Solve: 8p = 24
A p = 192
B p = 16
p=3
D p = 32

Answer:

\(y-4p\)

Step-by-step explanation:

Add/subtract like terms.

\(5y+2p-4y-6p\\5y-4y+2p-6p\\y-4p\)

Using the radius of the Ferris wheel and the angle between the two positions, the time spent on the ride when they're 28 meters above the ground is 12 minutes

The radius of the Ferris wheel is 30 / 2 = 15 meters.

The highest point on the Ferris wheel is 15 + 4 = 19 meters above the ground.

The time spent higher than 28 meters is the time spent between the 12 o'clock and 8 o'clock positions.

The angle between these two positions is 180 degrees.

The time spent at each position is 10 minutes / 360 degrees * 180 degrees = 6 minutes.

Therefore, the total time spent higher than 28 meters is 6 minutes * 2 = 12 minutes.

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Answer:

Derivative of sinx is cosx ...........

Answer:undefined

Step-by-step explanation:-5 is not in the ranges of 0 to 3, greater than three and it is not equal to three so undefined.

Answer:

\(\displaystyle\)\(\displaystyle f'(1)=-\frac{9}{e^3}\)

Step-by-step explanation:

Use Quotient Rule to find f'(x)

\(\displaystyle f(x)=\frac{3x^2+2}{e^{3x}}\\\\f'(x)=\frac{e^{3x}(6x)-(3x^2+2)(3e^{3x})}{(e^{3x})^2}\\\\f'(x)=\frac{6xe^{3x}-(9x^2+6)(e^{3x})}{e^{6x}}\\\\f'(x)=\frac{6x-(9x^2+6)}{e^{3x}}\\\\f'(x)=\frac{-9x^2+6x-6}{e^{3x}}\)

Find f'(1) using f'(x)

\(\displaystyle f'(1)=\frac{-9(1)^2+6(1)-6}{e^{3(1)}}\\\\f'(1)=\frac{-9+6-6}{e^3}\\\\f'(1)=\frac{-9}{e^3}\)

Answer:

\(f'(1)=-\dfrac{9}{e^{3}}\)

Step-by-step explanation:

Given rational function:

\(f(x)=\dfrac{3x^2+2}{e^{3x}}\)

To find the value of f'(1), we first need to differentiate the rational function to find f'(x). To do this, we can use the quotient rule.

\(\boxed{\begin{minipage}{5.5 cm}\underline{Quotient Rule for Differentiation}\\\\If $f(x)=\dfrac{g(x)}{h(x)}$ then:\\\\\\$f'(x)=\dfrac{h(x) g'(x)-g(x)h'(x)}{(h(x))^2}$\\\end{minipage}}\)

\(\textsf{Let}\;g(x)=3x^2+2 \implies g'(x)=6x\)

\(\textsf{Let}\;h(x)=e^{3x} \implies h'(x)=3e^{3x}\)

Therefore:

\(f'(x)=\dfrac{e^{3x} \cdot 6x -(3x^2+2) \cdot 3e^{3x}}{\left(e^{3x}\right)^2}\)

\(f'(x)=\dfrac{6x -(3x^2+2) \cdot 3}{e^{3x}}\)

\(f'(x)=\dfrac{6x -9x^2-6}{e^{3x}}\)

To find f'(1), substitute x = 1 into f'(x):

\(f'(1)=\dfrac{6(1) -9(1)^2-6}{e^{3(1)}}\)

\(f'(1)=\dfrac{6 -9-6}{e^{3}}\)

\(f'(1)=-\dfrac{9}{e^{3}}\)

The characteristic polynomial  x³ - 7x² + 16x - 12  The characteristic polynomial of a square matrix in linear algebra is a polynomial that is invariant under matrix similarity and has the eigenvalues as roots.

Its coefficients include the determinant and the trace of the matrix.

Characteristic polynomial of a 3×3 matrix A is given by ; x³ - trace(A)x² + (A​​​​​​11 + A​​​​​​22 + A​​​​​​33 )x - determinant(A)

Where A​​​​​​ii is the determinant of the matrix obtained by deleting i​​​​​​ th row and i th column.

Here trace(A) = sum of the diagonals = 12 - 7 + 2 = 7

A​​​​​​11 = -7 × 2 = -14

A​​​​​​22 = 2 × 12 = 24

A​​​​​​33 = ( 12×-7) - (-10×9) = 6

Determinant(A) = 12(-7×2 - 0) + 10(2×9 - 0) = 12

Substituting these values in above equation , we obtain;

x³ - 7x² + (-14 + 24 + 6)x - 12 = x³ - 7x² + 16x - 12.

Hence x³ - 7x² + 16x - 12 is the characteristic polynomial of A.

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The change that Grant received to the nearest cent after giving the delivery driver with a $100 bill is $ 32.6.

This is a question of percentages.

Given that:-

Price of bouquet of flowers = $ 55

Sales tax % = 6.5 %

Tip % = 15 %

Delivery fee= $10

We have to find the change that Grant received to the nearest cent after giving the delivery driver with a $100 bill.

Sales tax = (6.5/100)*55 = $3.575

$55 + $3.575 = $58.575

Tip = (15/100)*58.575 = $ 8.78625

Total money paid by Grant = 55 + 3.575 + 8.78625 = $ 67.36125 ≈ $ 67.4

Hence,

Change received by Grant = 100 - 67.4 = $ 32.6

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Answer:

∠ x = 58°

Step-by-step explanation:

the exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.

∠  BAD is an exterior angle of the triangle , then

x + 56° = 114° ( subtract 56° from both sides )

x = 58°

Answer:

\(\begin{cases}n+d = 27\\0.05n+0.10d = 2.75\\\end{cases}\)

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

Explanation:

n = number of nickels

d = number of dimes

The n and d are placeholders for positive whole numbers.

Since we have 27 coins, we know that n+d = 27. The two subcounts must add to the grand total of 27. That explains how the first equation is set up.

The second equation is set up by looking at the dollar amount each group of coin brings in.

0.05n = amount of money in dollars the nickels bring in

0.10d =  amount of money in dollars the dimes bring in

0.05n+0.10d = total amount of money in dollars = 2.75

The single curly brace to the left of the equations tells the reader we're dealing with a system of equations. The equations are tied together.

Answer:

3 days

Step-by-step explanation:

took the test

Answer:

6

Step-by-step explanation:

Answer: 6
The factors of 12 are: 1, 2, 3, 4, 6, 12

The factors of 18 are: 1, 2, 3, 6, 9, 18

The factors of 30 are: 1, 2, 3, 5, 6, 10, 15, 30

Then the greatest common factor is 6.

Answer:

333234

Step-by-step explanation:

333234$ for the next 4 years and the ecvation is 69$+-2$

The volume of the box will be → 980 square inches.

The volume of cuboid is found using the formula:

Volume = Length × Width × Height

Given is the volume of a box that is 14 inches long, 7 inches wide, and 10 inches high.

The volume of the box will be→

V= L x B x H

V= 14 x 7 x 10

v = 140 x 7

V= 980 square inches

Therefore, the volume of the box will be → 980 square inches

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Answer:

62.50

Step-by-step explanation:

Answer: (6,11π/6).

Step-by-step explanation:We need to find the radius r and the angle θ. Remember that r2=x2+y2, so

because of the signs of x and y, our angle is in quadrant IV. Therefore, we find that θ=11π/6.

So the final answer is (6,11π6).

Answer:

5 %  

Step-by-step explanation:

3020 *  x    = 151          x is the percentage in decimal form

x = 151 / 3020 = .05    which is 5 %

Answer: The man will make deposits for 66 - 45 = 21 years, or 21 x 4 = 84 quarters.

The quarterly interest rate is 4% / 4 = 1%.

Let's use the formula for the future value of an annuity:

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

where FV is the future value of the annuity, PMT is the periodic payment, r is the interest rate per period, and n is the number of periods.

In this case, PMT = $2500, r = 1%, and n = 84. Substituting these values into the formula, we get:

FV = $2500 x ((1 + 0.01)^84 - 1) / 0.01

FV = $2500 x (5.409 - 1) / 0.01

FV = $2500 x 540.9

FV = $1,352,250

Therefore, there will be $1,352,250 in the account when the man retires at age 71.

From the solution;

x = 62.62°

y = 8.9 cm

The sine rule (also known as the law of sines) is a mathematical formula that relates the sides and angles of a triangle. Specifically, it relates the ratios of the lengths of the sides of a triangle to the sine of the opposite angles.

By the use of the sine rule;

a/Sin A = c/Sin C

Sin C = cSin A/a

C = Sin-1(cSin A/a)

C = Sin-1(7.8 * sin 66.4/9.2)

C = 50.98°

B = 180 - (50.98° + 66.4)

B = 62.62°

Then;

a/Sin A = b/Sin B

9.2/Sin66.4 = b/Sin 62.62

b = 9.2 * Sin 62.62/Sin66.4

b = 9.2 * 0.89/0.92

b = 8.9 cm

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Answer: 2^3 - 16 : 2 +  5^2 = 25/1 = 25

Step-by-step explanation:

Exponentiation: 2 ^ 3 = 8Divide: 16 / 2 = 8Subtract: the result of step No. 1 - the result of step No. 2 = 8 - 8 = 0Exponentiation: 5 ^ 2 = 25Add: the result of step No. 3 + the result of step No. 4 = 0 + 25 = 25

Answer:

2b

Step-by-step explanation:

easy

Answer:

sorry if i read tht wrong but i think its 2b

Step-by-step explanation:

Using the parallelogram law to find m, the value of m is 50°.

The parallelogram law states that the sum of the squares for a parallelogram's four sides is equal to the sum of the squares for its two diagonals.

The parallelogram must have equal opposed sides in Euclidean geometry.

If ABCD is a parallelogram, then AB = DC and AD = BC, the parallelogram law is stated as:

2(AB)² + 2 (BC)² = (AC)² + (BD)²

If the parallelogram is a rectangle, the parallelogram law is stated as:

2(AB)² + 2 (BC)² = 2(AC)²

The value of the unknown angles in the parallelogram are as follows:

CED = 180 - (60 + 33 + 37)

CED = 50°

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Answer:

50

Step-by-step explanation:

5^3÷(13-8)×2

Using the BODMAS rule

Bracket first

13-8=5

5^3=125

Followed by division

125÷5=25

Then back to the multiplication

25×2=50

Answer:

50

Step-by-step explanation:

Using order of operations:

Input Equation:

= 5^3/(13-8)*2.

= 5^3/(5)*2.

= 5^3/5*2.

= 125/5*2.

= 25*2.

= 50

Hence, 50 is the correct Answer.

[RevyBreeze]

Answer: to solve this you can make a proportion.

264 x

---- = ----

3 1

to solve, cross multiply and divde

264 times 1 is 1. 264 divided by 3 is 88. the unit rate is 88 beats in one minute

Step-by-step explanation:

Deron's heart beat rate per minute is 64 beats/min.

A unitary method is a mathematical way of obtaining the value of a single unit and then deriving any no. of given units by multiplying it with the single unit.

Given, Deron recorded his heart rate as 204 beats in 3 minutes.

∴ How many times his heart beats in one minute or the unit rate in beats per minute can be obtained if we divide the total no. of beats by total no. of minutes which is,

= (204/3) beats per minute.

= 68 beats per minute.

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Answer:

24×10-6

First you multiply 24 and 10 which the answer is 240.

= 240-6

Then subtract 6 from 240

and your is...

=234

I used BODMAS which stands for

B - Brackets first

O - Operation second

D - Division third

M - Multiplication fourth

A - Addition fifth

S - Subtraction lastly

That's why we call it BODMAS...

Answer:

12.9

Step-by-step explanation:

Since the degree of the 10 is 1, move the decimal point of 1.29 to the right once.

Hi!

Your answer should be: 12.9.

Hope this helps!

Yours truly,

Answer:

y = x + 60

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

with (x₁, y₁ ) = (20, 80) and (x₂, y₂ ) = (40, 100) ← 2 points on the line

m = \(\frac{100-80}{40-20}\) = \(\frac{20}{20}\) = 1

the line crosses the y- axis at (0, 60 ) ⇒ c = 60

y = x + 60 ← equation of line