Evaluate (5 + 2)2 − 40 + 3 = __________.

NUMERICAL ANSWER EXPECTED!

Answer for Blank 1:

[tex]\bf ~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\\ P=\textit{original amount deposited}\dotfill & \$1500\\ r=rate\to 5\%\to \frac{5}{100}\dotfill &0.05\\ t=years\dotfill &1 \end{cases} \\\\\\ I=(1500)(0.05)(1)\implies I=75[/tex]

Chris will earn $75 in interest in the first year by depositing $1,500 into a savings account with an annual interest rate of 5%, calculated using the simple interest formula.

To calculate the amount of interest Chris will earn in the first year the money is in the savings account, we will use the formula for simple interest, which is Interest = Principal × Rate × Time. In this case, the principal amount is $1,500, the annual interest rate is 5% or 0.05 when expressed as a decimal, and the time is 1 year since we are looking for the interest for the first year only.

Therefore, the interest Chris will earn after one year is calculated as follows:

Interest = $1,500 × 0.05 × 1

Interest = $75

Thus, at the end of the first year, Chris will have earned $75 in interest.

Since p = x² - 7, you can substitute/plug in p for x² - 7

So:

(x² - 7)² - 4x² + 28 = 5

(p)² - 4x² + 28 = 5      You can factor out -4 from (-4x² + 28)

p² - 4(x² - 7) = 5        Plug in p

p² - 4p = 5        Subtract 5

p² - 4p - 5 = 0        Your answer is C

To find an equation equivalent to (x^2-7)-4x^2+28 in terms of p, substitute x^2-7 with p. The equation equivalent to (x^2-7)-4x^2+28 in terms of p is -4x^2+p+28.

To find an equation equivalent to (x^2-7)-4x^2+28 in terms of p, we can substitute x^2-7 with p. So we have (p)-4x^2+28. Now, we combine like terms by adding the coefficients of p and -4x^2, which gives us -4x^2+p+28.

Answer: 5,000

Step-by-step

Answer:

5,000

Step-by-step explanation:

just got my paper graded

Answer:

The answer is D

Step-by-step explanation:

for every increase in the product sold, the earnings increase by 300 respectively

I believe the correct answer to this question is 42 and 288. If im not wrong.

Answer:

the answer is 42 and 228

Step-by-step explanation:

165x165=27,225 and 123x123=15,129

27,225-15,129=12,096

if you multiply 4x288 you get 12,096 which is your answer from before.

Final answer:

The approximate area of a 212-degree sector with a 45m radius is 3371.26 m², and the approximate area of a 92-degree sector with a 9m diameter (4.5m radius) is 16.2 m².

Explanation:

To find the approximate area of a sector of a circle, we use the formula for the area of a circle, A = πr², and then adjust it for the sector by multiplying by the ratio of the central angle to 360 degrees. For Question 1, the central angle θ is approximately 212 degrees and the radius is 45 m. The formula for the sector area becomes A = (π × (45 m)² × (212/360)). A quick calculation gives us the following area:

For the first sector with a 212-degree angle and a radius of 45m:

A = 3.1415927 × (45 m)² × (212/360) = 3.1415927 × 2025 m² × 0.5889 ≈ 3371.26 m²

For Question 2, the central angle θ is approximately 92 degrees and the diameter is 9m, which makes the radius 4.5m. The formula for the sector area then becomes A = (π × (4.5 m)² × (92/360)). The calculation yields the following area:

A = 3.1415927 × (4.5 m)² × (92/360) = 3.1415927 × 20.25 m² × 0.2556 ≈ 16.2 m²

Answer:

Step-by-step explanation:

The domain of that function is all real numbers.  The x values will drop into negative infinity and will grow to positive infinity.

The range is found from the vertex form of a parabola, which is

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

where h indicates side to side movement of the vertex and k indicates up or down.  Our function has a +3 at the end of it and is positive (so it opens upwards), so the range is y ≥ 3.

To find the inverse of that function, switch the x and y coordinates and solve for the new y.  Let f(x) be y, then switch the x and y:

[tex]x=y^2+3[/tex]

Now solve for the new y:

y = ±[tex]\sqrt{x-3}[/tex]

To find the domain of a radical, set the radicand greater than or equal to 0 and solve for x (this is because the radicand cannot be a negative number or we are dealing with imaginary numbers and that's not what you want.  BTW, a radicand is the term under the radical sign).  

x - 3 ≥ 0  so   x ≥ 3.  The domain of the inverse is all real numbers greater than or equal to 3.

This is a sideways parabola (the inverse is), and it opens to the right starting at the x value of 3.  It will grow into positive values of y to infinity and will drop into negative values of y into negative infinity.

Just a little trick here to remember, and it ALWAYS holds true:  the domain of a function is the range of its inverse, and the range of a function is the domain of its inverse.  Look to our solution for your problem here and you'll see that it is true.

Answer:

So for every ounce of granola she uses a quarter ounces of raisins so a quarter of 24 is 6

Answer:6

Step-by-step explanation:

Answer:

  7/4 yard

Step-by-step explanation:

36 is a suitable common denominator for expressing these fractions. All measures are in yards.

  2/3 + 4/9 + 23/36 = (12·2)/(12·3) + (4·4)/(4·9) + 23/36

  = 24/36 + 16/36 + 23/36

  = 63/36 = (9·7)/(9·4)

  = 7/4 = 1 3/4 . . . . . yards

The formula is d=C/π.

The diameter is 2 times the radius

The formula for the circumference using the radius is 2πr.

in order to do this backwards, we would have to do 16÷2÷π, but we're not looking for the radius.

Therefore, we take out the ÷2 part, which would be 16÷π

16 is the circumference

16÷π=d

d=C÷π

Answer:

d = /π

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

$934.30

Step-by-step explanation:

We have been given that Alfred invest $60 a month in annuity that earns 4% APR and is compounded monthly. We are asked to find the future value of Alfred's account after 5 years.

[tex]FV=C_0\cdot (1+r)^n[/tex], where,

[tex]C_0=\text{Initial value}[/tex],

[tex]r=\text{APR in decimal form}[/tex],

[tex]n=\text{Number of times interest is compounded per year}[/tex].

[tex]r=4\%=\frac{4}{100}=0.04[/tex]

[tex]FV=\$60\cdot (1+0.04)^{12*5}[/tex]

[tex]FV=\$60\cdot (1.04)^{70}[/tex]

[tex]FV=\$60\cdot 15.57161835[/tex]

[tex]FV=\$934.2971[/tex]

[tex]FV\approx \$934.30[/tex]

Therefore, the future value of Alfred's account in 5 years would be $934.30.

Answer: 2

Step-by-step explanation:

The reason is for each meal to have one thing of food for every lunch special. So then you would go one by one, theres 2 appetizers so that means it'll only reach to 2 lunches. Then theres 5 main courses and you seperate those having 2 of the 5 with the appetizers. Onto the desserts, there are 5 desserts and 2 out of the 5 you put it together with the lunches that have a main course and appetizers. Next, there are 3 drinks and 2 of those 3 you would put it with the 2 meals that has an appetizer,main course,dessert, and now a drink. In the end, Its only possible that there are 2 lunch special being able to be made. With all the food

Answer: 150

Step-by-step explanation:

We know that a complete lunch meal consist of an appetizer , a main course , a dessert and a drink.

Given: The number of appetizers=2

The number of main courses=5

The number of desserts=5

The number of drinks=3

Therefore, the number of possible lunch meals will be :

[tex]2\times5\times5\times3=150[/tex]

Hence, there are 150 lunch meals are possible.

Answer:

  {x| x≤ 1/2 or x ≥ 3/4}

Step-by-step explanation:

The values of x that make the factors zero are 3/4 and 1/2. The product of these factors will be positive when both factors are negative (for x < 1/2) or when both factors are positive (x > 3/4). The matching answer selection is the third one.

2 minutes 21 seconds

take the square root of 36 and subtract 2 because √36= 6-2=4x

Answer:

take the square root of 36 and subtract 2 because √36= 6-2=4x

Step-by-step explanation:

Answer:  D) (-5, 1)

Step-by-step explanation:

Inverse is when the x's and y's are swapped.

f(x) has the coordinate (1, -5) --> the inverse of that is (-5, 1), which is option D.

Check the picture below.

Answer:

The correct answer is 23

Step-by-step explanation:

Answer:

[tex]\large\boxed{\left(-\dfrac{11}{2};\ -\dfrac{11}{2}\right)}[/tex]

Step-by-step explanation:

The formula of a midpoint of the segment"

[tex]\left(\dfrac{x_1+x_2}{2};\ \dfrac{y_1+y_2}{2}\right)[/tex]

We have the points W(-3, -7) and X(-8, -4).

Substitute:

[tex]x=\dfrac{-3+(-8)}{2}=\dfrac{-11}{2}\\\\y=\dfrac{-7+(-4)}{2}=\dfrac{-11}{2}[/tex]

The coordinates of the midpoint of a line segment with endpoints (-3, -7) and (-8, -4) are (-5.5, -5.5) using the midpoint formula.

The subject of this question is Mathematics, specifically dealing with geometry. The student is asked to find the midpoint of a line segment whose endpoints are given. The coordinates of the endpoints of the line segment are W(-3, -7) and X(-8, -4).

The formula to calculate the coordinates of a midpoint in a Cartesian plane is M = [(x1 + x2)/2, (y1 + y2)/2], where M denotes the midpoint, (x1, y1) and (x2, y2) are the coordinates of the endpoints of the line segment.

Thus, the midpoint M of the line segment WX is calculated as follows: M = [(-3 -8)/2, (-7 -4)/2] =  [-11/2, -11/2]. So, the coordinates of the midpoint of the line segment WX are (-5.5, -5.5).

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Answer:

0.3

Step-by-step explanation:

10y + 7 + 3(3y + 7) = 180

10y + 7 + 9y + 21 = 180

19y + 28 = 180

19y = 180 - 28

19y = 152

y = 152/19

y = 8

Plug back into Q and S.

Q = 10y + 7

Q = 10(8) + 7

Q = 80 + 7

Q = 87

S = 3(3y + 7)

S = 9y + 21

S = 9(8) + 21

S = 72 + 21

S = 93

Without solving for x to find the other angles, we can easily see that the answer is choice C.

Answer:

P = 61°

Q = 87°

R = 119°

S = 93°

Done!

Answer:

[tex]\sqrt[3]{-0.064}=-0.4[/tex]

Step-by-step explanation:

An on-line calculator can do this if your own doesn't.

For a cube root, you may have to use the exponentiation function with an exponent of 1/3. Usually, that fraction will need to be put in parentheses. (See the second attachment for the result from a TI-84 calculator.)

-Hello There-

If the probabilities are independent, the probability that a left-handed person will bring a glove is ...

 0.08×0.12 = 0.0096 ≈ 0.01

Hope This Helped!

Have A Great Day!

Stay Safe,

TheBlueFox

the answer would be 0.1

Answer:

170 ft²

Step-by-step explanation:

First let's calculate the height of this trapezoid.  Call it 'h.'  Look at the triangle on the right; the base is equal to (22 ft - 12 ft), or (10 ft).  Using the tangent function, we can find h:

                    h

tan 45° = ---------- = 1  and so we know that h = 10 ft

                  10 ft

The formula for the area of a trapezoid is

A = (average length)*(width)

Here we have:

A = [ (12 ft + 22 ft) / 2 ] * 10 ft, or

A  =           (17 ft)*(10 ft) = 170 ft²

Answer:

[tex]\theta=101.3\degree[/tex] to the nearest tenth

Step-by-step explanation:

The given vectors are;

u = – 3i + 3j and v = 3i + 2j

We use the dot product to find the angle between the two vectors.

[tex]u\bullet v=|u| |v|\cos \theta[/tex]

[tex](-3i+3j)\bullet (3i+2j)=|-3i+3j| |3i+3j|\cos \theta[/tex]

[tex](-3i+3j)\bullet (3i+2j)=\sqrt{(-3)^2+3^2} \sqrt{3^2+2^2}\cos \theta[/tex]

[tex]-9+6=3\sqrt{2} \sqrt{13}\cos \theta[/tex]

[tex]-3=3\sqrt{2} \sqrt{13}\cos \theta[/tex]

[tex]-1=\sqrt{26} \cos \theta[/tex]

[tex]-\frac{1}{\sqrt{26}}= \cos \theta[/tex]

[tex]\cos^{-1}(-\frac{1}{\sqrt{26}})= \theta[/tex]

[tex]\theta=101.3\degree[/tex]

Answer:

Step-by-step explanation:

If the point is translated across the y axis then the x coordinate will change sign.

If the point is translated upwards then the y coordinate will increase by 3

So the answers are B and D.

[tex]\bf b=ar^{n-1}~~ \begin{cases} b=1024\\ a=16\\ r=2 \end{cases}\implies 1024=16(2^{n-1})~~ \begin{cases} 1024=&2^{10}\\ 16=&2^4 \end{cases} \\\\\\ 2^{10}=2^4(2^{n-1})\implies \cfrac{2^{10}}{2^4}=2^{n-1}\implies 2^{10}\cdot 2^{-4}=2^{n-1}\implies 2^{10-4}=2^{n-1} \\\\\\ 2^6=2^{n-1}\implies \stackrel{\textit{same base, the exponents must be the same}}{6=n-1\implies 7=n}[/tex]

The value of n when b = 1,024, a = 16, and r = 2 is 7.

The student is asking to solve for n in the formula of the nth term of a geometric series given the formula b = ar^(n-1) and the values of b, a, and r. To find the value of n, we can substitute the known values into the formula and solve for n.

b = 1,024

a = 16

r = 2

Using these values:

Substitute the known values into the formula: 1,024 = 16 imes 2^(n-1)

Divide both sides by 16: 64 = 2^(n-1)

Recognize that 64 is 2 to the power of 6: 2^6 = 2^(n-1)

Therefore, n - 1 = 6

Add 1 to both sides to find n: n = 7

The value of n when b = 1,024, a = 16, and r = 2 is 7.

70 shirts per day

We simply need to find how many shirts would have been produced on the 8th day. This can be done by multiplying the number of extra shirts produced per day by the number of days extra shirts were produced. Since one day was skipped due to finishing early, there were 7 days of producing extra shirts.

7 times 10 equals 70. This means that 70 shirts would have been produced on the 8th day, which means the factory was planning on producing 70 shirts for every other day as well.

Answer:

t = 6: It takes 6 seconds for the object to hit the ground

Step-by-step explanation:

So, we need to find t when the height is 0. Since -5t² + 20t + 60 represents the height, that needs to equal 0.

Equation: -5t² + 20t + 60 = 0

Divide by -5: t² - 4t - 12 = 0

Find two numbers that add up to -4t and multiply to -12t²: -6t, 2t

Substitute: t² - 6t + 2t - 12 = 0

Factor: (t - 6)(t + 2) = 0

Answers: t = 6, t = -2

Since time can't be negative, t = 6.

To determine the time it takes for the object to hit the ground, the quadratic equation -5t^2 + 20t + 60 = 0 is solved, leading to the conclusion that it takes 6 seconds for the object to reach the ground.

The question asks, "How many seconds does it take for the object to hit the ground?" given the function f(t) = -5t2 + 20t + 60. To find when the object hits the ground, we need to determine when the height f(t) is equal to 0. This involves solving a quadratic equation.

Steps to Solve:

Set the equation equal to zero: -5t2 + 20t + 60 = 0.

Divide the entire equation by -5 to simplify: t2 - 4t - 12 = 0.

Use the quadratic formula: t = (-B ± √(B2 - 4AC)) / 2A, where A = 1, B = -4, and C = -12.

Calculate the discriminant: √((-4)2 - 4(1)(-12)) = √(16 + 48) = √64 = 8.

Substitute values into the formula: t = (4 ± 8) / 2, yielding t = 6 seconds or t = -2 seconds.

Dismiss the negative value, as time cannot be negative, leaving t = 6 seconds as the solution.

Therefore, it takes the object 6 seconds to hit the ground after it is launched.

Answer:

D) 8.6

Step-by-step explanation:

The Law of Sines tells you ...

c/sin(C) = a/sin(A)

The sum of angles in a triangle tells you ...

C = 180° -A -B = 180° -50° -60° = 70°

Then ...

c = a·sin(C)/sin(A) = 7·sin(70°)/sin(50°) ≈ 8.6 . . . . . above equation multiplied by sin(C)

_____

There are apps available for phone or tablet for solving triangles. Many graphing calculators have functions that will do the same. Also, there are on-line triangle solvers that will give you the answer.

We include the working here because you're supposed to know how to work the problem. If all you want is the answer, that can be found faster a number of different ways.

Answer:

3x (3x-2)(4x+1)

Step-by-step explanation:

36x^3 – 15x^2 – 6x

factor out the "3x"

3x (12x^2-5x-2)

3x(3x - 2) (4x + 1)

= 9x^2 - 6x (4x + 1)

= 36x^3 + 9x^2 + -  24x^2 - 6x

= 36x^3 - 15x^2 - 6x

hope this helps!

The product of prime polynomials is equivalent to Option (A)  [tex]3x(3x - 2)(4x + 1)[/tex].

In mathematics, an irreducible polynomial (or prime polynomial) is approximately a non-constant polynomial that cannot be factored into the product of two non-constant polynomials. The expression can be expressed in product of prime polynomial by converting it into the factored form.

Given polynomial expression = [tex]36x^{3} - 15x^{2} - 6x[/tex]

Solving the polynomial expression in factored form -

⇒ [tex]3x(12x^{2} - 5x - 2)[/tex]

⇒ [tex]3x(12x^{2} - 8x + 3x - 2)[/tex]

⇒ [tex]3x[4x(3x - 2) + 1(3x - 2)][/tex]

⇒ [tex]3x(3x - 2)(4x + 1)[/tex]

Therefore the product of prime polynomial is [tex]3x(3x - 2)(4x + 1)[/tex]

To learn more about product of prime polynomial, refer -

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