Rewrite each equation without absolute value for the given conditions. y= |x+5| if x>-5

Answer:

Use slope formula,m = StartFraction y 2 minus y 1 Over x 2 minus x 1 EndFraction, to find the slope of a line that passes through the points (–3, 8) and (4, –6).

m =

✔ -2

Use slope-intercept form, y = mx + b, to find the y-intercept (b) of the line.

b =

✔ 2

What is the new equation written in slope-intercept form, y = mx + b?

✔ y = -2x + 2

Step-by-step explanation:

Answer:

-11 YARDS

Step-by-step explanation:

Answer: -6

Step-by-step explanation:

Answer:

y = 5x - 1

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Calculate m using the slope formula

m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

with (x₁, y₁ ) = (1, 4) and (x₂, y₂ ) = (2, 9)

m = \(\frac{9-4}{2-1}\) = \(\frac{5}{1}\) = 5 , then

y = 5x + c ← is the partial equation

To find c use any ordered pair from the table and substitute into the partial equation.

Using (3, 14 ) , then

14 = 15 + c ⇒ c = 14 - 15 = - 1

y = 5x - 1 ← equation of line

Answer:

distance = 7.07 units

Step-by-step explanation:

x difference = 7

y difference = -1

using the Pythagorean theorem:

7² + -1² = d²

d² = 49 + 1 = 50

d = 7.07

Answer:

7.1

Step-by-step explanation:

distance between the x is 7 and y is 1

And to find the hypotenuse, you use the quadratic formula, 7^2 + 1^2 = c^2

c=50

and take the square root, which is 7.071, rounds to 7.1

Answer:

-45

Step-by-step explanation:

i hope this helps...

Answer: John walks a total of 360 yards from school.

Step-by-step explanation:

Let's represent the total distance John walks from school as "x".

According to the problem, John has already walked 15% of the way, which can be written as:

0.15x

We also know that he has walked 54 yards so far, which means:

0.15x = 54

To find the total distance John walks from school, we can solve for "x" by dividing both sides of the equation by 0.15:

x = 54 ÷ 0.15

x = 360

Therefore, John walks a total of 360 yards from school.

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Answer:

Step-by-step explanation:

Answer: ever got the answer?

Step-by-step explanation:

Answer:

b = 19

Step-by-step explanation:

To make it short and sweet, since one angle is 45 degrees and one angle is 90 degrees, the unknown angle is 45 degrees also. That makes it an isosceles triangle with both legs equal.

b = 19

Using it's concept, it is found that the probability that the coin shows tails and he rolls a 5 is of \(\frac{1}{12}\).

A probability is given by the number of desired outcomes divided by the number of total outcomes.

In this problem, the coin has two outcomes, one of which is tails, while the number cube has six outcomes, one of which is five. Since the coin and the number cube are independent, we just multiply the probabilities, hence:

\(p = \frac{1}{2} \times \frac{1}{6} = \frac{1}{12}\)

The probability that the coin shows tails and he rolls a 5 is of \(\frac{1}{12}\).

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Sampling variations refers to the fact that some samples represent populations well and some do not.

The correct answer is an option (D)

Weknow that sample variability is nothing but the increasing or decreasing sample sizes that leads to changes in the variability of samples.

For exa., a sample size of 50 people taken from the same population of 20000 will give you a very different result than a sample size of 300 people.

Sampling variation is simply the variation in a statistic from sample to sample.

It is nothing but how much an estimate varies between samples.

The common measure of sampling variability are variance (σ²) and standard deviation (σ).

Thus sampling variation is nothing but  the fact that some samples represent populations well and some do not.

The correct answer is an option (D)

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Answer:

15

Step-by-step explanation:

82 + (7s - 7) = 180

   - subtract 82 from both sides

7s - 7 = 98

   - add 7 to both sides

7s = 105

   - divide both sides by 7

s = 15

Given statement solution is :- The solutions for the Quadratic equation -2p² - 5p + 1 = 7p² + p are:

p₁ ≈ -0.207

p₂ ≈ -1.626

To solve the equation -2p² - 5p + 1 = 7p² + p, we can rearrange the terms to bring all the terms to one side and set the equation equal to zero:

-2p² - 5p + 1 - (7p² + p) = 0

Now, simplify the equation by combining like terms:

-2p² - 5p + 1 - 7p² - p = 0

Combine the p² terms:

-2p² - 7p² - 5p - p + 1 = 0

-9p² - 6p + 1 = 0

Now, we can solve this quadratic equation using the quadratic formula, which is given by:

p = (-b ± √(b² - 4ac)) / (2a)

In this equation, a = -9, b = -6, and c = 1. Substituting these values into the formula, we can find the solutions for p:

p = (-(-6) ± √((-6)² - 4(-9)(1))) / (2(-9))

Simplifying further:

p = (6 ± √(36 + 36)) / (-18)

p = (6 ± √(72)) / (-18)

p = (6 ± 6√(2)) / (-18)

Now, we can simplify the expression and find the two solutions for p:

p₁ = (6 + 6√(2)) / (-18)

p₂ = (6 - 6√(2)) / (-18)

Simplifying the expressions further:

p₁ = (1 + √(2)) / (-3)

p₂ = (1 - √(2)) / (-3)

Therefore, the solutions for the Quadratic equation -2p² - 5p + 1 = 7p² + p are:

p₁ ≈ -0.207

p₂ ≈ -1.626

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The choice which is closest to the y intercept of the function is Choice 1); 10

According to the question;

The y-intercept is the value of y when x = 0.

In essence;

.y = 10e⁰ + 1

therefore, the value which is closest to the y-intercept is 10.

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Critical angle for the total internal reflection icrit, β =  78.28⁰

Critical angle for the total internal reflection crit, α = 17,22⁰

We have the refractive index of core, \(n_c_o_r_e\) = 1.46

We have the refractive index of clad , \(n_c_l_a_d\) = 1.4

Critical angle can be defined as the incidence angle which results in the refraction angle being equal to  at that angle of incidence.

For Total Internal Reflection to occur, the incidence angle must be greater than the critical angle.

We know that the critical angle, θ is given by:

sinθ = \(\frac{n_c_l_a_d}{n_c_o_r_e}\)

sinθ = \(\frac{1.4}{1.46}\)

sinθ = 0.959 = sin⁻¹(0.979) = 78.28⁰

β = θ = 78.28⁰

Now, for α:

\(\frac{sin(90-\alpha )}{sin\alpha } = \frac{1}{n_c_o_r_e}\)

sinα = sin(90⁰-78.28⁰) × 1.46

sinα = sin(11.72⁰) × 1.46

α = sin⁻¹(0.296)

α = 17,22⁰

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Critical angle for total internal reflection icrit β = 78.28⁰

Critical angle for total internal reflection crit, α = 17.22⁰

The refractive index of the core is ncore = 1.46.

The refractive index of clad is nclad = 1.4.

We know that the critical angle, θ is given by:

sinθ = nclad/ ncore

sinθ = 1.4/1.46

sinθ = 0.959

sin⁻¹(0.979) = 78.28⁰

β = θ = 78.28⁰

Now, for α:

sin(90- α) / sin α = 1 / ncore

sinα = sin(90⁰-78.28⁰) × 1.46

sinα = sin(11.72⁰) × 1.46

α = sin⁻¹(0.296)

α = 17.22⁰

Critical angle for icrit β = 78.28⁰

Critical angle for crit α = 17.22⁰

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1. The inequality that can be used to determine d, the maximum number of days Melanie can afford to rent a car while staying within her budget is 33.27d + 3.5 ≤ 120.

2. For the second question, the correct inequality is D. 440 ≥ 25 + 62.12d.

Inequality is a mathematical expression that states that two values are not equal.

Inequality expressions employ one of these signs:  less than (<), greater than (>), less than or equal (≤), greater than or equal (≥), and the not equal symbol (≠).

Rental charge per day = $33.27

Rental charge per mile = $0.07

The number of miles Melanie intends to drive = 50 miles

The total rental charge for 50 miles = $3.50 ($0.07 x 50)

Melanie's budget for the rental = $120

33.27d = total rental charge for d days.

0.07m = total rental charge for m miles.

0.07m = 0.07 x 50 = 3.5

Budget constant: ≤ 120

Therefore, the inequality is:

= 33.27d + 3.5  ≤ 120

Thus, the inequality that can be used to determine d, the maximum number of days is 33.27d + 3.5 ≤ 120.

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The lengths of a,b,c, and d have been derived and expressed in terms of trigonometric ratios below.

As we can see from the figure itself, the value of a = sin θ

This can be written as such because = sin θ = Perpendicular / Hypotenuse

Here, the perpendicular = a and hypotenuse = radius = 1

= sin θ = a

The value of b = tan θ

This is because tan θ = perpendicular/base

Here, the base = radius = 1

= tan θ = b  

The value of c = sec θ

This is because sec θ = Hypotenuse / Base

= sec θ = c

The value of d = cos θ

This is because cos θ = Base / Hypotenuse

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Answer:

30x - 18y + 24

Step-by-step explanation:

When the distributive property is in play, you multiply all the numbers in the parenthesis by the number that's right next to it. In this case, you're multiplying 6 to all of the numbers in the paranthesis (5x - 3y +4).

For the matrix the true statement is given by option d. Both A and B are false.

Let's analyze each statement of the matrix as follow,

A) If A is a 3 times 5 matrix and T is a transformation defined by T(x) = Ax, then the domain of T is R⁵.

This statement is false.

The domain of the transformation T is not R⁵.

The domain of T is determined by the dimensionality of the vectors x that can be input into the transformation.

Here, the matrix A is a 3 times 5 matrix, which means the transformation T(x) = Ax can only accept vectors x that have 5 elements.

Therefore, the domain of T is R⁵, but rather a subspace of R⁵.

B) If A is a 3 times 2 matrix, then the transformation x right arrow Ax cannot be onto.

This statement is also false.

The transformation x → Ax can still be onto (surjective) even if A is a 3 times 2 matrix.

The surjectivity of a transformation depends on the rank of the matrix A and the dimensionality of the vector space it maps to.

It is possible for a 3 times 2 matrix to have a rank of 2,

and if the codomain is a vector space of dimension 3 or higher, then the transformation can be onto.

Therefore, as per the matrix both statements are false, the correct answer is d. Both A and B are false.

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The above question is incomplete, the complete question is:

Which of the following best characterizes the following statements:

A) If A is a 3 times 5 matrix and T is a transformation defined by T(x) = Ax, then the domain of T is R^5

B) If A is a 3 times 2 matrix, then the transformation x right arrow Ax cannot be onto

a. Only A is true

b. Only B is true

c. Both A and B are true

d. Both A and B are false

Answer:

e. -490

Step-by-step explanation:

-318+3= -315

-315/9= -35

So that would mean m= -35

-35*14= -490

Answer:

1x8 =8

Step-by-step explanation:

1x8=8

An expression is defined as a set of numbers, variables, and mathematical operations. An expression that is equal to 8 when simplified is |-8|.

In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.

PEMDAS is an acronym that refers to the sequence of operations to be employed when solving equations or expressions with multiple operations. PEMDAS is an acronym that stands for P-Parenthesis, E-Exponents, M-Multiplication, D-Division, A-Addition, and S-Subtraction.

A few of the expressions that are equal to 8 when simplified are,

Hence, an expression that is equal to 8 when simplified is |-8|.

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The area of the kitchen in square feet is 132\(ft^{2}\)

To find the area of the rectangular kitchen, we need to multiply the length by the width.

The length of the kitchen can be found by subtracting the x-coordinates of the two points on the same vertical side. So, the length is 8 - (-3) = 11 feet.

The width of the kitchen can be found by subtracting the y-coordinates of the two points on the same horizontal side. So, the width is 4 - (-8) = 12 feet.

Therefore, the area of the kitchen is:

Area = Length x Width = 11 ft x 12 ft = 132 square feet

So the answer is 132\(ft^{2}\).

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Option D is the correct answer (We are 95% confident that the proportion of coworkers who went on a vacation last year away from home for at least a week is between 50% and 66%)

Since the confidence interval is calculated for population proportion (parameter) based on sample data.

Because the figure is based on a sample of the population you are investigating; there is always uncertainty when you generate an estimate in statistics, whether it be a summary statistic or a test statistic. The confidence interval is the range of values. If you repeated your experiment or resampled the population in the same manner, you would anticipate your estimate to fall within a specific proportion of the time. The alpha value determines the confidence level, the proportion of times you anticipate being able to recreate an estimate between the top and lower boundaries of the confidence interval.

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The break-even point is the level of output at which total revenue (TR) equals total cost (TC). In this case, with TR(x) = 20x and TC(x) = 120 + 10x, we need to find the value of x where TR(x) = TC(x).

To find the break-even point, we set TR(x) equal to TC(x) and solve for x.
TR(x) = TC(x) can be expressed as:
20x = 120 + 10x
Simplifying the equation, we combine like terms:
20x - 10x = 120
10x = 120
To isolate x, we divide both sides of the equation by 10:
x = 12
Therefore, the break-even point occurs when x is equal to 12. At this level of output, the total revenue is equal to the total cost.

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The commission he earned last month was amount of $360.

The commission is determined by the product of the commission rate and the total sales.

A salesman receives a 6% commission on all merchandise sold.

He sold $6000 in merchandise last month.

Salesman earns 6% = 6/100 = 0.06

Now, we have to evaluate 6% of $6000

= 0.06 x 6000

Apply the multiplication operation, and we get

= 360$

Thus, the commission he earned last month was the amount of $360.

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The question seems incomplete, the complete question would be as:

A salesman earns 6% commission on all the merchandise that he sells. Last month he sold $6000 worth of merchandise. How much commission (in dollars) did he earn last month?

Answer:

Julio's number is 31.

Step-by-step explanation:

Okay, so -70 divided by -5 is 14.

14 plus 17 equals 31.

If you subtract 17 from 31, you get 14.

Then, if you multiply 14 times -5, you get -70.

Answer: 2

sqrt 41

Step-by-step explanation:

distance formula is just d=√((x2 – x1)² + (y2 – y1)²)

√(-2+8)^2+(-5-3)^2

√(-10)^2+(-8)^2

√100+64

2√41

The value of a is 30.1

The denominators of fractions must match in order to divide them. The numerators' quotient will be the quotient.

The phrase provided is,

a/12 = 30.1/12

We can directly cut the values if the denominator is the same. Since there is a 12 in the denominator on both the right and left sides in this case, remove 12 from both sides.

Thus, a = 30.1

Likewise, you can act in such manner,

a = (30.1 * 12) / 12

a = 30.1

Here, we take the right side of the left side denominator 12 and cancel 12.

Hence, A has a value of 30.1

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The probabilities are calculated assuming independence of each call and that the success probability remains constant throughout the calls.

a. The probability that, among five voters the student calls, exactly one supports candidate Smith can be calculated using the binomial probability formula. With a success probability of 64% (0.64) and exactly one success (k = 1) out of five trials (n = 5), the probability can be calculated as follows:

\[

P(X = 1) = \binom{5}{1} \times (0.64)^1 \times (1 - 0.64)^4

\]

The calculation results in approximately 0.369, or 36.9%.

b. The probability that, among five voters the student calls, at least one supports candidate Smith can be calculated as the complement of the probability that none of the voters support Smith. Using the binomial probability formula, with a success probability of 64% (0.64) and no success (k = 0) out of five trials (n = 5), the probability can be calculated as follows:

\[

P(X \geq 1) = 1 - P(X = 0) = 1 - \binom{5}{0} \times (0.64)^0 \times (1 - 0.64)^5

\]

The calculation results in approximately 0.997, or 99.7%.

c. The probability that the first voter supporting candidate Smith is reached on the fifth call can be calculated as the probability of not reaching a Smith supporter in the first four calls (0.36) multiplied by the probability of reaching a Smith supporter on the fifth call (0.64):

\[

P(\text{{First Smith Supporter on Fifth Call}}) = (1 - 0.64)^4 \times 0.64

\]

The calculation results in approximately 0.014, or 1.4%.

d. The probability that the third voter supporting candidate Smith is reached on the fifth call can be calculated as the probability of reaching two Smith supporters in the first four calls (0.64 for the first call, 0.36 for the second call, and 0.36 for the third call) multiplied by the probability of reaching a Smith supporter on the fifth call (0.64):

\[

P(\text{{Third Smith Supporter on Fifth Call}}) = (0.64)^2 \times (1 - 0.64) \times 0.64

\]

The calculation results in approximately 0.147, or 14.7%.

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The probabilities are calculated assuming independence of each call and that the success probability remains constant throughout the calls. The calculation results in approximately 0.369, or 36.9%.

a. The probability that, among five voters the student calls, exactly one supports candidate Smith can be calculated using the binomial probability formula. With a success probability of 64% (0.64) and exactly one success (k = 1) out of five trials (n = 5), the probability can be calculated as follows:

[P(X = 1) = \binom{5}{1} \times (0.64)^1 \times (1 - 0.64)^4\]

The calculation results in approximately 0.369, or 36.9%.

b. The probability that, among five voters the student calls, at least one supports candidate Smith can be calculated as the complement of the probability that none of the voters support Smith. Using the binomial probability formula, with a success probability of 64% (0.64) and no success (k = 0) out of five trials (n = 5), the probability can be calculated as follows:

[P(X \geq 1) = 1 - P(X = 0) = 1 - \binom{5}{0} \times (0.64)^0 \times (1 - 0.64)^5\]

The calculation results in approximately 0.997, or 99.7%.

c. The probability that the first voter supporting candidate Smith is reached on the fifth call can be calculated as the probability of not reaching a Smith supporter in the first four calls (0.36) multiplied by the probability of reaching a Smith supporter on the fifth call (0.64):

\[

P(\text{{First Smith Supporter on Fifth Call}}) = (1 - 0.64)^4 \times 0.64

\]

The calculation results in approximately 0.014, or 1.4%.

d. The probability that the third voter supporting candidate Smith is reached on the fifth call can be calculated as the probability of reaching two Smith supporters in the first four calls (0.64 for the first call, 0.36 for the second call, and 0.36 for the third call) multiplied by the probability of reaching a Smith supporter on the fifth call (0.64):

\[

P(\text{{Third Smith Supporter on Fifth Call}}) = (0.64)^2 \times (1 - 0.64) \times 0.64

\]

The calculation results in approximately 0.147, or 14.7%.

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