y=3x-34
у = 2x — 5
Help me with this

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 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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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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Answer:

Check out the image shown above/below

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

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

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: $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

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!

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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Answer:

A

Step-by-step explanation:

-2x + 9 < x - 9

-2x - x < -9 - 9

-3x < -18

x > -18/-3

x > 6

The simplified form in base 3 for ln(3) + ln(9) is 3ln(3)

logarithm, the exponent or power to which a base must be raised to yield a given number. Expressed mathematically, x is the logarithm of n to the base b if b^x = n, in which case one writes x = logb n.

In(9) can be written as ln3^2

which according law of logarithm is 2ln(3)

Expression becomes

ln(3) + 2ln(3) which is 3ln(3)

In conclusion, the simplified form of the expression in base 3 is 3ln(3)

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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.

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 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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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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There are $20468.55 must you deposit now in order to have $25,000 in 4 years in an account getting 5% interest compounded daily.

What is compound interest?

Compound interest, also known as interest on principal and interest, is the practice of adding interest to the principal amount of a loan or deposit.

Given:

A = Final amount = $25000

P = Initial principle balance

r = interest rate = 5% = 0.05

t = Number of time of years

n = number of times interest applied per time period = 365

Since, the formula for compound interest,

[tex]A = P(1+\frac{r}{n})^n^t[/tex]

Plug the values of A, r, n and t in the above formula

[tex]25000 = P(1 + \frac{0.05}{365})^3^6^5^*^4 \\25000 = P(1.0001369863)^1^4^6^0\\25000 = P(1.2213860258)\\P = 20,468.549231702[/tex]

P ≈ 20,468.55

Hence, there are $20468.55 must you deposit now in order to have $25,000 in 4 years in an account getting 5% interest compounded daily.

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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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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:

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

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

The probability of the customer wants to take snack B is 144/320 as they have already taken snack A

and the probability of the customer who has not taken snack A before

wants to take snack A =108/252

It is the ratio of favorable outcome to total possible outcome of an event.

based on given data, we calculated the number of customers who has taken snack A before may want to take snack B. The customers have not taken snack A yet may want to snack A.

hence, probability to take snack B = 144/320

probability to take A =108/252

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a) The probability a person who has eaten snack A before is 59/143.

b) The probability a person who has eaten snack A before is 84/143

What is probability?

Simply put, probability is the likelihood that something will occur. When we don't know how an event will turn out, we can discuss the likelihood or likelihood of several outcomes. Statistics is the study of events that follow a probability distribution.

Given that the total number of people that are taken for the event is 572.

The number of people who have eaten snack A before is 236.

The number of people who have not eaten snack A before is 336.

Probability = The number of outcomes of favorable event/ Total number of outcomes

The probability getting a person who has eaten snack A before is

= 236/ 572

= 59/143 [Divide denominator and numerator by 4]

The probability getting a person who has not eaten snack A before is

= 336/ 572

= 84/143 [Divide denominator and numerator by 4]

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The amounts of each type of coin that they have is given as follows:

The amounts of each type of coin are obtained using a system of equations, in which the variables are given as follows:

Kevin and Randy Muise have a jar containing 83 coins, hence:

x + y = 83.

The value of a nickel is of $0.05, while the value of a quarter is of $0.25. The total value of the coins in the jar is $12.95, hence:

0.25x + 0.05y = 12.95.

From the first equation, we have that:

y = 83 - x.

Replacing on the second equation, the amount of quarters is given as follows:

0.25x + 0.05(83 - x) = 12.95

0.2x = 8.8

x = 8.8/0.2

x = 44.

Then the amount of nickels is given as follows:

y = 83 - x = 83 - 44 = 39.

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The number of games that must be played for the cost to be the same at both places is 4.

Bowl o rama charges 2.50 a game plus 2 for shoe rental, and bowling pinz charges 2 a game plus 4 for shoe rental.

The number of games that must be played for the cost to be the same at both places is as follows:

Using system of equation,

let

x = number of games

Hence,

2.50x + 2 = 2x + 4

2.50x - 2x = 4 - 2

0.5x = 2

divide both sides by 0.5

x = 2 / 0.5

x = 4

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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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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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