for each equation, choose the statement that describes its solution. if applicable, give the solution.


5(y+1)-7 = 3(y-1)+2y


no solution


y = ?


all real numbers are solutions

Answer:

The volume of the pyramid is 128 cm³

Step-by-step explanation:

* Lets revise the volume of the pyramid

- The pyramid has one base and the number of side faces depends

 on the number of sides of the base

- The volume of any pyramid is 1/3 × Area of its base × its height

* Lets solve the problem

- The pyramid has a square base

- It has four side faces all of them are triangles

- It has five vertices and eight edges

- The area of the base = s², where s is the length of the side of

  the square

- The volume of the pyramid is 1/3 × s² × h, where h is the height

 of the pyramid

- The base edge length of the base is 2 cm longer than the height

 of the pyramid

- The height of the pyramid is 6 cm

∵ The length of the edge of the base is 2 cm longer than the

   height of the pyramid

∵ The height of the pyramid (h) = 6 cm

∴ The edge length of the base = 6 + 2 = 8 cm

- The area of the base = s²

∵ s = 8 cm

∴ The area of the base (s²) = 8² = 64 cm²

- The volume of the pyramid = 1/3 × s² × h

∴ Its volume = 1/3 × 64 × 6 = 128 cm³

* The volume of the pyramid is 128 cm³

The correct answer is:

128 cm^3

Hope this helps

Answer:

[tex]1.789*10^{3}[/tex]

Answer: 1.789 × 10 to the third power

Step-by-step explanation: the answer would be 1.789 x 10 to the third power because the A term has to be between 1 and 10

Answer:

A z coordinate is the third-dimensional coordinate in a volume pixel , or voxel . Together with x and y coordinates , the z coordinate defines a location in a three-dimensional space.

Step-by-step explanation:

Answer:

z coordinate =0 since this is xy plane.

Step-by-step explanation:

Given is a planar graph which contains a parallelogram.

The parallelogram is lying on xy plane.

The parallelogram is a planar figure drawn on xy plane.

We have in 3 dimensional cartesian system of coorindates in the xy plane z=0

Hence we have z coordinate =0

Answer:

A

Step-by-step explanation:

The volume (V) of a pyramid is

V = [tex]\frac{1}{3}[/tex] area of base × perpendicular height (h)

area of square base = 4² = 16 and h = 4, hence

V = [tex]\frac{1}{3}[/tex] × 16 × 4 = [tex]\frac{64}{3}[/tex] = 21 [tex]\frac{1}{3}[/tex] ft³

(a) The average price of brand A is higher than average price of brand B

(b) The price of brand B is more spread out than the price of brand A.

The mean of the distributions for the individual samples is given as;

Mean of Brand A = $50

Mean of Brand B = $40

Standard deviation of Brand A = $5

Standard deviation of Brand B = $8

From the mean and standard deviation of the samples we can conclude the following;

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Final answer:

The two true statements are that Brand A's prices are less spread out than brand B's prices (C), reflected in the smaller standard deviation, and that Brand A has a higher average price than brand B (D), as indicated by their respective means.

Explanation:

The question involves comparing means and standard deviations for samples of prices from two different brands of shoes, Brand A and Brand B. To select the two true statements among the given options, we consider the provided statistics for each brand:

Now let's analyze the statements:

Therefore, the two true statements are C and D: Brand A's prices are less spread out than brand B's prices, and Brand A has a higher average price than brand B.

8(-1) = -8

When a positive and a negative number is being multiplied the product is always negative, but when a negative and a negative number is being multiplied the product is positive

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:   y8

Step-by-step explanation:  You keep the base and add the exponents

The other answer is correct if you’re dealing with exponents. However, if your numbers are y5 x y3, then just multiply them: y5 x y3 = y15

This is because they are “like terms” can be directly multiplied

Answer:

no

Step-by-step explanation:

 Nathan has 6 letters in his name so he has a higher chance of winning

No, Katie has the advantage.

Katie has 5 distinct letters.

Nathan has 4 distinct letters.

They have one overlap (a).

Katie can expect to win 4 out of 26 games.

Nathan can expect to win 3 out of 26 games.

Since Katie has more distinct letters, she has the advantage, so it is not a fair game.

Answer:Substitute the given values in the Law of Sines and find that the measure is 24.72°

The measure of the missing angle is approximately 113.28°.

Assuming that the missing angle is opposite to side c, we can use the Law of Sines to find the measure of the missing angle. The Law of Sines states that for any triangle ABC:

a/sin(A) = b/sin(B) = c/sin(C)

Substituting the given values, we have:

16/sin(42°) = 10/sin(B) = c/sin(C)

Solving for sin(B), we get:

sin(B) = 10*sin(42°)/16 ≈ 0.4182

Using the inverse sine function, we can find the measure of angle B:

B ≈ sin⁻¹(0.4182) ≈ 24.72°

Now, we can use the fact that the angles of a triangle add up to 180° to find the measure of the missing angle:

A + B + C = 180°

A + 42° + 24.72° = 180°

A ≈ 113.28°

Therefore, the measure of the missing angle is approximately 113.28°.

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Answer:

D. 100 percent

Step-by-step explanation:

it is 100 percent because the reservoir is putting out 600k, but loses 300k, which would be easy to think it would be 50 percent because 300k is half of 600k, but however its peek outage is putting out 600k, therefore 600k = 600k, 100%.

27 is equivalent to the number 9

Answer:

[tex]2^{n-1}[/tex]

Step-by-step explanation:

Square 1 has 2^0 pennies.

Square 2 has 2^1 pennies.

Square 3 has 2^2 pennies.

Square 4 has 2^3 pennies. The exponent of 2 is 1 less than the square number, so ...

Square n has 2^(n-1) pennies.

Answer:

B

C

A

Step-by-step explanation:

Find the value of x in each equation then compare the solutions from the least to the greatest

In A

5( x-6)+3x=3/4(2x-8) ------------Open brackets

5x-30+3x=3/2x-6

5x+3x-30=3/2x-6

8x-3/2x=-6+30---------------collect like terms

16x-3x=48

13x=48-----------------dived both sides by 13

x=48/13 = 3.7

In B

2.7(5.1x+4.9)=3.2+28.9-------------open bracket

13.77x+13.23=32.1

13.77x=32.1-13.23---------------collect like terms

13.77x=18.87

x=18.87/13.77----------------------divide both sides by 13.77

x=1.37

In C

5(11x-18)=3(2x+7)--------------------open brackets

55x-90=6x+21

55x-6x=21+90-----------------------collect like terms

49x=111----------------------------------divide both sides by 49 to get x

x=111/49 = 2.27

From the solutions, the least value of x is in B, then C ,and finally A

Equation B:[tex]\(x \approx 1.371\)[/tex]

Equation C:[tex]\(x \approx 2.2653\)[/tex]

Equation A: [tex]\(x = \frac{48}{13}\)[/tex]

Order from least to greatest: B, C, A.

To solve each equation, let's start by simplifying each side of the equation step by step.

Equation A:[tex]\(5(x-6) + 3x = \frac{3}{4}(2x - 8)\)[/tex]

Step 1: Distribute the numbers:

[tex]\(5x - 30 + 3x = \frac{3}{4}(2x) - \frac{3}{4}(8)\)[/tex]

Step 2: Combine like terms:

[tex]\(8x - 30 = \frac{3}{2}x - 6\)[/tex]

Step 3: To get rid of the fraction, multiply both sides by 2:

(16x - 60 = 3x - 12)

Step 4: Move all (x) terms to one side by subtracting (3x) from both sides:

(16x - 3x - 60 = -12)

Step 5: Combine like terms:

(13x - 60 = -12)

Step 6: Add 60 to both sides to isolate (x):

13x = 48

Step 7: Divide both sides by 13 to solve for (x):

[tex]\(x = \frac{48}{13}\)[/tex]

Equation B: 2.7(5.1x + 4.9) = 3.2 + 28.9

Step 1: Distribute the number:

13.77x + 13.23 = 32.1

Step 2: Move the constant to the other side by subtracting 13.23 from both sides:

13.77x = 18.87

Step 3: Divide both sides by 13.77 to solve for (x):

x ≈ 1.371

Equation C: (5(11x - 18) = 3(2x + 7)

Step 1: Distribute the numbers:

55x - 90 = 6x + 21

Step 2: Move all (x) terms to one side by subtracting (6x) from both sides:

55x - 6x - 90 = 21

Step 3: Combine like terms:

49x - 90 = 21

Step 4: Add 90 to both sides to isolate (x):

49x = 111

Step 5: Divide both sides by 49 to solve for (x):

x ≈ 2.2653

Now, let's order these solutions from least to greatest:

[tex]\(x= 1.371\)[/tex] (from Equation B)

[tex]\(x = 2.2653\)[/tex] (from Equation C)

[tex]\(x = \frac{48}{13}\)[/tex] (from Equation A)

So, the order from least to greatest based on their solutions is Equation B, Equation C, and then Equation A.

4=$17.60

1=$17.60/4

1=$4.40

Hole this helps :)

The unit price of a padlock, when rounded to the nearest cent, is $4.40 per padlock.

To calculate the unit price of a padlock, you'll need to determine the cost per individual padlock within a pack. In this scenario, you have a pack of 4 padlocks that costs $17.60. To find the cost of a single padlock, you can use the following formula:

Unit Price = Total Cost / Number of Padlocks

In this case:

Total Cost = $17.60

Number of Padlocks = 4

Now, let's calculate the unit price:

Unit Price = $17.60 / 4 padlocks

Unit Price = $4.40 per padlock

So, the unit price of each padlock is $4.40 when rounded to the nearest cent.

Understanding the unit price is essential for making informed purchasing decisions. It allows you to compare prices and determine whether buying in bulk (in this case, a pack of 4 padlocks) is more cost-effective than purchasing items individually.

In summary, the unit price of a padlock is $4.40 per padlock when rounded to the nearest cent. This information helps consumers assess the value of buying items in larger quantities and ensures they get the best deal for their money.

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Answer:

Jimmy's second dive was [tex]\frac{4}{15}[/tex] of the pool deeper than the first one

Explanation:

We are given that:

First dive was [tex]\frac{1}{3}[/tex] of the way to the bottom

Second dive was [tex]\frac{3}{5}[/tex] of the way to the bottom

We know that the second dive was deeper than the first one since [tex]\frac{3}{5} > \frac{1}{3}[/tex]

To know how much deeper the second dive was compared to the first one, we will simply subtract the depth of the first dive from that of the second one

Therefore:

The second dive was [tex]\frac{3}{5} - \frac{1}{3} = \frac{9}{15} - \frac{5}{15} = \frac{4}{15}[/tex] of the pool deeper than the first one

Hope this helps :)

Final answer:

Jimmy's second dive was 4/15 of the pool deeper than his first dive, calculated by finding a common denominator and subtracting the fractions representing the depth of each dive.

Explanation:

Jimmy's second dive was 3/5 of the way to the bottom of the pool, which is deeper than his first dive at 1/3 of the way. To find out how much deeper the second dive was compared to the first, we subtract the two fractions:

Second dive - First dive = 3/5 - 1/3

To subtract fractions, they must have a common denominator. Multiplying top and bottom of 3/5 by 3 and 1/3 by 5 gives us:

9/15 - 5/15 = 4/15

Therefore, Jimmy's second dive was 4/15 of the pool deeper than his first dive.

$12,282.5 (20000x0.85x0.85x0.85)

The value of the copy machine depreciates at a rate of 15% each year. After calculating the depreciated value for 3 consecutive years, the copy machine that initially cost $20,000 is worth approximately $12,282.50 after 3 years.

The original cost of the copy machine is $20,000. Given that the copy machine depreciates, or loses value, at a rate of 15% each year, we need to calculate the value of the copy machine each year for 3 years by subtracting 15% of its current value.

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Final answer:

To calculate the number of different combinations of adult and children's tickets that would total $100, we can set up an equation: 5x + 3y = 100. We can find possible values of 'x' and 'y' that satisfy the equation. There are 6 different combinations of adult and children's tickets that would have totaled $100.

Explanation:

To calculate the number of different combinations of adult and children's tickets that would total $100, we can set up an equation:

5x + 3y = 100

Where 'x' represents the number of adult tickets and 'y' represents the number of children's tickets. We need to find whole number solutions for 'x' and 'y'.

We can start by finding the possible values of 'x' and 'y' that satisfy the equation and add up to $100. The possible combinations are:

x = 0, y = 33

x = 5, y = 31

x = 10, y = 29

x = 15, y = 27

x = 20, y = 25

x = 25, y = 23

Therefore, there are a total of 6 different combinations of adult and children's tickets that would have totaled $100.

Answer:

  To cancel a term, it is necessary to add the opposite of the term to both sides of the equation

Step-by-step explanation:

Adding opposites creates a sum of zero. Zero added to anything else does not change the its value. So, adding the opposite of a term effectively removes it from (that side of) the equation.

Answer:

Row B. J becomes (-2,-3), K becomes (-2,-5), and L becomes (1,-5)

The correct answer is B.

The coordinates of the triangle are ...

J = (-5, -1)

K = (-5, -3)

L = (-2, -3)

All you have to do is add 3 to all of the x's of the coords

And subtract 2 from all of the y's of the coords

Answer:

  4 cm

Step-by-step explanation:

The equation of a parabola with its vertex at the origin can be written as ...

  y = 1/(4p)x^2

The problem statement tells us that one point on the parabola is (x, y) = (12, 9). We can put these values into the equation and solve for p, the distance from the focus to the vertex.

  9 = 1/(4p)(12^2)

  9×4/144 = 1/p = 1/4 . . . . . . . . multiply by the inverse of the coefficient of 1/p

Then p = 4, and the bulb is 4 cm from the vertex.

4x-3(x-2)=21

4x-3x+6=21

4x-3x=21-6

x=15

is this right? let's check

4(15)-3(15-2) = 21? yes

For this case we have the following expression, we must find the value of the variable "x":

[tex]4x-3 (x-2) = 21[/tex]

We apply distributive property to the terms of the parenthesis taking into account that:

[tex]- * + = -\\- * - = +\\4x-3x + 6 = 21[/tex]

We add similar terms:

[tex]x + 6 = 21[/tex]

We subtract 6 on both sides of the equation:

[tex]x = 21-6\\x = 15[/tex]

Now, the value of x is 15

Answer:

[tex]x = 15[/tex]

Answer:

20

Step-by-step explanation:

A dodecahedron is a three-dimensional figure made out of 12 regular pentagons.  It resembles a soccer ball, just more rough on the edges.

So, it has 12 faces made out of regular pentagons.  Each summit/vertex is a meeting point for 3 different pentagons.

So, you can easily calculate the number of vertices:

How many pentagon vertices in total?

12 pentagons with 5 vertices / pentagon = 60 vertices in total

But each vertex meets with two others... so you have to divide the number of total vertices by 3... so 60 / 3 = 20.

Answer:

12 faces

Step-by-step explanation:

~apex

Answer

The solution for the two system of equations is (-4,2)

Explanation

Equation for slope-intercept

The equation for slope-intercept form is y = mx + b

-mx represents the slope of the equation

-b represents the y-intercept

Determine the slope and the y-intercept

The slope of the two equations can be found based on what the number in front of the x is, this term is also called the coefficient.

The y-intercept is in the form of b and is substituted normally by a positive or negative integer.

Slope: 1/4 and 2

Y-intercept: 3 and 10

You must graph these, for this problem I have provided one for you.

Determining the solution

Since this problem requires you to find the solution based on the graph you must graph the two lines and the solution is the point in which the two lines intersect.

Based on the graph I have provided for you, we can determine that the solution is (-4,2)

Checking your work

In math it's very important to check your work: plug in the solution and if it is a perfect math then the solution is correct.

[tex]\frac{1}{4} (-4)+ 3 = 2[/tex]

The solution applies to the first equation, however we must now check for the second equation.

[tex]2(-4) + 10 = 2[/tex]

The solution also applies to the second equation, so we now know that this solution is correct.

Answer:

1/4 bag for each batch.

Step-by-step explanation:

Start with 4 bags. If the cake requires 1/4 bag, then 3 3/4 bags of flour are left over for the cookies.  That's rather a nice number when you are dealing with 15 batches of cookies.

Start by changing the 3 3/4 into a decimal.

3 3/4 = 3.75

Now divide 3.75 by 15

3.75 / 15 = 0.25 bags which is 1/4 bag. You only have to come up with one value so this one will do.

Answer:

0

Step-by-step explanation:

[tex]p_1:~~y = x^2+2\\p_2:~~y = 3x^2+2\\ \\ V{p_1} = \Big(-\dfrac{b}{2a}, -\dfrac{\Delta}{4a}\Big) = \Big(-\dfrac{0}{2}, -\dfrac{0^2-4\cdot 2}{4}\Big) = \Big(0,2\Big) \\ \\ Vp_2 = \Big(x_V, -\dfrac{\Delta}{4a}\Big) = \Big(0, -\dfrac{0^2-4\cdot 3 \cdot 2}{4\cdot 3}\Big) = \Big(0,2\Big) \\ \\ \\ \text{The distance is }0,~~\text{Because the vertices are equal.}[/tex]

The distance between the vertices of the graphs is 0.

The distance between the vertices of the graphs corresponding to y = x2 + 2 and y = 3x2 + 2 can be found by finding the x-coordinates where the graphs intersect. To do this, we set the two equations equal to each other:

x2 + 2 = 3x2 + 2

Subtracting 2 from both sides gives: x2 = 3x2

Subtracting x2 from both sides gives: 0 = 2x2

Dividing both sides by 2 gives: 0 = x2

This equation has only one solution: x = 0. Therefore, the distance between the vertices of the graphs is 0.

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Answer:

Option A is correct.

Step-by-step explanation:

We need to find the difference of two matrices.

The matrices are:

[tex]\left[\begin{array}{cc}-4&8\\3&12\end{array}\right] - \left[\begin{array}{cc}2&1\\-14&15\end{array}\right][/tex]

We will subtract each row entry of Matrix 1 from the corresponding row entry of Matrix 2.

[tex]\left[\begin{array}{cc}-4-2&8-1\\3+14&12-15\end{array}\right]\\\left[\begin{array}{cc}-6&7\\17&-3\end{array}\right][/tex]

So, We get the answer

[tex]\left[\begin{array}{cc}-6&7\\17&-3\end{array}\right][/tex]

which matches Option A.

So, Option A is correct.

Answer:

A

Step-by-step explanation:

Subtract corresponding elements in second matrix from first matrix, that is

[tex]\left[\begin{array}{ccc}-4-2&8-1&\\3-(-14)&12-15&\\&&\end{array}\right][/tex]

= [tex]\left[\begin{array}{ccc}-6&7&\\17&-3&\end{array}\right][/tex]

Answer:

18%

Step-by-step explanation:

The number of graduates on financial aid = 1879

The total number of students = 10730

Probability = [tex]\frac{1879}{10730}[/tex] × 100% = 0.175 × 100% ≈ 18%

Answer:

Option C. 0.05x+0.10(x+6)=1.35

Step-by-step explanation:

Remember that

1 nickel=$0.05

1 dime=$0.10

Let

x-----> the number of nickels

y----> the number of dimes

we know that

0.05x+0.10y=1.35 -----> equation A

y=x+6 ----> equation B

substitute equation B in equation A and solve for x

0.05x+0.10(x+6)=1.35

The correct equation that can be used to determine x, the number of nickels Rhonda has, is 0.05x + 0.10(x+6) = 1.35, which is option C from the ones presented.

In this question, we are asked to find the equation that we can use to determine the number of nickels, represented by 'x', Rhonda has. Given that Rhonda has six more dimes than nickels, the cost of dimes in Rhonda's pocket can be represented by 0.10*(x+6) because each dime is worth $0.10 and she has six more dimes than nickels. Similarly, the cost of nickels in Rhonda's pocket could be represented as 0.05*x because each nickel is worth $0.05. As the total amount of money Rhonda has is $1.35, the two amounts should sum up to 1.35. Hence, the correct equation would be 0.05x + 0.10(x+6) = 1.35, so the answer is option C.

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This is a basic algebraic word problem. Make x equal the miles you traveled. multiply that by 2 and add the 3 initial dollars, then add the one dollar tip, finally make all this equal to 20. So your equation should look like this:

2x + 3 + 1 = 20

add the 3 and 1:

2x + 4 =20

move the 4 to the right side:

2x = 16

devide both sides by 2:

x = 8

So you traveled 8 miles.

Answer:

A. 27 π cubic inches

Step-by-step explanation:

The volume of a cylinder is calculated using the formula;

[tex]Volume=\pi r^2h[/tex]

From the given information, the smallest candle has a radius of 0.5 inches and a height of 3 inches.

We substitute [tex]r=0.5[/tex] and [tex]h=3[/tex] into the given formula.

The vlume of the smallest candle is

[tex]Volume=\pi \times0.5^2\times 3[/tex]

[tex]Volume=\frac{3}{4}\pi in^3[/tex]

from the given information, the other two candles are scaled versions of the smallest, with scale factors of 2 and 3.

The volume of the other two candles will be [tex]2^3\times \frac{3}{4}\pi=6\pi in^3[/tex] and [tex]3^3\times \frac{3}{4}\pi=\frac{81}{4}\pi in^3[/tex]

The wax needed to create one set of candle is

[tex]\frac{3}{4}\pi+6\pi+\frac{81}{4}\pi=27\pi\: in^3[/tex]

The correct answer is A

Answer:

27 pi in³

Step-by-step explanation:

I just took a test on Plato/Edmentum with this question and this was the right answer

~Please mark me as brainliest :)