Find the zeroes of the quadratic polynomial x
2
+ x−12 and verify the relationship between the zeroes
and the coefficients.

The point (-7, 1) is in fact a solution for the inequality y < 0.5x + 9

A point is a solution of a inequality only if it makes the truth value of the inequality true.

In this case, it would mean that the right side of the inequality is strictly larger than the left side.

So to check that, we just need to replace the values of the point on the inequality.

The values are x = -7 and y  = 1, replacing that in the given inequality we will get:

1 < 0.5*(-7) + 9

1 < -3.5 + 9

1 < 5.5

This is true, 5.5 is larger than 1, then we conclude that the point (-7, 1) is in fact a solution for the inequality y < 0.5x + 9

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The quadratic function of the jump is y = -0.22x^2 +0.89x + 6.11 if the jump changes so that the axis of symmetry becomes X=2 , the height stays the same 7 and also passes through the point (5,5)

Quadratic function involving vertex is given by

y = a(x-h)^2 + k

Where (h,k) is the vertex which is given as (2,7)

y = a(x-2)^2 + 7

y = a(x-2)(x-2)  + 7

y = a(x^2 -4x +4) + 7

Recall that

h = -b/2a

k = -(b^2 -4ac)/4a

2 = -b/2a

-b = 4a

b = -4a

Put b = -4a

k = -(b^2 -4ac)/4a

7= -(b^2 -4ac)/4a

7 = -((-4a)^2 -4ac)/4a

7 = -(16a^2 - 4ac)/4a

7 =  (-16a^2 + 4ac)/4a

7 = -4a + c

c = 7 + 4a

The path of the jump also passes through (5,5)

y = ax^2 + bx + c

5 = a5^2 + b5 + c

5= 25a +5b + c

Put b = -4a in above

5= 25a +5(-4a) + c

5= 25a -20a+ c

5 = 5a + c

Put c = 7 + 4a

5 = 5a + 7 +4a

Collect like terms

5-7 = 5a + 4a

-2 = 9a

a = -2/9

Put a in

y = a(x^2 -4x +4) + 7

y = -2/9(x^2 -4x +4) + 7

y = (-2x^2 +8x -8)/9 +7

Multiple through by 9

9y = -2x^2 +8x -8 + 63

9y = -2x^2 +8x + 55

Dividing through by 9

y = -0.22x^2 +0.89x + 6.11

Therefore the equation of the jump is

y = -0.22x^2 +0.89x + 6.11.

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The quotient of (x³+2 x²-x+6) / (x+3) is (B) x²-x+2.

So, find the quotient of (x³+2 x²-x+6) / (x+3) using the Polynomial long division method:

Therefore, the quotient of (x³+2 x²-x+6) / (x+3) is (B) x²-x+2.

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Answer:

m=2

Step-by-step explanation:

An equivalent form of the index 8.723 x 10-¹⁰ is 0. 0000000008723

The index form of a number is simply that number written as an exponential expression, or even as a single number that is raised to another number.

Index form is also known as standard form

Given the index form;

⇒ 8.723 x 10-¹⁰

⇒ 8. 723 × 10^ -(10)

This means that there 10 zero digits from the left end of the given decimal, it is expressed as;

0. 0000000008723

Thus, an equivalent form of the index 8.723 x 10-¹⁰ is 0. 0000000008723

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Moshde needs to carry out 55 cuts and style to save at least $1,278 per month

Moshde charges $42 per haircut and style

Her monthly expenses is $1040

She wants to save $1278

The number of cuts and styles required is

1040 + 1278 /42

= 2318/42

= 55.2

Hence Moshde need to make 55 cuts and style to save at least $1278 per month

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Answer:

17

Step-by-step explanation:

We can tell this is a right angle (90 degrees) by the square drawn in the angle.

So this becomes a two-step equation.

4x+22=90

4x+22-22=90-22

4x=68

4x/4=68/4

x=17

Answer:

im jk wdf is this goodluck

According to the question, the function f(x) is bounded with constant number. And the exponential function base e is not bounded. Similarly, logarithmic function base e is also not bounded.

Bounded values can be calculated with the help of asymptotes namely, vertical, horizontal and oblique. The vertical, horizontal and oblique asymptotes are constant values which grows the values of the function f(x) without bound.

A basic logarithmic function is a function with no horizontal shift as well as no vertical shift. All logarithmic function passes through a constant points and touches the horizontal axis which results into asymptotes. It either increases from left to right, or decreases from left to right.

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The measure of angle ABD (m ∠ABD) is 44°

The measure of angle CBD (m ∠CBD) is 44°

The measure of angle ABC (m ∠ABC) is 88°

From the question, we are to calculate the measures of the given angles

From the given, information, we have that BD bisects ∠ABC

Thus,

m ∠ABD = m ∠CBD

From the given diagram,

m ∠ABD = (6x + 14)°

and

m ∠CBD = (3x + 29)°

Then,

(6x + 14)° = (3x + 29)°

Solve for x

(6x + 14)° = (3x + 29)°

6x + 14 = 3x + 29

Collect like terms

6x - 3x = 29 - 14

3x = 15

x = 15/3

x = 5

Put the value of x into the equations

m ∠ABD = (6(5) + 14)°

m ∠ABD = (30 + 14)°

m ∠ABD = 44°

Since

m ∠ABD = m ∠CBD

Then,

m ∠CBD = 44°

and

m ∠ABC = m ∠ABD + m ∠CBD

m ∠ABC = 44° + 44°

m ∠ABC = 88°

Hence, the m ∠ABD = 44°, m ∠CBD = 44°, and m ∠ABC = 88°

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The product is smaller than the factors of the product.

Let's say that we have two real positive numbers A and B.

If we define 0 < A < 1

Then when we multiply A and B (a real positive number) we will have that:

A*B < B

So the value of B is decreased.

Now, if both numbers are in that range:

0 < A < 1

0 < B < 1

We will have that:

A*B < B

A*B < A

So the product is smaller than A and smaller than B, which are the factors of the product.

So the product is less than both of the factors.

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The property of real numbers illustrated by the given equation is associative property of multiplication.

Associative property states that the number in an equation can be grouped together in any way without the total value of the result changing. There are two types of associative property.

1. Associative property of addition which is given by:

(a+b)+c=a+(b+c)

2. Associative property of multiplication which is given by:

(ab)c=a(bc)

Associative property of multiplication states that the way factors are grouped in a multiplication equation does not change its product.

As the given equation 2. 3(3. 4. 12. 9)=(2. 3. 3. 4)(12. 9) contain multiplication operation, the property of real numbers illustrated is associative property of multiplication.

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The formula for converting from Celsius to Fahrenheit temperatures is F = 9/5 C + 32 then the inverse function is one-to-one.

The inverse function returns the original value for which the output of a function was given. When it comes to functions, f and g are inverse, with f(g(x)) = g(f(x)) = x. A function that is made up of its inverse returns the original value.

The formula for converting from Celsius to Fahrenheit temperatures is

F = 9/5 C + 32.

Let the Fahrenheit temperatures is F = 9/5 C + 32

Subtract 32 from both sides:

F - 32 = 9/5 C + 32 - 32

F − 32 = 9/5 C

Multiply both sides by 5:

5(F − 32) = 9C

Divide both sides by 9:

5/9 (F − 32) = C or C = 5/9 (F − 32)

For 27° F

⇒ C =  5/9 (27 - 32)

⇒ C =  5/9 (-5)

⇒ C = -25/9

⇒ -2.78 C° 2.dp.

Yes, the inverse is a one-to-one function.

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The correct option for showing the interval (-∞, -7) is Option C.

What is Interval?

An interval includes all the numbers that come between two particular numbers.

The given interval is (-∞, -7).

Now, On the number line (-∞, -7) is shown as;

The interval is open interval.

Hence, At point -7 the graph is in open circle.

And, The graph is going left side.

Hence, The correct option for showing the interval (-∞, -7) is Option C.

Which is shown in figure.

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Answer:

It has won 15 games.

Step-by-step explanation:

24*.625=15

Answer:

Range = 77

Step-by-step explanation:

1. Reorder all the values in your data set from low to high.

13, 45, 46, 56, 66, 67, 89, 90

2. Subtract the lowest number from the highest number.

90 - 13 = 77

Answer: 6

Step-by-step explanation:Shannon buys a bag online for $32.00 including tax, and the shipping is $4.00. If she decided to buy more of the same bags and it doesn't change the shipping cost, how many can she buy with $100.00

Answer:

Step-by-step explanation:

For 3 hours it cost him $78.25

25 + 17.75 + 17.75 + 17.75= 78.25

He had left from $102.17 subtract from $78.25 is $23.92

Answer:

23.92

Step-by-step explanation:

17.75x3=53.25

53.25+25=78.25

102.17-78.25=23.92

According to the question, the given rational expression can be simplified and as shown below:

Rational expression = [tex]\frac{49-z^{2} }{z+7}[/tex]

To simplify the given rational expression, calculate the factors of the numerator as well as denominator. And later divide it from each other. These expressions are also called as polynomial expressions.

Rational expression = [tex]\frac{(7-z)(7+z)}{z+7} =\frac{(7-z)}{1} =7-z[/tex]

Therefore, final expression of the given equation is [tex]7-z.[/tex]

What is polynomial expression?

Polynomial expression are those equation whose highest degree is two. It is also called as quadratic equation. And it is simplified by performing the factors on the given expressions.

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column A is the correct answer.

The distance versus time plot for a particular object shows a quadratic relationship. Which column of distance data is possible for this situation? Time (s) A. Distance (m) B. Distance (m) C. Distance (m) D. Distance (m) E. Distance (m) 0 0 2.00 9.00 ‡ ‡ 1 1.00 4.00 18.00 1.00 1.00 2 4.00 6.00 27.00 0.50 0.25 3 9.00 8.00 36.00 0.33 0.11 4 16.00 10.00 45.00 0.25 0.06 5 25.00 12.00 54.00 0.20 0.04 6 36.00 14.00 63.00

A quadratic relation means one variable is proportional to the square of the other variable.

for this problem, distance and time will be proportional to the following equation

d = kt² or t = kd²

where k is a (constant).

when y look at column A closely.  The numbers are all perfect squares: 1, 4, 9, 16...

This means d = kt²  with k=1:

at t = 0, d = 1 x 0² = 0

at  t = 1, d = 1 x 1² = 1

at  t = 2, d = 1 x 2² = 4

at   t = 3, d = 1 x 3² = 9

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The value of x is -1. Option B

From the information given, we have the equation as;

2x - 10/ 4 = 3x

Where;

Let's simplify the equation

cross multiply

2x - 10 = 3x × 4

2x - 10 = 12x

collect like terms

2x - 12x = 10

-10x = 10

Divide both sides by the coefficient of x

x = 10/ -10

x = -1

Thus, the value of x is -1. Option B

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Answer: B

Step-by-step explanation:

The inequality that can be used to determine v, the minimum number of visits Matthew needs to earn his first free movie ticket is 50 + 8.5v >= 185.

From the information, Matthew has a points card for a movie theater, he receives 50 rewards points just for signing up and earns 8.5 points for each visit to the movie theater.

Since he needs at least 185 points for a free movie ticket, the inequality will be:

50 + 8.5v >= 185

where v = the minimum number of visits Matthew needs to earn his first free movie ticket.

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A composite function exists as a function that depends on another function. The value for f/g(10) is 1/5

In mathematics, function composition exists as an operation ∘ that takes two functions f and g, and has a function h = g ∘ f such that h(x) = g. In this operation, the function g exists used to the result of applying the function f to x.

Function composition is a mathematical procedure where two functions, f, and g, are taken and a function, h = g ∘ f, is produced such that h(x) = g(f(x)). The function g exists used in this operation on the outcome of applying the function f to x.

Let the two functions be f(x) = x+5 and g(x) = x²-25

A function exists described as a relationship between one variable and another variable.

(f/g)(x) = f(x)/g(x) = (x+5) / (x²-25)

The domain of a function exists the set of all possible inputs for the function.

When the denominator is zero, the function remains undefined.

Hence, x cannot take the values 5 and -5.

The function (f/g)(x) is defined for all values of x except x = 5, -5.

Hence, the domain is all integers except x = 5, -5

⇒ (f/g)(10) = (10 + 5) / (100 - 25)

simplifying the above equation, we get

⇒ (f/g)(10) = (15) / (75)

⇒ (f/g)(10) =  1/5

Therefore, the value of (f/g)(10) is 1/5.

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The problems he got correct on the second test is 12.

Ratio expresses the relationship between two or more numbers. It shows the the number of times that one value is contained within other value(s). Ratio is used to compare two or more numbers. The sign used to represent ratio is :

The first step is to determine the total number of questions on the math test : (sum of ratios x answers gotten incorrect on the first test) / ratio of the answers gotten incorrect

(8 x 10) / 5 = 16

Answers gotten correct on the second test : (ratio of correct answers / sum of ratios) x total number of questions

(6/8) x 16 = 12

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The total surface area or surface area of the given sphere is 84.9 cm² rounded to 1 decimal place whose radius is 2.6cm

The total surface area or surface area of a sphere is given by the formula 4πr²

From the given figure it is clear that the radius of the sphere is 2.6cm

Here, we will use the value of π as 3.14 and not 22/7

So, Substituting the values in the formula of Total surface area of a sphere.

the total surface area =4 π (2.6)²

                                              4 × 3.14 × 6.76

                                              = 84.9056 cm²

Hence, the total surface area or surface area of the given sphere is 84.9056 cm² or 84.9 cm² rounded to 1 decimal place whose radius is 2.6cm

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The domain of the function {x ∈ R, x ≥ −7}

The inverse function would be [tex]f^{-1}(x)[/tex] = x² - 7

Range of the function be {y ∈R, y ≥ −7}

The domain of a relation's inverse is the same as the range of the original relation.

In other words, the y-values of the relation are the inverse's x-values.

Domain of f(x) = {x ∈ R, x ≥ −7} and Range = {y ∈ R, y ≥ 0}

Domain of [tex]f^{-1}[/tex](x)= {x ∈ R}, Range = {y ∈ R, y ≥ −7}

The domain of the function would be all x, such that x+7 ≥ 0, or x ≥ −7. Hence it is {x∈ R, x ≥ −7}.

Consider the range of the function y = √x + 7.

Since √x+7 ≥ 0, it is obvious that y ≥ 0.

Range would be {y ∈ R, y ≥ 0}

The inverse function would be [tex]f^{-1}(x)[/tex] = x² - 7

The domain of the inverse function is all real x, {x ∈ R}

For the range of the inverse function solve y = x²-7 for x.

It would be x = √y+7.

⇒ y + 7 ≥ 0.

Hence, the range of the function be {y ∈R, y ≥ −7}

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Answer:

Find the equation of a line that goes through the points (8, -9) and (-4, 15). ... with (x₁, y₁ ) = (8, - 9) and (x₂, y₂ ) = (- 4, 15).

Step-by-step explanation:

source: gogle

Find the equation of a line that goes through the points (8https://brainly.com › Mathematics › Middle School ©

March 21, 2020 — Find the equation of a line that goes through the points (8, -9) and (-4, 15). ... with (x₁, y₁ ) = (8, - 9) and (x₂, y₂ ) = (- 4, 15).

I Doublecheck it

Answer:

Step-by-step explanation:

well jar b's amount of sweets must be between 205 and 175