If f(x) = 5x + 4, which of the following is the inverse of f(x)?
​

Answer:

x = - 2 ± [tex]\sqrt{5}[/tex]

Step-by-step explanation:

Given

x² + 4x - 1 = 0 ( add 1 to both sides )

x² + 4x = 1

To complete the square

add (half the coefficient of the x- term )² to both sides

x² + 2(2)x + 2² = 1 + 2² ← complete the square on the left side

(x + 2)² = 5 ← take the square root of both sides

x + 2 = ± [tex]\sqrt{5}[/tex] ← subtract 2 from both sides

x = - 2 ± [tex]\sqrt{5}[/tex]

roots are x = - 2 - [tex]\sqrt{5}[/tex] or x = - 2 + [tex]\sqrt{5}[/tex]

Final answer:

To find the roots of the quadratic function x² + 4x - 1 = 0, the equation is rearranged, a perfect square is formed by adding (b/2)² to both sides, and the square root is taken to obtain the solutions x = √{5} - 2 and x = -√sqrt{5} - 2.

Explanation:

To find the roots of the quadratic function x² + 4x - 1 = 0 by completing the square, we need to follow a series of steps:

First, we'll arrange the equation so that the x-squared and x terms are on one side, leaving the constant on the other side. In this case, we add 1 to both sides to obtain x² + 4x = 1.

Next, we find the number that needs to be added to x^2 + 4x to make it a perfect square trinomial. This number is (b/2)², where b is the coefficient of x. Here, b is 4, so we need to add (4/2)² = 4 to both sides.

Our equation now reads x² + 4x + 4 = 5. Notice that the left-hand side is a perfect square, as it can be written as (x+2)².

Finally, we take the square root of both sides, giving us x + 2 = √{5} or x + 2 = -√{5}. Therefore, the solutions are x = √{5} - 2 and x = -√{5} - 2.

To check our solutions, we could substitute them back into the original equation and ensure that the left side equals zero.

Answer:

V =20.4 in^3

Step-by-step explanation:

The formula for volume of a triangular prism is

V = B *h

B is the area of the triangle which is 1/2 b*h

B = 1/2 (2.5) (3.4)

The height is 4.8 in

V = 1/2 (2.5) (3.4) * 4.8

V =20.4 in^3

Answer:

V =20.4 in^3 is your answer

Step-by-step explanation:

Answer:

Part 1: Find (f/g)(4) = 3

Part 2: Find (f+g)(4) = 28

Step-by-step explanation:

Part 1: Find (f/g)(4):

(f/g)(4) means divide f function by g function and simplify it. Then plug in 4 into x of that simplified function.

Let's do this:

[tex]\frac{x^2+2x-3}{x^2-9}\\=\frac{(x+3)(x-1)}{(x-3)(x+3)}\\=\frac{x-1}{x-3}[/tex]

Plugging in 4 into x gives us:

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

The answer is 3

Part 2: Find (f+g)(4):

(f+g)(4) means add f function and g function and simplify it. Then plug in 4 into x of that simplified function.

Let's do this:

[tex](x^2+2x-3)+(x^2-9)\\=2x^2+2x-12[/tex]

Plugging in 4 into x gives us:

[tex]2x^2+2x-12\\=2(4)^2+2(4)-12\\=28[/tex]

The answer is 28

Answer: the first one is -11 and the second one is 0

step-by-step explanation:

someone answered your question but it was wrong so i had too guess and got the real answers since you know ... i ended up getting it wrong lol so yea

Answer:

Yes, it does.

Step-by-step explanation:

Every regular shaped figure will have rotational symmetry, since they are built with identical segments all around.

To find the answer, ask yourself « If I rotate the shape, is there a time where I’ll find the exact same shape again with a different angle? »

So, a square has rotational symmetry, but not a rectangle.

A equilateral triangle has rotational symmetry, but not any other type of triangle.

The Ferris wheel shaped like a regular octagon would have rotational symmetry.

The rotational symmetry of a shape makes it possible for an object when rotated on its own axis, the shape of the object looks the same.

For a regular polygon with n sides, there would be n number of rotational symmetry,

The Ferris wheel shaped like a regular octagon would have rotational symmetry.

Find out more on rotational symmetry at: https://brainly.com/question/15178808

Answer:

Part A) The volume of the ice cream scoop is [tex]36\pi\ in^{3}[/tex]

Part B) The melted ice cream won't fill the cup

Part C) The melted ice cream exceeds the volume  of Anna's cup

Part D) The height of the smallest cylindrical cup is [tex]h=8\ in[/tex]

Step-by-step explanation:

Part A) Find the volume of the ice cream scoop

we know that

The volume of the sphere (ice cream scoop) is equal to

[tex]V=\frac{4}{3}\pi r^{3}[/tex]

we have

[tex]r=3\ in[/tex]

substitute

[tex]V=\frac{4}{3}\pi (3)^{3}=36\pi\ in^{3}[/tex]

Part B) Find the volume of Anna's cylindrical cup

we know that

The volume of a cylinder is equal to

[tex]V=\pi r^{2}h[/tex]

we have

[tex]r=3\ in[/tex]

[tex]h=6\ in[/tex]

substitute

[tex]V=\pi (3)^{2}(6)=54\pi\ in^{3}[/tex]

[tex]54\pi\ in^{3}> 36\pi\ in^{3}[/tex]

The volume of Anna's cup (cylinder) is greater than the volume of melted ice cream scoop

therefore

The melted ice cream won't fill the cup.

Part C) Will two scoop of melted ice cream fit in Anna's cup?

Multiply the volume of ice cream scoop by 2 and compare with the volume of Anna's cup

so

[tex](2)36\pi\ in^{3}=72\pi\ in^{3}[/tex]

[tex]72\pi\ in^{3}> 54\pi\ in^{3}[/tex]

The volume of Anna's cup (cylinder) is less than the volume of two melted ice cream scoop

therefore

The melted ice cream exceeds the volume  of Anna's cup

Part D) Find the smallest cylindrical cup that will hold two scoops of melted ice cream

we know that

The volume of a cylinder is equal to

[tex]V=\pi r^{2}h[/tex]

we have

[tex]V=72\pi\ in^{3}[/tex] ------> volume of two scoops of melted ice cream

[tex]r=3\ in[/tex]

substitute in the formula and solve for h

[tex]72\pi=\pi (3)^{2}h[/tex]

simplify

[tex]72=(9)h[/tex]

[tex]h=8\ in[/tex]

Answer:

[tex]m<1=92\°[/tex]

Step-by-step explanation:

we know that

The sum of the interior angles in a quadrilateral must be equal to 360 degrees

so

[tex]62\°+92\°+114\°+m<1\°=360\°[/tex]

solve for the measure of angle 1

[tex]268\°+m<1\°=360\°[/tex]

[tex]m<1=360\°-268\°=92\°[/tex]

Answer:

The answer is

B. 92 degrees.

Step-by-step explanation:

Answer:

3 : 8

Step-by-step explanation:

Two hours = 120 minutes

Alyssa:Elijah

45 : 120

3 : 8

Answer:

wrong its 5gallons

Step-by-step explanation:

Answer: [tex]x\geq6[/tex]

Step-by-step explanation:

g°h indicates that you must plug the function h(x) into the function g(x) as you can see below:

[tex]g\°h=\sqrt{(2x-8)-4}[/tex]

Now you must simplify by adding like terms, as following:

[tex]g\°h=\sqrt{2x-12}[/tex]

By definition you have that:

[tex]2x-12\geq0[/tex]

Theen you must solve for x:

[tex]2x\geq12\\x\geq6[/tex]

Therefore, the domain is:

{[tex]x[/tex] ∈R:[tex]x\geq6[/tex]}

Then the answer is [tex]x\geq6[/tex]

Answer:

Restriction on the domain is x ≥ 6.

Step-by-step explanation:

We have given two functions.

g(x) = √x-4 and h(x) = 2x-8

We have to find the restrictions on the domain of (g o f).

(g o h)(x) = g(h(x))

(g o h)(x) = g(2x-8)

(g o h)(x) = √2x-8-4

(g o h)(x) = √2x-12

Hence, 2x-12 ≥ 0

2x ≥ 12

x ≥ 6

Hence, restriction on the domain is x ≥ 6.

Answer:

I believe it is C

Step-by-step explanation:

since x+y=4 that could mean, 2+2=4 which means x and y has the same value, that is 2.

so if we make the equation

6(2)+6(2)= it WOULD equal to 24, and for that reason I think it is C.

(24,4)

Answer:

x = 2

Step-by-step explanation:

Similar triangles are triangles which have the same shape but not the same size. This means their angle measures are equal but their side lengths are not instead they are proportional. To solve, we will set up a proportion and solve.

A proportion is two equal ratios set equal to each other. We form the ratios by finding corresponding sides (sides which match to each other on both triangles by their position). Out ratios will be one side of the small triangle over the corresponding side on the big triangle as shown below:

[tex]\frac{little}{big} =\frac{little}{big}[/tex].

[tex]\frac{36}{36 + 12}=\frac{24}{24 + 6x - 4}[/tex]

To solve the proportion, we'll cross multiply by multiplying numerator with denominator across the equal sign.

[tex]36(24 + 6x - 4)=(36+12)(24)\\36(6x + 20)=48(24)\\216x + 720 = 1152 \\216x = 432\\\frac{216x}{216}=\frac{432}{216} \\x = 2[/tex]

question 1 is congruent. 2 is not congruent and 3 is congruent

Answer: 1) Congruent

2) Not congruent

3) Congruent

Step-by-step explanation:

We know that a rigid transformations preserves side-lengths and angle measures of a figure in such a way that the figure doesn't shrink or get enlarger. It creates congruent figures.

    a) reflections, b) rotations, c) translations

On the other hand a dilation changes the size of the image when the scale factor is not equal to 1. It does not produces congruent images.

So what they are trying to say is that they both have the same y-intercept. Easy!

Make y the subject:

5x - 2y = 3

2y = 5x - 3

y = 2.5x - 1.5

The y-intercept is -1.5.

Make y the subject:

x + y = a

y = -x + a

Therefore, a must be -1.5 !

The system of linear equations has a solution on the y-axis only when a = -3/2

We have the system of linear equations:

5x - 2y = 3

x + y = a

Now let's write both in slope-intercept form:

y = (-3/2) + (5/2)x

y = a - x

If we want the lines to intersect at the y-axis, then we will have x = 0, replacing that we get:

y = -3/2

y = a

So, for the system to be consistent, we must have a = -3/2.

If you want to learn more about systems of equations, you can read:

https://brainly.com/question/13729904

Answer:

2

Step-by-step explanation:

8 ( 4 - x ) = 7x + 2

(Expand brackets

32 - 8x = 7x + 2

(-7x from both sides)

-15x = -30

(Divide by -15 from both sides)

x=2

Answer:

x = 2

Step-by-step explanation:

8(4 - x) = 7x + 2

Distribute the 8 on the left side.

32 - 8x = 7x + 2

Subtract 7x from both sides.

32 - 15x = 2

Subtract 32 from both sides.

-15x = -30

Divide both sides by -15.

x = 2

Answer:

[tex]x^2+y^2=16[/tex]

Step-by-step explanation:

The equation of a circle with center (h,k) and radius r is given by the formula;

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

Given (h,k)=(0,0) and r=4, we substitute the values to obtain;

[tex](x-0)^2+(y-0)^2=4^2[/tex]

The required equation is

[tex]x^2+y^2=16[/tex]

The standard form of the equation for a circle centered at the origin with a radius of 4 is x2 + y2 = 16.

The equation of a circle in standard form with the center at the origin (0, 0) and a radius of 4 is given by x2 + y2 = r2, where x and y are the coordinates of any point on the circle, and r is the radius.

Plugging the given radius into the equation, we have x2 + y2 = 42. Simplifying this, we get the equation x2 + y2 = 16. This is the standard form of the equation for the given circle.

The possible values of x are -2.4,1.4,3.9

Step-by-step explanation:

F(x)=3x - 1

G(x)=x³-3x²-4x

when we will plot we are given two functions f(x) and g(x) as:

the graph of these two functions we could clearly see that the point of intersections are the possible solutions of the equation .

F(x)=G(x)

the points of the intersection of this equation is x= -2.4,1.4,3.9

Hence the solutions are  x= -2.4,1.4,3.9.

Answer:

[tex]\large\boxed{f(x)+(x-3)^2-7}[/tex]

Step-by-step explanation:

[tex]\text{The vertex form of equation}\ y=ax^2+bx+c:\\\\y=a(x-h)^2+k\\\\\text{We have the equation:}\\\\f(x)=x^2-6x+2=x^2-2(x)(3)+1=x^2-2(x)(3)+3^2-3^2+2\\\\\text{Use}\ (a-b)^2=a^2-2ab+b^2\to x^2-2(x)(3)+3^2=(x-3)^2\\\\f(x)=(x-3)^2-9+2=(x-3)^2-7[/tex]

Answer:

10oz:1lb

Step-by-step explanation:

divide by two

Answer:

Option D. [tex]y=3(x+2)^{2}+5[/tex]

Step-by-step explanation:

we know that

The equation of a vertical parabola in vertex form is equal to

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

where

(h,k) is the vertex of the parabola

If a> 0 then the parabola open up and the vertex is a minimum

If a< 0 then the parabola open down and the vertex is a maximum

In this problem the vertex is the point (-2,5)

so

the equation must be equal to

[tex]y=a(x+2)^{2}+5[/tex] and the value of a is positive

therefore

the answer is the option D

Answer:

y=3(x+2)^2+5

Step-by-step explanation:

y = 3(x+2)^2 + 5 Is the correct answer

Answer:

The answer would be D because both ordered pair that was substituted in the equation didn't equal to each other.

Explanation:

All you do is substitute the x and y numbers. (x,y)

A:

Substitute the x and y number

7(2) - 5 = 4(4) - 6

Multiply the number in the parentheses by the outside number on both sides.

14 - 5 = 16 - 6

Subtract both sides to get your solution.

9 = 10

Doesn't equal so that means it's not the solution.

B:

Substitute

7(3) - 5 = 4(6) - 6

Multiply the number in the parentheses by the outside number on both sides.

21 - 5 = 24 - 6

Subtract both sides to get your solution.

16 = 18

It also doesn't equal so that means that it's not the solution either.

C:

Both ordered pair didn't equal to each other so this is not the answer.

Hope this helps!

Answer:

Part 1) [tex]\frac{\sqrt{2}}{2}\ sec[/tex] or [tex]0.7\ sec[/tex]

Part 2) The side length of each piece Trinette used to make the pillow covers is [tex]30 in[/tex]

Part 3) Elton's hourly wage is [tex]\$6.50[/tex]

Step-by-step explanation:

Part 1)

Let

x------> the time in seconds

we have

[tex]f(x)=-16x^{2}+c[/tex]

In this problem the initial height is 8 ft

so

[tex]f(x)=-16x^{2}+8[/tex]

To find how long does it take the apple to reach the ground, equate the function to zero and solve for x

[tex]0=-16x^{2}+8[/tex]

[tex]16x^{2}=8[/tex]

[tex]x^{2}=1/2[/tex]

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

[tex]x=0.7\ sec[/tex]

Part 2)

step 1

The area of a square tablecloth is

[tex]A=3,600\ in^{2}[/tex]

Divided by 4

[tex]3,600/4=900\ in^{2}[/tex]

step 2

Find the length of each piece

[tex]A=b^{2}[/tex]

so

[tex]900=b^{2}[/tex]

[tex]b=30 in[/tex]

Part 3)

we know that

[tex]2x^{2} =84.50[/tex]

solve for x

[tex]x^{2} =42.25[/tex]

[tex]x=\sqrt{42.25}[/tex]

[tex]x=\$6.50[/tex]

D, 196,608.

The sequence is multiplying by -4 every time.

Answer:  The correct option is (D) 196608.

Step-by-step explanation:  We are given to find the 9th term of the following sequence :

3,    -12,    48,    -192,    .    .    .

Let a(n) denote the n-th term of the given sequence.

Then, a(1) = 3,  a(2) = -12,  a(3) = 48,  a(4) = -192,   .   .   .

We see that

[tex]\dfrac{a(2)}{a(1)}=\dfrac{-12}{3}=-4,\\\\\\\dfrac{a(3)}{a(2)}=\dfrac{48}{-12}=-4,\\\\\\\dfrac{a(4)}{a(3)}=\dfrac{-192}{48}=-4,~~.~~.~~.[/tex]

So, we get

[tex]\dfrac{a(2)}{a(1)}=\dfrac{a(3)}{a(2)}=\dfrac{a(4)}{a(3)}=~~.~~.~~.~~=-4.[/tex]

That is, the given sequence is a GEOMETRIC one with first term a = 3  and common ratio d= -4.

We know that

the n-th term of an geometric  sequence with first term a and common ratio r is given by

[tex]a(n)=ar^{n-1}.[/tex]

Therefore, the 9th term of the given sequence is

[tex]a(9)=ar^{9-1}=3\times(-4)^8=3\times 65536=196608.[/tex]

Thus, the 9th term of the given sequence is 196608.

Option (D) is CORRECT.

Answer:

to make 1000 gallons with 10% alcohol, we need 714.3 gallons of mixture that contains 5% alcohol and 285,7 gallons of mixture that contains 12% alcohol.

Step-by-step explanation:

According to the statement, there are two mixtures. One mixture contains 5% alcohol and the other contains 12% alcohol.

We want to make 1000 gallons with 10% alcohol, so we have the following system of equations:

A + B = 1000 gallons. [1]

0.05A + 0.12B = 0.1(1000) ⇒ 0.05A + 0.12B = 100 [2]

(Where 'A' represents the mixture that contains 5% alcohol and 'B' the one that contains 12% alcohol).

Solving the system of equations:

A + B = 1000 ⇒ A = 1000 - B [3]

[3] → [2]

0.05(1000 - B) + 0.12B = 100 ⇒ 50 - 0.05B + 0.12B = 100

⇒ 0.07B = 50 ⇒ B = 714.28 ≈ B=714.3 [4]

[4] → [1]

A + B = 1000 ⇒ A + 714.3 = 1000 ⇒ A = 285,7

Therefore, to make 1000 gallons with 10% alcohol, we need 714.3 gallons of mixture 'A' and 285,7 gallons of mixture 'B'

The approximate volume of the sphere is 4188.79 cubic units.

Calculating the volume of a sphere.

A sphere is a three-dimensional round object. The volume of a sphere can be calculated by using the formula [tex]\dfrac{4}{3} \pi r^3[/tex].

In the given question, the radius of the sphere is stated to be 10 units. So, the volume of the sphere can be determined by replacing the value of the radius into the equation. i.e.

[tex]V= \dfrac{4}{3}\pi r^3[/tex]

[tex]V= \dfrac{4}{3} \times \pi \times (10)^3[/tex]

V = 4188.79 cubic units.

Therefore, the approximate volume of the sphere is 4188.79 cubic units.

Answer:

D

Step-by-step explanation:

7 * 12 = 84

And 1/4 hours which is 7/4 which is $1.25 more.

So she got 85.25 dollars in total, which is a little less than $90.

Answer:

Answer:

B.

Explanation:

If you want to multiply a parenthesis by a number, you simply distribute the number to all the terms in the parenthesis.

Step-by-step explanation:

Answer:

B. [tex]15x-35[/tex]

Step-by-step explanation:

We are asked to simplify the expression [tex]5(3x-7)[/tex] using distributive property.

Distributive property states that we can multiply a quantity to sum by multiplying each addend separately and then add the products as:

[tex]a(b+c)=a\cdot b+a\cdot c[/tex]

Using distributive property, we will multiply 5 by [tex]3x[/tex] and [tex]-7[/tex] as:

[tex]5\cdot 3x-5\cdot 7[/tex]

[tex]15x-35[/tex]

Therefore, the simplified form of the given expression would be [tex]15x-35[/tex] and option B is the correct choice.

Answer:

[tex]w\leq 100\ pounds[/tex]

Step-by-step explanation:

Let

w------> the weight in pounds

we know that

A delivery company charges an extra fee for a package that weighs more than 100 pounds

so

For

[tex]w> 100\ pounds[/tex] -----> the company charges an extra fee

therefore

For

[tex]w\leq 100\ pounds[/tex] ----> the company not charge an extra fee

The inequality w ≤ 100 expresses the weight limit for Sonia's package. Jesse should use kilograms to weigh the box in the mailroom.

The inequality is: w ≤ 100

Since Sonia can ship packages without paying the extra fee for weights up to 100 pounds. Therefore, any package weighing 100 pounds or less would not incur the additional charge.

Jesse should use kilograms to weigh the box of books in the mailroom because it's a more appropriate metric unit considering the size and weight of the objects in the box.

Find the slope or the y-intercept.

It would be 83.

Reason it 83 units away from 0.

I hope this helps :)

Answer:

83

Step-by-step explanation: