10. (04.02 LC)
For the following system, if you isolated x in the second equation to use the substitution method, what expression would you substitute into the first equation? (1 point)
2x + y = 8
-x - 3y = -12
3y + 12
-3y + 12
3y - 12
-3y - 12

The composite function (f + g)(x) is (f + g)(x) = 9x² - x - 8

From the question, we have the following parameters that can be used in our computation:

f(x)=3x²+42-6

g(x)=62-5²-2

Express properly

So, we have the following representation

f(x) = 3x² + 4x -6

g(x) = 6x² - 5x - 2

The composite function is then calculated as

(f + g)(x) = f(x) + g(x)

So, we have

(f + g)(x) = 3x² + 4x -6 + 6x² - 5x - 2

Evaluate

(f + g)(x) = 9x² - x - 8

Hence, the function is (f + g)(x) = 9x² - x - 8

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The number of possible outcomes that do not show 1 on the first spinner and 4 on the second spinner is 2.

It is the total number of possible outcomes from a given set.

We have,

The sample space for when both the spinners are spun once.

S = {(1, 2, 3) x (3, 4, 5, 6)}

S = {(1, 3), (1, 4), (1, 5), (1, 6), (2, 3), (2, 4), (2, 5), (2, 6), (3, 4), (3, 4), (3, 5), (3, 6)}

Now,

The number of total outcomes = 12

The number of outcomes that do not show 1 on the first spinner and 4 on the second spinner.

= {(2, 4), (3, 4)}

= 2

Thus,

The number of required possible outcomes is 2.

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The required value of y is obtained as -2.

The given system of equation can either have a unique solution, more than one solutions or no solution.

On this basis they are divided into two parts consistent and inconsistent.

A consistent system has one or more solutions while for an inconsistent system there are no solutions.

The given system of equations is as below,

4x - y = 10             (1)

x - 4 = y               (2)

Substitute the value of y from equation (2) into equation (1) to get,

4x - (x - 4) = 10

=> 3x + 4 = 10

=> 3x = 6

=> x = 2

Then, substitute x = 2 in  x - 4 = y  to get,

y = 2 - 4  = -2

Hence, the value of y for the given system of equations is -2.

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The required explanation of probability distribution that has a mean of 0 and a standard deviation of 1 is describe below.

Probability distributions help to show our reality, empowering us to get evaluations of the likelihood that a specific occasion might happen, or gauge the inconstancy of event. They are a typical method for depicting, and potentially foresee, the likelihood of an occasion

The mean of the z-scores is dependably 0. The standard deviation of the z-scores is dependably 1. The chart of the z-score dissemination generally has a similar shape as the first conveyance of test values. The amount of the squared z-scores is dependably equivalent to the quantity of z-score values.

Thus, it is dependable.

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Correct question:

A normal probability distribution can have any value of the mean or must have a standard deviation of 1 and a mean of 0?

Answer:

Savings Account

Investment Account

The linear functions in this problem are given as follows:

1. y = -x/2 - 4.

2. y = -3x + 7.

Considering the options in these problems, the linear functions are defined in slope-intercept format, given as follows:

y = mx + b.

The coefficients of the function are given as follows:

The slope-intercept definition of the two equations presented in this problem are given as follows:

When two linear functions are parallel, they have the same slope, hence the two functions will be given as follows:

For item 1, when x = 2, y = -5, hence the intercept b is calculated as follows:

-5 = -0.5(2) + b

b = -5 + 1

b = -4.

For item 2, when x = 1, y = 4, hence the intercept b is calculated as follows:

4 = -3(1) + b

b = 7.

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Answer: 170678

Step-by-step explanation:

try it and you'll see.

The area of circle when π is 3.14 is 1017.36 inches².

What is the area of circle?

Area of the circle = πr²

= 3.14 * 18 * 18

= 3.14 * 324

= 1017.36 inches²

Hence, the area of circle when π is 3.14 is 1017.36 inches².

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The number a has to be greater than or equal to 1000.

As per the given data we have to determine that how large the number a has to be so that [tex]$$\int_a^{\infty} \frac{1}{1+x^2} \cdot d x < 0.001$$[/tex]

[tex]$$\Rightarrow \quad\left[\tan ^{-1}(x)\right]_a^{\infty} < 0.001$$[/tex]

[tex]$\Rightarrow \quad \tan ^{-1}(x)-\tan ^{-1}(a) < 0.001$[/tex]

[tex]$$\begin{array}{ll}\Rightarrow & \frac{\pi}{2}-0.001 < \tan ^{-1}(a) \\\\\Rightarrow & 1.5698 < \tan ^{-1}(a)\end{array}$$[/tex]

[tex]$$\begin{aligned}& \Rightarrow \quad \tan ^{-1}(a) > 1.5698 \\& \Rightarrow \quad a > \tan (1.5698)\end{aligned}$$[/tex]

[tex]$$\begin{aligned}& \Rightarrow \quad a > 999.999 \\& \Rightarrow \quad a \geqslant 1000\end{aligned}$$[/tex]

Therefore the answer is [tex]\quad a \geqslant 1000[/tex]

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ΔLMJ and ΔLKN are congruent by SAS congruence postulate.

What is SAS and ASA congruence rule for triangles?

SAS : If two sides and the included angle of a triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent.

ASA : If two angles and the included side of a triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent.

According to the given question:

The pair of overlapping congruent triangles in the diagram are:

ΔLMJ and ΔLKN

Now,

LM ≅ LK (Given)

LN ≅ LJ (Given)

∠LJM = ∠LNK (Angles opposite to equal sides are equal)

∴ ΔLMJ ≅ ΔLKN by SAS congruence of triangles

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Monica was wrong she will get less interest than Paul as Paul has invested a higher Principal amount than Monica.

What is simple interest?

Simple interest is based on the principal amount of a loan or the first deposit in a savings account.

                         [tex]A = P (1 + rt)\\\\A $ = final amount$\\P $ = initial principal balance$\\r $ = annual interest rate$\\t $ = time (in years)$[/tex]

Given that:

For Monica:

Principal (p) = $400

Rate (r) = 4.3% = 0.043

Year (t) = 1 year

Deposit Paul:

Principal = $500

Rate (r) = 4.2%  = 0.042

Year (t) = 1 year

Now calculate the interest amount for Monica and Paul, we get

For Monica:

             A = P(1 + rt)

             A = 400(1 + (0.043 × 1))

             A = 417.2

             A = $417.20

Now for Monica, Interest will be

           I = A - P

             = 417.20 - 400

           I = 17.20 dollars -----------(II)

For Paul:

             A = P(1 + rt)

             A = 500(1 + (0.042 × 1))

             A = 521

             A = $521 dollars

Now for Paul, Interest will be

           I = A - P

             = 521 - 500

           I = 21 dollars ---------------(II)

From (I) and (II), we can say that Paul will earn more interest than Monica.

Hence, Monica was wrong she will get less interest than Paul as Paul has invested a higher Principal amount than Monica.

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Answer:

117.12

Step-by-step explanation:

43.78+21.05 = 64.83

64.83+52.29 = 117.12

Answer:

Step-by-step explanation:

Given that $6000 is deposited into an account earning 5.9% compounded quarterly, you want the values of P, r, n used in the future-value formula, and you want the value after 9 years.

The problem statement tells you the values:

  amount deposited = P = 6000

  interest rate = r = 5.9% = 0.059

  compounding periods in a year = n = 4

Using these numbers in the formula, you find (with t=9) ...

  S(9) = 6000(1 +0.059/4)^(4·9) ≈ $10164.30

Answer:

Step-by-step explanation:

To solve the equation 3(x+1) = 4x-1, we need to use the rules of algebra to isolate the variable "x" on one side of the equation and simplify the other side.

First, we can distribute the 3 on the left side of the equation to obtain 3x + 31 = 4x-1. This gives us 3x + 3 = 4x-1.

Next, we can subtract 3x from both sides of the equation to obtain 3 + 3 = 4x-1-3x. This simplifies to 3 = x-1.

Now we can add 1 to both sides of the equation to obtain 3+1 = x. This gives us the final solution x = 4.

Therefore, the solution to the equation 3(x+1) = 4x-1 is x = 4.

After 8 years, the amount of money which Carl would have in the bank account is equal to $620.

Mathematically, simple interest can be calculated by using this formula:

S.I = PRT or S.I = A - P

Where:

Substituting the given parameters into the simple interest formula, we have the following;

S.I = 500 × 3/100 × 8

S.I = $120.

Now, we can calculate the future value (A) as follows;

Future value (A) = P + S.1

Future value (A) = 500 + 120

Future value (A) = $620.

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Answer:

NY: 4cm + 3cm = 7cm

XY: 8cm + 3cm = 11cm

Step-by-step explanation:

1. find the difference between XN and MN

2. use the difference to add to the value LN and LM

Answer:

d=c/pi

Step-by-step explanation

divide by pi then d=c/pi

Answer:

C / pi = d

Step-by-step explanation:

The formula for circumference is

C = pi * d

To solve for d, divide each side by pi

C / pi = d

The value of y in the given inequality 4y + 1/5 ≤ 4/5 is: y ≤ 3/20.

To solve any inequalities, apply the same knowledge used to solve a normal algebraic equation by isolating the value of the variable.

The given inequality is 4y + 1/5 ≤ 4/5. To solve for the value of y, follow the steps below:

4y + 1/5 ≤ 4/5 [given]

Subtract 1/5 from both sides of the inequality:

4y ≤ 4/5 - 1/5 [subtraction property of equality]

4y ≤ 3/5

Multiply both sides by 1/4:

4y × 1/4 ≤ 3/5 × 1/4

y ≤ (3 × 1) / (5 × 4)

y ≤ 3/20

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If the regular box has dimensions l, w, and h, then the dimensions of the family value box would be 1.25l, 1.25w, and 1.25h. This means that the volume of the family value box would be 1.25 * 1.25 * 1.25 = 1.953125 times the volume of the regular box. Since the family value box is 25% larger in each dimension, its volume is nearly double the volume of the regular box.

Step-by-step explanation:

5. the most significant challenge that small businesses face is financial problems.

Answer:

it would be C

hope this helps

Step-by-step explanation:

Since ,the amount is same in both jobs as valet and waiter thus the total amount of money he made is $538.9

Equation: a claim that two expressions with variable- and/or number-filled expressions are equivalent. Mathematical development has been sparked by the desire to find solutions to equations, which are really just questions.

Here,

Part A:

Jamal works as a valet made $10.25 an hour and an additional $50.10 in tips,

Thus number of hours be x

equation : 10.25x + 50.10 =0

or

Jamal works as a waiter made $6.75 an hour and an additional $125 in tips

equation : 6.75x + 125 = 0

Part B:

The total amount he made when both paychecks are same

=> 6.75x + 125 = 10.25x + 50.10

=> 10.25x-6.75x = 125-50.10

=>3.5x = 74.9

=>x=74.9/3.5 =21.4

Thus the total amount he made

10.25(21.4) + 50.1 = 269.45

and

Total amount = 2* 269.45=538.9

Since ,the amount is same in both jobs as valet and waiter thus the total amount of money he made is $538.9

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Answer:

x represents the number of hours.

(y) distance because the distance depends on the number of hours traveled.

H(x) = 50x

H(5) = 50(5)

H(5) - 250 miles

After 5 hours of driving at 50 miles per hour, the car has traveled 250 miles.

Step-by-step explanation:

The reason why simple random sampling will be a good way to do the selection of bad books is; Option C: He will have a more representative sample if he chooses randomly

A simple random sample is defined as a randomly selected subset of a particular population. In this method of sampling, it will be noticed that each member of the population has an exactly equal chance of being selected.

The importance of simple random sampling is that it removes every form of bias as every member has an equal chance of being selected. Thus, it will give a good representation of what we want to research.

Now, in this case, since the librarian wants to check a sample of books from the library to get an idea of how many need replacing, it means that a random sampling method is good because;

He will have a more representative sample if he selects randomly as the definition earlier stated makes clear.

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By solving a system of equations we will see that they sold 35 advanced tickets and 30 same-day ones.

Let's define the variables we will be using for this problem, these are:

x = number of same advance tickets.

y = number of same-day tickets.

With the given information we can write a system of equations:

x*$25 + y*$20 =  $1,450

x + y = 65

To solve the system we can isolate x on the second equation:

x = 65 - y

Now let's replace that in the other equation:

(65 - y)*$25 + y*$20 =  $1,450

$1,625 - y*$5 =  $1,450

$1,625 - $1,450 = $5*y

$175/$5 = y

35 = y

Then the value of x is:

x = 65 - 35 = 30

So they sold 35 advanced tickets and 30 same-day ones.

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Thus ,the statement about overhead expenses which is true is option (B). .

In the business world, an ongoing expense of operating a business is known as overhead or an overhead charge .In contrast to operating costs like raw material and labor, overheads are expenses that cannot easily be connected to or associated with any one revenue unit.

Here,

the statement about overhead expenses  which is true is option (B).

Explanation :The costs of operating a firm that aren't directly connected to providing an item or service are referred to as overhead. These expenses might be either fixed, like rent, or variable, like transportation expenditures. Additionally, they may be semi-variable, like utilities. Thus contribute directly to the running of a business.

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Therefore, the five steps are taken to localize the protein dynein in tissue sections of the esophagus and trachea.

Any procedure that involves moving, attaching to, or otherwise maintaining a cell, substance, or cellular entity in one place, like an organelle or protein complex. Substance localisation can also be accomplished through selective degradation.

In this case,

the steps that are done in order to localize the protein dynein in tissue sections of the esophagus and trachea are as follows:

1. Histoclear removes the medium to enable the labeling of the antibodies

2. to rehydrate the sample, add water.

3. Using BSA blocking solution after Triton X- 100, which ruptures membranes and makes antigens more accessible to antibodies

(4) Add the dynein antibody.

5. include a secondary antibody that is likewise peroxidase-active (adds specificity)

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f(x)=-25x^4+3x^2+2 = f'(x)=-100x^3+6x

Take derivation

f'(x)=d/dx(-25x^4+3x^2+2)

Formula

f'(x)=d/dx(-25x^4)+d/dx(3x^2)+d/dx(2)

Formula

f'(x)=-25(4x^3)+3(2x)+0

f'(x)=-100x^3+6x

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The number of sides of Alexandra's regular polygon is 12.

The number of sides of Maris's regular polygon is 15.

What is a regulars polygon?

A regular polygon is denoted a area. The area bounded by equal length of arms. The angel between any two consecutive arms will same any other pair of consecutive arms.

The number of line of symmetry of a polygon is the same is the number of arm or sides of that polygon.

Thus the number of sides of a polygon that has 12 lines of symmetry is 12.

The angle of rotational symmetry of a polygon is 360°/n, where n is the number of arms.

Therefore,

Angle of rotational symmetry = 360°/n

Putting Angle of rotational symmetry = 24°:

24° = 360°/n

Multiply both sides by n

24n = 360

Divide both sides by 24:

n = 360/24

n = 15

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The geometric sequence have a common ratio of 2

Geometric progression (GP) is a type of sequence where each next term is gotten by multiplying each previous term by a fixed number, which is called a common ratio.

In this problem, we must write out two equations to find the common ratio.

Let;

The nth term of a GP is given as;

Tn = arⁿ⁻¹

T₈ = ar⁷

256 = ar⁷ ...eq(i)

T₅ = 32

32 = ar⁴ ...eq(ii)

Dividing equation (i) by equation (ii)

256 / 32 = ar⁷ / ar⁴

8 = r⁷⁻⁴

8 = r³

r = ∛8

r = 2

The common ratio of the geometric sequence is 2

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