7. The top of a tree is 35 feet above ground level. The roots reach down 22 feet below ground
level. What is the difference between the top of the tree and the bottom of the roots?

The solutions to the equation in the interval are x = π/3, x = 5π/3 and x = π.

A formula for a mathematical equation is one that connects two expressions and expresses their equality using the equals sign (=). In English, an equation is defined as a properly written formula that consists of two expressions connected by an equals sign, however cognates of the word in other languages may have slightly different meanings. For instance, an equation is defined as having one or more variables in French. Finding the variables' values that cause the equality to be true is the first step in solving an equation with variables.

Let's assign a variable to the cosine function, cos(x), and say y = cos (x). Our phrase changes to

4y2 + 2y - 2 = 0

2(2y2 + y - 1) = 0

2y2 + y - 1

= 2y(y+1) - (y + 1)

= (2y - 1)(y + 1)

2(2y-1)(y+1) = 0

y + 1 = 0 = y = -1

The answers cos(x) = 1/2 and cos(x) = -1 result from replacing y with cos(x). Our solutions are x = /3, x = 5/3, and x = on the interval [0, 2], where cos(x) = 1/2 for x = /3 and x = 5/3 and cos(x) = -1.

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you need to draw the exact graph of f(x), but moved 3 units to the right and 5 units up.

First, we know the graph of f(x), and now we want to find the graph of the function:

f(x - 3) + 5.

Remember that a horizontal translation of N units is written as:

f(x + N)

Remember that a vertical translation of N units is written as:

f(x + N)

Then the function:

f(x - 3) + 5

Is a translation of 3 units to the right and 5 units upwards.

This means that you need to draw the exact graph of f(x), but moved 3 units to the right and 5 units up.

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Work Shown:

The floor area is length*width = 5*15 = 75 square meters

1 square meter = 5 dollars

75*(1 square meter) = 75*(5 dollars)

75 square meters = 375 dollars

Answer:

a = 7

b = -10

c = 3

That is all for this question.

Answer: x<2

Step-by-step explanation:  Isolate the variable by dividing each side by factors that don't contain the variable.

hope this was helpful!! - hailey_ <3 :)

Answer: The answer is C(3,11)

Step-by-step explanation:

If you replace x with 3 that will be 3 to the third power 3 x 3 is 9 so 9 plus 2 is 11 you can use 11 in y, therefor your answer is C.(3,11)

In 12 days a professional gamer got 6561 points

We know that average is ratio of the sum of all observations and the number of total observations.

For given question,

A professional gamer averaged a score of 534 points, every day, for 5 days.

⇒ 534 = (total score of 5 days) / 5

⇒ total score of 5 days = 534 × 5

⇒ total score points of 5 days = 2670 points

Then, for the next 3 days he scored a total of 1827 points.

So, the total points of 8 days would be,

total score points of 5 days +  total score points of 3 days

⇒ 2670 points + 1827 points = 4497 points.

In another 4 days he averaged a score of 516 points each day.

⇒ 516 = (total score of 4 days) / 4

⇒ total score of 4 days = 516 × 4

⇒ total score points of 4 days = 2064 points

So, the total number of points he did in 12 days:

total score points of 5 days +  total score points of 3 days + total score points of 4 days

= 2670 points + 1827 points + 2064 points

= 6561 points

Therefore, in 12 days a professional gamer got 6561 points

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The values of x are 1/ 5 and 11 respectively.

Algebraic expressions are expressions that are comprised of terms, constants, coefficients, variables and factors.

They are also made up of arithmetic operations made up of subtraction, addition, multiplication, division.

To determine the expressions, we have;

1. Let the number be x

We have the expression as;

6x - 8 = x - 7

collect like terms

6x - x = - 7 + 8

5x = 1

Make 'x' the subject

x = 1/ 5

2. Let the number be x

2x = x + 11

collect like terms

2x - x = 11

x = 11

Thus, the values of x are 1/ 5 and 11 respectively.

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The sequence of rigid transformations that will map the preimage ΔABC onto image ΔA'B'C' is Option(a) a reflection across the x-axis, a translation 8 units right, and then a reflection across the x-axis.

Co-ordinates of the points of ΔABC are,

A = (-4, 2)

B = (-6, 2)

C = (-2, 6)

point (x,-y) is the reflection of the point (x,y) across the x-axis.

So, new co-ordinates are,

A = (-4, -2)

B = (-6, -2)

C = (-2, -6)

point (x+8,y) is the translation of the point (x,y) by 8 units right.

So, new co-ordinates are,

A = (4, -2)

B = (2, -2)

C = (6, -6)

Then, the reflection of the point (x,y) across the x-axis is the point (x,-y).

So, new co-ordinates are,

A' = (4, 2)

B' = (2, 2)

C' = (6, 6)

These are the coordinates of ΔA'B'C' so the correct answer is Option(a).

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"The complete question is: Which sequence of rigid transformations will map the preimage ΔABC onto image ΔA′B′C′?

a) a reflection across the x-axis, a translation 8 units right, and then a reflection across the x-axis

b) a translation 4 units down and 10 units to the right

c) a reflection across the line y = x followed by a rotation 90° counterclockwise

d) a rotation 180° clockwise followed by a reflection across the x-axis."

The rule for the translation from LMN to L'M'N' is:

(x,y) -> (x + 3, y + 1).

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction either in it’s definition or in it’s domain. Examples are shift left/right or bottom/up, vertical or horizontal stretching or compression, and reflections over the x-axis or the y-axis.

For this problem, we have that each vertex of LMN was:

Thus the rule for the translation from LMN to L'M'N' is:

(x,y) -> (x + 3, y + 1).

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Answer:

10,540

Step-by-step explanation:

(5000*2)+(200+300)+40

10,000+500+40=10,500+40=10,540

Hope this helps!

Answer:

10540

Step-by-step explanation:

Using translation concepts, it is found that:

A. The triangle was reflected over the y-axis.

B. The coordinates for J' are (-5,-4).

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction either in it’s definition or in it’s domain. Examples are shift left/right or bottom/up, vertical or horizontal stretching or compression, and reflections over the x-axis or the y-axis.

For item a, we have that the rule applied at each vertex is given by:

(x,y) -> (-x,y).

This rule means that the triangle was reflected over the y-axis.

In item b, supposing point J(5,-4), the image is given by:

(5,-4) -> (-5,-4).

The coordinates for J' are (-5,-4).

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Answer:

I gotchu! The answer is 80.

Step-by-step explanation:

To find the mean, you need to add up all the scores and divide it by how many scores there are. In this case, there are 5 scores, so we can first add them all up.

70+75+80+85+90=400

Now, since there are 5 scores, you need to divide 400 by 5.

400/5=80

The mean would be 80.

Hope that helped!

Have a great day!

:D

The function f(x), representing the number of blocks Eva is away from her house after x minutes is

[tex]f(x) = \begin{cases} & 0\text{ if } x= 0\\ & x\text{ if } 0 < x\leq 3 \\ & 3\text{ if } 3 < x\leq 6\\ & x/2\text{ if } 6 < x\leq 12\\ & 6\text{ if } 12 < x\leq 18\\ & 24-x\text{ if } 18 < x\leq 24 \\ & 0\text{ if } x > 24 \end{cases}[/tex]

The graph for the same is attached.

In the question, we are asked to form a graph showing the number of blocks, that Eva is away from her home at x minutes, after she leaves her home.

To form the graph, we first try to make a function for x minutes, f(x), showing the number of blocks Eva is away from her home after x minutes.

Since x represents time, it cannot be negative.

At x = 0, f(x) = 0, as she is at her home at 0 minutes.

Then, Eva visits the store, 3 blocks away from her home at a speed of 1 block per minute.

Thus, she moves 1 block every minute up to 3 minutes.

Thus, we get f(x) = x, 0 < x ≤ 3.

After this, she spends 3 minutes at the store, giving f(x) = 3, 3 < x ≤ 6.

Then she moves towards the bank, in the same direction, 3 blocks away at the speed of 1 block every 2 minutes.

Thus, in every minute, she travels 1/2 block.

Thus, the function can be designed as follows:

f(x) = 3 + (1/2)(x - 6), 6 < x ≤ 12,

or, f(x) = x/2, 6 < x ≤ 12.

Now, we are given that she stops at the bank for 6 minutes.

Thus, we get, f(x) = 6, 12 < x ≤ 18.

Now, she drove back home, at the speed of one block every minute.

Thus, we get f(x) = 6 - (x - 18), 18 < x ≤ 24,

or, f(x) = 24 - x, 18 < x ≤ 24.

At the 24th minute, Eva reaches her house back, giving f(x) = 0, x > 24.

Thus, the complete function can be shown as:

[tex]f(x) = \begin{cases} & 0\text{ if } x= 0\\ & x\text{ if } 0 < x\leq 3 \\ & 3\text{ if } 3 < x\leq 6\\ & x/2\text{ if } 6 < x\leq 12\\ & 6\text{ if } 12 < x\leq 18\\ & 24-x\text{ if } 18 < x\leq 24 \\ & 0\text{ if } x > 24 \end{cases}[/tex]

The graph for this function is attached.

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6w^2z^2

I hope this helps!

Answer:

Step-by-step explanation:

The number of written in standard form is 9.45 × 10⁵

From the question, we are to write the given number in standard form

The given number is

Nine hundred forty-nine thousand

That is,

945000

To write a number in standard form, we will write the number as a decimal number between 1.0 and 10.0, multiplied by a power of 10.

The number, 945000, written in standard form is

9.45 × 10⁵

Hence, the number of written in standard form is 9.45 × 10⁵

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Answer:

1/3

Step-by-step explanation:

3/9 divide both sides by 3 for simplest form

1/3

768 cm'^2 is the trapezoid’s area.

What is  isosceles trapezoid?

Isosceles trapezoids have equal length non-parallel sides, hence the name "isosceles" which means "equal legs". The "legs" are another name for these equal sides.

Let 50 cm  = the bottom  base

We can find the area of one of the triangles that comprise the area of the trapezoid.....its sides are 30, 40 and 50  cm

Let s be the semi-perimeter of one of the triangle  = [ 50 + 40 + 30 ] / 2  = 60 cm

And the area of  of this triangle  =  sqrt  [ s ( s - a) (s - b) ( s -c) ]     where a,b, c are the sides

So...we have    sqrt [ 60 ( 60 - 30) (60 - 40) (60 - 50) ]  = sqrt [ 60 * 30 * 20 * 10 ] =

sqrt [ 1800 * 200]   =   sqrt [ 3600 * 100]  = 60 * 10  = 600 cm ^2

Now the base of this triangle = 50 and the height can be found as

follows :

Area =  (1/2) 50 * height

600 = 25 * height

height  =  24 cm   and this is the height of the trapezoid

Now....the top base can be found as   50  -  2 sqrt [ 30^2 - 24^2 ]  = 14 cm

So....the area of the trapezoid  = (1/2) height ( sum of the bases)  =  (1/2) (24) ( 50 + 14)  = 12 ( 64)  = 768 cm'^2

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The way to write the name of a segment differently than the name of a line is that  a line is written with the use of two arrowheads on the ends. While a line segment is just written down by an overbar with endpoints.

A line is known to be a kind of a one-dimensional figure that moves from infinitely in 2 directions.

A line segment is seen as a part of a line that is known to be made up of  definite attributes where it has two endpoints as well as a fixed length.

Therefore, The way to write the name of a segment differently than the name of a line is that  a line is written with the use of two arrowheads on the ends. While a line segment is just written down by an overbar with endpoints.

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O Zeema gets paid £1870 per month in equal monthly payments.

The amount paid each month to repay the loan over the course of the loan is known as the monthly payment. When a loan is taken out, not only the principal, or the original amount borrowed, but also the interest that accrues, must be repaid.

Now when the total amount earned in a month is given then the monthly payment is calculated by dividing the total amount by 12 as there are 12 months in a year.

Annual amount earned by O Zeema=£22,440

Therefore monthly amount earned=£22,440 ÷12=£1870

Hence O Zeema earns £1870 per month

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Answer: 1.65 × 10⁻³

Step-by-step explanation: hope this helps!!!

Answer:

Week 1:

Michelle makes the most with $237.50

Chris made $195 and Alex made $178.50

Week 2:

Michele makes the most with $232

Chris made $192.50 and Alex made $180.83

Week 3:

Alex makes the most with $234.50

Chris made $272.50 and Michelle makes $206

Step-by-step explanation:

For Chris in week 1, multiply 3/100 x 1500 to get what he makes on commission. That equals $45. $150 + $45 = $195

For Michelle in week 1, multiply 15 x 5 = 75. Also multiply 25 x 6.5 = 162.5 to find how much she gets payed by the Pringles. Add it up to get $237.50

For Alex in week 1, multiply 21 x 8.5 = $178.50

For Chris in week 2, multiply 1/40 x 1000 = $25 to get what he makes on commission for the first $1,000. Then multiply 7/200 x 500 = $17.50 to get when he makes on commission for the sales over $1,000. Add it all up and get $192.50

For Michelle in week 2, multiply 10 x 5 = 50 to find how much she gets payed by the Rogers'. Then multiply 28 x 6.5 = 182 to find how much she gets payed by the Pringles. Add it up to get $232

For Alex in week 2, multiply 25 x 7 = 175 to find out how much he earns for 5 hours each day. Then, since Alex worked another 50 minutes, multiply 5/6 x 7 = 5.83. Add it up to get $180.83

For Chris in week 3, multiply 3/200 x 1500  = 42.50 to get what he makes on commission. Then add it with the base salary of 250 to get $272.50

For Michelle in week 3, since the Pringles paid her double, she earned $13 an hour. So, multiply 13 x 12 = 156. Then add it with the $50 she makes from the Rogers' and get $206

For Alex in week 3, multiply 7 by the number of hours he works each day in the week. Get $234.50

Answer:

7 grids

Step-by-step explanation:

-start at one of your points

-count up or down the y-axis to the other point.

-count along the x-axis to your other point.

-add the 2 lengths.

The amount that the bank loaned out at 7.9% is $1,574.00

How do represent the amounts lent at different rates?

On the assumption that x amount was loaned at 7.9% and that the remaining amount, (8,200-x) was loan out at 7.4%, we can determine the interest charged on each loan as the loan multiplied by the interest rate

interest on 7.9% loan=7.9%*x=0.079x

interest on 7.4% loan=7.4%*(8200-x)

interest on 7.4% loan=606.80-0.074x

total interest=0.079x+606.80-0.074x

total interest=0.005x+606.80

total interest on loans=614.67

614.67=0.005x+606.80

614.67-606.80=0.005x

7.87=0.005x

x=7.87/0.005

x=amount loaned at 7.9%=$1,574.00

y=$8200-$1574

y=$6,626.00

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Answer: 210 cm

Step-by-step explanation:

1 inch=2.5 cm

1 foot=12 inches

1 foot*12 inches*2.5 cm=30 cm

1 foot=30 cm

7 feet=30*7=210 cm

Answer:

23

Step-by-step explanation:

you always do whatever is in the brackets first,

31 - 9 = 22

then the equation would be,

45 - 22

so the answer is 23

hope this helped xx