Write an expression in simplest form for the perimeter of a right triangle with leg lengths of 12a^4 and 16a^4.

Answer: [tex]2,412.74\ cm^2[/tex]

Step-by-step explanation:

You need to use the following formula for calculate the Total surface area of a solid hemisphere:

[tex]SA_{total}=3\pi r^2[/tex]

Where "r" is the radius.

 Since you cut a styrofoam ball in half, the total surface areas are equal.

The exercise gives you the diameter. Observe in the figure that this is:

[tex]d=32\ cm[/tex]

Since the radius is half the diameter, you know that:

[tex]r=\frac{d}{2}\\\\r=\frac{32\ cm}{2}\\\\r=16\ cm[/tex]

Finally, you can substitute the radius into the formula:

 [tex]SA_{total}=3\pi (16\ cm)^2=2,412.74\ cm^2[/tex] (Of each half of the styrofoam ball)

You can use the fact that along with the surface area of hemisphere, you need to add the surface area of the circle that's on the top of each hemisphere.(hemisphere means half of sphere)

The surface area of each half of the styrofoam ball is [tex]3\pi r^2 \: \rm unit^2[/tex]

Surface area of sphere = [tex]4 \pi r^2[/tex] sq. units where r is radius of sphere.

Since hemisphere is half of the sphere, thus,

Surface area of hemisphere = [tex]2\pi r^2[/tex] sq. units.

Since the foam ball is not hollow, if we slice it in half, each of the half piece is having surface = outer half sphere's surface + that circle which is formed due to slicing the ball

Thus, surface area of each half of the Styrofoam ball is calculated as

Surface area = Surface area of hemisphere + area of circle

Let the ball had radius r, then we have the needed surface area as:

[tex]S = 2\pi r^2 + \pi r^2 = 3\pi r^2 \: \rm unit^2[/tex]

S is surface area of each half of the styrofoam ball.

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Answer:

GB is 15 units

Step-by-step explanation:

see the attached figure to better understand the problem

we know that

The Centroid is a point of triangle where all 3 medians intersect

In this problem point G is the centroid of the triangle FDE

FA, EB and DC are medians of the triangle FDE.

Remember that centroid divides the median in 2:1

FA is a is median so FG:GA=2:1.

Find the value of x

[tex]\frac{FG}{GA}=\frac{2}{1}\\\\\frac{5x}{x+9}=\frac{2}{1}\\\\5x=2x+18\\\\5x-2x=18\\\\3x=18\\\\x=6[/tex]

Find the value of GB

GB=2x+3

substitute the value of x

[tex]GB=2(6)+3=15\ units[/tex]

Answer:

3875 feet above sea level

Answer:

[tex]3875[/tex]  [tex]feet[/tex]

Step-by-step explanation:

We first start at 7,000 feet above sea level, we then descend 4,500 feet closer to the sea level, therefore:

[tex]7,000 - 4,500[/tex]

[tex]==> 2,500[/tex]

Then we go up 1,375 feet farther from the sea level, so:

[tex]2,500 + 1,375[/tex]

[tex]==> 3,875[/tex]

Answer:

A. [tex]R=1,500+6x,\ x\le 800[/tex]

B. 584

Step-by-step explanation:

A band is performing at an auditorium for a fee of $1500.

In addition to this fee, the band receives 30% of each $20 ticket sold. Let x be the number of tickets sold, then these x tickets cost $20x. Calculate 30% of 20x:

[tex]20x\cdot 0.3=6x[/tex]

A. The total cost is

[tex]R=1,500+6x[/tex]

The maximum capacity of the auditorium is 800 people, so x≤800.

B. The band needs $5,000 for new equipment so

[tex]1,500x+6x\ge 5,000\\ \\6x\ge 3,500\\ \\x\ge \dfrac{3500}{6}\\ \\x\ge 583.333...[/tex]

So, it is enough 584 tickets to be sold.

The band's revenue equation is R = 1500 + 0.30 * 20 * x. To earn $5000 for new equipment, the band needs to sell at least 584 tickets, considering their fixed fee and the additional revenue from ticket sales.

Calculating Revenue for a Band's Performance

The band's total revenue (R) when x tickets are sold can be calculated using the equation: R = 1500 + 0.30 *20* x. This equation includes their fixed fee of $1500 plus the variable amount obtained from ticket sales, which is 30% of the ticket price ($20). For every ticket sold, the band adds $6 (30% of $20) to their revenue.

For the band to afford new equipment costing $5000, we need to determine how many tickets need to be sold. The equation becomes:

R = 1500 + 0.30 * 20 * x

$5000 = 1500 + 6 * x

$5000 - 1500 = 6 * x

$3500 = 6x

x = $3500 / 6

x = 583.33

Since the band cannot sell a fraction of a ticket, they would need to sell at least 584 tickets to meet their goal of $5000.

Answer:

Part a) The slope is [tex]m=-\frac{1}{3}[/tex]

Part b) The equation in point slope form is [tex]y-4=-\frac{1}{3}(x-3)[/tex]

Part c) The equation in slope-intercept form is [tex]y=-\frac{1}{3}x+5[/tex]

Step-by-step explanation:

we have the points (3,4) and (-3,6)

Part a) What is the slope of the line?

The formula to calculate the slope between two points is equal to

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

substitute the given points

[tex]m=\frac{6-4}{-3-3}[/tex]

[tex]m=\frac{2}{-6}[/tex]

[tex]m=-\frac{1}{3}[/tex]

Part b) Write the equation of the line in point-slope form

[tex]y-y1=m(x-x1)[/tex]

we have

[tex]m=-\frac{1}{3}[/tex]

[tex]point\ (3,4)[/tex]

substitute

[tex]y-4=-\frac{1}{3}(x-3)[/tex]  ---> equation in point slope form

Part c) Write the equation of the line in slope-intercept form

[tex]y=mx+b[/tex]

we have

[tex]y-4=-\frac{1}{3}(x-3)[/tex]

Isolate the variable y

distribute right side

[tex]y-4=-\frac{1}{3}x+1[/tex]

Adds 4 both sides

[tex]y=-\frac{1}{3}x+1+4[/tex]

[tex]y=-\frac{1}{3}x+5[/tex] ---> equation in slope intercept form

Answer: [tex]1.2675*10^{37}\ ergs[/tex]

Step-by-step explanation:

Let be "x" the amount of ergs the sun produces in[tex]3.25 * 10^3\ seconds[/tex].

According to the information provided in the exercise, in 1 second the sun produces [tex]3.9 * 10^{33}\ ergs[/tex] of radiant energy.

Then, in order to find the value of "x" you can write the following proportion:

[tex]\frac{ 3.9 * 10^{33}\ ergs}{1\ second}=\frac{x}{3.25 * 10^3\ seconds}[/tex]

Finally, you must solve for "x".

Therefore, you get:

[tex]x=\frac{( 3.9 * 10^{33}\ ergs)( 3.25 * 10^3 seconds)}{1\ second}\\\\x=1.2675*10^{37}\ ergs[/tex]

Answer: B

Step-by-step explanation:

-19 + (-23)

Answer:

-19-23 is basically 19+23 but in the negatives.

so B is your answer

Step-by-step explanation:

Answer:

22

Step-by-step explanation:

Answer:

Step-by-step explanation:

Steps:

1. Let x = #

2. "Five less than six times a number" can be written as: 6x - 5

3. "is at least" is the same as "greater than or equal to" and can be written as: >=

4. "nine subtracted from two times that number" can be written as: 2x - 9

5. the equation is: 6x - 5 >= 2x - 9

6. solve for x by grouping the x variable terms on one side and the constants on the other side:

6x - 5 >= 2x - 9

-2x +5 -2X +5

4x >= -4

7. divide each side by 4, and you get: x = -1

The solution according to the given statement is "x = -1".

According to the question,

The equation will be:

By adding "5" both sides, we get

→ [tex]6x - 5+5 \geq 2x - 9+5[/tex]

→             [tex]6x \geq 2x-4[/tex]

By subtracting "2x" form both sides, we get

→     [tex]6x-2x \geq 2x-4-2x[/tex]

→             [tex]4x \geq -4[/tex]

→               [tex]x \geq -\frac{4}{4}[/tex]

→               [tex]x = -1[/tex]

Thus the above answer is appropriate.

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Answer:

1.  0.8 cm

2.  1.6 cm

Step-by-step explanation:

1.

The scale for 2nd map is 1 cm to 50 km, that means "1 cm on map" is "50 km in real life".

We already know distance from Cleveland to Cincinnati is 40 km, which is less than 50, so we know the distance on map would be less than 1 cm.

So we set up ratio and figure out (let x be distance on map from Cleveland to Cincinnati):

[tex]\frac{1}{50}=\frac{x}{40}\\50x=40\\x=\frac{40}{50}\\x=0.8[/tex]

Hene, 0.8 centimeters would be the distance in 2nd map

2.

A scale of 1:50 means 1 cm equal 50 cm

So, 0.8m would be

0.8 * 100 = 80 cm

Hence, 80 cm would be represented by 80/50 on the map, that is:

[tex]\frac{80}{50}=1.6[/tex]

That is 1.6 centimeters

Answer:

A

Step-by-step explanation:

Given

4 - t = 3(t - 1) - 5 ← distribute and simplify right side

4 - t = 3t - 3 - 5

4 - t = 3t - 8 ( subtract 3t from both sides )

4 - 4t = - 8 ( subtract 4 from both sides )

- 4t = - 12 ( divide both sides by - 4 )

t = 3

Answer: -39g + 9

Step-by-step explanation:

PEMDAS states that multiplication must be performed before addition & subtraction

  (6g × 7) - (3²g × 9) + 3³

=     42g   -     81g     + 9

=           -39g             + 9

To expand (2x + 4) (3x^2 + 5x + 7), draw a rectangle with six regions, multiply the terms in each region and add them together. The final expanded form is 6x^3 + 22x^2 + 34x + 28.

To expand the polynomial expression (2x + 4) (3x2 + 5x + 7), we will use the rectangle (or area) method. This involves drawing a rectangle divided into six regions, each representing a product of a term from the first binomial and a term from the second trinomial.

First, draw a 2x3 rectangle, with the dimensions representing the two terms in the first binomial and the three terms in the second trinomial.

Label the length of the rectangle with the three terms from the second trinomial, 3x2, 5x, and 7.

Label the width of the rectangle with the two terms from the first binomial, 2x and 4.

Fill in each of the six regions by multiplying the term at the end of the row by the term at the top of the column. For example, the top-left region would be 2x multiplied by 3x2, giving 6x3.

Continue filling in the other five regions: 2x times 5x is 10x2, 2x times 7 is 14x, 4 times 3x2 is 12x2, 4 times 5x is 20x, and 4 times 7 is 28.

Combine like terms to get the final expanded form: 6x3 + 22x2 + 34x + 28.

[tex]\bf \stackrel{5}{~~\begin{matrix} 20 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~} \times \cfrac{3}{~~\begin{matrix} 4\\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}\implies 5\times 3\implies 15[/tex]

The simplest form of the expression 20 x 3/4 is 15, which is achieved by first multiplying 20 by 3 to get 60, and then dividing 60 by 4.

The student has asked to find the simplest form of the mathematical expression 20 x 3/4.

To simplify this expression, you multiply 20 by 3 and then divide the result by 4.

First, calculate 20 times 3, which equals 60.

20×3 = 60

Next, divide 60 by 4, which gives you 15.

[tex]\frac{60}{4} = 15[/tex]

So, the simplest form of the expression 20 x 3/4 is 15.

Answer:

[tex]\large\boxed{14:2=20:\dfrac{20}{7}}[/tex]

Step-by-step explanation:

[tex]14:2=20:x\\\\\dfrac{14\!\!\!\!\!\diagup^7}{2\!\!\!\!\diagup_1}=\dfrac{20}{x}\\\\\dfrac{7}{1}=\dfrac{20}{x}\qquad\text{cross multiply}\\\\7x=(20)(1)\\\\7x=20\qquad\text{divide both sides by 7}\\\\x=\dfrac{20}{7}[/tex]

Answer:

all work is shown and pictured

Answer:

0.34 cents

Step-by-step explanation:

You simply divide 1.02 by the 3 peppers.

Answer:

all work is pictured and shown

Final answer:

The equation of a line with a slope of 1 that passes through the point (2,5) in slope-intercept form is y = x + 3.

Explanation:

To write the equation of a line in slope-intercept form (y = mx + b), you need to know the slope (m) and the y-intercept (b). Since the slope is given as 1 and the line passes through the point (2,5), we can use the point-slope formula to find the y-intercept.

The point-slope formula is y - y1 = m(x - x1), where m is the slope and (x1, y1) is the point the line passes through. Plugging in the values we have:

y - 5 = 1(x - 2) → y - 5 = x - 2 → y = x + 3

So, the equation of the line in slope-intercept form is y = x + 3.

Answer:

53

Equation:

y = -2(6) + 65

y = -12 + 65

y = 65 - 12

y = 53

Answer:

53

Stp-by-step explanation:

Answer:

d= -9                                       d=9  

Step-by-step explanation:

-2d = 18                                 -2d=-18

divide by -2

d= -9                                       d=9  

Answer:

d=(18-1)/-2l

Step-by-step explanation:

i-2dl=18

-l        

-2dl=18-l

/-2l        

d=(18-1)/-2l

Answer:

Step-by-step explanation:

We can model a line with slope-intercept form:

[tex]y = mx + b[/tex]

where [tex]m[/tex] is the slope and [tex]b[/tex] is the Y-intercept.

We know that the new line is parallel to the given line, so the two lines have the same slope, or [tex]m = \frac{3}{2}[/tex]:

[tex]y = \frac{3}{2}x + b[/tex]

To determine [tex]b[/tex], we just need to plug in the given point that the line passes through, [tex](-2, 3)[/tex]:

[tex]y = \frac{3}{2}x + b[/tex]

[tex](3) = \frac{3}{2}(-2) + b[/tex]

[tex]3 = -3 + b[/tex]

[tex]b = 6[/tex]

This gives us the following equation:

[tex]y = \frac{3}{2}x + 6[/tex]

The equation of the line is y = (3/2)x + 6.

The equation of a line is given by:

y = mx + c

where m is the slope of the line and c is the y-intercept.

Example:

The slope of the line y = 2x + 3 is 2.

The slope of a line that passes through (1, 2) and (2, 3) is 1.

We have,

The equation of the line passes through the point (-2,3).

y = m(1)x + c

The equation of the line is parallel to the line whose equation is y=3/2x-4.

​This means,

y = (3/2)x - 4

This is in the form of y = m(2)x + c

m(2) = (3/2)

So,

m(1) = m(2)

Now,

(-2, 3) = (x, y)

y = m(1)x + c

3 = (3/2) x (-2) + c

3 = -3 + c

c = 3 + 3

c = 6

Now,

y = m(1)x + c

y = (3/2)x + 6

Thus,

The equation of the line is y = (3/2)x + 6.

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Answer:

The mean will be increased by 5

Step-by-step explanation:

Suppose a set of data [tex](2, 4, 6, 8, 10, 12)[/tex]

Mean is defined as sum of all the values given set of data divided by total number of values.

Mean1 = [tex]\frac{2+4+6+8+10+12}{6} = \frac{42}{6} = 7[/tex]

Now if we add 5 toeach value, the new set becomes [tex](7, 9, 11, 13, 15, 17)[/tex]

for which,

Mean2 = [tex]\frac{7+9+11+13+15+17}{6} = \frac{72}{6} = 12[/tex]

Mean2 - Mean1 = 5

Final answer:

A cube with a 5-inch edge has square-shaped faces, an area per face of 25 square inches, a total surface area of 150 square inches, and a volume of 125 cubic inches.

Explanation:

The question relates to the properties of a cube with an edge length of 5 inches. Here are the answers to each part:

b. Each face of the cube is a square shape.

c. The area of each face is 5 inches × 5 inches = 25 square inches.

d. The surface area of the cube is 6 × (area of one face) = 6 × 25 square inches = 150 square inches.

e. The volume of the cube is the cube of the side length, so 5 inches × 5 inches × 5 inches = 125 cubic inches.

Answer: 672 cars will have defective engine mounds

Step-by-step explanation: 25% of 2,688 is 672

The cost of a taxi ride can be calculated using the equation c = 1.75 + (m - 1/8) * 8 * 0.30, where c represents the total cost and m represents the total miles driven. Solving this equation for m when the total cost is $7.75 would yield the number of miles driven.

The subject of this question is the creation of an equation to calculate the cost of a taxi ride. According to the question, a taxi charges $1.75 for the first 1/8 mile and $0.30 for each additional 1/8 mile. First, we need to convert miles to 1/8 miles, since the pricing is based on this fraction. We know that each full mile is equal to 8 fractions of 1/8 mile. Therefore, to convert miles to 1/8 miles, we multiply the number of miles by 8.

Given this pricing structure, the costs associated with additional miles driven beyond the first 1/8 mile (which are already accounted for by the initial $1.75), can be represented by (m-1/8)*8*0.30. Here, (m-1/8) represents the additional miles traveled beyond the first 1/8 mile, and multiplying this by 8 converts these miles into 1/8 miles.

The total cost, c, can thus be represented by the equation c = 1.75 + (m - 1/8) * 8 * 0.30. If a ride cost $7.75, we can substitute this cost into the equation and solve for m to find the number of miles driven. This would give us the equation: 7.75 = 1.75 + (m - 1/8) * 8 * 0.30.

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Answer:

75 and 552 =627

Step-by-step explanation:

First=x

Second 7x+27

x+ 7x+27= 627

8x+27=627

8x=600

x=75

75*7+27 =525

525+27 = 552