(3x + 3)(2x + 6) =
(2x + 1)(x - 2) =
(x - 3)(x + 4) =
(2x - 4)(x - 5) =
(x + 3)(x + 2) =
(x + 2)(x + 2) =
(x + 3)(x - 3) =
(2x³ + 1)(x - 4) =

Answer:

1. Multiply each expression by a number to make a variable cancel out. The numbers can be different:

1(2x + 5y = 10)

5(x-y = -9)

Use the distributive property, then add the expressions together.

2x + 5y = 10

5x - 5y = -45

7x = -35

x = -5

2. Solve the inequality as if there was an equal sign.

-9x -6 < 3 - 2x

-7x < 9

Flip the inequality sign around if you have to multiply/divide by a negative number.

x > -1.2857...

3. Find the y-intercept and slope of each line. If the line is shaded below, it is <. If it is shaded above, it is >.

blue line: y < -0.5x - 3

red line: y > -1.5x -5

Answer:

Width = 3.773 inches

Length = 79.227 inches-

Step-by-step explanation:

g = 7(3w)             Eq. 1

166 = 2(g+w)       Eq. 2

g = length

w = width

From Eq, 1:

g = 21w              Eq. 3

Replacing Eq. 3 in Eq. 2

166 = 2(21w + w)

166 = 2(22w)

166 = 44w

166/44 = w

w = 3.773

From Eq. 3

g = 21(3.773)

g = 79.227

Check:

From Eq. 2:

166 = 2(79.227 + 3.773) = 2 * 83

Answer: (x > -3).

Step-by-step explanation:

To solve the inequality 4(1 - x) < 16, we will simplify and solve for x:

4(1 - x) < 16

Distribute the 4:

4 - 4x < 16

Subtract 4 from both sides:

-4x < 12

Divide both sides by -4. Note that when dividing by a negative number, the inequality sign flips:

x > -3

The solution to the inequality is x > -3. This means that x must be greater than -3 for the inequality to hold true.

To graph the solution on a number line, we mark a shaded region to the right of -3, indicating that all values greater than -3 satisfy the inequality:

The open circle at -3 indicates that -3 is not included in the solution since the inequality is strict (x > -3).

here's the graph for 4(1-x)<16

The left-hand side of the equation represents the logarithm of 64 with base x, and it is not possible to find a real value of x that satisfies the equation.

solve the equation logₓ(64) + 5 = 2, we can follow these steps:

Step 1: Move the constant term to the other side of the equation:

logₓ(64) = 2 - 5

logₓ(64) = -3

Step 2: Rewrite the equation in exponential form:

x^(-3) = 64

Step 3: Rewrite 64 as a power of x:

x^(-3) = x^6

Step 4: Set the exponents equal to each other:

-3 = 6

The equation -3 = 6 is not true, which means there is no real solution to the given equation.

Therefore, the equation logₓ(64) + 5 = 2 has no solution in the real number system.

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Answer:

i) Consecutive interior angles

ii) Supplementary angles

iii) The two oars are parallel by consecutive interior angles theorem

Step-by-step explanation:

i) m∠1  and m∠2 lie between two line and on the same side of the line passing through the two lines. Therefore, they are consecutive interior angles

ii)x = 10

m∠1 = 6x + 18

= 6(10) + 18

= 60 + 18

= 78

m∠2 = 9x + 12

= 9(10) + 12

= 90 + 12

= 102

m∠1 + m∠2 = 72 + 108 = 180

Since m∠1 and m∠2 add to 180, they are supplementary angles.

iii) The two oars are parallel

consecutive interior angle theorem:

If  a transversal cuts through two line and the consecutive interior angles are supplimentary, then the two lines are parallel

Answer:

C

Step-by-step explanation:

There has to be two variables it's being compared to, in which case this is the blood sugar level and the amount of sugar

Answer:

250 and 250.1

Answer:

250.1

Step-by-step explanation:

5002 divided by 20 equals 250.1

The other Washington DC landmark with coordinates (8,-10) is located in the fourth quadrant of the map.

To determine in which quadrant of the map a point with coordinates (8,-10) is located, we need to look at the signs of the x and y coordinates.

Since the x-coordinate (8) is positive and the y-coordinate (-10) is negative, this point is located in the fourth quadrant.

In general, the four quadrants of a Cartesian coordinate system are divided by the x and y-axes.

The first quadrant is located in the upper right-hand corner and contains points with positive x and y coordinates.

The second quadrant is located in the upper left-hand corner and contains points with negative x and positive y coordinates.

The third quadrant is located in the lower left-hand corner and contains points with negative x and y coordinates.

Finally, the fourth quadrant is located in the lower right-hand corner and contains points with positive x and negative y coordinates.

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A) The algebraic expression will be 12d + 7 = 91

B) He drives 7 miles per day to work.

For 11 days straight, Ms. Chung drove the same distance every day going to and coming from work.

The distance she drove on Saturday was; 0.9 miles.

The number of miles she drives per day:

84 miles/12

= 7 miles per day

Let the number of miles she travels be day = d

12d + 7 = 91 miles

12d + 7 = 91

12d = 91 - 7

12d = 84

d = 84/12

d = 7 miles per day

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Given:

price p = $25

number of x units = -8p + 400

Find: solve for the value of x

Solution:

To determine the value of x, simply replace the variable "p" in the equation with 25.

Then, solve.

Multiply -8 and 25.

Add -200 and 400.

Therefore, at $25, 200 units were sold.

Part F:

Since the equation of the revenue is R(x) = -8p² + 400p, then the graph must be a parabola opening down. Out of the 4 options, Only Options A and D show this.

However, upon comparing the two options, we see that the y-axis of the two graphs is different. Option A says that the y-axis is the price p while Option D says that the y-axis is the revenue R.

Since the given function is the revenue, then the y-axis should be R. The correct graph is Graph D.

Part G:

If the revenue is at least $4032, then let's replace the r(x) function with 4, 032.

To solve for p, let's equate the function to zero by subtracting both sides of the function by 4, 032.

Then, let's solve for the value of "p" using the quadratic formula.

Note that in the revenue function above, a = -8, b = 400, and c = -4032. Let's plug these values into the formula above.

Then, simplify.

Separate the plus and minus operations.

The values of p are 14 and 36.

Hence, the company should charge a price between a minimum of $14 and a maximum of $36 to have a revenue of at least $4,032.

Answer:

DE=23

Step-by-step explanation:

Since E is the midpoint of DF, we know that DE and EF are equal. Thus, we can set them equal to eachother and solve.

8x-1=6x+5

2x=6

x=3

After that, plug 3 back into DE.

6(3)+5= DE

18+5= DE

23=DE

Answer: No he is not correct the answer is 6 3/8

Step-by-step explanation: so what you have to do is add the 2 numbers you it should look like this(2 3/4+ 3 5/8) then you want to add the 2 and the 3 and add the 3/4 and 5/8 it should look like this (5+11/8) then you want to converse the number to a mixed number it should look like this (5+1+3/8) then you should add the

Answer:

No. Total distance = 6 3/8.

Step-by-step explanation:

\(2\frac{3}{4}+3\frac{5}{8}=\frac{11}{4}+\frac{29}{8}\\\\\)

            \(=\frac{11*2}{4*2}+\frac{29}{8}\\\\=\frac{22}{8}+\frac{29}{8}\\\\=\frac{22+29}{8}\\\\=\frac{51}{8}\\\\=6\frac{3}{8}\)

The equation of the line with a slope of -4 and passing through the point (-7, -7) is y = -4x - 35, the slope m = -4 and y-intercept b = -35.

The formula for equation of line is expressed as;

y = mx + b

Where m is slope and b is y-intercept.

Given that:

The line has a slope of -4 and passes through the point (-7,-7).

Plug these values into the point-slope form and solve for y:

y - y₁ = m(x - x₁)

Plug in m = -4, x₁ = -7 and y₁ = -7

y - (-7) = -4(x - (-7))

Simplify:

y + 7 = -4( x + 7 )

y + 7 = -4x - 28

Subtract 7 from both sides

y + 7 - 7 = -4x - 28 - 7

y = -4x - 28 - 7

y = -4x - 35

Therefore, the equation of the line is y = -4x - 35.

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Answer:

the magnitude of the velocity of the large fish just after it snapped up this meal is about 69.9 cm/s and the direction is about 2.9 degrees south of east. This can be obtained by applying the conservation of momentum principle to the two-dimensional collision of the two fish.

Step-by-step explanation:

Answer:

Slope is 1, in slope intercept form it will be y=1x+b

Step-by-step explanation:

You will use

y2-y1/x2-x1

a. The probability that a yellow disk will be selected is 1 out of 5.

b. It is **likely** that a yellow disk will be randomly selected from the bag.

a. The probability that a yellow disk will be selected can be calculated by;

P = 5 / 25

P = 1/5

The probability of randomly selecting a yellow disk is calculated by dividing the number of yellow disks by the total number of disks. In this case, there are 5 yellow disks and 25 total disks, so the probability is 5/25 = 1/5. This means that there is a 20% chance of randomly selecting a yellow disk.

b. The likelihood of randomly selecting a yellow disk is described as "likely" because the probability is greater than 1/10. A probability of 1/10 or less is considered "unlikely", while a probability of greater than 1/10 is considered "likely".

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The coordinates of the image of the point Q is Q'(3, 6).

Transformation of geometrical figures or points is the manipulation of a given figure to some other way.

Different types of transformations are Rotation, Reflection, Glide reflection, Translation and Dilation.

From the given graph, we have point Q(-4, 4).

Here the point is translated.

After translation, the original figure is shifted from a place to another place without affecting it's size.

The rule of translation is given as the point (x, y) is translated as (x + 1, y + 2).

So the given point is (-4, 4).

(-4, 4) after translation becomes by the definition (-4 + 1, 4 + 2).

So the required point is (-3, 6).

Hence the image of point Q is (-3, 6).

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Your question is incomplete, Probably, the correct graph for the question is given below.

Answer:

\(y = \frac{x}2 + 2.5\)

Step-by-step explanation:

Step 1) Finding the slope
The line is perpendicular to \(y = 1 - 2x\), therefore, its slope is equal to the negative invert of \(y\)'s slope.

\(y\)'s slope is -2 (the coefficient to \(x\)), and, therefore, the line's slope is \(m = [-(-2)]^{-1} = 2^{-1} = \frac12\)

Step 2) Building the Equation

We can now substitute the slope, along with the given point's coordinates, into the formula \(y - y_1 = m(x - x_1)\) :

\(y - 3 = \frac12(x - 1)\\\to y - 3 = \frac{x}2 - \frac12\\\to y = \frac{x}2 + 2.5\)

Answer:

g(x) is reflected across the x-axis and translated 6 units up compared to ƒ(x).

Step-by-step explanation:

Answer:

Step-by-step explanation:

g(x) is reflected across the x-axis and translated 6 units up compared to ƒ(x).

Answer:

it's no solution

Step-by-step explanation:

3(x^2 - 2*1/3*x+1/9) + 11/3 > 0

so it's no solution

Therefore, **x < 7** is the inequality that may be utilized to find x

A mathematical statement known as an inequality compares two expressions using an inequality sign, such as (less than), > (greater than), or (less than or equal to).

For instance, the inequality x + 2 5 signifies that "x + 2 is less than 5".

Let x represent how many days the client paid for pet sitting.

$15 per day plus a $20 fixed service fee equals the total cost of pet sitting.

We are aware that the customer's purchase was under $125. Consequently, we can write:

20 + 15x < 125

Putting this disparity simply:

15x < 105

x < 7

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Based on the graph which shows the relationship between time and the number of soda bottles a machine can make, this machine can make 20 soda bottles each minute.

In Geometry, the rate of change of any straight line simply refers to the  slope and it can be calculated by using this mathematical equation (expression);

Rate of change (slope), m = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Rate of change (slope), m = (y₂ - y₁)/(x₂ - x₁)

From the information provided in the graph above, we can logically deduce the following data points located on the line:

Substituting the given data points into the rate of change formula, we have the following;

Rate of change (slope), m = (y₂ - y₁)/(x₂ - x₁)

Rate of change (slope), m = (140 - 100)/(7 - 5)

Rate of change (slope), m = 40/2

Rate of change (slope), m = 20.

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The unit rate of the relationship will be 10/3. The correct option is C.

The given equation is,

y = 10/3x + 8

The general form of an equation of the line is,

y = mx +  c

here, the slope will be 10/3

Slope refers to the steepness or incline of a line on a graph. It is a measure of how much the dependent variable changes for a given change in the independent variable.

The slope of a line is represented by the ratio of the change in the y-axis (vertical) to the change in the x-axis (horizontal) between any two points on the line. It can also be interpreted as the rate of change of the dependent variable with respect to the independent variable.

A positive slope indicates an upward trend, while a negative slope indicates a downward trend. The slope of a line is often denoted by the letter m.

The unit relationship will be 10/3.

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To find arcsin, we need to use the identity:

sin(arcsin(x)) = x

Since arcsin is negative, sin(arcsin) is also negative. Therefore, we can say:

sin(arcsin) = -sqrt(1 - (cos)^2)

where (cos)^2 = 8/17

Substituting, we get:

sin(arcsin) = -sqrt(1 - (8/17))

Simplifying, we get:

sin(arcsin) = -sqrt(17/17 - 8/17)

Simplifying further, we get:

sin(arcsin) = -sqrt(9/17)

Therefore, arcsin = -sqrt(9/17)

To find arctan, we need to use the identity:

tan(arctan(x)) = x

Substituting, we get:

tan(arctan) = -8/17

Therefore, arctan = -8/17

So, arcsin is -sqrt(9/17) and arctan is -8/17.

For the function f(x) = 7/8x² - 14, the x-intercepts are x = -4 and x = 4.

What is a function?

In mathematics, a function is a unique arrangement of the inputs (also referred to as the domain) and their outputs (sometimes referred to as the codomain), where each input has exactly one output and the output can be linked to its input.

To find the x-intercepts of the function f(x), we need to solve the equation f(x) = 0.

f(x) = 7/8x² - 14

Substitute f(x) with 0 -

0 = 7/8x² - 14

Add 14 to both sides -

7/8x² = 14

Multiply both sides by 8/7 -

x² = 16

Take the square root of both sides -

x = ±4

Therefore, the x-intercepts of the function f(x) are x = -4 and x = 4.

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Answer:

1/4

1/8

1/12

1/100

1/1000

1/10000