Explain the difference between multiplying by powers of 10 when the exponent is a positive number and when the exponent is a negative number

The rule is add 3. The next three terms are 36, 39, 42

Answer:

D

Step-by-step explanation:

The sides of a regular hexagon are congruent

Given that 1 side = 15in, then

perimeter = 6 × 15 = 90 in → D

Answer:

A

Step-by-step explanation:

x^2 +8X = 33

x^2 +8X +(8/2)^2 = 33 + (8/2)^2

(x + 8/2)^2 = 49

(x +4)^2 = 49

x = -11

x = 3

The values of x in the given quadratic equation by completing the square are -11 and 3.

Hence, option A)-11,3 is the correct answer.

Quadratic equation is simply an algebraic expression of the second degree in x. Quadratic equation in its standard form is;

ax² + bx + c = 0

Where x is the unknown

Given th equation in the question;

x² + 8x = 33

Using completing the square method

First we take the half of the x term and square it

( 8/2 )² = 16

Now we add 16 to both sides

x² + 8x + 16 = 33 + 16

Next, we rewrite the perfect square on the left

( x + 4 )² = 33 + 16

( x + 4 )² = 49

We take square root of both sides

x + 4 = √49

x = -4 ± √49

x = -4 ± 7

x = -4 - 7 or -4 + 7

x = -11 or 3

x = -11, 3

The values of x in the given quadratic equation by completing the square are -11 and 3.

Hence, option A)-11,3 is the correct answer.

Learn more about quadratic equations here: brainly.com/question/1863222

#SPJ5

[tex]13 + 9 + 10 = 33[/tex]

Diego's neighbors paid him $33.

Answer:

0 your asking the following right? -8-8?  If yes, its 0 if you substitute m.

:) hope that helped

Answer:

[tex]49,987.24\ ft[/tex]

Step-by-step explanation:

Let

x-----> distance from the two towns

we know that

In the right triangle ABC

[tex]tan(32\°)=37,000/(x+y)\\x+y=37,000/tan(32\°)[/tex]

In the right triangle ABD

[tex]tan(76\°)=37,000/(y)\\y=37,000/tan(76\°)[/tex]

see the attached figure to better understand the problem

Remember that

(x+y)-y=x

so

[tex]x=\frac{37,000}{tan(32\°)} -\frac{37,000}{tan(76\°)}[/tex]

[tex]x=49,987.24\ ft[/tex]

Answer:

B: 192pi - 144

Step-by-step explanation:

Area of the sector = (120/360) * pi * r^2

Area of the sector = 1/3 * pi * 24 * 24

Area of the sector = 192 * pi

Now to find the area of the triangle.

The triangle is an isosceles triangle That means two of its sides are equal. They are equal to the radius of the circle, which is 24.

the small angles are equal to

2x + 120 = 180    Subtract 120 from both sides

2x = 60               Divide by 2

x = 60/2

x = 30

The height of the triangle is derived from sin(30) = opposite / hypotenuse

sin(30) = 1/2

hypotenuse = 24

1/2 = opposite / hypotenuse

1/2 = opposite / 24                      Multiply both sides by 24

1/2 * 24 = opposite

opposite = 12

The height = 12

r = 24

Area of the triangle = 1/2 * 12 * 24

Area of the triangle = 144

So the area of the shaded area = 192*pi - 144 which looks like B

The area of the shaded region of the circle in terms of pi is 192π - 144√3 m².

The correct option is B) 192π - 144√3 m².

The shaded area of the circle is a segment, to determine the area of the segment, we simply subtract the area of the triangle from the area of the sector.

Note that; the area of a sector is expressed as:

Area = (θ/360) × πr²

Area of a triangle can be expressed as:

Area = ab × (sinθ)/2

Hence, the area of the shaded region will be:

Area = ( (θ/360) × πr² ) - ( ab × (sinθ)/2 )

Plug in the values and simplify:

Area = ( (120/360) × π × 24² ) - ( 24 × 24 × (sin120)/2 )

Area = ( 192π ) - ( 144√3 )

Area = 192π - 144√3

Therefore, the shaded area measures 192π - 144√3 square meters.

Option B) 192π - 144√3 m² is the correct answer.

Learn more about area of sector here: https://brainly.com/question/32139306

#SPJ3

Gallons would provide a more precise measurement when measuring water evaporation from a swimming pool.

If you are measuring the amount of water evaporated from a swimming pool, gallons would give you a more precise measurement. Gallons is a larger unit of measurement than quarts and therefore provides a more accurate representation of the amount of water evaporated from a swimming pool due to its larger capacity.

Answer:

  65 miles

Step-by-step explanation:

The straight line distance between two points can be considered to be the hypotenuse of a right triangle. In this case, the legs of the triangle are the distance east and the distance north. The Pythagorean theorem describes the relation between the legs (a, b) and the hypotenuse (c).

  c² = a² +b²

  c² = 60² +25² = 3600 +625 = 4225

  c = √4225 = 65

The two airports are 65 miles apart.

__

Additional comment

You may recognize that the greatest common factor of 25 and 60 is 5, which means these numbers have the ratio 5 : 12. You may also recognize these as being the two smaller numbers in the Pythagorean triple {5, 12, 13}. That is, you expect the airports to be 5×13 = 65 miles apart.

The distance between the two airports is 65 miles.

Let's denote the distance east as [tex]$d_e = 60$[/tex] miles and the distance north as [tex]$d_n = 25$[/tex] miles. The distance between the two airports, which is the hypotenuse of the right-angled triangle formed by the two distances, can be calculated as follows:

[tex]\[ d = \sqrt{d_e^2 + d_n^2} \][/tex]

Substituting the given values:

[tex]\[ d = \sqrt{60^2 + 25^2} \] \[ d = \sqrt{3600 + 625} \] \[ d = \sqrt{4225} \] \[ d = 65 \][/tex]

Therefore, the distance between the two airports is 65 miles.

Answer:

Step-by-step explanation:

yes i did and it was sad because it was so hard mabey some questions where easy but other than that it was hard i whould cry throught the whole pert test but nah i didint

The PERT test's Math portion mainly covers algebra and geometry. It includes topics such as fractions, decimals, percentages, ratios and proportions, linear equations, inequalities, polynomials, quadratic equations, and basic geometry concepts. Preparation, practice, and study guides are recommended to perform well.

The PERT (Postsecondary Education Readiness Test) is a placement test used by colleges in Florida to assess a students' college readiness in Reading, Writing, and Mathematics. If you're concerned about the Math section, understanding the content breakdown can be very helpful.

The Math portion of the PERT test primarily includes algebraic and geometry questions, with the main focus being algebra. Topics include but aren't limited to fractions, decimals, percentages, ratios and proportions, linear equations, inequalities, polynomials, quadratic equations, and basic geometry concepts.

Preparing for this test may include using study guides, practice tests, and brushing up on your algebra and geometry skills. Remember utilizing all available resources and allotting ample time to study can greatly help you perform better on the test.

https://brainly.com/question/34144790

#SPJ11

Answer:

3 x 5 = 15

4 x 7 = 28

the answer is 15/28

;)

Answer:

The doubling time of this investment would be 9.9 years.

Step-by-step explanation:

The appropriate equation for this compound interest is

A = Pe^(rt), where P is the principal, r is the interest rate as a decimal fraction, and t is the elapsed time in years.

If P doubles, then A = 2P

Thus, 2P = Pe^(0.07t)

Dividing both sides by P results in 2 = e^(0.07t)

Take the natural log of both sides:  ln 2 = 0.07t.

Then t = elapsed time = ln 2

                                       --------- = 0.69315/0.07 = 9.9

                                         0.07

The doubling time of this investment would be 9.9 years.

To calculate the doubling time for an investment earning 7% interest compounded continuously, the Rule of 70 is used, which suggests that the investment will double in approximately 10 years.

To find the doubling time of an investment earning 7% interest compounded continuously, we can use the Rule of 70. The Rule of 70 is a quick and useful formula that estimates the number of years it takes for an investment to double given a fixed interest rate, specifically for interest rates below 10%. Here's how you can use it:

The Rule of 70 assumes continuous compounding. Thus, if an investment has a consistent return of 7% per year, compounded continuously, it will take roughly 10 years to double.

It's also worth noting that the Rule of 72 can be used in a similar way to estimate the doubling time more roughly. In this case, using the Rule of 72, dividing 72 by the interest rate of 7% would provide an estimation of approximately 10.3 years. This is a close approximation and often used due to its simplicity.

Answer:

x=3 (double root)

Step-by-step explanation:

We are told that y = x - 3.

Substituting x - 3 for y in the second equation yields:

x - 3 = x² - 5x + 6.

We need to rewrite this in the standard form of a quadratic equation:

Subtracting (x - 3) from both sides results in:

0 = x² - 5x + 6 - x + 3.

Combining like terms gives us:

0 = x² - 6x + 9,

which factors into (x - 3)(x - 3) = 0.  Thus, there are two real, equal roots:  x = 3 and x = 3.

Subbing 3 for x in the first equation gives us 3 - 3 = 0 = y..

Thus, the solution of this system of equations is (3, 0).

Answer:

(3,0)

Step-by-step explanation:

$260 divided by 10 weeks equals $26 a week

I say 8 is the answer.

Proof:

[tex]3 + 2 + 3 = 8[/tex]

So 8ft is my answer.

Answer:

36 square feet outdoor carpet will be required for this hole.

Step-by-step explanation:

A triangle colored in green with a rectangular hole has been given in the figure.

Area of the outdoor carpet will be calculated by the expression,

Area of the carpet = Area of the right triangle - Area of the rectangle removed from the triangle

Area of the right triangle = [tex]\frac{1}{2}(\text{Base})(\text{Height})[/tex]

                                         = [tex]\frac{1}{2}\times (12)\times (7)[/tex]

                                         = 42 square ft

Area of the rectangle = Length × Width

                                   = 3×2

                                   = 6 square ft

Area of the remaining area to be covered with the carpet = 42 - 6

= 36 square feet

Therefore, area of the outdoor carpet required for the hole = 36 feet²

Answer:

there are thirty kids in the class

Step-by-step explanation:

there are two boys to three girls so 18 divided by 3 is 6. 2 times 6 is 12. 12 plus 18 is 30.

The total number of students that are in Ms. Cunningham's class is 30 students.

Let the number of boys be represented by x.

2/3 = x/18

Cross multiply.

3 × x = 2 × 18

3x = 36

x = 36/2

x = 12

Boys = 12

Girls = 18

Total number of students = 12 + 18 = 30

Therefore, the total number of students that are in Ms. Cunningham's class is 30 students.

Read related link on:

https://brainly.com/question/12276219

Answer:

Option D. y=6x

Step-by-step explanation:

we know that

A relationship between two variables, x, and y, represent a direct variation if it can be expressed in the form [tex]y/x=k[/tex] or [tex]y=kx[/tex]

In a proportional relationship the constant of proportionality k is equal to the slope m of the line and the line passes through the origin

Verify each case

case a) y=(1/6)x+6

Is a linear equation, but is not a direct variation. The line not passes through the origin

case b)  y=6/x

The equation represent an inverse variation

case c) y=6x-6

Is a linear equation, but is not a direct variation. The line not passes through the origin

case d) y=6x

The equation represent a direct variation

Final answer:

Among the options provided, option d. y = 6x is the equation of a direct proportion because it follows the form y = kx where k is the constant of proportionality and there is no added or subtracted constant.

Explanation:

The equation of a direct proportion is one where the dependent variable changes at the same rate as the independent variable. In mathematical terms, if two variables y and x are directly proportional, it implies that y = kx, where k is the constant of proportionality.

Looking at the options provided:

a. y = 1/6x + 6 is not directly proportional because of the addition of the constant 6.

b. y = 6/x is an inverse proportion because y changes inversely with x.

c. y = 6x - 6 is also not directly proportional due to the subtraction of the constant 6.

d. y = 6x perfectly fits the definition of direct proportionality as there is no added or subtracted constant and it follows the form y = kx.

Therefore, the equation of a direct proportion among the options given is d. y = 6x.

Answer:

Add all the average amounts of items in each bag and you should get 23. Then, divide it by 3 since you are working with 3 numbers.

Answers for different places you have to round to:

Ones: 8

Tenths: 7.7

Hundredths: 7.67

Thousandths: 7.667

The average number of items in all the gift bags is [tex]7.4[/tex].

To find the average number of items in all the gift bags, we need to consider the distribution of the bags and their respective average items.

Given:

50% of the bags are green with an average of 8 items per bag.

20% of the bags are yellow with an average of 5 items per bag.

30% of the bags are blue with an average of 8 items per bag.

Let's calculate the average number of items across all gift bags:

1. Calculate the total number of bags:

Total bags = 50% (green) + 20% (yellow) + 30% (blue) = 100%

2. Calculate the weighted average of items:

[tex]\[ \text{Average items per bag} = \left(0.50 \times 8\right) + \left(0.20 \times 5\right) + \left(0.30 \times 8\right) \][/tex]

Green bags contribute [tex]\( 0.50 \times 8 = 4 \)[/tex] items on average.

Yellow bags contribute [tex]\( 0.20 \times 5 = 1 \)[/tex] item on average.

Blue bags contribute [tex]\( 0.30 \times 8 = 2.4 \)[/tex] items on average.

[tex]\[ \text{Average items per bag} = 4 + 1 + 2.4 \][/tex]

[tex]\[ \text{Average items per bag} = 7.4 \][/tex].

Answer:98 I believe

Step-by-step explanation:

Answer:

98.

Step-by-step explanation:

Number of cats = 28 * 3.5

= 98 cats.

That's a zoo!!

The system has Infinite solutions

15*18+12/3+9=103

(15*18=270)

(270+12=282)

(282/3=94)

(94+9=103)

Answer: option a

Step-by-step explanation:

You must apply the formula for calculate the distance between the two points. which is shown below:

[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

Therefore, keeping on mind that the points given in the problem are (6, 11), (0, 3), when you substitute values into the formula shown above, you obtain that the distance between these two points is the following:

[tex]d=\sqrt{(0-6)^2+(3-11)^2}\\d=10[/tex]

Answer:

a. 10

Step-by-step explanation:

We have been given two points (6, 11) and  (0, 3). Now we need to find the distance between points (6, 11) and  (0, 3) and check which of the following choices are correct:

(6, 11), (0, 3) a. 10 b. 14 c. 15 d. 100

Also we should round to the nearest tenth if necessary.

Apply distance formula :

[tex]distance =\sqrt{\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2}[/tex]

[tex]distance =\sqrt{\left(0-6\right)^2+\left(3-11\right)^2}[/tex]

[tex]distance =\sqrt{\left(-6\right)^2+\left(-8\right)^2}[/tex]

[tex]distance =\sqrt{36+64}[/tex]

[tex]distance =\sqrt{100}[/tex]

[tex]distance =10[/tex]

Hence correct choice is a. 10

31.5in² hopefully this helps

The area of a sector can be calculated using a given formula. After adjusting for the given radius and angle, the approximate area of the sector is 31.1 cm^2.

Without specifications about the figure, let's consider it as a sector of a circle.

The area of a sector can be calculated using the formula Area = (angle / 360) * π * (radius)^2.

But here we are given the base length, which is actually the diameter for the whole circle.

Hence, the radius would be base/2 which is 9/2 = 4.5 cm.

So, by substituting the given values in the formula, the area will be Area = (140 / 360) * π * (4.5)^2 = 31.07 cm^2 approx. So, the area of the figure to the nearest tenth is 31.1 cm^2.

Learn more about Area here:

https://brainly.com/question/32024069

#SPJ2

Hello.

To find our answer we need to do .25 x 100.

      0.25

x      1 00

_________     STEP 1: Calculate 5 x 1 to get 5.

      5 00

    --

    0.25

x    1 00

_______     STEP 2: Multiply 2 x 1 to get 2.

   2 5 00

We've simply have our answer, but are not done.

We have 2500 but we cannot forget about the decimal.

We need to move it over 2 times.

Our final answer is 25.00

So she will pay $25.00 total for 100 apples.

Have an amazing day & thanks for using Brainly!

Answer: C≈47.12m

Step-by-step explanation:

C=2π r=2· π· 7.5≈47.12389m

* Hopefully this helps:)Mark me the brainliest:)!!

Answer: 5.6?

Step-by-step explanation:

x^= 16+16

x^= 32

find the square root of 32 which is 5.6 pretty sure

Answer:

Least positive angle measurement = 280°

Step-by-step explanation:

Given in the question

angle = -80°

Co terminal angles are angles whose difference differs by multiple of 360°

To solve this all we have to do is add or subtract 360° over and over again until we get answer between 0° and 360°

Answer:

280 is the answer.

Step-by-step explanation:

Angles are said to be coterminal when the sum of angles 360 degrees.

-80 ± 360

Since its asking for positive angle ,therefore

-80+360 = 280 degrees

[tex]5(2x + 7) = 10x + 35[/tex]

The given expression 5(2x+7) is equivalent to (10x+35).

The distributive property is the property that expresses the distributive law of algebraic multiplication. similarly, in polynomial expression we can use the distributive property for example we can write a(c+b)  in the form of (ac+bc).

We have a polynomial expression:

= 5(2x+7)

By using the distributive property we get

=(5×2x+5×7)

= (10x+35)

Thus, the given expression 5(2x+7) is equivalent to (10x+35).

Learn more about the distributive property here:

https://brainly.com/question/5637942

Answer:

76.16

Step-by-step explanation:8 multiplied by 9.52