Solve this system of equations by substitution or by linear combination

Answer:

15 x [tex]3^{2}[/tex]

Step-by-step explanation:

since each side is increased by 3, total enlargement of area will be [tex]3^{2}[/tex] times

Answer:

Step-by-step explanation:

To find the x-intercepts of the polynomial function f(x) = x^4 - x^2, we need to set f(x) = 0 and solve for x. That is, we need to find the values of x that make the function equal to zero.

f(x) = x^4 - x^2

Setting f(x) = 0, we get:

x^4 - x^2 = 0

Factoring out x^2, we get:

x^2(x^2 - 1) = 0

Using the zero product property, we get:

x^2 = 0 or x^2 - 1 = 0

Solving for x in each case, we get:

x = 0 or x = ±1

Therefore, the x-intercepts of the polynomial function f(x) = x^4 - x^2 are (0, 0), (1, 0), and (-1, 0).

The probability of selected exactly three girls is A 0.022

Probability simply means the chance that a particular thing or event will happen. It is the occurence of likely events. It is simply the area of mathematics that deals with the numerical estimates of the chance that an event will occur or that a particular statement is true.

In this case, the probability of an event us usually represented as a number between 0 and 1. In this case, 0 denotes the impossibility of the event and 1 represents certainty.

In this situation, the probability of selected exactly three girls is 0.022. This can easily be seen in the table.

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The sum of the given series is -

6 ∑{1/(2n + 1)² - 1}.

Integration is a process of adding up small elemental volumes to find the larger volume.

Given is the series as -

6/(3² - 1) + 6/(5² - 1) + 6/(7² - 1) + ....

The given series is -

S = 6/(3² - 1) + 6/(5² - 1) + 6/(7² - 1) + ....

S = 6{1/(3² - 1) + 1/(5² - 1) + 1/(7² - 1) + ....}

S = 6 ∑ {1/(2n + 1)² - 1}

Therefore, the sum of the given series is -

6 ∑{1/(2n + 1)² - 1}.

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Answer:

Step-by-step explanation:

To represent the number of eighth-grade students, we can use the expression:

0.8s

This is because the problem states that there are 20% fewer students in the eighth grade than in the seventh grade, which means that the number of eighth-grade students is equal to 80% of the number of seventh-grade students.

To simplify this expression, we can use the distributive property:

0.8s = 1s - 0.2s

This shows that the number of eighth-grade students is equal to the number of seventh-grade students minus 20% of the number of seventh-grade students. We can further simplify this to:

0.8s = 0.8s

This means that the number of eighth-grade students is equal to 80% of the number of seventh-grade students, which is consistent with the original problem statement.

The runners can finish in 362880 possible results

What is Permutation?

Permutation is the different number of arrangements that can be formed by taking r things from the n available things.

The formula  n! = 1 × 2 × 3 × 4 × .......× n.

To get the order the runners could possibly finish,

= 9! = 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1

= 326880

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Answer:

C revenue

Step-by-step explanation:

from the student's perspective, eliminating the opened envelope would be a better choice as it doubles their chances of winning the dollar.

While from the team's perspective, keeping all 24 envelopes would be better as it reduces the probability of the student winning the dollar to 1/24. Therefore, the team would likely raise more money if they encourage the students to keep all 24 envelopes.

Assuming that the slips of paper are randomly distributed and the student does not have any information about the distribution, let's analyze the probabilities for each choice:

Thus, from the student's perspective, eliminating the opened envelope would be a better choice as it doubles their chances of winning the dollar. On the other hand, from the team's perspective, keeping all 24 envelopes would be better as it reduces the probability of the student winning the dollar to 1/24. Therefore, the team would likely raise more money if they encourage the students to keep all 24 envelopes.

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The slope of the line segment is -1/2 . Option A is correct.

What is slope ?

The slope of a line is a measure of its steepness. Mathematically, slope is calculated as "rise over run" (change in y divided by change in x).

The slope is the "rise over run" between any two points on the line.

Count out how much "up or down" vs "left or right" to find the slope:

   We go up 5 and right 5, giving us the fraction

Thus , slope is given by -5 /10 = -1 /2      

When counting, up and right are counted as positive; left and down are counted as negative.

Hence , the slope of the line segment is -1/2 . Option A is correct.

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The fraction of the teams which walked as part of the fundraiser for the library, that raised extra money, is D. 1 / 3.

You must count the number of teams that were able to walk more than 50 laps in order to determine the percentage of teams that raised the additional funds. The distance walked by teams more than 50 laps were :

There are 12 teams overall, which is equal to the number of leaves.

The fraction of teams that raised additional funds is:

= 4 teams / 12 total teams

= ( 4 ÷ 4 ) / ( 12 ÷ 4 )

= 1 / 3

In conclusion, the fraction of teams which raised extra money was 1 / 3.

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Answer:

-27/64 or -0.4219

Step-by-step explanation:

A fraction is a fragment of a whole number, used to define parts of a whole. The whole can be a whole object, or many different objects. The number at the top of the line is called the numerator, whereas the bottom is called the denominator.

To solve this, we can take the numerator and denominator, and cube them.

The new fraction is now [tex]-\frac{27}{64}[/tex].

Therefore, [tex]-\frac{3}{4}[/tex] cubed as a fraction is [tex]-\frac{27}{64}[/tex].

The expression as a fraction is -27/64.

We have,

Expression:

(-3/4)³

This can be written as,

-3³ / 4³

Now.

Simplifying each term.

-3³ = -3 x -3 x -3 = -27

4³ = 4 x 4 x 4  = 64

Now,

(-3/4)³ = -27/64

Thus,

The expression as a fraction is -27/64.

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Answer:

347

Step-by-step explanation:

Im not sure if that helps but thats the answer I got.

By using the long division method, The value of expression  8328 ÷ 24 after divide is,

⇒ 8328 ÷ 24

   = 347

Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications.

For example, To dividing 20 by 2 means splitting 20 into 2 equal groups of 10.

We have to given that;

The mathematical expression for divide is,

⇒ 8328 ÷ 24

Now, We can formulate;

We can use the long division method for the expression as;

⇒ 8328 ÷ 24

⇒ 8328 / 24

 24 ) 8328 ( 347

     -  72

       -----

        112

     -   96

        ------

             168

           -  168

            --------

                  0

Therefore, We get the correct answer,

By using the long division method,

The value of expression  8328 ÷ 24  after divide is,

⇒ 8328 ÷ 24

   = 347

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Answer:

c = -5

Step-by-step explanation:

[tex]\frac{1}{4} c+2=\frac{3}{4}[/tex]

Subtract 2 on both sides

[tex]\frac{1}{4} c=-1\frac{1}{4}[/tex]

Divide by [tex]\frac{1}{4}[/tex]

[tex]c=-5[/tex]

The number of years for the interest amount to reach $ 1,500 at 4 % is given by b = 10.35 years

Compound interest is interest based on the initial principle plus all prior periods' accumulated interest. The power of compound interest is the ability to generate "interest on interest." Interest can be added at any time, from continuously to daily to annually.

The formula for calculating Compound Interest is

A = P ( 1 + r/n )ⁿᵇ

where A = Final Amount

P = Principal

r = rate of interest

n = number of times interest is applied

b = number of time periods elapsed

Given data ,

Let the amount invested be P = $ 1,000

Let the number of years be = b

Let the number of times the interest is applied n = 1

Let the rate of interest be r = 4 %

Now , the compound interest + amount = $ 1,500

A = P ( 1 + r/n )ⁿᵇ

And , the number of years b = ln ( A / P ) / n [ ln ( 1 + r / n ) ]

On simplifying , we get

b = ln ( 1,500.00 / 1,000.00 ) / ( 1 × [ ln ( 1 + 0.04 ) ] )

b = 10.338 years

Hence , the number of years is 10.35 years

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The probability that he will make both free throws is 0.84.

What exactly is the meaning of probability?

Probability expresses the possibility of an event. This branch of mathematics studies the occurrence of a random event. The value ranges between 0 and 1. Probability is used in mathematics to anticipate the possibility of events occurring.

Probability refers to the likelihood of something occurring. This fundamental premise of probability theory is used by the probability distribution. We must first know the entire number of possibilities before we can assess the possibility of an event occurring.

P(E) is the probability of an event occurring divided by the total number of outcomes.

Now,

Given that player makes 92% of freethrows

that means p(making free throws)=92/100

=23/25

so making two free throws probability will be =23*23/25*25

=529/625

=0.84

Hence,

           The probability that he will make both free throws is 0.84.

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Answer:

0.1369

Step-by-step explanation:

(37/100)^2=0.1369

Answer:

Step-by-step explanation:

a) The slope of the line passing through the points (5,6) and (-1,6) can be calculated using the formula:

m = (y2 - y1) / (x2 - x1)

where (x1, y1) = (5,6) and (x2, y2) = (-1,6).

m = (6 - 6) / (-1 - 5) = 0 / -6 = 0

Therefore, the slope of the line is 0.

b) The slope of the line passing through the points (3,-2) and (3,-1) cannot be calculated using the previous formula since the points have the same x coordinate. This means that the line is vertical and therefore its slope is infinite (or undefined).

c) The slope of the line passing through the points (2,2) and (-5,2) can be calculated using the formula:

m = (y2 - y1) / (x2 - x1)

where (x1, y1) = (2,2) and (x2, y2) = (-5,2).

m = (2 - 2) / (-5 - 2) = 0 / -7 = 0

Therefore, the slope of the line is 0.

d) The slope of the line passing through the points (9,-2) and (-7,-2) can be calculated using the formula:

m = (y2 - y1) / (x2 - x1)

where (x1, y1) = (9,-2) and (x2, y2) = (-7,-2).

m = (-2 - (-2)) / (-7 - 9) = 0 / -16 = 0

Therefore, the slope of the line is 0.

e) The slope of the line passing through the points (-8,22) and (1,4) can be calculated using the formula:

m = (y2 - y1) / (x2 - x1)

where (x1, y1) = (-8,22) and (x2, y2) = (1,4).

m = (4 - 22) / (1 - (-8)) = -18 / 9 = -2

Therefore, the slope of the line is -2.

f) Since we know the slope m = 2 and one of the points is (3,6), we can use the formula:

y - y1 = m(x - x1)

where (x1, y1) = (3,6). Substituting m and (x1, y1) into the formula, we get:

y - 6 = 2(x - 3)

Expanding the formula and solving for y, we get:

y = 2x - 6 + 6

y = 2x

Therefore, the y-coordinate of the second point is y = 2(4) = 8. The second point is (4,8).

the answer is(C) equation x +y = 11; 2x 10y = 54.

In mathematics, an equation is a statement that asserts the equivalency of two expressions, generally containing one or further variables. An equation consists of two sides, frequently separated by an equal sign. The left- hand side( LHS) of the equation contains one expression, while the right- hand side( RHS) contains another. The equation asserts that the two sides are equal, meaning that they represent the same value, anyhow of the values assigned to the variables.

The correct system of equations that represents the number of one- on- one and platoon games being played is

x y = 11( since there are 11 basketball courts in total)

2x 10y = 54( since a one- on- one game requires 2 players and a platoon game requires 10 players)

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It takes the toy car 2.43 seconds to fall to the bottom floor,  answer choice is B. 9/4 seconds, which is equal to 2.25 seconds.

An equation is a mathematical statement that asserts that two expressions are equal. An equation consists of two sides, the left-hand side and the right-hand side, separated by an equal sign (=).

For example, 2x + 5 = 11 is an equation, where the left-hand side is 2x + 5 and the right-hand side is 11. This equation asserts that the expression 2x + 5 is equal to 11, and the value of x can be determined by solving for x.

Equations can be simple or complex, and they can involve one or more variables. They can also be linear or nonlinear, depending on the nature of the expressions involved.

Solving an equation involves finding the values of the variables that make the equation true. This may involve applying algebraic operations and simplification techniques to isolate the variable on one side of the equation.

Equations are used in many areas of mathematics, science, engineering, and economics, and they provide a powerful tool for modeling and analyzing real-world situations. They are also used extensively in computer programming and cryptography, where they play a critical role in the development of algorithms and data encryption methods.

We have the equation [tex]h = 94 - 16t^2[/tex], where h is the height of the toy car in feet and t is the time in seconds.

When the toy car reaches the bottom floor, its height will be h = 0. So we can set the equation equal to 0 and solve for t:

[tex]0 = 94 - 16t^216t^2 = 94t^2 = 94/16[/tex]

[tex]t = \sqrt{(94/16)} = \sqrt{(23.5/4)} = 2.43 seconds[/tex] (rounded to two decimal places)

Therefore, it takes the toy car 2.43 seconds to fall to the bottom floor.

The closest answer choice is B. 9/4 seconds, which is equal to 2.25 seconds.

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A + A(9%) = A(1.09) is matching with the amount Jess owes Julie from borrowing A with 9% interest.

What is interest?

In the study of finance and economics, interest is the predetermined amount that a borrower or deposit-taking financial institution pays to a lender or depositor above and beyond the principal amount. It differs from any fees the borrower may be required to pay the lender or another entity.

Suppose here A is 100

We put the value of A in the equation

A + A(9%) = A(1.09)

100+ 100*9/100 = 100*1.09

Or,100+9=100*109/100

Hence the correct answer is D, amount Jess owes Julie from borrowing A with 9% interest.

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Answer:

Step-by-step explanation:

deuyfheuf

The sequence of transformations that maps triangle ABC onto triangle A”B”C” is given as follows:

First we must look at one vertex of the original triangle, and I am going to choose vertex A, which has the coordinates given as follows:

A(-1,1).

From the change in the orientation of the triangle, we can see that it was reflected over the x-axis, transformation for which the rule is (x,y) -> (x, -y), hence:

A'(-1,-1).

The coordinates of vertex A'' are given as follows:

A(-4,-4).

This means that each coordinate of vertex A' was multiplied by 4, thus the second transformation is a dilation with a scale factor of 4.

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Function with the domain of [-3, 3] is f(x) = [tex]x^2[/tex]

A function is a mathematical formula that gives each input value in a set an individual output value. The domain and range are two sets that relate to one another in such a way that each element in the domain has a unique association with the elements in the range.

An equation or collection of rules that indicate how the output is determined depending on the input constitutes a function, which is often denoted by a symbol like f. The independent variable is the value of the inputs, and the dependent variable is the value of the outputs.

Here's an example of a function with the domain of [-3, 3]:

f(x) = [tex]x^2[/tex]

This function maps each value in the interval [-3, 3] to its square. For example, when x = -3, f(x) = [tex](-3)^2[/tex] = 9, and when x = 3, f(x) = [tex](3)^2[/tex] = 9. The graph of this function is a parabola that opens upward and has its vertex at the origin (0,0).

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The probability that the random sample of 100 male students has a mean gpa greater than 3. 42 is 0.9452.

A statistic known as the standard deviation is used to describe how volatile or dispersed a group of numerical values is. While a big standard deviation denotes that the values are scattered across a wider range, a low standard deviation indicates that the values tend to be close to the set mean.

From the given information, a scores random sample of 100 male students is selected and the GPA for each student is calculated which follows approximately normal with a mean of 3.5 and standard deviation of 0.5. That is,

µ = 3. 5 and σ = 0. 5

and the random sample of 100 male students has a mean GPA 3.42 is considered.

The z-score value is,

Z=( 3.42-3.5)/ (0.5/√100)

Z= -0.08/0.05

Z=-1.6

The value of z-score is obtained by taking the difference of x and µ. Then the resulting value is divided with the standard deviation by sample size.

The probability that the random sample of 100 male students has a mean GPA greater than 3.42 is obtained below:

The required probability is,

P(X>3.42)=P(z>-1.6)

= 1- P(Z≤-1.6)

From the “standard normal table”, the area to the left of Z=-1.6 is 0.0548.

P(X>3.42)= 1- P(Z≤-1.6)

=1-0.0548

=0.9452

The probability that the random sample of 100 male students has a mean GPA greater than 3.42 is 0.9452.

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Answer:

y= -6x+5

y= 2x+(-5)

Step-by-step explanation:

This is the equation of the line in point-slope form.
y - 5 = (-5/4)(x + 6)

The equation in slope-intercept form is y = (-5/4)x - 5/4.

And So the equation in standard form is 5x + 4y = -5.

To determine Kristina's refund or tax liability, we need to calculate her total tax liability and compare it to the total amount of federal withholding that was taken out of her paychecks throughout the year.

From the previous question, we know that Kristina's federal tax liability for the year is $668.00.

To calculate her total federal withholding, we need to multiply the amount taken out of each biweekly paycheck by the number of pay periods in a year. If $89.50 was taken out of each biweekly paycheck, then the total federal withholding for the year would be:

$89.50 x 26 = $2,327.00

To determine Kristina's refund or tax liability, we subtract her total federal withholding from her total tax liability:

$2,327.00 - $668.00 = $1,659.00

Since the result is a positive number, it means that Kristina will have a tax liability when she files her taxes. Specifically, she will need to pay $1,659.00 in federal taxes for the year.

Therefore, the answer is option B) Pay $1,011.75.

The values of k for which 2x² + kx - 5 can be factored as the product of two linear factors with integer coefficients are k = 3, 1, and 9.

What is a linear factor?

A linear factor is a polynomial of degree one, which means it has one variable raised to the first power and a constant coefficient. In other words, it is an expression of the form ax + b, where a and b are constants and x is the variable.

We can factor the quadratic 2x² + kx - 5 into the product of two linear factors with integer coefficients if and only if its discriminant is a perfect square.

The discriminant of the quadratic equation ax² + bx + c = 0 is given by the expression b² - 4ac. In this case, a = 2, b = k, and c = -5. Therefore, the discriminant is:

b² - 4ac = k² - 4(2)(-5) = k² + 40

For the quadratic to be factored into two linear factors with integer coefficients, k² + 40 must be a perfect square.

One way to proceed is to list the perfect squares that are 40 greater than a square, and see if k is one of the corresponding values. We can do this by solving the equation:

k² + 40 = m²

where m is an integer. Rearranging, we get:

k² - m² = -40

This is a difference of squares, so we can factor it:

(k + m)(k - m) = -40

We now need to find integer values of k and m that satisfy this equation. We can do this by considering all possible pairs of factors of -40 and solving for k and m.

The pairs of factors of -40 are:

(-1, 40), (-2, 20), (-4, 10), (-5, 8)

For each pair, we can solve the system of equations:

k + m = a

k - m = b

where a and b are the two factors in the pair. Adding these equations, we get:

2k = a + b

Subtracting them, we get:

2m = a - b

Solving for k and m, we obtain:

k = (a + b)/2

m = (a - b)/2

We can now check if the values of k and m are integers and if they satisfy the original equation.

For example, if we take the pair (-1, 40), we get:

k + m = -1

k - m = 40

Adding these equations, we get:

2k = 39

This implies that k = 39/2, which is not an integer, so this pair does not work.

Trying the other pairs, we find that:

(-2, 20) gives k = 9 and m = 11, which works

(-4, 10) gives k = 3 and m = 7, which works

(-5, 8) gives k = 1 and m = 3, which works

Therefore, the values of k for which 2x² + kx - 5 can be factored as the product of two linear factors with integer coefficients are k = 3, 1, and 9.

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The value of the integral ∫(1+3x) dx is equal to 14.

Integration is a process of adding up small elemental volumes to find the larger volume.

Given is to find the integral -

∫(1+3x)

We can find the equivalent values as -

∫(1+3x) dx = ∫1 dx + ∫3x dx

∫(1+3x) dx = x + 3x²/2

For the limit x = 1 to x = 3, we can write -

∫(1+3x) dx = (3 + 27/2) - (1 + 3/2)

∫(1+3x) dx = 33/2 - 5/2 = 14

Therefore, the value of the integral ∫(1+3x) dx is equal to 14.

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Answer:

D. [If D is saying "x = 4"]

Step-by-step explanation:

We can start solving the equation 216 = 62x - 1 by adding 1 to both sides to isolate the term with x:

216 + 1 = 62x

Simplifying the left side, we get:

217 = 62x

To solve for x, we can divide both sides by 62:

217/62 = x

Using a calculator, we can evaluate the quotient:

3.5 = x

Therefore, the solution to the equation 216 = 62x - 1 is x = 3.5.

Since none of the answer choices match this result exactly, we can round 3.5 to the nearest integer. Rounding 3.5 up to the nearest integer gives us x = 4.

Answer:

the sale price of the one-terabyte external hard drive is $274.13.

Step-by-step explanation:

To find the sale price of the one-terabyte external hard drive, we can use the following formula:

Sale price = Original price - Discount amount

where the discount amount is the amount by which the original price is reduced. The discount amount is equal to the discount rate times the original price. The discount rate is 21%, or 0.21, because the hard drive is on sale at a 21% discount.

Substituting the given values into the formula, we get:

Discount amount = 0.21 * $347 = $72.87

To find the sale price, we subtract the discount amount from the original price:

Sale price = $347 - $72.87 = $274.13

Therefore, the sale price of the one-terabyte external hard drive is $274.13.