Write the fraction as equivalent fraction with the given denominator

Given the expression:

5x + 6 (x-2) -8 (x-3)

Let's simplify the exression using the following steps:

Step 1.

Apply distributive property:

5x + 6x + 6(-2) - 8x - 8(-3)

5x + 6x - 12 - 8x + 24

Step 2.

Combine like terms:

5x + 6x - 8x - 12 + 24

3x + 12

Therefore, the simplified expression is:

3x + 12

ANSWER:

D. 3x + 12

After finding the difference between total measure of wood and cut off wood, she have remaining 8/9 wood.

In the given we have to find the remaining wood.

Ruth has a piece of wood that measures 2 2/9 feet.

Now converting the mixed fraction in improper fraction by multiplying the 2 and 9 then add 2 in the multiplication of 2 and 9.

So the improper fraction is 20/9.

So The measure of wood = 20/9 feet

She cut off 1 1/3 feet of wood for a project.

Now converting the mixed fraction in improper fraction by multiplying the 1 and 3 then add 1 in the multiplication of 1 and 3.

So the improper fraction is 4/3.

So, she cut the wood = 4/3 feet

Now the remaining wood = Total measure of wood−cut the wood

Remaining wood =20/9−4/3

Now equal the denominator of both values.

Remaining wood =20/9 −4/3 ×3/3

Remaining wood =20/9 −12/9

Remaining wood =(20−12)/9

Remaining wood =8/9

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The figure A when rotated through 180 degrees counterclockwis, figure B will be obtained

correct answer is OPTION B

We have the following:

Answer:

-22/9

Explanation:

If the equation of the parabola is

y = 5/9 (x - 1)² - 3

The y-coordinate for the point where the parabola intersects the x-axis can be calculated by replacing x = 0, so

y = 5/9 (0 - 1)² - 3

y = 5/9 (-1)² - 3

y = 5/9 (1) - 3

y = 5/9 - 3

y = -22/9

Therefore, the y-coordinate is -22/9

For two lines of the form:

The distance between the two lines is:

The traslated triangle would be:

We can conclude that it would be in the 3rd quadrant.

Answer: Option 3

Given the function:

Where A(t) shows the amount of drug in a body after t hours.

Let's solve for the following:

• (a). Initial dosage:

Apply the exponential functions:

Where:

a is the initial value

b is the change factor.

Thus, we have the following:

a = 40

b = 0.83

Therefore, the initial dose is 40 mg.

• (b). What percent leaves the body each hour?

Apply the function:

Where:

r is the decay rate.

Thus, we have:

b = 1 - r

r = 1 - b

r = 1 - 0.83

r = 0.17

The percent that leaves the body each hour will be:

0.17 x 100 = 17%

Therefore, 17 percent of the drug leaves the body each hour.

• (c). What amount of drug is left after 12 hours?

Substitute 12 for t and solve for A(12):

The amount left after 12 hours is 4.28 mg.

• (d). The first whole number of hours at which there is less than 6 mg left.

Plug in 5.9 for A(t) and solve for t.

Divide both sides by 40:

Take the natural logarithm of both sides:

Therefore, the first whole number of hours where there is less than 6 mg left is 10 hours.

ANSWER:

• (a) 40 mg

• (b) 17%

• (c). 4.28 mg

• (d). 10 hours

We have to find how many shirts (s) he has bought.

We know that each shirt costs $15, so the total cost of the shirts should be 15*s.

If we substract the discount, we have the total final cost C as:

If we know that this total cost was $36, we can find the number of shirts as:

Answer: He bought 3 shirts (s = 3).

Consider that the general form of a linear equation can be writen as follow:

y = mx + b

where m is the slope of the line and b the y-intercept

use the following formula for the calculation of m:

m = (y2 - y1)/(x2 - x1)

where (x1,y1) = (-10,-7) and (x2,y2) = (0,10). Replace these values of the coordinates into the formula for m:

m = (10 - (-7))/(0-(-10))

m = (17)/(10)

m = 1.7

The y-intercept of the line is the value of the y coordinate when x=0, from the point (0,10) you can notice that y=10 when x=0. Then, the y-interceot is b =10

FInally, replace the values of m and b into the general expression for y:

y = mx + b

y = 1.7x + 10

The slope is given by:

The standard form of a quadratic equation is the following:

Where a, b and c are numbers. In this case we are given a quadratic equation in vertex form:

We can expand the squared binomial:

Then the answer is the second option.

so the answer is

We will have the following:

We remember that:

SOLUTIONS

What is the least common multiple of 12, 48 and 72

Therefore the least common multiple of 12, 48 and 72 = 144

Cofficient of variable terms is :

So the first variable

so the cofficent is -2

and the cofficent of second variable is:

So the cofficent of second term is 8.

Answer:

38%

Step-by-step explanation:

Dog owners=57

Total population=157

Percentage of owners=(dog owners/total population) ×100=(57/157)×100=0.38×100=38%

Answer:

b = 60.7

d = 43.1

Explanation:

The angles of measure 60.7 and b are alternate interior angles because they are on opposite sides of the transversal and in the inside of the parallel lines m and n. These angles have the same measure, so

b = 60.7

Angle d and the angle of measure 136.9 form a straight line, so they sum to 180 degrees. Therefore, the measure of angle d is

d = 180 - 136.9 = 43.1

Therefore, the answers are

b = 60.7

d = 43.1

By using Quadratic formula, the solutions are

[tex]x = {3 + 2\sqrt{2}}[/tex] or [tex]x = {3 - 2\sqrt{2}}[/tex]

What is Quadratic equation?

At first it is important to know about equation

Equation shows the equality between two algebraic expressions by connecting the two algebraic expressions by an equal to sign.

A two degree equation is known as Quadratic equation.

If [tex]ax^2+bx + c = 0 (a\neq 0)[/tex] be a quadratic equation,

[tex]x = \frac{-b \pm \sqrt{b^2 -4ac}}{2a}[/tex]

This is the quadratic formula

Here,

The given quadratic equation is

[tex]3x^2 = 7x - 3\\3x^2 - 7x + 3 = 0\\[/tex]

a = 1, b = -6, c = 1

x =

[tex]\frac{-(-6)\pm\sqrt{(-6)^2 - 4\times 1 \times 1}}{2\times 1}\\\frac{6 \pm \sqrt{36 - 4}}{2}\\\frac{6 \pm \sqrt{32}}{2}\\\frac{6 \pm 4\sqrt{2}}{2}\\\frac{2(3 \pm 2\sqrt{2})}{2}\\{3 \pm 2\sqrt{2}}[/tex]

[tex]x = {3 + 2\sqrt{2}}[/tex] or [tex]x = {3 - 2\sqrt{2}}[/tex]

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The sine fuction we have is

If we want the y-intercept, we must put x = 0, then

Therefore the y-intercept is 3.

Answer: 0

Step-by-step explanation: trust me

Using the normal distribution, it is found that, the standard deviation is 0.86

Normal usually refers to the word "normal" in a normal distribution.

The normal distribution is somewhat similar where the main observation (mean or its surrounding) occurs frequently and as we go far from the mean, its chances decrease.

In a normal distribution with mean μ and standard deviation  σ, the z-score of a measure X is;

σ = √np(1- p)

After finding the z-score, we need the p-value associated with this z-score, which is the percentile of X.

The given parameters are:

n = 3 ---- the number of flips

p = 0.5 --- the probability

The standard deviation is calculated as:

σ = √np(1- p)

σ = √3 (0.5) (0.5)

σ = 0.86

Hence, the standard deviation is 0.86

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we have the equation

A) since H is an exponential function 180 represents the maximum posible value of H or the maximum temperature that the center of the cake can reach

b)

we have

H(t)= 22° C

when placed in the oven or t=0

the value of a is 158

C)

H(t)=150°C

we already know a=158

let's solve for t

now this is the time 29 minutes before taking the cake out of the oven

so the total time is 29+21.587

then the total time the baking thin was in the oven

is 50.587 minutes

The lowest common denominator is defined as the set of fraction denominators with the lowest common multiple. The lowest positive integer with more than one denominator in the set is LCD.

Given that the Peanuts are sold in 8-ounce and 12-ounce packages

We have to determine the number of ounces you can buy from each package to have equal amounts of each package size

8 = 2 × 2 × 2

12 = 2 × 2 × 3

The LCDs 8 and 12 are 24

Thus, three 8 oz packets and two 12 oz packets.

Therefore, you can buy from each package to have equal amounts of each package size the number o ounces as 3 packets of 8 ounces and 2 packets of 12 ounces.

Remember that the volume of a triangular pyramid can be calculated using the formula:

So first, let's calculate the area of the base:

Using this in the formula,

Thereby, the volume of the pyramid is 240 cubic centimiters

Suppose in routine 1 and 2, Melissa rune for t minutes.

She burns 42 calories walking and then she runs at a rate that burns 14.25 calories per minute in rouitne 1.

So, total calories she burns in routine 1 is

Again, in routine 2, she burns 25 calories walking and she runs at a rate that burns 18.5 calories per minute in rouitne 2.

So, total calories she burns in routine 2 is

Accordingly,

So, Melissa should run for minimum 4 minutes

According to the image given there is a right triangle formed in which we are missing one of the angles, for that we know that the sum of thr interior angles of every triangle has to be equal to 180°.

Using this information

we clear the equation for Y

The measure of angle Y is 42°.

Explanation

In the question, we are given that,

We will need to find the volume of the cone.

Therefore, we will have;

So for 12 hats with candy, we will have;

Answer: 636.1728 cubic inches

By definition, the slope of a line is:

You can observe that it is the change in "y" divided by the change in "x".

In this case, you have the following slope:

Then the change in "y" in 2 and the change is "x" is 3.

Given the point (-4,1), you can follow these steps to graph the line:

1. Plot the given point on the coordinate plane.

2. Knowing that the slope is

You must move 3 units to the right and then 2 units up. This will give you a new point.

3. Graph the line. It must pass through those points.

The graph is:

Let

x ------> measure of the two angles that have the same measure

y -----> teh larger angle

we have that

2x+y=180 --------> equation A

y=x+9 -------> equation B

substitute equation B in equation A

2x+(x+9)=180

solve for x

3x=180-9

3x=171

x=57 degrees

Find the value of y

y=x+9

y=57+9

y=66 degrees

therefore

The 2 SMALLER angles each have a measure of 57 degrees

The LARGER angle has a measure of 66 degrees

Answer:

The answer would be D

Step-by-step explanation:

The inequality x>1.5, or x is greater than 1.5, has to have a line going to the right because x has to be greater than 1.5, so answers B and C can't be it. Because the symbol is greater than instead of greater than or equal to, the circle will be open, and the circle for option A is closed, so the answer is D