Translate the sentence into an equation.Twice the difference of a number and 9 equals 6.Use the variable y for the unknown number.

The negative sign reflects the graph across the x axis

Then, the answer is number B. It reflects the graph across the x-axis.

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

correct answer is OPTION B

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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Explanation:

The absolute value of any number is always positive it doesn't matter if the number is positive or negative.

In this case we have that the absolute value of p is 12, therefore p could be 12 or -12

Answers:

• -12

• 12

Answer:

Step-by-step explanation:

12 and -12 is the answer

A and F

Given:

The coordinates of the figure ABC are,

A(-2,0)

B(-3,-4)

C(-1,-4)

To find the correct statement:

Let us find the coordinates after rotating the figure 90 degree clockwise direction.

As we know,

In a rotation of 90 degrees clockwise, every point (x,y) will be changed to (y, -x).

So, we get,

D(0,2)

E(-4, 3)

F(-4,1)

It perfectly matches with given graph.

So, Betty's statement is correct.

If we translate the figure two units up and two units right, the given point B (-3,-4) will be changed to (-1,-2) and its reflected point over the y-axis will be (1,-2).

But, this does not match with E(-4,3).

So, Veronica's statement is wrong.

Hence, Betty's statement alone is the correct one.

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°.

Let's look at the info we have for each term:

term 1 = 4

term 2 = 12

term 3 = 36

term 4 = 108

term 5 = ?

Notice that term 2 (12) is obtained from the previous term 1 (4) by multiplying it by the number 3:

12 = 4 * 3

Now, term number 3 is obtained from term 2 (the previous) also by multiplying it by 3:

36 = 12 * 3

term number 4 is obtained from multiplying the previous term (term 3) by the number 3 again:

108 = 36 * 3

Now, we can conclude that if the strategy carries on, term number 5 will be the product of the pervious term (108) times 3. That is:

term 5 = 108 * 3 = 324

Now, we need to decide on which formula better describes our function:

We find that the function is better described by the formula:

since we can verify:

term 1 =

term 2 =

term 3 =

term 4 =

So the correct answer is the second option they give you in the list.

EXPLANATION

The expression means that we need to compute the limit as the function f(x) approaches 3 from the right.

We need to use the lines that comes from the right of 3 and gets as close as we want to x=3.

That is the line that has the open circle around y=3

Therefore, the limit is equal to 3

The slope is given by:

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

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

ANSWER

48kg

EXPLANATION

In 1 minute, the factory makes 4.8kg of pumpkin pie filling, so in 10 minutes it will make,

In 10 minutes, the factory makes 48 kilograms of pumpkin pie filling.

Thus x= -1.4 and y=1.6

Given:

Required:

We need to find the domain and range of the given function.

Explanation:

Recall that the domain of a graph consists of all the input values shown on the x-axis.

Recall that the range is the set of possible output values, which are shown on the y-axis.

Final answer:

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.

The volume of cone is calculated using this formula:

So, to obtain the volume of a cone, the radius and the height must be known.

We then multiply the value of the constant pi by the square of the radius and the height, and then divide the final result by 3.

The unit is cubic unit.

Question 5:

Step 1

From the figure, we can say that vertically opposite angles are equal.

Step 2:

From the diagram,

Consider that the coefficient for the number of full bags is 7/8 and the number of bags is 5. By divinding these numbers you get the total amount of full bags:

when we have used division between fractions (Notice what we added a 1 denominator to 5).

Hence, the answer:

A. 7 divided by (8 x 5)

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

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

Here, we have a recipe that serves 4 people in the given ratio below;

Cider to Caramel syrup to Pumpskin spice = 4:1/4:1

Now to make for 8 people, we simply will multiply what we had in the original recipe by 2 since it was for 4 people initially

So the punch ratio for 8 people will be;

8 cups of Apple Cider

1/2 cups Caramel syrup

2 teaspoons of Pumpskin spice

For 12 people, we simply multiply what we had initially for 4 people by 3. This will be;

12 cups of Apple Cider

3/4 cups of Caramel syrup

3 teaspoons of Pumpskin spice

In any right triangle with acute angles x and y, then

The sum of x and y is 90 degrees

Then for part (1)

Since triangle XYZ is a right angle at Z

Then

Then X and Y are complementary angles

Part (2)

sin X = opposite/hypotenuse

sin Y = opposite/hypotenuse

cos X = adjacent/hypotenuse

cos Y = adjacent/hypotenuse

Part (3)

Part (4)

Since sin = cos, then

The sum of the 2 angles must be 90

One of them is 23 degrees, then the other must be

The answer is

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

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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Answer:

Yes

Explanation:

Yes, 3.0 is equal to 3.0000 because in Mathematics, once we have only zeros after the decimal point, we can discard them and write only the whole number part. So 3.0 and 3.0000 can both be written as 3.

The traslated triangle would be:

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

Answer: Option 3

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:

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.

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 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