What is the correct answer?

a:

Just divide both sides by 7. Since 7 is positive, you don't need to change the inequality sign:

[tex]7j>77\iff j>11\}[/tex]

In set notation, we write

[tex]\{j \in \mathbb{R}\ :\ j>11[/tex]

b:

Subtract 9 from both sides:

[tex]17\leq x+9 \iff 8\leq x[/tex]

In set notation, we write

[tex]\{x \in \mathbb{R}\ :\ x\geq 8\}[/tex]

To calculate taxes for each scenario, use the progressive tax rate schedules to find the correct tax bracket, apply the marginal tax rate, add any base tax amount, and complete the calculation for the head of household, single person, and married taxpayers filing jointly.

To calculate the amount of taxes for the given situations, we use the tax rate schedules provided. For each scenario, the tax is calculated based on the income brackets and the corresponding tax rates in the tax table, which align with a progressive tax system. Detailed calculations are needed with step-by-step explanations for accuracy.

The mentioned tax brackets and rates are based on example tax tables; the actual calculations would depend on the specific tax brackets and rates set forth by the IRS for the given tax year.

Answer:

B. 7/2, -8/3

Step-by-step explanation:

Move all the terms to the left side and set them equal to zero.  Then set each factor equal to zero.

Answer:

It's prime

Step-by-step explanation:

So there are no factors except 1 and 17

Answer:

x³ + 4 x² + x - 6

Step-by-step explanation:

( x - 1 ) ( x + 2 ) ( x + 3 )

( x - 1 ) ( x + 2 ) = x² + 2 x - 1 x - 2 = x² + x - 2

( x² + x - 2 ) ( x + 3 ) = x³ + 3 x² + x² + 3 x - 2 x - 6 = x³ + 4 x² + x - 6

The expression (x-1)(x+2)(x+3) can be written as x³ + 4x² + x—6 after multiplication of the expression.

It is defined as the combination of constants and variables with mathematical operators.

We have:

= (x-1)(x+2)(x+3)

After multiplying first and second terms:

[tex]\rm =\left(x^2+x-2\right)\left(x+3\right)[/tex]

Again multiplying:

[tex]\rm =x^3+4x^2+x-6[/tex]

Thus, the expression (x-1)(x+2)(x+3) can be written as x³ + 4x² + x—6 after multiplication of the expression.

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Answer:

Step-by-step explanation:

Weren't there possible answer choices?  Whenever there are, would you please share them.  Thank you.

n/4 - 13 could be written "13 less than one quarter of the number n."

Answer:

(x - 5)(2x + 3)

Step-by-step explanation:

To factorise the quadratic

Consider the factors of the product of the x² term and the constant term which sum to give the coefficient of the x- term

product = 2 × - 15 = - 30 and sum = - 7

The factors are - 10 and + 3

Use these factors to split the x- term

2x² - 10x + 3x - 15 ( factor the first/second and third/fourth terms )

= 2x(x - 5) + 3(x - 5) ← factor out (x - 5) from each term

= (x - 5)(2x + 3)

The factorization of the quadratic expression is presented as follows;

2·x² - 7·x - 15 is  (2·x + 3)·(x - 5)

A quadratic expression is an expression that can be presented in the form a·x² + b·x + c, where a ≠ 0, and a, b, and c are numbers.

In order to factorize the quadratic expression 2·x² - 7·x - 15, it is required to find two binomials with a product equivalent to the expression is to be found

The binomial can be found from the numbers p and q such that p + q = -7 and p·q = -30 (The product of the leading coefficient and the constant term)
A possible pair of such numbers is p = -10 and q = 3. Therefore, we get;

2·x² - 7·x -15 = 2·x² + (3·x - 10·x) - 15

The first two terms and the last two terms can be grouped and each group factorized separately as follows;

2·x² + (3·x - 10·x) - 15 = (2·x² + 3·x) +  (-10·x - 15)

x·(2 + 3) - 5·(2·x + 3)

The above expression can be further factorized by taking out the common factor (2·x + 3) as follows;

x·(2 + 3) - 5·(2·x + 3) = (2·x + 3)·(x - 5)

Therefore, the factored expression is; 2·x² - 7·x - 15 = (2·x + 3)·(x - 5)

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Answer:

[tex]\frac{2\sqrt{2} }{3}[/tex]

Step-by-step explanation:

The sine of an angle is defined as the ratio between the opposite side and the hypotenuse of a given right-angled triangle;

sin x = ( opposite / hypotenuse)

The opposite side to the angle x is thus 1 unit while the hypotenuse is 3 units. We need to determine the adjacent side to the angle x. We use the Pythagoras theorem since we are dealing with right-angled triangle;

The adjacent side would be;

[tex]\sqrt{9-1}=\sqrt{8}=2\sqrt{2}[/tex]

The cosine of an angle is given as;

cos x = (adjacent side / hypotenuse)

Therefore, the cos x would be;

[tex]\frac{2\sqrt{2} }{3}[/tex]

Answer:

[tex]cos(x) =\±2\frac{\sqrt{2}}{3}[/tex]

Step-by-step explanation:

We know that [tex]sen(x) =\frac{1}{3}[/tex]

Remember the following trigonometric identities

[tex]cos ^ 2(x) = 1-sin ^ 2(x)[/tex]

Use this identity to find the value of cosx.

If [tex]sen(x) =\frac{1}{3}[/tex] then:

[tex]cos ^ 2(x) = 1-(\frac{1}{3})^2[/tex]

[tex]cos ^ 2(x) =\frac{8}{9}[/tex]

[tex]cos(x) =\±\sqrt{\frac{8}{9}}[/tex]

[tex]cos(x) =\±2\frac{\sqrt{2}}{3}[/tex]

Answer:

1

Step-by-step explanation:

0 Triangles satisfy the given condition.

What is the triangle inequality?

Triangle inequality theorem that the sum of any two sides of a triangle is greater than or equal to the third side; in symbols, a + b ≥ c.

In this question:

a,b and A are three sides of triangle.

a=14

b=2 and

A=66

In this triangle

Therefore, no such triangle with given dimension can exist.

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Answer:

991 J

Step-by-step explanation:

At the bottom of the swing all of the potential energy has been converted to kinetic energy (assuming a lossless system).

Answer:

991 J

Step-by-step explanation:

At the highest point, an object has maximum potential energy and no kinetic energy. And at its lowest point, an object has maximum kinetic energy and no potential energy. All of the potential energy it had was converted into kinetic.

Answer:

48 miles

Step-by-step explanation:

1 Kilometer = 0.6 miles

80 kilometers = X miles

1 kilometer/0.6 miles = 80 kilometers/X miles

then cross multiply the ratio

X (1) = 80 (0.6)

X=48 miles

Answer:

48

Step-by-step explanation:

Answer:

C.

Step-by-step explanation:

Answer: 53 inches

Step-by-step explanation:

so to figure this out..

1. split the shape. there will be a 6 by 8 rectangle and a Height of 2 inches and the length of 5 inch triangle.

2.then find the area of 6 * 8 equals 48

3.Then find the area of the triangle. 5 * 2 equals 10. then  Divide 10 / 2 your answer will be 5

4.Then  add 48 and 5 together your answer will be 53

Answer:

see explanation

Step-by-step explanation:

Using the cosine addition identity

cos(x + y) = cosxcosy - sinxsiny

and cos([tex]\frac{\pi }{2}[/tex]) = 0, sin([tex]\frac{\pi }{2}[/tex]) = 1

cos(x + [tex]\frac{\pi }{2}[/tex])

= cosxcos([tex]\frac{\pi }{2}[/tex]) - sinxsin([tex]\frac{\pi }{2}[/tex])

= cosx × 0 - sinx × 1

= 0 - sinx

= - sinx

To obtain the graph of the function y = |x+2| we have to make a table of values of x to find the values of y. The absolute value or modulus of a real number is its numerical value without care its sign. For example, the absolute value of |4| and |-4| is 4.

In order to make a graph we are going to use the values (-3, -2, -1, 0, 1, 2, 3) for x.

x = -3

y = |-3 + 2| = |-1| = 1

x = -2

y = |-2 + 2| = |0| = 0

x = -1

y = |-1 + 2| = |1| = 1

x = 0

y = |0 + 2| = |2| = 2

x = 1

y = |1 + 2| = |3| = 3

x = 2

y = |2 + 2| = |4| = 4

x = 3

y = |3 + 2| = |5| = 5

 x   ║   y

-3        1

-2        0

-1         1

 0        2

 1         3

 2        4

 3        5

Obtaining the graph shown in the image attached.

.

Answer:

the forth one

Step-by-step explanation:

The answer above is right

A variable in mathematical terms is said to be Independent, if it's value does not depend on other variable.

For, example

 y=x²

Here , you can take any one among, x and y as independent and other as Dependent to get value of other.

For, example

 x=2, gives y=4.

So,variable y is dependent on variable x.So, y is Dependent and x is Independent.

Now, Among the given options

 The Naturally Occuring product found on earth are Independent ,and Man made product which is a combination of Natural and Human beings are Dependent.

⇒Option A

Gasoline

⇒Option F

Oil

Gasoline, tires, and oil are the independent variables from the given options.

The independent variables are the ones that can be directly controlled or manipulated in an experiment or analysis.

The independent variables would typically be:

Gasoline: The amount of gasoline can be controlled by choosing how much to put in the vehicle.

Tires: The type and condition of tires can be chosen and changed.

Oil: The choice and frequency of oil changes can be controlled.

Hence, the independent variables are gasoline, tires and oil.

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Answer:

The radius of the aquarium tank is [tex]8.25\ ft[/tex]

Step-by-step explanation:

we know that

Applying the Tangent Secant Theorem

[tex]DC^{2}=AC*8[/tex]

we have that

[tex]AC=(D+8)\ ft[/tex]

[tex]DC=14\ ft[/tex]

substitute

[tex]14^{2}=(D+8)*8[/tex]

[tex]196=8D+64[/tex]

Solve for D

[tex]8D=196-64[/tex]

[tex]8D=132[/tex]

[tex]D=16.5\ ft[/tex]

Find the radius

The radius is half the diameter

[tex]r=16.5/2=8.25\ ft[/tex]

Answer:

8.25

Step-by-step explanation:

DC = 14ft

AC = 8ft + the diametre

Lets use d for diametre

The equation we are using is the Segments of Secants and Tangents Theorem, which is [tex]DC^{2}[/tex] = 8ft (or the outside segment) * AC (the whole segment)

[tex]14^{2}[/tex] = 8 * (8 + d)

196 = 64 + 8d

Subtract 64 from 196 to get: 132 = 8d

Divide 8 from 132 to get: d = 16.5

Now the diametre is 16.5, but the radius is half the diametre, so now you have to do: 16.5 / 2

So the radius would end up being 8.25

Answer:

d^2 - 64

Step-by-step explanation:

This is the difference of squares. The middle 2 terms cancel out.

d^2 - 8d + 8d - 8*8

d^2 - 64

FOIL

FIRST

OUTSIDE

INSIDE

LAST

First:

(d-8)(d+8)

d * d

[tex]d^{2}[/tex]

Outside:

(d-8)(d+8)

d * 8

8d

Inside:

(d-8)(d+8)

-8 * d

-8d

Last:

(d-8)(d+8)

-8 * 8

-64

so...

d^2 + 8d + (-8d) + (-64)

d^2 - 64

Hope this helped!

Answer:

2 13/20

Dude the blue trail is trying to trick you. scratch it out.

Step-by-step explanation:

Make the denominators the same

3 1/4 -->3 5/20

3/5   -->  12/20

covert this to an improper fraction-->3 5/20 --> 65/20

Subtract 65/20 - 12/20= 53/20

simplify 53/20 --> 2 13/20

Final answer:

To find the distance hiked before it started to rain, the length of the red trail (3 1/4 miles) is multiplied by 3/5, giving a distance of 1.95 miles.

Explanation:

The student has asked about the distance hiked on the red trail before it started to rain. To find the distance, we need to calculate 3/5 of the red trail length, which is 3 1/4 miles long. First, we must convert the mixed number to an improper fraction. 3 1/4 miles can be expressed as (3 × 4 + 1)/4 = 13/4 miles. Then we multiply 13/4 by 3/5 to find the distance hiked: (13/4) × (3/5) = (13 × 3) / (4 × 5) = 39/20. Converting this back to miles gives us 1.95 miles.

-is a positive parabola

-has two roots at x= 1 and x= 5

- has a y-intercept at y=5

- has a minimum at (3, -4)

- axis of symmetry is x=3

What they said ^^^^^^^^^^^^^^^

Answer:

its 1/2

Step-by-step explanation:

Final answer:

The constant of proportionality (r) in the equation y=rx can be found by dividing y by x for any given pair of values. Using the pair (14, 7), the constant of proportionality is calculated as r = 7 / 14 = 0.5.

Explanation:

The quantities x and y are said to be proportional if they relate via a constant of proportionality, which we refer to as r in the equation y=rx. To find the constant of proportionality, you can choose any given pair of values for x and y and divide them. For example, using the given pair (14, 7), we can find r by dividing 7 by 14.

r = y / x = 7 / 14 = 0.5

Therefore, the constant of proportionality r is 0.5. You can check this value with other given pairs to confirm it is consistent. For further confirmation, using the pair (30, 15), we have:

r = 15 / 30 = 0.5

which matches our previously calculated constant of proportionality.

Answer:

Focus = (0, [tex]\frac{3}{4}[/tex])

Step-by-step explanation:

(± 3, 3) are at an equal distance from y-axis.

axis of parabola = y-axis

vertex = (0, 0)

Parabola will be of the form: x² = 4ay, passing through(± 3, 3)

(± 3)² = 4 × a × 3  ⇒ 9 = 12a   ⇒ a = [tex]\frac{9}{12}[/tex]

a = [tex]\frac{3}{4}[/tex]

Coordinates of focus are: (0, a)  ⇒  (0, [tex]\frac{3}{4}[/tex])

Answer:

The focus of the parabola is (0 , 3/4)

Step-by-step explanation:

* Lets revise some facts about the parabola

- The standard form of the equation of a parabola of vertex (h , k)

 is (x - h)² = 4p (y - k)  

- The standard form of the equation of a parabola of vertex (0 , 0)  is

  x² =  4p y, from this equation we can find:  

# The axis of symmetry is the y-axis,  x = 0  

# 4p equal to the coefficient of y in the given equation  

# If  p  >  0, the parabola opens up.  

# If  p <  0, the parabola opens down.

# The coordinates of the focus,  (0 , p)

# The directrix ,  y = − p

* Now lets solve the problem

∵ The vertex of the parabola is (0 , 0)

∴ The equation of the parabola is x² = 4p y

∵ the parabola passes through points (-3 , 3) and (3 , 3)

- Substitute the value of x and y coordinates of one point in the

 equation to find the value of p

∴ (3)² = 4p (3) ⇒ we use point (3 , 3)

∴ 9 = 12 p ⇒ divide both sides by 12

∴ p = 9/12 = 3/4

- Now lets find the focus of the parabola

∵ The focus of the parabola is (0 , p)

∵ p = 3/4

∴ The focus of the parabola is (0 , 3/4)

Answer:

D. 6^30

explanation:

(6^36)/(6^6)= 6^30

Answer:

[tex]490.9\ ft^{2}[/tex]

Step-by-step explanation:

we know that

The total area is equal to

[tex]A=10(h)+2\pi r(h)+10(h)[/tex]

we have

[tex]h=9\ ft[/tex]

[tex]r=5.5\ ft[/tex]

[tex]\pi=3.14[/tex]

substitute

[tex]A=10(9)+2(3.14)(5.5)(9)+10(9)[/tex]

[tex]A=490.9\ ft^{2}[/tex]

Answer:

Yes, the art supplies cost $29.73, and I believe she has what looks on the picture to be $57

Step-by-step explanation:

Answer:

(6,-11)

Step-by-step explanation:

Given

Point B' = (4,-8)

And the translation formula (x-2, y+3)

In order to get the coordinates of the point before translation, both given points have to be put equivalent.

So, for x-coordinate

x-2 = 4

x= 4+2

x= 6

And for y-coordinate

y+3 = -8

y = -8-3

y=-11

So the old coordinates of old point were (6,-11) ..

your answer is (6, -11)

Divide the total amount of money by the number of boys:

1.92/3 = 0.64 cents

Each boy gets 0.64 cents.

Answer:

Step-by-step explanation:

Look at the picture.

Therefore we have:

[tex]\dfrac{4}{3}=\dfrac{x}{2.25}[/tex]            cross multiply

[tex]3x=(4)(2.25)[/tex]

[tex]3x=9[/tex]             divide both sides by 3

[tex]x=3[/tex]