What is the completely factored form of 2x2 – 32?

Answer:

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Step-by-step explanation:

To find a solution to the linear equation y=7x-3, select a value for x, substitute it into the equation, and solve for y. The resulting ordered pair (x, y) is a solution. For instance, (1, 4) is a solution when x=1.

The question is asking for the solution to the linear equation y=7x-3. To find an ordered pair that satisfies this equation, we need to choose a value for x and then calculate the corresponding value of y using the equation. For example, if we choose x=1, we then substitute it into the equation to get y=7(1)-3, which simplifies to y=4. Therefore, the ordered pair (1, 4) is a solution to the equation y=7x-3.

In general, to find more solutions, we could select different values of x and calculate y each time. All the resulting ordered pairs would be solutions to the given equation and would lie on the line represented by this equation when plotted on a graph.

Answer:

The correct option is C.

Step-by-step explanation:

The given expression is

[tex]21x-18x+28xy[/tex]

The factors of each term are

[tex]21x=3\times 7\times x[/tex]

[tex]18x=3\times 6\times x[/tex]

[tex]28xy=2\times 2\times 7\times x\times y[/tex]

The common factor is x.

[tex]G.C.F.=x[/tex]

Therefore correct option is C.

Final answer:

The equation of the circle x² + y² - 2y - 15 = 0 is rewritten in vertex form by completing the square for the y terms, resulting in x² + (y - 1)² = 4², indicating a center at (0, 1) and a radius of 4.

Explanation:

To rewrite the equation of the circle in vertex form, you want to complete the square for both the x and y terms. The equation given is x² + y² - 2y - 15 = 0. First, we need to isolate the x and y terms:

Since there's no x-term to complete the square with, we can leave the x² term as it is. For the y-terms, add and subtract (1/2 * coefficient of y)2, which is (1/2 * -2)² = 1:

Now the equation inside the parentheses is a perfect square trinomial and can be factored as (y - 1)². After adjustment, we get:

So the circle in vertex form is x² + (y - 1)² = 4², with the center at (0, 1) and a radius of 4 units.

Ans

Step-by-step explanation:

Answer:200 %

Step-by-step explanation:

From 1980 to 1990 population increased by 100%

Let us Say initial population be x

therefore 100 % increase means it increases to 2x

From 1990 to 2000 population increased by 50%

i.e.[tex]2x \times 1.5=3x[/tex]

Total increase from 1980 to 2000

[tex]\frac{3x-x}{x}\times 100=200\%[/tex]

The probability of choosing one red bulb and then one yellow bulb from 27 bulbs (11 red, 9 yellow, and 7 purple) is calculated by multiplying the chance of picking a red bulb first and a yellow bulb second. This results in approximately 1 in 7.1, or roughly 0.14.

The question you are asking is about finding the probability that one bulb is red and one is yellow out of a total of 27 bulbs, with a distribution of 11 red, 9 yellow, and 7 purple bulbs. To calculate this probability, we use the following steps:

Using the multiplication rule of probability, we get:

P(Red then Yellow) = (11/27) × (9/26)  = 99/702 = 1/7.1 (approximately).

So the probability that one bulb is red and one is yellow is about 1 in 7.1, or approximately 0.14.

Answer:

The probability that 3 red balls are chosen is: 2.2%

Step-by-step explanation:

A bag contains 4 black, 5 red, and 6 pink balls.

Total balls in the bag= 4+5+6= 15 balls in the bag

We need to know what is the probability that 3 red balls are chosen without replacement?

[tex]P_r=\frac{R_b}{T_b}*\frac{R_b-1}{T_b-1}*\frac{R_b-2}{T_b-2}[/tex]

Where:

[tex]P_r:[/tex] Probability that 3 red balls are chosen

[tex]R_b:[/tex] Number of red balls

[tex]T_b:[/tex] Number of total balls

[tex]P_r=\frac{5}{15}*\frac{5-1}{15-1}*\frac{5-2}{15-2}\\P_r=\frac{5}{15}*\frac{4}{14}*\frac{3}{13}\\P_r=\frac{1}{3}*\frac{4}{14}*\frac{3}{13}\\P_r=\frac{2}{91}\\P_r=0.022[/tex]

[tex]P_r=0.022=2.2[/tex]%

The probability that 3 red balls are chosen is: 2.2%

Answer:

6

Step-by-step explanation:

Answer:  The correct option is (B) [tex]x\leq 5.[/tex]

Step-by-step explanation:  Given that Kylie has $70 to spend on clothes. She wants to buy a pair of jeans for $30 and spend the rest on t-shirts where each t-shirt costs $8.

We are to select the inequality that represents the number of t-shirts she can purchase.

Let x denote the number of t-shirts that she can buy.

Then, according to the given information, we have

[tex]30+x\times 8\leq 70\\\\\Rightarrow 30+8x\leq 70\\\\\Rightarrow 8x\leq 70-30\\\\\Rightarrow 8x\leq 40\\\\\Rightarrow x\leq \dfrac{40}{8}\\\\\Rightarrow x\leq5.[/tex]

Thus, the required inequality that represents the number of t-shirts she can purchase is [tex]x\leq 5.[/tex]

Option (B) is CORRECT.

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:

https://brainly.com/question/3118662

#SPJ3

Final answer:

To find the number of non-guppies in the aquarium, subtract the number of guppies (7) from the total number of fish (13), which equals 6 non-guppy fish.

Explanation:

The student's question requires basic arithmetic to solve a subtraction problem within a real-world context of counting fish in an aquarium. Given that there are 13 fish in an aquarium and 7 are guppies, we need to find the number of non-guppies. The total number of non-guppies can be found by subtracting the number of guppies from the total number of fish.

Let's perform the calculation:

Total number of fish in the aquarium = 13

Number of guppy fish = 7

Subtract the number of guppy fish from the total number of fish to find the number of non-guppy fish. 13 (total number of fish) - 7 (number of guppies) = 6

Therefore, there are 6 non-guppie fish in the aquarium.

Did you distribute the negative 1 across the second term?

8x^2-1+2x^3-7x^3+3x^2-1

The answer should be -5x^3 + 11x^2

Final answer:

To round 0.9998 to three decimal places, consider the fourth decimal digit (8). Since it's 5 or higher, the third decimal digit (9) rounds up, resulting in 1.000 after taking the carry-over into account.

Explanation:

To round the number 0.9998 to three decimal places, you need to look at the fourth decimal place to decide whether to round up the third decimal place. The fourth decimal place is 8, which is 5 or more, so we round up the third decimal place from 9 to 10. However, since the third place is already at the maximum digit (9), this causes a carry-over, changing the number to 1.000. But, rounding to three decimal places means you want three digits after the decimal point, so the rounded number is 1.000. Rounding introduces a small amount of imprecision, determined by the digits you're eliminating or adjusting. However, in this situation, it's clear that the number essentially rounds up to one.

0.0703 written in scientific notation is 7.03 × [tex]10^{-2[/tex], representing the original number more compactly with the mantissa (7.03) and exponent (-2).

To express 0.0703 in scientific notation, we first need to move the decimal point to the right until only one digit is to its left. Count the number of places you moved the decimal point, which gives us the exponent of 10. In this case, we move the decimal point three places to the right to obtain 7.03. Thus, we have 7.03 × [tex]10^{-2[/tex]. Since we moved the decimal point three places to the right, the exponent of 10 is -3.

Therefore, 0.0703 in scientific notation is 7.03 × [tex]10^{-2[/tex]. This notation represents the original number in a more compact form, where the mantissa (7.03) indicates the significant digits and the exponent (-2) denotes the power of 10 by which the mantissa is multiplied.