Thirty cities were researched to determine whether they had a professional sports team, a symphony, or a children's museum of these cities, 15 had a professional
sports team 15 had a symphony, 13 had a children's museum, 8 had a professional sports team and a symphony, 7 had a professional sports team and a children's
museum 7 had a symphony and a children's museum, and 3 had all three activities Complete parts a) through e) below​

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

-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

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....

Let P = Phil's age

P + 9 = 18

The correct equation representation for 'Phil's age increased by 9 years is 18 years' would be 'p + 9 = 18', which indicates that when you add 9 years to Phil's age, it equals 18. Hence, option D is the correct answer.

The student is seeking to translate a sentence into a mathematical equation. The sentence states: 'Phil's age increased by 9 years is 18 years.' Considering 'Phil's age' as 'p', the correct translation of the sentence into a mathematical equation would be 'p + 9 = 18' since this indicates that when we add 9 years to Phil's age, we get 18 years. Therefore, the correct answer among the provided choices is option D: p + 9 = 18.

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The complete question is here:

Write as an equation: Phil's age increased by 9 years is 18 years.

A. p+18=9

B. p-9=18

C. p=18+9

D. p+9=18

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:

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 = 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:

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:

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

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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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:

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^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:

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]

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:

Miles he drove on highway = 180 miles

Miles he drove in the city = 217 miles

Step-by-step explanation:

Lets assume that gallon used on highway = x

Miles driven on highway = y

(I) 36 miles per gallon on the highway.

36x = y    equation 1

(II) 31 miles per gallon in the city.He recently drove 397 miles on 12 gallons of gasoline

31(12-x)= 397-y    equation 2

372-31x= 397-y

Combine the constants:

-31x= 397-372-y

y-31x = 25

Now substitute the value of equation 1 in equation 2

y-31x=25

36x-31x=25

5x=25

Now divide both sides by 5

5x/5=25/5

x=5

Now substitute the value x=5 in equation 1

36x=y

36(5)=y

180= y

Now subtract the miles driven on highway from recently drove miles to get the miles driven in the city.

397-y = 389 - 180

= 217

Therefore,

Miles he drove on highway = 180 miles

Miles he drove in the city = 217 miles ....

Julio drove 0 miles on the highway and 2856 miles in the city.

To find out how many miles Julio drove on the highway and in the city, we can set up a system of equations. Let x represent the number of miles driven on the highway and y represent the number of miles driven in the city. We know that the total distance driven is 397 miles and the total amount of gas used is 12 gallons. Using the given miles per gallon ratings, we can set up the following equations:

x + y = 397

36x + 31y = 12

From the first equation, we can isolate x:

x = 397 - y

Substituting this value of x into the second equation, we can solve for y:

36(397 - y) + 31y = 12

14292 - 36y + 31y = 12

-5y = -14280

y = 2856

Now we can substitute the value of y back into the first equation to find x:

x + 2856 = 397

x = 397 - 2856

x = -2459

However, since we cannot have negative miles, we know that Julio did not drive any miles on the highway.

Therefore, Julio drove 0 miles on the highway and 2856 miles in the city.

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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:

yes it is a solution

Step-by-step explanation:

o>-4

0<1

yes both work out to be equal

Answer:

It is a solution

Step-by-step explanation:

Check and see if (0,0) satisfies both inequalities.

The first inequality is:

[tex]y \geqslant {x}^{2} + x - 4 [/tex]

When we put x=0, and y=0, we get:

[tex]0\geqslant {0}^{2} + 0 - 4[/tex]

[tex] \implies0\geqslant- 4[/tex]

This part is true.

The second inequality is:

[tex]y \leqslant {x}^{2} + 2 x + 1[/tex]

We put x=0 and y=0 to get:

[tex]0 \leqslant {0}^{2} + 2 (0) + 1[/tex]

[tex]0 \leqslant 1[/tex]

This part is also true.

Since the (0,0) not satisfy both, inequalities, it is a solution.

Answer:

The area in factored form is [tex]A=(x+2)(x-5)[/tex].

The area in standard form is [tex]A=x^2-3x-10[/tex].

Step-by-step explanation:

The area of a rectangle is length times width.

So the area here is (x+2)(x-5).

They are probably not looking for A=(x+2)(x-5) because it requires too little work.

They probably want A in standard form instead of factored form.

Let's use foil:

First x(x)=x^2

Outer: x(-5)=-5x

Inner: 2(x)=2x

Last: 2(-5)=-10

---------------------Adding together:  [tex]x^2-3x-10[/tex].

The area in factored form is [tex]A=(x+2)(x-5)[/tex].

The area in standard form is [tex]A=x^2-3x-10[/tex].

Final answer:

The equation describing the area of the rectangle in terms of x, given the sides x + 2 and x - 5, is A = x² - 3x - 10.

Explanation:

To find the equation that describes the area, A, of a rectangle in terms of x, we use the formula for the area of a rectangle, which is length times width. Given that the length is x + 2 and the width is x - 5, the equation for the area A in terms of x is A = (x + 2)(x - 5).

To express A as a polynomial, we can expand this equation:

A = x(x - 5) + 2(x - 5)

A = x² - 5x + 2x - 10

A = x² - 3x - 10

Therefore, the equation that describes the area of the rectangle in terms of x is A = x² - 3x - 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

Check the picture below.

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:

-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:

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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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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