Solve the problem below and show your work

Answer:

Step-by-step explanation:

(5x - 1) (5x - 1)

= \((5x - 1)^{2}\)

Using laws of exponents,

\((a - b)^{2} = a^{2} - 2ab + b^{2}\)

here, a = 5x, b = 1

so it becomes,

\(5x^{2}\) - 2 × 5x × 1 + \(1^{2}\)

\(25x^{2}\) - 10x + 1

Hope this helps

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The vector v+w has a magnitude of 2√2 and its direction is along the positive x-axis.

What is meant by vector?

A vector is a quantity that has both magnitude and direction. It is represented as an arrow with its length representing the magnitude and its direction representing the direction of the quantity.

What is meant by the x-axis?

The x-axis is the horizontal line on a coordinate plane that is used as a reference for plotting and describing the positions of points in two-dimensional space. It is often referred to as the "horizontal axis" or the "abscissa".

According to the given information

Here the vector v has a magnitude of 2 and a direction of 45° so the components of vector v are:

v_x = 2 cos 45° = √2

v_y = 2 sin 45° = √2

Vector w has a magnitude of 2 and a direction of 45° South of East. This means that the angle between vector w and the positive x-axis is 45°, and the angle between vector w and the negative y-axis is 45°. Therefore, the components of vector w are:

w_x = 2 cos 45° = √2

w_y = -2 sin 45° = -√2

Now we can add the components of vectors v and w to find the components of the vector v+w:

(v+w)_x = v_x + w_x = √2 + √2 = 2√2

(v+w)_y = v_y + w_y = √2 - √2 = 0

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Answer:

2

Step-by-step explanation:

The probability that the point that is selected randomly would be in the semicircular region would be = 0.28.

To calculate the probability of a selected point, the formula for probability should be chosen. That is;

Probably = possible outcome/sample space

Possible outcome is the area of the semicircle = πr²/2

where r = 5 in

Area of semicircle = 3.14×5×5/2

=78.5/2 = 39.25 in²

The sample space = area of semicircle+area of square.

But Area of the square;

= length×width

= 10×10 = 100in²

sample space = 100+39.25 =139.25

Probability = 39.25/139.25 = 0.28

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Answer:

4 - b

-1 - e

-4 - a

-5 - c

Step-by-step explanation:

The values of b = 4, e = -1, a = -4,  c = -5.

A matrix is a rectangular array or table of numbers, symbols, or expressions, arranged in rows and columns, which is used to represent a mathematical object or a property of such an object.

Here,

\(\left[\begin{array}{ccc}3&-1&3\\8&-1&-9\\4&-1&0\end{array}\right] - \left[\begin{array}{ccc}a&e&d\\f&b&h\\c&g&i\end{array}\right] = \left[\begin{array}{ccc}7&0&1\\-4&-5&1\\9&7&-4\end{array}\right]\)

\(\left[\begin{array}{ccc}3-a&-1-e&3-d\\8-f&-1-b&-9-h\\4-c&-1-g&0-i\end{array}\right] =\left[\begin{array}{ccc}7&0&1\\-4&-5&1\\9&7&-4\end{array}\right]\)

On comparing both sides, we get

3-a = 7                   ⇒ a = -4

-1-e = 0                  ⇒ e = -1

3-d = 1                   ⇒ d = 2

8-f = -4                  ⇒ f =12

-1-b = -5                ⇒ b = 4

-9 - h = 1               ⇒ h =-8

4-c = 9                  ⇒ c = -5

-1-g = 7                 ⇒ g = -8

-i = -4                    ⇒ i = 4

Thus, the values of b = 4, e = -1, a = -4,  c = -5.

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Answer:

the other side is 5 i think

The 95% confidence interval for the effectiveness of the blood-pressure drug is given as follows:

\(22.6 < \mu < 24.4\)

The mean, the standard deviation and the sample size for this problem, which are the three parameters, are given as follows:

\(\overline{x} = 23.5, \sigma = 12.2, n = 775\)

Looking at the z-table, the critical value for a 95% confidence interval is given as follows:

z = 1.96.

The lower bound of the interval is then given as follows:

\(23.5 - 1.96 \times \frac{12.2}{\sqrt{775}} = 22.6\)

The upper bound of the interval is then given as follows:

\(23.5 + 1.96 \times \frac{12.2}{\sqrt{775}} = 24.4\)

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The height is 114.83 ft and the distance of the ø if someone is observing below is 84.8.

The branch of mathematics that sets up a relationship between the sides and the angles of the right-angle triangle is termed trigonometry.

The trigonometric functions, also known as a circular, angle, or goniometric functions in mathematics, are real functions that link the angle of a right-angled triangle to the ratios of its two side lengths.

Given that at a given point of 67.7ft at the ground level of a covered court, the angle of elevation of a roof worker from the bottom is 38.6⁰ and the angle of elevation of the roof from the top is 42.4 degrees.

The base will be calculated as:-

tan(38.6) = P / B

tan(38.6) = 67.7 / B

B = 67.7 / tan(38.6)

B = 54.8 ft

The height will be calculated as:-

Cos(42.4) = B / H

H = 84.8 / Cos(42.4)

H = 114.83 ft

Therefore, If someone were to look down from above, they would be 114.83 feet from the object and 84.8 feet away.

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Answer:

I dont know the other homes but this one is $390 ( I think)

Step-by-step explanation:

4% of $375 is $15 so adding $15 on you would get $390.

I really hope this is right. And I hope this helped!

The guest will pay the amount of 15 dollars tax for the stay which is determined by the evaluation of 4% of $375.

The percentage is defined as a ratio expressed as a fraction of 100.

We have been given that the 4% tax is charged to hotel guests. A single guest's stay at the hotel costs $375 before taxes.

We have to determine the evaluation of 4% of $375.

⇒ 4% of $375

4%  is expressed as 4/100 in fractional form

⇒ (4/100)(375)

4/100 is expressed as 0.04 in decimal form

⇒ (0.04)(375)

Apply the multiplication operation, and we get

⇒ 15

Therefore, the guest will pay the amount of 15 dollars tax for the stay.

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Answer:

πr2h

3

Step-by-step explanation:

Answer: I believe it is C.

Step-by-step explanation: Because if you take 4 x 20 = 80

If  I am wrong sorry.

The work done by the force in 10 seconds is 250 Joules

This is the product of force and distance covered by a body

The formula for calculating the workdone is expressed as:

From the information given

Workdone = 25* (2*10) sin 30

Workdone = 500(0.5)

Workdone = 250 Joules

Hence the work done by the force in 10 seconds is 250 Joules

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Answer:

D:  {1/2, 4 1/2} or {0.5, 4.5}

Step-by-step explanation:

Start by simplifying this equation.  Divding both sides by 3, we get:

|2x - 5| = 4

Now divide all terms by 2 to isolate x inside the absolute value signs:

|x - 5/2| = 2

We regard 5/2 as the center; the two solutions are 2 units distant from this center on either side:

Case 1:  x = 5/2 + 2, or x = 9/2, or x = 4.5

Case 2:  x = 5/2 - 2, or x = 1/2, or x = 0.5

Check:  is 9/2 two units to the right of the 'center' 5/2?  Is 5/2 + 2 = 9/2?  YES

Is 12 two units to the left of the 'center' 5/2?  Is 5/2 - 4/2 = 1/2?  YES

The solution set is D:  {1/2, 4 1/2} or {0.5, 4.5}

Answer:

See explanation below.

Step-by-step explanation:

Given transformed function:

\(y=-2 \sin \left[2(x-45^{\circ})\right]+1\)

The parent function of the given function is:  y = sin(x)

The five key points for graphing the parent function are:

(See attachment 1)

Standard form of a sine function:

\(\text{f}(x)=\text{A} \sin\left[\text{B}(x+\text{C})\right]+\text{D}\)

where:

Therefore, for the given transformed function:

\(y=-2 \sin \left[2(x-45^{\circ})\right]+1\)

See attachment 2.

The maximum height reached by each stone is 40.5 meters.

The height of each stone above the ocean is given by the function:

h = -2t² + 2t + 40

This is a quadratic function in standard form, with a = -2, b = 2, and c = 40.

The maximum height reached by the stone occurs at the vertex of the parabolic curve described by this function.

The t-coordinate of the vertex is given as:

t = -b / 2a

Substitute the values of a and b,

t = -2 / (2×(-2)) = 0.5

So the maximum height is reached 0.5 seconds after the stone is thrown.

To find the maximum height, substitute the value of t into the function:

h = -2(0.5)² + 2(0.5) + 40 = 40.5 meters

Therefore, the maximum height reached by each stone is 40.5 meters.

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Answer: a

Step-by-step explanation:

Answer:

125 mph

Step-by-step explanation:

The river is going 25 mph every 20 minutes

Therefore we can paddle 125 miles at consistent rate.

Answer:

Shawn

Step-by-step explanation:

Shawn sells 36/4 = 9

Brett sells 56/7=8

Therefore , Shawn sells more vehicles per week

Answer: Shawn

Step-by-step explanation:

36 ÷ 4 = 9

56 ÷ 7 = 8

9 is greater than 8 and bc if we divide the numbers it equals how many vehicles per week.

Answer:

Set your calculator to Degree mode.

55^2 = 90^2 + 50^2 - 2(90)(50)cos(C)

3,025 = 10,600 - 9,000cos(C)

-7,575 = -9,000cos(C)

cos(C) = 101/120

C = cos^-1 (101/120) = 32.7°

A formula that describes the average revenue per person is:

average revenue per person = 1.4w

Average revenue per person is the ratio of the total revenue received to the number of people. It is calculated by dividing total revenue by the number of people.

We have:

Total revenue formula, M = 350w⁴

Total number of people formula, T = 250w³

Thus,

Average revenue per person = M/T

Average revenue per person = 350w⁴/250w³

Average revenue per person = 1.4w

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Answer:

no

Step-by-step explanation:

3^3=27

so 3^3+3^3+3^3=27+27+27=81

3^9=19683

Answer:

No it's not same because we cannot add degrees. 3^9 is much greater than 3^3+3^3+3^3.

27+27+27≠ 19, 683

81≠19,683

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Step-by-step explanation:

Answer:

P(A) = 0.57 (rounded to two decimal places).

Step-by-step explanation:

The probability of selecting a red marble from the hat can be found by dividing the number of red marbles by the total number of marbles:

P(red) = number of red marbles / total number of marbles

P(red) = 20/35

We can simplify this fraction by dividing both the numerator and denominator by 5:

P(red) = 4/7

So the probability of selecting a red marble from the hat is 4/7, or approximately 0.57 when rounded to two decimal places.

Therefore, P(A) = 0.57 (rounded to two decimal places).

Answer:

4+ (10/5) = 6-2 what is wrong with it is The left side

6

does not equal to the right side

4

Step-by-step explanation:

Answer:

No

Step-by-step explanation:

The ordered pair is not a solution to the equation.

Answer:

No

Step-by-step explanation:

The amount received from loans as a number in millions is 242,700 million rand.

Deducing value A requires computation of collective income sources, for which the following summation suffices:

Total Income = Tax + Loans + ASC + QP + Other income + Non-tax income = 1370 + 242.7 + 180.3 + 31.5 + A + 0 = 1825.5 + A

In this context, it follows that A amounts to (1825.5 - 1370 - 242.7 - 180.3 - 31.5) = 0 million rand.

Conversely determining missing value B necessitates subtraction of total expenditure from accumulated revenue, giving rise to the subsequent formula:

Total Income - Total Expenditure = B

(1825.5 - 112.7 - 278.4 - 262.4 - 222.6 - 211.0 - 209.2 - 208.5 - 202.2 - 0) = B

Following calculation, B equates to -77.1 million rand, indicating an overage in expenses during fiscal year 2019/20.

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The Surface area of Triangular Prism is 132 cm².

We have have the dimension of prism as

Sides = 3 cm, 4 cm, 5 cm

and, l = 10 cm

and, b= 4 cm

Now, Surface area of Triangular Prism as

= (sum of sides) l + bh

= (3 + 4 + 5)10 + 4 x 3

= 12 x 10 + 12

= 120 + 12

= 132 cm²

Thus, the Surface area of Triangular Prism is 132 cm².

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The answer is 53

It is the process of substituting values of individual respective variables and solving using elementary arithmetic operations.

Given here, the expression as 8 - (m/n) + p² & substituting  the values as m=8 , n=2 , p=7 we get

8- 8/2 + 7² = 8-4+53

                  = 53

Hence, the final answer is equal to 53

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The cost of food before the delivery fee will be $12.5.

Given that,

The total cost of lunch from a delivery truck = $13.75

i.e.

It includes the cost of the food and a delivery fee.

And,

The delivery fee = 10%

Now,

Let,

The cost of the food without the delivery fee = x

And,

The delivery fee = 10% of x = 0.1x

Now,

According to the question,

13.75 = x + 0.1x

i.e.

1.1x = 13.75

So,

x = 13.75/1.1

We get,

x = 12.5

i.e.

The cost of the food before the delivery fee is $12.5.

Hence we can say that the cost of food before the delivery fee will be $12.5.

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The area and arc length of each piece can be found using the

relationship between a circle and a sector of the circle.

Responses (b, c, and d are approximated):

a. 120°

b. 10.6 square inch

c. 28.3 in.

d. Area: 15.8 in.², Central angle: 89.1°

Given:

Diameter of the pan, d = 9-inch

Number pie pieces cut from the apple pie = 6

The pie pieces are sectors of a circular pie.

a. The central angle of one pie pieces = \(\dfrac{360^{\circ}}{6}\) = 60°

Therefore;

b. Area of circular pie = π·r²

Where;

\(r = \mathbf{\dfrac{d}{2}}\)

Therefore;

\(r = \dfrac{9}{2} = \mathbf{ 4.5}\)

\(The \ area \ covered \ by \ each \ pie \ piece = \dfrac{\pi \times 4.5^2}{6} \approx \mathbf{10.6}\)

c. The circumference of a circle = 2·π·r

The circumference of the original pie = 2 × π × 4.5 in. ≈ 28.3 in.

d. Let the arc length of the pie piece = 7 inches

\(\mathbf{Area} \ of \ the \ \mathbf{pie \ piece}= \dfrac{7}{2 \cdot \pi \cdot 4.5} \times \pi \times 4.5^2 = \dfrac{7}{2 } \times 4.5 = 15.75 \approx 15.8\)

\(The \ central \ angle \ of \ the \ pie \ piece = \dfrac{7}{2 \cdot \pi \cdot 4.5} \times 360^{\circ} \approx \underline{ 89.1^{\circ}}\)

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The amount of change that Tina got back would be = $10

The amount of hours Tina spent in canoeing = 6 hours

The amount paid per hour for canoeing = $4

Therefore the total amount spent on canoeing = 6×4 = $24

The cost of the life jacket = $6

Therefore the total amount Tina spent = total amount spent on canoeing + cost of the life jacket.

That is; 24+6 = $30

The change Tina will receive from the two twenty dollars bills = (2×20) - 30

= 40-30 = $10

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