Part A: A graph passes through the points (0, 4), (1, 8), and (2, 10). Does this graph represent a linear function or a non-linear function? Explain your answer in words.

Part B: Write one example of a linear function and one example of a non-linear function. (Use x and y as the variables)

250.

To determine the 4th term in a geometric sequence, start with the first term and use the common ratio. In this case, the first term is -2 and the common ratio is -5. The formula for finding the nth term of a geometric sequence is an = a1 * r(n-1).

Identify the values: a1 = -2, r = -5, n = 4.

Substitute into the formula: a4 = -2 * (-5)(4-1).

Calculate the 4th term: a4 = -2 * (-5)3 = -2 * (-125) = 250.

Answer:

Option (d) is correct.

[tex]\sqrt{10000x^{64}}=100x^{32}[/tex]

Step-by-step explanation:

Given : Expression [tex]\sqrt{10000x^{64}}[/tex]

We have to write a simplified form of the given expression [tex]\sqrt{10000x^{64}}[/tex]

Consider the given expression [tex]\sqrt{10000x^{64}}[/tex]

[tex]\mathrm{Apply\:radical\:rule\:}\sqrt[n]{ab}=\sqrt[n]{a}\sqrt[n]{b},\:\quad \mathrm{\:assuming\:}a\ge 0,\:b\ge 0[/tex]

[tex]=\sqrt{10000}\sqrt{x^{64}}[/tex]

Factor 10000 as [tex]10000=100^2[/tex]

[tex]\mathrm{Apply\:radical\:rule}:\quad \sqrt[n]{a^n}=a[/tex]

[tex]\sqrt{100^2}=100[/tex]

also, [tex]\mathrm{Apply\:radical\:rule\:}\sqrt[n]{a^m}=a^{\frac{m}{n}},\:\quad \mathrm{\:assuming\:}a\ge 0[/tex]

We have,

[tex]\sqrt{x^{64}}=x^{\frac{64}{2}}=x^{32}[/tex]

Thus, [tex]\sqrt{10000x^{64}}=100x^{32}[/tex]

Answer: D. 100x32

Step-by-step explanation:

Fraction with numerator as prime number and denominator as a square number between 0.5 and 0.9 is equals to 7/9.

"Fraction is defined as the part of whole number divided into equal parts."

According to the question,

'x / y' represents the required fraction

'x' represents numerator of the given fraction

'y' represents denominator of the given fraction

Condition given,

0.5 < ( x / y) < 0.9

Denominator is squared number

Numerator is a prime number

(5 / 10) < ( 6 / 10) <( 7 / 10) < (7 / 9)<  ( 9 / 10)

Hence, required fraction as per condition is ( 7 / 9).

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-225 divided by -15 is equal to 15.

A division is a process of splitting a specific amount into equal parts.

We have to find the value of the expression -225 divided by -15

By means of division we can find this value.

-225/(-15) = 15

Two hundred twenty five is the numerator and fifteen is the denominator.

We get 15

When we divide a negative number by a negative number, the result is a positive number.

Therefore, -225 divided by -15 is equal to 15.

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x+y = 4

x=4-y

52x+50y=204

52(4-y)+50y=204

208-52y+50y=204

208-2y=204

-2y=-4

y=2

x= 4-2=2

check 52*2=104

50*2 = 100

104+100=204

 so he traveled 2 hours at both 50 and 52 mph

We can solve for the value of x using the formula:

V = l w h

where,

h = x the size of the cut since it would form the walls of the rectangle

w = 8.5 – 2x        = it is subtracted by 2x since two sides will be cut

l = 11 – 2x

Substituting:

V = x (8.5 − 2x) (11 − 2x)

Expanding the expression:

V = 93.5 x – 39 x^2 + 4 x^3

To solve the maxima, we have to get the 1st derivative dV / dx then equate to 0. dV / dx = 0:

dV / dx = 93.5 – 78 x + 12 x^2

0 = 93.5 – 78 x + 12 x^2

We get:

x ≈ 1.585 in          and        x ≈ 4.915 in

Therefore Anya’s suggestion of 1.5 inches would create the larger volume since it is nearer to 1.585 inches.

There can be different volumes since volume refers to the amount of space inside the rectangle. They can only have similar perimeter and surface area, but not volume.

 It is restricted to 0 in. < x < 4.25 in. because our w is 8.5 – 2x. Going beyond that value will give negative dimensions.

Answer:

1/2

Step-by-step explanation:

no guarantees but the guy before me said 10/20 and of course if you divide 10 and 20 you get 0.5, and 0.5 is equal to 1/2.

The greatest amount of money that rounds to $105.40 is $105.41, while the least amount that rounds to $105.40 is $105.39.

The greatest amount of money that rounds to $105.40 would be the amount slightly greater than $105.40. Since rounding to the nearest cent, we would look at the hundredths place. Any amount greater than $105.405 would round up to $105.41. So the greatest amount of money that rounds to $105.40 would be $105.41.

The least amount of money that rounds to $105.40 would be the amount slightly less than $105.40. Again, looking at the hundredths place, any amount less than $105.395 would round down to $105.39. So the least amount of money that rounds to $105.40 would be $105.39.

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Final answer:

The inequality that represents the speed of the car while cruise control is being used is 62 ≤ s ≤ 68, where s is the car's speed and it shows the car's speed will be at least 62 mph and at most 68 mph.

Explanation:

The cruise control feature on a car is designed to maintain a steady speed, in this case, 65 miles per hour. However, it is acknowledged that the car's actual speed can fluctuate slightly. The question asks for an inequality that represents the potential speed of the car while cruise control is in use.

Considering the car's speed can vary by up to 3 mph more or less than the cruise control setting, we can set up an inequality to describe this range of speeds. The car's speed (s) should be no more than 3 mph above 65 mph and no less than 3 mph below 65 mph. Therefore, the inequality that represents the speed s of the car would be:

62 ≤ s ≤ 68

This inequality shows that the car's speed will be at least 62 mph and at most 68 mph, encompassing the 3 mph range of variation allowed by the cruise control setting.

To find the inverse of a function, replace f(x) with y, swap x and y, then solve for y. Thus, the inverse of f(x) = x + 5 is f^-1(x) = x - 5.

To find the inverse of a function like f(x) = x + 5, we use the following steps:

Replace the function notation f(x) with y. So, we get y = x + 5.

Swap the roles of x and y. This changes the equation to x = y + 5.

Solve for y to get the inverse function. By subtracting 5 from both sides, we acquire y = x - 5.

This implies that the inverse of the function f(x) = x + 5 is f-1(x) = x - 5.

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So what we do to one side of the equal sign, we must do to the other side as well.

We want to solve for f, so we need to subtract 15 on both sides of the equal sign in order to get f alone by itself on the left side:

[tex] f=20 [/tex]

So now we know that f = 20.

f + 15 = 35

Isolate the variable (f). Note the equal sign. What you do to one side, you do to the other.

Subtract 15 from both sides

f + 15 (-15) = 35 (-15)

f = 35 - 15

Simplify

f = 20

f = 20 is your answer

hope this helps

Answer:

Option E ⇒  x = 19

Step-by-step explanation:

See the attached figure.

TRAP is an isosceles trapezoid

The shown angles are supplementary angles

So, the sum of (5x+9) and (4x) is 180

So, 5x+9 + 4x = 180

solve for x

9x + 9 = 180

9x = 180-9 = 171

x = 171/9 = 19

The answer is option E

Answer:

Answer is 5.

Step-by-step explanation:

The given expression is :

[tex]4x^{3}y+8x^{2} +6x+5[/tex]

We have to tell the constant term here.

A constant term is one that remains same and does not change with change in values of x and y.

Here, other terms contains either x or y or both, that will change with change in x and y. Only 5 is the single term that will remain constant.

So, the answer is 5.

Answer:

[tex](6x^\frac{13}{2})[/tex]

Step-by-step explanation:

[tex](2x^6)(3x^\frac{1}{2})[/tex]

Use property of exponents

a^m * a^n = a^mn

When the exponents with same base are in multiplication then we add the exponents

2 times 3= 6

now we multiply x^6 and x^1/2

[tex](x^6)(x^\frac{1}{2})=x^{6+\frac{1}{2}}[/tex]

Make the denominators same to add the fractions

[tex]\frac{12}{2} +\frac{1}{2} =\frac{13}{2}[/tex]

[tex](6x^\frac{13}{2})[/tex]

Answer: a person on a trail at 12 miles per hour for 20 minutes

Step-by-step explanation:

just go it right!!!

A. The point estimate of μ1 − μ2 is calculated using the value of x1 - x2, therefore:

μ1 − μ2 = x1 – x2 = 7.82 – 5.99

μ1 − μ2 = 1.83

B. The formula for confidence interval is given as:

Confidence interval = (x1 –x2) ± z σ

where z is a value taken from the standard distribution tables at 99% confidence interval, z = 2.58

and σ is calculated using the formula:

σ = sqrt [(σ1^2 / n1) + (σ2^2 / n2)]

σ = sqrt [(2.35^2 / 18) + (3.17^2 / 15)]

σ = 0.988297

Going back to the confidence interval:

Confidence interval = 1.83 ± (2.58) (0.988297)

Confidence interval = 1.83 ± 2.55

Confidence interval = -0.72, 4.38