Quick algebra 1 question for 25 points!


Only answer if you know the answer, Tysm!

Answer:

[tex]f(g(x))[/tex]  = [tex]\sqrt{8x - 4}[/tex]

Step-by-step explanation:

• [tex]f(x) = \sqrt{x + 8}[/tex]

• [tex]g(x) = 8x - 12[/tex]

[tex]f(g(x))[/tex] is the combination of the functions [tex]f(x)[/tex] and [tex]g(x)[/tex] such that [tex]g(x)[/tex] is the input to the function [tex]f(x)[/tex] .

This means, we have to replace the original input of  [tex]f(x)[/tex], which is [tex]x[/tex], with the function  [tex]g(x)[/tex].

∴  [tex]f(g(x))[/tex] = [tex]f(8x - 12)[/tex]

               ⇒ [tex]\sqrt{8x - 12 + 8}[/tex]

               ⇒ [tex]\sqrt{8x - 4}[/tex]

Answer:

5.5

Step-by-step explanation:

For the first fold, we cut the 11-inch side in half, resulting in an 8.5-by-5.5-inch piece. After the second fold, we have a 4.25 by 5.5 piece after halving the 8.5 inch side. The length is 5.5 inches.

Answer:

Simplified: 2x/15 + 5y/8

Step-by-step explanation:

Simplify the expression.

Answer:

Answer: 2x/15 + 5y/8

Step-by-step explanation:

Just Simplify the expression dude.

The graph is shown in the attached image.

The final graph of y = -|x + 2| + 3 is a V-shaped curve that opens downwards and is shifted upwards by 3 units.

This curve intersects the x-axis at x = -4 and x = -0 and passes through the point (-2, 1).

The graph is given below.

A function has an input and an output.

A function can be one-to-one or onto one.

It simply indicated the relationships between the input and the output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

The graph of y = -x is a straight line that passes through the origin and has a slope of -1.

It extends infinitely in both directions and has a negative slope, which means that as x increases, y decreases.

The graph of y = |x + 2| - 3 is a bit more complex.

The absolute value function |x + 2| means that the value of x + 2 is taken, and then the absolute value of that value is calculated.

The absolute value function always returns a positive value, so the graph of y = |x + 2| is a V-shaped curve that opens upwards and passes through the point (-2, 0).

The minus sign outside the absolute value function means that the entire curve is reflected about the x-axis, so the graph of y = -|x + 2| is also a V-shaped curve, but this time it opens downwards.

Finally, the +3 at the end of the equation means that the entire graph of

y = -|x + 2| is shifted upwards by 3 units.

Thus,

The final graph of y = -|x + 2| + 3 is a V-shaped curve that opens downwards and is shifted upwards by 3 units.

This curve intersects the x-axis at x = -4 and x = -0 and passes through the point (-2, 1).

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The attached graph represents the graph of the linear equation y = 1000x - 5000 on a scale of 1 to 1000 units on both axes

Linear equations are equations that have constant average rates of change, slope or gradient

The equation of the linear function is given as:

y = 1000x - 5000

The x values are given as:

x = -3 to 8

This means that the domain of the function is [-3, 8] or -3 <= x <= 8

So, we set x = -3 and x = 8, and we calculate the y values.

So, we have:

y = 1000 * -3 - 5000 = -8000

y = 1000 * 8 - 5000 = 3000

So, we draw two points at (-3, -8000) and (8, 3000) and connect the dots

See attachment for the graph of the function

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His body temperature in the evening is 102.6 °F

The given parameters are:

Temperature in the morning = 99.2°F.

Temperature increase = 3.4°F.

His body temperature in the evening is calculated as:

New = Temperature in the morning + Temperature increase

So, we have

New = 99.2°F +  3.4°F

Evaluate the sum

New = 102.6 °F

Hence, his body temperature in the evening is 102.6 °F

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Step-by-step explanation:

cotθcosθ=1tanθ⋅1cosθ

The coordinates of F is (8.5, 7)

The coordinates of the points are given as:

D = (-2, -5)

F = (5, 3)

DF : FE = 4 : 2

Rewrite the ratio as

m = 4 : 2

The coordinate of the partition is calculated as:

F = 1/(m + n) * (mx2 + nx1, my2 + ny1)

This gives

(5, 3) = 1/(4 + 2) * (4 * x + 2 * -2, 4 * y + 2 * -5)

Evaluate the sum and the product

(5, 3) = 1/6 * (4x - 4, 4y - 10)

Multiply both sides by 6

(30, 18) = (4x - 4, 4y - 10)

By comparison, we have:

4x - 4 = 30

4y - 10 = 18

Solve the equations

x = 8.5

y = 7

So, we have:

F = (8.5, 7)

Hence, the coordinates of F is (8.5, 7)

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The algebraic expression of the part A is 6+7x. And the verbal expression for 3*(n+8) is "the triple of the sum between the numbers n and 8".

A linear expression can be represented by a line. The standard form for this equation is: y=ax+b , for example, y=2x+7.

First, you should choose a variable for unknow number. Here, the variable will be x. Then, 7 times a number can be represented for 7x.

The word more will be represented for the add symbol (+). Thus,

the algebraic expression is 6+7x.

The expression 3*(n+8) can be represented for the sentence:

The triple of the sum between the numbers n and 8.

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Answer:

Step-by-step explanation:

(4+8/2)*5-1

8*5-1

39 is your answer

The ratio is different from the other three is StartFraction 6 Over 10 EndFraction; 6/10.

A ratio is a number representing a comparison between two named things.

StartFraction 2 Over 5 EndFraction = StartFraction 6 Over 10 EndFraction = StartFraction 8 Over 20 EndFraction = StartFraction 12 Over 30 EndFraction

2/5 = 6/10 = 8/20 = 12/30

2/5 = 0.4

6/10 = 0.6

8/20 = 0.4

12/30 = 0.4

Therefore, the ratio is different from the other three is StartFraction 6 Over 10 EndFraction; 6/10

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The cubic meters of water did the hull of the titanic have to displace to stay afloat is known to be about 52,310 tons that is 51843.918 m³ of water.

The RMS Titanic is known to be a ship that is said to be owned by the White Star Line.

This is known to be the biggest British passenger liner that was said to have  sank when it was on its maiden voyage in the year 1912 in the North Atlantic Ocean.

Note that it sank because it was said to have hit an iceberg on Sunday, 14 April 1912.

The Titanic was said to be about 46,328 gross register tons and was known to have displaced about 52,310 tons of water.

So, 1 ton (displacement) ≈ 0.99109 cubic meters (m³)

Therefore, 52,310 tons

= 52,310 × 0.99109 m³

≈ 51843.918 m³

Therefore, The cubic meters of water did the hull of the titanic have to displace to stay afloat is known to be about 52,310 tons that is 51843.918 m³ of water.

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The statement is false as the sample is a few ATMs of the total ATMs in US.

The sample is only 860 ATMs and not total ATMs in US thus, a sample of 860 ATMs have taken and conducted the survey.

Thus, the statement is false as the sample is a few ATMs of the total ATMs in US.

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Compounded continuously the balance grows at a continuous rate of 1.7%.

What is compound interest ?

The model used for continuous compounding is

 f(t) = Pe^(rt)

where P is the principal amount, and r is the interest rate being compounded. Assuming a typo in your given equation, you have

 f(t) = 1000·e^(0.017t)

Matching the various parts of the equation, we see that P = 1000 and r = 0.017 = 1.7%.

Therefore, the balance grows at a continuous rate of 1.7%.

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The length of the function x = 2y is 2√5 units

According to the given question.

We have a function

x = 2y

Since, we know that the length of the function in the interval [a, b] is given by

l =    [tex]\int\limits^a_b\sqrt{1+(\frac{dx}{dy}) ^{2} } \,dy[/tex]

Where, l is the length of the function.

Now, differentiating the given function x = 2y w.r.t y.

Therefore,

dx/dy = 2

So, the length of the given function x = 2y  from y = -1 to y = 1 is given by

l =   [tex]\int\limits^1_{-1}{\sqrt{1+2^{2} } } \,dy[/tex]

⇒ l =   [tex]\int\limits^1_{-1} {\sqrt{1+4} } \,dy[/tex]

⇒ l =   [tex]\int\limits^1_{-1}{\sqrt{5} } \,dy[/tex]

⇒ l = √5[1 - (-1)]

⇒ l = √5(2)

⇒ l = 2√5

Hence, the length of the function x = 2y is 2√5 units.

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0.0016

reduce expression if possible by canceling the common factors

Answer:

the frequency is the number of times a particular value occurs in a given data.

Answer:

sub -2 into 12x^3 - 15

h(-2) = 12(-2)^3 -15

        = -111

hope this helps!!!! If it's incorrect I'm sorry :(

Answer:

[tex]h(-2) =\boxed{ \bf -111}[/tex]

Step-by-step explanation:

The function [tex]h(x)[/tex] is defined as:

[tex]h(x) = 12x^3 - 15[/tex]

To calculate the value of [tex]h(-2)[/tex], we have to replace the [tex]x[/tex] in the definition of [tex]h(x)[/tex] with -2:

[tex]h(-2)[/tex] = [tex]12(-2)^3 - 15[/tex]

       ⇒ [tex]12(-8) -15[/tex]

       ⇒ -96 - 15

       ⇒ -111

The Area of the kite with the given diagonals is: 125 square meters.

A kite can be described as a quadrilateral having four (4) sides, which can be categorized into two pairs of congruent sides, each of them is adjacent to the other. A kite has two diagonals that intersect, where by the longer diagonal divides the smaller diagonal into equal halves.

An example of a kite is shown in the image attached below, where:

JL and KM are the diagonals of the kite.

The formula for finding the area of a kite is given as:

Area = 1/2 × (product of the lengths of the diagonals)

Given the following:

Length of diagonal 1 = 10 meters

length of diagonal 2 = 25 meters

Area = 1/2 × (product of the lengths of the diagonals) = 1/2 × (10 × 25)

Area of kite = 1/2 × (250)

Area of kite = 1/2 × (250)

Area of kite = 125 square meters.

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Answer:

0

Step-by-step explanation:

A 0 horas, la temperature era 9.

The ounces of cheese Ellie uses to make tacos is 2

What is a unitary method?

The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.

Calculation :

1 pound = 16 ounces

Total cheese Ellie has = [tex]\frac{2}{8}[/tex] pound

Cheese required to make tacos = [tex]\frac{2}{8}[/tex]×[tex]\frac{1}{2}[/tex] = [tex]\frac{1}{8}[/tex] pounds

Ounces of cheese required to make cheese are [tex]\frac{1}{8}[/tex] × 16 = 2 ounces

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Answer:

8km  5mi

Step-by-step explanation:

20x400=8000meters a km = to 1000meters

8000/1000=8km

A mile is a kilometer/ 1.6  8/1.6=5 miles

Sanford ran approximately 8 kilometers and about 4.97 miles.

Given that a coach made someone run 20 laps on a 400 m track.

We need to find the number of mile he ran as well as number of kilometers he ran.

To find out how many kilometers Sanford ran, we can use the fact that 1 kilometer is equal to 1000 meters.

Similarly, to find out how many miles he ran, we'll use the conversion factor of 1 mile being equal to approximately 1609.34 meters.

Let's calculate it:

1 lap = 400 meters

20 laps = 20 x 400 = 8000 meters

Kilometers:

8000 meters ÷ 1000 meters/kilometer = 8 kilometers

Miles:

8000 meters ÷ 1609.34 meters/mile ≈ 4.97 miles

So, Sanford ran approximately 8 kilometers and about 4.97 miles.

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The function f(x) = ∛x - 3 is positive at the interval (3, oo)

The function is given as:

f(x) = ∛x - 3

The function is positive when the function value is greater than 0

This is represented as:

f(x) > 0

So, we have the following inequality expression

∛x - 3 > 0

Take the cube of both sides

x - 3 > 0

Add 3 to both sides

x > 3

Express as an interval notation

(3, oo)

Hence, the function f(x) = ∛x - 3 is positive at the interval (3, oo)

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Answer:

-3

Step-by-step explanation:

If you reflect over the y-axis and then move 2 units to the left(x-2), then ABCD will be 3 units above EHGF. Since you need to move it down 3 units to map ABCD onto EHGF, you will need to do y-3, which is the same as y+-3

The slope of tangent line at point(4, 2pi) is undefined.

For given question,

We have been given a polar equation r = 2 + 2cos(θ)

We need find dy/dx as well as the slope of tangent line at point(4, 2π).

We know that, for polar equation we use,

x = r cos(θ)   and  y = r sin(θ)

plug the given value of r into these equations we get:

⇒ x = r cos(θ)

⇒ x = (2 + 2cos(θ) ) ×  cos(θ)

⇒ x = 2(cos(θ) + cos²(θ))

⇒ x = 2cos(θ) + 2cos²(θ)

Similarly,

⇒ y = r sin(θ)

⇒ y = (2 + 2cos(θ) ) ×  sin(θ)

⇒ y =  2(sin(θ) + sin(θ)cos(θ))

⇒ y =  2sin(θ) + 2sin(θ)cos(θ)

Now we find derivative of x and y with respect to theta.

[tex]\Rightarrow \frac{dx}{d\theta} =-2sin(\theta)+2(-2cos(\theta)sin(\theta))\\\\\Rightarrow \frac{dx}{d\theta} =-2sin(\theta)-2sin(2\theta)[/tex]          .............(1)

Similarly,

[tex]\Rightarrow \frac{dy}{d\theta}=2cos(\theta)+2(cos^2(\theta)-sin^2(\theta))\\\\\Rightarrow \frac{dy}{d\theta}=2cos(\theta)+2(cos(2\theta))[/tex]          ..............(2)

Now we find dy/dx

⇒ dy/dx = (dy/dθ) / (dx/dθ)

From (1) and (2),

[tex]\Rightarrow \frac{dy}{dx} =\frac{2cos(\theta)+2cos(2\theta)}{-2sin(\theta)-2sin(2\theta)} \\\\\Rightarrow \frac{dy}{dx} =\frac{2(cos(\theta)+cos(2\theta))}{-2(sin(\theta)+sin(2\theta))}\\\\\Rightarrow \frac{dy}{dx} =-\frac{cos(\theta)+cos(2\theta)}{sin(\theta)+sin(2\theta)}[/tex]

We know that The slope of tangent line is given by dy/dx.

So, the slope is: [tex]m =-\frac{cos(\theta)+cos(2\theta)}{sin(\theta)+sin(2\theta)}[/tex]

Now we need to find the slope of tangent line at point(4, 2pi)

Substitute θ = 2π in above slope formula.

[tex]\Rightarrow m =-\frac{cos(2\pi)+cos(2\times 2\pi)}{sin(2\pi)+sin(2\times 2\pi)}\\\\\Rightarrow m=-\frac{1+cos(4\pi)}{0+sin(4\pi)}\\\\\Rightarrow m=-\frac{1+cos(4\pi)}{sin(4\pi)}[/tex]

⇒ m = ∞

The slope of tangent line at point(4, 2pi) is not defined.

This means, the tangent line must be parallel to Y-axis.

Therefore, the slope of tangent line at point(4, 2pi) is undefined.

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Answer:

5) 26

6) 18

Step-by-step explanation:

Substitute the value of the variables in the expression and evaluate.

x = 2 ; y = -3 and z = 1

Absolute value:  Absolute value of a real number is the non negative a value of x without regard its sign.

Example: I-3I = 3

               I 3I = 3

5) 24 + Ix - 4I =24 + I 2 - 4I

                      = 24 + I-2I

                      = 24 + 2

                      = 26

6) 13 + I 8 +y I = 13 + I 8 + (-3)I

                       = 13 + I 5 I

                       = 13 + 5

                       = 18

The probability of correctly picking the two numbers is 2/10.

Probability determines the chances that an event would happen. The probability the event occurs is 1 and the probability that the event does not occur is 0.

The more likely the event is to happen, the closer the probability value would be to 1. The less likely it is for the event not to happen, the closer the probability value would be to zero.

The probability of correctly picking the two numbers = (numbers that have to be selected to win / total numbers)

2/10

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