What are the steps needed to solve the following problem:

(2x - 3)(x + 4) = -5?

The formula for the area of a rhombus is s^2=A.  Plug in and solve:

s^2=25

*Take the square root of both sides*

s=5

Hope this helps!!

Answer:

The side length is 5 mm

Step-by-step explanation:

Since it is square, we know the area of a square is given by

A = s^2 where s is the side length of the square

25 = s^2

Take the square root of each side

sqrt (25) = sqrt(s^2)

5 = s

The side length is 5 mm

The simplified form of the given polynomial equation is:

                  [tex]-2x^2-x+7[/tex]

We are asked to simplify the given polynomial expression in terms of the variable x.

The algebraic expression is given as:

[tex](-9x^2+2x+13)-(-7x^2+3x+6)[/tex]

On taking out the terms from both the brackets the sign of the terms of the second bracket gets interchanged as there is a negative sign preceding it.

Hence, we get the expression as:

           [tex]=-9x^2+2x+13+7x^2-3x-6\\[/tex]

Now on combining the like terms we get:

       [tex]=-9x^2+7x^2+2x-3x+13-6\\\\\\=-2x^2-x+7[/tex]

Answer:

[tex]P = 0.25[/tex]

Step-by-step explanation:

The simulation shows a result composed of 20 data.

If January represents month 1 and February represents month 2 then September is represented by number 9.

According to this simulation, the probability of a randomly selected student having birthdays in September is:

[tex]P = \frac{X_9}{20}[/tex]

Where [tex]X_9[/tex] is the frequency of 9. That is, [tex]X_9[/tex] is the number of times the number 9 appears among the 20 data

Therefore:

[tex]P = \frac{5}{20}[/tex]

[tex]P = \frac{1}{4}[/tex]

[tex]P = 0.25[/tex]

Answer:

0.25

Step-by-step explanation:

gradpoint

To solve this all you need to do is take the fraction 2/5 and multiply it by a number (this means you multiply BOTH the denominator and the numerator)

1. Multiply the original fraction by 2:

[tex]\frac{2*2}{5*2} = \frac{4}{10}[/tex]

2. Multiply the original fraction by 3:

[tex]\frac{2*3}{5*3} = \frac{6}{15}[/tex]

3. Multiply the original fraction by 4:

[tex]\frac{2*4}{5*4} = \frac{8}{20}[/tex]

4. Multiply the original fraction by 5:

[tex]\frac{2*5}{5*5} = \frac{10}{25}[/tex]

5. Multiply the original fraction by 6:

[tex]\frac{2*6}{5*6} = \frac{12}{30}[/tex]

All of the fractions above are equal to 2/5 and to each other. You can keep doing this with higher numbers if you wold like, but these are just a few examples.

Hope this helped!

Hello There!

Some equivalent fractions of 2/5 are:

2/5 = 4/10 = 6/15 = 8/20 = 10/25 = 12/30 = 14/35 = 16/40 = 18/45 = 20/50 = 22/55 = 24/60 = 26/65 = 28/70 = 30/75 = 32/80 = 34/85 = 36/90 = 38/95 = 40/100 = 42/105

Equivalent fractions are fractions that equal each other, but they look different from each other. These fractions are represented differently.

Answer: Sasha has 20 bars to start of with. Let's assume Sasha keeps 6 bars for herself. The problem says Sasha has twice as many bars as Hanna, so Hanna HAS to have 3 bars. The problem says Kyle got 3 more bars than Hanna, so 3+3=6, and Hannah got 2 less bars than Noah.. Noah has to have bars because 5-3=2

Sasha 6, Kyle 6, Noah 5, Hanna 3= 6+6+5+3=20

Step-by-step explanation:

Final answer:

Using equations based on the relationship between the number of muesli bars each person has, we determine that Sasha ended up with 6 muesli bars.

Explanation:

The subject of this question is mathematics, specifically it involves solving a word problem by setting up equations based on the given relationships among the quantities. Let's find out how many muesli bars Sasha had in the end.

Let's denote the number of muesli bars Sasha, Hannah, Noah, and Kyle have as S, H, N, and K respectively. The problem gives us the following relationships:

H = N - 2 (Hannah has two fewer bars than Noah)

K = H + 3 (Kyle has three more bars than Hannah)

S = 2H (Sasha has twice as many bars as Hannah)

Since there are 20 muesli bars in total, we can write the equation:

S + H + N + K = 20

Substituting the relationships into the equation we get:

2H + H + (H + 2) + (H + 3) = 20

Combining like terms, we have:

5H + 5 = 20

Subtracting 5 from both sides, we get:

5H = 15

Dividing both sides by 5, we find H:

H = 3

Now, we can find S:

S = 2H = 2(3) = 6

So, Sasha had 6 muesli bars in the end.

The answer is X= 2a+2

Answer:

a = 1/2x - 1

Step-by-step explanation:

-8a + 3a = -9a + 2x - 4

-8a + 3a + 9a = 2x - 4

4a = 2x - 4

a = (2x - 4) ÷ 4

a = 1/2x - 1

Answer:

Approximately 53

Step-by-step explanation:

This is a geometric progression, because each term is found by multiplying the previous one by a constant factor.

In our case, the first term is know (a1 = 3), and the growth factor is also known (q = 1.333333).

What we are tasked to do is to find the 11th (n=11) term of the series, since it asks for AFTER the 10th roll..  That's easy with the base formula:

[tex]a_{n} = a_{1} q^{n-1}[/tex]

Let's place the values we have in the equation and solve it:

[tex]a_{10} = 3 * (1.333333)^{11-1} = 3 * (17.758) = 53.3[/tex]

So, after the 10th roll, you should need 53 dice, approximately.

Answer:

Step-by-step explanation:

f(x) + n - move the graph n units up

f(x) - n - move the graph n units down

f(x + n) - move the graph n units to the left

f(x - n) - move the graph n units to the right

--------------------------------------------------------------------------

G(x) = 1/x shifted 4 units up → G(x) + 4 = 1/x + 4

Answer: G(x)= 1/(x+4) +4

Step-by-step explanation:

Hello There! Your answer is D) about 54%.

To find your answer, start by adding together all of the totals for each gender.

Female: 119 + 150 + 447 + 735 + 1174 = 2625

Male: 103 + 171 + 512 + 710 + 756 = 2252

Total: 2625 + 2252 = 4877

The question is asking what percentage of the respondents was female. So, we are finding what precent of 4877 is equal to 2625. To do this, divide 2625 by 4877 and multiply what you get by 100.

2625 divided by 4877 =  0.53824072175 x 100 = 53.824072175%.

Out of the answer choices provided, D) about 54% is correct since 53.824072175% is very close to 54%.

I hope this helps, have a great day!

Answer:

D

Step-by-step explanation:

In total, there were 4877 respondents, among which 2625 of them were female. The percent of female respondents, therefore, would be

2625

4877

x 100 = 53.8% ~ 54%

part a: 1

part b: (3,5)

Answer:

252 cm²

Step-by-step explanation:

Area of a rectangle is width times length:

A = WL

If the width and length increase by a factor of 1.5:

A = (1.5 W) (1.5 L)

A = 2.25 WL

So the area increases by a factor of 2.25.

2.25 × 112 cm² = 252 cm²

The length of the hypotenuse of a right triangle formed inside the unit circle with a radius of 1 is simply 1.

The expression equal to the length of the hypotenuse of a right triangle formed inside the unit circle, with a radius of 1, can be found using the Pythagorean theorem. In a unit circle, the hypotenuse of any right triangle formed by a radius will always have a length of 1, because the radius of a unit circle is 1 by definition. So, the expression you are looking for is simply 1, since the hypotenuse in this case is the radius of the circle.

Answer:15.741

Step-by-step explanation: 4.95*3= 14.85, 14.85* 0.06= 0.891+14.85=15.741

Hope it helped!

Answer:

Step-by-step explanation:

[tex]5m=35\qquad\text{divide both sides by 5}\\\\\dfrac{5\!\!\!\!\diagup^1m}{5\!\!\!\!\diagup_1}=\dfrac{35\!\!\!\!\!\diagup^7}{5\!\!\!\!\diagup_1}\\\\\boxed{m=7}[/tex]

The current value of a future sum of money. The Present Value allows us to calculate what is the value of today that has an amount of money that we will not receive right now but later, in the future.

Present value seeks to reflect that it is always better to have an amount of money today than to receive it in the future. In fact, if we have the money today we can do something to make it productive, such as investing in a company, buying shares or leaving it in the bank that pays us interest, among other options. In addition, even if we do not have a certain plan to invest the money we can simply spend it to satisfy our tastes and we do not have to wait to receive the money in the future.

Answer:

A) The current value of a future sum of money

Step-by-step explanation:

on plato

Answer:

A firm determines its profit by subtracting "Total Cost" from "Total Revenue".

Step-by-step explanation:

Given statement is "A firm determines its profit by subtracting _____ from ______. Now we need to fill the blanks with suitable words.

We know that there are some initial costs associated with production of any product. So to get the profit, we need to subtract the cost that that is spent during production of the product from total sales.

Hence final answer can be written as:

A firm determines its profit by subtracting "Total Cost" from "Total Revenue".

Well, just looking at this problem we know 3 formulas that will help us. Firstly we have C (The Circumference) is Equal to 2π Times the Radius, r.

In Equation form that looks something like this:

C=2πr

We also know that the radius is half of the diameter, r=D/2  or D=2r

So, if C=62.8, then 62.8=2πr must also be true.

By doing some quick re arranging we get to the equation r=62.8/2π

This equation gives us 9.99, Which is essentially 10.

Now that we know that r=10, we can find that diameter, D=2r, is Equal to 20.

Therefore, your answers are

Radius = 10

Diameter = 20

Circumference = 62.8 (Given)

If there are any questions about anything I did please feel free to ask more questions and I will respond ASAP!

Answer:

$13,997.53

Step-by-step explanation:

The simplest, minimally acceptable answer would stem from multiplying by 5 the $247.43 monthly payment and subtracting the result from the amount initially owed:

$15,234.68

-$ 1,237.15

----------------

$13,997.53

To calculate the net change to the loan from Quiana's perspective over the past 5 months, subtract the total amount she has repaid from the initial loan amount. In this case, the net change is $13,997.53.

The amount owed to the lender = $15,234.68

Amount repaid = $247.43

Time = 5 months

To calculate the net change to the loan from Quiana's perspective over the past 5 months, we need to subtract the total amount she has repaid from the initial loan amount.

Since she repaid $247.43 each month for 5 months, the total amount repaid is $247.43 x 5 = $1237.15.

To find the net change to the loan, we subtract the total amount repaid from the initial loan amount:

= $15,234.68 - $1237.15

= $13,997.53.

Answer:

To have an infinite number of solutions, the equations must graph the same line. That means the equations must be equivalent. To form an equivalent equation, use the properties of equality to rewrite the given equation in a different form. Add, subtract, multiply, or divide both sides of the equation by the same amount.

A system of two linear equations in two variables has an infinite number of solutions if the slope and y-intercept of the two lines is same.

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line. If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

It is given that the equation is,

y = 2/3 x - 5

If the slope and y-intercept of the two lines are the same, a system of two linear equations in two variables has an infinite number of solutions.

The equations must graph the same line if there are infinitely many solutions. Therefore, the equations must be equal. The above equation may be rewritten in a different way using the equality principles to create an equivalent equation. Both sides of the equation should be increased, decreased, multiplied, or divided by the same quantity.

Thus, system of two linear equations in two variables has an infinite number of solutions if the slope and y-intercept of the two lines is same.

Learn more about the linear equation here:

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Answer:

The surface area is [tex]SA=3.596\ m^{2}[/tex]

Step-by-step explanation:

we know that

The surface area of the box is equal to

[tex]SA=2[LW]+2(L+W)H[/tex]

Let

[tex]L=1/4=0.25\ m[/tex]

[tex]W=0.36\ m[/tex]

[tex]H=2.8\ m[/tex]

substitute the values

[tex]SA=2[0.25*0.36]+2(0.25+0.36)(2.8)[/tex]

[tex]SA=0.18+3.416[/tex]

[tex]SA=3.596\ m^{2}[/tex]

Answer:

d). 22

Step-by-step explanation:

add the -1 for x then solve

Answer and explanation:

A) Yes, the sample gathered by surveying food critics only is most likely to be biased.

B) If the chef is going to survey only the food critics and not include the regular customers who visit the restaurant then this will result in a biased survey.

The reason being that there will exist a systematic error since the surveyed people will not cover the whole population as it will only be limited to the food critics.

Yes it is. 5\7 is a fraction, therefore it is rational; it can be written as a decimal, 0.714285...... [bar notation indication].

Answer: The quotient of (-5)÷(-7) is a rational number

Step-by-step explanation:

It is asked that the quotient of (-5) / (-7) is a rational number ?

Rational Number : A rational number  is a number which can be expressed in the form p/q  

We multiply the numerator and denominator  of the fraction by -1

[tex]\frac{(-5)(-1)}{(-7)(-1)}[/tex]

=[tex]\frac{5}{7}[/tex]

i.e. the number can be expressed in the form p/q where p=5 and q=7

So the quotient is a rational number

For this case we must find the value of "x", by trigonometric relations.

The tangent of an angle is given by the leg opposite the angle on the leg adjacent to the same angle.

[tex]tg (25) = \frac {10} {x}\\x = \frac {10} {tg (25)}\\x = \frac {10} {0.46630766}\\x = 21.4450691202[/tex]

Rounding:

[tex]x = 21.4[/tex]

Answer:

21.4

Answer:

x = 21.44506921

Step-by-step explanation:

Trigonometry

We need to find x or the adjacent

We are given the Opposite ( 10 )

We don't need the hypotenuse

So we use our formula triangles

TOA             SOH                  CAH

Since we don't need the hypotenuse, we look for a formula without ' H ' in it and it is TOA so we use it

Tan = Opposite ÷ Adjacent

We need to find the adjacent so we rearrange the formula into

Adjacent = Opposite ÷ Tan

Adjacent = 10 ÷ tan(25)

Adjacent = 21.44506921

Answer:

E,F and G

Step-by-step explanation:

we have

2x+y < 10 ---> inequality A

The solution of the inequality A is the shaded area below the dashed line

2x+y=10

Find the intercepts of the dashed line to plot the inequality A in the graph

The x-intercept is the point (5,0)

The y-intercept is the point (0,10)

2x-4y >8 ----> inequality B  

The solution of the inequality B is the shaded area below the dashed line 2x-4y=8

Find the intercepts of the dashed line to plot the inequality B in the graph

The x-intercept is the point (4,0)

The y-intercept is the point (0,-2)

The solution of the system of inequalities the shaded area

see the attached figure

If a ordered pair is a solution of the system of inequalities, then the ordered pair must lie on the shaded area of the solution of the system

In this problem the solutions are E,F and G

Answer:

24 in²

Step-by-step explanation:

The easy way:

The two legs, or shorter sides, of a right triangle form that triangle's base and height. Knowing that the area of a triangle is [tex]\frac{bh}{2}[/tex] (where b is the base and h is the height), we can use the 6 inch leg for the base and the 8 inch leg for the height to find an area of [tex]\frac{6(8)}{2}=\frac{48}{2}=24[/tex] in².

The harder but more general way

There's a nice formula for calculating the area of any triangle given its side lengths found by this Greek guy named Heron, and it's appropriately called Heron's formula:

[tex]A=\sqrt{s(s-a)(s-b)(s-c)[/tex]

a, b, and c are the lengths of triangle, and s here is half the triangle's perimeter (also called the semi-perimeter), or mathematically:

[tex]s=\frac{a+b+c}{2}[/tex]

For our problem, let's pick a = 6, b = 8, and c = 10. This would give us

[tex]s=\frac{6+8+10}{2} =\frac{24}{2}=12[/tex]

Substituting that s back into Heron's formula, we get

[tex]A=\sqrt{12(12-6)(12-8)(12-10)}=\sqrt{12(6)(4)(2)}\\=\sqrt{72(8)}=\sqrt{576}=24[/tex]

So our area is 24 in²

To find out how many weeks Tameca needs to save to have at least $100, we create an inequality, 5w + 55 >= 100, where 'w' represents the number of weeks. Solving this inequality gives w >= 9. Therefore, Tameca needs to save for at least 9 weeks.

The subject of this problem is linear inequalities, which falls under Mathematics. To solve this problem, let's denote the number of weeks that Tameca needs to save money as 'w'. Since she already has $55 and is saving $5 each week, the inequality that represents this situation is 55 + 5w >= 100.

In order to solve this inequality, we need to isolate 'w'. You can do this by subtracting 55 from both sides of the inequality to get 5w >= 45. Then, divide both sides by 5 to get w >= 9.

Therefore, Tameca must save for at least 9 weeks in order to have a minimum of $100 in her savings account.

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To find the mean just add all of them then divide the result by 8. To find the median put the numbers in order. So 3, 3, 4, 4, 13, 15, 15, 16 then find the middle number, if there is not middle number (which there isn’t) add the two middle numbers (4 and 13) to get 17 then divide 17 by 2 to get 8.5 which is the median

Let, that number = x

It would be: x * 0.65 = 52

x = 52 / 0.65

x = 80

So, that number and your answer is 80

18 is 45% of 40

45%/100 = 0.45

0.45*40=18

It is computed that loan Q's finance charge will be $83.73 greater than loan P's.

From the information, the payment for bank P will be:

= (0.058/12)(19450) / [1 - (1 + 0.058/12)^108

= 231.59

The future value will be:

= 231.59 × 12 × 9

= 25011.72

The finance charge for P will be:

= (25011.72 - 19450) + 925

= 6846.72

The payment for Q is 211.08. The future value will be:

= 211.08 × 12 × 10

= 25329.60

The finance charge for Q will be:

= (25329.60 - 19450) + 690.85

= 6570.45.

The difference will now be:

= 6570.45 - 6846.72

= $83.73

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Answer:

A

Step-by-step explanation:

Got it right