}[/tex]and [tex]$y_{1}[/tex]. The coordinates of the second points exist [tex]$x_{2} , y_{2} .[/tex]

The slope of the line exists the ratio of the rise to the run, or rise separated by the run.

[tex]$m = (y_{2} -y_{1})/(x_{2} - x_{1} )[/tex]

The Line, AB contains points A (8, −4) and B (1, −5).

Substitute the value of points in the equation then we get

[tex]$m = (y_{2} -y_{1})/(x_{2} - x_{1} )[/tex]

m = (-5-(-4))/(1 - 8)

Simplifying the above equation, we get

m = (-5+4)/(1 - 8)

m = (-1)/(-7)

m = 1/7

Therefore, the slope of line AB exists 1/7.

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The computation shows that the year that Helike disappeared is 2248 years in between.

From the information, Helike disappearance was denoted as -1/5w. The year that civil year ended was represented as c + 1/4c.

This implies that year Helike disappeared will be:

= c + 1/4c - +-1/5w)

= 2248 years.

Here is the complete question:

The year the Greek city of Helike disappeared is -⅕ times the year the US Civil War ended. Let w represent the year the Civil War ended. Write an expression in terms of w to represent the year of Helike’s disappearance.

Part G

Use the results from Part E and Part F to determine the year Helike disappeared. Express your answer in terms of BC or AD.

Part H

Using the results from parts D through G, write an expression that represents the number of years elapsed between the disappearance of the Greek city of Helike and the end of the US Civil War. Write the expression in terms of c and w. Then solve the expression to find out how many years separate these two events.

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After 24 hours, 35.4% of the initial dosage remains on the body.

The exponential decay is written as:

[tex]f(x) = A*e^{-k*x}[/tex]

Where A is the initial value, in this case 2.8mg.

k is the constant of decay, given by the logarithm of 2 over the half life, in this case, is:

[tex]k = ln(2)/16h[/tex]

Replacing all that in the above formula, and evaluating in x = 24 hours we get:

[tex]f(24h) = 2.8mg*e^{-24h*ln(2)/16h} = 0.9899 mg[/tex]

The percentage of the initial dosage that remains is:

[tex]P = \frac{0.9899mg}{2.8mg}*100\% = 35.4\%[/tex]

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The correct simplification of x^12z^11/x^2z^4 is [tex]x^{10}z^{7[/tex]

The expression is given as:

x^12z^11/x^2z^4

Rewrite properly as

[tex]\frac{x^{12}z^{11}}{x^2z^4}[/tex]

Apply the quotient law of indices

[tex]x^{12-2}z^{11-4}[/tex]

Evaluate the difference

[tex]x^{10}z^{7[/tex]

Hence, the correct simplification of x^12z^11/x^2z^4 is [tex]x^{10}z^{7[/tex]

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The  production department factory overhead rates for Cut and sew department is 89 and Pattern is 67.

a. Pattern Department            

Factory overhead rate=Total Overhead Cost/Direct Labor Hours

Factory overhead rate= 140,700/2700

Factory overhead rate=67

Cut and sew Department

Factory overhead rate=231,400/2600

Factory overhead rate=89

b.  Factory overhead per unit

Pattern Department:      

Small glove=.04 x 67

Small glove=2.68    

Medium glove= .05 x 67

Medium glove=3.35

Large glove= .06 x 67

Large glove=4.02

Cut and sew Department:      

Small glove=.07 x 89

Small glove=6.23    

Medium glove=.09 x 89

Medium glove=8.01  

Large glove=.11 x 89

Large glove=9.79

Therefore the  production department factory overhead rates for Cut and sew department is 89 and Pattern is 67.

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The complete question is:

Handy Leather, Inc., produces three sizes of sports gloves: small,

medium, and large. A glove pattern is first stenciled onto leather in the Pattern Department. The stenciled patterns are then sent to the Cut and Sew Department, where the glove is cut and sewed together. Handy Leather uses the multiple production department factory overhead rate method of allocating factory overhead costs. Its factory overhead costs were budgeted as follows:

Pattern department Overhead                $140,700

Cut and sew Department overhead        $231,400

Total    $372100

Direct labor labor estimated for each department was as follows:

Pattern   Dept. -                       2100 direct labor hours

Cut and Sew Department      2600

Total                                          4700 direct labor hours

Direct labor hours are used to allocate the production department overhead to the products. The direct labor hours per unit for each product for each production department were obtained from the engineering records as follows:

Production Departments        Small Glove    Medium Glove          Large Glove

Pattern dept. 0.04         0.05                          0.06

cut and sew dept.                             0.07                 0.09                          0.11

direct labor hours per unit               0.11                   0.14                          0.17

If required, round all per unit answers to the nearest cent.

a. Determine the two production department factory overhead rates.

Cut and sew department and Pattern

b. Use the two production department factory overhead rates to determine the factory overhead per unit for each product.

small glove, medium glove and large glove

The value of x in the proportion is x = 39/8

The proportion is given as:

3/8 =x/13

Cross multiply

8 * x = 3 * 13

Evaluate

8x = 39

Divide by 8

x = 39/8

Hence, the value of x in the proportion is x = 39/8

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Hello,

f'(x) = sin(x) - 65 → f(x) = -cos(x) - 65x

So, the graph of f(x - 2) is just the graph of f(x) translated 2 units to the right.

Sadly we don't have the original function f(x), but we can answer in a general form.

Remember that for a general function f(x), a horizontal translation of N units can be written as:

g(x) = f(x + N).

So, the graph of f(x - 2) is just the graph of f(x) translated 2 units to the right.

So you need to resketch f(x), but just move it 2 units to the right side (positive x-axis side).

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Answer:

This is the graph of y = 0.4x

Answer:

√-1

Step-by-step explanation:

The imaginary number i is defined as √(-1)

NOTE : i² = -1

Answer:

-1/2 and 13/2

Step-by-step explanation:

Using the coordinate geometry formula, the exact area of triangle DEF is: B. 18 square units.

The coordinate geometry formula is used to find the rea of a triangle with given coordinates of its vertices. It is given as: the absolute value of [Dx(Ey - Fy) + Ex(Fy - Dy) + Fx(Dy - Ey)]/2.

Dx = -3

Dy = 4

Ex = 3

Ey =-2

Fx = 3

Fy = 4

Plug in the values:

[-3(-2 - 4) + 3(4 - 4) + 3(4 - (-2))]/2.

[-3(-6) + 3(0) + 3(6)]/2.

[18 + 0 + 18]/2.

36/2

= 18 units²

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Finance charge is: d.) $69.25.

Using this formula

Finance charge=(Monthly payment× Number of payment)-(Purchase price-Down payment)

Let plug in the formula

Finance charge=($22.50×12)-($225.75-$25)

Finance charge=$270-$200.75

Finance charge=$69.25

Therefore the Finance charge is: d.) $69.25.

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The complement of the given set is:

A* = {-1, 0, 1, 4, 5}

For any set A on a universal set U, such that:

A ⊂ U.

The complement of A is the set of all the terms on U that do not belong to A.

Here we have:

U = {-3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7}

And the given set is:

A = {-3, -2, 2, 3, 6, 7}

Then the complement of A is:

A* = {-1, 0, 1, 4, 5}

(all the elements of U that are not in A).

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Hello and Good Morning/Afternoon

Let's take this problem step-by-step:

First step

⇒ consider the fact cotθ = 1 / (tanθ)

 [tex]\frac{1+tanx}{1+cotx} =\frac{1+tanx}{1+\frac{1}{tanx} }[/tex]

Second step

⇒ form a common denominator for the fraction in the 'denominator'

[tex]\frac{1+tanx}{1+\frac{1}{tanx} } =\frac{1+tanx}{\frac{tanx+1}{tanx} }[/tex]

Let's flip over the fraction on the denominator

[tex]\frac{1+tanx}{\frac{tanx+1}{tanx} } =(1+tanx) * \frac{tanx}{1+tanx} =tanx[/tex]

And there you go, you have proved the statement by following these steps!

 *note, I used 'x' because the equation creator didn't have 'θ' symbol

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Answer:

undefined - you can't divide by 0!

Step-by-step explanation:

m = [tex]\frac{y2-y1}{x2-x1}[/tex]

m = [tex]\frac{10-(-8)}{1-1}[/tex]

m = 18/0

In order to find the slope, we have the formula is

The change of Y (Also Y minus each other)

----------------------------------------------------------------- Over (As fraction

The change of X (Also X minus each other)

Now the first point is (1,10) The Y is 10

                                               The X is 1

Now the Second Point is (1,-8) The Y is -8

                                                     The X is 1

So now we plug the numbers in

10-(-8)

---------                which is equal to 18/0

1-1  

A quick tip is that you CAN'T divide by zero

Therefore the answer is unidentified, but now you know how to solve for slopes

The best measurement for the angle is less than 90°. The correct option is a. less than 90°

From the question, we are to determine which of the given options is the best measurement for the angle

In the given diagram, we can observe that the angle is an acute angle. Thus, the measure of the angle will be lesser than 90°.

Hence, the best measurement for the angle is less than 90°. The correct option is a. less than 90°.

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Answer:

36.

Step-by-step explanation:

try this option provided on the attached picture.