Cheryl is planning a garden that will be
8x7 feet. She wants it to be raised by 6 inches.
How many cubic feet of topsoil will she need
to add?

Answer:

4

Step-by-step explanation:

f⁻¹(x) = x²+3, but none of that matters, since f(f⁻¹(x)) = x

Answer:

Step-by-step explanation:

Any number between 0.390 and 0.400 will work.  For example, 0.391, 0.392, and 0.393.

Answer:

A. x=0 and x=4

Step-by-step explanation:

The roots of a quadratic function are the x intercepts of the parabola. In this case, the roots are 0 and 4 because the parabola intercepts the x axis twice in these points.

Your answer is A. x=0 and x=4

Hope I helped!

Answer:

A

Step-by-step explanation:

Answer:

Sorry, all I know is that after he got the 7 blocks of spruce he will have $3,600  left over. I don't know how many blocks he can buy with that.

Step-by-step explanation:

Answer:

Ted can buy 8 blocks of mahogany.

Step-by-step explanation:

Total amount Ted wishes to spend this month is $5000.

Mahogany costs $450 per block, and he has already bought 7 blocks of spruce at $200 each.

So, money spent on spruce = [tex]7\times200=1400[/tex] dollars

Money left after buying spruce = [tex]5000-1400=3600[/tex] dollars

Now as $450 will be spent on buying 1 block of mahogany.

So, $3600 will be spent on buying [tex]\frac{3600}{450}= 8[/tex] blocks of mahogany.

The answer is 8 blocks.

Answer:

The domain of the graph is all real number ⇒ the last answer

Step-by-step explanation:

* Remember that our original exponential formula was y = ab^x

- The b value is the growth factor

* Lets revise how to find the domain of this function

- The domain is all values of x that make the function defined

* Lets revise the composite function

- A composite function is a function that depends on another function.

- A composite function is created when one function is substituted

 into another function.

- For example, f(g(x)) is the composite function that is formed when

 g(x) is substituted for x in f(x).

∵ f(x) = 2^x

∵ g(x) = x - 2

∴ (f · g)(x) = f(x - 2)

∵ f(x) = 2^x

∴ (f · g)(x) = f(x - 2) = 2^(x - 2)

- For this function there is no values of x make the function undefined

∴ The Domain is all real numbers

- Look to the graph, the values of x go from -∞ to ∞

* The domain of the graph is all real number

Answer:

-4.5

Step-by-step explanation:

ANSWER

The midline y=3.6

EXPLANATION

The midline is the midpoint of the peak value and the least value.

The peak value is 5.20

The least value is 2

The midline is

[tex]y = \frac{5.20 + 2}{2} = \frac{7.2}{2} = 3.6[/tex]

Therefore the mid value is y=3.6

318.83484250503 mm^2

The area of the regular 15-gon with a radius of 10mm is approximately 247.2mm².

Formula for a Regular Polygon Area:

The area (A) of a regular polygon can be calculated using the following formula:

A = 1/2 * n * s^2 * r

where:

n is the number of sides in the polygon (15 for this case)

s is the side length of the polygon

r is the radius of the polygon

Finding the Side Length (s):

We don't directly have the side length (s) of the regular 15-gon. However, we can relate it to the radius (r) using the following formula:

s = 2r * sin(π / n)

In this case:

r = 10mm

n = 15

Substituting these values:

s = 2 * 10mm * sin(π / 15)

s ≈ 8.24mm (round to 2 decimal places)

Calculating the Area (A):

Now that we have the side length (s) and the radius (r), we can calculate the area (A) of the regular 15-gon:

A = 1/2 * 15 * 8.24mm² * 10mm

A ≈ 247.2mm^2 (round to 1 decimal place)

Therefore, the area of the regular 15-gon with a radius of 10mm is approximately 247.2mm².

Answer:

see explanation

Step-by-step explanation:

Given

4x - 8x ÷ 2

Under the rules of PEMDAS , division must be performed before subtraction.

Hence

4x - 8x ÷ 2 = 4x - 4x ← dividing - 8x by 2, then

4x - 4x = 0 ← correct answer

In this figure, ∠a and ∠b are supplementary. The answer is OPTION C.

A. Complementary angles are two angles whose sum is equal to 90 degrees. Since no information is given about the angles Za and Zb in the figure, we cannot determine if they are complementary. Therefore, this answer choice is not supported by the given information.

B. Equal angles have the same measure. Again, no information is given about the angles Za and Zb, so we cannot determine if they are equal. Thus, this answer choice is not supported by the given information.

C. Supplementary angles are two angles whose sum is equal to 180 degrees. Since the figure does not provide any specific angle measurements, we cannot directly determine if Za and Zb are supplementary. However, this answer choice is a possibility as supplementary angles are commonly encountered in geometry.

D. Vertical angles are a pair of non-adjacent angles formed by intersecting lines. Without any information about the lines or angles in the figure, we cannot determine if Za and Zb are vertical angles. Therefore, this answer choice is not supported by the given information.

In conclusion, the most accurate answer choice based on the given information is C. supplementary. However, without additional context or measurements, we cannot definitively determine the relationship between Za and Zb.

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According to the given figure, ∠a and ∠b are complementary angles.

The correct answer to the given question is option A.

These two could be any pair of angles and the relationship between them depends on their relative positions. If ∠a and ∠b are complementary, that means that the sum of their angle measures is 90 degrees.

This usually happens when two angles together form a right angle. On the other hand, if ∠a and ∠b are equal, that means that they have the same angle measure.

This usually happens when the angles are opposite each other in a shape with symmetry, such as an isosceles triangle or a rectangle. Should ∠a and ∠b be supplementary, it means that the sum of their angle measures is 180 degrees.

This usually happens when two angles form a straight line or the angles on a straight line sum to 180 degrees.

Finally, if ∠a and ∠b are vertical, that means they are opposite each other when two lines intersect.

Hence, ∠a and ∠b are complementary angles.

Therefore, the correct answer to the given question is option A.

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Answer:

[tex]\frac{95}{99}[/tex]

Step-by-step explanation:

The bar above 95 denotes that 95 is repeated, that is

0.959595,,,,

Create 2 equations with the repeating values after the decimal point, thus

let x = 0.9595.... → (1) ← multiply both sides by 100

100x = 95.9595.... → (2)

Subtract (1) from (2) eliminating the repeated value, so

99x = 95 ( divide both sides by 99 )

x = [tex]\frac{95}{99}[/tex]

Answer:

the answer is: 6z^3

Step-by-step explanation:

We need to solve this equation:

[tex]\sqrt{36z^6}[/tex]

We know that 6X6 = 36

and √ = 1/2

Solving:

[tex]=\sqrt{6*6*z*z*z*z*z*z}\\We\,\,know\,\,6X6=6^2\,\, and \,\,z*z=z^2\\=\sqrt{6^2*z^2*z^2*z^2} \\=(6^2)^{1/2}*(z^2)^{1/2}*(z^2)^{1/2}*(z^2)^{1/2}\\=6*z*z*z\\=6z^3[/tex]

So, the answer is: 6z^3

When doing volume you do Length x Width x Height (9 x 2.5 x 10) the answer is 225 if I’m not mistaken

The volume of the cereal box is 225 in³

Volume is a measure of three-dimensional space. It is often quantified numerically using SI derived units or by various imperial or US customary units. The definition of length is interrelated with volume.

Given that, a cereal box is 9 inches by 2.5 inches by 10 inches., we need to find its volume,

Volume of box = length x width x height

= 9 x 2.5 x 10

= 225

Hence, the volume of the cereal box is 225 in³

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Answer:

Perimeter of polygon B = 80 units

Step-by-step explanation:

Since both polygons are similar, their corresponding sides and perimeters are proportional. Knowing this we can setup a proportion to find the perimeter of polygon B.

[tex]\frac{side-polygonA}{side-polygonB} =\frac{perimeter-polygonA}{perimeter-polygonB}[/tex]

Let [tex]x[/tex] be the perimeter of polygon B. We know from our problem that the side of polygon A is 24, the side of polygon B is 15, and the perimeter of polygon A is 128.

Let's replace those value sin our proportion and solve for [tex]x[/tex]:

[tex]\frac{side-polygonA}{side-polygonB} =\frac{perimeter-polygonA}{perimeter-polygonB}[/tex]

[tex]\frac{24}{15} =\frac{128}{x}[/tex]

[tex]x=\frac{128*15}{24}[/tex]

[tex]x=\frac{1920}{24}[/tex]

[tex]x=80[/tex]

We can conclude that the perimeter of polygon B is 80 units.

Answer:80 units

Step-by-step explanation:

I'm doing it right now. You got this have a great day!

Answer:

50 degrees

Step-by-step explanation:

If angle A and angle B are complementary, that would mean that their sum is 90 degrees. A + B = 90 . We know that angle A is 40, so 40 + B = 90. It becomes a one step equation. Subtract both sides by 40. 90 - 40 = 50. Angle B is equal to 50 degrees.

Answer:

50 degrees

Step-by-step explanation:

we know that

If two angles are complementary, then their sum is equal to 90 degrees

so

A+B=90°

we have

A=40°

substitute and solve for B

40°+B=90°

B=90°-40°=50°

P: padre de Luis

h: hijo

P=32+h

P+h=78

Método: sustitución

*p + h = 78

(32 + h) + h = 78

32 + h + h = 78

2h + 32 = 78

2h = 78 - 32

2h = 46

[tex]h = \frac{46}{2} \\ \\ h = 23[/tex]

El hijo tiene 23 años

EL padre tiene 55 años

P = 32 + h

P = 32 + 23

P = 55

Answer: the range is 209

Step-by-step explanation: the biggest number minus the smallest will give you the range

The answer is 209. Hope this helps

Answer:

The friends will each have passed _33_ scales in _7_ weeks.

Step-by-step explanation:

We must write an equation for the number of scales that Nick approves and an equation for the number of scales that Mary approves.

For Nick we have:

5 initial scales

Nick has committed to approve 4 scales per week. Let's call x the number of weeks.

So the number of scales and for Nick is:

[tex]y = 5 + 4x[/tex]

For Mary we have:

12 initial scales

Mary has committed to approve 3 scales per week. Let's call x the number of weeks.

So the number of scales and for Mary is:

[tex]y = 12 + 3x[/tex]

To know when the two friends have passed the same number of scales we must equal both equations and solve for x:

[tex]12 + 3x = 5 + 4x[/tex]

[tex]12-5= 4x-3x[/tex]

[tex]x= 7\ weeks[/tex]

And

[tex]y=12+3*7\\\\y=33\ scales[/tex]

Final answer:

Nick and Mary will both have passed 33 scales in 7 weeks. This is determined by setting the equation for the number of scales Nick will pass equal to the number for Mary and solving for the number of weeks.

Explanation:

To determine when Nick and Mary will have passed the same number of scales, we can set up an equation based on the given information. Nick has currently passed 5 scales and will pass 4 scales each week. Mary has passed 12 scales and will pass 3 scales each week. The point at which they will have passed the same number of scales is when their total passed scales are equal.

Let's denote the number of weeks it will take to reach this point as w. For Nick, the total number of scales passed after w weeks will be 5 + 4w (his current count plus 4 times the number of weeks). For Mary, it will be 12 + 3w (her current count plus 3 times the number of weeks). Setting these two expressions equal to each other:

5 + 4w = 12 + 3w

Subtract 3w from both sides:

5 + w = 12

Subtract 5 from both sides:

w = 7

So, it will take 7 weeks for Nick and Mary to have passed the same number of scales. At that point, to find the total number of scales:

Nick: 5 + 4 x 7 = 33 scales

Mary: 12 + 3 x 7 = 33 scales

The friends will each have passed 33 scales in 7 weeks.

Answer:

1 = 60, 4 = 30, 5 = 30, 6 = 150, 7 = 110, 8 = 30, 9 = 60, 10 = 90.  2 = 47.5, 3 = 132.5

Step-by-step explanation:

Starting with angle 5:  knowing that arc BC = 30 and angle 5 is a central angle, it has an angle measure equal to the measure of the arc it intercepts.

Angle 6 is supplementary to angle 5, so 180 - 30 = 150.

Angle 9 = 60.  Ch is a diameter, so that means it splits the circle into 2 congruent halves, each measuring 180 degrees around the outside.  So if arcs AB and CB both measure 30, then arc AH measures 180 - 30 - 30 = 120.  By definition, the measure of angle 9 is half the measure of the arc it intercepts.

Angles 4 and 8 = 30 each.  Because you have AH parallel to CG, then CH is a transversal, creating a pair of alternate interior angles that are congruent.  Those angles are 4 and 8.  We find 8 to be an inscribed angle, cutting off arc ABC which measures 60 degrees.  An inscribed angle is half the measure of the arc it intercepts. Because angle 4 measures 30 degrees and is inscribed, the arc it cuts off, arc GH, measures twice the angle cutting it.  So arc GH measures 60.

Again, since CH is a diameter, then the semicircle CDEG measures 180.  Since we know from the description that arcs CD and DE are congruent, then arc CD + arc DE + arc EG (given as 50) + arc GH = 180.  Since arcs CD and DE are congruent, lets just call them "x" and we have two of them.  That gives us that 2x + 50 + 60 = 180.  x = 35.  Angle 1 is equal to half of the sum of its intercepted arcs ( 35 + 35 + 50) which is 60.

Angle COE intercepts arc CDE, and is central, so angle COE measures 70, and since angle 7 is supplemetray to angle COE, then angle 7 measures 180 - 70 = 110.

Angle 10 by definition is a right angle (refer to the theorem regarding a tangent line to a point on a circle).

Angle 2 is half of the sum of 35 (arc CD) and 60 (arc GH), so angle 2 measures 47.5 and that means that angle 3, supplementary to angle 2, measures 180 - 47.5 = 132.5.  I think those are all correct.  The only one I'm unsure of is angle 2.  

17) 5:6

18) 3:4

19) 4:5

20) 2:3

21) 3:4

22) 2:3

23) 3:5

24) 9:10

These answers are all simplified ratios

Final answer:

The questions involve finding the ratio of two quantities and simplifying them by dividing both numbers by their greatest common divisor. Each ratio gives a comparative relationship between two different counts of items or scores in different subjects.

Explanation:

The questions provided all relate to finding the ratio of two quantities.

In each case, the ratio is found by comparing two quantities and simplifying by dividing both numbers by their greatest common divisor (GCD).

To solve the equation Z + mx = yx for x, we first move 'mx' to the right side to get 'yx - mx = Z'. We then factor out 'x' to get 'x(y - m) = Z'. Finally, we divide by '(y - m)' to get 'x = Z / (y - m)'. This solution holds as long as y ≠ m.

Here, we're going to solve the equation for x: Z + mx = yx.

We can start by grouping the terms with 'x' together. This gives us: yx - mx = Z. Now, we can factor x out of the left side of the equation. This results in: x(y - m) = Z. Finally, to solve for x, we divide both sides of the equation by (y - m). This gives us the solution: x = Z / (y - m).

Note: This solution is under the assumption that y ≠ m because division by zero is undefined.

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Answer:

The answer would be A. 1.25

Weird. A period appears above this... huh.

Answer:

[Th]e cube has a greater value.

Step-by-step explanation:

What the word problem really wants us to get [is ]the question of 'Which is greater, A=6a^2 when 'a' [is] 18 or A=4[tex]\pi[/tex]r^2 when r = 9? And here's how to solve that.

Starting with the[ c]ube we have A=6a^2. A bit t[o]o simple, right?

A=6(18)^2 Substitute numbers.

A=6(324) Solve ex[p]onents.

A=1944 Mult[i]ply.

So w[e] know that the cube is 1944 meters cube[d ] in area. But what about the more [f]ormidable sphere? Fo[r] it we need a slightly m[o]re co[m]plicated formula, A=4[tex]\pi[/tex]r^2. However, instead of using the real pi I will be rounding to 3.14, since we have no calculator so anything more would take way too long and fry your[ bra]in.

A=4(3.14)(9)^2 Subst[i]tute numbers.

A=4(3.14)(81) Solve expone[n]ts.

A=12.56(81) Multip[ly].

A=1017.36 Multiply again[.]

Now, since I'm sure all of us can count, we know that 1944 is greater than 1017.36. Or in other words, the cube is bigger than the sphere.

And PLEASE don't copy this guys. Make your own iteration. Change it up!

Answer:

The correct answer to this problem is

C) 0; The slope indicates that Daniel is not moving.

Step-by-step explanation:

I know this because I just did the test

The slope from point D to point E on the graph represents Daniel's speed between these two points. The slope is 10 meters per minute.

The slope from point D to point E on the graph represents Daniel's speed between these two points. To determine the slope, we need to find the change in position and the change in time between the two points. The slope is calculated by dividing the change in position by the change in time.

Let's assume that the change in position from D to E is 100 meters and the change in time is 10 minutes. The slope would then be 100 meters divided by 10 minutes, which is equal to 10 meters per minute.

Therefore, the correct answer is A) 10; The slope indicates that Daniel's speed is 10 meters per minute.

The water station would be located approximately 2.9 miles from the start.

A mathematical number known as distance measures "how much ground an object has traveled" while moving. Distance is defined as the product of speed and time.

Let's call the distance from the start to the water station x. The distance from the water station to the finish line is 5 - x.

We know that the ratio of these two distances is 7:5, so we can write the following equation:

x / (5 - x) = 7/5

Expanding and solving for x, we get:

5x = 7(5) - 7x

12x = 35

x = 35/12 = 2.92 miles

So, the water station would be located approximately 2.92 miles from the start. Round to the nearest tenth of a mile, the answer is 2.9 miles.

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The water station will be placed approximately 2.9 miles from the start, rounding to the nearest tenth of a mile.

To find where to place the water station at a 7:5 ratio along a 5-mile race course, we must determine how many parts out of the total 12 parts (7+5) each section of the race is. Since the total race is 5 miles, we divide 5 miles by 12 parts, which gives us the length of one part. Multiplying that length by 7 will give us the distance from the start to the water station.

First, we find the length of one part:

Then, we find the distance to the water station:

The water station will be placed approximately 2.9 miles from the start, rounding to the nearest tenth of a mile.

For this case we must find the solution of the following expression:

[tex](x + 7) (x + 7) = 0[/tex]

If we isolate a term and we equate to zero, we have:

[tex]x + 7 = 0[/tex]

Subtracting 7 on both sides of the equation we have:

[tex]x + 7-7 = 0-7\\x = -7[/tex]

Thus, the solution of the expression is given by:

[tex]x = -7[/tex]

ANswer:

[tex]x = -7[/tex]

Answer:

x = -7, multiplicity 2.

Writing it as a set it is {-7, -7}.

Step-by-step explanation:

(x + 7)(x + 7 )= 0

When 2 expressions are multiplied and the result is zero either of them can be zero, so

x + 7 = 0

x = -7.

In this case, since the 2 factors are the same, there are duplicate roots.

We write  this as  x = -7, multiplicity 2.

Answer:

Width=5

Step-by-step explanation:

[tex]\bf \qquad \qquad \textit{direct proportional variation} \\\\ \textit{\underline{y} varies directly with \underline{x}}\qquad \qquad y=kx\impliedby \begin{array}{llll} k=constant\ of\\ \qquad variation \end{array} \\\\[-0.35em] ~\dotfill\\\\ \begin{cases} y=8\\ x=-2 \end{cases}\implies 8=k(-2)[/tex]

Answer:

4 Dimes

9 Nickels

Step-by-step explanation:

I did guess and check (if you have an equation leave a comment or answer!)

So I did kept playing with the numbers making them go down until I could subtract the number of coins and divide to get the rest:

85-40 (4 dimes)=45

45/5=9 nickels

4+9=13

I hope this helps!

To solve for the number of nickels and dimes amounting to $0.85 in 13 coins, we set up and solve a system of equations. We found that there are 9 nickels and 4 dimes in the wallet.

To find out how many nickels you have when you have 13 coins composed of nickels and dimes amounting to $0.85, we can set up a system of equations where the number of nickels is represented by n and the number of dimes by d.

The first equation comes from the total number of coins: n + d = 13.

The second is derived from the total amount of money: 0.05n + 0.10d = 0.85.

We have two equations:

n + d = 13

0.05n + 0.10d = 0.85

Now, let's multiply the second equation by 20 to get rid of the decimals:

n + 2d = 17

By subtracting the first equation from this new equation:

d = 4

Substitute d back into the first equation:

n + 4 = 13

Thus:

n = 9

So you have 9 nickels and 4 dimes.

Final answer:

Explaining how to calculate density using the mass and volume of a rock.

Explanation:

Density can be calculated using the formula: Density = Mass/Volume. Given that the mass of the rock is 50 g and the volume is 10 mL, we can plug these values into the formula to find the density.

Mass = 50 g

Volume = 10 mL = 10 cm³

Density = Mass/Volume = 50 g / 10 cm³ = 5 g/cm³

Answer:

Vertex ( 5 ,8) .

Step-by-step explanation:

Given  : f(x) = 2(x − 5)² + 8.

To find : Determine the vertex of the function .

Solution : We have given

f(x) = 2(x − 5)² + 8.

Vertex form of parabola  : f (x) = a(x - h)² + k, where (h, k) is the vertex.

On comparing f(x) = 2(x − 5)² + 8. with vertex form of parabola.

a = 2 , h = 5 , k = 8 .

Vertex ( 5 ,8) .

Therefore, Vertex ( 5 ,8) .

Answer: (5,8)

Step-by-step explanation:

The given function :[tex]f(x) = 2(x - 5)^2 + 8.[/tex]

We know that the vertex form of a quadratic equation is given by :

[tex]f (x) = m(x - a)^2+ b[/tex]   (1)

, where (a,b)= Vertex of the function f(x).

When we compare the given function [tex]f(x) = 2(x - 5)^2 + 8.[/tex] to equation (1) , we conclude that the given function is already in its vertex form.

with a= 5 and b= 8

Therefore , the vertex of the function [tex]f(x) = 2(x - 5)^2 + 8.[/tex] = (5,8)