Find the equation of the line shown. 10 9 8 6 5 4 3 2 1 1 23 4 5 67 8 9 10​

The quotient and remainder when -x⁴+6x³+7x²+3 is divided by x-7 is 12 and 73, respectively.

Using synthetic division, the quotient and remainder when -x⁴+6x³+7x²+3 is divided by x-7 is 12 and 73, respectively.


To solve this problem, start by writing out the synthetic division form, with the coefficients in the same order as the original problem:



  |-7 |6 7 3
 |1 -7
 |0 12
 |-73


Take the first coefficient of the divisor (-7) and multiply it by the first coefficient of the dividend (-1). The result is 7. Place this number at the top of the first column of the table.


Take the divisor’s first coefficient (-7) and add it to the dividend’s second coefficient (6). Place the result (–1) in the second column of the table.


Take the first coefficient of the divisor (-7) and multiply it by the second coefficient of the dividend (6). Place the result (-42) in the third column of the table.


Now add the first two numbers in the second column of the table (7 and -1). Place the result (6) in the fourth column.

The last number in the table (-73) is the remainder. The second number in the table (12) is the quotient.

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The value of 6 = 3 × 2³ is 24 by using PEMDAS operations, the correct option is (d).

To understand why, we can simplify the equation using the order of operations, which is PEMDAS (parentheses, exponents, multiplication/division, addition/subtraction). To evaluate the expression 3 x 2³, we first need to simplify the exponent, which means multiplying 2 by itself three times:

2³ = 2 x 2 x 2

2³ = 8

Now we can substitute the value of 2³ into the original expression:

3 x 2³ = 3 x 8

3 x 2³ = 24

However, the value of 6 = 3 x 2³, is equal to 24 the correct option is (d).

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The complete question is:

What is the value of 6 = 3 × 2³?

a. 16

b. 64

c. 42

d. 24

The measure of the height of the triangle measured by Manuel is given as follows:

5 feet.

The height of a triangle is the perpendicular distance from the base to the vertex opposite the base, and is used to calculate the area of the triangle.

Hence, the height is measured as the distance from the top vertex of the triangle to it's base.

In this problem, it is stated that:

"Manuel measured the distance from the top vertex of the triangle shown to its base".

He found the distance to be of 5 ft, hence the height of the triangle is of:

5 ft.

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To factor the trinomial 2x²+7x-4, you could rewrite it as 2x²+8x-2x-4, and then factor by grouping. The factor pairs of ac are (x+4), (2x-1).

To factor the trinomial 2x²+7x-4 by grouping, we need to find a factor pair of ac that sums to b. In this case, ac = (2)(-4) = -8 and b = 7.

The factor pair of -8 that sums to 7 is 8 and -1. Therefore, we can rewrite the trinomial as follows:

2x²+7x-4 = 2x²+8x-x-4

Next, we can group the first two terms and the last two terms:

(2x²+8x)+(-x-4)

Now, we can factor out the greatest common factor from each group:

2x(x+4)-1(x+4)

Finally, we can factor out the common factor of (x+4):

(x+4)(2x-1)

Therefore, the factored form of the trinomial 2x²+7x-4 is (x+4)(2x-1).

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The state income tax owed on a $40,000 per year salary is $1,500.

What is income tax?

A tax levied against people or organizations (taxpayers) in relation to their income or profits is known as an income tax. (commonly called taxable income). Tax rates multiplied by taxable income are typically used to calculate income taxes. Tax rates might change depending on the taxpayer's attributes and source of income.

To calculate the state income tax owed on a $40,000 per year salary, we need to determine which progressive tax range it falls into and apply the corresponding tax rate.

Since $40,000 falls within the range of $10,001 - $50,000, we will use the tax rate of 5% for this portion of the income.

First, we need to calculate the amount of income within this range -

$40,000 - $10,000 = $30,000

Next, we calculate the amount of tax owed on this portion of the income -

$30,000 x 0.05 = $1,500

Therefore, the value is obtained as $1,500.

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We have verified that A^-1A = I and AA^-1 = I for both matrices.

To compute the inverse of a matrix, we can use the formula: A^-1 = 1/det(A) * adj(A), where det(A) is the determinant of the matrix A and adj(A) is the adjoint of the matrix A.

(a) A = [1 1; 1 -4]

det(A) = (1*-4) - (1*1) = -4 - 1 = -5

adj(A) = [-4 -1; -1 1]

A^-1 = 1/-5 * [-4 -1; -1 1] = [4/5 1/5; 1/5 -1/5]

(b) A = [2 1 1; 3 1 2; -1 3 -1]

det(A) = (2*(1*-1) - 1*(2*3) + 1*(-1*3)) - (1*(1*-1) - 1*(2*-1) + 1*(3*3)) = -6 - 3 - 3 - 9 = -21

adj(A) = [-1 -2 7; 5 1 -8; 2 5 -7]

A^-1 = 1/-21 * [-1 -2 7; 5 1 -8; 2 5 -7] = [1/21 2/21 -7/21; -5/21 -1/21 8/21; -2/21 -5/21 7/21]

To verify that A^-1A = I and AA^-1 = I, we can simply multiply the matrices and check if the result is the identity matrix.

For (a):

A^-1A = [4/5 1/5; 1/5 -1/5] * [1 1; 1 -4] = [1 0; 0 1] = I

AA^-1 = [1 1; 1 -4] * [4/5 1/5; 1/5 -1/5] = [1 0; 0 1] = I

For (b):

A^-1A = [1/21 2/21 -7/21; -5/21 -1/21 8/21; -2/21 -5/21 7/21] * [2 1 1; 3 1 2; -1 3 -1] = [1 0 0; 0 1 0; 0 0 1] = I

AA^-1 = [2 1 1; 3 1 2; -1 3 -1] * [1/21 2/21 -7/21; -5/21 -1/21 8/21; -2/21 -5/21 7/21] = [1 0 0; 0 1 0; 0 0 1] = I

Therefore, we have verified that A^-1A = I and AA^-1 = I for both matrices.

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Answer:

4

Step-by-step explanation:

Step-by-step explanation:

just ignore the % sign and answer :

is 1/2 equivalent to 50 ? yes or no ?

no, of course.

1/2 = 0.5

50 = 50

clearly they are different.

Sam is confused, because 50% = 1/2 = 0.5.

but 50% is NOT 1/2%

1/2% is half of 1%, which by itself is 1/50 of 50%.

1/2% = 1/50/2 of 50% = 1/100 of 50% =

= 0.01 × 0.5 = 0.005

Based on the given mean and standard deviation of Sarah's finishing times, we can estimate that approximately 68% of her races will have finishing times between 61.5 and 64.5 seconds.

The empirical rule, also known as the 68-95-99.7 rule, is a useful tool for estimating the percentage of data that falls within a certain number of standard deviations from the mean in a normal distribution.

In this case, Sarah's finishing times in the 400-meter dash are normally distributed with a mean of 63 seconds and a standard deviation of 1.5 seconds. To use the empirical rule, we need to first calculate the z-scores for the lower and upper bounds of the range we're interested in.

For the lower bound of 61.5 seconds:

z = (61.5 - 63) / 1.5 = -1

For the upper bound of 64.5 seconds:

z = (64.5 - 63) / 1.5 = 1

These z-scores tell us how many standard deviations are away from the mean each time. Using the empirical rule, we know that approximately 68% of the data falls within one standard deviation of the mean, 95% falls within two standard deviations, and 99.7% falls within three standard deviations.

Since the range we're interested in is within one standard deviation of the mean, we can estimate that approximately 68% of Sarah's finishing times will be between 61.5 and 64.5 seconds.

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The system of inequalities that describes the graph is given as follows:

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

In which:

For the lower bound of the inequality, we have that:

Hence:

y ≥ -4/3x + 8

4x/3 + y ≥ 8

4x + 3y ≥ 24.

For the upper bound of the inequality, we have that:

Hence:

y ≤ -5x/8 + 5

5x/8 + y ≤ 5

5x + 8y ≤ 40.

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Answer:

x = 5

Step-by-step explanation:

 5x - 7 = 3x + 3

- 3x        -3x

2x - 7 =         3

      +7           +7

 2x =              10

Divide 2 from both sides

x = 5

Answer: 10

Step-by-step explanation:

2x - 7 = 3

add 7 to both sides = 2x = 10

now to solve:

once u have 2x = 10

divide both sides by 2

x=5

To determine whether the two statement forms are equivalent, we need to create a truth table for each statement form and compare the results.

First, let's create a truth table for the statement form (p∧q)∨∼(p∨q):


 
   p
   q
   p∧q
   p∨q
   ∼(p∨q)
   (p∧q)∨∼(p∨q)
 
 
   T
   T
   T
   T
   F
   T
 
 
   T
   F
   F
   T
   F
   F
 
 
   F
   T
   F
   T
   F
   F
 
 
   F
   F
   F
   F
   T
   T
 

Next, let's create a truth table for the statement form (p∨∼q)∧(∼p∨q):


 
   p
   q
   ∼q
   ∼p
   p∨∼q
   ∼p∨q
   (p∨∼q)∧(∼p∨q)
 
 
   T
   T
   F
   F
   T
   T
   T
 
 
   T
   F
   T
   F
   T
   F
   F
 
 
   F
   T
   F
   T
   F
   T
   F
 
 
   F
   F
   T
   T
   T
   T
   T
 

Comparing the results of the two truth tables, we can see that the two statement forms are not equivalent. The statement form (p∧q)∨∼(p∨q) is true when both p and q are true or when both p and q are false. The statement form (p∨∼q)∧(∼p∨q) is true when both p and q are true or when both p and q are false, but it is also true when p is false and q is true. Therefore, the two statement forms are not equivalent.

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In the word problem, the time (in seconds) the ball was in the air is D)0.50 seconds.

What is word problem?

Word problems are often described verbally as instances where a problem exists and one or more questions are posed, the solutions to which can be found by applying mathematical operations to the numerical information provided in the problem statement. Determining whether two provided statements are equal with respect to a collection of rewritings is known as a word problem in computational mathematics.

Here expression which describes height is,

h(t)= [tex]-18t^2+3t+2[/tex]

Now h(t)=0 then,

=> [tex]-18t^2+3t+2=0[/tex]

=> [tex]18t^2-3t-2=0[/tex]

=> [tex]18t^2-3t=2[/tex]

=> 3t(6t-1)=2

=> 3t=2 , 6t-1=2

=> t=2/3 , 6t=3

=> t=2/3 , t=1/2

=> t= 0.5 seconds.

Hence  the time (in seconds) the ball was in the air is D)0.50 seconds.

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The solution of the function f(h.g)(x) will be 6x³ -3x² + 5. The correct option is C.

In mathematics, expression is defined as the relationship of numbers, variables, and functions using mathematical signs such as addition, subtraction, multiplication, and division.

The given functions are,

h(x) = 3x +5

g(x) = 2x³ - x ²

The value of the function f(h.g)(x) will be calculated as,

f(h.g)(x) = 3 ( 2x³ - x² ) + 5

f(h.g)(x) = 6x³ - 3x² + 5

Therefore, the solution of the function f(h.g)(x) will be 6x³ -3x² + 5. The correct option is C.

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Answer: Your welcome!

Step-by-step explanation:

This linear model tells us that, on average, for every additional square foot of area in a home, the selling price increases by 122.2 dollars. Therefore, this model suggests that the larger the area of a home, the higher the selling price of the home will be.

Answer:

Step-by-step explanation:

The volume of the cone is approximately 94.25π cubic cm.

To find the volume of a cone, we use the formula V = 1/3πr²h, where V is the volume, r is the radius of the base, and h is the height or depth of the cone. In this case, we know that the depth of the cone is 14 cm and the base radius is 9/2 cm.

First, we need to calculate the radius of the base in terms of cm, since the formula requires it. We are given that the base radius is 9/2 cm, so we can substitute this value for r:

r = 9/2 cm

Next, we need to calculate the volume of the cone using the formula. We know that the depth of the cone is 14 cm, so we can substitute this value for h:

V = 1/3πr²h

V = 1/3π(9/2)²(14)

V = 1/3π(81/4)(14)

V = 1/3π(1134/4)

V = 1/3π(283.5)

V = 94.25π

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To average a 90 on all three tests, you must score a 95 on the next test.

To find the score you need to average exactly a 90 on all three tests, you can use the formula for the mean (average) of a set of numbers:

Mean = (Sum of all numbers) / (Total number of numbers)

Let's call the score you need on the next test x. We can plug in the known values and solve for x:

90 = (81 + 94 + x) / 3

Multiply both sides by 3 to get rid of the fraction:

270 = 81 + 94 + x

Subtract 81 and 94 from both sides to isolate x:

95 = x

So, you need to score a 95 on the next test to average exactly a 90 on all three tests.

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The expression that is equivalent to [tex](\frac{x^2}{x^-4})^5[/tex] is x³⁰

From the question, we have the following parameters that can be used in our computation:

[tex](\frac{x^2}{x^-4})^5[/tex]

An equivalent expression is a different way of writing the same mathematical statement using equivalent mathematical operations or properties.

Evaluate the quotients using the law of indices

So, we have the following representation

(x⁶)⁵

Remove the bracket using the law of indices

So, we have the following representation

x³⁰

Hence, the solution to the expression is x³⁰

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Answer:

D

Step-by-step explanation:

The line touches the graph at 2 different points so it doesnt pass the verticle line test

On dividing (x³ + 7x² + 9x - 5) by (x + 4), we get -

h(x) = x² + 3x - 3 + 7/(x + 4).

Division algorithm states that -

Dividend = (Divisor x Quotient) + Remainder

Given is to find the remainder when -

(x³ + 7x² + 9x - 5) ÷ (x + 4)

We can write -

f(x) = (x³ + 7x² + 9x - 5)

g(x) = (x + 4)

So -

h(x) = f(x) ÷ g(x)

h(x) = (x³ + 7x² + 9x - 5) ÷ (x + 4)

h(x) = (x³ + 4x² + 3x² + 9x - 5)/(x + 4)

h(x) = x² + (3x² + 9x - 5)/(x + 4)

h(x) = x² + 3x + (-3x - 5)/(x + 4)

h(x) = x² + 3x - 3 + 7/(x + 4)

Therefore, on dividing (x³ + 7x² + 9x - 5) by (x + 4), we get -

h(x) = x² + 3x - 3 + 7/(x + 4).

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Answer: 5x + 2y = 6

Step-by-step explanation:

The standard form is Ax + By = C

Subtract 5x from each side:

- 5x - 2y = - 6

The first term in the standard form must be positive, so multiply by -1 to change the sign.

5x + 2y = 6

Hope this helps!

Answer:

10

Step-by-step explanation:

Answer:

10

Step-by-step explanation:

1. 4(f+k)(x)=4(2x^2 - 5x - 8 + 2x + 4) = 8x^2 - 20x - 32.

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Lucky duck probabilities include:

A duck with a number:

Every duck has a number, so the probability of choosing a duck with a number is certain (1/1 or 100%).

A duck with a number greater than 10:

is 2/12 or 1/6, since there are 2 ducks with numbers greater than 10 out of a total of 12 ducks.

Duck number 4:

There is only one duck with the number 4, so the probability of choosing this duck is 1/12.

A duck with sunglasses:

There are no ducks with sunglasses so the probability is impossible.

A duck with a hat:

We don't know how many ducks wear hats, so we cannot determine the probability.

An even-numbered duck:

There are 6 even-numbered ducks (2, 4, 6, 8, 10, 12) out of 12 ducks in total, so the probability of choosing an even-numbered duck is 6/12, which simplifies to 1/2.

A duck with a number less than 7:

There are 6 ducks with a number less than 7 (1, 2, 3, 4, 5, 6) out of 12 ducks in total, so the probability of choosing a duck with a number less than 7 is 6/12, which simplifies to 1/2.

A duck with a mustache:

There are no ducks with mustaches, so the probability of getting a duck with a mustache is impossible, 0.

A duck with a bow tie:

Ducks with bowties are 8, so the probability of choosing a duck with bowtie is likely 8/12, 2/3

A duck with a number lower than 25:

All ducks have a number lower than 25, so the probability of choosing a duck with a number lower than 25 is certain (1).

A duck with a number greater than 5:

There are 7 ducks with a number greater than 5 (6, 7, 8, 9, 10, 11, 12) out of 12 ducks in total, so the probability of choosing a duck with a number greater than 5 is 7/12.

A duck with number that's a multiple of 3:

There are 4 ducks with a number that's a multiple of 3 (3, 6, 9, 12) out of 12 ducks in total, so the probability of choosing a duck with a number that's a multiple of 3 is 4/12, which simplifies to 1/3.

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Answer:

the answer is B. 2x(5x+1)

The difference between the two groups is likely due to chance and the two groups likely have the same mean.

To conduct the appropriate test of significance for a research situation, you must first identify whether you need to use a one-tailed or two-tailed test. A one-tailed test is used when you are looking to see if the mean of one group is greater or less than the mean of another group. A two-tailed test is used when you are testing the null hypothesis that the two groups have the same mean.

Once you have identified the type of test, you must determine if it is a one or two sample test. A one sample test is used when you are comparing the mean of one group to a known population mean, whereas a two sample test is used when you are comparing the means of two separate groups.

Next, you must select the appropriate alpha level. Alpha levels are a measure of the significance of the test and refer to the probability of rejecting the null hypothesis when it is actually true. Generally, an alpha level of 0.05 is used in research settings.

Once you have selected the appropriate test and alpha level, you can make a decision about the test significance. This is done by comparing the calculated test statistic to the critical value in the test statistic table. If the calculated test statistic is larger than the critical value, the test is statistically significant and the null hypothesis can be rejected. If the calculated test statistic is smaller than the critical value, the test is not statistically significant and the null hypothesis cannot be rejected.

Finally, you must interpret the results of the test. If the test is statistically significant, it means that the difference between the groups is not likely due to chance, and therefore the two groups are likely to have different means. If the test is not statistically significant, it means that the difference between the two groups is likely due to chance and the two groups likely have the same mean.

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A. Amplitude: 4,  Asymptotes: None,  Complete Period:  [tex]\(\frac{2\pi}{5}\)[/tex],  Period: [tex]\(2\pi/5\)[/tex],  Phase Shift:  [tex]\(\frac{\pi}{5}\)[/tex].
B. Amplitude: 1, Asymptotes:  [tex]\(x=\frac{\pi}{2}+\frac{2\pi}{3}n\)[/tex], Complete Period:  [tex]\frac{2\pi}{3}\)[/tex],     Period:  [tex]\(2\pi/3\)[/tex],  Phase Shift: [tex]\(\frac{\pi}{6}\)[/tex].

To find the amplitude, asymptotes, complete period, period, and phase shift for each of the given trigonometric functions, we need to use the standard form of the trigonometric functions:[tex]\[f(x)=A\sin(Bx+C)+D\][/tex] and [tex]\[g(x)=A\sec(Bx+C)+D\][/tex]

For function f(x), we have:
A = 4, B = 5, C = -π, and D = 0

The amplitude is |A| = |4| = 4

The period is  [tex]\(\frac{2\pi}{|B|}[/tex] = [tex]\frac{2\pi}{5}\)[/tex]

The phase shift is [tex]\(-\frac{C}{B}[/tex] = [tex]-\frac{-\pi}{5}[/tex] = [tex]\frac{\pi}{5}\)[/tex]

There are no asymptotes for the sine function.

For function g(x), we have:
A = -1, B = 3, C = -π/2, and D = 0

The amplitude is |A| = |-1| = 1

The period is [tex]\(\frac{2\pi}{|B|}[/tex] = [tex]\frac{2\pi}{3}\)[/tex]

The phase shift is [tex]\(-\frac{C}{B}[/tex] = [tex]-\frac{-\pi/2}{3}[/tex] = [tex]\frac{\pi}{6}\)[/tex]

The asymptotes occur when the cosine function is equal to zero, so the asymptotes are at  [tex]\(x=\frac{\pi}{2}+\frac{2\pi}{3}n\)[/tex] , where n is an integer.

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The perimeter of triangle QRS 60. Therefore, the correct answer is C: 60.

The perimeter of a triangle is the sum of the lengths of its sides. Therefore, the perimeter of triangle QRS is 14 + 19 + t.

Since t is the cube of an integer, we can write t as x³, where x is an integer. The perimeter of the triangle is then 14 + 19 + x³.

We also know that t is the longest side of the triangle, so it must be greater than both 14 and 19. This means that x³ must be greater than 19, so x must be greater than or equal to 3.

If x is 3, then t is 3³, or 27. The perimeter of the triangle is then 14 + 19 + 27, or 60.

Therefore, the correct answer is C: 60.

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Answer: a. To calculate the crude mortality rate in NJ in 2017, we need to divide the total number of deaths (74,846) by the total population (8,888,543) and then multiply by 1,000 to express the result per 1,000 population.

Crude Mortality Rate = (Total deaths / Total population) x 1,000

Crude Mortality Rate = (74,846 / 8,888,543) x 1,000

Crude Mortality Rate = 8.42 per 1,000 population

b. To calculate the cause-specific mortality rate due to diabetes in NJ in 2017, we need to divide the number of deaths due to diabetes (1,908) by the total population and then multiply by 1,000 to express the result per 1,000 population.

Cause-specific Mortality Rate due to Diabetes = (Deaths due to diabetes / Total population) x 1,000

Cause-specific Mortality Rate due to Diabetes = (1,908 / 8,888,543) x 1,000

Cause-specific Mortality Rate due to Diabetes = 0.21 per 1,000 population

c. To calculate the case-fatality percent of diabetes, we would need to know the number of people diagnosed with diabetes who died during the same time period. Specifically, the case-fatality percent of diabetes would be calculated by dividing the number of people with diabetes who died (numerator) by the total number of people with diabetes (denominator) and then multiplying the result by 100 to express the percentage. Therefore, the additional variable required is the number of people with diabetes in the population.

Step-by-step explanation:

The area of the hexagon is given by A = 585 units²

Six equilateral triangles make create a regular hexagon, which has six congruent sides and angles. The following is the formula to get the area of a regular hexagon.

Area of a hexagon A = 3 (√3)/ 2 ) a²

where, a represent the length of a side of the regular hexagon

Given data ,

Let the area of the hexagon be represented as A

Now , the value of A is

Let the side length of the hexagon be a = 15

Now , area of a hexagon A = 3 (√3)/ 2 ) a²

On simplifying , we get

The area of hexagon A = 3 (√3)/ 2 ) ( 15 )²

The area of hexagon A = 584.56715 units²

The area of hexagon A = 585 units²

Therefore , the value of A is 585 units²

Hence , the area of the hexagon is A = 585 units²

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