a) Evaluate the following calculation, giving your answer rounded to 3 decimal
places:
(4.01 +8.56)³ × (347-150) ½
b) Explain the steps you have taken in the calculation and why.

The values for f(x)-2 g(x) = -2x² + 8x - 1

Given :  f(x)=2 x+5

            g(x)=x²-3 x+2

Solution:

            2g(x)=2x²-6x+4

            f(x)-2 g(x) = 2 x+5 - (2x²-6x+4)

            f(x)-2 g(x) = 2 x+5 - 2x² + 6x - 4

            f(x)-2 g(x) = -2x² + 8x - 1

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The value of x from the given linear equation x/3-3=x/9+3 is 27.

What is linear equation?

A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included.

Given equation

x/3-3=x/9+3

=> x/3-x/9=3+3

=>(3x-x)/9=6

=>2x/9=6

=> x=9*6/2

x=27.

Therefore, the value of x from the given linear equation is 27.

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If the expression is log₄ 5x+log₄3x, then the expression in single logarithm form looks like [tex]log_{4} 15x^{2}[/tex].

Given that the expression is log₄ 5x+log₄3x.

We have to express the expression in single logarithm.

Product property of logarithm says that the logarithm of a product is equal to a sum of logarithms. Because logs are exponents which we have to multiply like bases, we can add the exponents.

The expression is log₄ 5x+log₄3x.

log₄ 5x+log₄3x=[tex]log_{4} 15x^{2}[/tex]     (We are not required to change the base)

Hence if the expression is log₄ 5x+log₄3x, then the expression in single logarithm form looks like [tex]log_{4} 15x^{2}[/tex].

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Answer: 19

Step-by-step explanation:

Answer:

3/4 of the members.

Step-by-step explanation:

4/12 simplifies to 3/4

Answer:

Simplify

x

=

35.99

dollar

11.33

dollar

.

x

=

3.1765225

Step-by-step explanation:

Answer:1133.5 mm²

Step-by-step explanation:

area= πr² where r is the radius

3.14x19²= 1133.5 mm²

Answer:

Step-by-step explanation:

5

2

−9x−10

Calculate 5 to the power of 2 and get 25.

25−9x−10

1

Calculate 10 to the power of 1 and get 10.

25−9x−10

Subtract 10 from 25 to get 15.

15−9x

1 apple contains a number of times calories = 95

In contrast to functions defined for other values, an arithmetic function is any mathematical function defined for integers (..., 3, 2, 1, 0, 1, 2, 3,...) and relies on the qualities of the integer itself as a number (real numbers, complex numbers, or even other functions)

Based on the given conditions, formulate: 20+6 * x = 590

Rearrange unknown terms to the left side of the equation: 6x = 590 - 20

Calculate the sum or difference:6x = 570

Divide both sides of the equation by the coefficient of variable: x = 570/6

Cross out the common factor: x = 95

get the result: x = 95

1 apple contains a number of times calories = 95.

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The scatter plot is shown in attached images and the line of best fit for the data set is y=1.9821x+2.1937.

The given data set is (0,2),(1,4),(2,6.5),(3,8.5),(4,10),(5,12),(6,14).

Plot the points on a coordinate plane.

Calculate the means of the x -values and the y -values.

[tex]\begin{aligned}\bar{X}&=\frac{0+1+2+3+4+5+6}{7}\\ &=\frac{21}{7} \text{ or } 3\\ \bar{Y}&=\frac{2+4+6.5+8.5+10+12+14}{7}\\ &=\frac{57}{7}\text{ or }8.14\end[/tex]

Now, we will calculate the [tex]\sum_{i=1}^{n}(x_{i}-\bar{X})(y_{i}-\bar{Y})[/tex] and [tex]\sum_{i=1}^{n}(x_{i}-\bar{X})^{2}[/tex], we get

[tex]\sum_{i=1}^{n}(x_{i}-\bar{X})^{2}=28[/tex]

and [tex]\sum_{i=1}^{n}(x_{i}-\bar{X})(y_{i}-\bar{Y})=55.5[/tex]

Calculate the slope.

[tex]\begin{aligned}m&=\frac{\sum_{i=1}^{n}(x_{i}-\bar{X})(y_{i}-\bar{Y})}{\sum_{i=1}^{n}(x_{i}-\bar{X})}\\ &=\frac{55.5}{28}\\ &=1.9821\end[/tex]

Calculate the y -intercept.

Use the formula to compute the y -intercept.

[tex]\begin{aligned}b&=\bar{Y}-m\bar{X}\\ &=8.14-(1.9821\times3)\\ &=8.14-5.9463\\ &=2.1937\end[/tex]

Use the slope and y -intercept to form the equation of the line of best fit.

The slope of the line is 1.9821 and the y -intercept is 2.1937 .

Therefore, the equation is y=1.9821x+2.1937 .

Draw the line on the scatter plot.

Hence, the scatter plot is shown in attached image and the line of best fit for given data set (0,2),(1,4),(2,6.5),(3,8.5),(4,10),(5,12),(6,14) is y=1.9821x+2.1937.

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answer: 7,602

explanation: 2×3×7×181

Answer:7602

Step-by-step explanation:First line up the numbers vertically and match the places from the right like this.

181

942

* ​____

​

Now multiply the first number with the 1 st  digit in 2 nd

 number to get intermediate results. That is Multiply 181 with 2. Write the result 362 at the end leaving 0 spaces to the right like this.

181

42

*​_____

362

​

Now multiply the first number with the 2nd digit in 2nd

 number to get intermediate results. That is Multiply 181 with 4. Write the result 724 at the end leaving 1 spaces to the right like this.

181

42

*______

362

724

​______-

Now add the intermediate results to get final answer.

181

42

*_____

362

724

______

​7602

​

Answer: use a picture math thing

Step-by-step explanation:0.0038 x 105=0.399 so move the decimal point over 1 then it should look like 0.038 x 10.5=0.399 then repeat.

Answer:

Personally, I think it depends on the amount of the product you’re buying. If the product is expensive, you should go the store with a percentage-off discount. If the product is not expensive, you should go to the store with coupon savings.

Step-by-step explanation:

For example, if you’re buying a $5 toy with a $1 coupon and 10% off, you should chose the coupon. Because if you chose the discount, it doesn’t change a lot of things. However, if you’re buying a million dollar airplane(just kidding), then you should definitely chose the discount. Because a million dollar minus 1 changes nothing. But a 10% discount can decrease the cost by 1 hundred thousand! Isn’t that surprising? Hope you understand it.

Answer: The answer is <

Step-by-step explanation:

Really can explain sorry

Using simultaneous equations in two variables we get that the cost of laminate is $ 0.65 per sq. feet and the cost of carpet is $ 4.12 per sq. feet.

Equations in algebra that involve two or more variables simultaneously, such as x and y, are referred to as simultaneous equations. The equations are referred to as simultaneous equations since they are solved simultaneously. There are countless possible solutions to just these equations.

A set of finite equations for which common solutions are sought makes up a system of equations, often known as an equation system.

Let the cost per sq feet of laminate be x and the cost per sq feet of carpet be y.

Now it is given that the cost of 750 sq feet of laminate and 525 square foot of carpet is $2717.25

∴ 750x+525y=2717.25

Again  the cost of 100 sq feet of laminate and 75 square foot of carpet is $374.75

∴ 100x + 75 y = 374.15

Now we solve the pair of simultaneous equations to find the value of x and y:

Multiplying the second equation by 7 and subtracting from the first we get:

750x + 525y =  2717.25

600x + 575 y = 2619.05

150x = 98.20

or, x = 0.654...

Substituting this  value in the first equation we get:

y= 4.115...

Therefore the solution of the simultaneous equation is:

x = $ 0.65 and y = $ 4.12

Therefore  the cost of laminate is $ 0.65 per sq. feet and the cost of carpet is $ 4.12 per sq. feet.

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Answer:

Step-by-step explanation:

If 8 panes cost 1880

then 1 pane cost 1880 divided by 8

1 pane = $ 235

3 pane = $235 x 3

            = $ 705

$1715 + $705 = $ 2420

Answer:

w=5

Step-by-step explanation:

3(w-2)=9

3w-6=9

w=5

Answer:

w = 5

Step-by-step explanation:

The equation is 3(w - 2) = 9
1st : Distribute 3 to w and -2
    Should equal 3w and -6
2nd : Add 6 on both sides
    Should equal 3w = 15
3rd : Divide 3 on both sides
    Should equal w = 5

Hope this helps!
--Blu

The gymnasts average score is 9.07

The scores are given as

8.9, 9.2, 9.15, 9.03

The gymnasts average score is calculated using'

Average = Sum/Count

So, we have

Average = (8.9 + 9.2 + 9.15 + 9.03)/4

Evaluate

Average = 9.07

Hence, the gymnasts average score is 9.07

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The domain of the expression is all real numbers except where the expression is undefined. In this case, there is no real number that makes the expression undefined.

Interval Notation:

                             ( -∞ , ∞ )

Set-Builder Notation:

                                  { x | x ∈ R }

The range is the set of all valid  y  values. Use the graph to find the range.

Interval Notation:

                               ( -∞ , ∞ )

Set-Builder Notation:

                                 { y | y ∈ R }

Determine the domain and range.

Domain:  ( −∞ , ∞ ), { x | x ∈ R }

Range:  ( −∞ , ∞ ), { y | y ∈ R }

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Answer:

58

Step-by-step explanation:

2-2x-3y5

2-2(2)-3(-4)5

-2+60

58

The solutions are;

1. U = {a, d, e, i, l, n, o, p, y}

2. E ∪ I = {a, d, e, i, l, n, o, p, y}

3. E ∩ I = { }

4. J' = {a, d, e, l}

5. I ∪ J = {p, i, n, a, o, y}

6.( J ∩ I ) ∪ E = {d, o, l, e, p, i, n, y}

7. E' = {a, i, n, p, y}

8. I' ∪ J = {d, e, l, o, p, i, n, y}

9. (E ∩ I) ∩ (I ∪ J) = { }

10. (J ∪ I)' = {d, e, l}

What is Union of the set?

Union of two or more set is the set containing all the elements of the given set.

Here, U is the universal set, which is the set of all elements of the three given sets.

And, Three sets are;

⇒ E = {d, o, I, e},     I = {p, i, n, a, y},     J = {p, i, n, o, y}

Now, We find the universal set as;

1. U = {{a, d, e, i, l, n, o, p, y}

2. And, E ∪ I =  {d, o, I, e} ∪ {p, i, n, a, y}

                = {a, d, e, i, l, n, o, p, y}

Hence, E ∪ I = {a, d, e, i, l, n, o, p, y}

3.  E ∩ I =  {d, o, I, e} ∩ {p, i, n, a, y}

Since, It cannot contain any common elements.

So, Intersection of E and I is null set.

Hence, E ∩ I = { }

4. Since, J' = U - J

J' = {a, d, e, i, l, n, o, p, y} - {p, i, n, o, y}

J' = {a, d, e, l}

Hence, J' = {a, d, e, l}

5. I ∪ J = {p, i, n, a, y} ∪ {p, i, n, o, y}

           = {p, i, n, a, o, y}

Hence,  I ∪ J = {p, i, n, a, o, y}

6. ( J ∩ I ) ∪ E = ({p, i, n, o, y} ∩ {p, i, n, a, y}) ∪ {d, o, I, e}

                     = {p, i, n, y} ∪ {d, o, I, e}

                     = {d, o, l, e, p, i, n, y}

Hence, ( J ∩ I ) ∪ E = {d, o, l, e, p, i, n, y}

7.  E' = U - E

       = {a, d, e, i, l, n, o, p, y} - {d, o, I, e}

       = {a, i, n, p, y}

Hence, E' = {a, i, n, p, y}

8.  I' ∪ J = (U - I) ∪ J

            = ( {a, d, e, i, l, n, o, p, y} - {p, i, n, a, y}) ∪ {p, i, n, o, y}

            = {d, e, l, o} ∪ {p, i, n, o, y}

            =  {d, e, l, o, p, i, n, y}

Hence, I' ∪ J = {d, e, l, o, p, i, n, y}

9. (E ∩ I) ∩ (I ∪ J) = ( {d, o, I, e} ∩ {p, i, n, a, y}) ∩ ({p, i, n, a, y} ∪ {p, i, n, o, y})

                          = { } ∩ {p, i, n, a, o, y}

                          = { }

Hence,  (E ∩ I) ∩ (I ∪ J) = { }

10. (J ∪ I)' = U - (J ∪ I)

              = {a, d, e, i, l, n, o, p, y} - ({p, i, n, a, y} ∪ {p, i, n, o, y})

              = {a, d, e, i, l, n, o, p, y} - {p, i, n, a, o, y}

              =  {d, e, l}

Hence,  (J ∪ I)' = {d, e, l}

So, The solutions are;

1. U = {a, d, e, i, l, n, o, p, y}

2. E ∪ I = {a, d, e, i, l, n, o, p, y}

3. E ∩ I = { }

4. J' = {a, d, e, l}

5. I ∪ J = {p, i, n, a, o, y}

6.( J ∩ I ) ∪ E = {d, o, l, e, p, i, n, y}

7. E' = {a, i, n, p, y}

8. I' ∪ J = {d, e, l, o, p, i, n, y}

9. (E ∩ I) ∩ (I ∪ J) = { }

10. (J ∪ I)' = {d, e, l}

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Answer:

x = -1, y = 1

Step-by-step explanation:

Solve the following system:

{y = 3 x + 4 | (equation 1)

y = x + 2 | (equation 2)

Express the system in standard form:

{-(3 x) + y = 4 | (equation 1)

-x + y = 2 | (equation 2)

Subtract 1/3 × (equation 1) from equation 2:

{-(3 x) + y = 4 | (equation 1)

0 x + (2 y)/3 = 2/3 | (equation 2)

Multiply equation 2 by 3/2:

{-(3 x) + y = 4 | (equation 1)

0 x + y = 1 | (equation 2)

Subtract equation 2 from equation 1:

{-(3 x) + 0 y = 3 | (equation 1)

0 x + y = 1 | (equation 2)

Divide equation 1 by -3:

{x + 0 y = -1 | (equation 1)

0 x + y = 1 | (equation 2)

Collect results:

Answer: {x = -1, y = 1

Answer:

1.33

Step-by-step explanation:

14÷10 1/2= 1.33

Answer:

(8,-14)

Step-by-step explanation:

mid piont is (4,-5) So let us consider that S(x,y)

Now,

from mid point formula,

[tex]4 = \frac{x + 0}{2} \\ x = 8[/tex]

[tex] - 5 = \frac{y + 4}{2} \\ - 10 = y + 4 \\ y = - 10 - 4 \\ y = - 14[/tex]

The expression is completely simplified to give 13√7

Surds are defined as square root values that cannot be further decreases to integers or whole numbers.

Another name for surds are irrational numbers.

Given the surd forms;

5√28 + √63

Now, let's find the factors of the value 28 with perfect squares.

√28 = √4 × 7

The factors of 63 with perfect squares

√63 = √9 × 7

Now, let's substitute the values

5√4 × 7 + √9 × 7

Find the perfect squares

5 × 2√7 + 3√7

Multiply through

10√7 + 3√7

Since the values have common roots, add the coefficient and keep the root the same.

We have;

13√7

Thus, the expression is completely simplified to give 13√7

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Area of the floor of the bandstand in regular octagon is  1931.2 ft²

dimensions of a square bandstand with the same area as the octagon is 43.94 ft

square bandstand has largest perimeter.

floor has the shape of a regular octagon

Area of a regular octagon = 2a²(1+[tex]\sqrt{2}[/tex])

a = length of the side of the octagon

here a = 20 ft

Area = 2a²(1+[tex]\sqrt{2}[/tex]) = 2(20)(20)(1+[tex]\sqrt{2}[/tex])

                           = 800(1+1.414)

                           = 800(2.414)

                           = 1931.2 ft²

square bandstand with the same area as the octagon

Area of square = b²

b = length of the side of the square

1931.2 = b²

b = 43.94 ft

Perimeter of regular octagon = 8a

                                                = 8(20)

                                                = 160ft

Perimeter of Square = 4b

                                  = 4(43.94)

                                  = 175.78ft

area of the floor of the bandstand in regular octagon is  1931.2 ft²

dimensions of a square bandstand with the same area as the octagon is 43.94 ft

square bandstand has largest perimeter.

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[tex](\stackrel{x_1}{-3}~,~\stackrel{y_1}{-3})\hspace{10em} \stackrel{slope}{m} ~=~ 3 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-3)}=\stackrel{m}{ 3}(x-\stackrel{x_1}{(-3)}) \implies y +3= 3 (x +3) \\\\\\ y+3=3x+9\implies {\LARGE \begin{array}{llll} y=3x+6 \end{array}}[/tex]