f(x)=-2x-5;g(x)=5x+2 find 10f(x)-5g(x)

Answer:

Ok, Sir, The answer is D.

Step-by-step explanation:

From the list of possible answers, the sides are 5 and 12 and the hypotenuse is 13, so sin(x) is either 5/13 or 12/13 depending on which of the two legs is opposite to angle x.

Out of the 400 surveyed students, 327 were either seniors or commuters.

To find the number of students who were either seniors or commuters out of the 400 surveyed students, we need to add the number of seniors and the number of commuters while avoiding double-counting those who fall into both categories.

According to the information given:

There were 262 seniors.

There were 215 commuters.

150 of the seniors were also commuters.

To avoid double-counting, we need to subtract the number of seniors who were also commuters from the total count of seniors and commuters.

Seniors or commuters = Total seniors + Total commuters - Seniors who are also commuters

= 262 + 215 - 150

= 327

Therefore, out of the 400 surveyed students, 327 were either seniors or commuters.

It's important to note that in this calculation, we accounted for the overlap between seniors and commuters (150 students who were both seniors and commuters) to avoid counting them twice.

This ensures an accurate count of the students who fall into either category.

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Answer:

To divide fractions, you need to follow these steps:

Flip the second fraction (the one you want to divide by) upside down (this is called taking the reciprocal).

Multiply the first fraction by the reciprocal of the second fraction.

Simplify the resulting fraction if possible.

Here is an example:

1/3 ÷ 2/5

Step 1: Flip the second fraction: 2/5 becomes 5/2.

Step 2: Multiply the first fraction by the reciprocal of the second fraction: 1/3 x 5/2 = 5/6.

Step 3: Simplify the resulting fraction if possible: 5/6 is already in its simplest form.

For more examples and explanatTo divide fractions, you need to follow these steps:

Flip the second fraction (the one you want to divide by) upside down (this is called taking the reciprocal).

Multiply the first fraction by the reciprocal of the second fraction.

Simplify the resulting fraction if possible.

Here is an example:

1/3 ÷ 2/5

Step 1: Flip the second fraction: 2/5 becomes 5/2.

Step 2: Multiply the first fraction by the reciprocal of the second fraction: 1/3 x 5/2 = 5/6.

Step 3: Simplify the resulting fraction if possible: 5/6 is already in its simplest form.

Step-by-step explanation:

brainliest pls

Answer:

Step-by-step explanation:

For dividing fractions:

Remember:

Keep Change Flip

Keep the first the same

Change the sign to multiplication

Flip the second fraction.

EX.

\(\frac{4}{5}\) ÷ \(\frac{1}{2}\)                           >Keep, Change Flip

=\(\frac{4}{5}\) * \(\frac{2}{1}\)                          >Now it's multiplication, reduce first if you can

                                    (nothing reduces in this problem), so mulitply

                                    across

= \(\frac{8}{5}\)

Answer:

Step-by-step explanation:

15+5x=20x

   -5x  -5x  => Subtract 5x from each side

You get

15 = 15x

Divide both sides by 15

1=x

Answer:

m<EAG = 132°

Step-by-step explanation:  

First we have to solve for x.

W=7x+12

G=8x-15

A=180-(12x+24)

All 3 of those added together should equal 180.

7x+12+8x-15+180-(12x+24)=180

7x+12+8x-15+180-12x-24=180

3x+153=180

3x=180-153

3x=27

x=9

SO, m<EAG = 12x+24 = 12(9)+24=108+24=132

Answer:

Step-by-step explanation:

The vertex is at (-3, -1)  and the leading coefficient is negative ( because  the curve is inverted)

y = -a(x + 3)^2 - 1

One point on the curve is (-2, -3) so

-3 = -a(-2+3)^2 - 1

-3 = -a - 1

-a = -2

So we have

y = -2(x + 3)^2 -  1

y = -2(x^2 + 6x + 9) - 1

y = -2x^2 - 12x - 19.

A 7800 yd² of artificial turf must be purchased to cover the field.

A rectangle is a 2-dimensional shape with parallel opposite sides equal to each other and four angles are right angles.

Area of a rectangle is expressed as;

Area = length × width

Given that;

Length of the field = 130 yd

Wdith of the field = 60 yd

To calculate the amount of artificial turf needed to cover a rectangular field, we need to find the area of the field.

Area = length × width

Plug in the values

Area = 130 yd × 60 yd

Area = 7800 square yards

Hence, to cover the entire field with artificial turf, you would need to purchase 7800 square yards of artificial turf.

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Answer:

Step-by-step explanation:

Solving in steps:

Answer:

She will not have enough money

Step-by-step explanation:

0.79x85=67.15

67.15+35=105.15

Given the values of z and w, as

we will find z w, as follow

Simplifying further

To express in polar and exponetial form

We need to get the angle between them

Thus, in the polar form, we will have

For the exponential form, we will have

Answer:

uhhh 28

Step-by-step explanation:

Answer:

The answer is A

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

Edge2021

Answer:

P(A) = 0.57 (rounded to two decimal places).

Step-by-step explanation:

The probability of selecting a red marble from the hat can be found by dividing the number of red marbles by the total number of marbles:

P(red) = number of red marbles / total number of marbles

P(red) = 20/35

We can simplify this fraction by dividing both the numerator and denominator by 5:

P(red) = 4/7

So the probability of selecting a red marble from the hat is 4/7, or approximately 0.57 when rounded to two decimal places.

Therefore, P(A) = 0.57 (rounded to two decimal places).

Interest is a fee charged by a lender to a borrower for the use of money or credit, usually expressed as a percentage of the amount borrowed or invested over a period of time. Brandon invested $\(4700\) at 3% interest and $\(1100\) at \(8\)% interest.  The total interest earned after one year is $229

How much was in each account?

Let x be the amount invested in the first account that pays 3% interest, and let y be the amount invested in the second account that pays 8% interest. Since the total amount invested is $5800, we have:

\(x + y = 5800\)

The amount of interest earned on the first account is 0.03x, and the amount of interest earned on the second account is 0.08y. Since the total interest earned after one year is $229, we have:

\(0.03x + 0.08y = 229\)

We now have two equations with two unknowns:

\(x + y = 5800\)

\(0.03x + 0.08y = 229\)

We can solve for x and y by using elimination or substitution method. Here, we will use the substitution method.

Solve the first equation for x:

\(x = 5800 - y\)

Substitute this expression for x into the second equation and solve for y:

\(0.03(5800 - y) + 0.08y = 229\)

\(174 - 0.03y + 0.08y = 229\)

\(0.05y = 55\)

\(y = 1100\)

Now substitute this value of y into either equation to solve for x:

\(x + 1100 = 5800\)

\(x = 4700\)

Therefore, Brandon invested $\(4700\) at 3% interest and $\(1100\) at \(8\)% interest.

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Answer: x=9/2

Step-by-step explanation: Step 1) subtract 5x from both sides 3x+7-5x=5x-2 -5x = -2x+7=-2

Step 2) Subtract 7 from both sides -2x+7-7= -2 -7 -2x=-9

Step 3) Divide both sides by -2   -2x/-2 = -9/-2  x=9/2

Answer:

Step-by-step explanation:

A lawnmower was reduced in a sale by 2%. The new price is £127.40. What was the original cost of the lawnmower?

127.40 = 98%

127.40 : 98 * 100 = 130

-------------------

check

130 - 2% = 127.40

the answer is good

Answer:

130 pounds

Step-by-step explanation:

Let's say the original price was x, that'd mean x*0.98=127.40, x=127.4/0.98, x=130

The width of the rectangle whose perimeter is 37 cm is 6.25 cm.

A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.

Variables are the name given to these symbols because they lack set values.

In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.

Given:

The length of a rectangle is 6 cm more than its width, w cm.

So, the length = w + 6

The perimeter of the rectangle is 37 cm.

Then, Perimeter of the rectangle = 37

2(l+ w) = 37

2( w+ 6 +w )= 37

2(2w + 6)= 37

4w + 12 = 37

4w = 25

w = 6.25 cm

and, length = w+ 6 = 6 + 6.25 = 12.25 cm

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Main Answer: The total surface area of cylinder B is approximately 476.7  square units.

Supporting Question and Answer:

How is the surface area of a cylinder calculated?

The surface area of a cylinder is the sum of the areas of its curved surface and two circular bases. It can be calculated using the formula:

A = 2πrh + 2π\(r^{2}\)

where "r" is the radius of the circular base, "h" is the height of the cylinder, and π (pi) is a mathematical constant that represents the ratio of the circumference of a circle to its diameter, approximately equal to 3.14159.

The first term, 2πrh, represents the area of the curved surface of the cylinder, while the second term, 2π\(r^{2}\), represents the combined area of the top and bottom circular bases.

Body of the Solution: Let the height and radius of cylinder A be "h" and "r" respectively. Then, the height and radius of cylinder B are "2h" and "R" respectively, since cylinder B has twice the height of cylinder A but the same radius.

The total surface area of a cylinder is given by the formula:

Area = 2πrh + 2π\(r^{2}\)

For cylinder A, we know that the surface area is 180, so we can substitute the values and solve for "r" as follows:

180 = 2πrh + 2π\(r^{2}\)

90 = πrh + π\(r^{2}\)

We can rearrange this equation to solve for r:

r² + rh - 90/π=0

Using the quAdratic formula,we get:

r = (-h ± √((h)² + 4(90/π)))/2

r = -h/2 ± √(h² + 4(90/π))/2

Now we have an expression for r in terms of h . We can use this expression to find the radius of cylinder B, since we know that cylinder B has twice the height of cylinder A.

R = 2r= -h ± √(h² + 4(90/π))

We can use this expression to find the surface area of cylinder B:

Surface area of cylinder B = 2πR² + 2πR(2h)

Surface area of cylinder B= 2π( -h ± √(h² + 4(90/π)))² + 4πh( -h± √(h² + 4(90/π)))

We can use the value we found for 2h using the quadratic formula in the expression to get:

Surface area of cylinder B = 476.7 square units (rounded to one decimal place)

Therefore, the total surface area of cylinder B is approximately 476.7  square units.

Final Answer: Therefore, the total surface area of cylinder B is approximately 476.7  square units.

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Answer:

5n

Step-by-step explanation:

Answer:

3) 21/60= 0.35

4) 5/4= 1.25

5) 9/15= 0.6 or 2/3

6) 378/15= 25.2 or 25 and 1/5

7) 1 1/2/ 2/3= 2.5

8) 28 1/3 / 3 1/3= 8.5

Step-by-step explanation:

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Taking the difference of compound interest and simple interest, the interest rate is 15%

Let's assume that the rate of interest is "r" percent per annum.

The simple interest on Rs. 8000 for 2 years at the rate of "r" percent per annum is:

SI = (P * R * T) / 100

\(= (8000 * r * 2) / 100\\= 160r\)

The compound interest on Rs. 8000 for 2 years at the rate of "r" percent per annum is:

CI = P[(1 + R/100)^T - 1]

\(= 8000[(1 + r/100)^2 - 1]\\= 8000[(100 + r)^2 - 10000] / 10000\)

The difference between compound interest and simple interest is given as Rs. 180:

CI - SI = 180

Substituting the values of CI and SI, we get:

\(8000[(100 + r)^2 - 10000] / 10000 - 160r = 180\)

Simplifying and taking the square root of both sides;

r = 15, r = -15

Taking the positive value, r = 15

The interest rate is 15%

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Answer:

See below for proof

Step-by-step explanation:

\(\displaystyle \frac{\sin x}{1-\cos x}=\frac{\sin x(1+\cos x)}{(1-\cos x)(1+\cos x)}\\\\\frac{\sin x}{1-\cos x}=\frac{\sin x(1+\cos x)}{1-\cos^2 x}\\\\\frac{\sin x}{1-\cos x}=\frac{\sin x(1+\cos x)}{\sin^2 x}\\\\\frac{\sin x}{1-\cos x}=\frac{1+\cos x}{\sin x}\\\\\frac{\sin x}{1-\cos x}=\frac{1}{\sin x}+\frac{\cos x}{\sin x}\\\\\frac{\sin x}{1-\cos x}=\csc x+\cot x\)

\(\\ \tt\bull\rightarrowtail h(x)=1/5(x^2-6)-8\)

\(\\ \tt\bull\rightarrowtail h(4)\)

\(\\ \tt\bull\rightarrowtail 1/5(4^2-6)-8\)

\(\\ \tt\bull\rightarrowtail 1/5(16-6)-8\)

\(\\ \tt\bull\rightarrowtail 10/5-8\)

\(\\ \tt\bull\rightarrowtail 2-8\)

\(\\ \tt\bull\rightarrowtail -6\)

The equation that represents the table, in slope-intercept form, is expressed as: y = 5x.

To write the equation of the table, find the slope (m) and the y-intercept (b), and express the equation as y = mx + b.

Let x represent time (min) and y represent water used (gal).

Slope (m) = change in y / change in x = 10 - 5 / 2 - 1 = 5/1

Slope (m) = 5

Find the y-intercept (b) by substituting m = 5 and (x, y) = (1, 5) into y = mx + b:

5 = 5(1) + b

5 - 5 = b

b = 0

Substitute m = 5 and b = 0 into y = mx + b:

y = 5x + 0

y = 5x

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The length of the rectangle is 96 m, the width of the rectangle is 77 cm , the length of the rectangle is 1/8 mile, the length and width of the rectangle is 7 m and 42 m respectively, VW is  11 units.

According to the question,

1) Perimeter of rectangle = 344 M

Width = 76 M

Perimeter of rectangle = 2(length + width)

2(length+76) = 344

length+76 = 172

length = 172-76

Length of the rectangle = 96 M

2) Area of a rectangular window = 7315 \(cm^{2}\)

Length of the window is 95 cm.

Area of rectangle = length*width

95*width = 7315

width = 7315/95

Width of the rectangle = 77 cm

3) The perimeter of a rectangular garden is 5/8 mile.

The width of the garden is 3/16 mile.

Perimeter of rectangle = 2(length+width)

2(length+3/16) = 5/8

length+3/16 = 5/(2*8)

length = 5/16-3/16

Length of the rectangle = 2/16 or 1/8 mile

4) The area of a rectangular window is 8256 \(m^{2}\).

The length of the window is 86 m.

Area of rectangle = length*width

86*width = 8256

width = 8256/86

Width of the rectangle = 96 m

5)  The length of a rectangle is six times its width. The perimeter of the rectangle is 98 m.

Let's take width of the rectangle to be x m.

Length of rectangle = 6x m

2(length+width) = 98

2(6x+x) = 98

2*7x = 98

14x = 98

x = 98/14

x = 7 m

Width = 7 m

Length = 7*6 m or 42 m

6) The perimeter of the pentagon is 58 units.

3z+10+z+3+2z-1+10 = 58

6z+10+3-1+10 = 58

6z+22 = 58

6z = 58-22

6z = 36

z = 36/6

z = 6 units

VW = 2z-1

VW = 2*6-1

VW = 12-1

VW = 11 units

Hence, the answer to 1 is 96 m , 2 is 77 cm, 3 is 1/8 mile , 4 is 96 m , 5 is 7 m and 42 m and 6 is 11 units.

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Answer:The correct answer is 16

Step-by-step explanation:

4^2= 16

16-6/2+3

16-3+3

13+3=16

Answer:

392

Step-by-step explanation:

I would separate this into 2 shapes a triangle and a square. So first take the area of the square

area of square = base x height

16x19=304

Than take the area of the triangle

area of triangle = 1/2(base x height)

you can find the height of the triangle by subtracting 19 from 30 which is 11, and the base is the same as the base of the square which is 16

1/2(16x11)= 88

Add them together

304+88=392