If x = 4, calculate the value of: 2x³ - 2x² + 2x - x

Answer: He received $6:05.

Step-by-step explanation:

I got this by subtracting $13.95 from $20.00.

Answer:

--

Step-by-step explanation:

Show all the options please

Not able to see all options

Answer:

$30.25

Step-by-step explanation:

55% of 55$ is $30.25. she wants 45 % off of 55$. which is $24.75. 55-24.75 is 30.25

$30.25

since it's 45% off, you need to subtract 45% from 100%

100%-45%=55%

then turn the % into a decimal

55%/100=0.55

now multiply the original price by 0.55

0.55*55=30.25

If x denotes the width (in feet) of the billboard, find a function in the variable x giving the area of the printed region of the billboard as a function of x is (150/x - 10)(x - 4).

A billboard designer has decided that a sign should have 5-ft margins at the top and bottom and 2-ft margins on the left and right sides.

x = width of the billboard designer

Total Area including margin = 150 ft^2

Height of the billboard = Area/width

Height of the billboard = 150/x

Before the height of the billboard = (150/x - 5 × 2)

Before the height of the billboard = (150/x - 10) ft

The width of the printed region billboard = (x - 2 × 2)

The width of the printed region billboard = (x - 4) ft

The area of the printed region of the billboard = The width of the printed region billboard × The height of the printed region billboard

The area of the printed region of the billboard = (150/x - 10)(x - 4)

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The complete question is:

A billboard designer has decided that a sign should have 5-ft margins at the top and bottom and 2-ft margins on the left and right sides. Furthermore, the billboard should have a total area of 150 ft^2 (including the margins).

If x denotes the width (in feet) of the billboard, find a function in the variable x giving the area of the printed region of the billboard.

Area as a function of x =

The statement translated to an algebra equation will give the value of the unknown number w = 11/5

Algebra is the branch of mathematics that helps to represent problems or values in the form of mathematical expressions using letters to represent unknown values.

Let us represent the unknown number with the letter w so that the statement can be written as the equation:

5w - 8 = 3

add 8 to both sides

5w - 8 + 8 = 3 + 8

5w = 11

divide through by 5

5w/5 = 11/5

w = 11/5

Therefore, the statement translated to an algebra equation will give the value of the unknown number w = 11/5

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The algebraic property illustrated is the commutative property of multiplication

The properties of algebra are those properties mostly used in simplifying algebraic expressions.

Algebraic properties are:

From the expression given we have

4/5 • 5/4 = 1

= 4/ 5 × 5/ 4

= 1

Thus, the algebraic property illustrated is the commutative property of multiplication

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Answer:

4/D a reflection fallowed by a rotation.

sorry if I am wrong

Answer:

the value of a - b is 4.

Step-by-step explanation:

We have been given the following two equations:

a + b = 10 ------------(1)

a² - b² = 40 -------(2)

We can factor the left-hand side of equation (2) using the difference of squares identity:

(a + b)(a - b) = 40

Substituting equation (1) into this equation, we get:

10(a - b) = 40

Dividing both sides by 10, we get:

a - b = 4

Therefore, the value of a - b is 4.

Step-by-step explanation:

if I understand this correctly :

a + b = 10

a² - b² = 40

(a² - b²) = (a + b)(a - b) = 40

10(a - b) = 40

(a - b) = 4

Missy will need a minimum of 570 square inches of wrapping paper to completely cover the box.

To calculate the minimum amount of wrapping paper needed to cover the box, we need to find the surface area of the box.

A rectangular box has six sides: a top, a bottom, two sides, and two ends.

The top and bottom sides have the same dimensions, which are 17.5 inches by 10 inches. So each of these sides has an area of 17.5 in × 10 in = 175 square inches.

The two side surfaces also have the same dimensions, which are 17.5 inches by 4 inches.

Each of these sides has an area of 17.5 in × 4 in = 70 square inches.

The two end surfaces have the same dimensions, which are 10 inches by 4 inches. Each of these sides has an area of 10 in × 4 in = 40 square inches.

To find the total surface area of the box, we add up the areas of all six sides:

175 in² (top) + 175 in² (bottom) + 70 in² (side 1) + 70 in² (side 2) + 40 in² (end 1) + 40 in² (end 2)

Total surface area = 570 in².

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A PARALLEL line has the same angular coeficient, so:

\(f(x) = 2x+b\)

\(f(4) = 5\)

\(5 = 2\cdot 4 +b\)

\(b = 5-8\)

\(b = -3\)

The line asked is:

\(f(x) = 2x-3\)

Answer:

-2x+y=-3

Step-by-step explanation:

Choose a point (4,5) that the parallel line will pass through.

Find the slope m=2

To find an equation that is parallel to   y=2x-4 the slopes must be equal. Using the slope of the equation, find the parallel line using the point-slope formula.

y-y1=m(x-x1) if m=2 and x1=4 and y1=5

y-5=2(x-4)

y-5=2x-8

Solve for  y --- > y=2x-3

-2x+y=-3

(-2x+y=-3)*-1

2x-y=3

Answer:

\(\huge\boxed{-3\overrightarrow{a}+5\overrightarrow{b}=\left<-21;\ 2\right>}\)

Step-by-step explanation:

\(\overrightarrow{a}=\left<2;\ 6\right>\\\\\overrightarrow{b}=\left<-3;\ 4\right>\\\\-3\overrightarrow{a}+5\overrightarrow{b}=-3\left<2;\ 6\right>+5\left<-3;\ 4\right>=\left<-3\cdot2;\ -3\cdot6\right>+\left<5\cdot(-3);\ 5\cdot4\right>\\\\=\left<-6;\ -18\right>+\left<-15;\ 20\right>=\left<-6+(-15);\ -18+20\right>=\left<-21;\ 2\right>\)

Answer:

Blue label

Step-by-step explanation:

All that matters here is # of bottles sold * profit per bottle.

If you multiply these 2 values for each row you will see the blue label has the highest amount of profit.

Among all the product ranges blue label generated the most profit of $5625.

Profit is basically the difference between the total revenue and the total cost of the product.

Profit=Total Revenue- Total cost.

We know that Average profit= total profit/ number of units.

So the profit will be as average profits* number of units.

So the profit of product ranges will be =average profit * number of bottles.

Profit of red label=1.12*3000

=$3360

Profit of black label=1.5*2000

=$3000.

Profit of gold label=2.75*1000

=$2750

Profit of white label=1.20*2750

=$3300

Profit of blue label=2.25*2500

=$5625.

Hence among all the product ranges blue label has generated maximum profit.

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Answer:

\(\frac{356}{559}\)

I hope this helps!

===================================================

Explanation:

Check out the diagram below.

The original L shape is indicated as "figure A".

Split the L shape into 2 rectangular prisms (aka blocks) labeled figure B and figure C. For now, we'll ignore the red regions, but we'll come back to that later.

Figure B is a block with dimensions of

The surface area is:

SA = 2*(L*W + L*H + W*H)

SA = 2*(5*10 + 5*30 + 10*30)

SA = 1000 square cm

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

Now move your attention to figure C.

SA = 2*(L*W + L*H + W*H)

SA = 2*(12*5 + 12*10 + 5*10)

SA = 460 square cm.

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

When combining those two surface areas (of figures B and C) we get a total surface area of 1000+460 = 1460 square cm.

But wait, we need to account for those red regions I mentioned earlier.

This region is not frosted as it's inside the cake rather than on the outside.

The area of the red rectangle is 10*5 = 50 sq cm. It's counted twice when we combined the two 3D blocks together to form the L shape again.

So we have to subtract off 2*50 = 100 sq cm to ignore the red region.

1460-100 = 1360 square cm is the final answer.

Answer:

4\(y^{\frac{3}{2} }\)

Step-by-step explanation:

using the rule of exponents/ radicals

\(\sqrt[n]{a^{m} }\) = \(a^{\frac{m}{n} }\)

then

4 \(\sqrt{y^{3} }\)

= 4\(y^{\frac{3}{2} }\)

Since the product of variables in inverse proportion is constant, the equation is \(xy=22\)

Dividing both sides by x, we get:

\(\boxed{y=\frac{22}{x}} \longrightarrow k=\boxed{22}\)

Answer:

ham

tam

mat

hat

at

ha

am

ma

Step-by-step explanation:

Answer:

It would be 10

Step-by-step explanation:

Its 10 because 12 is to long and the fact that 10 is a few inches shorter it looks correct :D

Answer:

A) 12

Step-by-step explanation:

Yes you have to do a² + b² = c²

So the bottom triangle is 3 and 4 so plug in.

4² + 3² = c² (simplify)

16 + 9 = c²

25 = c² (square root both sides)

5 = c

That gives us the vertical side of the second triangle.

So plug in again

5² + b² = 13² (simplify)

25 + b² = 169 (subtract 25 on both sides)

b² = 144 (square root both sides)

b = 12

x = 12

Hope this helps ya!!

Answer:

5:3

Step-by-step explanation:

140:84 =

35:21 =

5:3

Hope that helps! (If you're up for it, can you give me a brainliest? Thanks)

The ratio is 5:3

A ratio indicates how many times one number contains another. For example, if there are eight oranges and six lemons in a bowl of fruit, then the ratio of oranges to lemons is eight to six.

Given:

Total participants= 224

nonresidents =84

So, residents= 224-84 = 140

Now, ratio of residents to nonresidents

=140/84

=70/42

=10/6

=5/3

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1a. The accumulated factor is 1.5986.

b. The accumulated value is K9591.60

c. The total compound interest earned is K3591.60.

2. Deal 1 is better since it gives a higher amount, K3591.60, of interest earned compared to Deal 2, of K2273.60.

3. The annual compound interest rate used is 5.42%.

4a. Under Plan A, it would take 5.38 years to reach his target of K8000.

b. It would take him 3.65 years to reach his target. under Plan B.

5a. Accumulation factor is 1.0816, accumulated value is K5408, and the total compound interest earned is K408.

b. Accumulation factor is 1.2167, the accumulated value is K6083.50, and the total compound interest earned is K1083.50

6. Total interest she will earn 5 years after the original investment is K4,595.69.

7. Sharon will reach her target in approximately June 2002 which is approx. 1.07 years.

8. The customer will have to pay back K6757.61 after 12 weeks.

1. (a) The accumulated factor is calculated as follows:

i = 4.0% per year, compounded quarterly

n = 8 years × 4 quarters per year = 32 quarters

Using the formula for the accumulated factor for quarterly compounding:

F = \((1 + i)^{n}\) = \((1 + 0.04/4)^{32}\) = 1.5986

Accumulated factor = 1.5986.

(b) Accumulated value: accumulated factor * principal amount:

A = F × P = 1.5986 × K6000 = K9591.60

Accumulated value = K9591.60.

(c) The total compound interest earned: principal -accumulated value:

I = A - P = K9591.60 - K6000 = K3591.60

Compound interest earned =K3591.60.

2. To compare the two deals, we will calculate the total amount of interest earned under each one.  

Under Deal 1, interest is compounded quarterly:

I = A - P = K9591.60 - K6000 = K3591.60

Under Deal 2: We shall use the formula: I = P × r × t

P = principal amount,

r = interest rate,

t = time in years.

I = K6200 × 0.046 × 8 = K2273.60

This means that the first deal is better since it gives a higher total amount of interest earned.

3. The annual interest rate:

Given::

P = K200

A = K310

n = 2 (compounded twice per year)

t = 10 years

A = \(P (1 + r/n)^{(nt)}\)

A = accumulated value,

P = principal amount,

r = interest rate,

n = number of times the interest is compounded per year,

t = time in years.

310 = \(200 (1 + r/2)^{(2 * 10)}\)

1.55 = \((1 + r/2)^{20}\)

Taking the 20th root of both sides, we get:

1 + r/2 = 1.0271

r/2 = 0.0271

r = 0.0542

Annual compound interest rate = 5.42%.

4. (a) Under Plan A,

Using I = P × r × t, we have:

I = K8000 - K6200 = K1800

r = 5.4%

t = I / (P × r) = K1800 / (K6200 × 0.054)  = K334.80

To reach K8000, the tutor will need to earn K1800 in interest, so he is to invest for:

K1800 / K334.80 = 5.38 years

(b) Under Plan B, interest is compounded monthly. using the formula A = \(P (1 + r/n)^{(nt)}\)

Monthly interest rate:

0.048 / 12 = 0.004

The amount of interest earned in one month is:

K6200 x 0.004 = K24.80

To reach K8000, the tutor will need to earn K1800 in interest, so he has to invest for:

log(K8000/K6200) / log(1+0.004) = 43.76 months

= 43.76/12

= 3.65 years.

5(a) After 2 years, the accumulation factor is:

\((1 + 0.04)^{2}\) = 1.0816

The accumulated value is:

K5000 x 1.0816 = K5408

Total compound interest earned is:

K5408 - K5000 = K408

(b) After 5 years, the accumulation factor is:

(1 + 0.04)⁵ = 1.2167

The accumulated value is:

K5000 x 1.2167 = K6083.50

The total amount of compound interest earned is:

K6083.50 - K5000 = K1083.50

6. Amount invested is K5000 + K6000 = K11,000.

Interest rate = 5% per annum compounded quarterly, so the quarterly interest rate is 1.25%.

The number of quarters in 5 years is 20.

Accumulated value after 5 years is:

\(K11,000 (1 + 0.0125)^{20}\) = K15,595.69

The total interest earned is:

K15,595.69 - K11,000 = K4,595.69

7. To calculate the time taken to reach K10,000, we use the compound interest  formula:

\(K8000 (1 + 0.04/4)^{4t}\)  = K10,000

where t =  time in years.

t = log(K10,000/K8000) / (4 log(1 + 0.04/4)) = 4.28 quarters

4 quarters in a year is ≈ 1.07 years, so Sharon will reach her target in approximately June 2002.

8. Weekly interest rate = 2%,

So daily interest rate ≈ 0.0286%.

The amount owed after 12 weeks:

\(K5000 (1 + 0.000286)^{84}\) = K6757.61

The customer will pay back K6757.61 after 12 weeks

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Answer:

y - x = 69

Step-by-step explanation:

From the figure attached,

Number in each block is the sum of the numbers in the block beneath it.

Therefore, A + 21 = 32 ⇒ A = 11

A + 5 = B ⇒ B = 16

C = 5 + x

D = 32 + B ⇒ D = 32 + 16 = 48

E = B + C ⇒ E = 16 + (5 + x)

               ⇒ E = 21 + x

y = D + E ⇒ y = 48 + (21 + x)

                   y = 48 + 21 + x

                   y = 69 + x

              y - x = 69

Therefore, y - x = 69 will be the answer.

hello

according to metric table

1 decagram = 1000 centigram

Joni's mistake was not multiplying by 1000

the answer is option B

Answer:

x² + y² = 74

Step-by-step explanation:

given

(x - y) = 8 ( square both sides )

(x - y)² = 8² ← expand left side using FOIL

x² - 2xy + y² = 64 ← substitute xy = 5

x² - 2(5) + y² = 64

x² - 10 + y² = 64 ( add 10 to both sides )

x² + y² = 74

Answer:

45 = 50

not true

Answer:   45=50

Step-by-step explanation:

Answer: y=3.75x+1.9

Step-by-step explanation: the pick up fee would be the y-intercept and the per mile cost would be the slope.

The equation that can be used to determine the number of miles in the taxi ride is 1.90 + 3.75x = 80.65.

The number of miles traveled is 21 miles.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

We have,

Pick up fee charges = $1.90

Charges per mile = $3.75

Total fare = $80.65

The number of miles traveled = x

We can write an equation as:

1.90 + 3.75x = 80.65

The number of miles traveled:

1.90 + 3.75x = 80.65

Subtract 1.90 on both sides.

1.90 + 3.75x - 1.90 = 80.65 - 1.90

3.75x = 78.75

Divide both sides by 3.75.

x = 21.

Thus,

The equation that can be used to determine the number of miles in the taxi ride is 1.90 + 3.75x = 80.65.

The number of miles traveled is 21 miles.

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The relationship between logarithms and exponential functions is fundamental and provides a powerful tool for finding solutions in various mathematical and scientific contexts.

Logarithms are the inverse functions of exponential functions. They allow us to solve equations and manipulate exponential expressions in a more manageable way. By taking the logarithm of both sides of an exponential equation, we can convert it into a linear equation, which is often easier to solve.

One of the key properties of logarithms is the ability to condense multiplication and division operations into addition and subtraction operations. For example, the logarithm of a product is equal to the sum of the logarithms, and the logarithm of a quotient is equal to the difference of the logarithms.

Logarithms also help us solve equations involving exponential growth or decay. By taking the logarithm of both sides of an exponential growth or decay equation, we can isolate the exponent and solve for the unknown variable.

This is particularly useful in fields such as finance, population modeling, and radioactive decay, where exponential functions are commonly used.

Furthermore, logarithms provide a way to express very large or very small numbers in a more manageable form. The logarithmic scale allows us to compress a wide range of values into a smaller range, making it easier to analyze and compare data.

In summary, the relationship between logarithms and exponential functions enables us to simplify and solve equations involving exponential expressions, model exponential growth or decay, and manipulate large or small numbers more effectively.

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Answer: $227,226.51

Step-by-step explanation:

First, we need to convert the period to weeks.

9 1/2 years = 9.5 years

1 year = 52 weeks

9.5 years = 494 weeks

Next, we can use the formula for the future value of an annuity:

FV = (PMT x (((1 + r/n)^(n*t)) - 1)) / (r/n)

where:

PMT = payment amount per period

r = annual interest rate

n = number of compounding periods per year

t = number of years

Plugging in the given values:

PMT = $300

r = 0.055 (5.5% expressed as a decimal)

n = 52 (compounded weekly)

t = 9.5 years = 494 weeks

FV = ($300 x (((1 + 0.055/52)^(52*494)) - 1)) / (0.055/52)

FV = $227,226.51

Therefore, the future value of the annuity is approximately $227,226.51.

Answer:

1/sec x- tan x

Step-by-step explanation:

sec x+ tan x

= sec x+ tan x) (sec x - tan x)/(sec x , tan x)

=sec^2x-tan^2x)(sec x- tan x)

(sec^2x-tan^2x=1)

=1/sec x- tan x

-The answer is:

This is a quadratic expression, factored out. The roots are:

This tell us that the function in x 0 -1 and x = 4 is equal to zero. We what to find all the x for which the function is positive.

If we grapf the points in a line:

The red point are the places where the function is zero. We want to know what happends between those points. If the function is positive between -1 and 4, then the answer would we that interval. If the function is negative in that interval, then we want to know if the function is positive outside the interval:

Let's take a point between -1 and 4 and to make simpler: x = 0

Let's see whats the value: (0 - 4)(0 + 1) = (-4) * 1 = -4

It's negative, then the inequality (x - 4)(x +1) > 0 is false in the interval (-1, 4)

Let's see what happends outside the interval (-1, 49. Let's take the points x = -5 and x = 5, because -5 < -1 and 4 < 5

(5 - 4)(5 +1) = 1 * 6 = 6 It's positive.

(-5 - 4)(-5 + 1) = (-9)(-4) = 36 It's positive.

Then the answer are all the x's smaller than -1 and greater than 4.