A quadratic function y = f(x) is plotted on a graph and the vertex of the resulting parabola is (4, 6). What is the vertex of the function defined as g(x) = f(x +2) - 2?

Hence, when [tex]m=-3,b=6[/tex], so the equation of slope is [tex]y=-3x+6[/tex].

What is the slope of line?

The slope of a line gives the measure of its steepness and direction. The slope of a straight line between two points says [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] can be easily determined by finding the difference between the coordinates of the points.

The slope is usually represented by the letter [tex]m[/tex].

Here given that,

The linear function [tex]f(2)= 0[/tex] and [tex]f(4)=-6[/tex].

Let the linear function is

[tex]y=mx+b[/tex]

[tex]x=2,y=0[/tex]

Then

[tex]0=m(2)+b\\\\2m+b=0[/tex]      .......[tex](1)[/tex]

And for

[tex]f(4)=-6\\x=4,y=-6[/tex]

[tex]-6=m(4)+b\\\\4m+b=-6[/tex]       ......[tex](2)[/tex]

Solving equation [tex](1)[/tex] and [tex](2)[/tex], we get

In equation [tex](1)[/tex]

[tex]b=-2m[/tex]      ........[tex](*)[/tex]

Substitute [tex]b=-2m[/tex] in equation [tex](2)[/tex]

[tex]4m-2m=-6\\\\2m=-6\\\\m==\frac{6}{2}\\\\m=-3[/tex]

Put [tex]m=-3[/tex] in [tex](*)[/tex] equation

[tex]b=2m\\\\b=-2(-3)\\\\b=6[/tex]

Hence, when [tex]m=-3,b=6[/tex], so the equation of slope is [tex]y=-3x+6[/tex].

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The vertex of the parabola y = x² - 16x + 24 will be at (8, -40). Then the correct option is D.

Let the point (h, k) be the vertex of the parabola and a be the leading coefficient.

Then the equation of the parabola will be given as,

y = a(x - h)² + k

The equation is given below.

y = x² - 16x + 24

Convert the equation into vertex form, then we have

y = x² - 16x + 24

y = x² - 2·8·x + 8² - 8² + 24

y = (x - 8)² - 64 + 24

y = (x - 8)² - 40

The vertex of the parabola y = x² - 16x + 24 will be at (8, -40). Then the correct option is D.

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The area of the trapezium will be = 90[tex]mm^{2}[/tex]

According to the figure of the trapezium =

Let us consider the length of base a = 5mm

length of base b = 13mm

height h of the trapezium = 10mm

According to the formula of the area of trapezium

= (1/2) x h x (a + b)

= (1/2) x 10 x (13 + 5)

= 5 x 18

= 90[tex]mm^{2}[/tex]

Therefore, the area of the trapezium will be = 90[tex]mm^{2}[/tex]

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The complete question here could be- Find the area of the trapezium given base a= 5mm, base b= 13mm and height h= 10mm

Answer:

The expression is 2 * 3 - 2 + 4 = 8.

Step-by-step explanation:

In this expression, the variables a, b, and c are given specific values. Substituting these values into the expression, we have 2 * 3 - 2 + 4, which simplifies to 8.To evaluate an expression, we substitute the given values for the variables and carry out the operations according to the order of operations (i.e. parentheses, exponents, multiplication and division, addition and subtraction). In this case, the expression is already fully simplified, so we don't need to do any further calculations.

Answer:

5 buses

Step-by-step explanation:

Mrs. Smith will need to reserve buses for 7 classes of Fourth graders, with 20 students in each class, for a total of

7 * 20 = <<7*20=140>>140 students.

Since 30 students fit on a bus, Mrs. Smith will need to reserve

140 / 30 = <<140/30=4.67>>4.67 buses.

Since Mrs. Smith can't reserve a partial bus, she will need to reserve 5 buses for the trip.

Answer: 5 busses, you have to multiple the number of students by the amount of classes (7 x 20) to get a product of 140 students. If only 30 can fit on to each bus you have to divide 140 by 30 and you get 4.6666667 so you need to round up to get an answer of 5 busses

Step-by-step explanation:

The probability their average salary is less than $33,200 is = 0.6554

Given that,

Mean = $32,000

Standard deviation = $3,000

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.

Standard deviation (SD) is a widely used measurement of variability used in statistics. It shows how much variation there is from the average (mean). A low SD indicates that the data points tend to be close to the mean, whereas a high SD indicates that the data are spread out over a large range of values.

The Z score is used to calculate how many standard deviations above or below the mean the raw score is. It comes from,

z = (x- μ) / σ           (Equation-1)

Where,

x=raw score,

μ=mean,

σ=standard deviation

μ=32,000,

σ=3,000

Average salary is less than $33,200

x < 33,200

We can substitute values in Equation-1,

z = (33,200-32,000)/3000

z = 1200/3000

z = 0.4

Using the normal distribution table as a guide,

P(x < 33,200) = P(z < 0.4)

P(x < 33,200) = 1-P(z>0.4)

P(x < 33,200) = 0.6554

Therefore,

The probability their average salary is less than $33,200 is = 0.6554

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The point of intersection of f(x) and [tex]f^{-1}[/tex](x)   is (3, 3)

"It defines a relation between input and output values."

"In function, for each input there is exactly one output."

"The inverse function of x = f(m) is m =[tex]f^{-1}[/tex] , where x, m are real values"

For given question,

A function  f(x) and its inverse function [tex]f^{-1}(x)[/tex],  are both plotted on the same coordinate plane.

We know that the inverse function [tex]f^{-1}(x)[/tex]   is the mirror image of the function f(x.)

This means, both the functions must be symmetric about the line y = x.

The curve of inverse function [tex]f^{-1} (x)[/tex]  would cross the Y-axis at (0, 2), changes direction at (-1, -1) and crosses the X-axis at (-2, 0)

And both the functions intersect each other only on y = x

The point which satisfy the line y = x is (3, 3)

Therefore, the point of intersection of f(x) and[tex]f^{-1} (x)[/tex] is (3, 3)

The complete question is : If f(x) and its inverse function, f–1(x), are both plotted on the same coordinate plane, what is their point of intersection?

On a coordinate plane, a curve opens down and to the right in quadrants 3 and 4 and then changes direction and curves up and to the left in quadrants 1 and 4. The curve crosses the y-axis at (0, negative 2), changes direction at (1, negative 1, and crosses the x-axis at (2, 0).

A.(0, –2)

B.(1, –1)

C.(2, 0)

D.(3, 3)

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Using simple mathematical operations, we can conclude that Roanne will earn $10 in 1 hour.

A mathematical "operation" is the process of calculating a value utilizing operands and a math operator.

There are predefined rules associated with the math operator's symbol that must be applied to the supplied operands or numbers.

The order of operations refers to the rules that govern how to solve an expression with several operations.

Parentheses, Exponents, Multiplication, Division, Addition, and Subtraction are all referred to as PEMDAS (from left to right).

So, we know that:

Roanne earns $5 for 1/2 hour.

Roanne will earn in 1/2 * 2 = 1 hour:

5 * 2 = $10

Therefore, using simple mathematical operations, we can conclude that Roanne will earn $10 in 1 hour.

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Answer:

B. Just Minus expression with same one

Answer:

c)  36, 48, 60

Step-by-step explanation:

A Pythagorean Triple is a set of positive integers (a, b, c) that follows the rule:

[tex]\boxed{a^2+b^2=c^2}[/tex]

where a < c and b < c.

It always consists of:

When a and b are both even, c is even.

When one of a and b is odd and the other is even, c is odd.

(5, 7, 9) cannot be a Pythagorean Triple since it consists of all odd numbers.

(17, 20, 23) is not a Pythagorean Triple since:

[tex]\implies 17^2+20^2=23^2[/tex]

[tex]\implies 289+400=529[/tex]

[tex]\implies 689 \neq 529[/tex]

(36, 48, 60) is a Pythagorean Triple since:

[tex]\implies 36^2+48^2=60^2[/tex]

[tex]\implies 1296+2304=3600[/tex]

[tex]\implies 3600=3600[/tex]

(19, 22, 25) is not a Pythagorean Triple since:

[tex]\implies 19^2+22^2=25^2[/tex]

[tex]\implies 361+484=625[/tex]

[tex]\implies 845\neq 625[/tex]

By using the property of congruency, it can be calculated that

Length of line segment AC is 26 units

What are congruent triangles?

Two triangles are said to be congruent if their corrosponding sides are equal and the corrosponding angles are equal.

There are six axioms of congruency. They are

AAS axiom, SAS axiom, ASA axiom, SSS axiom, RHS axiom

In [tex]\Delta[/tex] ABC and [tex]\Delta[/tex] XYZ,

[tex]\angle[/tex]B = [tex]\angle[/tex]Y [Given]

[tex]\angle[/tex]C = [tex]\angle[/tex]Z [Given]

BC = YZ [Given]

[tex]\Delta[/tex] ABC [tex]\cong[/tex] [tex]\Delta[/tex] XYZ [ASA axiom]

AC = XZ [Corrosponding parts of congruent triangles are congruent]

AC = 26 units

Length of line segment AC is 26 units

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We have proved that tanθ.cosθ + cotθ.sinθ = sinθ + cosθ.

What are trigonometric identities?

Trigonometric Identities are the equalities that involve trigonometry functions and hold true for all the values of variables given in the equation. There are various distinct trigonometric identities involving the side length as well as the angle of a triangle.

                  tan∅ = sin∅/cos∅

                  cot∅ = cos∅/sin∅

Given:

tanθ.cosθ + cotθ.sinθ = sinθ + cosθ

Now LHS =  tanθ.cosθ + cotθ.sinθ

                = (sinθ/cosθ)cosθ + (cosθ/sinθ)sinθ

                = sinθ + cosθ

LHS = RHS

Hence, we have proved that tanθ.cosθ + cotθ.sinθ = sinθ + cosθ.

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The row of Pascal's triangle that is used to expand the binomial expression  (2x³ +3y³)⁷ is Row eight: 1 7 21 35 35 21 7 1.

A binomial expression is an expression that contains only two terms.

Pascal's triangle is an algorithm for finding the coefficients of a binomial expansion.

Since we require the expansion of the binomial expression (2x³ +3y³)⁷ using Pascal's triangle, we note that, the power of the binomial expression is always equal to the second and second to the last coefficient of the terms in the Pascal's triangle.

So, we see that the Row eight: 1 7 21 35 35 21 7 1, satisfies this condition.

So, the row of Pascal's triangle that is used to expand the binomial expression  (2x³ +3y³)⁷ is Row eight: 1 7 21 35 35 21 7 1.

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The value of expression will be;

⇒ 7 / 30

⇒ - 14/15

What is Distributive property?

By the rule of distributive property, multiplying the sum of two or more addends by a number gives the same result as when each addend is multiplied individually by the number and the products are added together.

Given that;

The expression is,

⇒ [ 7/5 × - 3/12 ] ± [ 7/5 × 5/12 ]

Now,

Since, The expression is,

⇒ [ 7/5 × - 3/12 ] ± [ 7/5 × 5/12 ]

Solve the expression by using distributive property as;

⇒ [ 7/5 × - 3/12 ] ± [ 7/5 × 5/12 ]

⇒ [ 7/5 ] × [ - 3/12 ±  5/12 ]

It gives two solution as;

⇒ 7/5 × [ - 3/12 + 5/12 }

⇒ 7/5 × 2/12

⇒ 7/5 × 1/6

⇒ 7 / 30

And,  7/5 × [ - 3/12 - 5/12 }

⇒ 7/5 × - 8/12

⇒ 7/5 × - 2/3

⇒ - 14 / 15

Thus, The value of expression will be;

⇒ 7 / 30

⇒ - 14/15

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Answer: The answer to this solution is 5.

If the margin error of the volume of the soap is 354.85 ml to 354.95 ml, then the volume of the soap that he measured is 354.9 ml

The margin of error = 354.85 ml to 354.95 ml

The margin error is defined as the difference between the actual and projected results in a random survey sample.  If the actual measurement is x, there is a chance of error in the measurement because of numerous reasons.

The margin of error in the measurement is 354.85 ml to 354.95 ml

In the given options the correct value is 354.9 ml, because it is the middle value of the given margin or error 354.85 ml to 354.95 ml

Therefore, the volume of soap that he measured is 354.9 ml

I have solved the question in general, as the given question is incomplete

The complete question is:

For the volume of soap in a bottle, Ryan determined the margin of error as 354.85 mL to 354.95 ml. What was the volume of soap that he measured? a) 354.8 mL b) 354.85 mL c) 354.9 mL d) 354.95 mL

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The correlation of the scatterplots are defined as;

The math and English scores show; A positive correlation.

The math and chemistry scores show; A negative correlation

In correlation in statistics, it could either be positive correlation, negative correlation or no correlation at all.

A positive correlation is defined as a relationship between two variables that tend to move in the same direction. Thus, a positive correlation exists in the event that one variable tends to decrease while the other variable decreases, or one variable tends to increase while the other variable increases.

A negative correlation is defined as a relationship between two variables whereby one variable increases while the other decreases, and vice versa.

No correlation means there is no relationship between the two variables.

Now, for scatterplot of the math and English scores shown, we see that majority of the english scores increase as the maths scores increase and as sch it is a positive correlation.

Meanwhile, for the math and chemistry scores shown, majority of the maths score decreases with an increase in the chemistry score and as such this is a negative correlation.

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Answer:

F

Step-by-step explanation:

15/10 = x+12/12

180=10x+120

x=6

x+12=18=AE

Answer:

11) KF = DB

12) DC=YZ

13) <C = <W

14) <S and <K

Step-by-step explanation:

11) For this question, we want to try and use SSS to prove the triangles are congruent. SSS stands for side-side-side postulate, so all sides have to be equivalent. We already have ED = FB as given, and DF = DF due to reflexive property. From this information, we already have two sides. Additional information that would be needed to figure out the third side is KF = DB, as it's the only side we are missing.

12) For this question, we want to use SAS postulate, which stands for side-angle-side. We already have one side congruent, which is BC=YX. We have one angle congruent which is <C = <Y. With this information, we have one side and one angle. This means that we need to find another side that is congruent. The side that we need to find here is DC=YZ, as it will help us prove the triangles are congruent with SAS.

13) For this question, we want to use AAS, which stands for angle-angle-side. We already have one angle congruent, which is <CDE = WDE. We have one side congruent as well, which is DE = DE due to reflexive property. With this given information, we have one angle and one side. We only need one more angle before the other angle to figure this out. The angles that are needed are <C = <W.

14) For this question, we want to use ASA, which stands for angle-side-angle. The one angle we have already is <KTM = <UTS, which is because of vertical angles are congruent. The one side that we have is ST=TK. With this, we have one angle and one side. We just need one more angle to prove this, which would be <S and <K.

Remember, for triangle congruency postulates, they have to be in order. They cannot just be out of order. For example, in question 14, we have to find the measures in order. First we need an angle, side, and then another angle. The first angle is <S and <K, then the side we have is ST=TK, and then our last angle, <KTM = <UTS.

The amount of interest earned quarterly at 0.5% interest rate compounded quarterly are;

a. Interest for the first quarter = $8.125

b. First quarter ending balance = $6,508.125

c. Interest for the second quarter = $8.13515625

d. Second quarter ending balance = $6,516.26015625

e. Interest for the third quarter = $8.1432520325

f. Third quarter closing balance = $6,524.40548145

g. Interest for the fourth quarter = $8.15550685975

h. The amount of interest earned in a year is about $32.56

What is an interest earned on an amount?

An interest is the amount a borrower pays to a lenders as to make use of the lender's funds.

The amount Fred deposited, P = $6,500

The interest paid by the account, r = 0.5% compounded quarterly

a. The first quarter interest can be found by the formula;

C.I. = P[tex](1+ r/4)^{4 . 1/4}[/tex] - P

Therefore

C.I. = 6500 x (1 + [tex]\frac{0.5/100}{4}[/tex]) - 6500 = 8.125

b. The first quarter ending balance is therefore;

A = P + C.I.

A = $6,500 + $8.125 = $6,508.125

c. The second quarter's interest can be found from the formula;

C.I. = 6508.125 x (1 + [tex]\frac{0.5/100}{4}[/tex]) - 6508.125 = 8.13515625

The second quarter's interest is $8.13515625

d. The second quarter ending balance is therefore;

A = $6,508.125 + $8.13515625 = $6,516.26015625

The second quarter ending balance is $6,516.26015625

e. The third quarters interest is therefore;

C.I. = 6516.26015625 x  (1 + [tex]\frac{0.5/100}{4}[/tex]) - 6516.26015625 = 8.1432520325

The third quarter's interest is about $8.1433

f. The third quarter's ending balance is therefore;

A ≈ $6516.26015625 + $8.1432520325 = $6,524.40548145

The third quarter's ending balance is $6,524.40548145

g. The fourth quarter's interest can be found as follows;

C.I. = 6524.40548145 x (1 + [tex]\frac{0.5/100}{4}[/tex]) - 6524.40548145 = 8.15550685975

The fourth quarter's interest is; $8.15550685975

h. The balance at the end of one year is therefore;

Balance = C.I. fourth quarter + Principal for the fourth quarter

Therefore;

Balance = $6,524.40548145 + $8.15550685975 = $6,532.56098831

i. The interest the account earns in a year is therefore;

$6,532.56098831 - $6,500 = $32.5609883

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Answer:

No

Step-by-step explanation:

If you look at the first numbers, 1 and 3, we can see that 1 is being multiplied by 3 to get 3.

But if you look at the second numbers, 2 and 4, then you can see that 2 is not being multiplied by 3 to get 4.

Therefore, it is not proportional.

The area of the front cover a face perpendicular to the thickness is 72in²

What is a rectangular prism?

Having six faces, a rectangular prism is a three-dimensional shape (two at the top and bottom, and four are lateral faces). The prism's faces are all rectangular in shape. There are three sets of identical faces as a result. A rectangular prism is often referred to as a cuboid because of its shape.

Here, we have

Given:

A new dictionary in the shape of a rectangular prism will have a thickness of 3 inches.

The volume of the dictionary will be 216in².

Volume = W×L×H

Surface = volume/ height

= 216/3

= 72in²

Hence, the area of the front cover of a face perpendicular to the thickness is 72in².

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Answer:

= 4.54545 × 10^-1

Step-by-step explanation:

[tex] \frac{45}{99} = \frac{5}{11} [/tex]

= 0.45454545

= 4.54545 × 10^-1

I hope this helped

Answer: $27,000

Step-by-step explanation:

Answer:

$2.92

Step-by-step explanation:

Divde $11.67 by the 4 gallons that Dennis bought.

11.67/4=2.9175

round to the nearst cent (or hundreths place)

since 7 is greater than 5, it rounds up

$2.92

Answer:

I use desmos; what do you need help with?

Answer:zegari6636 is king of brainlist

Step-by-step explanation:

My algebra teacher use Desmos and also thanks for the points have a good day do you need help

If a blood stain has a length of 3.0cm and a width of 1.5cm, the angle of impact is 30 degrees

The length of the blood stain = 3 cm

The width of the blood stain = 1.5 cm

The equation for measuring the angle of impact is

sin (angle of impact) = The width of the blood stain / The length of the blood stain

Angle of impact = sin^-1 (The width of the blood stain / The length of the blood stain)

Substitute the values in the equation

Angle of impact = sin^-1(1.5 / 3)

= sin^-1(0.5)

= 30 degrees

Therefore, the angle of impact is 30 degrees

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The value of f(x)+g(x) is 5x³+7x²+3x+10

Given that,

                 f(x)=3x³+4x²-2x+8

                 g(x)=2x³+3x²+5x+2

f(x)+g(x)=3x³+4x²-2x+8+2x³+3x²+5x+2

            =3x³+2x³+4x²+3x²+5x-2x+8+2

            =5x³+7x²+3x+10

Step-by-step explanation:

This question is a type of quadratic equation. To solve this type of question first, we have to put the values of f(x) and g(x). Then we have to put similar terms(which have similar coefficients with similar power)together. Then we add the similar term of f(x) with the similar term of g(x) like 3x³+2x³=5x³, 4x²+3x²=7x², 5x-2x=3x and 8+2=10

Therefore the value of f(x)+g(x) is 5x³+7x²+3x+10

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Answer:

£115

Step-by-step explanation:

After solving the equation the linear equation is x = 27/5 , y = 7/5.

What do you mean by linear equation?

Equations with the highest degree of 1 are called linear equations. This means that the exponent of the variable in the linear equation is greater than 1. The graph of a linear equation is always a straight line.

A linear equation is an algebraic equation in which each term has exponent 1, and the graph of this equation is always a straight line. For this reason, it is called a "linear equation".

Given system of equation:

7x - 7y = 28 ..........(1)

2x - 7y = 1 .............(2)

Solve this system of linear equation. Find the value of 7y from equation (1) and substitute in equation(2)

7x - 7y = 28

7x - 28 =7y .............(3)

Substitute this value in equation (2)

2x - (7x - 28) = 1

2x - 7x + 28 = 1

-5x + 28 = 1

5x = 28 - 1

5x = 27

x = 27/5

Substitute this value in equation (3)

7y = 7(27/5) - 28

7y = 189/5 - 28

7y = 49/5

y = 7/5

Therefore, x = 27/5 , y = 7/5

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