Complete the table below to solve the equation 2.5x − 10.5 = 64(0.5x).

x f(x) = 2.5x − 10.5 g(x) = 64(0.5x)
2
3
4
5
6

A newspaper started an online version of its paper 14 years ago. In a recent presentation to stockholders, the lead marketing executive stated, “The revenues for online ads are more than double that of the revenues for printed ads.”
Use the graph below to justify the lead executive’s statement.
Determine the approximate year that the two ad revenues were equal.
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Two ocean beaches are being affected by erosion. The table shows the width, in feet, of each beach measured at high tide where 1995 is represented by year 0:

Year number Western Beach width (in feet) Dunes Beach width (in feet)
0 100 20
5 90 45
10 80 70
11 78 75
12 76 80
15 70 95

Describe the patterns shown by the erosion data measurements shown for each of the beaches in the table.
Between which years will the beaches have approximately the same width?
Assuming these rates remain constant, what can you do to get a better approximation of when the two beaches will have the same width?

Using a calculator, the slope of the line of best-fit is of 7.2.

To find the equation, we need to insert the points (x,y) in the calculator.

In this problem, the points are given as follows:

(-4,-32), (-2,-8), (0,10), (2,8), (4,32).

Using the calculator, the equation is:

y = 7.2x + 2.

Hence the slope is of 7.2.

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Step-by-step explanation:

Here,

given length= 45 5/7 m( mixed fraction)

= 320/7 m( simple fraction)

similar breadth= 16 3/4 m

= 67/4 m

Now,

Area= length* breadth

= 320/7 * 67/4

=5360/7 m²

Step-by-step explanation:

I guess this means the garden is a rectangle.

the area is

length × breadth (or width or ...)

so,

45 5/7 × 16 3/4 =

= (45×7 + 5)/7 × (16×4 + 3)/4 =

= 320/7 × 67/4 = 320×67 / 7×4 = 80×67 / 7 =

= 5360/7 = 765 5/7 m²

The number of ways of the letters FGHIJ can be arranged with repetition and without repetition are 125 and 60 ways respectively.

Formula for permutation with repetition

[tex]^nPr = n^r[/tex]

Formula for permutation without repetition

[tex]^nPr = \frac{n!}{n-r!}[/tex]

We have = 5

r = 3

a. If repetition is allowed,

Permutation = [tex]5^3[/tex] = 125 ways

b. If repetition is not allowed,

Permutation = [tex]\frac{5!}{5-3!}[/tex]

Permutation = [tex]\frac{5*4*3*2*1}{2*1}[/tex]

Permutation = [tex]\frac{120}{2}[/tex]

Permutation = 60 ways

Thus, the number of ways of the letters FGHIJ can be arranged with repetition and without repetition are 125 and 60 ways respectively.

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Answer:

4

Step-by-step explanation:

5x + 2 = 2x + 14

5x-2x=14-2

3x=12

x=12/3

x=4

Answer:

The exact form: x = 4

The phrases that fit the graph of [tex]y = \sqrt x[/tex] are

The equation of the function is given as:

[tex]y = \sqrt x[/tex]

Next, we plot the graph of the function (see attachment)

From the attached graph, we have the following highlights:

The above represents the phrases that fit the graph

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Using a graphing application, graph y = √x. Sketch the graph below.

Select all phrases that fit the graph of y = √x

curve     straight      y-intercept = 1        positive x-values

quadrant IV         quadrant III       point (1, 1)        x-intercept = 0

quadrant I           y-intercept = 0        no y-intercept    negative y-values

no x-intercept     quadrant II     x-intercept = 1    point (-1, -1)

Answer:

Step-by-step explanation:

Area of a scaled figure is multiplied by the square of the scale factor; volume is multiplied by the cube of the scale factor.

When dimensions are multiplied by 3, the area is multiplied by 3² = 9.

Area of the larger figure is 9 times that of the smaller one.

When dimensions are multiplied by 3, the volume is multiplied by 3³ = 27.

Volume of the larger figure is 27 times that of the smaller one.

__

Additional comment

In general, the area of a figure is the sum of the products of two orthogonal dimensions. If each of those is multiplied by 3, then the product is multiplied by 3 twice, or 3² = 9.

Similarly, the volume of a figure is the sum of products of three orthogonal dimensions. When those are each multiplied by 3, the product is multiplied by 3 three times, or 3³ = 27.

Answer: [tex]\tan^2 t[/tex]

Step-by-step explanation:

[tex]\sin^{2} t+\cos^2 t=1 \implies 1-\cos^2 t=\sin^2 t\\\\\implies \frac{1-\cos^{2}t}{\cos ^2 t}=\frac{\sin ^2 t}{\cos^2 t}=\tan^2 t[/tex]

Answer:

70

Step-by-step explanation:

【Answer】The least common multiple of 35 and 70 is 70.

                          [tex]\orange{ {\hspace{50 pt}\above 1.2pt}\boldsymbol{\mathsf{Procedure}}{\hspace{50pt}\above 1.2pt}}[/tex]                        

To obtain the least common multiple (lcm) we must do it by simultaneous decomposition.

This method consists of extracting the common and uncommon prime factors, then

[tex]\large\displaystyle\text{$\begin{gathered}\sf \left.\begin{matrix} \blue{35 \ \ \ 70}\\ 35 \ \ \ 35\\ 7 \ \ \ \ 7\\ 1 \ \ \ \ 1 \end{matrix}\right|\begin{matrix} 2\\ 5\\ 7\\ \: \end{matrix} \end{gathered}$}[/tex]

                                        [tex]\sf{L.c.m.(35,70)=2\times5\times7}[/tex]

                                          [tex]\boxed{\boxed{\sf{L.c.m.(35,70)=70}}}[/tex]

Using the linear function given in this problem, the formula underestimates the median weekly earnings in 2013 by $3, as 657 < 660.

The function that estimates the median weekly earnings n years after 1980 is:

W = 13n + 231.

2013 is 2013-1980 = 33 years after 2000, hence the estimate is given by W when n = 33, that is:

W = 13 x 33 + 231 = 660.

657 < 660, hence the formula underestimates the median weekly earnings in 2013 by $3.

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The number of miles the bird can fly for 60 minutes is 20 miles.

A bird can fly 5 miles in 15 minutes.

Let's find the rate before we can find the number of miles the bird can fly in 60 minutes.

Therefore,

rate = distance / time

rate = 5 / 15  = 1 / 3 miles per minutes

Therefore,

1 / 3  = d / 60

cross multiply

60 = 3d

d = 60 / 3

d = 20 miles

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Answer:

9

Step-by-step explanation:

Answer:

Equilateral triangle: All three sides are equal.

Isosceles triangle: All two sides are equal.

Scalene triangle: No sides are equal.

Step-by-step explanation: Step 1: Label the given points as A, B, and C, and plot them as vertices of a triangle with connecting lines to draw the triangle we are working to identify.

Step 2: Calculate the side length AB using the distance formula.

Step 3: Calculate the side length BC using the distance formula.

Step 4: Calculate the side length AC using the distance formula.

Step 5: Compare the side lengths AB, BC, and AC from the previous steps to define the triangle type.

Answer:

Step-by-step explanation:

The interest that Jimmy's account has earned is $35.95.

Interest is the total increase in excess of the amount deposited in the account. Interest earned can be determined by subtracting the amount deposited from the current balance.

Interest = current balance - amount deposited

$3,485.95 - $3,450.00 = $35.95

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Answer: -2 1/3

Step-by-step explanation:

First, change the word into equation

9*x+3=6

Do division first, so 6/9, simplify into 2/3 then subtract it by 3 which is -2 1/3

Answer:

[tex]200 cm^2[/tex]

Step-by-step explanation:

A = (1/2)bh

A = (1/2)(18)(30)

A = 270 square cm

A = (1/2)(16)(25)

A = 200 square cm

Answer:

200 square centimeters

Step-by-step explanation:

The area of a triangle can be calculated using the formula: [tex]A = \frac{1}{2}bh[/tex] where b is the base and h is the height. So if the base is 16 cm and the height if 25 cm you simply plug the values into the equation to find the area

Plug Values In:

[tex]A = \frac{1}{2}(16 cm)(25 cm)[/tex]

Multiply 16 cm and 25 cm:

[tex]A = \frac{1}{2}(400 cm^2)[/tex]

Multiply by 0.5 (or technically divide by 2)

[tex]A = 200 cm^2[/tex]

Answer: x = 6

Step-by-step explanation:

B(7,3) maps onto B'(5,3).

The perpendicular bisector of [tex]\overline{BB'}[/tex] is x=6, so that is also the line of reflection.

Answer:

x = 6

Step-by-step explanation:

Taking test as we speak

Answer:

all shown below

Step-by-step explanation:

y-intercept means a dot's y coordinate is 8 and on the y axis, x-i intercept means a dot's x coordinate is 9 and on the x axis

Answer:

  see the attached graph

Step-by-step explanation:

The intercepts are the points where a graph crosses the coordinate axes.

The y-intercept is the the point where the graph crosses the y-axis. The value of x is zero there. The coordinates of the y-intercept are (0, 8).

The x-intercept is the point where the graph crosses the x-axis. The value of y is zero there. The coordinates of the x-intercept are (9, 0).

You graph these intercepts by plotting the points at these coordinates.

__

In the attached graph, the intercepts are blue dots, and we have drawn a line through them. The line is not part of the graph of the intercepts. It is merely an instance of a function that has these intercepts.

In base 13, we use the digits 0-9 along with A for 10, B for 11, and C for 12.

Then the number that comes after A59C₁₃ is

A59C₁₃ + 1₁₃ = A59(C + 1)₁₃

… = A59(10)₁₃

… = A5(9 + 1)0₁₃

… = A5A0₁₃

where I use parentheses to indicate we're adding C and 1 in the same digits place, then carry the 1 into the next digits place.

[tex]{ \red{ \bold{option \: (d)}}} \: { \green{ \tt{ {2}^{8p} = {2}^{5p + 3}}}} [/tex]

Step-by-step explanation:

I said option (d) is correct. Because, the answer of 2^8 is 256 i.e.,

[tex]{ \green{ \bold{ {2}^{8} }}} = { \green{ \tt{2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2}}}[/tex]

[tex]{ \green{ \bold{ {2}^{8} }}} = { \green{ \tt{256}}}[/tex]

The value of 16^2 = 256.

Also, the answer of 2^5 is 32. i.e.,

[tex]{ \green{ \bold{ {2}^{5} }}} = { \green{ \tt{2 \times 2 \times 2 \times 2 \times 2}}}[/tex]

[tex]{ \green{ \bold{ {2}^{5} }}} = { \green{ \tt{32}}}[/tex]

Answer:

y

Step-by-step explanation:

that easy just isolate the variables

Answer:

(x+2)²+(y-4)²=36

Step-by-step explanation:

1) to determine the coordinates of the centre of the given circle. It is point A (-2;4);

2) to determine the length of the radius: to calculate the distance between the point A(-2;4) and any point on the circle, it is 6 [units];

3) to make up the required equation according to the scheme:

(x-x₀)²+(y-y₀)²=r², where (x₀;y₀) - the coordinates of the centre, r - the length of the radius.

4) finally, (x+2)²+(y-4)²=6².

PS. for more details see the attachment.

Answer:

[tex]y = -2x + 5[/tex]

m = -1

b = 5

Step-by-step explanation:

Hello!

Slope - Intercept Form: [tex]y = mx+b[/tex]

The slope of the line is the rate of change, or how the graph changes in y as it changes in x.

Slope can be calculated by the formula: [tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]

We need two points on the line to get the x and y-values. I'm going to choose points (0,5) and (4,-3).

Calculate Slope

The slope is -2.

The y-intercept of the line is where the graph touches the y-axis (x = 0). It can be found by looking at the intersection of the graph and the axis.

The intersection happens at point (0,5), so the y-intercept is 5.

We found m, the slope, to be -2 and b, the y-intercept, to be 5. We can just plug it into the equation format.

Equation: [tex]y = -2x + 5[/tex]

The inference based on the information about ordering is that D. Yes, young Cosette 1, young Cosette 2, and young Cosette 3 are all different parts.

It should be noted that a inference simply means the conclusion that can be deduced based on the information given.

In the role of young Cosette for the drama, 3 girls should be casted.

If three are being casted then there is need for different parts because for same role there may be different stages of character.

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Answer:

if you are asking a real question the answer should be on your driving history on life 360 or maybe the average gps. How fast were you driving? I have no idea thats a answer only you know.

Step-by-step explanation:

Answer:

r = 70.59  miles / hour

Step-by-step explanation:

Comment

The first set of numbers gives you the distance you travelled.

Givens

t = 20 minutes = 20/60 = 1/3 of an hour

r = 60 miles / hour

d = ?

d =  r * t

d = 60 * 1/3

d = 20 miles  (The hours cancel)

So now you can find out what 17  minutes means

d = 20 miles

t = 17 minutes = 17/60 hours = 0.2833 hours.

r = d / t

r = 20 / 0.2833

r = 70.59  miles / hour

Answer:

t = 1.322

Step-by-step explanation:

4×(2^t) = 10

2^t = 10/4 = 2.5

t = log2(2.5)

now, the logarithm to the base 2 of 2.5 must be larger than 1, as 2.5 is larger than 2.

so, it can be only the 4th answer option.

now, to actually calculate it :

log2(2.5) = log10(2.5) / log10(2) = 1.321928095... ≈

≈ 1.322

we were correct.

Answer:

t = 1.322

Step-by-step explanation:

Given equation:

[tex]4(2^t)=10[/tex]

Divide both sides by 4:

[tex]\implies \dfrac{4(2^t)}{4}=\dfrac{10}{4}[/tex]

[tex]\implies 2^t=2.5[/tex]

Take natural logs of both sides:

[tex]\implies \ln 2^t = \ln 2.5[/tex]

[tex]\textsf{Apply the natural log power law}: \quad \ln x^n=n \ln x[/tex]

[tex]\implies t \ln 2 = \ln 2.5[/tex]

Divide both sides by ln 2:

[tex]\implies \dfrac{t \ln 2}{\ln 2} = \dfrac{\ln 2.5}{\ln 2}[/tex]

[tex]\implies t= \dfrac{\ln 2.5}{\ln 2}[/tex]

[tex]\implies t=1.321928095...[/tex]

[tex]\textsf{Apply log law}: \quad a^c=b \iff \log_ab=c[/tex]

[tex]\implies \log 2 (2.5)=t[/tex]

[tex]\implies t=1.321928095...[/tex]

Therefore, the solution that is nearest to the exact solution is t = 1.322

A heat engine is a device that turns heat into mechanical energy that may subsequently be utilized to do mechanical labour. The total rate of heat rejection to the environment is 298.4458 kJ/min.

A heat engine is a device that turns heat into mechanical energy that may subsequently be utilized to do mechanical labour. It accomplishes this by transferring a functioning ingredient from a higher to a lower state temperature.

For the following condition, the diagram can be made as shown below. Also, the Heat Engine Sink temperature, [tex]T_H[/tex] = 900 K

Heat Engine surrounding temperature, [tex]T_L[/tex] = 300 K

Refrigerator surrounding temperature, [tex]T'_C[/tex] = 215 C + 273 =  488 K

Refrigerator sink temperature, [tex]T'_H[/tex] = 300 K

The heat removed by the refrigerator, [tex]Q'_{in}[/tex] = 250 kJ/min

A.) For a Carnot refrigerator, the COP or the coefficient of performance is given by,

[tex]COP = \dfrac{T'_C}{T'_H-T'C}[/tex]

COP = (488)/(488-300)

COP = 2.596

The COP is also the ratio of the Heat input and the work output.

[tex]COP = \dfrac{Q'_{in}}{W}[/tex]

2.596 = 250/W

W = 96.302 kJ/min

The Carnot engine efficiency is expressed as,

[tex]\eta = 1- \dfrac{T_C}{T_H}[/tex]

η = 1 - (300/900)

η = 0.6667

Also, the Carnot engine efficiency is defined as,

[tex]\eta = \dfrac{W}{Q_{in}}\\\\[/tex]

[tex]0.6667 = \dfrac{96.302}{Q_{in}}\\\\Q_{in} = \rm 144.4458\ kJ/min[/tex]

Hence, the rate of heat supplied to the heat engine is 144.4458 kJ/min.

B.) The total work done by the engine is 96.302 kJ/min, while the heat input is 144.4458 kJ/min. Therefore, the heat output of the system is,

[tex]W = Q_{in} - Q_{out}\\\\Q_{out} = 48.1438\rm\ kJ/min[/tex]

Thus, the total rate of heat rejection to the environment,

[tex]\text{Total Heat rejection} = Q_{out}+Q'_{in}\\[/tex]

                               = 48.4458 kJ/min + 250 kJ/min

                                = 298.4458 kJ/min

Hence, the total rate of heat rejection to the environment is 298.4458 kJ/min.

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Step-by-step explanation:

(3x+6)= 48(Alternate angles)

3x=48-6

3x=42

x=14

2y+48=5y-9 (Sum of two opposite interior angles= exterior angle)

48+9=5y-2y

57=3y

y=19