solve f(x)=x²+7x+12/-x²-3x+4

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

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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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:

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:

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.

The explicit rule for the decreasing arithmetic sequence 13, 10.5, 8, 5.5, 3, 0.5, ... is 'aₙ = 15.5 - 2.5n'. This rule reflects the initial term and the common difference between terms.

The sequence provided is 13, 10.5, 8, 5.5, 3, 0.5, and we are finding the explicit rule for this sequence. To find the explicit rule, we will look at the differences between the terms. The differences are consistently -2.5, thus the sequence decreases by 2.5 each time. Assume the first term corresponds to n=1, the next step is to find the initial value at n=1.

Starting with the first term, when n=1, the value is 13. Keeping in mind the sequence decreases by 2.5 with each step, if we reverse one step back (which would be 0 steps), we would be at the initial value, which is 13 + 2.5 = 15.5. Therefore, the explicit rule can be written in the form aₙ = initial value - difference times (n-1), which simplifies to aₙ = 15.5 - 2.5n.

So, given the options provided, the explicit rule for the given sequence is aₙ = 15.5 - 2.5n.

Answer:

Step-by-step explanation:

"A ratio of 4 to 5" means that dividing the two angles (whatever they may be) simplifies to 4/5. One example is 40 degrees and 50 degrees so 40/50 = 4/5. Another example is the pair of angles 20 and 25, so 20/25 = 4/5

For now, we don't know the angles. Let's call them x and y. Based on the info above, we can say

x/y = 4/5

also we know that x and y add to 90 degrees because the angles are complementary. So x+y = 90 which solves to y = 90-x if you isolate y.

Let's cross multiply on the first equation to get...

x/y = 4/5

5*x = 4*y

Now replace y with 90-x. Solve for x

5x = 4(90-x)

5x = 360 - 4x

5x+4x = 360

9x = 360

x = 360/9

x = 40

Use this to find y

y = 90 - x = 90 - 40 = 50

So the two angles are 40 degrees and 50 degrees.

To find two complementary angles with a ratio of 4 to 5, set up the equation 4x + 5x = 90, where x is the common multiplier. Solve for x to find each angle's measure. Check that the sum equals 90 degrees to confirm the solution.

To determine the measures of two complementary angles with a ratio of 4 to 5, you first need to understand that complementary angles add up to 90 degrees. Let's call the angles A and B, with A being the smaller angle. Since they are in a ratio of 4 to 5, we can represent them as 4x and 5x, respectively, where x is a common multiplier. The equation to solve for x is set up based on the definition of complementary angles:

4x + 5x = 90

Combine like terms to simplify:

9x = 90

Now, divide both sides by 9 to solve for x:

x = 90 ÷ 9

x = 10

Once you have the value of x, you can find the measures of the angles:

A = 4x = 4(10) = 40 degrees

B = 5x = 5(10) = 50 degrees

Always check your answer to confirm it makes sense. In this case, A + B should equal 90 degrees, which it does (40 + 50 = 90).

Answer:

there would be 420 cards in total

Step-by-step explanation:

Answer: ITS B

Step-by-step explanation:

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:

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.

The claim that people do better with the new edition regarding the given situation is false at 0.01 level of significance.

There are two hypotheses. First one is called null hypothesis and it is chosen such that it predicts nullity or no change in a thing. It is usually the hypothesis against which we do the test. The hypothesis which we put against null hypothesis is alternate hypothesis.

Null hypothesis is the one which researchers try to disprove.

For this case, the hypothesis we'll lay down are:

Null hypothesis: People are performing less than or equal(compared with old performance) with the new edition

Alternate hypothesis: People are doing better with the new edition

This can be symbolically written as:

Null hypothesis: [tex]H_0: \mu_2 \leq 75\\[/tex]
Alternate hypothesis: [tex]H_1: \mu_2 > 75[/tex]

(where [tex]\mu_1[/tex] = 75 is mean test score with old edition, and [tex]\mu_2[/tex] is mean test score with new edition(of the population) )

Mean score with old edition is given to be [tex]\mu_1= 75[/tex]

Mean score with new edition(of the sample) is ratio of sum of scores to total count of scores = [tex]\overline{x} = \dfrac{830}{10} = 83[/tex] ([tex]\overline{x}[/tex] is representative of the population mean with new edition)

The standard deviation for both cases is: [tex]\sigma = 10.5[/tex]

Since sample size = 10 < 30, thus, we'll perform t-test for single mean (as first mean is mean of population and not of any sample).

Degree of freedom =  sample size - 1 = 9

Level of significance = 0.01

t test statistic's value for given case = [tex]\dfrac{\overline{x} - \mu_1}{s / \sqrt{n}} = \dfrac{ 83-75 }{9.82/\sqrt{10}} \approx 2.57[/tex]

(where s is sample standard deviation)

From the p-value calculator, we get the p-value for t = 2.57 at 0.01 level of significance with d.f.= 9 as : p = .015 > level of significance = 0.01

Thus, as p value is bigger than the level of significance, we fail to reject the null hypothesis, and thus, conclude that there is no significant improvement because of the new edition.

Thus, The claim that people do better with the new edition regarding the given situation is false at 0.01 level of significance.

Learn more about hypothesis testing here:

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A one-sample t-test is used to determine if there's a significant difference in mean scores between the old and new textbook. The null hypothesis is not rejected because the t-score is lesser than the critical value, implying that there is not sufficient evidence that the new textbook is more helpful at the 0.01 significance level.

To determine if the newly designed textbook is more helpful for learning material than the old edition, we can use a one-sample t-test. The null hypothesis (H0) is that there is no difference in mean scores between the old and the new textbooks, meaning the mean score with the new textbook is 75. The alternative hypothesis (Ha) is that the mean score with the new textbook is greater than 75.

We're given that the standard deviation (σ) is 10.5, the sample size (n) is 10, and the sample mean (μ) is calculated from the provided scores. To perform the t-test, we first calculate the sample mean (μ) = (92 + 83 + 93 + 74 + 85 + 97 + 88 + 70 + 69 + 79) / 10 = 830 / 10 = 83.

Next, we calculate the t-score using the formula: t = (sample mean - population mean) / (standard deviation / sqrt(n)).

t = (83 - 75) / (10.5 / sqrt(10)) = 8 / (10.5 / 3.162) = 8 / 3.316 = 2.412.

With a significance level of 0.01 and 9 degrees of freedom (n-1), we look up the critical t-value from the t-distribution table or use a statistical software to find that the critical value for a one-tailed test is approximately 2.821. Since our t-score of 2.412 is lesser than the critical value, we do not reject the null hypothesis, suggesting that there is not enough evidence to support that the new textbook is more helpful at the 0.01 significance level.

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.

For more information:

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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            

Answer:

She should borrow the money for 3.1161... years so that she can afford the monthly payment.

Step-by-step explanation:

Monthly payment formula is:    [tex]M=P*\frac{r(1+r)^n}{(1+r)^n -1}[/tex]  , where

M = Monthly payment amount, P = Loan amount, r = rate of interest per month and n = total number of months.

Given that, Cynthia wants to take out a $8500 loan with a 4.75% APR and she can afford to pay $245 per month.

That means,  [tex]P= 8500, M= 245[/tex] and [tex]r= \frac{0.0475}{12}= 0.0039583[/tex]

Plugging these values into the above formula, we will get........

[tex]245=8500*\frac{0.0039583(1+0.0039583)^n}{(1+0.0039583)^n-1} \\ \\ 245=\frac{33.64555(1.0039583)^n}{(1.0039583)^n -1}\\ \\ 245(1.0039583)^n -245=33.64555(1.0039583)^n\\ \\ 211.35445(1.0039583)^n=245\\ \\ (1.0039583)^n=\frac{245}{211.35445}=1.15919\\ \\ n= log_{1.0039583}(1.15919)=37.39327[/tex]

So, [tex]n= 37.39327 months =\frac{37.39327}{12} years = 3.1161... years[/tex]

That means, she should borrow the money for 3.1161... years so that she can afford the monthly payment.

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:

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.

C

You want to choose an assignment of numbers that makes the number of numbers that represent each color be the same.

Numbers 0–33 include 34 numbers. Numbers 0–99 include 100 numbers, so blue blocks are over-represented by scenario A.

Scenario B suffers the same problem as scenario A in that 0–3 includes 4 numbers and 0–9 includes 10 numbers.

Scenario D has the opposite problem: 1–31 is 31 numbers, but 32–63 is 32 numbers. Blue blocks are under-represented in this scenario.

___

Scenario C has 3 of 9 numbers representing each color—just what you want.

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:

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: 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

In quadrant III, cosine is negative

In quadrant III, sine is negative

x^2+y^2 = 1 represents the unit circle. This is a circle centered at the origin with radius 1. The point (x,y) is on the unit circle where x = cos(theta) and y = sin(theta)

If theta is between 180 and 270 degrees, then

x = cos(theta) leads to -1 < x < 0, ie x is some negative number between -1 and 0

y = sin(theta) leads to -1 < y < 0, so y has similar properties to x above.

Because we don't know what value theta is exactly, we can only comment on the fact that each result is positive or negative.

The four quadrants are set up where quadrant 1 is in the upper right corner. Then you move counter-clockwise to sweep through the other quadrants 2 through 4.

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%

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.

Answer:

$30

Step-by-step explanation:

x*0.70=21

21/0.70= 30

[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]

Answer:

The value is 180

Step-by-step explanation:

The formula for z score is given by

       x - mean

z=    -------------

       standard deviation

We know z= 2.4

We know the standard deviation =20

and we know the mean = 132

We can   find  x

         x - 132

2.4 =  ----------------

           20

Multiply each side by 20

2.4 *20 = x-132

48 = x-132

Add 132 to each side

48+132 = x -132+132

180 = x

Answer:

The value that has a z score of 2.4 is 180.

Step-by-step explanation:

Given : If a normal distribution has a mean of 132 and a standard deviation of 20.

To find : What is the value that has a z score of 2.4?

Solution :

The formula of z-score is given by

[tex]z=\frac{x-\mu}{\sigma}[/tex]

where, z=2.4 is z score value

[tex]\mu=132[/tex] is the mean of the normal distribution

[tex]\sigma=20[/tex] is the standard deviation

x is the value of z score.

Substituting all the values in the formula,

[tex]2.4=\frac{x-132}{20}[/tex]

[tex]2.4\times 20=x-132[/tex]

[tex]48=x-132[/tex]

[tex]x=180[/tex]

Therefore, The value that has a z score of 2.4 is 180.