David performed the following mathematical operation:
2x+3
x+3)2x2 +9x+9
He was left with a remainder of zero. Which of the following statements must
be true?

Answer:

Width equals 11, and length equals 12.

Step-by-step explanation: It is helpful to memorize your multiplication tables up to 12. I personally couldn't figure out a formula for this, but I knew that 12 x 11 equals 132, and the length is greater than the width, so length is 12 and width is 11. Hopefully somebody else can figure it out. P.S. I meant the formula, not the answer, my answer is correct.

Answer:

\(l(l - 1) = 132\)

\( {l }^{2} - l - 132 = 0 \)

\((l - 12)(l + 11) = 0\)

\(l = 12 \: or \: l = - 11\)

\(length \: must \: be \: postive\)

\(integers\)

\(l = 12 \: and \: w = l - 1 = 11\)

plato

Answer:

For parallel:

gradient is 1/5

\(y = mx + c\)

consider (5, -2):

\( - 2 = ( \frac{1}{5} \times 5) + c \\ - 2 = 1 + c \\ c = - 3\)

\({ \boxed{ \bf{equation : y = \frac{1}{5}x - 3 }}}\)

For perpendicular:

gradient, m1:

\(m _{1} \times m_{2} = - 1 \\ m _{1} \times \frac{1}{5} = - 1 \\ \\ m _{1} = - 5\)

gradient = -5

\(y = mx + c \\ - 2 = (5 \times - 5) + c \\ - 2 = - 25 + c \\ c = 23\)

\({ \boxed{ \bf{equation :y = - 5x + 23 }}}\)

Answer:

Parallel: \(y=\displaystyle \frac{1}{5}x-3\)

Perpendicular: \(y=-5x+23\)

Step-by-step explanation:

Hi there!

What we must know:

Finding the Parallel Line

\(y=\displaystyle \frac{1}{5} x-3\)

Given this equation, we can identify that its slope (m) is \(\displaystyle \frac{1}{5}\). Because parallel lines always have the same slope, the slope of the line we're currently solving for would be \(\displaystyle \frac{1}{5}\) as well. Plug this into \(y=mx+b\):

\(y=\displaystyle \frac{1}{5}x+b\)

Now, to find the y-intercept, plug in the given point (5,-2) and solve for b:

\(-2=\displaystyle \frac{1}{5}(5)+b\\\\-2=1+b\\-2-1=b\\-3=b\)

Therefore, the y-intercept is -3. Plug this back into \(y=\displaystyle \frac{1}{5}x+b\):

\(y=\displaystyle \frac{1}{5}x+(-3)\\\\y=\displaystyle \frac{1}{5}x-3\)

Our final equation is \(y=\displaystyle \frac{1}{5}x-3\).

Finding the Perpendicular Line

\(y=\displaystyle \frac{1}{5} x-3\)

Again, the slope of this line is \(\displaystyle \frac{1}{5}\). The slopes of perpendicular lines are negative reciprocals, so the slope of the line we're solving for would be -5. Plug this into \(y=mx+b\):

\(y=-5x+b\)

To find the y-intercept, plug in the point (5,-2) and solve for b:

\(-2=-5(5)+b\\-2=-25+b\\-2+25=b\\23=b\)

Therefore, the y-intercept is 23. Plug this back into \(y=-5x+b\):

\(y=-5x+23\)

Our final equation is \(y=-5x+23\).

I hope this helps!

Answer:

will it be 2000 feet.....

Step-by-step explanation:

cause she basically just did an extra 4 minute and if she does 1000 feet every 4 minutes, she does 2000 feet every 8 minutes.

Answer:

c. domain: {-2, 0, 2}, range: {-1, 1, 3}

Step-by-step explanation:

From the given points (negative 2, negative 1), (0, 1), (2, 3), we can determine the domain and range.

The domain represents the set of all possible x-values of the points, and the range represents the set of all possible y-values of the points.

In this case, we can see that the x-values are -2, 0, and 2, and the corresponding y-values are -1, 1, and 3.

Therefore, the correct answer is:

c. domain: {-2, 0, 2}, range: {-1, 1, 3}

Answer:(2,-3)

Step-by-step explanation:

\( \rightarrow4 \times \frac{3}{5} = 12 \times \frac{1}{5} \\ \)

\( \rightarrow \frac{12}{5} = \frac{12}{5} \\ \)

\( \rightarrow \: lhs \: = \: rhs\)

Hence , 4 x 3/5 =12 ×1/5

Let's see

We know

So

Hence verified

Answer:

Step-by-step explanation:

Tree as an autotroph can prepare its own food and which animals and humans feed upon, so the tree is a producer

Answer:

f(-5)=-125

Step-by-step explanation:

we have

\(f(x)=x^3\\\\x=-5\\\\f(-5)=(-5)^3\\\\f(-5)=-125\)

Answer: f(-5)=-125

Step-by-step explanation:

For this problem, we are given f(x)=x³ and x=-5. Since we are given x=-5, we plug that into f(x) and solve.

f(x)=x³            [plug in x=-5]

f(-5)=(-5)³      [exponent]

f(-5)=-125

Now, we know that f(-5)=-125.

Answer:

y=(1/4)x + 9      OR      y=x/4 +9

Step-by-step explanation:

Perpendicular lines have a slope/gradient of -1/n

Because the slope of this line is -4, the slope of a line perpendicular to it would be 1/4.

y=(1/4)x+b

(0,9) is the y-intercept, so b = 9

y=(1/4)x + 9      OR      y=x/4 +9

Output values are 25 times the input values, and the expression can be given as y = 25x.

An algebraic expression is consists of variables, numbers with various mathematical operations.

The given input values are,

1, 2, 3, and 4

The output values are,

25, 50, 75, and 100.

Let x represents the input values, and y represents the output values,

The expression for the input and output values can be give by,

y = k x        (1)

Substitute x =1 , and  y = 25

25 = k (1)

k = 25

To find the required expression, substitute k = 25 in equation (1),

y = 25x

y = 25x is the expression, in which y is 25 times the value of x.

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The sum of the geometric progression is the sum S₃ = 32

The sum of terms of a geometric progression is given by

Sₙ = a(rⁿ - 1)/(r - 1) where

Given the geometric progression, aₙ = 4(2)ⁿ⁻¹ comparng it with the general term of a geometric sequence aₙ = arⁿ⁻¹, then

Now, we desire S₃, that is Sₙ when n = 3.

So, S₃ = a(r³ - 1)/(r - 1)

= 4(2³ - 1)/(2 - 1)

= 4(8 - 1)/1

= 4(8)

= 32

So, the sum S₃ = 32

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Answer:

No solution

Step-by-step explanation:

4x = 4x + 1

0 unequal to 1

Answer: D. No solution

please mark Brainliest :)

Answer:(6, 5)

Give me brainliest

The categories of the solutions are

The graph represents the given parameter

As a general rule, when two lines or curves intersect, then the point of intersection represents the solution to the system of equations

In this case, the graph intersect at points B and F

This means that the solution to the system are Point B and Point F

While other points do not represent the solutions

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Answer:

j

Step-by-step explanation:

j

The return on equity for  the firm is 18.75%.

Return on equity=Return on assets +[ (Debt/Equity ratio)×(Return on assets-Return on debt)]

Let plug in the formula

Return on equity=.15+ [(.75)× (.15-.10)]

Return on assets=.15+ (.75×0.05)

Return on assets=.15+0.0375

Return on equity=0.1875×100

Return on equity=18.75%

Therefore the return on equity ratio is 18.75%.

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This equation is separable,

\(\dfrac{dA}{dt} = -6A \implies \dfrac{dA}A = -6\,dt\)

Integrate both sides and solve for \(A\) :

\(\displaystyle \int \frac{dA}A = -6 \int dt\)

\(\ln|A| = -6t + C\)

\(e^{\ln|A|} + e^{-6t+C}\)

\(\implies A(t) = Ce^{-6t}\)

Solve for \(C\) using the initial value.

\(A(0) = 6 \implies 6 = Ce^0 \implies C=6\)

Then the particular solution is

\(\boxed{A(t) = 6e^{-6t}}\)

Therefore , the solution of the given problem of volume comes out to be the cone has a height of 7 units.

A three-dimensional object's volume, which is expressed in cubic units, indicates how much space it takes up. These symbols for cubic measurements are litre and in3. Nonetheless, assessing an object's volume allows one to ascertain its dimensions. The weight of the item is often converted into mass units like grammes or kilogrammes.

Here,

If r is the radius of the base and h is the height, then (1/3)r2h can be used to define the volume of a right cone.

As the base's diameter is specified as 6 units, the radius is equal to half that amount, or 3 units.

We can solve for the height by substituting the given volume of 21 units3 into the formula:

=> (1/3)π(3²)h = 21π

=>  9h = 63

=>  h = 7

As a result, the cone has a height of 7 units.

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Angles of similar triangles are always congruent a: 63, b: 88, c: 29 and x = 53.75

Based on the information available, there are numerous equations for calculating the area of a triangle. As indicated in the calculator above, please use the Triangle formula for additional information and equations for calculating the area of a triangle as well as determining the sides of a triangle using whatever information is available.

find the ratio between the two triangles:

40 on the left corresponds to 50 on the right = 40/50 = 43/x

to find x:

40x = 43 × 50

40x = 215

x = 215/40

x = 53.75

"angles of similar triangles are always congruent."

a: 63

b: 88

c: 29

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Full question:

Given a pair of similar triangles, find the missing length x and the missing angles A, B, and C.

Answer:

what is the question?

Step-by-step explanation:

Answer:

The equation of this line is y = -4.

Answer:

y=-4

Step-by-step explanation:

zero slope m=0

y-y1=m(x-x1)

y-(-4)=0(x-(-9))

y+4=0

y=-4

Out of the 400 surveyed students, 327 were either seniors or commuters.

To find the number of students who were either seniors or commuters out of the 400 surveyed students, we need to add the number of seniors and the number of commuters while avoiding double-counting those who fall into both categories.

According to the information given:

There were 262 seniors.

There were 215 commuters.

150 of the seniors were also commuters.

To avoid double-counting, we need to subtract the number of seniors who were also commuters from the total count of seniors and commuters.

Seniors or commuters = Total seniors + Total commuters - Seniors who are also commuters

= 262 + 215 - 150

= 327

Therefore, out of the 400 surveyed students, 327 were either seniors or commuters.

It's important to note that in this calculation, we accounted for the overlap between seniors and commuters (150 students who were both seniors and commuters) to avoid counting them twice.

This ensures an accurate count of the students who fall into either category.

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Answer:we cant really answer this without the image

Step-by-step explanation:

Answer:

-129

Step-by-step explanation:

2x+5=0

x=-5/2 [By the remainder theorem]

f(-5/2)=8(-5/2)^3+4(-5/2)^2+13(-5/2)+3

=-125+25-65/2+3

=-129.

Answer:

0.0418 = 4.18% probability that the average income level in the neighborhoods was less than $38,000.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean \(\mu\) and standard deviation \(\sigma\), the zscore of a measure X is given by:

\(Z = \frac{X - \mu}{\sigma}\)

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean \(\mu\) and standard deviation \(\sigma\), the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \(\mu\) and standard deviation \(s = \frac{\sigma}{\sqrt{n}}\).

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

Jean knows that the mean income level in the country is $40,000, with a standard deviation of $2,000.

This means that \(\mu = 40000, \sigma = 2000\)

Jean selected three neighborhoods and determined the average income level.

This means that \(n = 3, s = \frac{2000}{\sqrt{3}} = 1154.7\)

What is the probability that the average income level in the neighborhoods was less than $38,000

This is the pvalue of Z when X = 38000. So

\(Z = \frac{X - \mu}{\sigma}\)

By the Central Limit Theorem

\(Z = \frac{X - \mu}{s}\)

\(Z = \frac{38000 - 40000}{1154.7}\)

\(Z = -1.73\)

\(Z = -1.73\) has a pvalue of 0.0418

0.0418 = 4.18% probability that the average income level in the neighborhoods was less than $38,000.

Answer:

40 students have given their speeches

24 students need to give their speeches

5/8 of the students have given their speeches

3/8 of the students need to give their speeches

Step-by-step explanation:

Answer:

40 students gave their speeches.

Step-by-step explanation:

Anytime in math that it says the word "of" it means multiplication. So, in this situation, we are multiplying:

(5/8) x 64.

But, when you are multiplying a fraction by a number, you are actually dividing instead of multiplying. Think of it this way: the question is asking you 5/8 of 64, meaning you must find how many is 5/8 of the amount of students that gave their speeches is. Also, that slash between the 5 and the 8 in the fraction is actually a division symbol. So, by placing 5/8 into 64, we get:

(5/8) x 64 = 40.

I'm quite sure why it asked for "simplest form" when the answer is not a decimal or fraction, but this is the answer to the problem that you have posted.

I hope that this helps.

Answer:

a. See explanation for table

b. The 7th hour

Step-by-step explanation:

Given

Ski Resort

\(Base\ Snow = 75in\)

\(Rate = 1in\) hourly

Mt. Winterpark

\(Base\ Snow = 68in\)

\(Rate = 2in\) hourly

First, we need to illustrate the amount of snow as an equation in both cases.

\(Amount = Base\ Snow + Rate * Time\)

Let x be number of hours. and y be the amount of snow

So:

Ski Resort

\(y= 75 + 1* x\)

\(y= 75 + x\)

Mt. Winterpark

\(y= 68 + 2 * x\)

\(y= 68 + 2x\)

Next, we make a table to show the data.

When \(x = 0\)

Ski Resort: \(y = 75 + 0 = 75\)

Mt. Winterpark: \(y = 68 + 2(0) = 68\)

When \(x = 1\)

Ski Resort: \(y = 75 + 1 = 76\)

Mt. Winterpark: \(y = 68 + 2(1) = 70\)

When \(x = 2\)

Ski Resort: \(y = 75 + 2 = 77\)

Mt. Winterpark: \(y = 68 + 2(2) = 72\)

When \(x = 3\)

Ski Resort: \(y = 75 + 3 = 78\)

Mt. Winterpark: \(y = 68 + 2(3) = 74\)

When \(x = 4\)

Ski Resort: \(y = 75 + 4 = 79\)

Mt. Winterpark: \(y = 68 + 2(4) = 76\)

When \(x = 5\)

Ski Resort: \(y = 75 + 5 = 80\)

Mt. Winterpark: \(y = 68 + 2(5) = 78\)

When \(x = 6\)

Ski Resort: \(y = 75 + 6 = 81\)

Mt. Winterpark: \(y = 68 + 2(6) = 80\)

When \(x = 7\)

Ski Resort: \(y = 75 + 7 = 82\)

Mt. Winterpark: \(y = 68 + 2(7) = 82\)

When \(x = 8\)

Ski Resort: \(y = 75 + 8 = 83\)

Mt. Winterpark: \(y = 68 + 2(8) = 84\)

When \(x = 9\)

Ski Resort: \(y = 75 + 9 = 84\)

Mt. Winterpark: \(y = 68 + 2(9) = 86\)

When \(x = 10\)

Ski Resort: \(y = 75 + 10 = 85\)

Mt. Winterpark: \(y = 68 + 2(10) = 88\)

Hence, the table is:

x ---- Ski Resort ---- Mt. Winterpark

0 --------75 ----------- 68

1 --------76 ----------- 70

2 --------77 ----------- 72

3 --------78 ----------- 74

4 --------79 ----------- 76

5 --------80 ----------- 78

6 --------81 ----------- 80

7 --------82 ----------- 82

8 --------83 ----------- 84

9 --------84 ----------- 86

10 -------85 ----------- 88

(b)

From the table, the amount of snow is the same at the 7th hour and the snow is 82 inches