Rate of change from the line

Answer:  [tex]y=(x +3)^2 -6[/tex]

Step-by-step explanation:

The equation of a parabola in Vertex form is:

[tex]y=a(x-h)^2+k[/tex]

Where [tex](h,k)[/tex] is the vertex of the parabola

We can rewrite the function [tex]f(x)= x^2 + 6x + 3[/tex] as:

 [tex]y= x^2 + 6x + 3[/tex]

 In order to convert it into vertex form we need to Complete the square:

Take the coefficient of the x term, divide it by 2 and square it:

[tex](\frac{6}{2})=3^2[/tex]

Add and subtract 3² on the right side:

[tex]y= x^2 + 6x+3^2 + 3-3^2[/tex]

Now we must convert the right side to a squared expression, then we get:

 [tex]y=(x +3)^2 -6[/tex]

Answer:

27

Step-by-step explanation:

Answer:

27 units on edge.

Answer:

12

Step-by-step explanation:

2(a+3)

Given a = 3, all you need to do is just plug in a = 3 into the expression

2(3 + 3)

= 2 (6)

= 12

Answer:

2(3+3)

6x2

12

Step-by-step explanation:

Answer:

The volume of the sphere is 24 cm³

Step-by-step explanation:

* Lets explain the difference between the cylinder and the sphere

- The cylinder has two circular bases and a curved surface

- The bases of the cylinder have radius r and the curved surface has

 a height h

- The volume of the cylinder = area of its base × its height

∵ The area of the circle is πr²

∴ The volume of the cylinder is V = π r² h

- A sphere is a perfectly round geometrical object in three-dimensional

 space

- It the set of points that are all at the same distance r from a given point

 that means its radius equals its height

- The volume of the sphere = 4/3 π r³

* Now lets solve the problem

∵ The cylinder and the sphere have the same radius and height

∵ The volume of the cylinder is 18 cm³

- Lets equate the rule of the volume of the cylinder by 18

∵ The volume of the cylinder = π r² h

∴ π r² h = 18 ⇒ divide both side by π

∴ r² h = 18/π

- The sphere and the cylinder have the same radius and height

∴ The radius and height of the sphere have the same value of the

   cylinder

∵ The the height of the sphere is its radius

∴ r²h of the cylinder = r³ in the sphere

∴ r³ = 18/π

- Substitute this value in the rule of the volume of the sphere

∵ The volume of the sphere = 4/3 π r³

∴ The volume of the sphere = 4/3 π (18/π) ⇒ cancel π's

∴ The volume of the sphere = 4/3 (18) = 24 cm³

* The volume of the sphere is 24 cm³

Answer:

Step-by-step explanation:

I think you meant 3([7/5]x + 4) - 2(3/2 - [5/4]x).  If that's the case, then identify the LCD:  It is 20.  Multiply both [7/5]x + 4 and 3/2 - [5/4]x by 20 and then divide the resulting expression by 20:

3(28x + 80) - 2(30 - 25x)

------------------------------------

               20

Next, perform the indicated multiplication:

 84x + 240 - 60 + 50x

----------------------------------

                 20

This simplifies to:

 34x + 180        17x + 9

---------------- = ----------------

       20                 10

Next time, please share the answer choices.

Answer:

67x/10 + 9

Step-by-step explanation:

Simplify 7/5x to 7x/5

3(7x/5 + 4) -2(3/2 - 5/4x)

Simplify 5/4x to 5x/4

3(7x/5 + 4) -2(3/2 - 5x/4)

Expand

21x/5 + 12 - 3 + 5x/2

Collect like terms

(21x/5 + 5x/2) + (12 - 3)

Simplify

67x/10 + 9

Answer: $16.850

Step-by-step explanation:

Subtract 2x^2+55x+10 - (2x^2 -15x-40)

70x+50

Then put in 240 for x

Answer:

Part 1) [tex]10\°\ C=50\°\ F[/tex]

Part 2) [tex]87\°\ F=30.6\°\ C[/tex]

Part 3) [tex]-5\°\ C=23\°\ F[/tex]

Part 4) [tex]10\°\ F=-12.2\°\ C[/tex]

Step-by-step explanation:

we know that

The formula to convert degrees Celsius to degrees Fahrenheit is equal to

[tex]F=(\frac{9}{5}C)+32[/tex]

The formula to convert degrees Fahrenheit to degrees Celsius is equal to

[tex]C=(F-32)\frac{5}{9}[/tex]

Part 1) we have

10 degrees Celsius

Convert to degrees Fahrenheit

[tex]F=(\frac{9}{5}10)+32[/tex]

[tex]F=50\°[/tex]

Part 2) we have

87 degrees Fahrenheit

Convert to degrees Celsius

[tex]C=(87-32)\frac{5}{9}[/tex]

[tex]C=30.6\°[/tex]

Part 3) we have

-5 degrees Celsius

Convert to degrees Fahrenheit

[tex]F=(\frac{9}{5}(-5))+32[/tex]

[tex]F=23\°[/tex]

Part 4) we have

10 degrees Fahrenheit

Convert to degrees Celsius

[tex]C=(10-32)\frac{5}{9}[/tex]

[tex]C=-12.2\°[/tex]

Answer:

Degree Celsius:        Degree Fahrenheit:

10                                         50

30.6                                     87

-5                                         23

-12.2                                     10

Step-by-step explanation:

Hope this helps!!

Answer:

It would be (-2,11)

Step-by-step explanation:

I used desmos for this, since it says graphing.

desmos.com/calculator/glijhd4ksg

look at the link to view the graph and solution.

Normally, you would plot points from one line, connect them, then do the same for the other line.

Hope this helps!

When using a graph to find the solution you must look at where the lines intersect. Look at the graph provided below:

As you can see the graph below shows that the two lines intersect at point (-2, 11)

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:

Option B [tex]f(x)=-x^{2}+12x-32[/tex]

Step-by-step explanation:

we know that

For the given values, the quadratic function is a vertical parabola open downward (vertex is a maximum)

The equation in vertex form is equal to

[tex]f(x)=a(x-h)^{2} +k[/tex]

where

(h,k) is the vertex

a is a coefficient

we have

(h,k)=(6,4)

so

[tex]f(x)=a(x-6)^{2} +4[/tex]

Find the value of a

For x=8, y=0 -----> the y-intercept

substitute

[tex]0=a(8-6)^{2} +4[/tex]

[tex]0=a(2)^{2} +4[/tex]

[tex]0=4a +4[/tex]

[tex]a=-1[/tex]

substitute

[tex]f(x)=-(x-6)^{2} +4[/tex]

Convert to standard form

[tex]f(x)=-(x^{2}-12x+36) +4[/tex]

[tex]f(x)=-x^{2}+12x-36+4[/tex]

[tex]f(x)=-x^{2}+12x-32[/tex]

The graph in the attached figure

Answer:

16 36 169 100

Step-by-step explanation:

just square them

16, 36, 169, 100

square of 4

[tex]4^{2}=16[/tex]

square of 6

[tex]6^{2}=36[/tex]

square of 13

[tex]13^{2}=169[/tex]

square of 10

[tex]10^{2} = 100[/tex]

In the mathematics squaring is easy to understand. Squaring the number means multiplying it by itself. Squaring is written on mathematical symbols by putting a two above the number you are squaring to show that it is multiplied two times

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To solve this you must use Pythagorean theorem:

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

a and b are the legs (the sides that form a perpendicular/right angle)

c is the hypotenuse (the side opposite the right angle)

In this case...

a = 5

b = 8

c = x

^^^Plug these numbers into the theorem

[tex]5^{2} +8^{2} =x^{2}[/tex]

simplify

25 + 64 = [tex]x^{2}[/tex]

89 = [tex]x^{2}[/tex]

To remove the square from x take the square root of both sides to get you...

√89 = x  

(choice A)

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:

The correct answer is first option  √89

Step-by-step explanation:

Points to remember

Pythagorean theorem

For a right triangle,

Base² + Height² = Hypotenuse²

To find the vale of x

From the figure we can see a right triangle,

Base = 8 units and height = 5 units

Hypotenuse² = Base² + Height²

x² = 8² + 5²

 = 64 + 25

 = 89

x = √89

The correct answer is first option  √89

Answer:

C. triangles

Step-by-step explanation:

Pythagoras Theorem is a theorem which states you can work out a side of a right - angled triangle using the other 2 sides. Pythagoras will not work on shapes except from a right - angled triangle and square

Answer:

D

Step-by-step explanation:

[tex]1/3)^{x}[/tex] = [tex]\frac{1}{3^{x} }[/tex] = [tex]3^{-x}[/tex]

and

[tex]27^{x+2}[/tex] = [tex](3^{3})^{x+2}[/tex] = [tex]3^{3(x+2)}[/tex] = [tex]3^{3x+6}[/tex]

Hence expression D is equivalent

Answer with explanation:

Pre image= Coordinates of point X= (3,4)

When point ,(x,y) is rotated by an angle of 180°, then coordinates of image that is point (x,y) after rotation = (-x, -y)

⇒≡Coordinates of point X(3,4) after rotation by an angle of 180°=X'(-3,-4)

The coordinates after a rotation of 180 degrees about the origin is: X'(-3, -4)

There are different types of transformation such as:

Translation

Rotation

Reflection

Dilation

The transformation rule for the rotation about 180 degrees (180°) about the origin is (x,y)→(−x,−y) .

Thus:

X(3, 4) → X'(-3, -4)

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Answer:

The given expression is equivalent to 3(2^(3/8))x.

Step-by-step explanation:

The given expression (3 root 8^1/4 x) can be written as:

3√(8^(1/4))x

we know that 2^3 = 8

= 3√(2^(3/4))x

We know that √x = (x)^(1/2)

= 3(2^((3/4)(1/2))x

Powers multiply with each other, 3*1/4*2 = 3/8

= 3(2^(3/8))x

B^2 for B = 9 means squaring the value of 9, resulting in 9^2, which equals 81. Therefore, B^2 for B = 9 is 81.

To evaluate B^2 for B = 9, you simply substitute the value of B into the expression and then perform the calculation. Here's how it's done:

B^2 means "B squared," which is equivalent to multiplying B by itself. So, for B = 9, we have:

[tex]\(B^2 = 9^2 = 9 \times 9\)[/tex]

Now, calculate the product:

[tex]\(9 \times 9 = 81\)[/tex]

So, B^2 for B = 9 is equal to 81.

In summary, when you substitute B = 9 into the expression B^2, you get 9^2, which equals 81. Therefore, B^2 for B = 9 is 81.

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For this case we have that by definition, the equation of a line in the slope-intersection form is given by:

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

Where:

m: It's the slope

b: It is the cut-off point with the y axis

[tex]m = \frac {y2-y1} {x2-x1}[/tex]

We have the following points:

[tex](x1, y1): (- 7,25)\\(x2, y2): (- 4,13)[/tex]

Substituting the values:[tex]m = \frac {13-25} {- 4 - (- 7)} = \frac {-12} {- 4 + 7} = \frac {-12} {3} = - 4[/tex]

Thus, the line is of the form:

[tex]y = -4x + b[/tex]

We substitute one of the points and find "b":

[tex]13 = -4 (-4) + b\\13 = 16 + b\\b = 13-16 = -3[/tex]

Finally we have to:

[tex]y = -4x-3[/tex]

Answer:

The equation es [tex]y = -4x-3[/tex]

Answer:

She mixed up the slope and y-intercept when she wrote the equation in step 3.

ANSWER

C) (6,-8)

EXPLANATION

The equations are:

[tex]y = \frac{1}{3}x - 10[/tex]

and

[tex]2x+y=4[/tex]

We substitute the first equation into the second equation to get:

[tex]2x + \frac{1}{3}x - 10 = 4[/tex]

We multiply through by 3 to get:

[tex]6x + x - 30= 12[/tex]

Group similar terms,

[tex]6x + x = 30 + 12[/tex]

[tex]7x = 42[/tex]

Divide both sides by 7 to get,

[tex]x = \frac{42}{7} = 6[/tex]

Put this value of x into the first equation to get;

[tex]y = \frac{1}{3} (6) - 10[/tex]

[tex]y = 2 - 10 = - 8[/tex]

Answer:

(9m-1)(9m+1)

Step-by-step explanation:

This is a difference of squares

(9m)^2-1^2

Use a^2-b^2=(a-b)(a+b)

So the answer is (9m-1)(9m+1)

Answer:

Step-by-step explanation:

[tex]81m^2-1=9^2m^2-1^2=(9m)^2-1^2\\\\\text{use}\ a^2-b^2=(a-b)(a+b)\\\\=(9m-1)(9m+1)[/tex]

Answer:

y = 2x + 2

Step-by-step explanation:

Start at point (2, 6).

Go up 2 units up (rise = 2) and 1 unit right (run = 1). Now you are at point (3, 8) which is on the graph.

slope = rise/run = 2/1 = 2

The slope of the graph is 2. m = 2

Now look at point (0, 2). The y-intercept is 2. b = 2

The equation is

y = mx + b

y = 2x + 2

Answer:

y = 2x + 2

Step-by-step explanation:

Here we're asked to come up with a linear function relating x and y.

First we find the slope of the line.  As we move from (0, 2) to (3, 8), x increases by 3 and y by 6.  Thus, the slope is

m = rise / run = 6 / 3 = 2.  

Plugging givens into the slope-intercept formula y = mx + b, we find b:

2 = 2(0) + b, so that b = 2.

Then the desired relationship between x and y is y = 2x + 2.

The percentage of bags contain between 65 and 85 potato chips is 95%.

Step-by-step explanation:

A probability distribution that is symmetric and the data near the mean are more frequent than far is known as a normal distribution. Normal distributions are important in statistics and are often used to represent real-valued random variables.

The formula for finding the percentage of bags using normally distributed is given as

f(x) = (1 / sigma * square root 2 *pi) * e^((-1/2)*((x-u)/sigma))

Substituting the values of mean and standard deviation,

The percentage of bags contain between 65 and 85 potato chips is 95%.

Final answer:

Using the empirical rule, approximately 95% of potato chip bags will contain between 65 and 85 chips, as this range spans two standard deviations away from the mean in a normal distribution.

Explanation:

The question is regarding the percentage of potato chip bags that contain a specific number of chips based on a normal distribution. With a mean of 75 and a standard deviation of 5, the range of chips in the bags is between 65 and 85. To find this percentage, we use the empirical rule, sometimes referred to as the 68-95-99.7 rule, which states that approximately 68% of the data within one standard deviation of the mean, 95% within two standard deviations, and 99.7% within three standard deviations.

Since the range from 65 to 85 chips spans two standard deviations from the mean (65 is 10 chips away from 75 which is two standard deviations as 5*2=10, and the same logic applies for 85), we can say that approximately 95% of the bags will contain between 65 and 85 potato chips.

Answer:

solution = (1.-2)

Step-by-step explanation:

put x= 1 and y = -2 in this system  :  y=-4x+2 and y + 2x = 0

you have :  - 2 = - 4(1)+2  and -2 +2(1)=0

-2=-2 and 0=0 .....right

The required solution of the given system of equations is (1, -2), and a graph of the solution has been shown.

Simultaneous linear equations are two- or three-variable linear equations that can be solved together to arrive at a common solution.

Here,
y=-4x+2 - - - -(1)
y + 2x = 0 - - - (2)

Equating equations,
-4x +2 = -2x
x =  1

Put x = -2 in equation 1
y = -4(1) + 2
y = -2

Thus, the required solution of the given system of equations is (1, -2).

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Answer:

f(x)=4(3)^2

(2,36)

36=4(3)^2

36=4(9)

36=36

Step-by-step explanation:

Answer: Hi! here you want a function that pases through the point (2,36)

it means, a function f(x) so f(2) = 36.

Also, f(x) must be an exponential function, this means that f(x) = [tex]a^{x}[/tex]

where a is a real number.

then  [tex]a^{2}[/tex] = 36

so a = [tex]\sqrt{36}[/tex] = ± 6.

then your function can be f(x) = [tex]-6^{x}[/tex] or [tex]6^{x}[/tex].

Notice that i used a very simplest example of exponential function. You actually can found lots of exponential functions F(x) that passes through the point (2,36).

Answer:

c)

Step-by-step explanation:

-2 is the slope so that y equals -2x and the y intercept is positive 4 so that the equation is y=-2x+4

Answer:

c)  y = -2x+4

Step-by-step explanation:

The slope intercept form of a line is

y = mx+b  where m is the slope and b is the y intercept

Substituting in

y = -2x +4

Answer:

A

Step-by-step explanation:

First find the median of the data set.

The median is the middle value of the data set arranged in ascending order

10, 11, 12, 15, 17, 19, 22, 24, 29, 33, 38

The median = 19

The first quartile ( lower) is the middle value of the data to the left of the median.

10, 11, 12, 15, 17

The first quartile is 12 → A

Answer:

Step-by-step explanation:

Use the cosine law (look at the picture).

We have:

[tex]a=a\\b=4\\c=3\\\gamma=32^o[/tex]

[tex]a^2=4^2+3^2-2(4)(3)\cos32^o[/tex]

[tex]\cos32^o\approx0.848[/tex] → look at the second picture

[tex]a^2=16+9-24(0.848)\\\\a^2=25-20.352\\\\a^2=4.648\to a=\sqrt{4.648}\\\\a\approx2.2[/tex]

Answer:

h = (10 ft)(4.01) = 40.1 ft

Step-by-step explanation:

The tangent function relates this elevation to the horizontal distance (10 ft) and the angle of elevation (76 degrees):

                               opp           h

tan 76 degrees = --------- = ------------- = 4.01

                                adj         10 ft

Therefore , h = (10 ft)(4.01) = 40.1 ft

Answer: 40 ft

Step-by-step explanation:

You can find the height of the statue by solving the right triangle.

In this case the adjacent side of the triangle is the horizontal distance to the statue (10 ft). The height of the statue is the opposite side to the angle of 76 °.

By definition, the tangent of an angle is:

[tex]tan(\theta) = \frac{opposite}{adjacent}[/tex]

In this case

[tex]\theta=76\°\\\\opposite = h\\\\adjacent = 10\ ft[/tex]

Therefore

[tex]tan(76) = \frac{h}{10}[/tex]

[tex]h=tan(76) * 10\\\\h=40\ ft[/tex]

Answer:

15

Step-by-step explanation:

-225/-15 = 15

A negative divided by a negative is a positive

225/15 = 15

Answer:

15

Step-by-step explanation:

The value of expression -225 divided (-15) :

-225/-15 = 15

Answer:

[7, -4, -8]

Step-by-step explanation:

Just simply plug in each choice into the equations to confirm their authenticities.