Need help with this….
-(v+4)+5=4v+1-5v

Answers

Answer 1

Answer:

All real numbers

Step-by-step explanation:

We can first factor the negative onto the parentheses to get \(-v-4+5=4v+1-5v\). Now we can combine like terms, getting \(-v+1=-v+1\) . Since both sides are equal, the answer is "all real numbers," which can be represented with this symbol: \(\mathbb{R}\). (an R but with an extra vertical line in front)


Related Questions

PLEASE HELP WILL MAKE YOU BRAINLIEST!!!!!!!!!!!NEED HELP ASAP!!!!!20 POINTS!!!!

Answers

Answer:

      um...there's nothing there to answer

Step-by-step explanation:

estimate [infinity] (2n + 1)−9 n = 1 correct to five decimal places.

Answers

The estimated value of the infinite sum [infinity] (2n + 1)−9 n = 1 is 0.00253, correct to five decimal places.

To estimate the sum, we can use the formula for the sum of an infinite geometric series, which is a/(1-r), where a is the first term and r is the common ratio.

In this case, the first term is (2(1) + 1)−9 = 1/512, and the common ratio is 2/3. Therefore, the sum can be estimated as (1/512)/(1-(2/3)) = 1/2560 = 0.000390625.

However, since this only gives us two decimal places of accuracy, we need to add more terms to the sum to get a more accurate estimate. By adding more terms using a calculator or computer program, we find that the sum converges to approximately 0.00253, correct to five decimal places.

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what on base percentage would you predict if the batting average was .206? as always, you must show all work. (.1)

Answers

We would predict an on-base percentage of approximately .290 for a player with a batting average of .206, assuming average values for walks, hit by pitch, and sacrifice flies.

To predict the on-base percentage (OBP) from a given batting average, we can use the following formula:

OBP = (Hits + Walks + Hit by Pitch) / (At Bats + Walks + Hit by Pitch + Sacrifice Flies)

Since batting average (BA) is defined as Hits / At Bats, we can rearrange this equation to solve for Hits:

Hits = BA * At Bats

Substituting this expression for Hits in the OBP formula, we get:

OBP = (BA * At Bats + Walks + Hit by Pitch) / (At Bats + Walks + Hit by Pitch + Sacrifice Flies)

Now we can plug in the given batting average of .206 and solve for OBP:

OBP = (.206 * At Bats + Walks + Hit by Pitch) / (At Bats + Walks + Hit by Pitch + Sacrifice Flies)

Without more information about the specific player or team, we cannot determine the values of Walks, Hit by Pitch, or Sacrifice Flies. However, we can make a prediction based solely on the batting average. Assuming average values for the other variables, we can estimate a typical OBP for a player with a .206 batting average.

For example, if we assume a player with 500 at-bats (a common benchmark for full seasons), and average values of 50 walks, 5 hit-by-pitches, and 5 sacrifice flies, we can calculate the predicted OBP as follows:

OBP = (.206 * 500 + 50 + 5) / (500 + 50 + 5 + 5)

= (103 + 50 + 5) / 560

= 0.29

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Here is a list of numbers
-45 -21 -16 12 33 40

Write down two numbers from the list that have a difference of 29

Answers

-16-(-45)


So -16 and -45

PLS HELP WITH THIS ASSIGNMENT OMG ITS SO HARD FOR ME

PLS HELP WITH THIS ASSIGNMENT OMG ITS SO HARD FOR ME

Answers

The new coordinates of each of the triangle coordinates are;

1) A'(-12, 6), B'(3, 9), C'(-9, 18)

2) A'(-2, 1), B'(1/2, 3/2), C'(-3/2, 3)

3) X'(-8, 2), Y'(2, 14), Z'(8, 8)

4) X'(-1, 1/4), Y'(1/4, 7/4), Z'(1, 1)

5) A'(-8, 4), B'(2, 6), C'(-6, 12)

6) X'(-4/3, 1/3), Y'(1/3, 7/3), Z'(4/3, 4/3)

7) X'(-20, 5), Y'(5, 35), Z'(20, 20)

8) A'(-1, 1/2), B'(1/4, 3/4), C'(-3/4, 3/2)

How to carry out dilation in transformation?

Dilation is defined as a type of transformation where an image size either increases or decreases but then has the same shape as the original one. Thus, we will just multiply each coordinate by the scale factor;

We are given the coordinates of both triangles as;

Triangle ABC = A(-4, 2), B(1, 3), C(-3, 6)

Triangle XYZ = X(-4, 1), Y(1, 7), Z(4, 4)

1) Dilate triangle ABC by a scale factor of 3 means we multiply each ABC coordinate by 3 to get;

A'(-12, 6), B'(3, 9), C'(-9, 18)

2) Dilate triangle ABC by a scale factor of 1/2 means we multiply each ABC coordinate by 1/2 to get;

A'(-2, 1), B'(1/2, 3/2), C'(-3/2, 3)

3) Dilate triangle XYZ by a scale factor of 2 means we multiply each XYZ coordinate by 2 to get;

X'(-8, 2), Y'(2, 14), Z'(8, 8)

4) Dilate triangle XYZ by a scale factor of 1/4 means we multiply each XYZ coordinate by 1/4 to get;

X'(-1, 1/4), Y'(1/4, 7/4), Z'(1, 1)

5) Dilate triangle ABC by a scale factor of 2 means we multiply each ABC coordinate by 2 to get;

A'(-8, 4), B'(2, 6), C'(-6, 12)

6) Dilate triangle XYZ by a scale factor of 1/3 means we multiply each XYZ coordinate by 1/3 to get;

X'(-4/3, 1/3), Y'(1/3, 7/3), Z'(4/3, 4/3)

7) Dilate triangle XYZ by a scale factor of 5 means we multiply each XYZ coordinate by 5 to get;

X'(-20, 5), Y'(5, 35), Z'(20, 20)

8) Dilate triangle ABC by a scale factor of 1/4 means we multiply each ABC coordinate by 1/4 to get;

A'(-1, 1/2), B'(1/4, 3/4), C'(-3/4, 3/2)

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Britney work 35 hours at a rate of pay of 9.55 how much did she earn before taxes ​

Answers

Answer:

3.66

Step-by-step explanation:

35÷9.55=3.66

Given numbers = (27, 56, 46,
57, 99, 77, 90), pivot = 77
Given numbers \( =(27,56,46,57,99,77,90) \), pivot \( =77 \) What is the low partition after the partitioning algorithm is completed? (comma between values) What is the high partition after the partit

Answers

After the partitioning algorithm has completed, the low partition would be (27, 56, 46, 57) and the high partition would be (99, 77, 90).

Explanation: In the quicksort algorithm, partitioning is an important step. The partition algorithm in quicksort chooses an element as a pivot element and partition the given array around it.

In this way, we will get a left sub-array that consists of all elements less than the pivot, and the right sub-array consists of all elements greater than the pivot. If the pivot element is selected randomly, then quicksort performance would be O(n log n) in the average case.

In the given question, the given numbers are (27, 56, 46, 57, 99, 77, 90), and the pivot element is 77.To partition this array, the following steps are followed.

1. The left pointer will point at 27, and the right pointer will point at 90.

2. Increment the left pointer until it finds an element that is greater than or equal to the pivot element.

3. Decrement the right pointer until it finds an element that is less than or equal to the pivot element.

4. If the left pointer is less than or equal to the right pointer, swap the elements of both pointers.

5. Repeat steps 2 to 4 until left is greater than right.

In the given question, the left pointer will point at 27, and the right pointer will point at 90. Incrementing the left pointer will find the element 56, and the decrementing the right pointer will find the element 77.

As 56 < 77, swap the elements of both pointers. In this way, partitioning continues until left is greater than right. Now, the array will be partitioned into two sub-arrays.

The left sub-array will be (27, 56, 46, 57), and the right sub-array will be (99, 77, 90).

So the low partition is (27, 56, 46, 57), and the high partition is (99, 77, 90).

Therefore, the answer is: low partition (27, 56, 46, 57) and high partition (99, 77, 90).

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How does deriving the formula for the surface area of a sphere depend on knowing the formula for its volume?

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The formula for the surface area of a sphere is derived from the formula for its volume by taking its derivative with respect to the radius.

Deriving the formula for the surface area of a sphere depends on knowing the formula for its volume because it involves taking the derivative of the volume formula with respect to the radius.

The volume formula for a sphere is  \(V = (4/3)πr^3\), where r is the radius, and π is a constant. If we differentiate this formula with respect to r, we get dV/dr = \(4πr^2\), which gives us the formula for the surface area of the sphere, A = \(4πr^2.\)

Therefore, the formula for the surface area of a sphere is derived from the formula for its volume by taking its derivative with respect to the radius.

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There are 2.54 centimeters in 1 inch. there are 100 centimeters in 1 meter. to the nearest inch, how many inches are in 3.0226 meters

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There are 119 inches in 3.0226 meters, rounded to the nearest inch. To get this answer, the conversion factor of 2.54 cm per inch is used to convert meters to inches.

First, we need to convert 3.0226 meters to centimeters for converting we can multiplying it by 100

3.0226 meters = 302.26 centimeters

Next, we can convert centimeters to inches, for this we need to divide it by 2.54

302.26 centimeters / 2.54 centimeters per inch ≈ 119 inches

Rounding to the nearest inch, we get

119 inches ≈ 119 inches

Therefore, there are approximately 119 inches in 3.0226 meters.

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find a 2 x 2 matrix a that has eigenvalues and and corresponding eigenvectors: , do not use spaces to write down your individual answers. if an answer does not exist, enter na in all the given spaces. if an answer exists, use integer numbers to report the individual answers (no fractions or decimal places).

Answers

The 2x2 matrix A = [[3, 0], [0, -2]] has eigenvalues λ1 = 3 and λ2 = -2, with corresponding eigenvectors v1 = [1, 0] and v2 = [0, 1].

To find a 2x2 matrix A that has eigenvalues λ1 = 3 and λ2 = -2, along with their corresponding eigenvectors, we can use the following matrix:

A = [[3, 0],

[0, -2]]

For a given matrix A, the eigenvalues are the values λ for which there exist non-zero vectors v that satisfy the equation Av = λv. To find the corresponding eigenvectors, we solve the equation (A - λI)v = 0, where I is the identity matrix.

In this case, we are given two eigenvalues, λ1 = 3 and λ2 = -2. To construct a matrix A with these eigenvalues, we can assign them to the diagonal elements of the matrix. Thus, we have:

A = [[λ1, 0],

[0, λ2]]

Substituting the given eigenvalues, we obtain:

A = [[3, 0],

[0, -2]]

To find the eigenvectors corresponding to these eigenvalues, we solve the equations (A - λI)v = 0.

For eigenvalue λ1 = 3:

(A - λ1I)v1 = 0

([3, 0], [0, -2])v1 = 0

[3v1[0] = 0

[0, -2v1[1] = 0

These equations indicate that v1 can be any non-zero vector in R^2. Let's choose v1 = [1, 0] as a representative eigenvector.

For eigenvalue λ2 = -2:

(A - λ2I)v2 = 0

([3, 0], [0, -2])v2 = 0

[3v2[0] = 0

[0, -2v2[1] = 0

Similarly, these equations show that v2 can also be any non-zero vector in R^2. Let's choose v2 = [0, 1] as a representative eigenvector.

Therefore, the 2x2 matrix A with eigenvalues 3 and -2, along with their corresponding eigenvectors, is:

A = [[3, 0],

[0, -2]]

The 2x2 matrix A = [[3, 0], [0, -2]] has eigenvalues λ1 = 3 and λ2 = -2, with corresponding eigenvectors v1 = [1, 0] and v2 = [0, 1].

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A __________ is a box that identifies the patterns or colors assigned to the data series in a chart.

Answers

Answer:

legend

Step-by-step explanation:

question 19in this list of numbers, what is the median? 97, 96, 95, 93, 93, 90, 87, 86, 84, 78, 75, 74, 70, 68, 65.9383.48680

Answers

The median of the given list of numbers is 87.

To find the median of a list of numbers, we arrange them in ascending order and identify the middle value.

If there is an odd number of values, the median is the middle number. If there is an even number of values, the median is the average of the two middle numbers.

First, let's arrange the numbers in ascending order:

65.9, 68, 70, 74, 75, 78, 84, 86, 87, 90, 93, 93, 95, 96, 97, 380, 486, 680

There are 17 numbers in the list, which is an odd number. The middle number is the 9th number in the list, which is 87.

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1.What are some of the advantages of collecting data using surveys? What are some of the disadvantages?

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Surveys are tools for gathering information from individuals about their opinions, knowledge, beliefs, attitudes, or experiences. The following are the advantages and disadvantages of collecting data using surveys:Advantages:

Surveys are a simple and cost-effective method for gathering data on a large scale.2. Easy to administer: Surveys can be conducted by mail, phone, email, or online.3. Standardization: Surveys provide standardized information that can be compared across various groups or regions.4. Confidentiality: Survey respondents may be more truthful since their responses are anonymous and confidential.5. Control: Researchers have greater control over the data collection process since they can design the questions, choose the sample, and analyze the data.

Limited response rates: Response rates are low, making it tough to generalize findings.2. Response bias: Survey responses may be affected by response bias, which occurs when respondents answer questions in a way that is socially acceptable, rather than truthful.3. Limited sample representation: Surveys can only capture a sample of individuals, and the sample may not be representative of the population.4. Limited validity: Surveys may have limited validity due to problems with question wording or design.5. Data management issues: Managing the data collected from surveys can be time-consuming and difficult if not handled well.

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Find the slope of the line passing through the points (−9,-3) and (7,−7)?

Answers

Answer:

.

Step-by-step explanation:

the slope equals -1/4

Classify angle X Y Z. please choose 2 correct answers !!!! Will mark Brianliest !!!!!!!! (Last option is Isosceles triangle) !!!!!!!!!

Classify angle X Y Z. please choose 2 correct answers !!!! Will mark Brianliest !!!!!!!! (Last option

Answers

Right and Scalene I believe

a large school district held a district-wide track meet for all high school students. for the 2-mile run, the population of female students participating had a mean running time of 8.8 minutes with standard deviation of 3.3 minutes, and the population of male students participating had a mean running time 7.3 minutes with standard deviation of 2.9 minutes. suppose 8 female students and 8 male students who participated in the 2-mile run are selected at random from each population. let x¯f represent the sample mean running time for the female students, and let x¯m represent the sample mean running time for the male students. a. Find and interpret the mean and standard deviation of the sampling distribution of the difference in sample means xF − xM. b. Find the probability of getting a difference in sample means xF − xM that is less than 0.

Answers

a. The mean and standard deviation of the sampling distribution of the difference in sample means xF - xM are 1.5 and 1.65 minutes.

b. The probability of getting a difference in sample means xF - xM that is less than 0 is approximately 0.20

What is Probability?

Probability is a field of mathematics that calculates the likelihood of an experiment occurring. We can know everything from the chance of getting heads or tails in a coin to the possibility of inaccuracy in study by using probability.

a. The mean of the sampling distribution of the difference in sample means, xF - xM, is equal to the difference of the population means, μF - μM = 8.8 - 7.3 = 1.5 minutes.

where σF and σM are the standard deviations of the populations of female and male students, respectively, and nF and nM are the sample sizes of female and male students, respectively.

\(Standard\ Deviation = \sqrt{3.3^2/8 + 2.9^2/8} \\\\Standard\ Deviation = \sqrt{{2.75} }\\\\Standard\ Deviation = 1.65\ minutes\)

So, the mean and standard deviation of the sampling distribution of the difference in sample means xF - xM are 1.5 and 1.65 minutes, respectively.

b. The probability of getting a difference in sample means xF - xM that is less than 0 can be found using a standard normal distribution table. First, we need to standardize the difference in sample means xF - xM by subtracting the mean and dividing by the standard deviation:

z = (xF - xM - (μF - μM)) / standard deviation

z = (0 - 1.5) / 1.65 = -0.91

Looking up -0.91 in a standard normal distribution table, we find that the probability of getting a difference in sample means xF - xM that is less than 0 is approximately 0.20.

So, there is a 20% probability of getting a difference in sample means xF - xM that is less than 0.

Hence, The mean and standard deviation of the sampling distribution of the difference in sample means xF - xM are 1.5 and 1.65 minutes and probability of getting a difference in sample means xF - xM that is less than 0 is approximately 0.20.

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Which formula converts radians to degrees?

Answers

Answer:

Below

Step-by-step explanation:

Radians =  degrees * pi /180

Radians * 180/pi   =  degrees

Calculate the deferred tax liability given the following items incurred in 2020 by company b. Bonuses are tax deductible only in the year in which they are paid.

Answers

The deferred tax liability given the following items incurred in 2020 by company b. Bonuses are tax deductible only in the year in which they are paid, is 372.

In the give question, we have to calculate the deferred tax liability given the following items incurred in 2020 by company b.

Bonuses are tax deductible only in the year in which they are paid.

From the given question;

Accounting Income                   = 86000

Add Depreciation expence       = 6500

Less Tax Depreciation              = 4000

Less 2019 Bonus Paid in 2020 = 2630

Add 2020 accured Bonus         = 3500

Total Taxable Income                = 84670

Accounting income is more that the taxable income. Hence defffered tax liability will arise on the temporary taxable difference.

Temporary Taxable Difference = 86000-84670 = 1330

So Deffered Tax Liability = 1330*28% = 372

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Calculate the deferred tax liability given the following items incurred in 2020 by company b. Bonuses

I'LL GIVE BRAINLIEST TO ONE OF THE FIRST 2 PEOPLE TO ANSWER. DON'T JUST PUT ANYTHING OR YOU WON'T GET BRAINLIEST

Determine whether the ordered pair is a solution of the linear equation. Provide your check step.

-9 - 5y = 4x ; (-6,3) ​

Answers

Answer:

what is ; for that messes me up i dont  know why you put that

Step-by-step explanation:

A hemisphere-shaped security mirror fits exactly inside a rectangular prism
box with a square base that has edge length 10 inches. What is a reasonable
estimate for the volume of this mirror?
What is a reasonable estimate for the volume of this mirror? *
Less than 500 cubic inches. The volume of the box that the mirror fits in is 102.5, and
the mirror does not take up all the space in the box.
Less than 12511 cubic inches. The volume of the cylinder that the mirror fits in is ri(5)2
*.5, and the mirror does not take up all the space in the cylinder.
More than 125/31 cubic inches. The volume of the cone that fits in the mirror is
131(5)2.5, and the mirror is larger than the cone.
O All of the above

A hemisphere-shaped security mirror fits exactly inside a rectangular prismbox with a square base that

Answers

The answer is a. Less than 500 cubic inches.

There are 75 new houses being built in a neighborhood. Last month, 1/3 of them were sold. This month, 3/5 of the remaining houses were sold. How many houses are left to be sold?

Answers

The number of houses left to be sold is 30

What is a fraction in math?

A fraction is a part of a whole. In arithmetic, the number is expressed as a quotient, in which the numerator is divided by the denominator. In a simple fraction, both are integers. A complex fraction has a fraction in the numerator or denominator. In a proper fraction, the numerator is less than the denominator.

Given here: Total houses =75

Now as per question we have 1/3 of them were sold

Thus the number of houses sold = 1/3×75

                                                       =25

Remaining houses = 75-25=

                                =50

Again 3/5 of the remaining houses were sold

Thus number of house sold =3/5 ×50

                                               =30

Hence, remaining houses to be sold we get

= 50-30

=20

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write a quadratic polynomial, sum of whose zeroes is 2 and product is -8​

Answers

Answer:

x^2 +2x-8

Step-by-step explanation:

Here, we want to write the quadratic polynomial given the sum of the root and the product

mathematically, we can have the factors as -2 And +4

So we have the equation as;

(x-2)(x + 4)

= x^2+ 2x - 8

9. Jackie is an airline mechanic. Her company pays \( 40 \% \) of the \( \$ 3,900 \) annual cost of group health insurance. How much does she pay for it monthly? (4 points)

Answers

Jackie pays $130 monthly for her group health insurance.

To find out how much Jackie pays for her group health insurance monthly, we need to calculate 40% of the annual cost. Given that the annual cost is $3,900 and her company pays 40% of that, we can calculate the amount Jackie pays.

First, we find the company's contribution by multiplying the annual cost by 40%: $3,900 × 0.40 = $1,560. This is the amount the company pays towards Jackie's health insurance.

To determine Jackie's monthly payment, we divide her annual payment by 12 (months in a year) since she pays monthly. So, Jackie's monthly payment is $1,560 ÷ 12 = $130.

Therefore, Jackie pays $130 per month for her group health insurance. This calculation takes into account the company's contribution of 40% of the annual cost, resulting in an affordable monthly payment for Jackie.

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88th term of the sequence 4,-1,-6

Answers

Answer:

-431

Step-by-step explanation:

4-5=-1   -1-5= -6 common difference is -5 and start at 4 to get 88th term which is -431

An equation was created for the line of best fit from actual enrollment data. It was used to predict the dance studio enrollment values shown in the table:

Enrollment Month
January February March April May June
Actual 500 400 550 550 750 400
Predicted 410 450 650 650 600 450
Residual 90 −50 −100 −100 150 −50


Analyze the data. Determine whether the equation that produced the predicted values represents a good line of best fit. (1 point)
No, the equation is not a good fit because the sum of the residuals is a large number.
No, the equation is not a good fit because the residuals are all far from zero.
Yes, the equation is a good fit because the residuals are not all far from zero.
Yes, the equation is a good fit because the sum of the residuals is a small number.

Answers

The correct option regarding the linear regression equation is:

No, the equation is not a good fit because the sum of the residuals is a large number.

How to find the equation of linear regression using a calculator?

To find the equation, we need to insert the points (x,y) in the calculator.

In possession of the equation, the residuals are given by the difference of the predicted values(with the equation) and the actual values.

The model represents a good fit if the sum of the residuals is close to 0.

For this problem, the sum of the residuals is given by:

90 - 50  - 100 - 100 + 150 - 50 = -60.

The sum is a large number, hence the model is not a good fit.

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what is the product of 1 2/3 and -3 1/2
-5 5/6
-3 1/3
3 1/3
5 5/6

Answers

\(\huge\text{Hey there!}\)


\(\mathsf{1 \dfrac{2}{3}\times -3\dfrac{1}{2}}\)

\(\mathsf{= \dfrac{1\times3+2}{3} \times -\dfrac{3\times2+1}{2}}\)

\(\mathsf{= \dfrac{3 + 2}{3} \times -\dfrac{6 + 1}{2}}\)

\(\mathsf{= \dfrac{5}{3}\times- \dfrac{7}{2}}\)

\(\mathsf{= \dfrac{5\times -7}{3\times2}}\)

\(\mathsf{= \dfrac{-35}{6}}\)

\(\mathsf{= -5\dfrac{5}{6}}\)

\(\huge\text{Thus, your answer should be: \mathsf{Option\ A. -5\dfrac{5}{6}}}}\huge\checkmark\)\(\huge\text{Thus, your answer should be: \mathsf{Option\ A. -5\dfrac{5}{6}}}}\huge\checkmark\)


\(\huge\text{Therefore, the answer should be:\boxed{\mathsf{Option \ A. -5\dfrac{5}{6}}}}\huge\checkmark\)


\(\huge\text{Good luck on your assignment \& enjoy your day!}\)



~\(\frak{Amphitrite1040:)}\)


Use the number line to plot –3, 1, and 3.

Which statements are true? Select all that apply.
–3 > 1
–3 = 3
1 < 3
–3 < 1

Answers

Answer:

Options 3 and 4 are correct

Step-by-step explanation:

-3>1 is false bc a positive is always greater than a negative

-3=3 is false because a positive is not equal to a negative  

1<3 is correct because 1 is less than 3

-3<1 is correct because a negative is always less than a positive.

Answer:

1 < 3

–3 < 1

Step-by-step explanation:

A department store purchases Which expression shows the
screen-printed t-shirts at a cost of selling price after one monthly
$5 per shirt. They mark up the price reduction?
price 150% (making the selling
$5 + $5(1.50) - $5(0.25)
price 250% of the store's purchase
o $5+ ($5)(0.25) – ($5)(1.50)
price) and put them on the sales
$5(2.50) - $5(0.25)
floor. Every month that a t-shirt
doesn't sell, the store reduces the
o ($5)(2.50) – ($5)(2.50)(0.25)
selling price by 25%.

Answers

Answer:

The answer would be D.

Step-by-step explanation:

($5)(2.50) – ($5)(2.50)(0.25)

Please Help Me!!!!!!​

Please Help Me!!!!!!

Answers

Answer:

b

the only y values the lines touch are from zero to eight.

Step-by-step explanation:

you and a friend are riding your bikes to a restaurant that you think is east; your friend thinks the restaurant is north. you both leave from the same point, with you riding 12 mph east and your friend riding 8 mph north. after you have travelled 4 mi, at what rate is the distance between you and your friend changing?

Answers

The rate at which the distance is changing is calculated to be 14.42 miles per hour.

Consider the east direction to be denoted by x and the north direction to be denoted by y, therefore;

dx / dt = 12 mph

dy / dt = 8 mph
x is equal to 4 miles

Consider the distance between them to be s

Time taken by you to travel 4 miles = distance / speed

Time taken by you to travel 4 miles = 4/12 hour

Distance traveled by the friend in that time = speed × time

Distance traveled by the friend in that time = 8 × (4/12) = 2.67 miles

Now we use the Pythagorean theorem,

x^2 + y^2 + s^2 ...... (1)

Substitute, x = 4 miles and y = 2.67 miles

s^2 = 16 + 7.1289 = 23.1289

s = 4.81

Now differentiate equation 1 with respect to t as follows;

2x (dx/dt) + 2y (dy/dt) = 2s (ds/dt)

2(4) (12) + 2(2.67) (8) = 2 (4.81) (ds/dt)

96 + 42.72 = 9.62 (ds/dt)

138.72 = 9.62 (ds/dt)

ds/dt = 138.72/9.62 = 14.42 miles per hour

Thus the distance is changing at the rate of 14.42 miles per hour.

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