A student factors 10x^2+3x-27 to the following


A. The expression is equivalent, and it is completely factored

Answer:

-7

Step-by-step explanation:

4x-12=16+8x

-12-16=8x-4x

-28÷4=x

x=-7

Answer:

-7 :)

Step-by-step explanation:

a) Finance Charge ≈ $18.01  the interest rate is 1.8 % per month.

b) The finance charge is approximately $18.01, and the new balance is approximately $1018.74.

To calculate the finance charge using the previous balance method, we'll need to follow these steps:

a) Find the finance charge on May 3:

Calculate the average daily balance for the billing period.

Average Daily Balance = (Total of daily balances) / (Number of days in the billing period)

Determine the number of days in the billing period (from April 3 to May 2). There are 30 days in this billing period.

Find the daily balances by considering the transactions during the billing period:

Daily balance from April 3 to May 2 = Previous balance on April 3 + Charges during the period - Payments during the period

Daily balance from April 3 to May 2 = $1495.39 + $305.34 - $800

Calculate the average daily balance:

Average Daily Balance = (Total of daily balances) / (Number of days in the billing period)

Average Daily Balance = [(1495.39 + 305.34 - 800) * 30] / 30

Average Daily Balance = $1000.73

Calculate the finance charge using the previous balance method:

Finance Charge = (Average Daily Balance) * (Monthly Interest Rate)

Finance Charge = $1000.73 * (0.018) [0.018 is the monthly interest rate as a decimal]

Finance Charge ≈ $18.01

b) Find the new balance on May 3:

New Balance = Previous balance + Charges during the period - Payments during the period + Finance Charge

New Balance = $1495.39 + $305.34 - $800 + $18.01

New Balance ≈ $1018.74

So, on May 3, the finance charge is approximately $18.01, and the new balance is approximately $1018.74.

To know more about Finance Charge click here :

https://brainly.com/question/29216351

#SPJ2

Final answer:

The finance charge on May 3 using the previous balance method is $26.92, assuming a monthly interest rate of 1.8%. The new balance on May 3, after adding the finance charge, additional charges, and subtracting the payment, is $1027.65.

Explanation:

To calculate the finance charge using the previous balance method, we take the balance due on the April 3 billing date, which was $1495.39, and apply the monthly interest rate of 1.8%. The charge is computed as follows:

Finance Charge = Previous Balance × Monthly Interest Rate
Finance Charge = $1495.39 × 0.018
Finance Charge = $26.91702

Since financial amounts are usually rounded to cents, the finance charge would be $26.92.

To find the new balance on May 3, we will take the previous balance and add the finance charge and any additional charges, then subtract any payments made. This looks like:

New Balance = Previous Balance + Finance Charge + Additional Charges - Payments
New Balance = $1495.39 + $26.92 + $305.34 - $800
New Balance = $1027.65

Therefore, the new balance on May 3 is $1027.65.

For this case we must solve the following quadratic equation:

[tex]2x ^ 2 -7x -15 = 0[/tex]

We must apply the following formula:

[tex]x = \frac {-b \pm \sqrt {b ^ 2-4 (a) (c)}} {2a}[/tex]

We have to:

[tex]a = 2\\b = -7\\c = -15[/tex]

Substituting we have:

[tex]x = \frac {- (- 7) \pm \sqrt {(- 7) ^ 2-4 (2) (- 15)}} {2 (2)}\\x = \frac {7 \pm \sqrt {49 + 120}} {4}\\x = \frac {7 \pm \sqrt {169}} {4}\\x = \frac {7 \pm13} {4}[/tex]

Thus, the solutions are:

[tex]x_ {1} = \frac {7 + 13} {4} = \frac {20} {4} = 5\\x_ {2} = \frac {7-13} {4} = \frac {-6} {4} = - \frac {3} {2}[/tex]

ANswer:

[tex]x_ {1} = 5\\x_ {2} = - \frac {3} {2}[/tex]

Answer:

{-3/2, 5} would be the right choice

Answer:

(1,-1)

Step-by-step explanation:

A translation of (x,y) ⟶ (x + 4, y – 2) means that the coordinates of the pre-image have moved four units to the right and two units down.

To get the coordinates of the pre-image rom the image, we must reverse the procedure.

That is, we must go two units up and four units to the left.

The coordinates of Point P' are (5, -3), so those of P must have been (1, -1).

Answer:

(1,-1) is the answer

Step-by-step explanation:

Hope this helps

Answer:

The number of child tickets = 39

Step-by-step explanation:

It is given that,child admission is $5.20 and adult admission is $8.60

Total sales = $868.00

To find the number of child tickets

Le 'x' be the number of children then number of adults = 2x

(x * 5.20) + (2x * 8.60) = 868

5.2x + 17.2x = 868

22.4x = 868

x = 868/22.4

 = 38.75 ≈ 39

Therefore the number of child tickets = 39

Answer:

IbI

Step-by-step explanation:

The square root of [tex]\( b^2 \)[/tex] is [tex]\( b \),[/tex] as the square root of any positive number is its positive root.

The square root of [tex]\( b^2 \)[/tex]  can be calculated step by step as follows:

Step 1:

Understand the concept.

The square root of a number is a value that, when multiplied by itself, gives the original number. For any real number [tex]\( b \), \( b^2 \)[/tex]  represents [tex]\( b \)[/tex]multiplied by itself.

Step 2:

Apply the square root property.

The square root of [tex]\( b^2 \)[/tex]  is [tex]\( b \)[/tex] because [tex]\( b \times b = b^2 \).[/tex] The square root of any positive number is its positive root.

Step 3:

Interpret the result.

Since the square root of [tex]\( b^2 \)[/tex] is [tex]\( b \),[/tex]  regardless of the value of \( b \), the square root of [tex]\( b^2 \)[/tex] is simply [tex]\( b \)[/tex] . This property holds true for any real number [tex]\( b \).[/tex]

So, the square root of [tex]\( b^2 \)[/tex] is [tex]\( b \).[/tex]

Answer:

Step-by-step explanation:

METHOD 1:

Calculate what fraction of 1600 is 3100 and convert it to the percent:

[tex]\dfrac{3100}{1600}=\dfrac{31}{16}\\\\\dfrac{31}{16}\cdot100\%=\dfrac{3100}{16}\%=193.75\%[/tex]

METHOD 2:

[tex]\begin{array}{ccc}1600&-&100\%\\\\3100&-&p\%\end{array}\qquad\text{cross multiplu}\\\\\\1600p=310000\qquad\text{divide bpth sides by 1600}\\\\p=193.75\ (\%)[/tex]

Answer:

x ≈ 50.8

Step-by-step explanation:

Given

sin80° = [tex]\frac{50}{x}[/tex]

Multiply both sides by x

x × sin80° = 50 ( divide both sides by sin80° )

x = [tex]\frac{50}{sin80}[/tex] ≈ 50.8 ( to 1 dec. place )

Answer:

[tex]\large\boxed{x\approx50.77}[/tex]

Step-by-step explanation:

[tex]\text{Look at the picture.}\\\\\sin80^o\approx0.9848\\\\\text{Substitute it the the equation}\ \sin80^o=\dfrac{50}{x}:\\\\0.9848=\dfrac{50}{x}\\\\\dfrac{9848}{10000}=\dfrac{50}{x}\qquad\text{cross multiply}\\\\9848x=(10000)(50)\\\\9848x=500000\qquad\text{divide both sides by 9848}\\\\x\approx50.77[/tex]

Answer:

d

Step-by-step explanation:

In an axiomatic system, the definition is 'the accepted meaning of a term'. An axiom is an accepted unproven fact. A fact proven by using logic is a theorem.

In an axiomatic system, the phrase that best describes the 'definition' would be option A - 'the accepted meaning of a term.' An axiomatic system is a sort of framework within mathematics where definitions, axioms, and propositions work together. A definition in this context offers the precise description or meaning of a term used within that mathematical system.

An axiom (option B) would most accurately be described as an accepted fact that is not proven, but instead accepted as truth within an axiomatic system (option C). A fact proven by using logic, on the other hand, would be a theorem (option D).

https://brainly.com/question/18405381

#SPJ3

Answer:

option B

Step-by-step explanation:

Paul bought 6 pounds of hamburger. He used 3 1/ 2  pounds to make burgers. Paul says he has 2 1/ 2  pounds of hamburger left.

To find out pounds of hamburger left we subtract 3  1/2 from 6 pounds

[tex]3 \frac{1}{2} =\frac{3*2+1}{2}=\frac{7}{2}[/tex]

Now we subtract the fraction from 6

[tex]6 - \frac{7}{2} = \frac{12}{2} - \frac{7}{2} =\frac{5}{2}[/tex]

Now we convert 5/2 into mixed fraction

[tex]\frac{5}{2} = 2\frac{1}{2}[/tex]

Paul's answer is correct. because when we add [tex]3\frac{1}{2} + 2\frac{1}{2}[/tex] we will get 6

Answer:

Option B

Step-by-step explanation:

we know that

The volume of a solid is the amount of space occupied by a solid object. The volume of solid is expressed as cubic units.

therefore

It is the amount of three -dimensional space inside the solid

Answer:

B. It is the amount of three-dimensional space inside the solid.

Step-by-step explanation:

Volume is defined as the amount of three-dimensional space enclosed by a close surface. Volume is the product of the three dimensions of a body. The SI unit of volume is m³.

eg. Volume of cube = a³

Volume of cuboid = L×B×H

Volume of sphere = [tex]\frac{4}{3}\pi r^3[/tex]

Volume of cylinder = πr²h

Volume of cone = [tex]\frac{1}{3}\pi r^2h[/tex]

Answer:

The answer is option B : $30,000.

Step-by-step explanation:

To avoid Primary Mortgage Insurance or PMI, one need to have the loan balance to be 80% or less of the home value.

Hence, Bella needs to deposit a down payment of at least 20% of $150,000

This value becomes:

[tex]0.20\times150000=30000[/tex] dollars

Therefore, the answer is option B : $30,000.

Answer:

B $30,000

Step-by-step explanation:

PMI then with the given amount is how we find the answer

[tex]\bf 40a^2+20a-30=(-1)(15a^3+30)\implies 40a^2+20a~~\begin{matrix} -30 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~=-15a^3~~\begin{matrix} -30 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix} \\\\\\ 40a^2+20a=-15a^3\implies 15a^3+40a^2+20a=0\implies 5a(3a^2+8a+4)=0 \\\\\\ 5a(3a+2)(a+2)=0\implies a= \begin{cases} 0\\ -\frac{2}{3}\\ -2 \end{cases}[/tex]

Step-by-step answer:

If one is constrained to move to the right, or up, or diagonally upwards (i.e. remain in the first quadrant), then

there are three choices at A.

At the next position, whichever path one has taken, there are also three choices.

At the following position, there are no more choices.

Therefore, there are 3*3 = 9 different paths.

Answer:

usually means establishing a series of equal monthly payments that will provide

a principal payment that will cause the unpai principal balance to decrease each month so that the principal balance will be zero at the time of the final payment

Answer:

To amortize a loan refers to equal and periodic payments (monthly in most of the cases), on which the lender runs some interest ratio due to the amortization.

In other words, it means that the total amount of money the lender is going to "give" you is divide in smaller amount of moneys, which he is gonna lend you periodically, monthly. For example, if you need a $60,000 loan, and your lender propose to lend that money with a 4% of annual interest, that means he is gonna give your $1771.4 per month, he won't give you the whole money, instead he amortize the loan and give your a certain quantity based on the interest rate.

The answer to 4+4 is 8

4+4=8

Answer:

[tex]m = \frac{y2 - y1}{x2 - x1} [/tex]

Step-by-step explanation:

slope formula

Answer:

[tex]\frac{rise}{run}[/tex]

Step-by-step explanation:

The slope of a line is calculated by dividing the rise by the run.

In the attached example, the rise is 1 and the run is 2, so the slope is 1/2.  The rise is the distance the line goes up.  The run is the distance the line goes to the right for each (rise) units.  The line below goes up 1 and right 2 over and over again.

Answer:

23

Step-by-step explanation:

plug and chug: 5(4)+3=20+3=23

Hello There!

The answer would be "23"

When we have an expression like this, the "x" next to a number means that we multiply the number next to the variable by it.

In this case, if "x" equals 4, then we multiply 5 by 4 and we get a product of 20 and we add 3 to get a sum of 23.

Have A Great Day!

Be Safe!

TheBlueFox

The equation that represents the given situation is 3x - (50 - x) - 0.5(50 - x) = 110. This equation is derived from the fact that Desiree gets 3 points for each correct answer, 1 point deducted for each wrong answer, and 0.5 point deducted for each unanswered question.

The equation that represents the given situation is 3x - (50 - x) - 0.5(50 - x) = 110.

This eqUation is derived from the fact that Desiree gets 3 points for each correct answer, 1 point deducted for each wrong answer, and 0.5 point deducted for each unanswered question.

By solving the equation, you can find the value of x, which represents the number of questions Desiree answered correctly.

Konichiwa~! My name is Zalgo and I am here to help you out today. The factorization of your equation is 4 (2a+b) (2a-b). If you do not understand this, it means 4 multiplied by 2a+b which is also multiplied 2a-b.

I hope that this helps! :P

"Stay Brainly and stay proud!" - Zalgo

(By the way, can you mark me as Brainliest? I'd greatly appreciate it! Arigato~! XT)

Answer:

4(2a+b)(2a-b)

Step-by-step explanation:

Distributive property: A(B+C)=ab+ac

4²=4*4=16

4*4a²-4b²

Term of 4.

4 (4a²-b²)

Simplify, to find the answer.

4a²-b²= (2a+b)-(2a-b)

(2a+b)-(2a-b) is the correct answer.

I hope this helps you, and have a wonderful day!

Answer:

The width of the base = the volume ÷ (length × height)

w = V/lh

Step-by-step explanation:

* Lets take about how to re-arrange any formula

- The formula of the volume of the rectangular prism is:

  V = lwh, where l is the length of the base , w is the width of the

  base and h is the height of the prism

- To find the formula of the width from the formula of the volume,

  we must isolate the width in one side and all other dimensions in

  other side

∵ V = lwh ⇒ divide both sides by l and h

∵ V/(lh) = (lwh)/(lh) ⇒ cancel lh up with lh down

∴ V/(lh) = w

∴ w = V/(lh)

∴ w = V ÷ (lh)

* The width of the base = the volume ÷ (length × height)

Answer:

Width=[tex]\frac{Volume}{(Length)*(height)}[/tex]

Step-by-step explanation:

You only have to clear the start of the formula:

V=L*W*H

Since lenght and height are multiplying the width of the base you have to clear them and take them to the other side of the equation dividing:

[tex]\frac{V}{l*h}[/tex]

So you can calculate the width of the base by dividing the volume between the product of the Height times the length.

Answer:

B

Step-by-step explanation:

Answer:

Step-by-step explanation:

volume of a pyramid is V=(lwh)/3

For this case we have that by definition, the volume of a pyramid is the third part of the volume of a prism that has the same area of the base and equal height.

Thus:

[tex]V = \frac {b * h} {3}[/tex]

Where:

b: It is the area of the base

h: It's the height

Answer:

[tex]V = \frac {b * h} {3}[/tex]

Answer:

The answer should be: B. (9,3)

Answer:  B. (9,3)

Step-by-step explanation:

To solve this problem, we start organizing the equation to the Slope intercept form:

[tex]y=5(x-9)+3[/tex]

[tex]y=5x-45+3[/tex]

[tex]y=5x-42[/tex]

Where 5 is the positive slope of the line, and -42 is the y-axis intercept. knowing the y-intercept, we may infer that choices C or D are incorrect, because values must be lower than -42. Thus, we replace the x value of choices A and B to verify which one applies:

Choice A

[tex]y=5(3)-42[/tex]

[tex]y=-27[/tex]

[tex]27\neq 9[/tex]

Choice B

[tex]y=5(9)-42[/tex]

[tex]y=3[/tex]  Correct!

Answer: 10 units.

Step-by-step explanation:

The equation of the circle in Center-radius form is:

[tex](x - h)^2 + (y - k)^2 = r^2[/tex]

Where the center is (h,k) and "r" is the radius.

The equation of the circle given is:

[tex]x ^2 + y^2 = 100[/tex]

You can observe that is written in Center-radius form.

Then, you can identify that:

[tex]r^2=100[/tex]

Knowing this, you need to solve for "r" to find the lenght of the radius.

This is:

[tex]r=\sqrt{100}\\\\r=10[/tex]

Therefore, the lenght of the radius is 10 units.

Answer:

16/9

Step-by-step explanation:

Step 1 : {Apply exponent rule}

Step 2: repeat

For this case we must simplify the following expression:[tex]7 (\sqrt [3] {2x}) - 3 (\sqrt [3] {16x}) - 3 (\sqrt [3] {8x})[/tex]

We rewrite:

[tex]16x = 2 ^ 3 * 2x\\8x = 2 ^ 3 * x[/tex]

We rewrite the expression:

[tex]7 (\sqrt [3] {2x}) - 3 (\sqrt [3] {2 ^ 3 * 2x}) - 3 (\sqrt [3] {2 ^ 3 * x}) =[/tex]

By definition of properties of powers and roots we have:

[tex]\sqrt [n] {a ^ m} = a ^ {\frac {m} {n}}[/tex]

Then, taking the terms of the radical:

[tex]7 (\sqrt [3] {2x}) - 3 (2 \sqrt [3] {2x}) - 3 (2 \sqrt [3] {x}) =\\7 \sqrt [3] {2x} -6 \sqrt [3] {2x} -6 \sqrt [3] {x} =[/tex]

We add similar terms:

[tex]\sqrt [3] {2x} -6 \sqrt [3] {x}[/tex]

Answer:

Option C

The answer is:

The fourth option,

{s | s <90}

Solving inequalities involves almost the same process of solving equalities for variable isolation.

We are given the inequality:

[tex]\frac{1}{3}s-6<24[/tex]

So, solving we have:

[tex]\frac{1}{3}s-6<24\\\\\frac{1}{3}s-6+6<24+6\\\\\frac{1}{3}s<30\\\\\frac{1}{3}s*3<30*3\\\\s<90[/tex]

Hence, we have that the correct option is the fourth option:

{s | s <90}

Have a nice day!

Answer:

{s | s < 90}   D is the correct answer

Step-by-step explanation:

It is.