Find the lengh of AB

Answer:

it's

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32.36

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Answer:

134217728

Step-by-step explanation:

The geometric sequence formula is:

[tex]\displaystyle{a_n = a_1r^{n-1}}[/tex]

We know that [tex]\displaystyle{a_1=8}[/tex] and [tex]\displaystyle{r=2}[/tex], we also want to find the 25th term, substitute n = 25:

[tex]\displaystyle{a_{25}=8\cdot 2^{25-1}}\\\\\displaystyle{a_{25}=8\cdot 2^{24}}\\\\\displaystyle{a_{25}=134217728}[/tex]

Therefore, the 25th term of sequence is 134217728

Answer:

  H.  99 ft²

Step-by-step explanation:

Area is proportional to the number of tiles.

The total area of the bathroom is 6×9 = 54 tiles. Of these, 12 are shaded. The proportion can be written as ...

  total area / shaded area = total tiles / shaded tiles

  total area / (22 ft²) = 54/12 . . . . . use given numbers

  total area = (22 ft²)×(54/12) = 99 ft² . . . . . multiply by 22 ft²

The total floor area of the bathroom is 99 square feet.

Alex had $444.231 in the beginning.

Two or more expressions with an Equal sign is called as Equation.

Let, x = the money Tierra had in the beginning

y = the money Nico had in the beginning

z = the money Alex had in the beginning

Tierra, Nico and Alex had $865 altogether

x + y + z = 865

Tierra spent 2/5 of her money and now she has: x - (2/5)x = 3x/5 left

Nico spent $40 and now has y - 40 left

Alex spent twice as much as Tierra and now has z - 2(2/5)x = z - 4x/5 left

the three friends had the same amount of money left

3x/5 = y - 40

y - 40 = z - 4x/5

by solving the system of equations

x + y + x = 865

3x/5 = y - 40

y - 40 = z - 4x/5

we find

x= $317.308

y = $230.385

z = $444.231

Alex had $444.231 in the beginning.

Hence, Alex had $444.231 in the beginning.

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Answer:

2nd answer option

Step-by-step explanation:

the domain is the interval or set of valid x values. the range is the same for valid y values.

so, what is the smallest x value we see in the functional graph ?

x = 0

there is no functional value for any x smaller than that.

and then the function goes on and on to the right in all eternity. that means it goes to infinity.

so, domain = [0, infinity)

please consider the round bracket at the end, because "infinity" is not a number.

now for the range and the y values.

in this case I start to ask for the largest y value.

y = 4

for no x value do we get a larger y value.

but it goes down and down in all eternity, going also to infinity, but -infinity (down is negative for y).

so, the range = (-infinity, 4]

"-infinity" is also not a number and therefore not included (hence the round bracket).

Answer:

gradient: 1.5

Explanation:

Take two points from the graph: (2, 0), (0, -3)

[tex]\sf gradient : \dfrac{y_2 - y_1}{x_2- x_1} = \dfrac{\triangle y}{\triangle x} \ \ where \ (x_1 , \ y_1), ( x_2 , \ y_2) \ are \ points[/tex]

So here given:

Inserting values

[tex]\rightarrow \sf gradient : \dfrac{-3-0}{0-2} = \dfrac{-3}{-2} = 1.5[/tex]

Using it's concept, it is found that the period of the function is of 20 units.

The period of a function is given by the distance between it's repetitions.

Looking at the graph, the distance between the repetitions is of 20 units, which is the period of the function.

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Answer: Sorry If I'm wrong but if you are asking for the missing angle on the bottom, I think it is 30 degrees.

Step-by-step explanation: All the angles in a triangle add up to 180 degrees. we already know that one is 50 degrees. The 2nd angle is a bit wider than a 90 degree angle, and the third angle is 30 degrees, so 50 degrees + 100 degrees + 30 degrees add up to 180. So, I think your answer would be 30 degrees.

Answer:

x = 25

Step-by-step explanation:

I added a drawing down below to guide you through!

First, we should remember, that if a line crosses two parallel lines, then the adjacent angles will have the same value. Since Line D and Line E are parallel and line BC is crossing it, angles ABC and 105 will be the same.

Now that we know one of the missing angles, we can find x easily!

All angles in a triangle add up to 180, so in this case, the equation will be: 50 + 105 + x = 180.

155 + x = 180

x = 25.

So x will equal to 25 degrees!

Answer:

a=30,b=60,c=105

Step-by-step explanation:

a = 30 vertical angle therom

b = 180-120 = 60 using triangle sum therom

c = 180-75 = 105 because a line is always 180 degrees

A. The exponential growth function that models the data is: [tex]A(t) = 5.89{0.0106t}[/tex]

B. Using the function, the population will be 11 million by 2059.

The function is given by:

[tex]A(t) = A(0)e^{kt}[/tex]

In which:

Item a:

We have that:

A(0) = 5.89, A(50) = 10.

We use this to find k, hence:

[tex]A(t) = A(0)e^{kt}[/tex]

[tex]10 = 5.89e^{50k}[/tex]

[tex]e^{50k} = \frac{10}{5.89}[/tex]

[tex]\ln{e^{50k}} = \ln{\frac{10}{5.89}}[/tex]

[tex]50k = \ln{\frac{10}{5.89}}[/tex]

[tex]k = \frac{\ln{\frac{10}{5.89}}}{50}[/tex]

k = 0.0106.

Hence the equation is:

[tex]A(t) = 5.89{0.0106t}[/tex]

Item b:

We have to solve for t when A(t) = 11, hence:

[tex]A(t) = A(0)e^{kt}[/tex]

[tex]11 = 5.89e^{0.0106t}[/tex]

[tex]e^{0.0106t} = \frac{11}{5.89}[/tex]

[tex]\ln{e^{0.0106t}} = \ln{\frac{11}{5.89}}[/tex]

[tex]0.0106t = \ln{\frac{11}{5.89}}[/tex]

[tex]t = \frac{\ln{\frac{11}{5.89}}}{0.0106}[/tex]

t = 58.9

Rounding up, the population will be of 11 million in 2059.

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By solving a system of equations we will see that the two-digit number is 84.

"The tens digit of a number is twice the ones digit"

"The sum of the digits is 12".

A two-digit number can be written as:

a*10 + b

Where a is the tens digit and b is the ones digit.

The word problem can then be written as:

a = 2*b

a + b = 12

So we have a system of equations.

To find the number we need to solve these, if we replace the first equation into the second one:

a + b = 12

(2b) + b = 12

3b = 12

b = 12/3 = 4

Then:

a = 2b = 2*4 = 8

So the two-digit number is 84.

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The true statements are:

The marked up price of chicken before 10pm is $6

The 50% mark down is taken off the marked up price

Percentage can be described as a fraction out of an amount that is usually expressed as a number out of hundred.

Price after the mark up= (1 + mark up) x initial price

1.50 x 4 = $6

Price after the mark down = (1 - percentage mark down) x price after mark up

0.50 x $6 = $3

Here are the options:

The marked up price of chicken before 10pm is 6

The 50% mark down is taken off the marked up price

The chickens sell for $4 after 10pm

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The two roots [tex]a +\sqrt{b}[/tex] and [tex]a -\sqrt{b}[/tex] are called conjugate radicals

The conjugate of a radical is the value which when multiplied with the radical expression clears the radical. Conjugates have the same numbers but the opposite sign in the middle.

The given roots are

[tex]a +\sqrt{b}[/tex] and [tex]a -\sqrt{b}[/tex]

They have the same numbers but opposite signs in the middle.

Hence, the two roots [tex]a +\sqrt{b}[/tex] and [tex]a -\sqrt{b}[/tex] are called conjugate radicals

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The fraction of pizza each of her friends get if they split it evenly is 1/8

Number of pizza each friend gets = Quantity of pizza Elaine has ÷ Number of Elaine friends

= 5/8 ÷ 5

= 5/8 × 1/5

= (5 × 1) / (8 × 5)

= 5/40

= 1/8

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Using proportions, it is found that the new minimum price you need to set for the remaining watercolor paintings in order to pay for the materials is of $2.89.

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

To pay for the materials, you need to sell 18 paintings at $2.25 each, hence the total is:

T = 18 x 2.25 = $40.5.

If you lose four paintings, you will sell 14, and still need to make $40.5, hence the price will be of:

P = $40.5/14 = $2.89.

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[tex]\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: {\large{\textsf{\textbf{\underline{\underline{Answer : \:}}}}}}[/tex]

[tex] \bold{ \blue{Answer:} \sf{x = \sqrt{2} - 3, - \sqrt{2 } - 3 }}[/tex]

[tex]\bold{Step \: \: by \: \: step \: \: explanation }[/tex]

1: The expression x² + 6x + 7 fits the form a x²+ bx + c Let's complete the square, where:

[tex] \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf{a = 1} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \sf{ b = 6} \\ \sf{c = 7}[/tex]

2: Enter the constant k, which is 9 in our case.

[tex] \sf{x {}^{2} + 6x {}^{} + 9 - 9 + 7}[/tex]

3: Use Sum Square (a + b) ² = a² + 2ab + b².

[tex] \sf{(x + 3) {}^{2} - 9 + 7}[/tex]

4: Simplify

[tex] \sf{(x + 3) { }^{2} - 2}[/tex]

5: Substitute the above back into the original equation.

[tex] \sf{( x + 3) {}^{2} - 2 = 0}[/tex]

6: Add 22 to both sides.

[tex] \sf{(x + 3) {}^{2} = 2}[/tex]

7: Take the square root of both sides.

[tex] \sf{x + 3 = ± \sqrt{2}} [/tex]

8: Divide the problem into these 2 equations.

[tex]\sf{x + 3 = \sqrt{2} } \\ \: \: \: \: \: \sf{x + 3 = - \sqrt{2} }[/tex]

9: Solve the 1st equation:

[tex] \sf{ x + 3 = \sqrt{2} } \\ \sf{x = \sqrt{2} - 3 }[/tex]

10: Solve the 2nd equation.

[tex] \sf{ x + 3 = - \sqrt{2} } \\ \sf{x = - \sqrt{2} - 3 } [/tex]

11: Collect all the solutions.

[tex] \sf{x = \sqrt{2} - 3, - \sqrt{2} - 3 }[/tex]

I hope I've helped : )

Answer:

z=2

Step-by-step explanation:

We are given that a line has a slope of 3.

The line passes through the points (-10, z) and (-8, 8)

We want to find the value of z.

To do that, we can calculate the slope.

The slope can be calculated using the formula [tex]\frac{y_2-y_1}{x_2-x_1}[/tex], where [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] are points

Even though we already have 2 points, let's label their values to avoid any confusion.

[tex]x_1=-10\\y_1=z\\x_2=-8\\y_2=8[/tex]

Now substitute those values into the formula, and set it equal to 3. Remember that the formula uses subtraction.

[tex]\frac{8-z}{-8--10}[/tex] = 3

We can simplify this first.

[tex]\frac{8-z}{-8+10}[/tex] = 3

[tex]\frac{8-z}{2}[/tex] = 3

We can multiply both sides by 2 to clear the fraction and make it easier to calculate.

2([tex]\frac{8-z}{2}[/tex])  = 2(3)

Multiply.

8 - z = 6

Subtract 8 from both sides

-z = - 2

Multiply both sides by -1.

-1(-z) = -1(-2)

Multiply.

z = 2

The number of people that studied only one subject is 108.

A set is a collection of well-defined objects.

Objects in a set are called elements or members of a set.

Set notation or the use of Venn diagrams are the methods used to solve set problems.

Analysis:

let P = physics

C = chemistry

M = mathematics

n(P) = 70

n(C) = 46

n(M) = 100

n(M n P n C) = 18

n(M n P) = 30

n(M n P n C') = 30 - 18 = 12

n(M n C) = 28

n(M n C n P') = 28 - 18 = 10

n(P n C ) = 23

n(P n C n M') = 23 - 18 = 5

n(P n C' n M') = 70-(12+18+5) = 70 - 35 = 35

n(P' n C n M') = 46-(18+5+10) = 46-23 = 13

n(P' n C' n M) = 100 - (10+18+12) = 100 - 40 = 60

people that studied only one subject are = 35 + 13 + 60 = 108

In conclusion 108 students studied only one type of subject.

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Answer:

The answer is B. [tex]y = x^2 + 6x + 5[/tex]

Step-by-step explanation:

Because [tex]y = (x + 3)^2 - 4 = x^2 + 6x + 9 - 4 = x^2 + 6x + 5[/tex]

So the answer in this question is B.

Answer:

(z+2)(z+3)(x-8)

Step-by-step explanation:

z² + 5z + 6 can be factored into (z+3)(z+2)

zx + 2x − 8z-16 can be factored into (x-8)(z+2)

the LCM would be (z+2)(z+3)(x-8)

if you were to multiply the two expressions together, you would multiply (z+2)^2, which is not necessary for LCM, which is why you factor them first

Answer:

-2

Step-by-step explanation:

you will group the like terms and add and subtract the remaining digits

Answer:

523.6

Step-by-step explanation:

Volume of sphere= 4/3πr^3

V=4/3π(5^3)

V=523.6 (correct to 1 dp)

Answer: 6 triangles

Step-by-step explanation:

hope this helps :)

Considering the volume of the rectangular prism, you will need 2240 bags will be needed for the patio.

The volume of a rectangular prism of length l, width w and height h is given by:

V = lwh.

In this problem, the dimensions are:

l = 14 ft, w = 12 ft, h = 8 ft.

Hence the volume is:

V = 14 x 12 x 8 = 1344 ft³

Each bag yields 0.6 ft³, hence the number of bags is:

n = 1344/0.6 = 2240 bags.

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Answer:

30 pupils

Step-by-step explanation:

first you divide 75 and 2.5 to get 30.

Answer:

30 prefer red

Step-by-step explanation:

Multiply the fraction by the number of students:

[tex]75(\frac{2}{5})=\frac{(75)(2)}{5} =\frac{150}{5} =30[/tex]

Hope this helps