Which equation, when graphed, has x-intercepts at (2, 0) and (4, 0) and a y-intercept of (0, –16)?

f(x) = –(x – 2)(x – 4)
f(x) = –(x + 2)(x + 4)
f(x) = –2(x – 2)(x – 4)
f(x) = –2(x + 2)(x + 4)

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:

(a)

Step-by-step explanation:

The line y = x + 1 has a solid circle at x = 2 indicating that x is valid for this value, thus

y = x + 1 for x ≤ 2

The line y = x + 2 has an open circle at x = 2 indicating that x = 2 is not part of the solution but that values greater than 2 are valid, that is

y = x + 2 for x > 2

The definition for the function is (a)

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.

Final answer:

The probability that a student takes theatre given that the student is taking choir is found using conditional probability and is calculated to be 0.3, or 30%.

Explanation:

To find the probability that a student takes theatre given that the student is taking choir, we use the definition of conditional probability. In this scenario, the probability of a student taking theatre and choir (joint probability) is given as 0.078, and the probability of a student taking choir (marginal probability) is 0.26.

The formula for conditional probability is:

P(A | B) = P(A and B) / P(B)

Let A represent the event of a student taking theatre, and B represent the event of a student taking choir. Substituting the given values into the formula yields:

P(A | B) = 0.078 / 0.26

Performing the division gives us:

P(A | B) = 0.3

Therefore, the probability that a student takes theatre given that the student is taking choir is 0.3, or 30%.

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.

For more such information on: unit price

https://brainly.com/question/29023044

#SPJ2

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.

Answer:

y = -4x - 2

Step-by-step explanation:

Parallel has same slope

so

y - 2 = -4(x + 1)

y - 2 = -4x - 4

y = -4x - 2

Equation

y = -4x - 2

Answer:

Step-by-step explanation:

This may look daunting, but let us approach it step by step.

multiply 1/10 by x - 3

0.1x - 0.3 = -40

In algebra, the goal is always to undo all the operations and get back to the original problem so that the mystery value can be determined. In this case since 0.3 was removed, we must add it back.

0.1x = -39.7

0.1x/0.1 = x

39.7/0.1 = -397

Answer seems to be B. -397, but we should still check it.

0.1(-397) - 0.3 = -40

-39.7 - 0.3 = -40

-40 = -40 Correct

If the answer was incorrect, this would show that there had been a flaw in our calculations. But everything checks out, so we are done!

Our final answer is B. -397.

PLEASE MARK BRAINLIEST

Answer:

The answer is -397

Step-by-step explanation:

Answer:

B. <Q = <R

Step-by-step explanation:

Angles are related to their intercepted arcs. An intercepted arc is found by finding the arc segment on a circle whose endpoints connect with the segments that make up an angle.

In this case, TQ and SQ make up <Q, so TS is the intercepted arc of <Q. However, TR and SR make up angle <R as well, making TS the intercepted arc of <R as well.

This means that because the angles share an intercepted arc, they are congruent.

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%.

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

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:

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:

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.

https://brainly.com/question/31486776

#SPJ2

26 different outcomes include at least two heads.

There are [tex]26[/tex] different outcomes that include at least two heads when a coin is tossed [tex]5[/tex] times.

The total number of outcomes when a coin is tossed [tex]5[/tex] times is [tex]\(2^5 = 32\)[/tex], since each toss has [tex]2[/tex] possible outcomes (heads or tails).

To find the number of outcomes with at least two heads, we can find the total number of outcomes with exactly one head and no heads, and subtract that from the total number of outcomes.

1. Number of outcomes with no heads: There is only [tex]1[/tex] outcome with no heads ([tex]5[/tex] tails).

2. Number of outcomes with exactly one head: This can be calculated using combinations. There are [tex]5[/tex] ways to choose which toss will be heads, and for each of these, the remaining [tex]4[/tex] tosses must be tails. So, there are [tex]\(5 \times 1 = 5\)[/tex]outcomes with exactly one head.

Therefore, the number of outcomes with at least two heads is:

[tex]\[ 32 - 1 - 5 = 26 \][/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

(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;

Learn more about standard deviation here: https://brainly.com/question/12402189

#SPJ2

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.

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:

the answer is c

Step-by-step explanation:

The events are illustrations of probability, and the events A and B are not independent events because P(A∣B) ≠ P(A)

From the complete table, we have the following parameter:

P(A∣B) ≠ P(A)

Two events A and B are independent if

P(A∣B) = P(A)

Given that:

P(A∣B) ≠ P(A)

It means that the events are not independent.

Hence, the events A and B are not independent events because P(A∣B) ≠ P(A)

Read more about probability at:

brainly.com/question/251701

#SPJ2

Answer:

The balance of Dianne's register should be $359.41

Step-by-step explanation:

We can begin at the ending balance on the bank statement at $578.30

Then a check is written for $219.25, so a debit

Next a deposit is made for $140.36, so a credit

Then a withdrawal is made for $140.00, so a debit

This means we can make the equation

[tex]578.30-219.25+140.36-140.00=359.41[/tex]

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 :)

27 is equivalent to the number 9

$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.

https://brainly.com/question/17827672

#SPJ3

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

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]

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.

let's recall that a cube is just a rectangular prism with all equal sides, check picture below.

[tex]\bf \textit{volume of a cube}\\\\ V=s^3~~ \begin{cases} s=&length~of\\ &a~side\\ \cline{1-2} V=&27000 \end{cases}\implies 27000=s^3\implies \sqrt[3]{27000}=s\implies 30=s \\\\[-0.35em] ~\dotfill\\\\ \textit{surface area of a cube}\\\\ SA=6s~~\begin{cases} s=&length~of\\ &a~side\\ \cline{1-2} s=&30 \end{cases}\implies SA=6(30)\implies SA=180[/tex]

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:

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.