HELPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPP

Answer:

The slope is 0

Step-by-step explanation:

Slope = (y2 - y1) / (x2 - x1)

Where the values of x and y are from the known points

Here the points are (-2,2) and (-1,2)

So we have (x1,y1) = (-2,2) and (x2,y2) = (-1,2)

This means, x1 = -2 , x2 = -1 , y1 = 2 and y2 = 2

We now plug these values into the slope formula

Recall slope = (y2 - y1) / (x2 - x1)

==> plug in x1 = -2 , x2 = -2 , y1 = 2,  y2 = 2

Slope = (2 - 2) / (-1 - (-2)

==> remove parenthesis

Slope = (2-2)  / (-1 + 2)

==> simplify addition and subtraction

Slope = 0 / 1 = 0

Answer:

\((\frac{1}{2}+\frac{\sqrt{3}}{2}i)^5=\frac{1}{2}-\frac{\sqrt{3}}{2}i\)

Step-by-step explanation:

Convert 1/2 + i√3/2 to rectangular form

\(\displaystyle z=a+bi=\frac{1}{2}+\frac{\sqrt{3}}{2}i\\\\r=\sqrt{a^2+b^2}=\sqrt{\biggr(\frac{1}{2}\biggr)^2+\biggr(\frac{\sqrt{3}}{2}\biggr)^2}=\sqrt{\frac{1}{4}+\frac{3}{4}}=\sqrt{1}=1\\\\\theta=\tan^{-1}\biggr(\frac{b}{a}\biggr)=\tan^{-1}\biggr(\frac{\frac{\sqrt{3}}{2}}{\frac{1}{2}}\biggr)=\tan^{-1}(\sqrt{3})=\frac{\pi}{3}\\\\z=\cos\frac{\pi}{3}+i\sin\frac{\pi}{3}\)

Use DeMoivre's Theorem

\(\displaystyle z^n=r^n(\cos(n\theta)+i\sin(n\theta))\\\\z^5=1^5\biggr(\cos\biggr(\frac{5\pi}{3}\biggr)+i\sin\biggr(\frac{5\pi}{3}\biggr)\biggr)\\\\z^5=\frac{1}{2}-\frac{\sqrt{3}}{2}i\)

Answer: 172 ounces

Step-by-step explanation:

We are given 10 pounds and 12 ounces to convert to ounces.

There are 16 ounces in 1 pound.

We can create a proportion to find out how much ounces 10 pounds is.

10 pounds / x ounces = 1 pound / 16 ounces

We need to solve for x by isolating the variable x.

10/x = 1/16

10 = x/16

10 * 16 = x

160 ounces = x

so 10 pounds is equivalent to 160 ounces. But we are not done yet.

We were asked to convert 10 pounds and 12 ounces.

So add together the ounces to find the total ounces:

160 ounces + 12 ounces = 172 ounces.

Answer:

Step-by-step explanation:

yes cdrj

ejkfkj

ennejw

Answer:

(10-4)*4+8

=6*4+8

=24+8

=32

Answer:

32

Step-by-step explanation:

Following PEMDAS we first do the stuff in the parentheses and we get \(6x4+8\)

Then since there are no exponents, we go straight to doing the multiplication and division, which leaves us with \(24+8\).

Finally when we add the last 2 terms together we get our answer of 32.

Hope this helps!

Answer:

The walkway should be 2ft wide.

Step-by-step explanation:

Let x be the width of the walkway surrounding the pool.

The area including the pool is 560ft².

Let's solve for the value of x.

The length plus twice the width of the pool is multiplied by the width plus twice the width of the pool. This makes up the whole area.

A = lw

560 = (24 + 2x)(16 + 2x)

560 = 384 + 48x + 32x + 4x²

4x² + 80x + 384 - 560 = 0

4x² + 80x - 176 = 0

Divide the whole equation by 4

x² + 20x - 44 = 0

(x + 22)(x -2) = 0

x = -22; x = 2

Since we are dealing with dimensions, take the one with the positive value.

x = 2ft

Let's check

560ft² = (24ft + 2x)(16ft + 2x)

560ft² = (24ft + 2(2ft)) (16ft + 2(2ft))

560ft² = (24ft + 4ft)(16ft + 4ft)

560ft² = (28ft)(20ft)

560ft² = 560ft² ✔

Answer:

d + 85

Step-by-step explanation:

Look at it like this,

suppose you have 1 DVD, and the mother buys 85 DVDs then you have 1 + 85 = 86 DVDS

or when you have 2 DVDs, then you have 2 + 85 = 87 DVDs afterwards.

notice that you always take the number of DVDs you already have, and add 85 to it.

d is just a number, but you just don't know it yet. you can change d by any number, and you know d+85 is the number of DVDs afterwards

The amount of water left in the tub after 5 minutes is; 24 gallons

The given recursive formula is expressed as;

aₙ = aₙ ₋ ₁ - 12

We are told that a₀ represents the amount of water left, in gallons, in a bathtub n after the drain stopper was pulled.

Thus, when n = 1, we have;

a₁ = a₁ ₋ ₁ - 12

a₁ = a₀ - 12

a₁ = 84 - 12

a₁ = 72

Then;

a₂ = a₁ - 12

a₂ = 72 - 12

a₂ = 60

It will seem that it follows a sequence pattern of;

aₙ = 84 - 12n

Thus;

a₅ = 84 - 12(5)

a₅ = 24 gallons

Read more about Recursive Formula at; https://brainly.com/question/1275192

#SPJ1

Answer:

answer is the first one

Step-by-step explanation:

i dont know how to explain it

Answer:

3 + √5

Step-by-step explanation:

Find the square root of 14+6√5​

Change to √ ( 14 + 6√5 ) = √x + √y

1️⃣ Square.

14 + 6√5 = x + y + 2√xy

14 + 2√45 = ( x + y) + 2√xy

2️⃣ Compare.

(x + y) = 14

xy = 45

3️⃣ Solve.

(x - y)² = (x+y)² - 4xy

( x - y)² = 14² - 180

( x - y)² = 196 - 180

( x - y)² = 16

( x - y) = 4

x + y = 14

x - y = 4

2x = 18

x = 9 .

y = 5 .

14 + 6√5 = √9 + √5 = 3 + √5 .

Answer: 3 + √5 .

Done ✔

1) Number of participants whose headache remained is: 62

2) The probability of randomly selecting an individual whose headache remained is: 0.4133

3) The probability of randomly selecting an individual whose headache remained and took a placebo is: 0.2933

From the table, we have the parameters as:

Number of participants that took medicine and headache went away = 120

Number of participants that took placebo and headache went away = 68

Number of participants that took and headache remained = 18

Number of participants that took placebo and headache remained = 44

1) Number of participants whose headache remained = 18 + 44 = 62

2) The probability of randomly selecting an individual whose headache remained is:

62/(62 + 120 + 68)

= 62/150

= 0.4133

3) The probability of randomly selecting an individual whose headache remained and took a placebo is:

44/150 = 0.2933

Read more about  probability of random selection at: https://brainly.com/question/251701

#SPJ1

Step-by-step explanation:

tan0=opp/adj

where opposite =3,adjacent =x,=70

tan 70=3/x

2.7474=3/x

2.7474x=3

divide both sides by 2.7474

x=3/2.7474

x=1.0919

x=1.10 to 1 d.p

Answer:

The interval of converges of a power series is the interval of input values for which the series converges.

Step-by-step explanation:

Answer:

4n

Step-by-step explanation:

It's basically like 4 times n which equals 4×n

Answer:

Step-by-step explanation:

4n

i think

Answer:

34 laps

Step-by-step explanation:

the specific answer is 33.3 but u have to round the whole number

Answer and Step-by-step explanation:

To find out how many more yards of red fabric Reuben used, we need to subtract the amount of yellow fabric from the amount of red fabric. Since the two fractions have different denominators, we need to find a common denominator before subtracting them. The least common multiple of 8 and 4 is 8, so we can rewrite both fractions with a denominator of 8:

7/8 - 1/4 = 7/8 - (1/4) * (2/2) = 7/8 - 2/8 = (7 - 2)/8 = 5/8

So, Reuben used 5/8 yards more red fabric than yellow fabric.

Answer:

10^3 = 1000

Step-by-step explanation:

10 * 10 * 10 = 1000

Answer:

1000

Step-by-step explanation:

it is ten to the third power so 10*10*10  and then you get the answer of:

1000

I hope this helped!

To determine the area of the remaining piece of cardboard expressed in terms of x when a square of side length x inches is cut out from a rectangular piece of cardboard having a length of 6x+2 inches and a width of 2x-4 inches, use the following steps.

Draw and label a diagram of the problem. The rectangle should be labeled as 6x+2 inches by 2x-4 inches, and the square cut out should be labeled as x inches by x inches. This is how the diagram looks like: Determine the area of the rectangle, Arect.

The area of the rectangle is given by the product of its length and width. Thus, Arect = (6x + 2)(2x - 4) Determine the area of the square, Asq. The area of the square is given by the square of its side length. Thus, Asq = x²Step 4: Determine the area of the remaining cardboard after the square is cut out, Ar.

This is the difference between the area of the rectangle and the area of the square. Thus, Ar = Arect - Asq= (6x + 2)(2x - 4) - x²= 12x² - 20x - 16

Simplify the expression. The final answer is given in terms of x. Thus, Ar = 12x² - 20x - 16.The area of the remaining piece of cardboard is expressed in terms of x as 12x² - 20x - 16.

For more such questions on square

https://brainly.com/question/27307830

#SPJ8

The actual distance represented by 23.7 cm on the map is 355.5 km.

To find the ratio of the amount of money Mabaso has to the amount of money Thabo has and the amount of money Ally has, we can divide each amount by the smallest amount (which is R35) to simplify the ratio.

Mabaso has R140, Thabo has R70, and Ally has R35.

The ratio of Mabaso's money to Thabo's money is:

R140 ÷ R35 = 4

The ratio of Mabaso's money to Ally's money is:

R140 ÷ R35 = 4

Therefore, the ratio of the amount of money Mabaso has to the amount of money Thabo has and to the amount of money Ally has is 4:1:1.

To calculate the percentage discount of a steel table, we need to find the difference between the original price and the discounted price, and then divide it by the original price. Finally, we multiply the result by 100 to get the percentage.

Original price: R750

Discounted price: R600

Discount: R750 - R600 = R150

Percentage discount: (R150 ÷ R750) × 100 = 20%

So, the table has a 20% discount on Black Friday.

To convert 125 grams to kilograms, we divide the amount in grams by 1,000 (since there are 1,000 grams in a kilogram).

125 g ÷ 1,000 = 0.125 kg

Therefore, 125 grams is equal to 0.125 kilograms.

If a green grocer packs 12 apples in a plastic bag and has 285 apples, we divide the total number of apples by the number of apples per bag to determine the number of bags needed.

Number of bags needed: 285 apples ÷ 12 apples/bag = 23.75 bags

Since we can't have a fraction of a bag, we round up to the nearest whole number. Therefore, the green grocer would need 24 bags.

If the scale of a map is 1,500,000 and the measurement on the map is 23.7 cm, we can use the scale to determine the actual distance.

1 cm on the map represents 1,500,000 cm in reality.

23.7 cm on the map represents x cm in reality.

x = 23.7 cm × 1,500,000 cm = 35,550,000 cm

To convert cm to km, we divide by 100,000 (since there are 100,000 cm in a kilometer).

35,550,000 cm ÷ 100,000 = 355.5 km

For more such questions on distance

https://brainly.com/question/30395212

#SPJ8

Answer: No its not a function.

Step-by-step explanation: Its not a function because the y coordinate has the same x coordinates. This fails the vertical line test.

Given the data attached; the corresponding scatter plot is:

A scatter plot matrix shows all pairwise scatter plots for many variables. If the variables tend to increase and decrease together, the association is positive.

Hence, the statement that best describes the data in the scatter plot is:

ANSWER

A. The data appears linear with positive association.

Answer:

C

Step-by-step explanation:

\(\left(\frac{f}{g} \right)(x)=\frac{f(x)}{g(x)} \\ \\ \frac{f(x)}{g(x)}=\frac{\sqrt[3]{2x}}{2x+1}\)

The denominator cannot equal 0, so:

\(2x+1 \neq 0 \implies x \neq -\frac{1}{2}\)

The round trip distance in miles from city 1 to city 3 is given as follows:

30 miles.

The matrix corresponding to the distances between each of the cities is given by the image presented at the end of the answer.

Looking at row 1, column 3, we have that the distance from city 1 to city 3 is of 15 miles.

For the round trip distance, we have to go back from city 3 to city 1, more 15 miles, hence the distance is given as follows:

2 x 15 = 30 miles.

More can be learned about matrices at https://brainly.com/question/2456804

#SPJ1

The relation that can not be supported by the evidence in the image is option B

Corresponding angles are those that are located on the same side of the transversal and in identical relative positions to the parallel lines. Angles that correspond to one another have the same measure.

Alternate interior angles are those that are located on the transverse and within the area between the parallel lines, respectively. Congruent alternate interior angles exist.

Alternate external angles are those that are outside of the space between the parallel lines and on the opposing sides of the transversal. Congruent external angles exist between the two.

Learn more about transversal:https://brainly.com/question/17987539

#SPJ1

The manufacturer can produce 12 Basic sets,  21 Homeowner sets and 4 Pro sets each day.

What is Substitution method ?

In the substitution approach, we will first examine the two equations to determine which variable will be the simplest to solve for, allowing us to write one of the equations as or. Then, we will substitute the or the in the other equation as necessary. The outcome will be a single-unknown equation that we can solve.

Let the manufacturer can produce 'x'  Basic sets,  'y' Homeowner sets and 'z' Pro sets each day.

So, The equations can be written as :

1.6x + 1.8y + 2.5z = 67

0.7x + 1.5y + 1.6z = 46.3

1x + 0.5y + 1.2z = 27.3

Now, [0.7x + 1.5y + 1.6z = 46.3] × 1

        0.7x + 1.5y + 1.6z = 46.3.  ....... equation 1

and,    [1x + 0.5y + 1.2z = 27.3] × 3

          3x + 1.5y+ 3.6z = 81.9. ....... equation 2

equation 2 - equation 1,

We get, 2.3x + 2z = 35.6

             x = (35.6 - 2z)/ 2.3 .........equation 3

Similarly,

              1.6x + 1.8y + 2.5z = 67

              1.6x + 1.8y + 2.5z = 67 .........equation 4

and,      [1x + 0.5y + 1.2z = 27.3] × 1.6

              1.6x + 0.8y + 1.92z = 43.68 ........equation 5

Now, equation 4 - equation 5

We get, y + 0.58z = 23.32

             y = 23.32 - 0.58z  ........equation 6

We know,    

         1x + 0.5y + 1.2z = 27.3

substituting the value of x and y in the above equation

We get, [(35.6 - 2z)/ 2.3] + 0.5 ×[23.32 - 0.58z]  +  1.2z = 27.3

             (35.6/2.3) - (2z/2.3) + 11.66 - 0.29z + 1.2z = 27.3

            1.2z - 0.29z - (2z/2.3) = 27.3 -  (35.6/2.3) - 11.66

 after taking LCM,

z [12× 230 - 29× 23 - 20× 100]/2300 = [273 ×230 - 356× 100 - 1166× 23]/2300

z [ 2760-667-2000]= 62790-35600-26818

z = 372/93

 z= 4

Substituting z = 4 in equation 3 and 6.

We get, x = 12 and y = 21.

Learn more about Substitution method from the link below,

https://brainly.com/question/22340165

#SPJ1

The height of the monument is 30 meters.

We have,

Let's assume the height of the monument is "h" meters.

From the top of the building, the angle of elevation to the top of the monument is equal to the angle of depression to the foot of the monument. This forms a right triangle with the building, the monument, and the ground.

In this triangle, the opposite side of the angle of elevation is the height of the building, which is given as 30 meters.

The opposite side of the angle of depression is the height of the monument, which is "h" meters.

Since the angles of elevation and depression are equal, the triangle is an isosceles triangle.

Therefore, the opposite sides are equal in length.

By setting up the equation:

h = 30

Thus,

The height of the monument is 30 meters.

Learn more about triangles here:

https://brainly.com/question/25950519

#SPJ1

Answer:

Step-by-step explanation:

563 people / 15 classes= 37 8/15. They should offer 38 classes.

2146 questions in 45 weeks.

2146/45= 47 31/45. round to 48 questions a week.

I would choose the first one. Even though the 2000 is an underestimate, the 50 weeks is overestimate , when divided it comes out to 50 questions a week which is closer to the 48 it actually is. I'd rather write too many questions then not enough.

The first step is to combine the terms by multiplication so that it becomes one term. We have

√(3/x) * √(x^2/12)

= √3x^2/12x

= √(x)/2

Option B is correct