Given the functions k(x) = 2x^2 − 5 and p(x) = x − 3, find (k ∘ p)(x).

a. (k ∘ p)(x) = 2x^2 − 6x + 4
b. (k ∘ p)(x) = 2x^2 − 12x + 13
c. (k ∘ p)(x) = 2x^2 − 12x + 18
d. (k ∘ p)(x) = 2x2 − 8

Answer:

The range is all real number y<3.

Step-by-step explanation:

[tex](u \circ v)(x)=u(v(x))[/tex]

So we have to have v(x) exist for input x.

Let's think about that.  v(x)=1/x so the domain is all real numbers except 0 since you cannot divide by 0.  v(x)=1/x will also never output 0 because the numerator of 1/x is never 0. So the range of v(x)=1/x is also all real numbers except y=0.

Now let's plug v into u:

[tex]u(x)=-2x^2+3[/tex]

[tex]u(v(x))=u(\frac{1}{x}[/tex]

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

The domain of will still have the restrictions of v; let's see if we see any others here.

Nope, there are no, others, the only thing that is bothering this function is still the division by x (which means we can't plug in 0).

[tex]u(v(x))=\frac{-2}{x^2}+3[/tex]

Let's thing about what are y's value will not ever get to be.

Let's start with that fraction. -2/x^2 will never be 0 because -2 will never be 0.

So we will never have y=0+3 which means y will never be 3.

There is one more thing to notice -2/x^2 will never be positive because x^2 is always positive and as we know a negative divided by a positive is negative.

So we have (a always negative number) +  3 this means the range will only go as high as 3 without including 3.

The range is all real number y<3.

Answer:

[tex]574.62\ in^3[/tex]

Step-by-step explanation:

First we calculate the volume of the cylinder.

[tex]V=\pi r^2*l[/tex]

Where r is the radius and l is the length of the cylinder.

We know that:

[tex]r = \frac{diameter}{2}[/tex]

[tex]r = \frac{4}{2}[/tex]

[tex]r = 2\ in[/tex]

Then:

[tex]V=3.14* 2^2*48[/tex]

[tex]V=602.88\ in^3[/tex]

Assuming that the cannon balls are spherical then the volume of the 2 spheres is:

[tex]V=2*\frac{4}{3}\pi r^3[/tex]

[tex]V=2*\frac{4}{3}(3.14)(\frac{3}{2})^3[/tex]

[tex]V=2*\frac{4}{3}(3.14)(\frac{3}{2})^3[/tex]

[tex]V=28.26\ in^3[/tex]

So the space left inside the cannon is

[tex]V=602.88\ in^3 - 28.26\ in^3\\\\V=574.62\ in^3[/tex]

Answer:

-7

Step-by-step explanation:

Lets count back.

1,0,-1,-2,-3,-4,-5,-6

We are going back, so -7

Answer:

f-¹(x) =(1-5x) /3x.

Step-by-step explanation:

f(x)=1/(3x+5)

Let y=1/(3x+5)

Exchanging x and y,

x=1/(3y+5)

3y+1=1/x

3y=1/x-5

3y=(1-5x) /x

y=(1-5x)/3x

f-¹(x) =(1-5x) /3x.

Answer:

y=3(x-5)

Step-by-step explanation:

Answer:

31877 people with live in the town in 2016 if the population increases at a rate of 6% every 2 years

Step-by-step explanation:

The formula used will be

A(t) = P(1+r)^t

A(t) = Future value

P = population

r = rate

t = time

P= 20,000

r =6% or 0.06

t = 16

Since population is increased every 2 years, so t = 16/2 = 8

Putting value:

A(16) = 20,000(1+0.06)^8

A(16)= 20,000(1.06)^8

A(16) = 31876.9 ≈ 31877

So, 31877 people with live in the town in 2016 if the population increases at a rate of 6% every 2 years

Answer:

m∠C = 55°

Step-by-step explanation:

A triangle's sum of all angles = 180°

Set the equation: m∠A + m∠B + m∠C = 180°

m∠A = 50° ; m∠B = 75°

Plug in the corresponding numbers to the corresponding variables:

50 + 75 + m∠C = 180

Simplify. Combine like terms:

(50 + 75) + m∠C = 180

125 + m∠C = 180

Isolate the variable. Note the equal sign, what you do to one side, you do to the other. Subtract 125 from both sides:

m∠C + 125 (-125) = 180 (-125)

m∠C = 180 - 125

m∠C = 55

m∠C = 55°

Check: All the angles added together must equal 180°:

50 + 75 + 55 = 180

125 + 55 = 180

180 = 180 (True)

~

Answer:

[tex](5\pi-11.6)\ ft^{2}[/tex]

Step-by-step explanation:

we know that

The area of the shaded region is equal to the area of the sector minus the area of the triangle

step 1

Find the area of the circle

the area of the circle is equal to

[tex]A=\pi r^{2}[/tex]

we have

[tex]r=5\ ft[/tex]

substitute

[tex]A=\pi (5)^{2}[/tex]

[tex]A=25\pi\ ft^{2}[/tex]

step 2

Find the area of the sector

we know that

The area of the circle subtends a central angle of 360 degrees

so

by proportion find out the area of a sector by a central angle of 72 degrees

[tex]\frac{25\pi}{360}=\frac{x}{72}\\ \\x=72*25\pi /360\\ \\x=5\pi\ ft^{2}[/tex]

step 3

Find the area of triangle

The area of the triangle is equal to

[tex]A=\frac{1}{2}(2.9+2.9)(4)= 11.6\ ft^{2}[/tex]

step 4

Find the area of the shaded region

Subtract the area of the triangle from the area of the sector

[tex](5\pi-11.6)\ ft^{2}[/tex]

In Mathematics, quadratic functions such as y=ax^2 and cubic functions such as y=ax^3, will have their vertex at the origin, represented by (0,0). These functions show this characteristic because there are no shifts involved in the equation.

In Mathematics, there are different functions that can have their vertex at the origin (0,0). For instance, when we speak of quadratic functions, a function in the form of y = ax^2 will have its vertex at the origin as it's a parabola that opens upward or downward.

Similarly, for the case of cubic functions, a function in the form of y = ax^3 will have the vertex at the origin.

Important to note is that, for all these cases, the vertex is at the origin because there are no horizontal or vertical shifts involved in the equation. That is, the h & k in (x-h)^2+k and (x-h)^3+k are both zero.

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Check the picture below.

Answer:

Your slope of the line is -3/10.

Step-by-step explanation:

Use the following equation:

m (slope) = (y₂ - y₁)/(x₂ - x₁)

Let:

(x₁ , y₁) = (-2 , 7)

(x₂ , y₂) = (18 , 1)

Plug in the corresponding numbers to the corresponding variables:

m = (1 - 7)/(18 - (-2))

Simplify. First solve the parenthesis, then divide:

m = (-6)/(18 + 2)

m = -6/20

Simplify.

m = (-6/20)/(2/2) = -3/10

Your slope of the line is -3/10.

~

Answer:

[tex]\displaystyle \frac{-3}{10}[/tex]

Step-by-step explanation:

Slope formula:

[tex]\displaystyle \frac{y_2-y_1}{x_2-x_1}[/tex]

[tex]\displaystyle\frac{1-7}{18-(-2)}= \frac{-6}{20}=\frac{-6\div2}{20\div2}=\frac{-3}{10}=-\frac{3}{10}[/tex]

Therefore, the slope is -3/10, and the correct answer is -3/10.

Answer:

161 is 4.6% of 3500

Step-by-step explanation:

Divide:

 161

-------- = 0.046

3500

Now multiply this result by 100%:  4.6%.

161 is 4.6% of 3500.

Answer:

4.6%

Step-by-step explanation:

To find what percent number A is of number B, divide A by B and multiply by 100.

To find what percent 161 is of 3500, divide 161 by 3500 and multiply by 100.

percent = 161/3500 * 100 = 0.046 * 100 = 4.6%

161 is 4.6% of 3500

Answer:

Clayton could use the relationship (x,y)→ (y,x) to find the points of the image

C’ will remain in the same location as C because it is on the line of reflection

The image and the pre-image will be congruent triangles

The image and pre-image will not have the same orientation because reflections flip figures

Step-by-step explanation:

Verify each statement

case A) Clayton could use the relationship (x,y)→ (y,x) to find the points of the image

The statement is true

we know that

The rule of the reflection of a point across the line y=x is equal to

(x,y)→ (y,x)

case B) Clayton could negate both the x and y values in the points to find the points of the image

The statement is false

case C) C’ will remain in the same location as C because it is on the line of reflection

The statement is true

If a point is on the line of reflection (y=x), then the point remain in the same location because the x and y coordinates are equal

case D) C’ will move because all points move in a reflection

The statement is false

Because C' is on the line of reflection (y=x), then the point remain in the same location

case E) The image and the pre-image will be congruent triangles

The statement is true

Because the reflection not change the length sides of the triangle or the measure of its internal angles. Reflection changes only the orientation of the figure

case F) The image and pre-image will not have the same orientation because reflections flip figures

The statement is true

Because in a reflection across the line y=x, the x coordinate of the pre-image becomes the y-coordinate of the image and the y-coordinate of the pre-image becomes the x-coordinate of the image

Answer:

y=-5x-6

Step-by-step explanation:

Parallel means you are looking for an equation that has the same slope as the one given.

The slope of y=-5x+9 is -5.

All I did was compare it to y=mx+b where m is slope and b is y-intercept.

So our equation is in the form y=-5x+b.

We want to find b such that y=-5x+b goes through (3,-21).

So we can plug in our point that is on this line so that that happens.

-21=-5(3)+b

-21=-15+b

Add 15 on both sides

-6=b

b=-6

So the line that is parallel to y=-5x+9 while going through (3,-21) is y=-5x-6.

Answer:x^2+2x+3

Step-by-step explanation:

I’m assuming you meant 2x^4+4x^3+6x^2...

So you can pull out 2x^2 from all of the polynomials...

And this equation isn’t able to be simplified anymore. Hope this helps!

The polynomial 2x^4 + 4x^3 + 6x^2 is factored by first finding the GCF 2x^2, resulting in 2x^2(x^2 + 2x + 3). The quadratic inside the parentheses cannot be factored further with real coefficients.

To factor the polynomial 2x^4 + 4x^3 + 6x^2, we first look for the greatest common factor (GCF) that can be factored out. In this case, each term has at least a factor of 2 and an x^2. Factoring out the GCF, we get:

2x^2(x^2 + 2x + 3)

Now, we look at the quadratic inside the parentheses to see if it can be factored further. However, the quadratic x^2 + 2x + 3 does not factor neatly over the integers because the discriminant, b^2 - 4ac, is negative (2^2 - 4(1)(3) = 4 - 12 = -8). Since we are only looking for real coefficients and not complex ones, we conclude that the quadratic cannot be factored further, and so the polynomial is fully factored as 2x^2(x^2 + 2x + 3).

Answer:

-43

Step-by-step explanation:

Follow PEMDAS as well as the left -> right rule.

Note that: PEMDAS =

Parenthesis

Exponents (& Roots)

Multiplication

Division

Addition

Subtraction

First, solve the multiplication:

23 + (5 * 3) - 100 + 19

23 + (15) - 100 + 19

Simplify. Follow the left-> right rule:

(23 + 15) - 100 + 19

38 - 100 + 19

(38 - 100) + 19

-62 + 19 = -43

-43 is your answer.

~

Answer:

-43

Step-by-step explanation:

Steps to PEMDAS:

P: parenthesis - There are no parenthesis in this equation.

E: exponents - There are no exponents in this equation.

M: multiplication 5 x 3 = 15

D: division There is no division in this equation.

A: addition 23 + previous 15 + 19 = 57

S: subtraction Previous answer 57 - 100 = -43

Therefore, the answer is -43.

Answer:

f(x) = (x-1)² + 3

Step-by-step explanation:

f(x)  = 4+x²-2x   or f(x)  = x²- 2x + 4   -----> eq 1

consider the top-most choice

f(x) = (x-1)² + 3 = x² + 2·x·(-1) + 1²  +  3

f(x) = x² - 2x+ 1  +  3

f(x) = x² - 2x+ 4  -----> compare this with eq 1 above (they match!)

hence f(x) = (x-1)² + 3 is the answer

Answer:

Jane drank 1 3/4 quarts of water.

Jane drank more water than Tom

Step-by-step explanation:

Tom drank  = 1 1/4 quarts of water

Jane drank = 1.75 quarts of water

We have to write the amount of water Jane drank in fraction.

There are some steps to convert decimal into fraction.

Step 1:

Value is 1.75:

Put the 1 aside and just work on 0.75

Write down the decimal value divided by 1

Like, 0.75/1

Step 2:

Now multiply both the numerator and denominator by 100.

We will multiply the numerator and denominator by 100 because 1.75 has two values after the decimal.

0.75 *100/1*100

75/100

Step 3:

Simplify the fraction.

divide the fraction by 5.

=15/20

=3/4

Now bring back the 1: and the fraction will become.

1 3/4

Jane drank 1 3/4 quarts of water.

Now who drank more water?

Jane drank more water than Tom

Reason:

Tom drank 1 1/4 = 5/4

Jane drank  1 3/4 = 7/4

Both the fractions have same denominator, so the value with the greater numerator drank more water than the other.

Therefore Jane drank more water than Tom....

Answer:

r<280

Step by step explanation:

Subtract 28 from both sides of the equation r+28<308.

r+28 subtracted by 28 leaves us with r<.

308-28 is 280.

Hence the equation becomes r<280.

The expression or inequality is 28 > r < 308 which represents 28 greater than r is less than 308.

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

The question is incomplete.

The complete question is:

Write the expression for the word expression "28 greater than r is less than 308"

It is given that:

The statement is:

28 greater than r is less than 308:

Here r is the real number.

Inequality can be defined as the expression in mathematics in which both sides are not equal they have mathematical signs either less than or greater than known as inequality.

28 > r < 308

Thus, the expression or inequality is 28 > r < 308 which represents 28 greater than r is less than 308.

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Check the picture below.

We are asked to find m ∠AKE, which is the measure of angle MAK. Therefore, MAK = 70 degrees. So, m∠AKE = 70 degrees.

To find m∠AKE, we need to use the properties of angles in a triangle. First, let's identify the triangle we are dealing with. Based on the information provided, we have the following triangle:

  A

 / \

/   \

/_____\

K E

Given that MAB = 110 and MDE = 130, we can use the fact that the sum of angles in a triangle is 180 degrees.

Since A is a common vertex to both angles MAB and MAE, we can write:

MAB + MAE + MAK = 180

Substitute the given values:

110 + MAE + MAK = 180

Now, we need to find MAE + MAK:

MAE + MAK = 180 - 110

MAE + MAK = 70

We are asked to find m∠AKE, which is the measure of angle MAK. Therefore, MAK = 70 degrees.

So, m∠AKE = 70 degrees.

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Answer:

D.

Step-by-step explanation:

h(x)=f(x)g(x) means multiply the expression for f to the expression for g.

That is the problem is just asking you to do (11x-5)(-2x-4).

Let's use foil.

First:  11x(-2x)=-22x^2

Outer: 11x(-4)=-44x

Inner: -5(-2x)=10x

Last: -5(-4)=20

------------------------Add together!

-22x^2-34x+20

D.

h(x) = [tex]-22x^{2} -34x+20[/tex]

Option D is correct.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Given equations

f(x) = 11x - 5

g(x) = - 2x - 4

h(x) = f(x) g(x)

h(x) = [tex](11x -5) \times (-2x-4)[/tex]

h(x) = [tex]11x \times (-2x) +11x \times (-4) -5 \times (-2x) -5 \times (-4)[/tex]

h(x) = [tex]-22x^{2} -44x+10x+20[/tex]

h(x) = [tex]-22x^{2} -34x+20[/tex]

Option D is correct.

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Answer:

y = 7.5x and y = 5.5x + 10

Step-by-step explanation:

this is for if you get the graph or not!

Answer:

5 classes

37.50 monthly cost for both gyms

Step-by-step explanation:

2022 edge

Answer:

0.08

Step-by-step explanation:

A standard deck of 52 cards has four aces.

The sample space is:

n(S) = 52

Let A be the event that an ace is drawn from the deck.

Then,

n(A) = 4

So,

[tex]P(A) = \frac{n(A)}{n(S)}\\ =\frac{4}{52} \\=0.0769[/tex]

Rounding off to the nearest hundredth will give us:

0.08 ..

The theoretical probability of drawing an ace from a standard deck of 52 cards is 0.08. The calculation is based on dividing the number of aces (4) by the total number of cards (52).

The theoretical probability of an event occurring is calculated by dividing the number of ways an event can occur by the total number of possible outcomes. In this scenario, the question is asking about the theoretical probability of drawing an ace from a standard deck of 52 cards.

In a standard deck of cards, there are 4 aces. So, the number of ways the event 'drawing an ace' can occur is 4. The total number of possible outcomes, which is the total number of cards in the deck, is 52. Therefore, the probability of drawing an ace, P(Ace), is calculated as follows:

P(ace) = Number of aces in the deck / Total number of cards

P(ace) = 4 / 52

When you simplify this fraction or convert it into decimal form (rounded to the nearest hundredths), it gives:

P(ace) = 0.08

So, the theoretical probability of drawing an ace from a deck of 52 cards is 0.08.

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Answer:

1 Ounce = 28.3495231 Grams

Step-by-step explanation:

Answer:

28.38 grams to the nearest hundredth.

Step-by-step explanation:

By proportion there is 454 / 16

= 28.38 grams in an ounce.

Answer:

B

Step-by-step explanation:

The entry A is the result of multiplying - x and 3x, that is

- x × 3x = - 3x² → B

Answer:

-3x^2

Step-by-step explanation:

A  3x * -x = -3x^2  so A = -3x^2

We can also find the value of B

B  -x *5 = -5x

and C

C = 3x*2 = 6x

Answer:

The correct answer is third option.  22 units

Step-by-step explanation:

Points to remember

If a right angled triangle with angles are 45°, 45° and 90° then the sides are in the ratio 1 : 1 : √2

To find the length of one leg of the triangle

From the figure we can see a right angled triangle with hypotenuse = 22√2 units

The other two legs are equal. Therefore the right angled triangle with angles 45°, 45° and 90°

Therefore the given triangle sides are in the ratio,

1 : 1 : √2 = x : x : 22√2

Therefore x = 22 units

The correct answer is third option.  22 units

Answer:

A

Step-by-step explanation:

Use the property

[tex]\sqrt[n]{a^m}=a^{\frac{m}{n}}[/tex]

The numerator can be simplified as

[tex]\sqrt[7]{x^2}=x^{\frac{2}{7}}[/tex]

The denominator can be simplified as

[tex]\sqrt[5]{y^3}=y^{\frac{3}{5}}[/tex]

Also remindr property

[tex]\dfrac{1}{a^n}=a^{-n}[/tex]

Thus, the expression is equivalent to

[tex]\dfrac{\sqrt[7]{x^2} }{\sqrt[5]{y^3} }=\dfrac{x^{\frac{2}{7}}}{y^{\frac{3}{5}}}=\left(x^{\frac{2}{7}}\right)\cdot \left(y^{-\frac{3}{5}}\right)[/tex]

Answer:

x ≥ 4

Step-by-step explanation:

Given

- 4(8 - 3x) ≥ 6x - 8 ← distribute parenthesis on left side

- 32 + 12x ≥ 6x - 8 ( subtract 6x from both sides )

- 32 + 6x ≥ - 8 ( add 32 to both sides )

6x ≥ 24 ( divide both sides by 6 )

x ≥ 4

Answer:

x ≥ 4

Step-by-step explanation:

4(8 - 3x) ≥ 6x - 8  distribute parenthesis on left side

32 + 12x ≥ 6x - 8 (subtract 6x from both sides)

32 + 6x ≥ - 8 (add 32 to both sides)

6x ≥ 24 (divide both sides by 6)

= x ≥ 4

Answer

-18√2-6√6

Step-by-step explanation:

(√12 +6) (-√8-√2)

=√12(-√8-√2)+6(-√8-√2)

= -√96-√24-6√8-6√2

= -4√6-2√6-12√2-6√2

= -6√6-18√2

= -18√2- 6√6

Step-by-step explanation:

To prove that two sides are parallel on a graph, we must show that their slopes are the same. Plotting this on Desmos, we get the first image attached.  Finding the slopes of each line, we get

[tex]TOP\\\frac{5-3}{6-1} =2/5\\BOTTOM\\\frac{-1-(-1)}{7-2} =2/5\\RIGHT\\-4\\LEFT\\-4[/tex]

As the top slope is the same as the bottom, and the right is the same as the left, this is a parallelogram.

To prove that two sides are congruent, we must find their lengths. The distance formula is

[tex]\sqrt(x_{1}+x_{2})^2+(y_{1}+y_{2})^2 } \\[/tex]

Finding the distances, we get

TOP: [tex]\sqrt{29}[/tex]

BOTTOM: [tex]\sqrt{29}[/tex]

RIGHT:[tex]\sqrt{17}[/tex]

LEFT:[tex]\sqrt{17}[/tex]

As the lengths are the same, the sides are congruent