an online store begins selling a new kind of baskelballshoe. At week zero, 30 pairs of shoes were sold.
In week 3, the store sold 240 pairs of shoes. Write an exponential model that relates the number of shoes sold to the week number, and use the model to predict how many shoes will be sold during week 7.

10. |x - 4| - 4 = 1/2x

⇒ Multiplying by 2,

2 |x - 4| - 8 = x

So, x - 4 = (x + 8)/2

             = -(x + 8)/2

When,

x - 4 = (x + 8)/2

2x - 8 = x + 8 (Multiplying by 2)

2x - x = 8 + 8 (Adding 8 and subtracting x to both sides)

x = 16

When,

x - 4 = - (x + 8)/2

2x - 8 = -x - 8 (Multiplying by 2)

2x + x = -8 + 8 (Adding 8 and x to both sides)

3x = 0

x = 0

Hence, the solution is x = 16 and x = 0.

13. (3/4)x = 2x - 10

⇒ Subtract 2x from both sides.

-5x/4 = -10

Multiply both sides by 4/(-5).

(-5x/4)×4/(-5) = -10 × 4/(-5).

x = 8 is the solution of the equation.

15. x² - 7x - 8 > 0

⇒ Solve the quadratic equation by splitting the middle term,

x² - 8x + x - 8 > 0

x(x - 8) + 1(x -8) > 0

(x + 1)(x- 8) > 0

-1 and 8 are the critical points of the inequality.

x < -1 and x > 8 are the solutions of the inequality which are represented by the shaded red region in the graph.

16. x - 5 > - 2x + 4

⇒ Adding 2x to both sides.

3x - 5 > 4

Adding 5 to both sides.

3x > 9

Divide both sides by 3.

x > 3 is the required solution represented by blue shade region in the graph.

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Cormariah, this is the solution:

a + 2b - 3a + 8 ​

• Terms: a, 2b, -3a, 8

• Like terms: a, -3a

• Coefficients: 2 for b; -1 and 3 for a

• Constant: 8

• Variables: a, b

Answer:

3.09

Step-by-step explanation:

21 - 17.91=3.09

This means that the difference between 17.91 and 21 is 3.09 which means for 17.91 to be equal to 21 you must add 3.09

The approximate height of the tree is given as follows:

45.6 ft.

The geometric mean theorem states that the length of the altitude drawn from the right angle of a triangle to its hypotenuse is equal to the geometric mean of the lengths of the segments formed on the hypotenuse.

The altitude segment for this problem is given as follows:

14.5 ft.

The bases are given as follows:

5.2 ft and x ft.

Hence the value of x is given as follows:

5.2x = 14.5²

x = 14.5²/5.2

x = 40.4 ft.

Hence the height of the three is given as follows:

5.2 + 40.4 = 45.6 ft.

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Answer:

$61.29 per day.

Step-by-step explanation:

Checking account balance on February 1st: $443

Checking account balance on February 7th: $872

Difference in balances: $872 - $443 = $429

Number of days between February 1st and February 7th: 7 days

Rate of change = Difference in balances / Number of days

Rate of change = $429 / 7 days

To find the rate of change per day, divide the difference in balances by the number of days:

Rate of change = $429 / 7 days ≈ $61.29 per day

Therefore, the rate of change in your checking account balance during that period was approximately $61.29 per day.

Answer:

d = 5

Step-by-step explanation:

1.Combine multiplied terms into a single fraction

2.5d + 9.75 = 1 + 4.25d

5d/2+9.75 = 1+4.25d

2.Combine multiplied terms into a single fraction

5d/2 + 9.75 = 1 + 4.25d

5d/2 + 9.75 = 1 + 17d / 4

3.Subtract 9.75 from both sides of the equation

5d/2+9.75 = 1 + 17d/4

5d/2 +9.75 - 9.75 = 1 + 17d/ 4 - 9.75

4.Simplify

Subtract the numbers

Subtract the numbers

5d/2 = -8.75 +17d/4

5. Multiply all terms by the same value to eliminate fraction denominators

5d/2 = -8.75 + 17d/4

2 * 2 * 5d/2 = 2 * 2( -8.75 + 17d/4)

6. Simplify

Cancel multiplied terms that are in the denominator

Multiply the numbers

Multiply the numbers

Distribute

Cancel multiplied terms that are in the denominator

Rearrange terms

10d = 17d - 35

7. Subtract 17d from both sides of the equation

10d = 17d - 35

10d - 17d = 17d - 35 - 17d

8. Simplify

Combine like terms

Combine like terms

-7d = -35

9. Divide both sides of the equation by the same term

-7d = -35

-7d/7 = -35/-7

10. Simplify

Cancel terms that are in both the numerator and denominator

Divide the numbers

d = -35/-7

d=5

Answer:

D= -35/27 (improper fraction)

Step-by-step explanation:

If you want it as a mixed fraction:

-1 8/27 (8 is the numerator)

The equation of a line perpendicular to y = -10 + 3x that passes through the point (9,2) is y = -1/3x + 1

The equation of the line is given as

y = -10 + 3x

Rewrite the equation as

y = 3x - 10

A linear equation is represented as

y = mx + c

Where

Slope = m

So, we have

m = 3

The slopes of perpendicular lines are opposite reciprocals

This means that

m2 = -1/m1

So, we have

m = -1/3

Evaluate

m = -1/3

The equation of the perpendicular line is then calculated as

y = m(x - x1) + y1

Where

(x1, y1) = (9, -2)

This gives

y = -1/3(x - 9) - 2

Evaluate

y = -1/3x + 3 - 2

Evaluate the sum and the difference

y = -1/3x + 1

So, the equation of a line perpendicular to y = -10 + 3x that passes through the point (9,2) is y = -1/3x + 1

Hence, the required equation of a line perpendicular to y = -10 + 3x that passes through the point (9,2) is y = -1/3x + 1

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Answer:

You have 7,167

Step-by-step explanation:

If this was to be converted into a whole number, it would be:

7,167

Answer:3

Step-by-step explanation:

edg

The second pair represent a unit rate. And the graph is shown.

An ordered pair is a pair made up of two parts that are written inside parantheses and are separated by commas. For instance, the ordered pair (x, y) denotes an ordered pair where "x" is the first member and "y" is the second element. These elements, which can either be variables or constants depending on the context in which they are used, have distinct names.

In an ordered pair, the element order is somewhat significant. It implies that (x, y) may not always be equivalent to (y, x).

When describing a point's location on the coordinate plane with respect to the origin, a coordinate geometry ordered pair is employed.

Hence the graph is attached and the second pair represents the unit rate.

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Answer:

  see attached

Step-by-step explanation:

The boundary lines are drawn by considering the relation as an equation.

The first "equation" describes a line with slope -8/3 through the y-intercept point (0, 6). Another point on that line would be 8 units down and 3 units right of (0, 6), at (3, -2). Both inequalities include the "or equal to" case, so both boundary lines are solid lines.

Since we have y ≥ ( ), the shading is above the line.

__

The second "equation" describes a line with a slope of 5/3 through the y-intercept point (0, -7). Another point would be 5 units up and 3 units right of (0, -7), at (3, -2). Since we have y ≤ ( ), the shading is below the line.

That is, the solution region is in the right-hand quadrant of the X where the lines cross. It includes the lines themselves.

Answer: I believe

M = 80

Step-by-step explanation:

100 - 20 = 80

Answer:

53\(x_{123}\) == 134 cf

Step-by-step explanation:

A - on the po boyds at a emase the foot, 1, of building. He. Observes an obje- et on the top, P of the building at an angle of ele- building of 66 Aviation of 66 Hemows directly backwards to new point C and observes the same object at an angle of elevation of 53° · 1P) |MT|= 50m point m Iame horizontal level I, a a​

The height of the building is approximately 78.63 meters.

The following is a step-by-step explanation of how to solve the problem. We'll need to use some trigonometric concepts and formulas to find the solution.

Therefore, the height of the building is approximately 78.63 meters.

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Answer: 6

Step-by-step explanation:

2/3 of 9 is basically 2/3 times 9

Answer:

6, because this and that is this and that bam boom bap, just trust me bro

Answer:

4x^2 - 12x + 9

Explanation:

(2x - 3)^2

(2x - 3)(2x - 3)

2x(2x - 3) -3 (2x - 3)

4x^2 - 6x - 3 (2x - 3)

4x^2 - 6x - 6x + 9

4x^2 - 12x + 9

Answer:

answer is 0.0092505089

Step-by-step explanation:

if tan =0

tan=opposite/adjacent

tan0=8÷15

tan0=0.533333

tan0.53333=0.0092505089

Answer:

1/2x

Step-by-step explanation:

Slope is

Rise over run  In a fraction the rise is the numerator and the run is the denominator

From getting one point to another

You rise 1 and run 2

Which is the equivalent of 1/2

Answer:

Step-by-step explanation:

(-1, -4) (1, -3)

(-3 + 4)/(1 + 1) = 1/2

Answer:

Step-by-step explanation:

Given relation

Its range is the set of second values in the pairs

In the ascending order

Answer:

{-4, -2, 2}

Step-by-step explanation:

The relation is {(3, -2), (1, 2), (-1, -4),(-1, 2)}

The range is all possible y values apart from any duplicates.

y = -2, 2, -4, 2

Removing all duplicates we get.

y = -2, 2, -4

Put them in order.

y = -4, -2, 2

Best of Luck!

Answer:

D

Step-by-step explanation: for p(x), the slope from 0 to 3 is 30, meaning if linear every time x increases by 3, the y value should as well, meaning that six as an x value to be linear should have been 90, but it was not.

For q(x), the slope from 0 to 3 is 90, and following the same thing from above, this means for every 3 units moved on the x, it should increase by 90 units on the y. This means 6 to be linear should have been 200 but instead was 380 making it also nonlinear

Answer:

26

Step-by-step explanation:

One leg measures 7.

One leg measures 8.

a² + b² = c²

7² + 8² = c²

c² = √113 = 10.630 = 11

perimeter = 7 + 8 + 11

perimeter = 26

Examining the number line, the value of y is calculated to be 5

The value of RS and ST are 33 and 28 respectively

A number line is a horizontal representation of number parts with equal intervals

The numbers in a number line is arranged to be increasing from left to right , hence drawing a number line will have the smaller values to the left of the bigger values

In the problem, the given data include:

RS = 6y + 3​,

ST = 4y + 8​,

RT = 61.

From the number line we can say that

RT = RS + ST

61 = 6y + 3 + 4y + 8

collecting like terms

61 - 8 - 3 = 6y + 4y

10y = 50

divide through by 10

y = 5

RS = 6y + 3​,

RS = 6 * 5 + 3​ = 30 + 3 = 33

RS = 33

ST = 4y + 8​,

ST = 4 * 5 + 8 = 20 + 8 = 28

ST = 28

​

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Answer:

The water level would rise by \(5\; \rm cm\).

Step-by-step explanation:

Assume that the initial water level is \(h\; \rm cm\).

Before the cube was placed in the tank, the volume of the water was the same as the volume of a rectangular prism with a length of \(160\; \rm cm\), a height of \(80\; \rm cm\), and a height of \(h\; \rm cm\):

\(\begin{aligned} & 160\; {\rm cm} \times 80\; {\rm cm} \times h\; {\rm cm} \\ =\; & (80 \times 160) \, h \; \rm cm^{3} \end{aligned}\).

Let the rise in the water level in the tank be \(x\; \rm cm\). The new water level would be \((x + h)\; \rm cm\).

The volume of the water and the submerged cube, combined, would be the same as that of a rectangular prism with a length of \(160\; \rm cm\), a width of \(\rm 80\; \rm cm\), and a height of \((x + h)\; \rm cm\):

\(\begin{aligned} & 160\; {\rm cm} \times 80\; {\rm cm} \times (x + h)\; {\rm cm} \\ =\; & (80 \times 160) \, (x + h) \; \rm cm^{3} \end{aligned}\).

In other words:

Therefore, the volume of the submerged cube could be expressed as:

\(\begin{aligned} & (80 \times 160) \, (x + h) \; {\rm cm^{3}} - (80 \times 160) \, h \; \rm cm^{3} \\ =\; &(80 \times 160)\, x\; {\rm cm^{3}}\end{aligned}\).

On the other hand, the volume of the cube could be expressed as:

\((40\; \rm cm)^{3} = 64000\; \rm cm^{3}\).

Equate these two expressions for the volume of the cube and solve for \(x\), the rise in the water level in the tank:

\((80 \times 160)\, x = 64000\).

\(x = 5\).

In other words, the rise in the water level in this tank would be \(5\; \rm cm\).

Step-by-step explanation:

y=x+1

y=5x+13

=13x/1

=5x/x

Yes ,induction can be used to prove the following is true for every nonnegitive integer n.

If P (n) is true, so is P (n + 1) because this argument holds true for any nonnegative integer n, it establishes the second fact required by the induction proof. As a result of the Induction Principle, the predicate P (m) is true for all nonnegative integers, m.

Mathematical induction is a technique for proving the truth of a statement, theorem, or formula for each and every natural number n. This is generalized as the 'Principle of Mathematical Induction,' which we would use to prove any mathematical statement.

For instance, 13 +23 + 33 +..... +n3 = (n(n+1) / 2)

The statement is assumed to be true for all natural number values in this case.

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Answer:

See graph attached

Step-by-step explanation:

Our life is simple because the equation \(y=2x+2\) is already put in slope-intercept form.

This form is called slope-intercept because it states exactly what it's called: The number multiplied by \(x\) (the constant of proportionality, in this case, 2) is the slope - and the y-intercept is what is being added to the equation (in this case, also 2, since there is a +2 at the end.)

With this info, we can start graphing.

We know that the y-intercept is 2, meaning one point will be (0,2).

We also know that the slope is 2, meaning every time x increases by 1, y will increase by 2. So the next point is (1, 4), the next is (2, 6), and so on.

Hope this helped!

The graph of the function y = 2x + 2 is added as an attachment

From the question, we have the following parameters that can be used in our computation:

y = 2x + 2

The above function is a linear function that has been transformed as follows

Next, we plot the graph using a graphing tool by taking not of the above transformations rules

The graph of the function is added as an attachment

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Okay, I attached the image, if you have questions about graphing, go to use desmos

Answer:

16 oatmeal cookies

Step-by-step explanation:

We can represent this situation as an equation.

Step 1: Add 7 to both sides.

Therefore, Lisa baked 16 oatmeal cookies.

Answer:

There are 4 questions to answer here and the answers are given below:

1. COMBINATION

2. SET 2  

3. {S2, S3, S4, S5}

4. { }  OR  ∅

Step-by-step explanation:

The key topics here are PERMUTATION & COMBINATION and SETS & VENN DIAGRAMS.

The assignment has 5 questions in all. The options for each question are listed below and separated by commas:

1. True, False

2. True, False

3. A, B, C, D

4. A, B, C, D

5. A, B, C, D

Mr. Montes derives his answers from a random answer generator; same way Amisha generated her answers by random selection.

QUESTION 1

If you want to find the odds that Amisha got at least 3/5 of the answers correctly, would you use a permutation or a combination?

ANSWER TO QUESTION 1

You would use a combination. Note that as much as 'permutation' is distinctly defined from 'combination', in many complex cases both are used to derive the solution. In this case though, a combination is used. For each of the 5 questions, there are a number of possible answers. Questions 1 and 2 have only two possible answers (also known as options) while questions 3, 4 and 5 have four possible answers/options to choose from. Amisha can only have one set of five answers; each to each question. So this is a combination! If you want to find the odds that Amisha got at least 3 of her 5 answers correct, you would use a combination of the various possible answers to check.

QUESTION 2

Find "Set 1 ∩ Set 2" and explain the notation in the sentence.

ANSWER TO QUESTION 2

First list out relevant information:

- The correct answers to questions 3, 4 and 5 are respectively C, B, A

- The universal set consists of five students: S1, S2, S3, S4, S5 hence

Ц = {S1, S2, S3, S4, S5}

Next, enlist the elements of each defined set

Set 1: {S1, S2, S3, S4, S5}     Set 2: {S2, S3, S4}     Set 3: {S4, S5}

Note: Set 1 is equal to the universal set.

Now this notation "∩" means "intersect". It requires an action - checking out which elements in one set also appear in a second set and then bringing those elements to form a new set.

In the case of this question, we're to find Set 1 intersect Set 2. The elements present in Set 1 and also present in Set 2 are {S2, S3, S4}.

If you look closely, you'll observe that these are the same elements in Set 2! This brings to remembrance, one of the laws of sets:

The intersect of any subset and the universal set (recall that Set 1 happens to be equal to or have the same elements as the universal set) is equal to that subset.

So the answer to question 2 is

Set 1 ∩ Set 2 = Set 2

QUESTION 3

Find "Set 2 ∪ Set 3" and explain the notation in the sentence.

ANSWER TO QUESTION 3

The notation ∪ represents "union". This is the act of putting together the elements in two sets, to form a new set. In this activity, if an element appears in both sets, it is only written once in the new set, not twice.

So, Set 2 union Set 3 = {S2, S3, S4, S5}

As earlier stated, Student 4 isn't appearing twice in the new set.

QUESTION 4

Find the ' of Set 1 and explain the notation in this sentence.

ANSWER TO QUESTION 4

The symbol ' means "complement of a set". Finding the complement of a set is like subtracting the elements of that set from the universal set.

Since Set 1 contains the same elements as the universal set, subtracting Set 1 from the universal set will give you nothing. In this case, the complement of Set 1 is a null set!

Set 1 ' Ц = { }  or  ∅

where the empty bracket symbol and the slashed zero symbol represent null set.

Kudos!

Answer:

  96°

Step-by-step explanation:

You want the value of angle C in the diagram with two parallel lines and a triangle between them.

The sum of angles in a triangle is 180°, so the missing angle in the triangle is ...

  180° -60° -24° = 96°

Angle C and the one we just found are alternate interior angles with respect to the parallel lines and the transversal that forms those angles. As such, they are congruent:

  C = 96°

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