Which expression is equivalent to (a^-8b/a^-5b^3)^-3

As per the concept of arithmetic sequence, there are 259 multiples of three between 10 and 787

To solve this problem, we need to find the first and last multiples of three within the given range and then count how many integers are there in between

Step 1: Find the first multiple of three greater than or equal to 10.

The first multiple of three greater than or equal to 10 is 12.

Step 2: Find the last multiple of three that is less than or equal to 787.

The largest multiple of three less than or equal to 787 can be calculated as follows:

Divide 787 by 3:

787 ÷ 3 ≈ 262.33

The largest multiple of three less than or equal to 787 is:

262 × 3 = 786

Step 3: Count the multiples of three within the range.

Now that we have found the first and last multiples of three within the range, we need to count the number of multiples of three between them, including the endpoints.

The multiples of three between 12 and 786 are:

12, 15, 18, ..., 783, 786.

Step 4: Calculate the total count of multiples.

To calculate the total count, we can use the formula for finding the number of terms in an arithmetic sequence:

Number of terms = (last term - first term) / common difference + 1.

In this case, the first term is 12, the last term is 786, and the common difference (the difference between consecutive terms) is 3.

Number of terms = (786 - 12) / 3 + 1

Number of terms = 774 / 3 + 1

Number of terms = 258 + 1

Number of terms = 259.

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The solution to the system of linear equations is (3, 0.5).

To solve the system of linear equations by graphing, we'll plot the two equations on the same set of axes and find the point of intersection, which represents the solution.

The solution is (3, 0.5). Confirming for the first equation: y = -3 - 7 = -10 and for the second equation: 3 + 2(0.5) = 4. The coordinates match both equations.

Answer:

situation 1 : flat rate of 50....1.50 per movie.....after 1 month her bill is 66.25

66.25 = 1.50x + 50

situation 2 : flat rate of 60....1.25 for every movie...

y = 1.25x + 60

both situations have a flat rate fee plus a charge for every movie. In situation 1, u can solve for x (the number of movies rented) because u know how much she was charged. However, in situation 2, without more information, u cannot solve this equation...what u would need to solve it would either be the number of movies rented or the total bill showing what she was charged. So basically, in situation 1, u are given more information then in situation 2.....enough information to be able to solve for the variable x...whereas, in situation 2, u are not given enough info to solve for a variable and get a numerical answer

BRAINLIEST PLEASE!!!!!

Answer: Situation 1 involves one independent variable that stands for the number of movies Melinda rented. Situation 1 gives a total for the monthly bill, but situation 2 does not give a total for the monthly bill. Because situation 2 leaves the total value out, it needs an additional variable. Therefore, situation 2 involves two variables—the number of movies Kimberly rented (the independent variable) and the monthly cable bill (the dependent variable). In this situation, we can’t solve for one variable without knowing the other.

Step-by-step explanation: ed.men.tum answer. DO NOT copy and paste!

Answer:

The factors of 2q²-5pq-2q+5p are (2q-5p) (q-1)....

Step-by-step explanation:

The given expression is:

2q²-5pq-2q+5p

Make a pair of first two terms and last two terms:

(2q²-5pq) - (2q-5p)

Now factor out the common factor from each group.

Note that there is no common factor in second group. So we will take 1 as a common factor.

q(2q-5p) -1(2q-5p)

Now factor the polynomial by factoring out the G.C.F, 2q-5p

(2q-5p) (q-1)

Thus the factors of 2q²-5pq-2q+5p are (2q-5p) (q-1)....

Answer:

[tex]\frac{5}{2\sqrt{6} }[/tex]

Step-by-step explanation:

Since Θ is in fourth quadrant then cosΘ > 0, as is secΘ

Given

sinΘ = - [tex]\frac{1}{5}[/tex], then

cosΘ = [tex]\sqrt{1-(-1/5)^2}[/tex]

         = [tex]\sqrt{1-\frac{1}{25} }[/tex] = [tex]\sqrt{\frac{24}{25} }[/tex] = [tex]\frac{2\sqrt{6} }{5}[/tex]

Hence

secΘ = [tex]\frac{1}{\frac{2\sqrt{6} }{5} }[/tex] = [tex]\frac{5}{2\sqrt{6} }[/tex]

Answer:

[tex]\sec(\theta)=\frac{5\sqrt{6}}{12}[/tex]

The answer is the last one.

Step-by-step explanation:

If we are in quadrant 4, then x (cosine) is positive and y (sine) is negative.

Since cosine is positive, secant is positive because secant is the reciprocal of cosine.

So we already know the answer is not the 1st one or the 3rd one.

I'm going to use a Pythagorean Identity to find cosine value of theta.

[tex]\cos^2(\theta)+\sin^2(\theta)=1[/tex]

Enter in -1/5 for [tex]\sin(\theta)[/tex]:

[tex]\cos^2(\theta)+(\frac{-1}{5})^2=1[/tex]

Simplify a bit:

[tex]\cos^2(\theta)+\frac{1}{25}=1[/tex]

Subtract 1/25 on both sides:

[tex]\cos^2(\theta)=1-\frac{1}{25}[/tex]

Write 1 as 25/25 so you have a common denominator on the right hand side:

[tex]\cos^2(\theta)=\frac{25}{25}-\frac{1}{25}[/tex]

[tex]\cos^2(\theta)=\frac{24}{25}[/tex]

Take the square root of both sides:

[tex]\cos(\theta)=\pm \sqrt{\frac{24}{25}}[/tex]

[tex]\cos(\theta)=\pm \frac{\sqrt{24}}{\sqrt{25}}[/tex]

I will worry about simplifying the square root part when finding secant.

We said that cosine was positive because we were in the fourth quadrant.

[tex]\cos(\theta)=\frac{\sqrt{24}}{\sqrt{25}}[/tex]

Now recall that cosine and secant are reciprocals of each other:

[tex]\sec(\theta)=\frac{\sqrt{25}}{\sqrt{24}}[/tex]

Let's simplify the square part not.

Usually people hate the square root on both and also if you look at your choices none of the choice have square root on bottom.

So we are going to multiply top and bottom by [tex]\sqrt{24}[/tex]. I'm going to also write 5 instead of [tex]\sqrt{25}[/tex].

[tex]\sec(\theta)=\frac{5}{\sqrt{24}} \cdot \frac{\sqrt{24}}{\sqrt{24}}[/tex]

[tex]\sec(\theta)=\frac{5\sqrt{24}}{24}[/tex]

Now let's simplify the square root of 24.

We know 24 is not a perfect square, but 24 does contain a factor that is a perfect square. That factor is 4.

[tex]\sec(\theta)=\frac{5\sqrt{4}\sqrt{6}}{24}[/tex].

[tex]\sec(\theta)=\frac{5(2)\sqrt{6}}{24}[/tex]

[tex]\sec(\theta)=\frac{10\sqrt{6}}{24}[/tex]

Now both 10 and 24 share a common factor of 2 so let's divide top and bottom by 2:

[tex]\sec(\theta)=\frac{5\sqrt{6}}{12}[/tex]

The answer is the last one.

Answer:

(a) Plan B, $4 more

(b) 140, Plan A

Answer:

41.04 meters

Step-by-step explanation:

The questions which involve calculating the angles and the sides of a triangle either require the sine rule or the cosine rule. In this question, the two sides that are given are adjacent to each other the given angle is the included angle. The initial position is given by A. The tree is denoted as C and the fence post is denoted as B. Since the use of sine rule will complicate the question, it will be easier to solve this question using the cosine rule. Therefore, cosine rule will be used to calculate the length of BC. The cosine rule is:

BC^2 = AB^2 + AC^2 - 2*AB*AC*cos(BAC).

The question specifies that AC = 70 meters, BAC = 25°, and AB = 35 meters. Plugging in the values:

BC^2 = 35^2 + 70^2 - 2(35)(70)*cos(25°).

Simplifying gives:

BC^2 = 1684.091844.

Taking square root on the both sides gives BC = 41.04 meters (rounded to two decimal places).

Therefore, the distance between the point on the tree to the point on the fence post is 41.04 meters!!!

To determine the average number of pies eaten by each participant in a contest with 9 participants and 46 pies, divide the total pies by the total participants. The result is approximately 5.11 pies per person, indicating they ate very evenly with most having eaten about 5 pies.

The question asks us to find out how many pies each person ate in a pie eating contest with 9 participants and 46 pies consumed. To calculate this, we divide the total number of pies by the number of participants. Here's the calculation:

Divide 46 pies by 9 participants to get the average number of pies per person.

The result is approximately 5.11 pies per person.

Since we can't have a fraction of a pie eaten in a real context, it suggests that participants ate either 5 or 6 pies each, if they are very evenly matched.

Therefore, the best description of how many pies each person ate, assuming they are very evenly matched, would be approximately 5 pies per person, with some participants possibly having eaten 6 pies to account for the total of 46 pies.

Answer:

the probability is the event is certain to happen

Step-by-step explanation:

Answer:

This event is certain to happen.

The probability is 1.

Step-by-step explanation:

Probability theory aims to explain the chance of an event occurring. In this case, there are 3 yellow balls, 4 blue balls and 8 red balls. The total of balls will be 3 + 4 + 8 = 15

If a random ball is removed, it can be any of three colors. The color that has the most balls will have a higher chance of being chosen from the 15 totals.

Likelihood of drawing a red ball: 8/15

Probability of a yellow ball: 3/15

Blue ball probability: 4/15

The question explains that only one ball will be removed and explains that there are only 3 colors. Therefore, when removing a ball, it will certainly be one of three colors.

This can be confirmed by adding the probability of each ball: 8/15 + 3/15 + 4/15 = 15/15 = 1

Thus, if a primary ball is removed, it will certainly be one of three colors. Moreover we can say that chance of being red is greater than being blue, which is greater than being yellow.

Answer:

Explanation:

The rotation of a point 180 degrees about the origin follows the rule:

That means that both the x-coordinate and the y-coordinate transform into their negative values.

So, - 3 transforms into - (-3) = 3, and - 2 transforms into - (-2) = 2.

The result is (-3, -2) → (3,2).

Answer:

-2

Step-by-step explanation:

Before a dilation you have the point (x,y).

After a dilation of a scale factor of r you have (r*x,r*y).

Let's look at one pair of corresponding points.

A(-11,7)  and A'(22,-14)

We need to figure out what we can multiply to -11 to get 22.

We need to figure out what we can multiply to 7 to get -14.

Hopefully it is the same number or this isn't a dilation.

So to get from pre-image to image you need to multiply by -2 because -11*-2=22 and 7*-2=-14.

The scale factor is -2.

The dilation is this: (x,y)->(-2x,-2y)

The required scale factor is -2

The scale factor is a measure for similar figures, who look the same but have different scales or measures.

Let's consider one pair of corresponding points.

Clearly we need to multiply by -2.

This is applicable for all the points

So, the scale factor is -2.

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Answer:

Step-by-step explanation:

[tex]\left\{\begin{array}{ccc}y=x+3&(1)\\4x+y=18&(2)\end{array}\right\\\\\text{substitute (1) to (2):}\\\\4x+(x+3)=18\\\\(4x+x)+3=18\qquad\text{subtract 3 from both sides}\\\\5x=15\qquad\text{divide both sides by 5}\\\\x=3\\\\\text{put the value of x to (1):}\\\\y=3+3\\\\y=6[/tex]

55% off the regular price means she paid 45% of the regular price. ( 100% - 55% = 45%

Multiply the original price by 45%:

39 x 0.45 = 17.55

She paid $17.55

(If you need to know how much she saved:  39 - 17.55 = $21.45)

Answer:

Ashley bought the item for $17.55

The area of the circle is found using the formula Area = PI x r^2

The area of a triangle is found using the formula Area = 1/2 x base x height.

Using the given dimensions:

Area of the circle = 3.14 x 3.8^2 = 45.3416 square units.

The area of the triangle is 1/2 x 5 x 10 = 25 square units.

To find the area of the unshaded part, subtract the area of the shaded triangle from the circle:

Area = 45.3416 - 25 = 20.3416

Round to two decimal places = 20.34

The answer is D. 20.34

D. 20.34

In this case, we must calculate first the Areas of the Triangle ([tex]A_{t}[/tex]), in square units, and the Circle ([tex]A_{c}[/tex]), in square units, later we subtract the Area of the former from the Area of the latter to determine the Area of unshaded region ([tex]A_{u}[/tex]), in square units. The Area formulas for each figure are, respectively:

Triangle

[tex]A_{t} = \frac{1}{2}\cdot b\cdot h[/tex] (1)

Circle

[tex]A_{c} = \pi\cdot r^{2}[/tex] (2)

Unshaded Area

[tex]A_{u} = A_{c} - A_{t}[/tex] (3)

Where:

[tex]h[/tex] - Height of the triangle.

[tex]b[/tex] - Base of the triangle.

[tex]r[/tex] - Radius of the circle.

If we know that [tex]h = 10[/tex], [tex]b = 5[/tex] and [tex]r = 3.8[/tex], then the area of the unshaded region is:

[tex]A_{t} = \frac{1}{2}\cdot (5)\cdot (10)[/tex]

[tex]A_{t} = 25[/tex]

[tex]A_{c} = \pi\cdot 3.8^{2}[/tex]

[tex]A_{c} \approx 45.365[/tex]

[tex]A_{u} = 45.365-25[/tex]

[tex]A_{u} = 20.365[/tex]

The correct answer is D.

Please see this question related to Area problems: https://brainly.com/question/16151549

First we can rewrite the equation to,

[tex]x^2+2x-3=0[/tex]

Which factors to,

[tex](x+3)(x-1)=0[/tex]

And this leads towards two solutions,

[tex]x_1\Longleftrightarrow x+3=0\Longrightarrow x_1=-3[/tex]

and,

[tex]x_2\Longleftrightarrow x-1=0\Longrightarrow x_2=1[/tex]

The answer is A.

Hope this helps.

r3t40

Answer:

c

Step-by-step explanation:

Given

x² + 2x = 3

To complete the square

add ( half the coefficient of the x- term )² to both sides

x² + 2(1)x + 1 = 3 + 1

(x + 1)² = 4 ( take the square root of both sides )

x + 1 = ± [tex]\sqrt{4}[/tex] = ± 2 ( subtract 1 from both sides )

x = - 1 ± 2, hence

x = - 1 - 2 = - 3 and x = - 1 + 2 = 1

Answer:

The value of the expression is -3.

Step-by-step explanation:

Consider the provided expression.

[tex]-3(-3+2)-6[/tex]

Step 1: Solve the parentheses.

[tex]-3(-1)-6[/tex]

Step 2: Open the parentheses.

[tex]3-6[/tex]

Step 3: Subtract the like terms.

[tex]-3[/tex]

Hence, the value of the expression is -3. The required steps is shown above.

Answer:

A) 32

Step-by-step explanation:

I will assume the function is

f(x) = 32 (1.5)^x

This is in the form

y =a b^x

in which a is the initial value, b is the growth rate, x is the time

a =32, which is the initial population

b= 1.5, which means 1.5-1 = .5. which means it grows at a 50% increase

x = number of  years

Answer:

I'll be referring to this form: ax^2-bx+c

The 4x^2 is the rate that it goes up. If a is greater than 1, then that means the graph gets narrower from the parent function x^2. You can clearly see that in that graph.

The c is always the y-intercept. In this case, you can see that it's 7. The graph clearly shows 7 as it's y-intercept as well, so that matches well.

Sadly, I do not know how to compare the 8x into this situation without a calculator, but that information should be quite enough to see how that function is in that graph.

Let the number of geese be x.

Then number of goats is 22-x.

A goose has 2 legs, and a goat has 4.

There are a total of 82 legs.

So,

2x + 4(22-x) = 82

2x + 88 - 4x = 82

-2x = -6

x = 3

There are 3 geese and (22-3=) 19 goats.

Please mark Brainliest if this helps and feel free to ask doubts!

I believe the answer would be 12.4 the first choice.

Answer:

=12.4 units

Step-by-step explanation:

We can use the Pythagoras theorem to find the lengths of EF, FG, and HE

(GF)²=(ΔX)²+(Δy)²

(GF)²=(2--1)²+(4-3)²

=3²+1²

=10

GF=√10=3.16 units

(EF)²=(Δx)²+(Δy)²

=(2--1)²+(6-4)²

=3²+2²

=9+4

=13

EF=√13=3.61 units

(HE)²=(Δx)²+(Δy)²

=(-1--3)²+(6-3)²

=2²+3²

=4+9

=13

HE=√13=3.61 units

GH=(-1--3)=2 units

Perimeter =GF+EF+EH+HG

=3.16+3.61+3.61+2

=12.38 units

=12.4 units to 1 decimal place.

Answer:

V≈2770.88

Step-by-step explanation:

The volume of a cylinder that has a radius of 7 and a height of 18 is 2770.88.

In order to find the answer, you should use the formula πr²h.

R means radius and H means Height.

V=πr2h=π·72·18≈2770.88472

Answer:

V = 882pi units^3

or approximately

2769.48 units^3

Step-by-step explanation:

The column of a cylinder is given by

V = pi * r^2 * h

We know the radius is 7 and the height is 18

V = pi * 7^2 *18

V =pi *49 *18

V =882 pi

If we want an approximate answer, we can approximate pi by 3.14

V = 3.14 * 882

V =2769.48

Answer:

Step-by-step explanation:

The solution of the system of equations is the coordinates of the intersection of the lines.

(1, -3)

Answer:

B.(1, -3)

Wherever the lines intersect is the solution. Hope this helps!

Step-by-step explanation:

Answer:

The answers would be:

1) 1/2

2) 1/10

3) 3/4

Step-by-step explanation:

Percentages are always calculated by multiplying the percentages with 100. Like in this example, 50% means 0.5. This 0.5 was multiplied before by 100 to get this percentage. So to find out the equivalent forms, we would simplify the percentage like:

50%-------> 0.5

10%--------> 0.1

75%--------> 0.75

So

0.5 means 1/2 of the total value

0.1 means 1/10 of the total value

0.75 means 3/4 of the total value.

Answer:

Took Quiz 100%.... 50%= 0.50 and 10%= 0.10 and 75% =0.75

Answer:

parent funtion is most basic

Step-by-step explanation:i just took the test

Answer:

Answer:

89

°

to the nearest degree.

Explanation:

The base of the triangle 7 can be divided in half by a line of symmetry of the isosceles triangle, which will bisect the vertex angle. This creates two right triangles:

Each with a base of 3.5 and a hypotenuse of 5.

The side opposite the half of the vertex angle is 3.5, the hypotenuse is 5.  

The sine function can be used to find the angle.

sin

θ

=

o

p

p

h

y

p

sin

θ

=

3.5

5

=

0.7

Use the inverse sin function or a table of trig functions to find the corresponding angle . (Arcsin)

arcsin  

0.7

=

44.4

°

Remember that this is the value of half of the vertex angle so double the value to find the vertex angle.

2

×

44.4

=

88.8

°

rounded off to the nearest whole degree =  

89

°

Answer:

[tex]m=-\frac{4}{5}[/tex]

Step-by-step explanation:

We can take 2 arbitrary points in the graph and solve for slope using the formula shown below.

Note: we will use the 2 points (2,-3) & (-3,1)

Where x_1 = 2, y _1 = -3  and  x _ 2 = -3 and y _ 2 = 1

The formula:

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

Let's plug the numbers and find the slope:

[tex]m=\frac{1-(-3)}{-3-2}\\m=\frac{4}{-5}\\m=-\frac{4}{5}[/tex]

Hence, thsi is the slope.

[tex]3D-2E=3\left[\begin{array}{cc}5&5\\-3&7\\1&3\end{array}\right] -2\left[\begin{array}{cc}6&7\\2&-7\\0&5\end{array}\right] \\\\3D-2E=\left[\begin{array}{cc}15&15\\-9&21\\3&9\end{array}\right] -\left[\begin{array}{cc}12&14\\4&-14\\0&10\end{array}\right] \\\\3D-2E=\left[\begin{array}{cc}3&1\\-13&35\\3&-1\end{array}\right][/tex]

Answer:

16.3 units ( to 1 dec. place )

Step-by-step explanation:

Using the distance formula

d = √ (x₂ - x₁ )² + (y₂ - y₁ )²

with (x₁, y₁ ) = A(- 1, 3) and (x₂, y₂ ) = B(11, - 8)

AB = [tex]\sqrt{(11+1)^2+(-8-3)^2}[/tex]

     = [tex]\sqrt{12^2+(-11)^2}[/tex]

     = [tex]\sqrt{144+121}[/tex]

     = [tex]\sqrt{265}[/tex] ≈ 16.3 ( to 1 dec. place )