basketball goal 10 ft high casts a shadow 36 ft long. Find the elevation to the sun

Final answer:

To subtract the polynomials, we subtract the coefficients of like terms: the a⁴ terms give -4a⁴, there are no changes to the ab² term since it's not present in both polynomials, and for the a terms, we get 46a. So, the result is -4a⁴ + 2ab² + 46a.

Explanation:

The question asks us to perform polynomial subtraction. Specifically, the question requires subtracting 7a⁴ - 4a²b² + 67a from 3a⁴ + 2ab² + 113a. To do this, we subtract the coefficients of like terms, which are terms with the same variable raised to the same power.

Let's subtract step-by-step:

Putting it all together, the result of our subtraction is -4a⁴ + 2ab² + 46a.

Answer:

2. It can be solved by using the multiplication property of equality.

3. The equation should be: [tex]\frac{x}{18}=109.8[/tex]

6. The answer is 1,976.4.

Step-by-step explanation:

Let x be the number.  

We have been given that the quotient of a number and 18 is 109.8.

Since we know that in a division problem the number which is being divided called dividend and by which number we divide is called divisor.

[tex]\text{Dividend}\div \text{Divisor }=\text{ Quotient}[/tex]

We can represent our given information as:

[tex]\frac{x}{18}=109.8[/tex]

By using multiplication property of equality we will get,

[tex]18*\frac{x}{18}=18*109.8[/tex]

[tex]x=18*109.8[/tex]

[tex]x=1976.4[/tex]

Upon looking at our given choices we can see that 2nd, 3rd and 6th statements are correct choices.

Answer: [tex]\bold{(A)\ \dfrac{\text{51 miles}}{\text{1 hour}}}[/tex]

Step-by-step explanation:

Consider the formula "distance (d) = rate (r) x time(t)" and solve for r.

d = r · t

÷ t  ÷ t  

[tex]\dfrac{d}{t}=r[/tex]

Now plug in the given d and t values from the table to solve for r:

[tex]r=\dfrac{\text{204 miles}}{\text{4 hours}}[/tex]

    [tex]=\dfrac{\text{51 miles}}{\text{1 hour}}[/tex]   simplified the fraction

You can check this by plugging in the other 3 values from the table:

[tex]r=\dfrac{\text{306 miles}}{\text{6 hours}}[/tex]

    [tex]=\dfrac{\text{51 miles}}{\text{1 hour}}[/tex]  

[tex]r=\dfrac{\text{408 miles}}{\text{8 hours}}[/tex]

    [tex]=\dfrac{\text{51 miles}}{\text{1 hour}}[/tex]  

[tex]r=\dfrac{\text{510 miles}}{\text{10 hours}}[/tex]

    [tex]=\dfrac{\text{51 miles}}{\text{1 hour}}[/tex]  

Answer:

4/15

Step-by-step explanation:

Experimental probability is the actual times the event occurs divided by the number of trials

Actual times : 8

Number of trials: 30

Experimental probability of a 2: 8/30 = 4/15

Answer:

There were 275 computers

Step-by-step explanation:

Computers replaced = total computers * percent replaced

What do we know?

The percent replaced is 20  = .2

55 computers were replaced.

Substitute this in

55 = total computers * .2

Divide each side by .2

55/.2 = total computers *.2 /.2

275 = total computers

There were 275 computers

Answer:

the answer is 3

Step-by-step explanation:

3 pizzas equal $9.00 so in order to know how much each pizza was, we will have to do division:

9 divided by 3

9/3

3

Answer:

8 movies or video games.

Step-by-step explanation:

Let x be the number of movies or video games on rent.  

We have been given that Omar has a choice of belonging to a video club with a monthly fee of $12 and $1-a-day rental fee for any movie or game. We can represent the charges for x movies or video games for a member of club as: [tex]x+12[/tex].

Omar can be a non-member and pay $2.50-a-day rental fee for any movie or game. We can represent the charges of a non-member for x movies or video games as: [tex]2.5x[/tex].

To find the number of movies for one day for the cost to be equal we will equate our both expressions.

[tex]x+12=2.5x[/tex]

[tex]x+12-x=2.5x-x[/tex]

[tex]12=1.5x[/tex]

[tex]x=\frac{12}{1.5}[/tex]

[tex]x=8[/tex]

Therefore, Omar must rent 8 movies or video games for one day for the cost to be equal between membership and non-membership.

By renting 8 movies or video games charges for membership will be: 8+12=20.

By renting 8 movies or video games charges for a non-membership be: 2.5*8=20.

Hence charges of renting 8 movies or video games are same for both membership or non-membership.

Omar needs to rent 8 movies or video games in one month for the costs of a membership and nonmembership to be the same. The membership includes a monthly fee of $12, and rentals cost $1 per day. Non-membership rentals cost $2.50 per day.

Omar wants to determine how many movies or video games he must rent for the cost of membership and non-membership to be equal. To find this, we will set up an equation comparing the two costs.

Membership Plan:

Non-membership Plan:

Rental fee: $2.50 per movie/game per day  

Let's denote the number of movies or games rented by x.

For the membership plan, the total cost is: $12 + $1x

For the non-membership plan, the total cost is:$2.50x

We set the two costs equal to find x: $12 + $1x = $2.50x

Subtract $1x from both sides: $12 = $1.50x

Divide both sides by $1.50: x = 8

Omar must rent 8 movies or video games in one month for the costs of membership and non-membership to be equal.

Answer:

there would be 420 cards in total

Step-by-step explanation:

Answer:

The numbers are 8 and 13

Step-by-step explanation:

In order to find this, we set the smaller number as x. Then we can set the larger one as x + 5, since it is 5 more than the smaller.

Given these two, we can then set them equal to 3x - 3, since the answer is three less than three times the larger.

x + x + 5 = 3x - 3

2x + 5 = 3x - 3

5 = x - 3

8 = x

Now to find the larger number, put into the larger number equation.

x + 5

(8) + 5

13

The numbers are 8 and 13.

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The algebraic expression is,

''One number is five more than another and their sum Is there less than three times the smaller''.

Now,

Let the smaller number = x

Then, The another number = x + 5

Write the expression as;

x + x + 5 = 3x - 3

2x + 5 = 3x - 3

2x - 3x = - 3 - 5

- x = - 8

x = 8

And, The another number = x + 5

                                        = 8 + 5

                                        = 13

Thus, The numbers are 8 and 13.

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Answer:

x ---> 1

y ---> 5

Step-by-step explanation:

We are given paired values for two variables x and y and we are to determine the constant number by which each term is increased such that they are in a proportional relationship.

For x, we have the following paired values:

[tex]x: 1, 2, 3, 4[/tex]

So here the difference between each consecutive term is 1 so the constant is 1.

And for y, we have:

[tex]y: 5, 10, 15, 20[/tex]

In this case, the difference between each consecutive term is 5 so the constant is 5.

Answer:

We put the value of "y" into the second equation:

x * 5 = -15

x = -15 / 5

x = -3

Step-by-step explanation:

[tex]3 log 2x=4\ /:3\\log2x=\frac{4}{3}\\10^{\frac{4}{3}}=2x\ /:2\\x=\frac{10\sqrt[3]{10} }{2}\\x=5\sqrt[3]{10}[/tex]

The membership went up by 10%.

There are now 55 total students in the club.

The formula for calculating the percentage change is

[tex]p=\frac{N-O}{O}.100[/tex]

where p is the percent change, N is the New Value and O is the Old Value.

In this problem we are given the Old Value (50) and the percent change (10). We can substitute this into the formula and solve for N:

[tex]10=\frac{N-50}{50} .100\\10=2(N-50)\\5=N-50\\N=55[/tex]

There are now 55 total students in the club.

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Answer:

Option d is correct.

Both the x and y coordinates of the point on δa'b'c' have opposite signs from the corresponding points on δabc.

Step-by-step explanation:

The rule of 180 degree rotation about the origin is:

[tex](x, y) \rightarrow (-x , -y)[/tex]

Since a Rotation of a point through 180°, about the origin when a point a(h, k)  is rotated about the origin through 180° in anticlockwise or clockwise direction.

then, By the rule of 180 degree rotation;

[tex]a(h, k) \rightarrow a'(-h , -k)[/tex]

so, it takes the new position i.e, [tex]a'(-h , -k)[/tex]

Therefore, both the x and y coordinates of the point on δa'b'c' have opposite signs from the corresponding points on δabc.

Answer:

Commutative property.

Step-by-step explanation:

Commutitive property suggests that, for example; b + c = c + b

'a' is used as a constant here.

Answer:

20%

Step-by-step explanation:

Percentage means out of 100

We need to get 2/10 to be out of 100

Multiply by 10/10

2/10*10/10

= 20/100

This is 20%

Answer:

Step-by-step explanation:

Answer:

$30

Step-by-step explanation:

x*0.70=21

21/0.70= 30

Answer: c

Step-by-step explanation:

the number with one dot < on the left side means its the smaller number

Answer:

c    x< 9

Step-by-step explanation:

A number less than 9

x must be less than 9

No equals sign because it is less than

The inequality faces the larger number

x < 9

Answer:

[tex]\frac{5}{8}[/tex]

Step-by-step explanation:

We have been given that our Einstein has baked a cake and cut it into 8 slices. So each slice will be equal [tex]\frac{1}{8}[/tex].

He hands out 3 slices to his guests. Let us find out part of the cake given to guests.

[tex]\text{The part of the cake given to guests}=\frac{1}{8}+\frac{1}{8}+\frac{1}{8}[/tex]

[tex]\text{The part of the cake given to guests}=\frac{1+1+1}{8}[/tex]

[tex]\text{The part of the cake given to guests}=\frac{3}{8}[/tex]

To find the fraction of left cake we will subtract [tex]\frac{3}{8}[/tex] from 1 as Einstein has 1 whole cake.

[tex]\text{fraction of cake is left}=1-\frac{3}{8}[/tex]

[tex]\text{fraction of cake is left}=\frac{8}{8}-\frac{3}{8}[/tex]

[tex]\text{fraction of cake is left}=\frac{8-3}{8}[/tex]

[tex]\text{fraction of cake is left}=\frac{5}{8}[/tex]

Therefore, [tex]\frac{5}{8}[/tex] of the cake is left.

Answer:

As per the given statement: Our Einstein has baked a cake and cut it into 8 slices.

⇒ Total slice of cake Einstein has baked = 8

Also, it is given that if he hands out 3 slices to his guests.

⇒ Number of slice he hands out to his guests = 3

Remaining slice of a cake Einstein left with = 8 -3 = 5.

We have to find the fraction of the cake is left.

Fraction states that a fraction is a number that represents a part of a whole. Also, It consists of a numerator and a denominator, where numerator represents the number of equal parts of a whole, while the denominator is the total number of parts.

Fraction of the cake is left = [tex]\frac{\text{Slices of cake left}}{\text{Total number of slices of a cake}}[/tex]

Substitute the given values we get;

[tex]\text{Fraction of the cake is left} =\frac{5}{8}[/tex]

therefore, the fraction of the cake is left is,  [tex]\frac{5}{8}[/tex]

Answer: x = 3

Step-by-step explanation:

If 3x is the midsegment of the triangle, then it is half the length of the base, which implies that the length of the base equals twice the length of the midsegment:

base = 2 * midsegment

 18   =  2 (3x)

  18  =   6x

  ÷6     ÷6  

   3   =  x

Answer:$38.75

Step-by-step explanation:

35(number of feet) * $1.75(cost per foot) = $61.25(total cost)

$100(bill used) - $61.25(total cost) = $38.75(amount given in change)

Answer:

$38.75

Step-by-step explanation:

We have given that : The trim cost per foot  =$1.75

for 35 feet of window trim cost = 35×1.75 = $61.25

Now, Fatima paid $100.00 bill

Amount she received = Amount she pay - cost of trim she buy

                                     = $100 - $61.25

                                      =$38.75            

180-(x+50)+180-4x+180-(2x+40)+180-3x=360

720-x-50-4x-2x-40-3x=360

630 - 10x=360

-10x=360-630

-10x=-270  /:(-10)

x=27

Answer: ITS B

Step-by-step explanation:

Answer:

3

Step-by-step explanation:

The zero at the point x=3 is a result of a factor of even degree, because the function does not change sign as the value of (x -3) changes sign. Since a cubic only has 3 factors, the even degree must be 2. That is, (x -3)² is a factor of f(x) and the root at x=3 has multiplicity 2.

Answer:

the footballer's average pay would be $4 million/annum.

Answer:

x = 5

Step-by-step explanation:

Refer the attached image.

B is midpoint of AC

D is midpoint of CE

So,

[tex]AB=BC=CD=DE[/tex]

[tex]BD=BC+CD= AB+DE=\frac{1}{2}(AE)[/tex]

[tex](3x+5)=\frac{1}{2} (4x+20)[/tex]

Solving for 'x' we get,

[tex]3x+5=2x+10[/tex]

[tex]3x-2x=10-5[/tex]

[tex]x=5[/tex]

So the value of 'x' is 5.

Erin needs to make a -$50.76 entry in her register to reconcile her check register with her bank statement. This takes into account deposits not reported on her bank statement, along with outstanding checks and an ATM withdrawal.

To reconcile Erin's check register, we need to account for all transactions not yet reported on the bank statement. First, add the value of the deposits not reported ($125.56 + $50 + $212.34 = $387.90) to the balance of the bank statement ($844.93 + $387.90 = $1232.83). Then, subtract the amount of the outstanding checks and ATM withdrawal ($15 + $78.25 + $40 = $133.25) from this sum ($1232.83 - $133.25 = $1099.58).

The reconciled balance in Erin's check register should be $1099.58. Consequently, Erin needs to adjust her register to reflect the correct balance. Given that Erin’s original balance was $1150.34 and the reconciled balance is $1099.58, Erin needs to subtract $50.76 from her register.

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Final answer:

Starting with Saul in the 3rd position and counting the 3 children between him and Enid, Enid is determined to be in the 7th position in the line.

Explanation:

To find the position of Enid in line, we start with Saul who is third in line. If there are 3 children between Saul and Enid, and Enid is last, we need to count the positions:

Saul is 3rd in line.

1st child after Saul is in the 4th position.

2nd child after Saul is in the 5th position.

3rd child after Saul is in the 6th position.

Enid is after the 3rd child, placing her in the 7th position.

Therefore, Enid is in the 7th position in line.