Solve this expression
(8c²) (9c)

The tringles ΔKLM, ΔXYZ, and ΔUVW are similar to the ΔHIJ.

What is the similarity of the triangles?

When it comes to Euclidean geometry, two things are said to be comparable if they have the same shape or the same shape as each other's mirror image. One can be created from the other more precisely by evenly scaling, possibly with the inclusion of further translation, rotation, and reflection.

We have,

In ΔHIJ

∠HIJ = 64°

∠JHI = 96°

and the side are

HI = 2 unit

IJ = 5.5 unit

HJ = 5 unit

So, the third angle will according to the sum of the angles of a triangle:

∠IJH = 20°

the triangles similar to ΔHIJ are:

A) It is similar to ΔHIJ cause,

∠HIJ ≅ ∠KLM

∠IJH ≅ ∠LMK

so, the third also will be equal:

∠JHI ≅ ∠LKM

D) It is similar to ΔHIJ cause,

∠IJH ≅ ∠XZY

HI/YX = 2/4 = 1/2

HJ/YZ = 5/10 = 1/2

C) It is similar to ΔHIJ cause,

HI/UV = 2/4 = 1/2

HJ/UW = 5/10 = 1/2

IJ/VW = 5.5/11 = 1/2

Hence, the tringles ΔKLM, ΔXYZ, and ΔUVW are similar to the ΔHIJ.

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Answer:

x = -2

Step-by-step explanation:

The first thing we can notice about this figure is that the two small outer triangles are congruent because of the given side congruence markings as well as the fact that the large triangle ABC is isosceles, thus angle A is congruent to angle C.

Using the above information, we can construct the equation:

3x + 2 = 2x

and solve it for x.

x = -2

The equation we constructed simply equates the corresponding sides of the two small outer triangles, as they are congruent by the CPCTC theorem.

Step-by-step explanation:

chances of rolling 1= 1/6

chances of rolling 2=1/6

chances of rolling anything else=2/3

2x+5y=18 equ(1)

x-3y=-2 equ(2)

from equ (2) make x the subject of the formula

x=-2+3y

substitute x=2+3y in equ (1)

2+(-2+3y)+5y=18

-4+6y+5y=18

6y+5y=18+4

11y/11=22/11

y=2

substitute y=2 in equ(2)

x+3(2)=-2

x-6=-2

x=-2+6

x=4

x=4 and y=2

The measure of angle A of the triangle is 50°.

How to find angles of the triangle?

Similar side interior angles therefore:

So, ∠C = ∠A

∠A = 50°

Hence, the measure of angle A of the triangle is 50°.

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Part a: P(A) = 1/2; P(B) =  2/3; P(C) = 1/12; P(A ∩ B ∩ C) = 1/36.

Part b: Part b: A, B, and C independent events.

Rolling a dice twice has 36 possible results, hence the following is the sample space:

S = {(1,1),(1,2),(1,3),(1,4),(1,5),(1,6),(2,1),(2,2),(2,3),(2,4),(2,5),(2,6),(3,1),(3,2),(3,3),(3,4),(3,5),(3,6),(4,1),(4,2),(4,3),(4,4),(4,5),(4,6),(5,1),(5,2),(5,3),(5,4),(5,5),(5,6),(6,1),(6,2),(6,3),(6,4),(6,5),(6,6)}

For the stated question-

Part a:  P(A), P(B),P(C), and P(A ∩ B ∩ C).

P(A) = 18/36 = 1/2

P(B) = 24/36 = 2/3

P(C) = 3/36 = 1/12

P(A ∩ B ∩ C) = 1/36

Part b: A, B, and C independent or not.

For the events to be independent,

P(A ∩ B ∩ C) = P(A).P(B).P(C)

P(A).P(B).P(C) = 1/2*2/3*1/12 = 1/36

As, P(A ∩ B ∩ C) = P(A).P(B).P(C).

Thus, the events are independent.

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Answer: -3/2

yeah use rise over run

Answer:

-2/3

Step-by-step explanation:

slope = rise/run

First find the y-intercept (point of crossing on the y-axis (the vertical one)), then find the next point that intercepts a box PERFECTLY, this next point is (4, -2)

Looking at the y-intercept's coordinates (0,1), count how many blocks down it takes to get to to 4 (2 blocks which is the RISE) and now count how many blocks to the right it takes to get to -2 (3 blocks)

Therefore it is 2/3 but it is also negative because it is going DOWN from left to right which is a negative decine

By solving the system of linear equations by elimination we get the value of x= 2 and y = 1.

What is the system of linear equations?

A grouping of one or more linear equation containing the same variables is known as a system of linear equations.

Here, we have

Given:  8x - 5y = 11....(1), 4x - 3y = 5...(2)

We solve equation(2) and find the value of x

4x = 5+ 3y

x = 5/4 + 3y/4

Now, we put the value of x in equation (1) and we get

8(5/4 + 3y/4) - 5y = 11

5×2 + 2×3y - 5y = 11

10 + y = 11

y = 1

Now, we put the value of y in equation(2) and we get

4x = 5+ 3(1)

4x = 8

x = 2

Hence, by solving the system of linear equations by elimination we get the value of x= 2 and y = 1.

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Hello,

I hope you and your family are doing well!

(a) The exponential growth model is given by the equation P(t) = P0 * r^t, where P(t) is the population t years after 2010, P0 is the population in 2010 (7420), and r is the annual growth rate (2.3%).

Substituting the given values into the equation gives us:

P(t) = 7420 * 1.023^t

This is the equation that estimates the population t years after 2010.

(b) To estimate the population of the town in 2022, we can substitute t = 12 into the equation:

P(12) = 7420 * 1.023^12

Calculating this gives us:

P(12) = 7420 * 1.023^12 = 7420 * 1.291891 = 9593.45

So the estimated population of the town in 2022 is approximately 9593

Happy to help!

Answer:

x = -6

Step-by-step explanation:

-6/3-4= -6

Answer:

18

Step-by-step explanation:

6-4=2

2x4=8

10+8=18

Answer:

Check out the image shown above/below

The total surface area of this triangular prism = 976

Surface area is the amount of space covering the outside of a three-dimensional shape.

A triangle would be divided in half, but since there are two, the ratio would remain the same.

 14 x 24 = 336

 10 x 25 = 250[ because there are two of them, multiply by 2.]

 10 x 14 = 140

The total surface area of this triangular prism = 336 + 250 + 140

                                                                            = 976

Therefore, the total surface area of this triangular prism = 976

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The values of x in the given equation, x² - 5x = -4, are x = 4 and x = 1

From the question, we are to solve the given equation by factoring

The given equation is

x² - 5x = -4

To solve the equation by factoring, transfer the constant to the other side of the equation

x² - 5x + 4 = 0

Factorize the left hand side expression

x² -x -4x + 4 = 0

x(x - 1) -4(x -1) = 0

(x - 4)(x - 1) = 0

x - 4 = 0 OR x - 1 = 0

x = 4 OR x = 1

Hence, the values of x are 4 and 1

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The number of acres owned for which the average intake is 2200 calories per day is 2 acres obtained by the algebraic expression that relates the acres of land and the calories per day.

It is given that, the number of calories consumed daily by a person owing x acres of land is given by the algebraic expression,

C(x) = 270 ln(x+1) + 1900

The average intake of calories consumed per day is given by C(x) = 2200

Here x is the number of acres of land. Then, the required number of acres of land is

C(x) = 270 ln(x+1) + 1900

⇒ 2200 = 270 ln(x+1) + 1900

⇒ 270 ln(x+1) = 2200 - 1900

⇒ 270 ln(x+1) = 300

⇒ ln(x+1) = 300/270 = 10/9

Applying base 'e' on both sides, we get

⇒ (x+1) = [tex]e^\frac{10}{9}[/tex]

⇒ x+1 = 3.0377

⇒ x = 3.0377 - 1 = 2.0377

When rounding the final answer to the nearest tenths, we get x = 2 acres.

When rounding the final answer to the nearest thousand, we get x = 2.038 acres.

Thus, for an average intake of 2200 calories per day, the number of acres of land owned is approximately 2 acres.

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The correct inequality which has no solution will be;

⇒ x ≤ –2 and 2x ≥ 6

⇒ x ≤ –1 and 5x ≤ 5

What is Inequality?

A relation by which we can compare two or more mathematical expression is called an inequality.

Given that;

There are some inequality is shown.

Now,

Find the inequality which has no solution as;

a) x ≤ –2 and 2x ≥ 6

⇒ x ≤ - 2

⇒ 2x ≥ 6 = x ≥ 6/2 = x ≥ 3

We get;

⇒ x ≤ - 2 and x ≥ 3

Which is not possible.

Hence, it has no solution.

b) x ≤ –1 and 5x ≤ 5

⇒ x ≤ - 1

⇒ 5x ≤ 5 = x ≤ 1

We get;

⇒ x ≤ - 1 and x ≤ 1

Which is not possible.

Hence, it has no solution.

c) x ≤ –1 and 3x ≥ –3

⇒ x ≤ - 1

⇒ 3x ≥ - 3 = x ≥ - 1

We get;

⇒ x ≤ - 1 and x ≥ - 1 ⇒ x = - 1

Thus, It has solution.

d)  x ≤ –2 and 4x ≤ –8

⇒  x ≤ –2 and

⇒ 4x ≤ - 8 = x ≤ - 2

Thus, It has solution.

Therefore, The correct inequality which has no solution will be;

⇒ x ≤ –2 and 2x ≥ 6

⇒ x ≤ –1 and 5x ≤ 5

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Answer: $3.55

Step-by-step explanation:

Started at 2.50 increased 4.75 which means the stock is 7.25 then decreased 1.25 making it 6 then another decrease of 2.45 making it $3.55

Answer:

6(4)-4=3(4)+8

24-4=12+8

20=20

Step-by-step explanation:

To prove x=4, substitute four into the equation

6(4)-4=3(4)+8

24-4=12+8

20=20

Therefore x=4 is proved

Answer:

(Answer in Image)

Step-by-step explanation:

6x-4=3x+8

6x-4-3x=3x+8-3x                    subtract -3x on both sides

3x-4=8                                    

3x-4+4=8+4                               add four on both sides

3x=12                                      simplify

3/3x=12/3                                       divide both sides by 3

x=4

12.6

Step-by-step explanation:

We need to find the hypotenuse

hyp² = opp² + adj²

hyp²= 2² + 3²

hyp²= 4 + 9

hyp²= 13

hyp=√13

hyp=3.6

sinθ=opp/hyp

sinθ=2/3.6

sinθ=5.6

cosθ=adj/hyp

cosθ=3/3.6

cosθ= 0.8

tan θ=sinθ/cosθ

tanθ= 5.6/0.8

tanθ=7

tan θ+sinθ

=7+5.6

=12.6

The system of equations that Tristan needs to solve is:

x*0.05 + y*0.10 = 1.40

x = 2*y

Let's define the variables:

x = number of nickels.

y = number of dimes.

Knowing that the net is $1.40 and that he has twice as many nickels as dimes, we can write:

x*0.05 + y*0.10 = 1.40

x = 2*y

That is our system of equations that Tristan can use to find the numbers of nickels and dimes.

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Answer:

(0,-5) , (3, -6) , (6, -7) ,(9, -8)

Step-by-step explanation:

I apologize for being unable to graph, but here are some of the points.

(0,-5) <-- The "y intercept"

slope is y2-y1/x2-x1, so "-1" is added to the "y" of the coordinate, and 3 is added to the "x"

(3,-6)

(6,-7)

(9,-8)

Hope this helps :)

C. x + 3y = 27 lines are perpendicular to 3x – y = 10

A line has length but no breadth, making it a one-dimensional figure. A line is made up of a collection of points that may be stretched indefinitely in opposing directions. In a two-dimensional plane, it is specified by two points. The term "collinear points" refers to two points that are on the same line.

As we know,

When two lines are perpendicular then the product of their slope is -1.

The slope is given by: y = mx+c

where, m is the slope.

Thus, the given equation:

3x – y = 10

y = 3x - 10

Comparing this equation with y = mx+c, we get

m₁ = 3

So, the slope of the given equation (m₁) = 3

Now find slope of others lines:

A) y = 3x + 5, Comparing this equation with y = mx+c, we get -

m₂ = 3

When two lines are perpendicular then the product of their slope is -1.

Here, product of the slope is:

= m₁ × m₂

= 3×3 (putting the values we get)

= 9 ≠ -1

So, this line is not perpendicular to given line.

B) y = –13x + 17, Comparing this equation with y = mx+c, we get -

m₃ = -13

When two lines are perpendicular then the product of their slope is -1.

Here, product of the slope is:

= m₁ × m₃

= 3× (-13) (putting the values we get)

= -39 ≠ -1

So, this line is not perpendicular to given line.

C) x + 3y = 27

3y = 27 - x

y = 9 - x/3, Comparing this equation with y = mx+c, we get -

m₄ = -1/3

When two lines are perpendicular then the product of their slope is -1.

Here, product of the slope is:

= m₁ × m₄

= 3× (-1/3) (putting the values we get)

= - 1

So, this line is perpendicular to given line.

D) y – 2 = 13(3x + 36)

y = 39x +470, Comparing this equation with y = mx+c, we get -

So, m₅ = 39

When two lines are perpendicular then the product of their slope is -1.

Here, product of the slope is:

= m₁ × m₅

= 3× (39) (putting the values we get)

= 117 ≠ -1

So, this line is not perpendicular to given line.

Therefore, option C is correct.

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Hello,

I hope you and your family are doing well!

If a ticket to the circus was 10% less on a Tuesday than it was on a Saturday, then it was 90% of the Saturday ticket price. If you paid $27 each to attend Tuesday's show, then the Saturday ticket price was $27 / 0.9 = $30.

Since you bought two tickets, the total cost of attending the circus on Saturday would have been 2 * $30 =60

Therefore, your total cost would have been $60 had you attended the circus on Saturday.

Please rate this answer 5 stars and brainliest if you find it helpful.

Happy Holidays and New Year!

Answer:

it is 3/5

Step-by-step explanation:

cos is the adjuacent devided by hypotenuse so it is 27/45 and that is 3/5

Answer:

A

Step-by-step explanation:

-2x + 9 < x - 9

-2x - x < -9 - 9

-3x < -18

x > -18/-3

x > 6

Yes, it is a proportional relationship. The relationship is distance (d) is directly proportional to time(t). The equation of the relationship is d= 65t

Direct Variation is said to be the relationship between two variables in which one is a constant multiple of the other. For example, when one variable changes the other, then they are said to be in proportion. If d( distance) is directly proportional to t( time) the equation is of the form d= kt (where k is a constant).

When d =65miles and t= 1hour, k =d/t

k= 65/1= 65

for other values of d and t, k = 65

Therefore the relationship between the distance and time is a proportional relationship. And the equation of the relationship is d= 65t

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The number of notebook is 36.

An equation is the statement that illustrates the variables given. In this case, two or more components are taken into consideration to describe the scenario.

Let the notebook be n.

Let the t shirt be t.

The equation will be:

n + t = 60 ..... i

7n + 12t = 540 ..... ii

From I n = 60 - t ..... iii

Put equation III into ii

7n + + 12t = 540 .

7(60 - t) + 12t = 540

420 - 7t + 12t = 540

5t = 540 - 420

5t = 120

Divide

t = 120 / 5

t = 24

Notebook will be:

= 60 - 24

= 36

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