Four-fifths of a number
decreased by eight is four.
Find the number.

Answer:

A. the angular speed is 3771.4 rad/min

b. 5921 rpms

Step-by-step explanation: I just got this same question right on a test.

Answer:

True

Step-by-step explanation:

The easiest way to understand this problem is to first breakdown the notation. In words, the problem is stating 9 is NOT an element of the set containing the elements 4, 1, 8, and 7. Since 4\(\neq\)9, 1\(\neq\)9, 8\(\neq\)9, and 7\(\neq\)9 then 9 is not an element of this set and the statement is true.

Part 1

The equation is \(y=a(x+8)(x-72)\).

Using the point \((62, -490)\) to solve for \(a\),

\(-490=a(62+8)(62-72) \implies a=\frac{7}{10}\\\\\therefore \boxed{y=\frac{7}{10}(x+8)(x-72)}\)

Part 2

When \(x=-8\), \(y=0\).

When \(x=2\), \(y=-490\).

So, the average rate of change is \(\frac{-490-0}{2-(-8)}=\boxed{-49}\)

The best description of the graph is "a quadratic function with a constant difference of 2."

A quadratic function is a function of the form f(x) = ax^2 + bx + c, where a, b, and c are constants. In a quadratic function, the graph forms a parabola.

In the given graph, if the differences between consecutive points on the graph are constant and equal to 2, it indicates a constant difference in the y-values (vertical direction) as the x-values (horizontal direction) increase. This is a characteristic of a quadratic function.

On the other hand, an exponential function with a growth factor of 2 would result in a graph that increases at an increasing rate, where the y-values grow exponentially as the x-values increase. This is not observed in the given graph.

Therefore, based on the information provided, the graph best represents a quadratic function with a constant difference of 2.

Learn more about quadratic equation here:

https://brainly.com/question/30164833

#SPJ8

The experimental probability that an arrangement will contain at least one yellow balloon is 0.767. Then the correct option is C.

Given that:

Each balloon arrangement in Ethan's class has four balloons in it. The likelihood of each balloon being red, blue, or yellow is equal. To represent this possibility, Ethan made a spinner.

ybrr, bybb, rbbb, rrry, rbbb, rryy, yybb, ryry, ryyr, rbyr, ryyr, rryy, rrrr, yrby, bbyy, byyr, byyr, byyb, rbby, ybry, rryy, rbrr, rybb, bbbr, rrbr, ybry, ryrr, rryb, rrrb, rryr

The experimental probability that an arrangement will contain at least one yellow balloon is calculated as,

P = 23 / 30

P = 0.767

Thus, the correct option is C.

More about the probability link is given below.

https://brainly.com/question/795909

#SPJ1

The possible values for angles 1, 2, and 3 given that lines a and b are parallel lines include the following:

In Mathematics and Geometry, parallel lines are two (2) lines that are always the same (equal) distance apart and never meet or intersect.

Note: Assuming angle 1 is equal to 60 degrees.

In Mathematics and Geometry, the vertical angles theorem states that two (2) opposite vertical angles that are formed whenever two (2) lines intersect each other are always congruent, which simply means being equal to each other:

m∠1 ≅ m∠3 = 60°.

Based on the linear pair postulate, the measure of angle 2 can be determined as follows;

m∠1 + m∠2 = 180°

60° + m∠2 = 180°

m∠2 = 180° - 60°

m∠2 = 120°

Read more on parallel lines here: https://brainly.com/question/12783631

#SPJ1

The statement "In both cases, subtract 6 from both sides, but reverse the inequality sign when doing that for the inequality" best describes the process used to solve the equations.

In the equation -3x + 6 = 21, to isolate the variable x, we subtract 6 from both sides of the equation, which yields -3x = 15. Then, we divide both sides by -3 to solve for x, resulting in x = -5. This process is applicable to equations where we aim to find the exact value of the variable.

Similarly, in the inequality -3x + 6 < 21, we want to find the range of values for x that satisfy the inequality. By subtracting 6 from both sides, we obtain -3x < 15.

However, since we performed the same operation on both sides of the inequality, the direction of the inequality sign remains the same.

Thus, the correct inequality is -3x < 15. To isolate x, we divide both sides by -3. However, since we reversed the inequality sign, we must also reverse it again, resulting in x > -5.

This process allows us to determine the range of values for x that satisfy the inequality.

Therefore, the statement accurately describes the process for solving both the equation and the inequality, highlighting the significance of reversing the inequality sign when manipulating inequalities.

for such more questions on  equations

https://brainly.com/question/17145398

#SPJ8

Answer:

50

Step-by-step explanation:

Answer:

50

Step-by-step explanation:

substitue z, then multiply by 5

Answer:

If f(-5) = 7, then the point P(-5, 7) will be on the graph of f

where -5 is the x-coordinate and 7 is the y-coordinate

Step-by-step explanation:

Answer:

The answer is 104

Step-by-step explanation:

8x14 = 104

104/8 = 13

104 is the answer :)

Answer:

$23.85

Step-by-step explanation:

Linear foot- sold by the lenght.

Therefore you dont worry about the 3.2 feet wide

So now we multiply 10.6 * 2.25

which is...

$23.85

Answer:

To solve for x using the exterior angle thm:

3x + 6x = 99

9x = 99

x = 11

m<T:

3x

3(11)

33

m<W:

6x

6(11)

66

m<TUW:

180 - 99

81

Answer:

The answer is 47°

Step-by-step explanation:

Total angles in a triangle is 180°

so 31+x+102 = 180

x= 180-133

x=47°

Answer:

D I'm not sure if it is correct but I'm sorry if wrong Good luck!

Answer:

8

Step-by-step explanation:

7 - (-1) =

7 + 1 =

8

Hope that helps!

Answer:

∡C=53°

∡F=102°

AB=11

DF=27

Step-by-step explanation:

Similar triangles have the same shape but not necessarily the same size. If two triangles are similar, their corresponding angles are equal and their corresponding sides are proportional.

Some of the properties of similar triangles:

For the question:

In ΔABC and ΔEFD

Since the respective corresponding angles are equal.

so,

∡A=∡E=25°

∡B=∡F=102°

∡C=∡D=53°

so, ΔABC  \(\sim\)  ΔEFD

Again

Since their corresponding sides are proportional.

First, we need to find the ratio of their respective side:

DE: CA=63:14=9:2 when compared to big triangle to small triangle.

CA: DE=14:63=2:9 when compared to big triangle to small triangle.

AB=2/9*EF=2/9*49.5=11

DF=9/2*CB=9/2*6=27

By answering the presented question, we may conclude that Evelyn will equation need to sell roughly 281 masks in order to cover her initial project expenditures and begin generating a profit.

A math equation is a technique that links two assertions and denotes equivalence using the equals sign (=). In algebra, an equation is a mathematical statement that proves the equality of two mathematical expressions. For example, in the equation 3x + 5 = 14, the equal sign separates the numbers 3x + 5 and 14. A mathematical formula may be used to understand the link between the two phrases written on either side of a letter. The logo and the programmed are usually interchangeable. As an example, 2x - 4 equals 2.  

Initially, we must determine the entire cost of producing and transporting one mask:

Total cost per mask = $1.25 plus $2.15 for delivery = $3.40

Profit per mask is selling price minus total cost per mask, which equals $5 - $3.40 = $1.60.

As a result, Evelyn will profit $1.60 for each mask she sells. We may use the following calculation to calculate how many masks she needs to sell to recoup her $450 initial project costs:

Total beginning project expenditures / profit per mask = number of masks to sell

Total number of masks to be sold = $450 / $1.60 per mask = 281 masks

Evelyn will need to sell roughly 281 masks in order to cover her initial project expenditures and begin generating a profit.

To know more about equation visit:

https://brainly.com/question/649785

#SPJ1

Probability helps us to know the chances of an event occurring. The probability of pulling a purple or green card is 7/50.

Probability helps us to know the chances of an event occurring.

\(\rm Probability=\dfrac{Desired\ Outcomes}{Total\ Number\ of\ outcomes\ possible}\)

The probabilities of different color cards being pulled are 1/20 for yellow, 1/10 for green, 1/15 for red, and 1/25 for purple. Therefore, the probability of pulling a purple or green card is,

Probability = 1/25 + 1/10

                  = (10 + 25) /250

                  = 35/250

                  = 7/50

Hence, the probability of pulling a purple or green card is 7/50.

Learn more about Probability:

https://brainly.com/question/795909

#SPJ1

Answer:

26 feet

Step-by-step explanation:

The perimeter of a rectangle is 2 times its length and 2 times its width, or \(2l+2w=P\). Let's plug in the given values for the width and perimeter and solve.

\(2l+2(22)=96\)

Simplify.

\(2l+44=96\)

Subtract 44 on both sides.

\(2l+44-44=96-44\)

Simplify.

\(2l=52\)

Divide by 2 on both sides.

\(\frac{2l}{2} =\frac{52}{2}\)

Simplify again to find the value of \(l\).

\(l=26\)

The length is 26 feet.

Good luck <3

ANSWER:

-9: NO

3: NO

4: NO

15: YES

STEP-BY-STEP EXPLANATION:

We have the following inequality:

We solve for x:

Which means that the solution is all numbers equal to or greater than 10.

Therefore:

Which means that -9, 3 and 4 are not solutions of the inequality.

15 if it is a solution it is of the inequality

Given statement solution is :- The present value of R13,000 per year invested for 8 years at 10% compound interest is approximately R69,776.60.

To calculate the present value of an investment with compound interest, we can use the formula for the present value of an annuity:

PV = A *\((1 - (1 + r)^(-n)) / r\)

Where:

PV = Present value

A = Annual payment or cash flow

r = Interest rate per period

n = Number of periods

In this case, the annual payment (A) is R13,000, the interest rate (r) is 10% per year, and the investment is made for 8 years (n).

Using the formula and substituting the given values, we can calculate the present value:

PV = \(13000 * (1 - (1 + 0.10)^(-8)) / 0.10\)

Calculating this expression:

PV = \(13000 * (1 - 1.10^(-8)) / 0.10\)

= 13000 * (1 - 0.46318) / 0.10

= 13000 * 0.53682 / 0.10

= 6977.66 / 0.10

= 69776.6

Therefore, the present value of R13,000 per year invested for 8 years at 10% compound interest is approximately R69,776.60.

For such more questions on present value

https://brainly.com/question/30390056

#SPJ8

The length AC in the kite is 8.7 cm.

A kite is a quadrilateral that has two pairs of consecutive equal sides and

perpendicular diagonals. Therefore, let's find the length AC in the kite.

Hence, using Pythagoras's theorem, let's find CE.

Therefore,

7² - 4² = CE²

CE = √49 - 16

CE = √33

CE = √33

Let's find AE as follows:

5²- 4² = AE²

AE = √25 - 16

AE = √9

AE = 3 units

Therefore,

AC = √33 + 3

AC = 5.74456264654 + 3

AC = 8.74456264654

AC = 8.7 units

learn more on kite here: https://brainly.com/question/27975644

#SPJ9

Answer:uu

Step-by-step explanation:

Answer:

I think 7 is the answer

hope it helps

Answer:

x-7y=84

x-7y-84=0

Step-by-step explanation:

y=mx+c

y=ax+b

ax+by=c or ax+by-c=0

m= 1/7

y=1/7x-12

x-7y=84

x-7y-84=0

Answer:

28.274

Step-by-step explanation:

Use the circle formula

A=pi(r)^2

Radius is 3

A=pi(3)^2=28.274

Hope this helps : )

Answer: $20.

Step-by-step explanation: The price of onions was $32 per kg, this price decreased by $12, so you need to subtract 12 from 32. 32 - 12 is $20.