Match each quadratic function given in factored form
with its equivalent standard form listed on the left.
-f(*) = (x + 2)(x - 6)
f(x) = (x - 4)(x + 3)
f(x) = (x - 12)(x 1)
f(x) = (x -3)(x + 4)

The supplied lines' point of intersection has the x coordinate  is 6.

A coordinate system is a method for determining how to position points or other geometrical objects on a manifold, such as Euclidean space, uniquely using one or more numbers, or coordinates.

The x coordinate of the location where the ensuing lines intersect must be chosen.

3x + 5y = 78 ...........................(1)

2x - y = 0 ...............................(2)

The given system of equations must be solved in order to determine the x coordinate of the site of intersection.

Equation (ii) provides us with

2x = y

y = 2x ........................(3)

Equation I yields the result when the value of y from equation (iii) is substituted.

3x + 5(2x) = 78

3x + 10x = 78

13x = 78

x = 78/13

x = 6.

As a result, the supplied lines' point of intersection has the x coordinate  6.

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I understand that the question you are looking is :

3x 5y = 78 2x - y = 0 the point of intersection of the lines has an x-coordinate of _____.

A.  7

B.8

C. 6

D. -6

The total number of students that plotted the number of books they read was 18, making the 4th option, a correct choice, using the dot plot.

Any data that may be shown as dots or tiny circles is called a dot plot. Given that the height of the bar created by the dots indicates the numerical value of each variable, it is comparable to a bar graph or a simple histogram. Small amounts of data are shown using dot plots.

In the question, we are informed that Mrs. Kelley asked her students to plot the number of books they read over the summer. a dot plot titled books read over the summer goes from 0 to 7. 0 has 1 dot, 1 has 3 dots, 2 has 6 dots, 3 has 2 dots, 4 has 3 dots, 5 has 1 dot, 6 has 2 dots, and 7 has 0 dots.

We are asked to find the total number of students that plotted the number of books they read using the dot plot.

The dot plot is attached to the solution.

The total number of students = The total number of dots = 1 + 3 + 6 + 2 + 3 + 1 + 2 + 0 = 18.

Thus, the total number of students that plotted the number of books they read was 18, making the 4th option, a correct choice, using the dot plot.

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we can see that the center is (-3, 3) and the radius is 9 units.

The general circle equation, for a circle with a center (a, b) and radius R is given by:

(x - a)^2 + (y - b)^2 = R^2

Here we have the equation:

x^2 + y^2 + 6x = 6y + 63

Let's complete squares:

x^2 + y^2 + 6x - 6y =  63

(x^2 + 6x) + (y^2 - 6y) = 63

(x^2 + 2*3x) + (y^2 - 2*3y) = 63

Now we can add and subtract 9, (two times) so we get:

(x^2 + 2*3x + 9) - 9 + (x^2 - 2*3x + 9) - 9 = 63

(x + 3)^2 + (y - 3)^2 = 63 + 9 + 9 = 81 = 9^2

(x + 3)^2 + (y - 3)^2 = 9^2

Comparing with the general circle equation, we can see that the center is (-3, 3) and the radius is 9 units.

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Answer:

5/222

Step-by-step explanation:

you need to add all the cards together first

13 + 10 + 8 + 6 = 37

then you take out 1 card to find the first probability of the blue card (there are 6 blue cards out of 37)

so 6/37

that will be your first probability

then for the 2nd probability, you will have 1 less card grom the deck making it only 36 cards (after taking out the first one, there will be only 5 blue cards left)

making it 5/36

that will be the 2nd probability

then you multiply both these probabilities to find the answer

6/37 × 5/36 = 5/222

[tex]\huge \mathbb{ \underline{EXPLANATION:}}[/tex]

▪ [tex] \bold{\: x + y + z = 20}[/tex]

[tex]\\[/tex]

◆ As we have a [tex]\small\bold{sum \: of \: three \: integers}[/tex] equal to 20 and less than 10, we know the integers have to be between 2 and 9 (1 and 0 don't apply because the sum wouldn't be equal to 20 between three integers.

[tex]\large\tt{Note:}[/tex]

The first value would be X value, second Y value and third Z value.

[tex]\huge \mathbb{ \underline{ANSWER:}}[/tex]

[tex] \large\boxed{ \sf 36 \: solution}[/tex]

the graphed equation is:

y = -|x| + 1

On the graph, we can see an absolute value equation, which opens downwards, and passes through the points (1, 0) and (0,1).

The general absolute value equation is:

y = a*|x - b| + c

Because the vertex is at the point (0, 1), we know that:

b = 0, c = 1

Replacing that we get:

y = a*|x| + 1

Now, this must be zero when we evaluate in x = 1, then:

0 = a*|1| + 1

a = -1

Then the graphed equation is:

y = -|x| + 1

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Answer:

153 in²

Step-by-step explanation:

[tex]\sf \boxed{\text{\bf Area of rectangle = length * width}}[/tex]

[tex]\sf \boxed{\text{\bf Area of square = side *side}}[/tex]

Figure I:

   length = 12 in

   width = 6 in

Area of figure I = 12 * 6

                         = 72 in²

Figure II:

      length = 13 in

      width = 5 in

Area of figure II = 13 * 5

                          = 65 in²

Figure III:

       side = 4 in

Area of figure III = 4 * 4

                           = 16 in²

Area of irregular shape = 72 + 65 + 16

                                      = 153 in²

Step-by-step explanation:

Plug in known values

[tex]13.4 = 5.825\sqrt[3]{\frac{3590}{p}}\\[/tex]

Divide both sides by 5.825

[tex]2.3004 = \sqrt[3]{\frac{3590}{P}}\\[/tex]
Cube both sides

[tex]12.1738 = \frac{3590}{P}[/tex]

Multiply both sides by P

[tex]12.1738P = 3590[/tex]

Divide both sides by 12.1738

[tex]P = 294.895[/tex]

Round to nearest hp

[tex]P = 295[/tex]

So if you look at the radical, it's possible for it to be mistake for a square root, and not a cube root. This was Daniels mistake, so his steps were

[tex]13.4 = 5.825\sqrt[3]{\frac{3590}{p}}\\[/tex]

Divide both sides by 5.825

[tex]2.3004 = \sqrt[3]{\frac{3590}{P}}\\[/tex]

Square both sides

[tex]5.29197 = \frac{3590}{P}[/tex]

Multiply both sides by P

[tex]5.29197P = 3590[/tex]

Divide both sides by 5.29197

[tex]p\approx 678.385[/tex]

He also probably rounded during his steps, which would explain how he got 679 instead of 678 when rounding in the final, but either way his answer is completely off, and this is due to him mistakenly thinking the cube root was a square root.

Answer:

3.049

Step-by-step explanation:

Move the decimal place in 304.9% to the left two places in order to convert from a percentage to a decimal. 3.049 is the answer.

Brainliest, please :) Hope this helps!

The equation for the variable 'c' is c = d(q² + 1)/(q² - 1). By using simple arithmetic operations on the original equation, the required equation can be obtained.

An equation is a relationship between two expressions given by a mathematical statement.

There are different types of equations. They are linear equations, quadratic, polynomial, etc.

The given equation is

q = √((c + d)/(c - d))

Squaring on both, root gets canceled out

⇒ q² = (c + d)/(c - d)

⇒ q²(c - d) = (c + d)

⇒ cq² - dq² = c + d

Separating like terms  aside,

cq² - c = d + dq²

⇒ c(q² - 1) = d(q² + 1)

⇒ c = d(q² + 1)/(q² - 1)

Therefore, the required equation is c = d(q² + 1)/(q² - 1).

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Sophie will pay money equivalent to $ 100 for 15 m at the same store.

The term "money" in mathematics refers to a form of payment, such as bills, coins, and demand deposits, that is used to purchase goods and services. Money is used to pay for the worth or price of an item or service.

A country's monetary system is referred to as its currency.

In the case of Gareth,

Money paid for 9 m of climbing = $ 60

Money paid per m of climbing = $ 60/9

Thus, money paid by Sophie for 15 m of climbing = 15 * 60/9

                                                                                    = $ 100

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Answer:

f(x) = -x²

Step-by-step explanation:

Writing f(x) = -x² in vertex form gives f(x)=-(x-0)^2+0 which shows that the vertex (h,k) is at (0,0)

The other equations written in vertex form do not have (h,k) = (0,0)

Answer:

D

Step-by-step explanation:

Let x be the first batch

let y be the second batch

y=2x

His brothers each received 9 rolls from the second batch i.e. 9×4=36

So

2x= 36+ (10÷6)x

2x - (10÷6)x = 36

12x-10x = 216

x=108

and y= 2 × 108= 216

Answer:

382 cm²

Step-by-step explanation:

Front face + Back face:

A = 2(a + b)h/2

A = 2(14 cm + 8 cm)(7 cm)/2

A = 154 cm²

Left face:

A = 7 cm × 6 cm = 42 cm²

Right face:

A = 9 cm × 6 cm = 54 cm²

Bottom face:

A = 14 cm × 6 cm = 84 cm²

Top face:

A = 6 cm × 8 cm = 48 cm²

Total surface area =

= (154 + 42 + 54 + 84 + 40) cm²

= 382 cm²

The standard deviation of the x distribution is 0.2.

According to the statement

we have given that the the sample n is 64 and we have to find the standard deviation of the given sample.

So, For this purpose, we know that the

The standard deviation of the sample is the standard deviation of population divided by the square root of the length of the sample.

In this problem, we have that the value of alpha is

[tex]\alpha = 1.6[/tex]

Suppose that for aluminum alloy sheets of a particular type,

If X is the sample mean Young's modulus for a random sample of n = 64 sheets, and the standard deviation of the X distribution is given by

[tex]s = \frac{\alpha}{\sqrt{64} }[/tex]

then solve it then the standard deviation

s =  {1.6} / {8 }

s = 0.2

So, The standard deviation of the x distribution is 0.2.

Disclaimer: This question was incomplete. Please find the full content below.

Question:

Given that Young's modulus is a quantitative measure of stiffness of an elastic material. Suppose that for aluminum alloy sheets of a particular type, its mean value and standard deviation are 70 GPa and 1.6 GPa, respectively.

a. If X is the sample mean Young's modulus for a random sample of n = 64 sheets, the sampling distribution of X centered at 70 GPa, and the standard deviation of the X distribution is given by

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Answer:

y=[4]x + [12]

Step-by-step explanation:

Remember that parallel lines have identical slopes; and to make a line which passes through a point we will use point-slope form.

Familiarize yourself with point-slope form:

[tex]y-y1=m(x-x1)[/tex]

If the line is parallel to [tex]y=4x+11[/tex] the slope must be 4.

[tex]y-y1=4(x-x1)[/tex]

And we know the point it must pass through is (-2,4), so we can fill those values in too.

[tex]y-4=4(x+2)[/tex]

Now all we have to do is solve for y:
[tex]y-4=4(x+2)\\y-4=4x+8\\y=4x+12[/tex]

Answer:

[tex]y = 4x + 12[/tex]

Step-by-step explanation:

The solution is in the attached image

The solution of the given equation is :

cosθ = 1/2 when θ = π/3 + 2kπ or 5π/3 + 2kπ

cosθ = -1 when θ = π + 2kπ

Since cos2θ + sin2θ = 1, sin2θ = 1 - cos2θ

So, the given equation is equivalent to 2(1 - cos2θ) - cosθ = 1

-2cos2θ - cosθ + 1 = 0

2cos2θ + cosθ - 1 = 0 (multiplying the entire equation by -1)

(2cosθ - 1)(cosθ + 1) = 0 (taking common)

cosθ = 1/2 or cosθ = -1 (on equating it to zero)

cosθ = 1/2 when θ = π/3 + 2kπ or 5π/3 + 2kπ

cosθ = -1 when θ = π + 2kπ

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Answer:

27/30

Step-by-step explanation:

9/10 x3 to both sides = 27/30

Answer:

[tex]\dfrac{27}{30}[/tex]

Explanation:

In a normal fraction such as [tex]\frac{a}{b}[/tex], a is the numerator and b is the denominator.

Here the given fraction is [tex]\frac{9}{10}[/tex], to rewrite the fraction with a denominator of 30. Multiply both the numerator and denominator by 3.

[tex]\rightarrow \dfrac{9}{10}[/tex]

[tex]\rightarrow \dfrac{9\:\times\:3}{10 \:\times \: 3}[/tex]

[tex]\rightarrow \dfrac{27}{30}[/tex]

Both the fractions are equivalent to each other.

[tex]\frac{(-12)(3)+(-5)(9)}{3^2 + 9^2} \langle 3, 9 \rangle \\ \\ =-\frac{9}{10} \langle 3, 9 \rangle \\ \\ =\langle -\frac{27}{10}, -\frac{81}{10} \rangle[/tex]

So, the correct answer is Option 1.

The key features of the above given functions are correctly matched to their corresponding definition.

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Answer:

length = 235 yd

width = 58 yd

Step-by-step explanation:

Let the width be W.

L = 4W + 3

perimeter = 2(L + W)

perimeter = 2(4W + 3 + W)

perimeter = 2(5W + 3) = 10W + 6

We are told the perimeter = 586 yd

10W + 6 = 586

10W = 580

W = 58

L = 4W + 3 = 4(58) + 3 = 232 + 3 = 235

length = 235 yd

width = 58 yd

The function [tex]f(x)=4\sqrt[3]{x}[/tex] is a cube root function and the function end behavior is: [tex]x[/tex] → [tex]+[/tex] ∞, [tex]f(x)[/tex] → [tex]+[/tex] ∞, and as [tex]x[/tex] → - ∞, [tex]f(x)[/tex] → [tex]+[/tex] ∞

To determine the end behavior:

[tex]x[/tex] → [tex]+[/tex] ∞, [tex]f(x)[/tex] → [tex]+[/tex] ∞, and as [tex]x[/tex] → - ∞, [tex]f(x)[/tex] → [tex]+[/tex] ∞

Therefore, the function [tex]f(x)=4\sqrt[3]{x}[/tex] is a cube root function and the function end behavior is: [tex]x[/tex] → [tex]+[/tex] ∞, [tex]f(x)[/tex] → [tex]+[/tex] ∞, and as [tex]x[/tex] → - ∞, [tex]f(x)[/tex] → [tex]+[/tex] ∞

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The complete question is given below:

What is the end behavior of the function f of x equals negative 4 times the cube root of x?

As x → –∞, f(x) → –∞, and as x → ∞, f(x) → ∞.

As x → –∞, f(x) → ∞, and as x → ∞, f(x) → –∞.

As x → –∞, f(x) → 0, and as x → ∞, f(x) → 0.

As x → 0, f(x) → –∞, and as x → ∞, f(x) → 0.

Answer:

As x → –∞, f(x) → –∞, and as x → ∞, f(x) → ∞.

Step-by-step explanation:

I got it right on the test.

Answer:

p - 4

Step-by-step explanation:

Prime number is a number that only has 2 factors, 1 and the number itself. Therefore, multiplying p by 2 or 7 means giving the number more than 2 factors, which would make the number no longer prime. Squaring the prime number itself does the same.

Let p = 7.

2p = 2*7 = 14                  14 = 1*2*7*14

7p = 7*7 = 49                 49 = 1*7*49

p - 4 = 7 - 4 = 3              3 = 1*3

p^2 = 7^2 = 49               49 = 1*7*49

1. The value of the linear correlation coefficient r is given as 0.8159. The correct option is a. There is insufficient evidence to support the claim of a nonlinear correlation between the two variables

2. The scatterplot reveals a distinct pattern that is not a straight-line pattern.

This is the data that we get when we try to get the existing relationship that is in existence between the variables that are used in a regression equation.

The value of r was calculated using a statistical tool online. The graph showed us it was not a straight line. The value of the r = 0.8159

The results of the test is in the attachment

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Answer:

-1.8

Step-by-step explanation:

its bigger than -9 and -4.2

Answers:

a) 49 square tiles - did the work on paper.

b) 83 circular tiles - did the work on paper.

c) C: could be even or odd - all patterns had both even and odd amounts of square and circular tiles.

Step-by-step explanation:

I did all the work on paper it took a while to do it. pls mark brainliest

Answer:

Step-by-step explanation:

15 rows adding 4 additional seats to each. Once at end add all seats in rows together for the final answer.

1-25

2-29

3-33

4-37

5-41

6-45

7-49

8-53

9-57

10-61

11-65

12-69

13-73

14-77

15-81

Add all togther. 25+29+33+37+41+45+49+53+57+61+65+69+73+77+81=795

So there are 795 seating capacity.