The perimeter of a parallelogram is 180 cm. One side exceeds the other by 10 cm.
What are the lengths of adjacent sides of the parallelogram?

Answer:

b) x = 4

Explanation:

[tex]2x^2 - x + 10 = 38[/tex]

collect variables

[tex]2x^2 - x + 10 - 38 = 0[/tex]

simplify

[tex]2x^2 - x - 28 = 0[/tex]

breakdown

[tex]2x^2 -8x + 7x - 28 = 0[/tex]

factor out

[tex]2x(x - 4) + 7(x - 4) = 0[/tex]

collect into groups

[tex](2x + 7)(x - 4) = 0[/tex]

set to zero

[tex]2x + 7 = 0, x - 4 = 0[/tex]

relocate variable

[tex]2x = -7, x = 4[/tex]

final solutions

[tex]x = -3.5, x = 4[/tex]

The answer is b.

To find the value of x, we need to convert this into the form of a quadratic equation.

Subtract 38 from each side.

Solve by splitting the middle term.

The expression which is not equivalent to (8 + (n - 4)) is (12+n) and this can be determined by using the arithmetic operations.

Given :

Expression - 8 + (n - 4)

To simplify the given expression following steps can be used:

Step 1 - Rewrite the given expression.

= (n - 4) + 8

Step 2 - Now, remove the parenthesis in the given expression.

= n - 4 + 8

Step 3 - Now, write 8 as the addition of 4 and 4.

= n - 4 + 4 + 4

Step 4 - Subtract 4 by 4.

= n + 4

Therefore, the correct answer is (12+n).

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Answer:

1. Cube

2. Square-based pyramid

Step-by-step explanation:

Answer:

Below.

Step-by-step explanation:

a) Cube

b Pyramid

"The function has one real zero and two nonreal zeros. The graph of the function intersects the x-axis at exactly one location."

Polynomial functions are equations such as quadratic and cubic equations that take only the non-negative integer power of a variable or a positive integer exponent. For example, 2x + 5 is a polynomial with an exponent equal to 1.

A polynomial function is an expression that is a combination of variables of different degrees, non-zero coefficients, positive exponents (of variables), and constants. For example, f (b) = 4b2 – 6 is a polynomial of'b'and has a degree of 2.

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See below for the interpretation of the graph

From the graph, the initial values of x and y are 0

As x increases, y decreases.

This means that the first statement is

Slope is calculated as:

[tex]m = \frac{y_2 - y_1}{x_2 -x_1}[/tex]

Using the graph values at the interval x =0 to x = 3, we have:

[tex]m = \frac{-3 - 0}{3 - 0}[/tex]

m = -1

This means that the second statement is

From the graph, y = -3, when x = 3

As x increases at this point, y increases.

This means that the third statement is

Using the graph values at the interval x = 3 to x = 5, we have:

[tex]m = \frac{3 + 3}{5 - 3}[/tex]

m = 3

This means that the fourth statement is

All y values at x = 0 to x = 4 are less than 0, while all y values at x = 4 to x = 8 are greater than 0

So, the last two statements are

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20 terms on the right side of the given equation [tex]20=20+18+16+...+x[/tex].

The first n terms of the arithmetic sequence are added together to form the sum of the first n terms of AP.

Therefore, we can only evaluate the sum of n terms in a sequence if we are aware of the type of sequence it is. Usually, when calculating the sum of an n-number of terms, we take into account arithmetic progression. The common distinction between each following term and each preceding term remains unchanged throughout this progression. Natural numbers are an illustration of Arithmetic Progression, where the common difference is 1. We must therefore be familiar with the formula in order to calculate the sum of natural numbers.

We can use formula for sum of n terms-

[tex]S = \frac{n}{2}(2a + (n-1)d)[/tex]

where, S- sum of n terms

n- number of terms

a- first term

d- difference between two consecutive terms

Here, S= 20 , a = 20, d= -2

we have to find n,

[tex]S = 20 = \frac{n}{2}(2(20) + (n-1)(-2)) \\20 = \frac{n}{2}(40-(2n-2))\\40 = n(40-2n+2)\\40 = 42n-2n^2\\2n^2 -42n +40 = 0[/tex]

solving this quadratic equation-

[tex]2n^2 -42n +40 = 0\\2n^2 -40n-2n+40=0\\2n(n-20)-2(n-20) = 0\\(2n-2)(n-20)=0[/tex]

when,

[tex]2n-2 = 0\\n=1[/tex]

When,

[tex]n-20=0\\ n=20[/tex]

as we can see that there are more than 1 terms present in the series so answer will be 20 terms.

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Completing the squares, we have that:

The equation of a quadratic function, of vertex (h,k), is given by:

y = a(x - h)² + k

In which a is the leading coefficient.

For the parabola of standard form y = x² - 6x + 17, we have that it can be written as follows, completing the squares:

y = x² - 6x + 17 = (x - 3)² + 8, hence the extreme value is (3,8).

For the parabola of standard form y = x² + 8x + 21, we have that it can be written as follows, completing the squares:

y = x² + 8x + 21 = (x + 4)² + 5, hence the extreme value is (-4,5).

For the parabola of standard form y = x² - 16x + 60, we have that it can be written as follows, completing the squares:

y = x² - 16x + 60 = (x - 8)² - 4, hence the extreme value is (8,-4).

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The expression which shows the earning of Mrs. Fresneda is 4x and the money that she will earn by selling 26 bars of soap is $144.

Given that price of soap is $4.00 per bar.

We have to find the expression which shows the earning of Mrs. Fresneda after selling soap bars and the money that she will earn by selling 26 bars of soap.

let the number of soap bars be x.

We know that the revenue is the product of price and quantity.

Money that Mrs.Fresneda earns is 4*x

=4x

Expression is 4x which shows that money that Mrs. Freneda will earn by selling soap bars.

We have to just put x=26 in the expression to calculate the money after selling 26 bars of soap.

Money=4*26

=$144

Hence the expression is 4x and the money that Mrs.Freneda will earnby selling 26 bars of soap is $144.

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The ramp with the following dimension won't obey the ADA guideline because the angle is more than 4.8 degrees.

The angle of elevation of the ramp can be found using trigonometric ratios.

Therefore,  the angle of elevation must be equal to 4.8 degrees to obey the ADA guidelines .

Hence,

tan ∅ = opposite / adjacent

opposite side = 3.5 ft

adjacent side = 40 ft

Therefore,

tan ∅ = 3.5 / 40

∅ = tan ⁻¹ 0.0875

∅ = 5.00064459756

∅ = 5 degrees

Therefore, the ramp with the following dimension won't obey the ADA guideline because the angle is more than 4.8 degrees.

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The effect that  'h' have on the graph of a parabola is Horizontal shift or translation .

A translation is the movement of  a shape up, down , this can also be movement from side to side.

Even though there is movement,   its appearance remains the same in any other way, hence, h values cause left or right movement with respect to the graph.

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Answer: 127

Step-by-step explanation:

angle b is 127 as well because they're vertical angles and vertical angles are equal to each other.

total expenses= 1/4 + 1/8

the denominators should be equal to add the values.

1/4×2(divide both the numerator and denominator by two)

=2/8

=2/8+1/8

3/8//

3/8(fraction of the salary he spent)

3/8 of the salary

3/8×50,000

R.s 6250

balance = 50,000-6,250

= R.s 43,750//

after 6.2 hours the dose will decay to 70% in your bloodstream.

We know that the half-life is 12 hours. Then the exponential relation for an initial dosage of A is:

[tex]D(t) = A*e^{-t*ln(2)/12h}[/tex]

If the dosage needs to decay to a 70% of the initial dosage, then we must have:

[tex]e^{-t*ln(2)/12h} = 0.7[/tex]

Now we need to solve that for t:

If we apply the natural logarithm in both sides, we get:

[tex]ln(e^{-t*ln(2)/12h}) = ln(0.7)\\\\-t*ln(2)/12h = ln(0.7)\\\\t = -ln(0.7)*12h/ln(2) = 6.2h[/tex]

So after 6.2 hours the dose will decay to 70% in your bloodstream.

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Answer:

-36 and 36

Step-by-step explanation:

moving the 9x to the left it changes to -9x and that plus -27x is -36x

-27-9 = -36

moving -27x to the right it changes to 27x so that plus 9x is 36x

27+9 = 36

Answer:

A. -36

F. 36

Step-by-step explanation:

Step-by-step explanation:

volume = length • width • height

by making width subject

V=LWH

W=V/LH

W= 54/8×3

W=54/24

W=9/4

W=2.25

The equation of the line containing the points (3,1) (9,3) and (27,9) is y = 1 / 3x

The equation of a line can be found as follows:

y = mx + b

where

Therefore,

using  (3,1) (9,3)

m =  3 - 1 / 9 - 3 = 2 / 6 = 1 / 3

using (3, 1)

1 = 1 / 3(3) + b

1 = 1 + b

b = 0

Therefore,

y = 1 / 3x

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Answer:

  (a)  x = -7, 1

Step-by-step explanation:

In most cases, it is useful to follow the directions. This can be solved easily by completing the square.

The square is completed by adding the square of the x-term coefficient to both sides.

  x² +6x +9 = 7 +9 . . . . . add 9

  (x +3)² = 16 . . . . . . . . simplify . . . . write the left side as a square

The square is now complete. We finish the solution by taking the square root.

  x +3 = ±√16 = ±4 . . . . take the square root

  x = -3 ±4 . . . . . . . . . subtract 3

  x = -7, 1

The mean of the sample is x-bar is determined to be 59.2 and population standard deviation, σ, is known to be 3.8. The 90% confidence interval about μ if the sample size, n, is 45 be  58.27< μ<60.13

A simple random sample of size n is drawn from a population whose population standard deviation, σ, is known to be 3.8. The sample mean, x-bar, is determined to be 59.2.

Hence,

n=45

σ=3.8

x-bar=59.2

The z value for the 90% confidence interval is z=1.645.

Then, μ=(x-bar)±(z×σ/[tex]\sqrt{n}[/tex])

μ=59.2±(1.645×3.8/[tex]\sqrt{45}[/tex])

μ=59.2±0.9318

59.2-0.9318<μ<59.2+0.9318

58.27< μ<60.13

Therefore, The 90% confidence interval about μ if the sample size, n, is 45 be  58.27< μ<60.13

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The equation of that is parallel to the graph is y = 1 / 2 x + 3 and the equation perpendicular to the graph is y = -2x + 1

Equation that are parallel have the same slope.

Equation that are perpendicular gives negative 1 when multiplied .

Therefore, using slope intercept equation,

y = mx + b

where

Hence, the equation of the graph can be calculated as follows:

(0, 6)(2, 7)

m = 7 - 6  / 2 - 0 = 1 / 2

Therefore,

y = 1 / 2 x + 6

Therefore, the equation that are parallel to the graph are as follows:

The equation that are perpendicular to the graph is as follows;

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The acute angles of a right triangle are complementary, so [tex]\boxed{m\angle F=34^{\circ}}[/tex].

Using right-angle trigonometry, we know that

[tex]\cos 56^{\circ}=\frac{26}{DF}\\\\DF=\frac{26}{\cos 56^{\circ}}\\\\\boxed{DF \approx 46.5}[/tex]

[tex]\tan 56^{\circ}=\frac{FE}{26}\\\\FE=26 \tan 56^{\circ}\\\\\boxed{FE \approx 38.5}[/tex]

If the sales had dropped 23% then music store had sold 551 units in the second quarter.

Given that a music store had sold 715 units in first quarter and sales had dropped by 23%.

We are required to determine the sales in the second quarter.

Percentage is the number or ratio expressed in terms of 100. It is expressed as %.

Sales in first quarter=715 units

Decrease in sales=23%

In units ,decrease=715*23%

=715*23/100

=164.45

Sales of second  quarter=715-164.45

=550.55

After rounding we will get 551.

Hence if the music store sold 715 units in first quarter then the units sold by music store in second quarter 551 units.

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Answer:

x = 21.013155617496

Step-by-step explanation:

we have a right triangle then ,

[tex]\cos \left( 36\right) =\frac{17}{x}[/tex]

Then

[tex]x=\frac{17}{\cos \left( 36\right) } = 21.013155617496[/tex]

Then

x ≈ 21

Step-by-step explanation:

imagine this right-angled triangle is the sine and cosine scenario in a circle. just turn it in your mind or on the paper until it looks like this.

the point with the 36° angle is the center of this circle.

x is the radius of the circle, that is under 36° connecting the center of the circle with the arc of the circle.

17 is the cosine of the angle multiplied by the radius (as the standard cosine function is normed for the standard circle with radius 1).

and the other leg is the sine of the angle multiplied by the radius (this is FYI, we don't need that for the solution here).

so,

17 = cos(36) × x

x = 17/cos(36) = 21.01315562...

we conclude that the sequence has 8 terms.

Here we have the geometric sequence:

2/81, 4/27, 8/9, ..., 6912

Notice that each term is equal to 6 times the previous term, such that:

2/81*6 = 4/27

4/27*6 = 8/9

Then the n-th term is equal to:

[tex]a_n = a_1*r^{n-1}[/tex]

Where in this case:

[tex]a_1 = 2/81\\\\r = 6[/tex]

Now we need to find the value of n such that:

[tex](2/81)*6^{n-1} = 6912\\\\6^n = 6*6812*(81/2) = 1,679,616[/tex]

If we apply the natural logarithm to both sides, then:

[tex]n*ln(6) = ln(1,679,616)\\n = ln(1,679,616)/ln(6) = 8[/tex]

Then we conclude that the sequence has 8 terms.

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Answer:

Hello,

Step-by-step explanation:

All is in the following picture:

Answer:

8(5) + 8(2)

Step-by-step explanation:

8 (5 + 2) is 8 (7) or 56

If I distribute the 8 through the problem, I will get the same answer

8(5) + 8(2)

40 + 16

56

The speed is:

S = 742.5ft

The distance that the parachutist falls in 5 seconds is:

D = 742.5ft

We know that the speed in free fall is:

S = 45 m/s.

We know that:

1 m = 3.3ft

Then we can rewrite the speed as:

S = 45 m/s = 45 *(3.28ft)/s = 148.5 ft/s

Then, the distance that the parachutist falls during 5 seconds is:

D = S*5s = (148.5 ft/s)*5s = 742.5ft

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Answer:

1. pi.      2.49-12.25pi

Step-by-step explanation: