Re-write the quadratic function below in Standard Form y=-5(x+1)²+7

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:

y= 2x + 10

Step-by-step explanation:

The variable depends on the $2 so, the green box should be 2

Step-by-step explanation:

log 6 = log (2×3) = log 2 + log 3 = 0.3010+0.4771

=0.7781

Answer:

[tex]\sf \log_{10}6=0.7781[/tex]

Step-by-step explanation:

Given:

[tex]\sf \log_{10} 2 = 0.3010[/tex]

[tex]\sf \log_{10} 3 = 0.4771[/tex]

To find log₁₀ 6, first rewrite 6 as 3 · 2:

[tex]\sf \implies \log_{10}6=\log_{10}(3 \cdot 2)[/tex]

[tex]\textsf{Apply the log product law}: \quad \log_axy=\log_ax + \log_ay[/tex]

[tex]\implies \sf \log_{10}(3 \cdot 2)=\log_{10}3+\log_{10}2[/tex]

Substituting the given values for log₁₀ 3 and log₁₀ 2:

[tex]\begin{aligned} \sf \implies \log_{10}3+\log_{10}2 & = \sf 0.4771+0.3010\\ & = \sf 0.7781 \end{aligned}[/tex]

Therefore:

[tex]\sf \log_{10}6=0.7781[/tex]

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Let hats be x

Let shirts be y

We can set up a system of equations to figure out the cost of one hat.

5x+3y = 176 and 3x+5y = 208

Since we are finding the cost of the hats, we will need to isolate x from the equation. We can first get rid of y. One way we can do that is by multiplying the first equation with 5 and the second one with -3, effectively making y add up to 0 when we solve for x.

5(5x+3y = 176) --> 25x+15y = 880

-3(3x+5y = 208) --> -9x-15y = -624

We can now add the 2 equations together and solve for x.
25x+15y = 880

-9x-15y = -624

+>>>>>>>>>>>>>>>

16x = 256

x = 16

So the the cost of one hat is 16 dollars.

Answer:

$16

Step-by-step explanation:

Define the variables:

Create two equations using the defined variables and the given information.

Equation 1

Five hats and three shirts cost $176.

⇒ 5x + 3y = 176

Equation 2

Three hats and five shirts cost $208.

⇒ 3x + 5y = 208

Rewrite Equation 2 to make y the subject:

[tex]\implies \sf 3x+5y-3x=208-3x[/tex]

[tex]\implies \sf 5y=208-3x[/tex]

[tex]\implies \sf \dfrac{5y}{5}=\dfrac{208-3x}{5}[/tex]

[tex]\implies \sf y=\dfrac{208-3x}{5}[/tex]

Substitute the found expression for y into Equation 1 and solve for x:

[tex]\implies \sf 5x+3\left(\dfrac{208-3x}{5} \right)=176[/tex]

[tex]\implies \sf 5x+\dfrac{624-9x}{5}=176[/tex]

[tex]\implies \sf 5x+124.8-1.8x=176[/tex]

[tex]\implies \sf 3.2x+124.8=176[/tex]

[tex]\implies \sf 3.2x+124.8-124.8=176-124.8[/tex]

[tex]\implies \sf 3.2x=51.2[/tex]

[tex]\implies \sf \dfrac{3.2x}{3.2}=\dfrac{51.2}{3.2}[/tex]

[tex]\implies \sf x=16[/tex]

Therefore, the cost of one hat is 16 dollars.

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Answer:

Step-by-step explanation:

[tex]\dfrac{ 1 }{ 2 } \times 12\times 15\times \sin ( 110 )[/tex]

==> 84.57

Answer:

[tex]e^{4x}=e^4+4e^4(x-1)+8e^4(x-1)^2+...[/tex]

[tex]\displaystyle e^{4x}=\sum^{\infty}_{n=0} \dfrac{4^ne^4}{n!}(x-1)^n[/tex]

Step-by-step explanation:

Taylor series expansions of f(x) at the point x = a

[tex]\text{f}(x)=\text{f}(a)+\text{f}\:'(a)(x-a)+\dfrac{\text{f}\:''(a)}{2!}(x-a)^2+\dfrac{\text{f}\:'''(a)}{3!}(x-a)^3+...+\dfrac{\text{f}\:^{(r)}(a)}{r!}(x-a)^r+...[/tex]

This expansion is valid only if [tex]\text{f}\:^{(n)}(a)[/tex] exists and is finite for all [tex]n \in \mathbb{N}[/tex], and for values of x for which the infinite series converges.

[tex]\textsf{Let }\text{f}(x)=e^{4x} \textsf{ and }a=1[/tex]

[tex]\text{f}(x)=\text{f}(1)+\text{f}\:'(1)(x-1)+\dfrac{\text{f}\:''(1)}{2!}(x-1)^2+...[/tex]

[tex]\boxed{\begin{minipage}{5.5 cm}\underline{Differentiating $e^{f(x)}$}\\\\If $y=e^{f(x)}$, then $\dfrac{\text{d}y}{\text{d}x}=f\:'(x)e^{f(x)}$\\\end{minipage}}[/tex]

[tex]\text{f}(x)=e^{4x} \implies \text{f}(1)=e^4[/tex]

[tex]\text{f}\:'(x)=4e^{4x} \implies \text{f}\:'(1)=4e^4[/tex]

[tex]\text{f}\:''(x)=16e^{4x} \implies \text{f}\:''(1)=16e^4[/tex]

Substituting the values in the series expansion gives:

[tex]e^{4x}=e^4+4e^4(x-1)+\dfrac{16e^4}{2}(x-1)^2+...[/tex]

Factoring out e⁴:

[tex]e^{4x}=e^4\left[1+4(x-1)+8}(x-1)^2+...\right][/tex]

Taylor Series summation notation:

[tex]\displaystyle \text{f}(x)=\sum^{\infty}_{n=0} \dfrac{\text{f}\:^{(n)}(a)}{n!}(x-a)^n[/tex]

Therefore:

[tex]\displaystyle e^{4x}=\sum^{\infty}_{n=0} \dfrac{4^ne^4}{n!}(x-1)^n[/tex]

For the given function f(x) = 5x² + 2x - 3,

Part A: The x-intercepts of the graph f(x) are: (-1, 0) and (3/5, 0).

Part B: The vertex of the graph of f(X) is going to be a minimum and its coordinates are (-0.2, -3.2).

Part C: The values obtained in the part A and Part B are used for graphing the given function. Since the vertex is minimum, the parabola opens upwards.

The x-intercepts of a function or equation are obtained at y = 0.

Then, on substituting y = 0 in the function gives the x-coordinate i.e., the x-intercept.

To calculate the x coordinate of vertex(h, k), use the formula mentioned below:

h = -b/2a

When the function is in the form of ax² + bx + c.

Then, to calculate the y-coordinate of the vertex, substitute obtained h value in the place of x in the function.

Thus, the required coordinates of the vertex are obtained as (h, k).

It is given that,

f(x) = 5x² + 2x - 3

Part A: Finding the x-intercepts:

Substituting y = 0 i.e., f(x) = 0;

⇒ 5x² + 2x - 3 = 0

On simplifying/factorizing,

⇒ 5x² + 5x - 3x - 3 = 0

⇒ 5x(x + 1) - 3(x +1) = 0

⇒ (5x - 3)(x + 1) =0

∴ x = 3/5 or x = -1

Thus, the x-intercepts are (3/5, 0) and (-1, 0).

Part B: Finding the vertex of the given function:

We have h = -b/2a

From the given function 5x² + 2x - 3; a = 5, b = 2 and c = -3

So, h = -2/2(5) = -1/5 = -0.2

Then, on substituting h = x = -0.2 in the function we get

k = 5(-0.2)² + 2(-0.2) - 3

k = -3.2

Thus, the coordinates of the vertex are (h, k) = (-0.2, -3.2).

Since a > 0 i.e., 5 > 0, the vertex of the graph is going to be minimum and the graph of f(x) opens upwards.

Part C: Steps to graph f(X):

Step 1: Plot the x-intercepts in the coordinate plane

Step 2: Plot the vertex of the function

Step 3: draw a curve line passing through them, opening towards up.

Thus, the graph of the given function is plotted as shown below.

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The total surface area of the figure is 92 m².

The surface area of a figure is the sum of the whole sides of the figure.

Therefore,

surface area = 4 × 4 + 4 × 4 + 6 × 4 + 2 × 4 + 1 / 2 (2 + 6)3.5 +  1 / 2 (2 + 6)3.5

Hence,

surface area = 16 + 16 + 24 + 8 + 14 + 14

Therefore,

surface area = 32 + 24 + 8 + 28

surface area = 56 + 8 + 28

surface area = 92 m²

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we conclude that the distance to the other side is 467 feet.

We know that the width of the river is 602ft. This means that the distance from shore to shore is 602 feet.

If the boy is at a distance of 135 from the shore, then the distance to the other side is given by the difference:

d = 602ft - 135ft = 467ft

Then, we conclude that the distance to the other side is 467 feet.

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Answer:

x = 1; y = 2

Step-by-step explanation:

y = 3x − 1

y = -4x + 6

In the first equation, y = 3x - 1.

Substitute 3x - 1 for y in the second equation.

3x - 1 = -4x + 6

7x = 7

x = 1

Substitute 1 for x in the first original equation.

y = 3x - 1

y = 3(1) - 1

y = 3 - 1

y = 2

Solution: x = 1; y = 2

Answer: (-5, -5)

Step-by-step explanation:

(-4, 0)

Here, -4 is our x value and 0 is our y value

The x value moves horizontal (left and right) while the y value moves vertical (up and down)

If we move 1 unit left, we change x by -1 so, -4 -1 = -5

If we move 5 units down, we change y by -5 so, 0 -5 = -5

Therefore,

our new endpoint is: (-5, -5)

[tex]\boldsymbol{\sf{Therefore \to \ 5.75\not{h}*\dfrac{60 \ min}{1\not{h}} =345 \ min }}[/tex]

5.75 hours is equal to 345 minutes.

Answer:

1. Given.

2. Alternate Interior Angles Theorem.

3. m<2 + m<7 = 180 by definition of supplementary angles. By definition of congruent angles, m<2 = m<4 and m<5 = m<7, therefore m<4 + m<5 = 180 by substitution property of equality. By definition of supplementary angles, <4 is supplementary to <5.

4. Converse of Consecutive Angles Theorem.

Answer:

C. slope

Greetings !

The symbol for slope is "m". Slope can be calculated by taking any two locations along a line and calculating the ratio of the RISE to the RUN (the ratio of the difference between vertical positions of the locations to the difference between horizontal positions of the locations).

Answer: slope.

Step-by-step explanation:

Based on the given data; the table represent an inverse variation and the equation that model the data in the table is y = 8/x

y = k × x

4 = k × 2

4 = 2k

k = 4/2

k = 2

when y = 2 and x = 4

y = k × x

= 2 × 4

y = 8

y = k/x

4 = k / 2

8 = k

when y = 2 and x = 4

y = k/x

2 = k/4

2 × 4 = k

k = 8

So,

y = k/x

y = 8/x

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The measure of the angle rst is [tex]105^{o}[/tex].

According to the theorem, a quadrilateral can be inscribed by a circle if and only if its opposing angles are supplementary. A quadrilateral that may be encircled by a circle is known as a cyclic quadrilateral.

The sum opposite angles of a quadrilateral is 180 degrees.

We can see that the angles rst and angle tqr are opposite angles of quadrilateral qrst, hence supplementary angles.

Therefore,

<RST + <TQR = 180

5x+15 + 4x+ 3 = 180

9x + 18 = 180

9x = 180 - 18

9x = 162

x = 162/9

x = 18

Since <RST = 5x+15

<RST = 5(18) + 15

<RST = 90 + 15

<RST = 105degrees

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Answer:

B. Property right are assigned to the party who is being

The predicted value (in dollars) for maintenance expenses when a truck is 7 years old is $626.3.

In this question,

The equation for least regression line to this data set is

y' = 76.82x + 88.56 ------- (1)

Number of years, x = 7

The general form of equation for least regression line is

y' = a + bx

where y is the dependent variable, x is the independent variable, a is the intercept of regression line and b is the slope of regression line.

The predicted value (in dollars) for maintenance expenses when a truck is 7 years old can be calculated as

y' = 76.82x + 88.56

Substitute the value of x in the above equation, we get

y' = 76.82(7) + 88.56

y' = 537.74 + 88.56

y' = 626.3

Hence we can conclude that the predicted value (in dollars) for maintenance expenses when a truck is 7 years old is $626.3.

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The value of the Population Variance is 100.

According to the statement

we have given that the A population of N = 10 scores has μ = 50 and σ = 5. And we have to find the population variance.

So, For this purpose,

we know that the population variance can be defined as the average of the distances from each data point in a particular population to the mean squared, and it indicates how data points are spread out in the population.

Population variance = mean /(standard deviation/number of samples)

Population variance = μ / (σ /N )

Substitute the values in it and then

Population variance = 50 / (5 /10 )

Population variance = 50 / (0.5 )

Population variance = 100.

So, The value of the Population Variance is 100.

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

Question:

A population of N = 10 scores has μ = 50 and σ = 5. What is the population variance?

a. 10

b. the square root of 5

c. the square root of 50

d. 25

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Answer:

When dividing both sides by a negative.

Step-by-step explanation:

When dividing OR multiplying both sides by a negative, we need to flip the inequality signs.

The general term for the arithmetic sequence; -13, -11, -9, -7 is Tn = -15 - 2n.

-13, -11, -9, -7

Common difference, d = Second term - first term

= -11 - (-13)

= -11 + 13

= 2

Therefore,

Tn = a + (n - 1)d

Where,

Tn = a + (n - 1)d

= -13 + (n - 1)2

= -13 - 2n - 2

Tn = -15 - 2n

So therefore, the general term for the arithmetic sequence; -13, -11, -9, -7 is Tn = -15 - 2n.

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Answer: x= 3.4

Step-by-step explanation:

Solve for x by simplifying both sides of the equation, then isolating the variable.

Answer:

x = 3.4

Step-by-step explanation:

[tex]10x - 4.5 + 3x = 12x -1.1 \\ 13x - 4.5 = 12x - 1.1 \\ 13x - 12x - 4.5 = 12x - 12x - 1.1 \\ x - 4.5 = - 1.1 \\ x - 4.5 + 4.5 = - 1.1 + 4.5 \\ x = 3.4[/tex]

Answer: 2000 meters

Step-by-step explanation: A kilometer means 1,000 meters a kilo means 1000. So, 2 x1000 = 2000 meters.

Answer: D

Step-by-step explanation:

The first term is 3 and the common difference is 2.

Substituting into the explicit formula for an arithmetic sequence gives D as the correct answer.

Answer:

Read explanation

Step-by-step explanation:

I answered another one of your questions just like this in detail so I'll keep this one shorter.

Domain: (-∞, 0]

Range: (-3,∞)

x-intercept: Approximately -3.75

y=intercept: -3

Answer:

11/20

Step-by-step explanation:

You could turn them all into equivalent fractions, but the common denominator would be 1,763,580.  Yuck.

Look at the relationship for the numerators to the denominators.  The only numerator that is more than half of its denominator is 11/20.  Half of 20 would be 10 and 11 has a larger value than 10, so as a decimal, it would be more than .5.  All of the other numerators are less than half, so that they have to less than .5.

If you changed all of the numbers to decimals, you would see that 11/20 has the largest value.

Answer: About (-2.414, 0) and (0.414, 0)

Step-by-step explanation:

       Let us graph the equation given and see what the x-intercepts are. These are points where the line intercepts the x-axis. See attached.

       This means our x-intercepts are at about (-2.414, 0) and (0.414, 0).

                        These are also equal to [tex]-1-\sqrt{2}[/tex] and  [tex]-1+\sqrt{2}[/tex]

Answer:

[tex]x = \bold{0.414} \textrm{ and } x= \bold{-2.414}[/tex]

Step-by-step explanation:

See attached graph for a visual

The x-intercepts of a graph are where the graph crosses the x-axis ie where the value of y = 0 The equation of the graph is y=-x^{2}-2x+1

Setting y = 0 and solving for the resultant equation will provide the x-intercepts

[tex]0=-x^{2}-2x+1or-x^{2}-2x+1=0[/tex]

Reversing the signs gives us

[tex]x^{2}+2x-1=0[/tex]

This is a quadratic equation of the form [tex]ax^{2}+bx+c=0[/tex] with a = 1, b = 2 and c=-1

For an equation of this form the roots of the equation ie the values of x which satisfy the equation are given by

[tex]\frac{-b\pm\sqrt{{b^{2}-4ac}}}{2a}[/tex]

Substituting we get the two roots as

[tex]x=\frac{-2\pm\sqrt{{2^{2}-4(1)(-1}}}{2}=\frac{-2\pm\sqrt{{4-(-4)}}}{2}x=\frac{-2\pm\sqrt{8}}{2}8 = 4(2)\sqrt{8}=\sqrt{4}\sqrt{2} = 2\sqrt{2}[/tex]

So the two roots are

[tex]x=\frac{-2\pm2\sqrt{2}}{2}[/tex]

Dividing by 2 we get the two roots(x-intercepts) as

[tex]x=-1\pm\sqrt{2}\\\\x_{1}=-1+\sqrt{2} =-1+1.414=\bold{0.414}[/tex]

[tex]x_{2}=-1-\sqrt{2}=-1-1.414=\boldsymbol{-2.414}[/tex]

Answer:

176 square feet

Step-by-step explanation:

add the areas of the rectangle and triangle

rectangle area is

16 times 8 which is

128

rectangle area is

1/2 times 12 times 8 which is

48

then add them

128 plus 48 is

176 square feet

Rotating 90 degrees counterclockwise: [tex](x,y) \longrightarrow (-y,x)[/tex]

[tex]A(-4,4) \longrightarrow A'(-4, -4)\\\\B(-3, 4) \longrightarrow B'(-4, -3)\\\\C(-3, 1) \longrightarrow C'(-1, -3)\\\\D(-4, 1) \longrightarrow D'(-1, -4)[/tex]

Translate along [tex]\langle 3, 4 \rangle[/tex]: [tex](x,y) \longrightarrow (x+3, y+4)[/tex]

[tex]A'(-4, -4) \longrightarrow A''(-1, 0)\\\\B'(-4, -3) \longrightarrow B''(-1, 1)\\\\C'(-1, -3) \longrightarrow C''(2, 1)\\\\D'(-1, -4) \longrightarrow D''(2, 0)[/tex]