Alan has $400 in his checking account. He withdraws $50 each week. The amount remaining in his account, f(x), after x weeks is
represented by a function. What is the range of the function?

The set of ordered pairs that represents a function is (D) {(-6, -3), (-4, -3), (-3, -3), (-2, -3), (0, 0)}.

A set of ordered pairs represents a function if each unique input (x-value) is associated with only one output (y-value).

{(-4, -3), (-2, -1), (-2, 0), (0, -2), (0, 2)}

In this set, both (-2, -1) and (-2, 0) have the same x-value but different y-values. Therefore, this set does not represent a function.

{(-5, -5), (-5, -4), (-5, -3), (-5, -2), (-3,0)}

In this set, all the ordered pairs have the same x-value (-5). Since (-5, -5), (-5, -4), (-5, -3), and (-5, -2) have the same x-value but different y-values, this set does not represent a function.

{(-4, -5), (-4, 0), (-3, -4), (0, -3), (3, -2)}

In this set, (-4, -5) and (-4, 0) have the same x-value but different y-values. Therefore, this set does not represent a function.

{(-6, -3), (-4, -3), (-3, -3), (-2, -3), (0, 0)}

In this set, each unique x-value is associated with a single y-value. There are no repeated x-values. Therefore, this set represents a function.

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Answer:

c=200+0.4Yd find determine equlibirum level investment is =400

Answer:im pretty sure its D

Step-by-step explanation:it goes through the origin

Answer:

That’s easy it is 282

Step-by-step explanation:

He will now have 282 bucks altogether.

Step-by-step explanation:

We already know that he has 237 bucks before his birthday, but now he has an additional 45 bucks that he got from his birthday. With this, you can create an equation that looks like this: 237+45. You then solve the equation by adding 45 to 237, which gets you 282 bucks altogether.

The slope of the line that passes through the points (7,-4) and (11,-4) is 0.

The slope of a line is found by using the formula:

slope = (change in y)/(change in x)

To find the change in y, subtract the y-coordinate of one point from the y-coordinate of the other point:

-4 - (-4) = 0

To find the change in x, subtract the x-coordinate of one point from the x-coordinate of the other point:

11 - 7 = 4

Now we can use the formula to find the slope:

slope = 0/4 = 0

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Answer: -4 x 16, -48

Step-by-step explanation:

word phrase: -4 x 16

symplified = -48

product means multiply

Answer:

\( \dfrac{2}{x} - 9\)

Step-by-step explanation:

the quotient of 2 and x:

\( \dfrac{2}{x} \)

9 less than the quotient of 2 and x:

\( \dfrac{2}{x} - 9\)

Answer:

12 216

Step-by-step explanation:

exponents multiplyed by each other

Answer: I think its 12^18

Step-by-step explanation: because you add the exponents together.

Answer:I think it would be 84 + 0.45m + 108.

Which simplified could be 0.45m + 192.

hope this helps!

Step-by-step explanation:

Answer:

392

Step-by-step explanation:

49+343

Answer: 392

Step-by-step explanation: The term “squared“ means times two. And the term “cubed” times three. So multiply 7*7 then add that to 7*7*7

If you found this answer helpful, give it a five-star rating and a thanks!

(Maybe even a brainliest if you feel like it ;D)

Answer:

what does cos theta mean

Step-by-step explanation:

i need to know

Step-by-step explanation:

if to apply the Piphagorean theoreme, then one of the angles is 90° (opposite to the side with the length 5):

3²+4²=5²; ⇔ 9+16=25.

Answer:

The answer is D- A(x)=25+10x

Step-by-step explanation:

I cant really explain how i got the answer but i got it right

The function A(x) has greater value then F(x) for x = 2.5.

A function is a relation between a independent variable and a dependent variable such that the value of dependent variable depends upon the independent one.

Given are two functions of [x] as follows -

F(x) = 80 - 15x

A(x) = 25 + 10x

We have the following functions -

F(x) = 80 - 15x

A(x) = 25 + 10x

Now, we will evaluate each function at x = 2.5.

F(2.5) = 80 - 15 x 2.5 = 42.5

and

A(2.5) = 25 + 10 x 2.5 = 50

It can be seen that A(2.5) > F(2.5)

So, the function A(x) has greater value then F(x) at x = 2.5

Therefore, the function A(x) has greater value then F(x) for x = 2.5.

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The solution of the given inequality is y ≤ -3.

The given inequality is -

3y ≤ −9

We have to solve this given inequality.

Now, we have the inequality as -

3y ≤ −9

=> y ≤ -3

Thus, the solution of the given inequality is y ≤ -3.

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Answer:

3/2

Step-by-step explanation:

Y2-Y1

_____

X2-X1

= 5-2

____

-6-(-3)

=3/2

Answer:

X = 30

Step-by-step explanation:

You can find the answer by solving for line RS through the corresponding ratio and adding it to the known value of ST.

Answer:

About 7 minutes

Step-by-step explanation:

3 minutes + 4 minutes= 7 minutes memory used for two songs

-1 does not equal 0, the equation is not true for any value of "a". This means that there is no value of "a" for which the function f(x) is continuous at x = 1.

To determine the value of "a" for which the function f(x) is continuous at x = 1, we need to check if the left-hand limit and the right-hand limit of f(x) as x approaches 1 are equal, and if the value of f(x) at x = 1 is equal to these limits.

First, let's calculate the left-hand limit of f(x) as x approaches 1. For x < 1, the function is given by f(x) = (ax² - 1). To find the left-hand limit, we substitute x = 1 into this expression:

lim(x→1-) f(x) = lim(x→1-) (ax² - 1) = a(1²) - 1 = a - 1.

Next, let's calculate the right-hand limit of f(x) as x approaches 1. For x > 1, the function is given by f(x) = (a(x² - 2x + 1)). Substituting x = 1 into this expression, we have:

lim(x→1+) f(x) = lim(x→1+) (a(x² - 2x + 1)) = a(1² - 2(1) + 1) = a(1 - 2 + 1) = a.

For the function f(x) to be continuous at x = 1, the left-hand limit and the right-hand limit should be equal. Therefore, we have:

a - 1 = a.

To solve this equation for "a," we subtract "a" from both sides:

-1 = 0.

Since -1 does not equal 0, the equation is not true for any value of "a". This means that there is no value of "a" for which the function f(x) is continuous at x = 1.

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Answer:

yes

Step-by-step explanation:

if the denomentators are dividable, than it is a equivalent equation

Answer:

$150

Step-by-step explanation:

discount=60%

let the price=x

(100-60)% of x=$60

40% of x=60

x=60×(100/40)=150

Answer:

21/2 or 10 1/2

Answer:

a = M/G - h

Step-by-step explanation:

G(a + h) = M

G/G(a + h) = M/G

a + h = M/G

a + h - h = M/G - h

a = M/G - h

The value of the expression in the form of 'a' is a = M/G - h.

Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.

The given expression is,

G(a + h) = M

Divide G on both sides.

G/G(a + h) = M/G

a + h = M/G

Subtract h on both sides.

a + h - h = M/G - h

a = M/G - h

Therefore, the value of the expression in the form of 'a' is a = M/G - h.

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Answer:

Yes

Step-by-step explanation:

yes because when you place 5 in the x spot you arrive a final answer of 15=15

Answer:

answer B would be the answer due to the amount of the space is shaded.

Answer:

C

Step-by-step explanation:

since the diagonal of the square is 36 inches:

by pythagoras:

c--> side

c^2 + c^2 = 36^2

2c^2 = 1296

c^2 = 648

c = 25.46 inches

thus the perimeter:

4c = 4 x 25.46 = 102

and the area:

c^2 = 648

The steps of completing the square assuming a parabolic equation of the form ax² + bx  + c is done to get

y = a(x + b/2a)² - (b² - 4ac)/4a = a(x - h)² + k

vertex is given by v(h, k) for h = b/2a and k = -(b² - 4ac)/4a

The standard equation of a parabola is ax² + bx  + c

completing the square is done as follows

write the equation ax² + bx  + c such that c is the other side of the equation

ax² + bx  = -c

divide through by a to get

x² + (b/a)x  = -c/a

add (b/2a)² to the both sides of the equation

x² + (b/a)x + (b/2a)² = (b/2a)² - c/a

solving each side differently,

(x + b/2a)² = x² + (b/a)x + (b/2a)² and

(b/2a)² - c/a = b²/4a² - c/a = (b² - 4ac)/4a²

hence

(x + b/2a)² = (b² - 4ac)/4a²

multiplying by a

a(x + b/2a)² = (b² - 4ac)/4a

rewriting the equation

y = a(x + b/2a)² - (b² - 4ac)/4a = a(x - h)² + k

therefore

h = b/2a

k = -(b² - 4ac)/4a

and vertex is v(h, k)

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The value of integral is 3.

Let's evaluate the integral over the positive half of the interval:

∫[0 to π] (cos(x) / √(4 + 3sin(x))) dx

Let u = 4 + 3sin(x), then du = 3cos(x) dx.

Substituting these expressions into the integral, we have:

∫[0 to π] (cos(x) / sqrt(4 + 3sin(x))) dx = ∫[0 to π] (1 / (3√u)) du

Using the power rule of integration, the integral becomes:

∫[0 to π] (1 / (3√u)) du = (2/3) . 2√u ∣[0 to π]

Evaluating the definite integral at the limits of integration:

(2/3)2√u ∣[0 to π] = (2/3) 2(√(4 + 3sin(π)) - √(4 + 3sin(0)))

(2/3) x 2(√(4) - √(4)) = (2/3) x 2(2 - 2) = (2/3) x 2(0) = 0

So, the value of integral is

= 3-0

= 3

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Answer:

\(3-\displaystyle \int^{\pi}_{-\pi} \dfrac{\cos x}{\sqrt{4+3 \sin x}}\; \text{d}x\approx 0.806\; \sf (3\;d.p.)\)

Step-by-step explanation:

First, compute the indefinite integral:

\(\displaystyle \int \dfrac{\cos x}{\sqrt{4+3\sin x}}\; \text{d}x\)

To evaluate the indefinite integral, use the method of substitution.

\(\textsf{Let} \;\;u = 4 + 3 \sin x\)

Find du/dx and rewrite it so that dx is on its own:

\(\dfrac{\text{d}u}{\text{d}x}=3 \cos x \implies \text{d}x=\dfrac{1}{3 \cos x}\; \text{d}u\)

Rewrite the original integral in terms of u and du, and evaluate:

\(\begin{aligned}\displaystyle \int \dfrac{\cos x}{\sqrt{4+3\sin x}}\; \text{d}x&=\int \dfrac{\cos x}{\sqrt{u}}\cdot \dfrac{1}{3 \cos x}\; \text{d}u\\\\&=\int \dfrac{1}{3\sqrt{u}}\; \text{d}u\\\\&=\int\dfrac{1}{3}u^{-\frac{1}{2}}\; \text{d}u\\\\&=\dfrac{1}{-\frac{1}{2}+1} \cdot \dfrac{1}{3}u^{-\frac{1}{2}+1}+C\\\\&=\dfrac{2}{3}\sqrt{u}+C\end{aligned}\)

Substitute back u = 4 + 3 sin x:

                            \(= \dfrac{2}{3}\sqrt{4+3\sin x}+C\)

Therefore:

\(\displaystyle \int \dfrac{\cos x}{\sqrt{4+3\sin x}}\; \text{d}x= \dfrac{2}{3}\sqrt{4+3\sin x}+C\)

To evaluate the definite integral, we must first determine any intervals within the given interval -π ≤ x ≤ π where the curve lies below the x-axis. This is because when we integrate a function that lies below the x-axis, it will give a negative area value.

Find the x-intercepts by setting the function to zero and solving for x in the given interval -π ≤ x ≤ π.

\(\begin{aligned}\dfrac{\cos x}{\sqrt{4+3\sin x}}&=0\\\\\cos x&=0\\\\x&=\arccos0\\\\\implies x&=-\dfrac{\pi }{2}, \dfrac{\pi }{2}\end{aligned}\)

Therefore, the curve of the function is:

So to calculate the total area, we need to calculate the positive and negative areas separately and then add them together, remembering that if you integrate a function to find an area that lies below the x-axis, it will give a negative value.

Integrate the function between -π and -π/2.

As the area is below the x-axis, we need to negate the integral so that the resulting area is positive:

\(\begin{aligned}A_1=-\displaystyle \int^{-\frac{\pi}{2}}_{-\pi} \dfrac{\cos x}{\sqrt{4+3\sin x}}\; \text{d}x&=- \left[\dfrac{2}{3}\sqrt{4+3\sin x}\right]^{-\frac{\pi}{2}}_{-\pi}\\\\&=-\dfrac{2}{3}\sqrt{4+3 \sin \left(-\frac{\pi}{2}\right)}+\dfrac{2}{3}\sqrt{4+3 \sin \left(-\pi\right)}\\\\&=-\dfrac{2}{3}\sqrt{4+3 (-1)}+\dfrac{2}{3}\sqrt{4+3 (0)}\\\\&=-\dfrac{2}{3}+\dfrac{4}{3}\\\\&=\dfrac{2}{3}\end{aligned}\)

Integrate the function between -π/2 and π/2:

\(\begin{aligned}A_2=\displaystyle \int^{\frac{\pi}{2}}_{-\frac{\pi}{2}} \dfrac{\cos x}{\sqrt{4+3\sin x}}\; \text{d}x&= \left[\dfrac{2}{3}\sqrt{4+3\sin x}\right]^{\frac{\pi}{2}}_{-\frac{\pi}{2}}\\\\&=\dfrac{2}{3}\sqrt{4+3 \sin \left(\frac{\pi}{2}\right)}-\dfrac{2}{3}\sqrt{4+3 \sin \left(-\frac{\pi}{2}\right)}\\\\&=\dfrac{2}{3}\sqrt{4+3 (1)}-\dfrac{2}{3}\sqrt{4+3 (-1)}\\\\&=\dfrac{2\sqrt{7}}{3}-\dfrac{2}{3}\\\\&=\dfrac{2\sqrt{7}-2}{3}\end{aligned}\)

Integrate the function between π/2 and π.

As the area is below the x-axis, we need to negate the integral so that the resulting area is positive:

\(\begin{aligned}A_3=-\displaystyle \int^{\pi}_{\frac{\pi}{2}} \dfrac{\cos x}{\sqrt{4+3\sin x}}\; \text{d}x&= -\left[\dfrac{2}{3}\sqrt{4+3\sin x}\right]^{\pi}_{\frac{\pi}{2}}\\\\&=-\dfrac{2}{3}\sqrt{4+3 \sin \left(\pi\right)}+\dfrac{2}{3}\sqrt{4+3 \sin \left(\frac{\pi}{2}\right)}\\\\&=-\dfrac{2}{3}\sqrt{4+3 (0)}+\dfrac{2}{3}\sqrt{4+3 (1)}\\\\&=-\dfrac{4}{3}+\dfrac{2\sqrt{7}}{3}\\\\&=\dfrac{2\sqrt{7}-4}{3}\end{aligned}\)

To evaluate the definite integral, sum A₁, A₂ and A₃:

\(\begin{aligned}\displaystyle \int^{\pi}_{-\pi} \dfrac{\cos x}{\sqrt{4+3\sin x}}\; \text{d}x&=\dfrac{2}{3}+\dfrac{2\sqrt{7}-2}{3}+\dfrac{2\sqrt{7}-4}{3}\\\\&=\dfrac{2+2\sqrt{7}-2+2\sqrt{7}-4}{3}\\\\&=\dfrac{4\sqrt{7}-4}{3}\\\\ &\approx2.194\; \sf (3\;d.p.)\end{aligned}\)

Now we have evaluated the definite integral, we can subtract it from 3 to evaluate the given expression:

\(\begin{aligned}3-\displaystyle \int^{\pi}_{-\pi} \dfrac{\cos x}{\sqrt{4+3 \sin x}}\; \text{d}x&=3-\dfrac{4\sqrt{7}-4}{3}\\\\&=\dfrac{9}{3}-\dfrac{4\sqrt{7}-4}{3}\\\\&=\dfrac{9-(4\sqrt{7}-4)}{3}\\\\&=\dfrac{13-4\sqrt{7}}{3}\\\\&\approx 0.806\; \sf (3\;d.p.)\end{aligned}\)

Therefore, the given expression cannot be zero.

Answer:

The sale price was 54.55 but if you round it up its 55 hope i helped!

Step-by-step explanation:

Answer:

Kerri

calculate z scores z= (x - xbar)/stdev

Kerri = 1.7

Cade = .7

Vincent = 1

Step-by-step explanation:

Answer:

B.) -2.5 z + 5 y - 8

Step-by-step explanation:

- 6 z + ( - 5.5 ) + 3.5 z + 5 y - 2.5

combine like terms

- 6 z + 3.5 z + 5 y -5.5 - 2.5

- 2.5 z + 5 y - 8

Answer:

11.1

Step-by-step explanation:

0.5(−77.8−11)/−4

=(0.5)(−88.8)/−4

=−44.4/−4

=11.1