What is the linear function equation represented by the graph? Enter your answer in the box. f(x) =​

[tex]\bold{\huge{\underline{ Solution }}}[/tex]

• [tex]\sf{ Polynomial :- ax^{2} + bx + c }[/tex]

• The zeroes of the given polynomial are α and β .

Here, we have polynomial

[tex]\sf{ = ax^{2} + bx + c }[/tex]

We know that,

Sum of the zeroes of the quadratic polynomial

[tex]\sf{ {\alpha} + {\beta} = {\dfrac{-b}{a}}}[/tex]

And

Product of zeroes

[tex]\sf{ {\alpha}{\beta} = {\dfrac{c}{a}}}[/tex]

Now, we have to find the polynomials having zeroes :-

[tex]\sf{ {\dfrac{{\alpha} + 1 }{{\beta}}} ,{\dfrac{{\beta} + 1 }{{\alpha}}}}[/tex]

Therefore ,

Sum of the zeroes

[tex]\sf{ ( {\alpha} + {\dfrac{1 }{{\beta}}} )+( {\beta}+{\dfrac{1 }{{\alpha}}})}[/tex]

[tex]\sf{ ( {\alpha} + {\beta}) + ( {\dfrac{1}{{\beta}}} +{\dfrac{1 }{{\alpha}}})}[/tex]

[tex]\sf{( {\dfrac{ -b}{a}} ) + {\dfrac{{\alpha}+{\beta}}{{\alpha}{\beta}}}}[/tex]

[tex]\sf{( {\dfrac{ -b}{a}} ) + {\dfrac{-b/a}{c/a}}}[/tex]

[tex]\sf{ {\dfrac{ -b}{a}} + {\dfrac{-b}{c}}}[/tex]

[tex]\bold{{\dfrac{ -bc - ab}{ac}}}[/tex]

Thus, The sum of the zeroes of the quadratic polynomial are -bc - ab/ac

Product of zeroes

[tex]\sf{ ( {\alpha} + {\dfrac{1 }{{\beta}}} ){\times}( {\beta}+{\dfrac{1 }{{\alpha}}})}[/tex]

[tex]\sf{ {\alpha}{\beta} + 1 + 1 + {\dfrac{1}{{\alpha}{\beta}}}}[/tex]

[tex]\sf{ {\alpha}{\beta} + 2 + {\dfrac{1}{{\alpha}{\beta}}}}[/tex]

[tex]\bold{ {\dfrac{c}{a}} + 2 + {\dfrac{ a}{c}}}[/tex]

Hence, The product of the zeroes are c/a + a/c + 2 .

We know that,

For any quadratic equation

[tex]\sf{ x^{2} + ( sum\: of \:zeroes )x + product\:of\: zeroes }[/tex]

[tex]\bold{ x^{2} + ( {\dfrac{ -bc - ab}{ac}} )x + {\dfrac{c}{a}} + 2 + {\dfrac{ a}{c}}}[/tex]

Hence, The polynomial is x² + (-bc-ab/c)x + c/a + a/c + 2 .

• Polynomial is algebraic expression which contains coffiecients are variables.

• There are different types of polynomial like linear polynomial , quadratic polynomial , cubic polynomial etc.

• Quadratic polynomials are those polynomials which having highest power of degree as 2 .

• The general form of quadratic equation is ax² + bx + c.

• The quadratic equation can be solved by factorization method, quadratic formula or completing square method.

Step-by-step explanation:

See the attached pics it explains everything

Answer:

Corresponding Angles Theorem

When a straight line intersects 2 parallel lines, the angles in the same relative position are congruent (equal).

Alternate Exterior Angles Theorem

When a straight line intersects 2 parallel lines, the alternate exterior angles are congruent (equal).

Vertical Angle Theorem

When two straight lines intersect, the vertical angles are congruent (equal).

Q1.   As  s ║ c  we can apply the Corresponding Angles Theorem:

⇒ 11x - 5 = 116

⇒ 11x - 5 + 5 = 116 + 5

⇒ 11x = 121

⇒ 11x ÷ 11 = 121 ÷ 11

⇒ x = 11

Q2.   As  s ║ c  we can apply the Alternative Exterior Angles Theorem:

⇒ 12x - 4 = 148

⇒ 12x - 4 + 4 = 148 + 4

⇒ 12x = 152

⇒ 12x ÷ 12 = 152 ÷ 12

⇒ x = 38/3 = 12.7 (nearest tenth)

Q1.   As  j ⊥ r  then the sum of the angles is 90°

⇒ 4x + 6x + 10 = 90

⇒ 10x + 10 - 10 = 90 - 10

⇒ 10x = 80

⇒ 10x ÷ 10 = 80 ÷ 10

⇒ x = 8

Q2.  As  j ⊥ r   we can apply the Vertical Angles Theorem:

⇒ 5x - 10 = x + 70

⇒ 5x - 10  + 10 = x + 70 + 10

⇒ 5x = x + 80

⇒ 5x - x = x + 80 - x

⇒ 4x = 80

⇒ 4x ÷ 4 = 80 ÷ 4

⇒ x = 20

Answer: Length of side QR is 16 units.

Step-by-step explanation: Given that dimensions of  PQR

QPR= 90degrees

The u-x and o-x from the given parameters of the population and the sample size will be u =28 and standard deviation is 5.

From the information given about the population and sample mean, the values include:

u=27 o=5 n=14

The standard deviation will be:

= 5/✓14

= 5/3.74

= 1.34

Therefore, u-x and o-x from the given parameters of the population and the sample size will be u =28 and standard deviation is 1.34.

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Answer:

The graph has been moved 7 units to the left and 8 units down.

Step-by-step explanation:

When numbers are added directly to the "x" value, the graph shifts to the left. If negative numbers are added directly to the "x" value, the grap shifts to the right. Therefore, if there is a +7 directly altering the "x" value, the function shifts 7 units to the left.

When a number is added to the overall function, it shifts upwards. If this number is negative, the entire function shifts downwards. Therefore, if there is a -8 outside altering the function, then it has been shifted 8 units down.

Answer:

A ≈ 43.3 cm²

Step-by-step explanation:

the area (A) of an equilateral triangle is calculated as

A = [tex]\frac{s^2\sqrt{3} }{4}[/tex] ( s is a side of the triangle )

given perimeter = 30 cm , then

s = 30 cm ÷ 3 = 10 cm

then

A = [tex]\frac{10^2\sqrt{3} }{4}[/tex] = [tex]\frac{100\sqrt{3} }{4}[/tex] = 25[tex]\sqrt{3}[/tex] ≈ 43.3 cm² ( to the nearest tenth )

Answer:

Step-by-step explanation:

The parabola y=x^2 is shifted up by 7 units and to the left by 1 unit.

Answer:

y=(x+1)^2 +7

When the parabola y=x² is  shifted up by 7 units and to the left by 1 unit then the equation of the new parabola is y = (x-1)² + 7.

When a parabola is shifted vertically or horizontally, its equation changes accordingly.

In this case, the parabola y = x² is shifted up by 7 units and to the left by 1 unit.

Adding a constant value to the function shifts the graph vertically.

In this case, adding 7 to the original function y = x² will shift it up by 7 units:

y = x² + 7

Subtracting a constant value from the input of the function shifts the graph horizontally.

In this case, subtracting 1 from the x-values of the function y = x² + 7 will shift it to the left by 1 unit:

y = (x-1)² + 7

Hence,  the equation of the new parabola after both shifts is y = (x-1)² + 7.

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Step-by-step explanation:

it is very simple, once you remember that "kilo" means 1000, "mili" means 1/1000, and "centi" means 1/100.

and therefore 1 cg = 10 mg, or 1 cm = 10 mm.

"deci" means 1/10.

and therefore 1 dm = 100 mm, 1dg = 100 mg.

1.

9.32 kg = 9.32×1000 = 9320 g

2.

1.429 g = 1.429/1000 = 0.001429 kg

3.

287 g = 287/1000 = 0.287 kg

4.

4.6 L = 4.6×1000 = 4600 mL

5.

0.119 L = 0.119×1000 = 119 mL

6.

9936 mL = 9936/1000 = 9.936 L

7.

26793 mL = 26793/1000 = 26.793 L

8.

0.06 L = 0.06×1000 = 60 mL

9.

170 cg = 170×10 = 1700 mg

10.

2674 cm = 2674/100 = 26.74 m

11.

9.05 mm = 9.05/100 = 0.0905 dm

12.

2 L = 2×1000 = 2000 mL

13.

62.4 L = 62.4×1000 = 62400 mL

14.

99.9 mm = 99.9/1000 = 0.0999 m

15.

4.34 g = 4.34×100 = 434 cg

16.

10 km = 10×1000 m = 10×1000×1000 = 10000000 mm

17.

65 cL = 65/100 = 0.65 L

18.

105 mL = 105/1000 = 0.105 L

19.

0.27 g = 0.27×100 = 27 cg

20.

7777 m = 7777/1000 = 7.777 km

The value of the constant a will the system of linear equations 6x-5y=3 and 3x+ay=1 have no solution is -5/2

For a system of equation to have no solution, the expression on both sides must be different.

Given the system of equation

6x-5y=3 and

3x+ay=1

For the equations to have no solution, the a1/a2= b1/b2

Substitute

6/3 = -5/a

Cross multiply

2 = -5/a

a= -5/2

Hence the value of the constant a will the system of linear equations 6x-5y=3 and 3x+ay=1 have no solution is -5/2

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Answer:

a. 1/760

b.1/1140

c.27/8000

d.3/5000

I chose D, is this correct

Step-by-step explanation:

Based on the calculations below, the weekly gross pay of John Pelson is $1,339.90.

Let G represents weekly gross pay. The gross pay can now be calculated as follows:

Net pay = G – FIT – SIT – CIT - Health insurance – Charity ……………….. (1)

Substitute all the relevant values into the equation (1) and solve as follows:

$972.11 = G – $185.00 – 0.05G – 0.02G – $64.00 – $25.00

$972.11 + $185.00 + $64.00 + $25.00 = G – 0.05G – 0.02G

$1,246.11 = (1 – 0.05 – 0.02)G

$1,246.11 = 0.93G

G = $1,246.11 / 0.93

G = $1,339.90

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Answer:

P (blue) = 23 / 82

Step-by-step explanation:

There are 23 blue out of 82 (28 + 21 + 23 + 10 = 82) balls

or,

23 / 82

So, the probability of a blue ball being chosen is  23/82  

(or a 28% chance [rounded])

The first step to solving almost any problem is to determine what the question is asking and what is given to us to help solve that problem.  Looking at the problem statement, they are asking for us to determine which option best describes the value of m in the expression provided.  The only thing that we are provided with is an expression which we need to solve for m.

Let's begin to solve the expression for m by first dividing both sides by -5.  However, since we are dividing by a negative, that means that we must flip the sign.

Divide both sides by -5

The next step that we must take is to subtract 1 from both sides but before that let's convert it into an improper fraction with a denominator of 5 so we can easily deal with it with the other fraction.

Subtract both sides by 1

We have finally came up to our final answer which would state that m is greater than or equal to negative 28 over 5.  The options that you have provided seem like the formatting has messed up but I'm sure that on your side you can see the correct answer.

Answer:

C

Step-by-step explanation:

A quadrilateral is a shape with 4 sides.

A is a triangle, 3 sides

B is a pentagon, 5 sides

D is a hexagon, 6 sides

C is a quadrilateral, 4 sides

Answer:

Step-by-step explanation:

c

a quadrillateral quadrilateral has four sides

Answer:

the revenue is 280 by 190

The area of a 2D form is the amount of space within its perimeter. The surface area of the cone is 108.79967 units².

The area of a 2D form is the amount of space within its perimeter. It is measured in square units such as cm2, m2, and so on. To find the area of a square formula or another quadrilateral, multiply its length by its width.

Given the diameter of the cone is 6 units, therefore, the radius of the cone is 3 units, and the height of the cone is 8 units. Thus, the surface area of the right cone is,

A=πr [r+√(h²+r²)]

A = 108.79967 units²

Hence, the surface area of the cone is 108.79967 units².

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Answer:

True

Step-by-step explanation:

Rays have one endpoint and one arrow, which means that they extend forever in one direction.

The cosine ratio is given as:

[tex]\cos(\theta) = \frac{\sqrt 3}{2}[/tex]

See attachment for the graph of [tex]\cos(\theta) = \frac{\sqrt 3}{2}[/tex] under the domain of [0,∞)

From the graph, we can see that some values of [tex]\theta[/tex] when [tex]\cos(\theta) = \frac{\sqrt 3}{2}[/tex] are:

[tex]\theta = \frac{\pi}{6}[/tex]    [tex]\theta = \frac{11\pi}{6}[/tex] and [tex]\theta = \frac{13\pi}{6}[/tex]

We have:

θ = 495°

Convert to radians

[tex]\theta = 495 * \frac{\pi}{180}[/tex]

Evaluate

[tex]\theta = \frac{11\pi}{4}[/tex]

The value of sec θ is then calculated as:

[tex]\sec(\theta) = \sec(\frac{11\pi}{4})[/tex]

Using a calculator, we have:

[tex]\sec(\theta) = -1.414[/tex]

Hence, the value of [tex]\sec(\theta)[/tex] is -1.414

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The option that depicts a translation is option B. See the attached image and the explanation for this answer below.

Translation in Math refers to the movement of a shape vertically or horizontally along the x or y-axis without altering its original dimensions.

Going by the above definition, it is clear that Option B is the translated image (assuming that the original image is as given in the image attached.

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The factorized expression of x = a²b² + 2a + a⁴ is x = a(ab² + 2 + a³)

The expression is given as:

x = a²b² + 2a + a⁴

Factor out a from the expression

x = a(ab² + 2 + a³)

The above expression cannot be further factorized.

Hence, the factorized expression of x = a²b² + 2a + a⁴ is x = a(ab² + 2 + a³)

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Using proportions, it is found that the number of cups per student is of 1.97. hence there will not be enough for each student to have 2 cups.

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

Each gallon is worth 16 cups, hence, since each grade is given 15 gallons of water, and the trip consists of three grades, the number of cups is given by:

C = 3 x 15 x 16 = 720.

There is a total of 370 students, hence the number of cups per student is given by:

n = 720/370 = 1.97.

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Answer:

y=-1/7+48/7

Step-by-step explanation:

You want to isolate the Y so you subtract the x to the other side.

Next you divide both numbers on the right hand side by 7 and that gives you

y=-1/7+48/7

Answer:

Step-by-step explanation:

Ar of circle

A= 49π

B=100π

C=169π

D=121π

Ar of circle A is less than Ar of circle D

Answer:

Step-by-step explanation:

Note: The first point should be (1, - 4)

According to the points, the sequence is:

or

We can observe it is a geometric sequence with common ratio of - 2, as:

The following term is:

The coordinates of same term are:

As we see the correct answer choice is D.

Answer:

  a)  ΔCED ~ ΔCAB

  b)  157.5 m

Step-by-step explanation:

The similarity statement for geometric figures lists the corresponding vertices in the same order. Corresponding sides of similar figures are proportional. That fact can be used to find the missing side length.

__

The right angles are corresponding. Angle C corresponds to itself, so the similarity statement can be written ...

  ΔCED ~ ΔCAB

__

Corresponding sides are proportional, so we can write ...

  AB/AC = ED/EC

  AB/(50+160) = 120/160 . . . . . using the numerical values

  AB = 210 × 120/160 = 157.5 . . . meters

The length of the lake is 157.5 meters.

The annual percentage rate for a 35 month loan that charges $22.38 per every $100 financed is seen from the table to be 14%.

From the table, the APR for 35 months loan that charges $22.38 per every $100 financed is seen to be 14%.

Thus, we can conclude that the annual percentage rate for a 35 month loan that charges $22.38 per every $100 financed is seen from the table to be 14%.

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Answer:

a. 13%

Step-by-step explanation:

E2020!

Answer:

players on both teams are about the same height on average

Step-by-step explanation:

because both are same