where is the opposite of 8 located on a number line?

The player needs to score at least 3 consecutive goals to raise his shots-on-goal percentage to at least 20%.

An expression contains one or more terms with addition, subtraction, multiplication, and division.

We always combine the like terms in an expression when we simplify.

We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.

Example:

1 + 3x + 4y = 7 is an expression.

3 + 4 is an expression.

2 x 4 + 6 x 7 – 9 is an expression.

33 + 77 – 88 is an expression.

We have,

Let's first calculate how many total shots-on-goal the player has attempted so far:

Total shots-on-goal attempted = 24

Total goals scored = 3

Shots-on-goal percentage.

= (Total goals scored / Total shots-on-goal attempted) x 100%

Shots-on-goal percentage = (3 / 24) x 100% = 12.5%

Now, let's assume that the player scores x consecutive goals in his next x consecutive shots-on-goal.

Therefore, his new total goals scored will be:

New total goals scored = 3 + x

His new shots-on-goal percentage will be at least 20%:

New shots-on-goal percentage.

= (New total goals scored / New total shots-on-goal attempted) x 100%

≥20%

Substituting the values, we get:

(New total goals scored / (24 + x)) x 100% ≥ 20%

Simplifying and solving for x:

(New total goals scored / (24 + x)) ≥ 0.2

New total goals scored ≥ 0.2 (24 + x)

3 + x ≥ 4.8 + 0.2x

0.8x ≥ 1.8

x ≥ 2.25

Therefore,

The player needs to score at least 3 consecutive goals to raise his shots-on-goal percentage to at least 20%.

Learn more about expressions here:

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Nadia needs 2 buckets of water to fill the fish tank.

To calculate the volume of water needed to fill the fish tank, we need to find the volume of the tank and subtract the volume of the empty space. The volume of the tank is 2 ft x 1 ft x 1.5 ft = 3 ft³. The volume of the empty space is 2 ft x 1 ft x 0.25 ft = 0.5 ft³. Therefore, the volume of water needed is 3 ft³ - 0.5 ft³ = 2.5 ft³.

Next, we divide the volume of water needed by the volume of water in each bucket to find the number of buckets needed. 2.5 ft³ divided by 1.25 ft³/bucket = 2 buckets. Therefore, Nadia needs 2 buckets of water to fill the fish tank.

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2x+3+x<30

3x<27

x<9

The answer would be D. 

Answer:  The probability of getting 100 % on the quiz is 0.0625.

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Step-by-step explanation:

Since we have given that

Number of true-false questions = 4

Number of chances of answer = 2

1) True,

2) False

Probability of getting correct answer is given by

[tex]\frac{1}{2}[/tex]

Probability of getting 100% on the quiz by randomly guessing the answer to all 4 questions is given by

[tex]\frac{1}{2}^4\\\\=\frac{1}{2}\times \frac{1}{2}\times \frac{1}{2}\times \frac{1}{2}\\\\=\frac{1}{16}\\\\=0.0625[/tex]

Hence, The probability of getting 100 % on the quiz is 0.0625.

Answer:

30

Step-by-step explanation:

The weekly cost as a function of the unit price x can be calculated by subtracting the revenue from the total cost. The revenue is given by the demand equation q = -40x + 800, and the total cost is the sum of the fixed cost and the variable cost. Therefore, the weekly cost as a function of the unit price x is -160x + 3600.

The weekly cost as a function of the unit price x can be calculated by subtracting the revenue from the total cost.

Revenue is given by the demand equation q = -40x + 800, where q is the number of shirts sold at price x.

Total cost is the sum of the fixed cost and the variable cost. The fixed cost is $400 per week for use of the facilities, and the variable cost is $4 per shirt.

Therefore, the weekly cost as a function of the unit price x is given by:

Cost(x) = 400 + 4q = 400 + 4(-40x + 800) = 400 - 160x + 3200 = -160x + 3600

So, the weekly cost as a function of the unit price x is -160x + 3600.

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24.99 rounded to the nearest tenth is 25.0.

To round 24.99 to the nearest tenth, we need to look at the digit in the hundredths place. The number 24.99 has a 9 in the tenths place and a 9 in the hundredths place.

Since the hundredths place in 24.99 is 9 (which is higher than 5), we round up the tenths place from 9 to the next whole number which is 10, and it causes the digit in the ones place to increase by 1.

Therefore, 24.99 rounded to the nearest tenth is 25.0.

To solve the given system of linear equations, subtract one equation from the other to eliminate the y-variable, then solve for x and substitute back to find y. The solution is x = 2, y = -1.

To solve the system of equations 6x + 3y = 9 and 2x + 3y = 1, we can use the subtraction method. We want to find the values of x and y that satisfy both equations simultaneously. Observing that both equations have the term 3y, we can subtract the second equation from the first to eliminate the y-terms:

The solution to the system of equations is x = 2, y = -1.

To find the similarity ratio of ΔABC to ΔXYZ, compare the corresponding sides of the triangles. The ratio will be one of the named proportions based on the specific measurements of the triangles, which are not provided in the question.

The question pertains to finding the similarity ratio of two similar triangles. The similarity ratio of triangles is the ratio of any two corresponding lengths in the triangles. This question specifically asks for the ratio of triangle ΔABC to triangle ΔXYZ. Without the specific lengths provided, a general solution is to compare the corresponding sides of the triangles. For instance, if the length of side AB in ΔABC is twice the length of side XY in ΔXYZ, then the similarity ratio would be 2:1. If it was the other way around, the ratio would be 1:2. Similarly, if AB was three halves the length of XY, the ratio would be 3:2, and if AB was two thirds the length of XY, the ratio would be 2:3. The correct ratio would be one of the options given based on the specific lengths provided in the problem, which are not included in the question as stated.

Final answer:

Without specific side lengths, it's impossible to provide the similarity ratio of ΔABC to ΔXYZ. Additional measures of corresponding sides are needed for such a calculation.

Explanation:

To determine the similarity ratio of two similar triangles, you need to compare the lengths of corresponding sides. However, in the provided question, no specific measurements for the triangles are given, so it is not possible to calculate the exact similarity ratio of ΔABC to ΔXYZ. We would need additional information, such as the lengths of corresponding sides from both triangles, to be able to determine the correct ratio.

The process would involve dividing the length of a side from ΔABC by the length of the corresponding side from ΔXYZ. For instance, if side AB of ΔABC measures 6 cm and the corresponding side XY of ΔXYZ measures 3 cm, then the similarity ratio is 6:3 or simplified as 2:1.

The decimal number 2.18 can be written as the mixed number 2 9/50, considering that .18 is equivalent to the fraction 18/100, which simplifies to 9/50.

The number 2.18 is not technically a mixed number, but it can be written in a format similar to a mixed number. A mixed number is defined as a number that includes both a whole number and a proper fraction. In this case, the whole number is 2 and the decimal .18 could be viewed as a type of fraction. If we want to express .18 as a fraction, we can convert it to 18/100. This fraction, however, can be further simplified to 9/50 by dividing both the numerator and the denominator by 2. Therefore, we could write 2.18 as the mixed number 2 9/50.

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The correct answer is:

a. all real numbers

When we reflect a function across the y-axis, the x-values change their signs. For the function [tex]\( f(x) = 6(0.25)^x \)[/tex], the domain consists of all real numbers since the function is defined for all real values of x.

When we reflect this function across the y-axis to get g(x), the domain of g(x) remains the same as the original function f(x). This is because reflecting across the y-axis does not affect the x-values for which the function is defined.

So, the correct answer is:

a. all real numbers

Answer with explanation:

  The given function is :

            [tex]y= f(x)=2^x+2[/tex]

To plot the graph of this function , we find x, for different integral values of y and x for different integral values of y and plot these points in x y plane.

  x      0     1      2     3

  y      3     4     6     10

Join these points to get required curve.

Final answer:

The original price of the item was $60, and after a 70% reduction, the new price is $18.

Explanation:

The original price of an item was $60. After being reduced by 70%, we need to calculate what the new price will be. We can calculate the amount of discount by multiplying 70% with the original price, which is $60.

To find the discount amount: $60 × 0.70 = $42

Now, subtract the discount amount from the original price to find the new price: $60 - $42 = $18.

Therefore, after a 70% reduction, the new price of the item is $18.

Final answer:

To factor the expression 4x² − 8x − 60 completely, factor out the greatest common factor of 4, then factor the resulting quadratic expression, which results in C. 4(x − 5)(x + 3).

Explanation:

The question asks you to factor completely the quadratic expression  [tex]4x^2 - 8x - 60[/tex]To factor this expression, first, look for any common factors among the terms. Here, the common factor is 4. Factoring out the 4 gives you [tex]4(x^2 - 2x - 15).[/tex]Next, we factor the quadratic expression within the parentheses.

We look for two numbers that multiply to give − 15 (the constant term) and add to give − 2 (the coefficient of x). These numbers are − 5 and + 3, so the expression factors further into 4(x − 5)(x + 3).

The completely factored form of the quadratic expression  [tex]4x^2 - 8x - 60[/tex] is C. 4(x − 5)(x + 3).