The graph shows two functions, f(x) and g(x).

If the functions are combined so that h(x) = f(x) – g(x), then the domain of the function h(x) is x ≥ ____ .

Answer:

sorry

Step-by-step explanation:

i dont know

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Answer:

30000 : 20000

Step-by-step explanation:

Given the ratio

\(\frac{1}{10}\) : \(\frac{1}{15}\) ( multiply both parts by 30 the LCM of 10 and 15, to clear the fractions )

= 3 : 2

sum the parts of the ratio, 3 + 2 = 5 parts

Divide the amount by 5 to find the value of 1 part of the ratio

50000 ÷ 5 = 10000 ← value of 1 part of the ratio, then

3 parts = 3 × 10000 = 30000

2 parts = 2 × 10000 = 20000

Then

50000 = 30000 : 20000 in the ratio 3 : 2

Hey there!

The answer is 100 square meters.

The formula for area is length times width, therefore we do 10 * 10, which gets us 100 square meters.

Have a terrificly amazing day! :D

Answer:

1/2 hour

Step-by-step explanation:

he ran 1.25 miles in 7.5 mins

so

1.25x=37.5

x=30 MINS

30 mins =.5 hours or 1/2 hours

Answer:

50%

Step-by-step explanation:

Answer: 50%

Step-by-step explanation:

31 is half of 62, so it was a 50% decrease.

Taxpayers in California may need to calculate the itemized deduction limitation when filing their state income taxes. This limitation sets a cap on the amount of itemized deductions that can be claimed, based on the taxpayer's federal adjusted gross income (AGI) and other factors.

Calculating the California itemized deduction limitation involves several steps and considerations to ensure compliance with the state tax regulations. To calculate the California itemized deduction limitation, taxpayers should first determine their federal AGI. This can be found on their federal tax return. Next, they need to identify any federal deductions that are not allowed for California state tax purposes, as these will be excluded from the calculation. Once the applicable deductions are determined, taxpayers must compare their federal AGI to the threshold specified by the California Franchise Tax Board (FTB). The limitation is typically a percentage of the federal AGI, and the percentage may vary depending on the taxpayer's filing status. If the federal AGI exceeds the threshold, the itemized deductions will be limited to the specified percentage. Taxpayers should consult the official guidelines and instructions provided by the California FTB or seek professional tax advice to ensure accurate calculation and compliance with the state tax regulations. Calculating the California itemized deduction limitation is an important step in accurately reporting and calculating state income taxes. It helps determine the maximum amount of itemized deductions that can be claimed, ensuring that taxpayers adhere to the tax laws and regulations of the state.

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-6x-1=23

=> -6x=1+23

=> -6x=24

=> x= 24/-6

=> x= -4

Hope it helps!

Step-by-step explanation:

Hey there!

Given;

\( - 6x - 1 = 23\)

~ Shift "-1" on right side.

\( - 6x = 23 + 1\)

\( - 6x = 24\)

~Divide 24 by -6.

\(x = \frac{24}{ - 6} \)

Therefore, x= -4.

Hope it helps...

Each of the following events result in a tax payment, an example of a direct tax is D. Javier owes money to the federal government based on job earnings.

A direct tax is one that is paid by an individual or group of individuals directly to the body that levied it. Taxes on assets, real estate, personal property, and income are a few examples that are all paid by an individual taxpayer directly to the government.

Direct taxes are those that you pay to the government directly. You have paid a direct tax, for instance, if you pay income tax, property tax, or capital gains tax. On the other side, an indirect tax is when you make a purchase and someone else subsequently pays the tax on your behalf through a sales tax.

Therefore, option D is correct.

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Answer:

(2) The statement is true.

-1 < r < 1

The value of the function at f(4) is 14.

When a function is defined using the notation, the set of rational data, or, is implicitly taken into account to be the function's range and small-space requirement. When a function is defined, the domain and codomain are not usually explicitly stated; one may just be aware that the function's domain is a subset of a larger set without having to perform any (potentially challenging) computations.

the given function is

f (x) = 3x + 2

f(4) = 3(4) +2

f(4) = 14

The area is assumed to be the largest subset of the set if the formula may be evaluated at any real number. In mathematical analysis, the phrase "a function from X to Y" is frequently used to describe a function that has a permissible subset of X as its domain.

The value of the function at f(4) is 14.

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Answer:

$35,000.00 - $1,000.00 = 34,000.00

Answer:

Hey there!

20^2+54/9

400+54/9

400+6

406

Hope this helps :)

Answer:

406

Step-by-step explanation:

20²+6

=400+6

=406

Between 48% and 54% believe that their health is extremely important.

According to the statement

Given that a random sample of 1001 Americans aged 18-24 years showed that 51% believe their health is extremely important.

Here

Sample size n =1001

sample proportion p = 0.51

By these values we calculate the Standard error of proportion.

So, Standard error of proportion = 0.0158.

Since sample size is sufficiently large we can take Z critical value for confidence interval

Z critical value for 95% = 1.96

Margin of error = ±1.96*std error

= ±0.0310

confidence interval = 0.51 ±0.0310

= (0.48, 0.54)

So, Between 48% and 54% believe that their health is extremely important.

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Answer:

B

Step-by-step explanation:

point-slope form is y-y1=m(x-x1)

x1=-3

y1=-1

m=2

Now plug it in!

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

Simplify it to

y+1=2(x+3)

Therefore, it should be B

Hope this helps!

The probability of A or B would be 0.3269. Probability can be used to make predictions and make decisions based on uncertain information in fields such as finance, engineering, and science.

Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, with 0 indicating that an event will not occur and 1 indicating that an event will definitely occur. Events with probabilities closer to 1 are considered more likely to happen, while events with probabilities closer to 0 are considered less likely.

Since A and B are mutually exclusive events, they cannot occur at the same time. Therefore, the probability of A or B is the sum of their individual probabilities.

p(A or B) = p(A) + p(B) = 0.07692 + 0.25 = 0.32692

To four decimal places, the probability of A or B is 0.3269.

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Answer:

Step-by-step explanation:

Probability of P.B.J. : milk : cookie being picked is; 1:12

Twelve possible combos one is P.B.J. : milk : cookie

There are three possible relations R on the set A {a, b, c, d} that have exactly two equivalence classes.

To determine the possible relations R with exactly two equivalence classes on the set A {a, b, c, d}, we need to consider the different ways in which the elements of A can be related to each other.

1. Relation with two equivalence classes: { {a, b, c}, {d} }

In this relation, elements a, b, and c are related to each other, forming one equivalence class, and element d is related only to itself, forming the second equivalence class. This relation satisfies the properties of reflexivity, symmetry, and transitivity.

2. Relation with two equivalence classes: { {a, b}, {c, d} }

In this relation, elements a and b are related to each other, forming the first equivalence class, and elements c and d are related to each other, forming the second equivalence class. There are no connections between elements from different equivalence classes. This relation satisfies the properties of reflexivity, symmetry, and transitivity.

3. Relation with two equivalence classes: { {a}, {b, c, d} }

In this relation, element a is related only to itself, forming the first equivalence class, and elements b, c, and d are related to each other, forming the second equivalence class. There are no connections between elements from different equivalence classes. This relation satisfies the properties of reflexivity, symmetry, and transitivity.

These three relations are the only possible ones on the set A {a, b, c, d} that have exactly two equivalence classes. Each relation partitions the set A into two subsets or equivalence classes based on the defined relationships between the elements.

It's important to note that there can be other relations on A with different numbers of equivalence classes, but for exactly two equivalence classes, the three relations described above are the only possibilities.

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The mean of the output of the LTI system is m/a.

To find the mean of the output of the system, we can use the property that the mean of the output of an LTI system is given by the convolution of the input mean and the impulse response.

Given:

Input random process: X(t)

Mean of the input random process: E{X(t)} = m

Impulse response of the LTI system: h(t) = \(e^{(-at)}u(t)\), where a is a constant and u(t) is the unit step function.

The output random process Y(t) of the LTI system is given by the convolution of the input random process X(t) and the impulse response h(t):

Y(t) = X(t)× h(t)

The mean of the output random process is then given by:

E{Y(t)} = E{X(t)× h(t)}

Using the property of linearity of expectation, we can write:

E{Y(t)} = E{X(t)}× E{h(t)}

Since the input random process X(t) has a mean of m, we have:

E{X(t)} = m

Now we need to calculate the mean of the impulse response h(t). To do this, we integrate h(t) over its range and divide by the range of integration. In this case, the impulse response h(t) is given by:

h(t) = \(e^{(-at)}\)u(t)

Integrating h(t) over its range, we get:

∫[0,∞] \(e^{(-at)}\) dt = [-1/a× \(e^{(-at)}\)] [0,∞] = [-1/a×(0 - 1)] = 1/a

So, the mean of the impulse response h(t) is 1/a.

Finally, substituting the values in the expression for the mean of the output random process, we have:

E{Y(t)} = E{X(t)} ×E{h(t)} = m × (1/a) = m/a

Therefore, the mean of the output of the LTI system is m/a.

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Answer:

W: (-3,5)

W': (-3,-5)

Y coordinate

Step-by-step explanation:

if you want me to explain it I can in the comments thing

In the plot the coordinates of W is (-3 , 5 ) , and the reflection will be W' (-3 , -5)

A reflection is a transformation representing a flip of a figure. Figures may be reflected in a point, a line, or a plane.

When reflecting a figure in a line or in a point, the image is congruent to the preimage.

A reflection maps every point of a figure to an image across a fixed line.

So in the plot the coordinates of W is (-3 , 5 )

and the reflection will be W' (-3 , -5)

The plot of W and W' is attached with the answer.

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The type of transformation represented is rotation

Transformation techniques is the process of changing the position of an object on the xy-plane.

The transformation technique that we have include;

From the diagram, you can see that the vertices ABC rotates clockwisely to generate the position A'B'C'. Hence the type of transformation represented is rotation

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Answer:

  see below for the meaning of a, b, c, k, p, q.

Step-by-step explanation:

You want the minimum value of a quadratic function.

The extreme will be a minimum if the sign of the leading term is positive. It will be a maximum if the sign of the leading term is negative.

The standard form equation of a parabola is ...

  f(x) = ax² +bx +c

The x-coordinate of the extreme value (maximum or minimum) is ...

  x = -b/(2a)

The y-coordinate of the extreme value, the maximum or minimum, is ...

  y = -b²/(4a) +c

The extreme point is (-b/(2a), -b²/(4a) +c).

The vertex form equation of a parabola is ...

  f(x) = a(x -h)² +k

The coordinates of the vertex (extreme point) are (h, k).

The factored form of the equation of a parabola is ...

  f(x) = a(x -p)(x -q)

where p and q are the x-intercepts.

The coordinates of the extreme point are ((p+q)/2, -a/4(p-q)²).

__

Additional comment

As you can see, the way you find the minimum (or maximum) value depends on what you're starting with. In general that value is the y-value of the vertex. We have also shown the x-value of the vertex, because you may be asked for the coordinates of the minimum (or maximum) point.

You may see the quadratic function in other forms. Generally, those forms can be rearranged to one of these forms. Obviously, if you're looking for the vertex, the "vertex form" is the easiest place to start.

The value of 'a' is the leading coefficient in every case.

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To find the minimum value of a quadratic equation, you can use either the vertex formula or completing the square method. The minimum value occurs at the vertex of the parabola.

To find the minimum value of a quadratic equation, you can use either the vertex formula or completing the square method.

Vertex Formula:

Completing the Square:

By using either of these methods, you can find the minimum value of a quadratic equation.

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Answer: To find the number of liters of water in the first pool after x minutes have passed, we can use the formula:

972 + 17x

To find the number of liters of water in the second pool after x minutes have passed, we can use the formula:

44x

Note that both of these formulas assume that the pools are being filled continuously, without any interruptions. If the flow of water into either pool is interrupted at any point, the actual amount of water in the pools may be different from what these formulas predict.

Answer:

a)

17x + 972

44x

b)

972 + 17x = 44x

Step-by-step explanation:

The example of the associative property of multiplication is 7 • (3 • 5) = (7 • 3) • 5

The associative property of multiplication states that

(a * b) * c = a * (b * c)

Using the above equation as a guide, we have the following equation

7 • (3 • 5) = (7 • 3) • 5

The above equation is the option (3) of the associative property of multiplication

Hence, the example of the associative property of multiplication is 7 • (3 • 5) = (7 • 3) • 5

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Answer:

hey, good afternoon

Step-by-step explanation:

-4x^2+16x+84 you put the -4x^2+16x in parenthesis. so it looks like this

(-4x^2+16x)+84  

-4(x^2 - 4x -21)

-4(x^2+3x-7x-21 the bold numbers are the common factors.

the solution to this problem is

-4(x-7)(x+3)

i think this is right hope this helps

Answer:

x= +- 2+\(\sqrt{3}\) /4

Step-by-step explanation:

The transformation of f(x) to g(x) is g(x) = (x + 6)² + 4

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

The functions f(x) and g(x)

Where, we have

f(x) = x²

The translation 6 units left and 4 units up means that

g(x) = f(x + 6) + 4

So, we have

g(x) = (x + 6)² + 4

This means that the transformation of f(x) to g(x) is g(x) = (x + 6)² + 4

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Answer:

1, 1/5, 3/50, 17/25, 21/50 I think

The value of cos A in the triangle is 1 / 9.

The triangle is given as ABC. The side lengths are a, b and c. Therefore, cos A of the triangle can be found using cosine rule as follows:

a² = b² + c² - 2bc cos A

a = 4

b = 3

c = 3

Therefore,

4² = 3² + 3² - 2(3)(3) cos A

16  = 9 + 9 - 18 cos A

16 - 18 = - 18 cos A

-2 = - 18 cos A

divide both sides by - 18

cos A = - 2 / - 18

cos A = 1 / 9

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The capacity of a car radiator is 20 quarts. If it's full of a 55% antifreeze solution,Let the capacity of the radiator be 20 quarts.

Let x quarts be drained off and replaced by an 80% solution.We know that the radiator is full of a 55% antifreeze solution. After draining x quarts of this solution, there will be (20 - x) quarts of the 55% solution in the radiator. So, the amount of antifreeze in the radiator will be 0.55(20 - x).The x quarts drained off will be replaced by an 80% solution. So, the amount of antifreeze in this solution will be 0.80x.

The total amount of antifreeze in the final solution (20 quarts of a 70% solution) will be:

0.70(20) = 14 quarts

.We can set up an equation that equates the total amount of antifreeze before and after the replacement:

0.55(20 - x) + 0.80x = 0.70(20

Simplifying and solving for

x:11 - 0.55x + 0.80x = 14-0.55x + 0.80x = 30/50

(we divided 14/20 by 10)0.25x = 0.6x = 2.4

The number of quarts that must be drained off and replaced by an 80% solution to give 20 quarts of a 70% solution is 2.4 quarts.

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The argument can be symbolized as follows:

1. CI (Cat is ill)

2. FI (She was fighting)

3. AE (She ate too many mice)

4. FI ⟺ A (She was fighting only if she was attacked)

5. A ⟺ (LS ∨ SB) (She was attacked only if either the large Siamese or the small Beagle was out)

6. LS ⟺ S (The large Siamese was out only if it was sunny)

7. SB ⟺ W (The small Beagle was out only if it was warm)

8. ¬W ∧ ¬S (It was neither warm nor sunny)

To prove that she ate too many mice given the provided premises, we need to establish a logical deduction based on the symbols and relationships given.

1. CI (Cat is ill) - Given

2. FI ∨ AE (If the cat is ill, either she was fighting or ate too many mice) - Provided in the first sentence

3. FI ⟺ A (She was fighting only if she was attacked) - Provided in the second sentence

4. A ⟺ (LS ∨ SB) (She was attacked only if either the large Siamese or the small Beagle was out) - Provided in the third sentence

5. LS ⟺ S (The large Siamese was out only if it was sunny) - Provided in the fourth sentence

6. SB ⟺ W (The small Beagle was out only if it was warm) - Provided in the fourth sentence

7. ¬W ∧ ¬S (It was neither warm nor sunny) - Given

Now, we can start constructing the proof by applying logical deductions step by step.

8. ¬(W ∨ S) (De Morgan's Law, from 7)

9. ¬(SB ⟺ W) (Equivalence Law, from 6)

10. ¬(LS ⟺ S) (Equivalence Law, from 5)

11. ¬(A ⟺ (LS ∨ SB)) (Equivalence Law, from 4)

12. ¬(FI ⟺ A) (Equivalence Law, from 3)

13. ¬(FI ∨ AE) (Equivalence Law, from 2)

14. ¬FI ∧ ¬AE (De Morgan's Law, from 13)

15. ¬FI (Simplification, from 14)

16. ¬AE (Simplification, from 14)

17. ¬FI ∧ CI (Conjunction, from 15 and 1)

18. ¬(CI ⟶ ¬FI) (Implication Law, from 17)

19. CI ⟶ ¬FI (Contrapositive, from 18)

Since the negation of FI (not fighting) is true based on the premises, we can conclude that AE (ate too many mice) must be true. Therefore, the final deduction is AE (She ate too many mice).

Thus, the proof establishes that she ate too many mice based on the given premises and logical deductions.

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