Which input value produces the same output value for the two functions on the graph

Answer:

x=7, y=-7

Step-by-step explanation:

3x – y = 28

3x + y = 14

Add the two equations together

3x – y = 28

3x + y = 14

---------------------

6x = 42

Divide by 6

6x/6 = 42/6

x = 7

3x – y = 28

3x + y = 14

Multiply the second equation by -1, then add

3x – y = 28

-3x - y = -14

-------------------

      -2y=14

Divide by -2

-2y/-2 = 14/-2

y = -7

Answer:

5r^3 + 4r^2 - 8r + 16

Step-by-step explanation:

(8 + 5r^3 - 2r^2) - (8r - 8 - 6r^2) =

The first set of parentheses is there just to show you that what is inside is a polynomial. The second set of parentheses has a second polynomial inside. The subtraction sign just to the left of the second set of parentheses shows that you are subtracting the second polynomial from the first one.

The first set of parentheses is not needed and can be dropped.

You are subtracting the second polynomial fromt he first one, so you can think of the the subtraction sign as a -1, and you need to distribute the -1 by the second polynomial, That will result in all signs inside the second set of parentheses changing.

Below, just the first set of parentheses is removed.

= 8 + 5r^3 - 2r^2 - (8r - 8 - 6r^2)

Now, we change every sign inside the second set of parentheses by distributing -1.

= 8 + 5r^3 - 2r^2 - 8r + 8 + 6r^2

Now we need to combine like terms. Like terms have the same variable part. We can rearrange the terms grouping like terms together before combining them. Also, it is customary to list the terms in descending order of degree.

= 5r^3 - 2r^2 + 6r^2 - 8r + 8 + 8

Now we combine like terms.

= 5r^3 + 4r^2 - 8r + 16

Answer:

The probability is 0.9973 or 99.73%

Step-by-step explanation:

* Lets explain how to solve the problem

- For the probability that a < X < b (X is between two numbers, a and b),

 convert a  and b into z-scores and use the table to find the area

 between the two z-values.

- Lets revise how to find the z-score

- The rule the z-score is z = (x - μ)/σ , where

# x is the score

# μ is the mean

# σ is the standard deviation

* Lets solve the problem

- For certain workers, the mean wage is $5.00/hr, with a standard

 deviation of $0.25

∴ μ = 5 and σ = 0.25

- The worker wage is between $4.25 and $5.75

∴ 4.25 < X < 5.75

∵ z = (x - μ)/σ

∴ z = (4.25 - 5)/0.25 = -0.75/0.25 = -3

∴ z = (5.75 - 5)/0.25 = 0.75/0.25 = 3

- Use the z table to find the corresponding area

∵ P(z > -3) = 0.00135

∵ P(z < 3) = 0.99865

∴ P(-3 < z < -2) = 0.99865 - 0.00135 = 0.9973

∵ P(4.25 < X < 5.75) = P(-3 < z < 3)

∴ P(4.25 < X < 5.75) = 0.9973 = 99.7%

* The probability is 0.9973 or 99.73%

Using the z-score method, we found that there is approximately a 99.74% chance that a randomly chosen worker's wage is between $4.25 and $5.75, given the wages follow a normal distribution.

To determine the probability that a randomly chosen worker's wage is between $4.25 and $5.75 when the mean wage is $5.00/hr with a standard deviation of $0.25, we'll use the properties of the normal distribution. First, we need to convert the wages into z-scores, which are measures of how many standard deviations away from the mean a value is.

To find the z-score for $4.25: Z = (4.25 - 5.00) / 0.25 = -3. To find the z-score for $5.75: Z = (5.75 - 5.00) / 0.25 = 3. Using these z-scores, we can look up the corresponding probabilities in a standard normal distribution table or use a calculator equipped with a normal distribution function.

The probability of a z-score between -3 and 3 is approximately 0.9974, meaning there is about a 99.74% chance that a randomly chosen worker's wage is between $4.25 and $5.75, given the distribution of wages is normal.

Answer: 15%

Step-by-step explanation: i just subtracted 714 from 840 then i started by multiplying by 10% and increasing until it gave me 126 which is what you get from subtracting 714 from 840

Answer:

B

Step-by-step explanation:

you add the like terms together and find the value of x multiple by 4

[tex]3b-7<32\\3b<39\\b<13[/tex]

Answer:

5[tex]\sqrt[4]{x}[/tex]

Step-by-step explanation:

Here we are given a verbal expression, we need to convert it to algebraic expression.

5 times x to the one fourth power.

Word                       Meaning

Times                          *(Multiplication)

one fourth                     [tex]\frac{1}{4}[/tex]

So, 5 times x to the one fourth power is = 5*[tex]x^{\frac{1}{4}}[/tex]

Now we have to write in using radical sign.

[tex]x^{\frac{1}{4} } = \sqrt[4]{x}[/tex]

Therefore, 5*[tex]x^{\frac{1}{4}}[/tex] = 5[tex]\sqrt[4]{x}[/tex]

Answer:

x=1 and x=0

Step-by-step explanation:

We need to find the points at which the graphs y = x^2 + x – 2 and y = 2x – 2 intercept.

We know that:

x^2 + x – 2 =  2x – 2

x^2 - x = 0

Factorizing:

x(x-1) = 0

Therefore, the solution to the system of equation is x=1 and x=0.

Answer:

(a) The two ordered pairs are (0 , 340) and (4 , 285)

(b) The slope is m = -55/4

The slope means the rate of decreases of the owl population was 55/4

per year (P decreased by 55/4 each year)

(c) The model equation is P = -55/4 t + 340

(d) The owl population in 2022 will be 216

(e)  At year 2038 will be no more owl in the park

Step-by-step explanation:

* Lets explain how to solve the problem

- The owl population in 2013 was measured to be 340

- In 2017 the owl population was measured again to be 285

- The owl population is P and the time is t where t measure the numbers

 of years since 2013

(a) Let t represented by the x-coordinates of the order pairs and P

   represented by the y-coordinates of the order pairs

∵ t is measured since 2013

∴ At 2013 ⇒ t = 0

∵ The population P in 2013 was 340

∴ The first order pair is (0 , 340)

∵ The time from 2013 to 2013 = 2017 - 2013 = 4 years

∴ At 2017 ⇒ t = 4

∵ The population at 2017 is 285

∴ The second order pair is (4 , 285)

* The two ordered pairs are (0 , 340) and (4 , 285)

(b) The slope of any lines whose endpoints are (x1 , y1) and (x2 , y2)

     is [tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

∵ (x1 , y1) is (0 , 340) and (x2 , y2) is (4 , 285)

∴ x1 = 0 , x2 = 4 and y1 = 340 , y2 = 285

∴ [tex]m = \frac{285-340}{4-0}=\frac{-55}{4}[/tex]

* The slope is m = -55/4

∵ The slope is negative value

∴ The relation is decreasing

* The slope means the rate of decreases of the owl population was

  55/4 per year (P decreased by 55/4 each year)

(c) The linear equation form is y = mx + c, where m is the slope and c is

    the value of y when x = 0

∵ The population is P and represented by y

∵ The time is t and represented by t

∴ P = mt + c , c is the initial amount of population

∵ m = -55/4

∵ The initial amount of the population is 340

∴ P = -55/4 t + 340

* The model equation is P = -55/4 t + 340

(d) Lets calculate the time from 2013 to 2022

∵ t = 2022 - 2013 = 9 years

∵ P = -55/4 t + 340

∴ P = -55/4 (9) + 340 = 216.25 ≅ 216

* The owl population in 2022 will be 216

(e) If the model is accurate , then the owl population be be zero after

    t years

∵ P = -55/4 t + 340

∵ P = 0

∴ 0 = -55/4 t + 340

- Add 55/4 t to both sides

∴ 55/4 t = 340

- Multiply both sides by 4

∴ 55 t = 1360

- Divide both sides by 55

∴ t = 24.7 ≅ 25 years

- To find the year add 25 years to 2013

∵ 2013 + 25 = 2038

* At year 2038 will be no more owl in the park

Answer:

Option B x=6 units

Step-by-step explanation:

we know that

If two figures are similar, then the ratio of its corresponding sides is proportional and its corresponding angles are congruent

In this problem

Triangles ABC and DEF are similar

therefore

∠A≅∠D

∠B≅∠E

∠C≅∠F

and

AB/DE=BC/EF=AC/DF

Find the value of x

AB/DE=BC/EF

substitute the given values

x/3=16/8

x=3*16/8

x=6 units

44 is 11% of 400. To find the number that 44 is 11% of, you divide 44 by 0.11.

The question asks for an equation to represent the scenario where 44 is 11% of a number. In algebraic terms, this is represented as:

44 = 0.11  times x

To find x, divide both sides of the equation by 0.11:

x = 44 / 0.11

Calculating this gives us x = 400, which means that 44 is 11% of 400.

Answer:

Step-by-step explanation:

The y-intercept is exist for x = 0.

We have the equation of the function: f(x) = x² + 3x + 5 → y = x² + 3x + 5.

Put x = 0:

y = 0² + 3(0) + 5 = 0 + 0 + 5 = 5

The correct option is option D: The y-intercept of the graph of the function will be (0,5).

The y-intercept of the function is determined by the point where the graph intercepts the y-axis.

At the point where the graph meets the y-axis, the x coordinate will be 0.

So by putting the x value =0 in the graph function, we can determine the y-intercept of the graph function. i.e. y=f(0)

Here, the function is given by f(x)=x²+3x+5

At the y-intercept point the x coordinate=0

So putting x=0, we can determine the y-intercept of the graph.

f(0)=0²+0+5=5

The y-coordinate of the y-intercept is 5.

The x-coordinate of the y-intercept is 0.

So the coordinate of the y-intercept is (0,5).

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Answer:

3)5x-4y=-3

6x+4y=14

Step-by-step explanation:

The system of equations is given

5x-4y=-3

3x+2y=7

Multiplying both sides of the lower equation by 2, we get

6x + 4y = 14

That means your answer 3)

The system with the same solution as the given system of equations is the one where the second equation is a multiple of the original. In this case, option 2) 5x - 4y = -3 and 6x + 2y = 14 shows the same solution set, as it is the only one that is equivalent to the original system after multiplying the second equation by 2.

The student is trying to identify which system of equations has the same solution as the original system given by:

When comparing this system to the provided options, we look for a system that is equivalent after applying some algebraic operations, since the solutions of equivalent systems are the same. For the second equation in each system, it must be a multiple of the original (3x + 2y = 7), or it must be alterable to be equivalent through multiplicative or additive operations.

In case of options:

The only system that is equivalent to the original one is the second option because doubling the second equation of the original system (3x + 2y = 7) gives us 6x + 4y = 14, which has the same solution set as the original system.

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Answer:

f(x)=(7(x-2)(x+5))/((x-1)(x+1))

Step-by-step explanation:

The vertical asymptotes should be in the denominator. The x-interceps should be in the numerator. Because the horizontal asymptote is y=7, you have to put 7 in the numerator because the horizontal asymptote is the coefficient of the numerator ÷ the coefficient of the denominator, when we have the same degree of the numerator and the denominator.

Answer:

12

Step-by-step explanation:

48 x 1/4

Multiply the total number of people by 1/4:

48 x 1/4 = 48/4

Simplify by dividing 48 by 4:

48 / 4 = 12

12 people had blue swimsuits.

Answer:

Step-by-step explanation:

1 yard = 3 feet

5yd 2ft = (5)(3)ft + 2ft = 17ft

6yd 1ft = (6)(3)ft + 1ft = 19ft

The formula of an area of a rectangle:

A = wl

w - width

l - length

Substitute w = 19ft and l = 17ft:

A = (19)(17) = 323 ft²

Answer:

15 teachers

Step-by-step explanation:

Given:

number of children is c

number of teachers is t

[tex]\frac{c}{t}[/tex] = [tex]\frac{14}{3}[/tex] (rearrange)

t = [tex]\frac{3}{14}[/tex] x C

When C = 70,

t = [tex]\frac{3}{14}[/tex] x 70

t = 15 teachers

Answer:

[tex] \frac{c}{t } = \frac{14}{3} [/tex]

as c=70 so put value of c in above formula we get

[tex] \frac{70}{t} = \frac{14}{3} [/tex]

by cross multiplication

[tex]70 \times 3 = 14t[/tex]

[tex]210 = 14t[/tex]

[tex] \frac{210}{14} = t[/tex]

t=15

i hope u will understand

Answer: 61.1

Step-by-step explanation: The answer would be 61.1 because .062 is greater than .05, which means that it rounds up.

Answer:

x^2 / 25 + y^2 / 9 = 1

Step-by-step explanation:

The major axis is along the x axis and the minor axis is on the y axis.

Major axis = 2a =  5--5 =10 so a = 5 and a^2 = 25.

Similarly b^2 = 3^2 = 9.

Answer:

[tex]\frac{x^2}{25}+\frac{y^2}{9}=1[/tex]

Step-by-step explanation:

Equation of ellipse is of form [tex]\frac{x^2}{a^2}+\frac{y^2}{b^2}=1[/tex] where [tex](a,0) , (-a,0)[/tex] are the x-intercepts and [tex](0,b) , (0,-b)[/tex] are the y-intercepts . If [tex]a > b[/tex] then it is a horizontal ellipse and if [tex]a < b[/tex] then it is a vertical ellipse .

For horizontal axis ,

Here, [tex](a,0) , (-a,0)[/tex] are known as the vertices of ellipse and [tex](0,b) , (0,-b)[/tex] are the co-vertices of ellipse .

Horizontal axis is known as the major axis and vertical axis is known as the minor axis .

Here, x-intercepts are [tex](5,0) , (-5,0)[/tex] , take a = 5

y-intercepts are [tex](0,3) , (0,-3)[/tex] , take b = 3

As [tex]a > b[/tex] , it is a horizontal ellipse .

On putting a = 5 and b = 3 , we get equation as

[tex]\frac{x^2}{5^2}+\frac{y^2}{3^2} =1\\ \frac{x^2}{25}+\frac{y^2}{9} =1[/tex]

Answer:

a) 50

Step-by-step explanation:

The angle formed by two chords is the average of the arc angles.

7x = (5x + 90) / 2

14x = 5x + 90

9x = 90

x = 10

So the measure of arc EC is 5x = 50°.

The measure of arc EC is  a) 50

The angle of a complete circle is 360°

The angle formed by two chords angle= arc/radius

  ⇒7x = (5x + 90) / 2

  ⇒14x = 5x + 90

  ⇒ 9x = 90

  ⇒x = 10

So the arc EC is 5x = 50°.

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Check  the picture below.

Answer: X=5

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

Answer:

Not geometric

Step-by-step explanation:

In a geometric sequence, each term is multiplied by a common ratio to get the next term.

So if this is a geometric sequence, then dividing each term by the one before it should result in the same common ratio.

42 / 21 = 2

126 / 42 = 3

504 / 126 = 4

The ratios are different.  This is not a geometric sequence.

Answer:

Some tips for the future, when trying to find if its arithmetic or geometric sequence we can do this to find the common ratio. Arithmetic; subtraction test Geometric; division test

Ex; 19, 25, 31, 37

Subtract-

37-31= 6

31-25= 6

25-19= 6

6 is the common difference for this arithmetic sequence

Ex; 4, 8, 16, 32

Divide-

32/16= 2

16/8= 2

8/4= 2

The common ratio for the geometric sequence is 2

Step-by-step explanation:

21, 42, 126, 504

504/126= 4

126/42= 3

42/21= 2

This is not a geometric sequence, there is no common ratio.

Answer:

40 degrees

Step-by-step explanation:

The alternate interior angles are equal when parallel lines are cut by transversal.

Basically the angle 70 would be equal to the 2 angles (x and 30). Thus we can say:

70 = 30 + x

x = 70 -30

x = 40

Hence x is 40 degrees

Graph C

This is a piecewise-defined function because it is defined by two equations over a specified domain and this domain is [tex][0,5][/tex]. The first function comes from the pattern of the square root function [tex]f(x)=\sqrt{x}[/tex] and the second one is a linear function.

The graph of [tex]3\sqrt{x+1}[/tex] has been shifted one unit to the left of [tex]f(x)=\sqrt{x}[/tex] and stretched vertically where each y-value is multiplied by 3.

Moreover, we can prove that:

The graph of [tex]3\sqrt{x+1}[/tex] passes through points (0,3) and (3,6):

[tex]y= 3\sqrt{x+1} \\ \\ \\ \bullet \ (0,3): \\ \\ let \ x=0: \\ \\ y= 3\sqrt{0+1} \therefore y=3\sqrt{1} \therefore y=3(1) \therefore y=3 \\ \\ \\ \bullet \ (3,6): \\ \\ let \ x=3: \\ \\ y= 3\sqrt{3+1} \therefore y=3\sqrt{4} \therefore y=3(2) \therefore y=6[/tex]

It passes through these points.

The graph of [tex]5-x[/tex] passes through points (5,0) and (3,2):

[tex]y=5-x \\ \\ \\ \bullet \ (5,0): \\ \\ let \ x=5: \\ \\ y=5-0 \therefore y=5 \\ \\ \\ \bullet \ (3,2): \\ \\ let \ x=3: \\ \\ y=5-3 \therefore y=2[/tex]

It passes through these points.

____________________

Ans:

24 chairs in 9th row and 144 chairs in ist 9th rows

Step-by-step explanation:

ist row= 8

2nd = 10

3rd =  12

.

.

.

9th row = 24

and if we add all chairs = 8+10+12+14+16+18+20+22+24= 144

The requried, there are 24 chairs in the 9th row and there are 144 chairs in total in the first 9 rows.

Arithmetic progression is the series of numbers that have common differences between adjacent values

The first row has 8 chairs, and each subsequent row has 2 more chairs than the previous row. So the number of chairs in each row can be given by the equation:

number of chairs = 8 + 2(row - 1)

To find the number of chairs in the 9th row, we substitute row = 9 into the equation:
number of chairs = 8 + 2(9 - 1) = 8 + 2(8) = 24

So there are 24 chairs in the 9th row.

To find the total number of chairs in the first 9 rows, we need to add up the number of chairs in each row from 1 to 9. This can be done using the formula for the sum of an arithmetic series:

sum = (n/2)(first term + last term)
where "n" is the number of terms in the series.

In this case, the first term is 8, the last term is 24, and there are 9 terms (i.e. the first 9 rows). Substituting these values into the formula, we get:

sum = (9/2)(8 + 24) = 9(16) = 144

So there are 144 chairs in total in the first 9 rows.

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Answer:

First one.

Step-by-step explanation:

You don't need the diagram.

You need the congruence statement.

In a congruence statement, it tells you the correspond parts (the congruent parts).

Angle T = Angle L because T and L are both in 2nd position.

Segment TD=Segment SG is false because while D and G share the same position, T and S don't.

Segment MT=Segment GL is false because M and G do not share the same position while T an L do.

Use the order. The order does matter.

Answer:

Step-by-step explanation:First one.

Step-by-step explanation:

You don't need the diagram.

You need the congruence statement.

In a congruence statement, it tells you the correspond parts (the congruent parts).

Angle T = Angle L because T and L are both in 2nd position.

Segment TD=Segment SG is false because while D and G share the same position, T and S don't.

Segment MT=Segment GL is false because M and G do not share the same position while T an L do.

Use the order. The order does matter.

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Answer:

1) Cubic

2) 2

3) -3

4) [tex]\frac{1}{9}x^{3}[/tex]

5) [tex]\frac{1}{9}[/tex]

Step-by-step explanation:

The given polynomial is:

[tex]\frac{1}{9}x^{3}-3[/tex]

The degree i.e. the highest exponent of the variable involved is 3. So the polynomial is a Cubic polynomial.

The terms in a polynomial can be distinguished by addition and subtraction symbols. So, for the given polynomial there are 2 terms.

The constant term is the term without any variable. So the constant term in given polynomial is -3.

Leading term is the term with variable having highest exponet which defines the degree of the polynomial. So leading term of the given polynomial is [tex]\frac{1}{9}x^{3}[/tex]

Leading coefficient is the coefficient of the leading term. So for given polynomial the leading coefficient would be [tex]\frac{1}{9}[/tex]

Answer:

(x - 3)(x - 1)

Step-by-step explanation:

Consider the factors of the constant term (+ 3) which sum to give the coefficient of the x- term.

The factors are - 3 and - 1, since

- 3 × - 1 = + 3 and - 3 - 1 = - 4, hence

x² - 4x + 3 = (x - 3)(x - 1) ← in factored form

Answer:

Factors are (x-1) (x-3)

Step-by-step explanation:

X^2-4x+3 = 0

x² - x - 3x + 3 =0

x(x - 1) -3(x - 1) = 0

        (x-1) (x-3) =0

The symbol [tex]\lor[/tex], from the latin "vel", which means "or", is indeed the logical "or" operator.

This operator puts together two statements A and B, and [tex]A\lor B[/tex] is true whenever at least one between A and B is true.

So, in this case, [tex]p \lor q[/tex] is true whenever either p is true, or q is true, or both are true.

So, every number which is less than -3 or more than 3 makes [tex]p \lor q[/tex] true.

Mathematically, this is the same as claiming that [tex]|x|>3[/tex]