Find the perimeter of the rectangle. Then, find the area of the rectangle. Round your
answer to the nearest tenth, if necessary.
(Lesson 2-3)

Answer:

-7

Step-by-step explanation:

To add a positive number, 5, and a negative number, -12, take the absolute value of both numbers.

You get 5 and 12.

Subtract the smaller absolute value from the larger absolute value.

12 - 5 = 7

The sign of the answer is the same sign as the number that has the larger absolute value. The absolute of 5 is 5. The absolute value of -12 is 12. -12 has the larger absolute value, and -12 is negative, so the answer is negative.

5 + (-12) = -7

Answer:

a=A/8

Step-by-step explanation:

This MIGHT be the answer, I am 99% sure!

[tex]i {}^{372} = 1 \\ i {}^{527 } = - i[/tex]

Step-by-step explanation:

Greetings !

Note that:-

[tex]i {}^{2n} = 1.\: if \: n \: is \: even \\ \: \: \: \: \: \: \: = - 1. \: if \: n \: is \: odd[/tex]

And also

[tex]i {}^{2n + 1} = i. \: if \: n \: is \: even \\ \: \: \: \: \: \: \: \: \: \: = - i.\: if \: n \: is \: dd[/tex]

Thus, remembering these general formula plug in values in the place of n and solve.

Therefore,

[tex]i {}^{2(186)} = i {}^{372} = 1[/tex]

where n is even thus its 1 from the above explanation

[tex]i {}^{2(263) + 1} = i {}^{527} = - i[/tex]

following the same procedure the values exceeds to be -i.

Hope it helps !!!

Answer: irrational

Step-by-step explanation:

because it still cant be turned into a fraction after adding 9 to pi

Answer:

  E = mc²

Step-by-step explanation:

You want an example of a literal equation.

A literal equation is one that uses variable names to represent numerical values.

Any equation that has no numbers is a literal equation.

One of the more famous literal equations in the world is Einstein's relation between mass and energy:

  E = mc²

We use literal equations as formulas for length, area, volume, and relations between chemical and engineering properties.

  P = 2(L+W) . . . . perimeter of a rectangle with length L and width W

  V = I·R . . . . voltage in a circuit with current I and resistance R

  PV = nRT . . . . ideal gas law relating pressure, volume, temperature, and quantity of gas

Answer:

x = 6

Step-by-step explanation:

4x/3 = 8

Solve for x

Multiply each side by 3

4x/3 *3 = 8*3

4x = 24

Divide each side by 4

4x/4 = 24/4

x = 6

Answer:

[tex] \sf \large \: x=6[/tex]

Step-by-step explanation:

Let's solve your equation step-by-step.

4x/3 =8

Step 1: Multiply both sides by 3.

4x/3=8

(4x/3)*(3)=(8)*(3)

4x=24

Step 2: Divide both sides by 4.

4x/4 = 24/4

x=6

Group C ran more miles than Group D

the central value of a set of data is expressed by the average of a list of data. It is defined mathematically as the ratio of the total number of data points to the number of units in the list. In terms of statistics, the term "mean" also refers to the average of a certain set of numerical data. The average of 2, 3, and 4 is, for instance, (2+3+4)/3 = 9/3 = 3. The center value of 2, 3, and 4 in this instance is 3, thus. Finding the mean value of a bunch of numbers is the definition of average.

Average = Total Values / Total Values

Group C = 27/4 = 6.75

Group D = 39 /6 = 6.5

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the height will be 50 ft after 0.575 seconds and after 5.424 seconds.

The equation that models the height is:

h(t) = 96*t - 16*t^2

Here we want to find the time such that the height is 50ft, then we need to solve the equation:

h(t) = 50 = 96*t - 16*t^2

Now we can solve that for t, we have the quadratic equation:

50 = 96*t - 16*t^2

0 = -16*t^2 + 96*t - 50

Then the solutions are:

t = (-96 ± √(96*96 - 4*(-50)*(-16))/(2*-16)

t = (-96 ± 77.6)/(-32)

The two solutions are:

This means that the height will be 50 ft after 0.575 seconds and after 5.424 seconds.

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Answer:

1/9

Step-by-step explanation:

[tex]y = - 9x - 4[/tex]

The slope of the perpendicular line is the interverse(opposite) of the slope of the original line.

Hope this helps!

Have any questions? Feel free to ask!

The equivalent expression of 4 − 3(x + 2) + 2(3 − 2x) is -7x + 4

The expression is given as:

4 − 3(x + 2) + 2(3 − 2x)

Open the brackets

4 − 3(x + 2) + 2(3 − 2x) = 4 - 3x - 6 + 6 - 4x

Collect the like terms

4 − 3(x + 2) + 2(3 − 2x) = - 3x - 4x + 4 - 6 + 6

Evaluate the like terms

4 − 3(x + 2) + 2(3 − 2x) = -7x + 4

Hence, the equivalent expression of 4 − 3(x + 2) + 2(3 − 2x) is -7x + 4

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The amount he would pay is $46.40.

Percentage can be described as the fraction of an amount that is expressed as a number out of hundred. The sign used to represent percentages is %.

The amount paid = list price of the first shirt + [list price of the second shirt x ( 1 - percentage discount)]

$29 + [$29 x (1 - 0.4)]

$29 + ($29 x 0.6) = $46.40

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The energy required is 30 watts second.

In order to accomplish work and to produce heat and light, energy must be transferred to a body or to a physical system. Energy is the quantitative attribute that does this. Energy is a preserved resource; according to the rule of conservation of energy, energy can only be transformed from one form to another and cannot be created or eliminated.

The voltage of a battery is 12 V and;

The charge is 2.5C.

Now, energy can be defined as the product of voltage and charge.

Therefore,

E = V × C

E = 12 × 2.5

E = 30 watt second

Hence, the energy needed by the 12 V battery to move 2.5 C through the electrical circuit is 30 watts second.

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Answer:

Q3

Slope = 5

Standard= y=5X+15

Q5

Slop =-4

Standard= y=-4x+4

Step-by-step explanation:

m=-5-5/-4+2=-10/-2= 5

y-5=5(x+2)

y-5=5x+10

y=5x+15

For the time period of  the projectile at least 192 feet above the ground is between 2 second and 6 second

Since s=128t-16t2, we want to know the 2 times where 128t-16t2=192, as those two values will be the begin and end times of the interval in question. We can rewrite that equation in standard quadratic equation form:

16t2-128t+192=0 or, simplified, 8t2-64t+96=0

or t2-8t+12=0

since it is now in quadratic form, we can solve using the quadratic formula:

t = 2 and 6

So the time period from approximately 2 second and 6 second has the projectile above 192 feet.

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answer and steps to get it in the picture

Answer:

The total amount of apples sold is 63.  There were 49 red apples and 14 green apples

Step-by-step explanation:

red: green : total

7          2       7+2

7          2          9

When we use the ratios, the total is 9

We are given the total is 63

63 divided by 9 is 7

We need to multiply each number by 7

red: green : total

7*7      2*7       9*7

49       14             63

The total amount of apples sold is 63.  There were 49 red apples and 14 green apples

Answer:

the answer is red apples 49 and green apples 14.

Answer:

120

Step-by-step explanation:

60 gallons of 30% antifreeze means there are 18 gallons of antifreeze.

Let the number of gallons of 60% antifreeze be x. Then,

[tex]\frac{0.6x+18}{x+60}=\frac{1}{2} \\ \\ 1.2x+36=x+60 \\ \\ 0.2x=24 \\ \\ x=129[/tex]

m= 15

b= 45

y= 15x +45

Overall equation

The equation of a line in slope-intercept form is given by y= mx +b, where m is the slope and b is the y-intercept.

Slope, m

The slope is the measure of how steep the line is. It also defines how the y-axis changes with respect to the x-axis. The formula for finding slope is as shown below.

[tex]\boxed{\text{Slope}=\frac{y_1-y_2}{x_1-x_2} }[/tex]

where [tex](x_1,y_1)[/tex] is the first coordinate and [tex](x_2,y_2)[/tex] is the second coordinate

y-intercept, b

This is the y-value in which the line cuts through the y-axis (vertical axis).

Slope, m

Let's identify two pairs of coordinates on the line.

2 square units on the y-axis represent $30. Thus, 1 unit on the y-axis represents $15.

The 2 points are: (0, 45) and (5, 120)

Substitute the 2 points into the slope formula:

Slope

= [tex]\frac{120-45}{5-0}[/tex]

= [tex]\frac{75}{5}[/tex]

= 15

Thus, m= 15.

y-intercept, b

From the graph, the line cuts through the y-axis at y= 45.

Thus, b= 45.

Overall equation

Substitute m= 15 & b= 45 into y= mx +b:

∴ The equation of the line is y= 15x +45.

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The values of x and y are 25° and 33° respectively.

It is important to note the following;

From the information given, we have that

Angles 5x + 4 and 3x - 24 are supplementary.

This is represented as;

5x + 5 + 3x - 24 = 180

collect like terms

8x = 180 + 20

add lik terms

8x = 200

x = 200/8

x = 25°

Also,

2y and 114 are on a straight line

This is represented as;

2y + 114 = 180

collect like terms

2y = 180 - 114

2y = 66

Make 'y' the subject

y = 66/2

y = 33°

Thus, the values of x and y are 25° and 33° respectively.

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[tex]{\sf{12 \times ( - 4) = -48}}[/tex]

Let the terms be a, ar, ar², ...

The sum to infinity being 27 means that:

[tex]\frac{a}{1-r}=27 \implies a=27(1-r)[/tex]

The sum of the first two terms being 15 means:

[tex]a+ar=15 \\ \\ (27-27r)+r(27-27r)=15 \\ \\ 27-27r+27r-27r^2 =15 \\ \\ 27r^2 -12=0 \\ \\ 27r^2 =12 \\ \\ r^2=\frac{12}{27}[/tex]

Since all the terms are positive, r>0.

[tex]\boxed{r=\frac{2}{3}} \\ \\ \implies a=27\left(1-\frac{2}{3} \right)=\boxed{9}[/tex]

Answer:

Step-by-step explanation:

create the cartesian system, sign the points, because the new triangle is reflected, so we need to use the straight lines which points on its ends, perpendicular to the x-axis, then we get A(0,-6), B(3,0), C(4,-3)

Answer:

formula for the derivative of x*lnx is equal to 1 + lnx.

Step-by-step explanation:

we need to find derivative of f(x) = x*lnx,

so we take the limiting value as x approaches x + h.

To simplify this, we set x = x + h,

and we want to take the limiting value as h approaches 0.

Now according to first derivative formula we have;

f'(x) = [tex]\lim_{h \to \zer0}[/tex]f(x+h) - f(x)]/[(x+h) - x]

[tex]\lim_{h \to \zer0}[/tex][ ln (1 + x) ] / x = 1

ln a - ln b = ln(a/b)

Using the above formulas, we have

d(xlnx)/dx = [tex]\lim_{h \to \zer0}[/tex][(x+h) ln(x+h) - xlnx]/[(x+h) - x]

= [tex]\lim_{h \to \zer0}[/tex][x ln(x+h) + h ln(x+h) - xlnx]/h

= [tex]\lim_{h \to \zer0}[/tex][x ln(x+h) - x lnx + h ln(x+h)]/h

= [tex]\lim_{h \to \zer0}\\[/tex][x(ln(x+h) - lnx) + h ln(x+h)]/h

=[tex]\lim_{h \to \zer0}[/tex][x ln [(x+h)/x] + h ln(x+h)]/h

=[tex]\lim_{h \to \zer0}[/tex][x ln (1+h/x) + h ln(x+h)]/h

=[tex]\lim_{h \to \zer0}[/tex] [x ln (1+h/x)]/h + limh→0 ln(x+h)

= [tex]\lim_{h \to \zer0}[/tex][ ln (1 + h/x) ] / (h/x) + limh→0 ln(x+h)

= 1 + lnx --- [Using limit formula [tex]\lim_{h \to \zer0}[/tex] [ ln (1 + x) ] / x = 1]

Hence, we have proved that the formula for the derivative of x*lnx is equal to 1 + lnx.

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Answer:

Step-by-step explanation:

In this section, we will determine the differentiate of xlnx using the first principle of derivatives, that is, the definition of limits. To derive the derivative of f(x) = xlnx, we take the limiting value as x approaches x + h. To simplify this, we set x = x + h, and we want to take the limiting value as h approaches 0. We will use the following formulas to prove the result:

f'(x) = limh→0[f(x+h) - f(x)]/[(x+h) - x]

limx→0 [ ln (1 + x) ] / x = 1

ln a - ln b = ln(a/b)

Using the above formulas, we have

d(xlnx)/dx = limh→0[(x+h) ln(x+h) - xlnx]/[(x+h) - x]

= limh→0[x ln(x+h) + h ln(x+h) - xlnx]/h

= limh→0[x ln(x+h) - x lnx + h ln(x+h)]/h

= limh→0[x(ln(x+h) - lnx) + h ln(x+h)]/h

= limh→0[x ln [(x+h)/x] + h ln(x+h)]/h

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Answer:

631

Step-by-step explanation:

This problem can be expressed as:

0.05x + 15 = 21.55
0.05x + 15 - 15 = 21.55 - 15
0.05x = 6.55
0.05x/0.05 = 6.55/0.05
x = 131

We also know that:

0.05x + 15 = x + 500

If x = 131:

x + 500
131 + 500
631

Answer:

33.33

Step-by-step explanation:

    Well, we already know the amount of time it takes to make the lemonade, and we know the rate as well.

We need to find out how many pitchers you can make in an hour. If you can make one pitcher in 10 minutes, then you can make 6 pitchers in 60 minutes, AKA an hour.

So we make 6 pitchers per hour.

If we make 6 an hour, then we multiply 6 by 200 to get the number of pitchers we can make in 200 hours.

We can make 33.33 pitchers in 200 hours

The volume of the sphere when it is completely closed is 4508.58 cubic inches

The formula for calculating the volume of a sphere is expressed as:

V = 4/3πr³

where

r is the radius = 20.5/2

radius = 10.25 in

Substitute

V = 4/3 (3.14)*10.25³

V = 4/3(3.14)
V =4508.58 cubic inches

Hence the volume of the sphere when it is completely closed is 4508.58 cubic inches

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Answer:

Approximately 1.86 times smaller

Step-by-step explanation:

5×10-7 = (5×10=50) = 50-7 = 43

8.5×10-4 = (8.5×10=84) = 84- 4 = 80

80/43 = approximately 1.86

43×1.86 = approximately 80

80/1.86 = approximately 43