2(x- 4) + 3x- 17 for x = 3

Yes. Parabola is possible to write an equation in the form f(x) = (x-a)(x-b)

Parabola is a symmetrical open plane curve formed by the intersection of a cone with a plane parallel to its side. The path of a projectile under the influence of gravity follows a curve of this shape.

A parabola can be described in the form of a general equation

[tex]y=ax^{2} +bx+c[/tex], with a, b, c is integers.

The form f(x)=(x-a)(x-b) can be made in other forms :

[tex]y=(x-a)(x-b)[/tex]

[tex]y=x^{2} -bx-ax+ab[/tex]

[tex]y=x^{2} -(b+a)x+ab[/tex]

That form of the equation is the same as : [tex]y=ax^{2} +bx+c[/tex]

With :  

a = 1

b = -(b+a)

c = ac  

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Answer:

A:(4,12)

B: In image

C. Yes, it does because it shows that the two lines intersect at the same point.

Step-by-step explanation:

-Hope this helped & Happy Holidays!

Answer:

cos S = 3/4

sin T = 3/4

Step-by-step explanation:

cos S = adj/hyp = 3/4

sin T = opp/hyp = 3/4

cos S and sin T are the sine and cosine of complementary angles arnd are equal.

The remainder of 5x³ + 7x +57 over x+2  is 3.

What is expression?

In mathematics, an expression that incorporates variables, constants, and algebraic operations is known as an algebraic expression (addition, subtraction, etc.). Terms comprise expressions.

Given expressions are 5x³ + 7x +57 and x+2.

Remainder theorem: According to the remainder theorem, the remainder equals f(a) when a polynomial, p(x), is divided by (x - a).

Assume that P(x) = 5x³ + 7x +57.

Equate x + 2 to zero and find the value of x:

x + 2 = 0

x = -2

Putting x = -2 in the polynomial P(x) = 5x³ + 7x +57:

P(-2) = 5(-2)³ + 7(-2) +57

P(-2) = 5(-8) + 7(-2) +57

P(-2) = -40 - 14 +57

P(-2) = 3

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The leftmost three digits of nn would be 816.

Solution:

The two-digit perfect squares are $16, 25, 36, 49, 64, 81$. We try making a sequence starting with each one:

The largest is 81649, so our answer is [816].

The leftmost three digits of nn would be 816.

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First we find number of passengers on each train.

4752/3 = 1584

Each train has 1584 passengers and 8 cars.

To find passengers per car, divide 1584 by 8.

198

Hope this helps :)

If you need any more explanation, feel free to ask.  If this really helps, consider marking brainliest.

- Jeron

Answer:

Step-by-step explanation:

x=-40

The Variable x varies inversely with y, and x = 132 when y = 4 then the value of x is 16.5 when y = 32.

So, the correct option is option(D).

Inverse variation can be expressed by the formula, xy=k or y=kx

That is, if there is a non-zero constant k such that xy = k or y = kx (x≠0,y≠0), then y varies inversely with x.

We have given that,

x varies inversely with y and we need to find x when y = 4 when x = 132

X varies inversely with y there exist a constant of proportionality say k such that :

=> (x)(y) = k ----(1)

Put the value of x and y in equation (1) to find the value of k

=> (132)(4) = k

Therefore, k = 528 , We get

=> (x)(y) = 528

Now, we find x when y = 32, so plug the value of y in equation (1)

=> (x)(32) = 528

=> x = 528/32

=> x = 16.5

Hence, the value of x is 16.5 when y = 32 .

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Using the formula of surface area to calculate the height and using the formula for volume , The answer is 24.98 [tex]cm^{3}[/tex] .

A cone is a three-dimensional geometric structure with a smooth transition from a flat base—often but not always circular—to the point at the top, also known as the apex or vertex.

The required formula are :

[tex]SA = \pi r (r + \sqrt {h^{2} + r ^ {2}})[/tex]  (Surface Area)

[tex]V = \pi r^{2} \frac {h}{3}[/tex] (Volume)

radius = 3 cm

Area= 66 [tex]cm^{2}[/tex]

[tex]SA = \pi r (r + \sqrt {h^{2} + r ^ {2}})[/tex]

h = 2.65 cm

[tex]V = \pi r^{2} \frac {h}{3} = \pi * 3^{2} * \frac {2.65}{3}[/tex]

=24.98 [tex]cm^{3}[/tex]

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Answer:

B

Step-by-step explanation:

To draw a dilation with a scale factor 1/2 , multiple every coordinates of pre-image with 1/2 and join the obtained points

A dilation is a transformation that alters the size of an image.

There is a centre and a scale factor in all dilations. The centre serves as the dilation's reference point (like the vanishing point in a perspective drawing)

The scale factor indicates how much the figure expands or contracts. A scale factor is usually denoted by the letter "k," and it is always greater than zero.

To draw a dilation with a scale factor of 1/2, follow these steps:

Step 1: Determine the scale factor and the dilation centre.

Step 2: Identify an image vertex. Draw a line through one of the image's vertices from the center of dilation.

Step 3: Find the horizontal distance and the vertical distance between the center of dilation and the vertex.

To find the horizontal and vertical distances from the centre of dilation to a new vertex, multiply the distances by the scale factor 1/2.

Step 4: Determine the new horizontal and vertical distances from the centre of dilation. Make a point plot.

Step 5: Join the new vertices together to create the dilated image.

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To find maximum value and minimum value in a set we have to use ven diagram from set theory.

Here we are taking an example?

Let A and B be 2 sets having elements 4 and 7 respectively. Then write the maximum number of elements that A∪B can have.

Let us assume that:

Number of elements of A is equal to n (A).

Number of elements of B is equal to n (B).

Number of elements of A∩B is equal to n (A∩B).

Now, the formula for the elements of A U B is as follows:

n(A∪B)=n(A)+n(B)−n(A∩B)

It is given in the question that, number of elements in set A is equal to 4 and number of elements in set B is equal to 7. So, we can write:

n (A) = 4, n (B) = 7

n (A∩B): the number of elements which are common in both the sets A and B.

We have to find the maximum number of elements which are in n(A∪B). So, the maximum of n(A∪B) is when n(A∩B) is minimum and the minimum of n(A∩B) is 0.

n(A∪B)=n(A)+n(B)−n(A∩B)⇒n(A∪B)=4+7−0⇒n(A∪B)=11

Hence, the maximum number of elements in A∪B is 11.

Note: You might be wondering, why for maximizing the n (A∪B) we have to minimize n (A∩B) and why the minimum value of n (A∩B) is 0.

In the formula for n (A∪B),

n(A∪B)=n(A)+n(B)−n(A∩B)

L.H.S will be maximized when in the R.H.S; the term after minus sign will be minimized. Hence, n (A∩B) must be minimized.

The minimum possible value of n (A∩B) is 0 means that the elements in the set A and B are such that there is not a single element is common in both the sets. And it could be possible that we have two sets and the sets have no element in common.

When no elements is common in both the sets, the n (A∩B) is ∅.

The set which has no element in it is called a null set or an empty set.

By this we can find maximum and minimum value in a set.

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Answer: It would be -48

Step-by-step explanation: Hope it helps:)

The Linear equations can have 2 or more answers if the lines overlap each other .

In the question ,

it is asked that can two linear equations have 2 answers or solutions .

We know that ,

(1) two linear equations can have No Solution / Zero Solution if two lines are parallel .

(2) two linear equations can have One Solution/Unique Solution if two line intersect at a point .

(3) two linear equations can have infinitely many solution if lines overlap on each other .

So from (3) , we can conclude that linear equations can have 2 or more solutions when the line are overlapping .

Therefore , Yes, the linear equations can have two answers .

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Answer:

68, 68, 44

x = 68

x - 24 = 44

Step-by-step explanation:

If you have a shape with three interior angles, it is a triangle. The three angles in a triangle add up to 180. Use this idea to write and solve an equation.

x + (x - 24) + 68 = 180

Combine like terms.

2x + 44 = 180

Subtract 44.

2x = 136

Divide by 2.

x = 68

So we can find x - 24

68 - 24 is 44.

The three angles are 68 (given), 68 (because x = 68), and 44 (because x-24)

The angles are 68, 68, and 44

Hence, the factors of [tex](10x+1)^2=100x^2+1+20x[/tex].

What are the factorization?

Factorisation or factoring is defined as the breaking or decomposition of an entity into a product of another entity, or factors, which when multiplied together give the original number.

Here given expression is

[tex]100x^2+1[/tex]

[tex](10x)^2+(1)^2[/tex]

[tex](10x+1)^2[/tex]

As we know that,

[tex](a+b)^2=a^2+b^2+2ab[/tex]

Here

[tex]a=10x\\b=1[/tex]

So,

[tex](10x+1)^2=(10x)^2+(1)^2+2(10x(1))\\\\(10x+1)^2=(10x)^2+(1)^2+20x\\\\(10x+1)^2=100x^2+1+20x[/tex]

Hence, the factors of [tex](10x+1)^2=100x^2+1+20x[/tex].

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The factors of the expression 100x² + 1 are (10x+i) (10x-i).

A polynomial function with one or more variables, where the largest exponent of the variable is two, is referred to as a quadratic function. In other terms, a "polynomial function of degree 2" is a quadratic function.

The given expression is 100x² + 1.

The given expression is a quadratic function.

The standard form of quadratic function:

ax²+bx +c, where a is not equals to zero.

Comparing with the standard form we get,

a = 100, b = 0 and c = 1

Simplifying,

100x² + 1

=  100x² - (-1)

= (10x)² - (-1)

= (10x)² - (i)²   ,{i² = -1}

= (10x+i) (10x-i)

Therefore, (10x+i) (10x-i) are the factors.

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The question is a spam as the correct question should be:

Which transformations could have taken place to map △ABC to △A"B"C".

The following answer has been given keeping in mind the above question.

The transformations that should have been taken place are a rotation and a dilation.

What is a rotation?

Rotation is when we rotate a figure to a certain degree. In a rotation, points and figures are turned on a coordinate plane. Majorly, rotations are about to the origin. Rotating a point about the origin can be, imagine a line connecting the origin to a point, and then rotate the line clockwise by the correct angle of rotation.

What is a dilation?

Dilation is a process of transformation in which something can be made larger or smaller. In a dilation, a point, a set of points can be expanded or contracted in relation to the origin. In expansion, the points in a figure move far away from the origin, and the side lengths of the figure increase. In a contraction, the points of the figure move closer to the origin, and the side lengths in the figure tend to reduce.

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There is 4 bottles in each of the packs when Andre and Jillian were shopping at the same grocery store for bottles of sports drinks for their kickball teams. Andre bought 3 packs of bottled drinks, plus 11 single bottles. Jillian purchased 5 packs, plus 3 singles. Andre and Jillian discovered that they had purchased the same number of bottles

The bottles in each of the packs can be calculate as follows:

Expressions that indicate the total number of bottles purchased

The formula 3p + 11 can be used to express how many bottles André purchased.

The formula that can be used to express how many bottles Jillian purchased is 5p + 3

Where:

P is the number of bottles in the purchased packs.

Counting how many bottles are in the pack

The expressions of Andre and Jillian would be equal if they each had the same number of bottles.

3p + 11 = 5p + 3

Take the subsequent actions to find the value of p:

Combine related words

5p - 3p = 11 - 3

2p = 8

Subtract 2 from both sides of the equation.

p = 4

Your question is incomplete but most probably your full question was

Andre and Jillian were shopping at the same grocery store for bottles of sports drinks for their kickball teams. Andre bought 3 packs of bottled drinks, plus 11 single bottles. Jillian purchased 5 packs, plus 3 singles. Andre and Jillian discovered that they had purchased the same number of bottles. How many bottles were in each of the packs? (All of the packs have the same number of bottles.)

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Answer:

7.5

Step-by-step explanation:

perimeter = 4 × side

√120 = 4s

s = (√120)/4

A = s²

A = [(√120)/4]²

A = 120/16

A = 7.5

The equation of the straight line passing through the point (1/2, 0) and parallel to the line y = 3x + 1 is y = 3x - ½ with slope m1 = 3 and m2 = 3.

Given line is y = 3x + 1

We need to find equation of line parallel to this line

Let us consider the equation of line as y = mx + c

We know that two lines are parallel if they have same slope i.e. m1 = m2

Here m1 = 3

So slope of required line m2 = 3

We need to find the value of c

Let us take a point (x1, y1) common to both lines

We know that (1/2, 0) is common to both lines

So x1 = 1/2, y1 = 0

Substituting these values in y = mx + c

0 = 3(1/2) + c

=> c = -1/2

Hence the equation of straight line passing through the point (1/2, 0) and parallel to the line y = 3x + 1 is y = 3x - 1/2.

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Answer:

Z= -3

Step-by-step explanation:

-6z-3z=27

-9z=27

/-9.   /-9

z= -3

Hopes this helps please mark brainliest

Answer:

D=74

D solution 8.60233

Step-by-step explanation:

Answer:

Therefore, when s is equal to 30, t is equal to 30 / 5 = <<30/5=6>>6.

Step-by-step explanation:

Direct variation means that the ratio between two variables is always constant. In this case, the constant ratio between s and t is equal to 20/4 = 5. This means that when t is equal to 4, s is equal to 20 and the ratio between the two is 5. If s is equal to 30, we can find the corresponding value of t by setting up the following equation:

s / t = 5

We can then solve for t by multiplying both sides of the equation by t to get:

s = 5 * t

If we substitute 30 for s, we get:

30 = 5 * t

We can solve for t by dividing both sides of the equation by 5:

t = 30 / 5

Therefore, when s is equal to 30, t is equal to 30 / 5 = <<30/5=6>>6.

The permutation combination of license plate is 35152000.

Numbers can be 10 digits (0, 1, 2, …, 9) and 26 letters (A, B, C, ..., Z).

Repetition is allowed, leaving 26 next choices for each letter used and 10 next choices for each digit used.

Therefore, according to the multiplication principle, the total number of different letter permutations.

26× 26 × 26 = 17576

and the total number of digit permutation: 10 × 10 × 10 = 1000

now,  they can be in any order:

⁶C₃ = 6!/(6−3)!3!

We have to consider 20 different combinations of positions.

So the total number of different license plates possible by the multiplication principle is

17576 × 1000 × 20 = 351520000

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The equation of the line is [tex]2x+y=1[/tex] passing through the points [tex](-1,3)[/tex] and [tex](2,3)[/tex]

The general equation can be written as [tex]y=mx+c[/tex]

where m is the slope and c is the intercept

The equation of a line passing through the points [tex](x_{1,} y_{1})[/tex] and [tex](x_{2,} y_{2})[/tex]

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

The equation is [tex]y-y_{1} =m(x-x_{1} )..........(1)[/tex]

[tex]m=\frac{y_{2}-y_{1} }{x_{2} -x_{1} }\\m=\frac{-3-3}{2-(-1)} \\m=\frac{-6}{3} \\m=-2[/tex]

Put this value in 1 equation

[tex]y-3=-2(x+1)\\y-3=-2x-2\\y=-2x+1\\2x+y=1[/tex]

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Answer: Second Pic, Probably the third.

Step-by-step explanation: little bit of guesswork

The required sample size of the given problem with a margin of error of at most 0.01 in a 99% confidence interval is 16590.

A margin of error is a factual estimation that records for the distinction among genuine and extended brings about an irregular overview test. In less complex terms, the margin of error you to measure the degree of unconventionality in information and exploration results.

Let p be the population proportion of cyanobacteria.

Given : E = 0.01

Critical value for 99% confidence interval : z = 2.576

If Ian does not want to rely on previous knowledge , then we assume p=0.5 because the largest standard error is at p=0.5.

Now, the required sample size = n

⇒0.5(1 - 0.5)([tex]\frac{2.576}{0.01}[/tex])^2

⇒ 0.25(257.6)^2

⇒ 0.25(66357.76)

⇒ 16589.44 ≈≈ 16590

Thus, the size of sample is 16590.

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