Questions:
1. What did you do to the numerators? What did you do too to the denominators?
2. Did you find like terms among the collected terms of the numerator? What did you do
to terms?
3. What factoring techniques did you apply?
4. How did you simplify your sum?​

Answer: 29 ft

Step-by-step explanation:

Based on the description we are given. we know that we can form a right triangle, where 20 and 21 are the legs. The length from the girl to the bike would be the hypotenuse. To do this, we need to use the Pythagorean Theorem, which is [tex]a^2+b^2=c^2[/tex], where a and b are legs, and c is hypotenuse. We can go ahead and plug them in.

[tex]20^2+21^2=c^2[/tex]            [exponent]

[tex]400+441=c^2[/tex]            [add]

[tex]841=c^2[/tex]                      [square root both sides]

[tex]c=29[/tex]

Therefore, the distance from the girl to the bike is 29 ft.

The output of function g(r) = -5x + 13 when r is 3 is -2.

A function is a relationship between inputs where each input is related to exactly one output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

g(r) = -5r + 13

Input r = 3

g(3)

= -5 x 3 + 13

= -15 + 13

= - 2

Thus,

The output is -2.

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I dont know

I would just pick c

Answer:

30

Step-by-step explanation:

The sum of the greatest common factor (HCF) and least common multiple (LCM) of 3 and 6 is 9.

The H.C.F. defines the highest common factor present in between given two or more numbers, while L.C.M. defines the least common multiple number which is exactly divisible by two or more numbers.

factors of 3 are 1 and 3

factors of 6 are 1, 2, 3, and 6

3 = 1 × 3

6 = 2 × 3

LCM = 2 × 3

LCM = 6

HCF = 3

sum of HCF and LCM of 3 and 6 = 3 + 6

sum of HCF and LCM of 3 and 6 = 9

Therefore, 9 is the sum of the greatest common factor HCF least common multiple LCM of 3 and 6.

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1) The formula for area is,

⇒ Area of rectangle = Length × Width

And, The formula for perimeter is,

⇒ Perimeter = 2 (Length + width)

2) An expression for the length of the south side of the yard is,

⇒ Length = (5x + 2) + (x² - 9) + (x² - 7x + 12)

3) The simply expression for the length of the south side of the yard is,

⇒ Length =  2x² - 2x + 5

4) An expression for the perimeter of the pool area is,

⇒ Perimeter = 2 ( (x² + 10) + (8x + 8) )

5) 5) The simply expression for the perimeter of the pool area is,

⇒ Perimeter = 2x² + 16x + 36

A rectangle is a two dimension figure with 4 sides, 4 corners and 4 right angles. The opposite sides of the rectangle are equal and parallel to each other.

Given that;

The Johnson family is redesigning their backyard this spring. They want to include a sandbox area, a swing set area, a patio area, a pool area and a grill area.

Now,

1) The formula for area is,

⇒ Area of rectangle = Length × Width

And, The formula for perimeter is,

⇒ Perimeter = 2 (Length + width)

2) An expression for the length of the south side of the yard is,

⇒ Length = (5x + 2) + (x² - 9) + (x² - 7x + 12)

3) The simply expression for the length of the south side of the yard is,

⇒ Length = (5x + 2) + (x² - 9) + (x² - 7x + 12)

                = 5x + 2 + x² - 9 + x² - 7x + 12

                = 2x² - 2x + 5

4) An expression for the perimeter of the pool area is,

⇒ Perimeter = 2 ( (x² + 10) + (8x + 8) )

5) The simply expression for the perimeter of the pool area is,

⇒ Perimeter = 2 ( (x² + 10) + (8x + 8) )

                    = 2 (x² + 10 + 8x + 8)

                    = 2 (x² + 8x + 18)

                    = 2x² + 16x + 36

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Answer:

The 4th would be 0.25

Step-by-step explanation:

The slope formula, or the ratio of the change in the y values to the change in the x values, is m=(y2-y1)/(x2-x1).

A line's steepness and direction are measured by the line's slope.

Without actually using a compass, determining the slope of lines in a coordinate plane can assist in forecasting whether the lines are parallel, perpendicular, or none at all.

A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes.

The y coordinate's net change is y, and the x coordinate's net change is x.

Hence, The slope formula, or the ratio of the change in the y values to the change in the x values, is m=(y2-y1)/(x2-x1).

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Answer:

6

Step-by-step explanation:

delta math

The required measure of the other leg will be 6 cm in the given right triangle.

Pythagoras's theorem states that in a right-angled triangle, the square of one side is equal to the sum of the squares of the other two sides.

We have been given that one of the legs of a right triangle measures 8 cm and its hypotenuse measures 10 cm.

Let the measure of the other leg would be x cm.

According to Pythagoras's theorem,

⇒ c² = a² + b²  ....(i)

As per the given question, we have

c = 10cm, a = 8 cm and b = x

Substitute the values in the above formula, and solve for x

⇒ 10² = 8² + x²

⇒ 100 = 64 + x²

⇒  x² = 100 - 64

⇒  x² = 36

⇒  x² = 6²

⇒  x = 6

Therefore, the required measure of the other leg will be 6 cm in the given right triangle.

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Answer:

5 kg.

Step-by-step explanation:

2 kg for $0.96 is more expensive than 5 kg for $1.95

Answer:

B

Step-by-step explanation:

Answer:

Mean: 3x

Median: 3x

Mode: None

Step-by-step explanation:

The mean is the sum of all the numbers divided by how many there are.

x + 2x + 3x + 4x + 5x = 15x and 15x/5 = 3x. So the mean is 3x.

The median is the number in the middle when the values are in order from least to greatest. The median is 3x.

The mode is the number that appears most often in the data set. In this case, the mode is none because no number appears more than the other numbers.

The expression to convert celcius to Fahrenheit isn't given.

Answer:

59°F

Step-by-step explanation:

However, the expression required for the conversion is :

Temperature (°F) = [Temperature (°C) * 1.8] + 32

Therefore, using the expression, we can convert a celcius temperature of 15°C to Fahrenheit ;

Temperature (°F) = (15 * 1.8) + 32

Temperature °F = 27 + 32

Temperature °F = 59°F

Therefore, there are 12 bandages in 2 boxes, which is the answer to the unitary method presented problem.

The term "unitary" refers to a single or separate unit or variable . As a result, this strategy's objective is to establish values in terms of a single unit. For instance, if a car travels 44 kilometres on two litres of gas, the unitary technique can be used to determine how many kilometers it will drive on one.

Here,

Given: Each box of bandages has three packs, with two bandages in each pack.

Now, determine how many bandages there are in two boxes.

Therefore, we solve using the unitary method:

One pack contains two bandages.

In 3 packs, there are therefore = 2*2 = 6 bandages.

One box contains three packs as stated.

Consequently, we multiply 2 by 6 to obtain the bandages in 2 boxes:

=> 2 * 6 = 12

Therefore, there are 12 bandages in 2 boxes, which is the answer to the unitary method's presented problem.

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If her monthly payment is P3,000 and interest is compounded semi-annually at 9%, the cost of the TV set comes to P17,545.08.

Compound interest, also known as interest on principal and interest, is the practice of adding interest to the principal amount of a loan or deposit.

It occurs when interest is reinvested, or added to the loaned capital rather than paid out, or when the borrower is required to pay it, so that interest is generated the next period on the principal amount plus any accumulated interest.

In finance and economics, compound interest is common.

In contrast to simple interest, which does not compound since past interest is not added to the principal for the current period, compound interest allows interest to build over time.

The interest per period multiplied by the number of periods in a year yields the simple annual interest rate.

According to our question-

9% = 0.09 / 2

=0.045 + 1 =1.045^(1/6)

=1.00736312 - 1 x 12 x 100

=8.836%

PV=0;

PMT=3000;

R=0.08836/12; N=6; PV

=PMT*(((1 + R)^N - 1)*((1 + R)^-N)* R^-1)

PV==17,545.08

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The difference between logarithmic and exponential functions can be determined by looking at the form of the equation and by performing a calculation.

A logarithmic equation is written as log_b(x) = y, where b is the base and x and y are variables. An exponential equation is written as b^x = y, where b is the base and x and y are variables.

To determine if an equation is logarithmic or exponential, begin by comparing the form of the equation to the two equations above. If the equation is written in the form of log_b(x) = y, then it is a logarithmic equation. If the equation is written in the form of b^x = y, then it is exponential.

To perform a calculation, plug in a known value for x and then solve for y. For example, if the equation is log_2(x) = 4, then plug in x = 8. The calculation would then be:

log_2(8) = 4

This is a logarithmic equation, as the form of the equation matches log_b(x) = y.

If the equation is b^x = 16, then plug in x = 4. The calculation would then be:

2^4 = 16

This is an exponential equation, as the form of the equation matches b^x = y.

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Answer:

1357.17 cubic feet

Step-by-step explanation:

The volume of a cylinder is

[tex]\pi {r}^{2} h[/tex]

We know the height is 12, and the radius is simply half our diameter, which in this case is

[tex] \frac{12}{2} = 6[/tex]

plug these two numbers into our formula and we have found our volume.

The simplest form of the value of the trigonometric identity cos(A-B) is

1508/1517.

What is are the trigonometric identities?

Trigonometric Identities are equality conditions that apply to all values of the equation's variables and which require trigonometry functions.

There are numerous unique trigonometric identities that involve both the side length and angle of a triangle. Only the right-angle triangle is  valid for the trigonometric identities to work.

cos(A-B) = cosA cosB + sinA sinB

Given,

    tan A = 12 / 35

So sin A = 12 / [tex]\sqrt{12^2 + 35^2}[/tex]  = 12 / 37

    cos A = 35 / 37

Now,

    sin B = 9/41

     cos B = [tex]\sqrt{1 - sin^{2} B }[/tex] = [tex]\sqrt{1 - (\frac{9}{41} )^{2} }[/tex] = 40/41

  Now substituting the above values in the cosine formula

cos(A-B) = cosA cosB + sinA sinB

              = (35/37) (40/41) + (12/37) (9/41)

              = 1508/1517 = 0.994

Therefore the simplest form of cos(A-B) is 1508/1517.

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Answer:

x = 30

Step-by-step explanation:

Plug in 56 in place of  y, then solve for x.

56 = 1.5x + 11

Subtract 11.

45 = 1.5x

Divide both sides by 1.5.

45/1.5 = x

30 = x

Answer:202

Step-by-step explanation:

I did it

The Value of the two constants K and R are 5 and 3 respectively.

a) To find u2, you can substitute u1 = 8 into the term-to-term rule to get:

u2 = 2u1 + 20 = 2(8) + 20 = 36

So u2 = 36.

b) To find the values of k and r, you can use the given values of u1, u2, and u3 to set up a system of equations. Using the term-to-term rule:

Substituting in the given values:

Solving for r and k, we get:

k = 5 and r = 3.

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The third side of a triangle, the following formula can be used c² = a² + b² - 2abcos(C)

To calculate the third side of a triangle, first find the lengths of the other two sides and the angle opposite the third side. Then plug these values into the formula above and solve for c.

Where c is the third side of the triangle, a and b are the other two sides, and C is the angle between them.

For example, for a triangle with two sides of length 4 and 6, and an angle between them of 75 degrees, the formula would look like this:

c² = 42 + 62 - 2(4)(6)cos(75)

Solving for c yields a third side length of 8.4.

To solve for c, first square the two side lengths: 42 = 16 and 62 = 36. Then, multiply the two side lengths together and multiply by the cosine of the angle between them: 2(4)(6)cos(75) = 43.9. Finally, add the two squared values together and subtract the result of the multiplication: 16 + 36 - 43.9 = 8.1. Then, take the square root of this result to get the length of the third side: √8.1 = 8.4.

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Answer:

The like terms in this expression are 24a and -8a, and -12b and 12b.

Step-by-step explanation:

The like terms 24a and -8a can be combined by adding the coefficients and the variables, which gives us 24a - 8a = 16a.

The like terms -12b and 12b can be combined by adding the coefficients and the variables, which gives us -12b + 12b = 0.

So the like terms in this expression are 24a, -8a, and -12b, 12b.

Answer:

1=B

Step-by-step explanation:

Answer:

it's -63

good luck if you want explanation comment

Answer: 63

Step-by-step explanation:

All triangles' angles added up should be 180 degrees, so 70+47=117 and 180-117=63.

180 = a+b+c

180 = 47 + 70 + c

180 - 47 - 70 = c

or,

180 - (47+70) = c

Answer:

A

Step-by-step explanation:

If you substitute each x value from the input boxes into the equations, you can find your answer.

The first input value is 1, and the output value is 12, so plug those into the first equation in the answer options.

y = 4x + 8

(12) = 4(1) + 8

12 = 4 + 8

12 = 12

Because the simplified equation ended in a true equality statement, that pair works with the equation.

The next x value is 3 and the y value is 20:

y = 4x + 8

(20) = 4(3) + 8

20 = 12 + 8

20 = 20

Again, it ends in  true equality statement, so it also works with the equation.

(28) = 4(5) + 8 = 28 so that one works as well.

Then check the second equation with the second set of input and output values.

(2) = -7(-1) - 5 = 2

The first x and y values of that system work.

(9) = -7(-2) - 5 = 9

The second one works as well.

(16) = -7(-3) - 5 = 16

The last one is equal as well.

So the equations in A, or the first option, work with all of the inputs and outputs.

Answer:

5, 9, 13, 17, 21, 25

Step-by-step explanation:

Given a₁ = 5 and d = 4

Add d = 4 to the previous term, that is

a₁ = 5

a₂ = a₁ + 4 = 5 + 4 = 9

a₃ = a₂ + 4 = 9 + 4 = 13

a₄ = a₃ + 4 = 13 + 4 = 17

a₅ = a₄ + 4 = 17 + 4 = 21

a₆ = a₅ + 4 = 21 + 4 = 25