Help me with this question please!! :)

The inverse function of [tex]f(x) = -\frac 12\sqrt{x + 3}[/tex] is[tex]f^{-1}(x) = 4x^2- 3[/tex]

The function is given as:

[tex]f(x) = -\frac 12\sqrt{x + 3}[/tex]

Rewrite as;

[tex]y = -\frac 12\sqrt{x + 3}[/tex]

Swap the positions of x and y

[tex]x = -\frac 12\sqrt{y + 3}[/tex]

Multiply through by -2

[tex]-2x = \sqrt{y + 3}[/tex]

Square both sides

4x^2 = y + 3

Subtract 3 from both sides

y = 4x^2 - 3

Express as an inverse function

[tex]f^{-1}(x) = 4x^2- 3[/tex]

Hence, the inverse function of [tex]f(x) = -\frac 12\sqrt{x + 3}[/tex] is[tex]f^{-1}(x) = 4x^2- 3[/tex]

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Answer:

So, the vertex form of your function is  [tex]y(x)=2*(x+2)^2-7[/tex].

The vertex is at [tex](-2|-7)[/tex]

Step-by-step explanation:

Given function:

[tex]y(x)=2*x^2+8x+1[/tex]

Steps:

[tex]y(x)=2*x^2+8x+1\\[/tex]

[tex]y(x)=2(x^2+4x+\frac{1}{2} )[/tex]    (Factor out)

[tex]y(x)=2(x^2+4x+2^2-2^2+\frac{1}{2} )[/tex]  (Complete the square)

[tex]y(x)=2((x+2)^2-2^2+\frac{1}{2} )[/tex]  (Use the binomial formula)

[tex]y(x)=2((x+2)^2-\frac{7}{2} )[/tex]  (Simplify)

[tex]y(x)=2*(x+2)^2-7[/tex] (Expand)

Answer: 3 answers

Step-by-step explanation:

Answer: It’s a trinomial

Step-by-step explanation: It has three terms, so it’s classified as a trinomial. (Tri=three)

Answer:

[tex]y=-\frac{3}{2}x+\frac{7}{2}[/tex]

Step-by-step explanation:

So when two lines are parallel there slopes are the same, but there y-intercepts are different, since if they had the same y-intercept, then they would be the same exact line. To convert an equation into slope-intercept form you simple isolate y by moving everything else to the other side, and then divide by the coefficient of y so the coefficient of y becomes 1. This will give you the equation in the form: y=mx+b where m is the slope and b is the y-intercept (because when the linear equation crosses the y-axis, the x is 0, thus mx will be 0, leaving only b, so the y-intercept is b).

Original Equation:

3x + 2y = 4

Subtract 3x from both sides

2y = -3x + 4

Divide both sides by 2

y = -3/2x + 2

Generally any parallel line will be in the form:

[tex]y=-\frac{3}{2}x + b\ \ \ \ \ b\ne2[/tex]. Since as stated before if two lines have the same slope and y-intercept, they're the same line, which is not the same as parallel, since parallel lines never intersect.

So since we're given a point in the parallel line (-1, 5) we can plug those values into the equation to find the value of b

[tex]5=-\frac{3}{2}(-1) + b[/tex]

Multiply and

[tex]5=\frac{3}{2}+ b[/tex]

Convert 5 into a fraction with a denominator of 2

[tex]\frac{5}{1} * \frac{2}{2} = \frac{10}{2}[/tex]

Write equation using this form of 5:

[tex]\frac{10}{2}=\frac{3}{2}+b[/tex]

Subtract 3/2 from both sides

[tex]\frac{7}{2}=b[/tex]

Now take this value and input it into the slope-intercept form to finish the equation: [tex]y=-\frac{3}{2}x+\frac{7}{2}[/tex]

49^2m-m : Not equivalent

7^2m-2m : Not equivalent

7^2m-m : Not equivalent

This is actually a trick question. All of the following are actually false statements. Want to know why? Let me show you.

For exponents, if you are dividing a number to some power (i.e 5^3) by the SAME number to a different power (i.e 5^2), then the expression is 5^3-2 or 5^1 = 5. This is true for any number a such that a^b ÷ a^c = a^b-c.

Since 7 and 49 are not the same number, this rule does not apply and thus cannot be simplified any further.

Let me prove why. 5^3 = 125, and 5^2 = 25, and 125 ÷ 25 = 5. This is also the same as 5^3-2 = 5^1 = 5. We just proved this as so.

But, what about 7 and 49, or 2 different numbers. Well it doesn't apply. 7^3 = 343, and 49^2 = 2401, and 343 ÷ 2401 ≈ 0.14. Thus, this is NOT equal to 7^3-2 which is 7. We just proved that a^y ÷ b^z ≠ a^y-z. Congratulations!

Hope this helped!

you need to start from the beginning add 2 and 3

Step-by-step explanation:

1) [tex]7y=8x-14, y=6[/tex] [given]

2) [tex]7(6)=8x-14[/tex] [substitution]

3) [tex]56=8x[/tex] [addition property of equality]

4) [tex]7=x[/tex] [division property of equality]

5) [tex]x=7[/tex] [symmetric property of equality]

A two columns proof is given in the attached image below as per the concept of solving equations.

A two columns proof is given below:

Statement | Reasons

y = 6 | Given

7y = 8x - 14 | Given

7(6) = 8x - 14 | Substitution (Substitute y with 6 in statement 2)

42 = 8x - 14 | Simplification

42 + 14 = 8x | Addition Property of Equality (Add 14 to both sides)

56 = 8x | Simplification

56/8 = x | Division Property of Equality (Divide both sides by 8)

7 = x | Simplification (Simplify the fraction 56/8)

x = 7 | Symmetric Property of Equality (Rearrange statement 9)

In this two-column proof, we start with the given information that y is equal to 6 (statement 1).

Then, we substitute the value of y into the equation 7y = 8x - 14 (statement 2) to get 42 = 8x - 14 (statement 3).

We simplify the equation to isolate 8x and find that 56 = 8x (statement 6). Dividing both sides of this equation by 8 (statement 7) gives us x = 7 (statement 8).

Finally, we use the symmetric property of equality to rearrange the equation and conclude that x is indeed equal to 7 (statement 9).

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[tex]z=\dfrac{kx^3}{y^3}\\\\\\59=\dfrac{k\cdot 8^3}{8^3}\\k=59\\\\\\z=\dfrac{59x^3}{y^3}\\\\\\z=\dfrac{59\cdot 3^3}{4^3}=\dfrac{1593}{64}[/tex]

Answer:

S= 4

Step-by-step explanation:

add 9 to -5

= 4

s=4

Answer:

13 feet

Step-by-step explanation:

A^2 + B^2 = C^2

A=5 ^2 = 25

B=12 ^2 = 144

144 +25 = 169

C=13

The equation of function g is f(x) = 7^3x + 1

The function f(x) is given as:

f(x) = 7^x + 1

The rule of horizontal compression by a factor of 3 is represented as

g(x) = f(kx)

Where k = 3

So, we have:

f(x) = 7^3x + 1

Hence, the equation of function g is f(x) = 7^3x + 1

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the school purchased 742 items in total.

Just add 256+332+154

which equals...742. :)

Answer:

742 items

Step-by-step explanation:

Add up all the items that the cafeteria purchased. 256+332+154=742!

Answer:

cos4B =1-8sin^2(B)+8sin^4(B)

Step-by-step explanation:

cos4B =1-8sin^2(B)+8sin^4(B)

(x² + 2√xy) = 5/4

2y - √2xy = 0

From the first equation

(2x-1)²+8√2xy=4

Expand the bracket

(2x-1) (2x+ 1) + 8√2xy = 4

4x² + 2x -2x - 1 + 8√2xy = 4

4x² - 1 + 8√2xy = 4

Collect like terms

4x² + 8√2xy = 4 + 1

4x² + 8√2xy = 5

Find the common factor

4(x² + 2√xy) = 5

(x² + 2√xy) = [tex]\frac{5}{4}[/tex]

For equation 2, we have

4y-√8xy-1=1​

4y - [tex]\sqrt{4 *2 xy }[/tex] = 1 -1

4y - [tex]2\sqrt{2xy}[/tex] = 0

Find the common factor

[tex]2(2y - 2\sqrt{2xy} ) = 0[/tex]

[tex]2y - 2\sqrt{2xy} = 0[/tex] × 2

[tex]2y - \sqrt{2xy} = 0[/tex]

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The number of red tiles in the box given the chance ratio of red to blue tiles is 18

= 12 + 2x

Number of red tiles = 3 / 8 × 12+2x

x = 3(12 + 2x) / 8

x = (36 + 6x) / 8

8x = 36 + 6x

8x - 6x = 36

2x = 36

x = 36/2

x = 18 tiles

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Answer: 28

Step-by-step explanation:

Answer:

All real numbers

Step-by-step explanation:

See attached graph.

Answer:

just hey effect me II rieirjttjhg shewtha

Answer:

[tex]-\frac15[/tex]

Step-by-step explanation:

Hello!

We can utilize the slope formula to find the slope.

Slope Formula: [tex]S = \frac{y_2-y_1}{x_2-x_1}[/tex]

Remember that a coordinate is written in the form (x,y)

The slope of the line is [tex]-\frac15[/tex].

Answer:

-1/5

Step-by-step explanation:

To find the slope of the line, we use the slope formula: (y₂ - y₁) / (x₂ - x₁)

Plug in these values:

(-4 - (-2)) / (5 - (-5))

Simplify the parentheses.

= (-4 + 2) / (5 + 5)

= -2 / 10

Simplify the fraction.

-2/10

= -1/5

This is your slope.

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Applying the angles of intersecting chords theorem, m∠BEC = 109°.

According to the angles of intersecting chords theorem, the measure of angle BEC equals half the sum of the measures of arcs AD and BC.

arc mAD = 103°

arc mBC = 115°

Therefore, we would have:

m∠BEC = 1/2(103 + 115)

m∠BEC = 109°

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Answer:

x=23

Step-by-step explanation:

put it in desmos and was right

Answer:

I think that's the answer

The liquid that will be the least dense liquid in the density column is; The  liquid floating on the top.

The formula for density is;

Density = Mass/Volume

Thus, the greater the mass, the more the density. Thus, it means that heavier objects will sink while lighter ones will float.

Thus, this means that the liquid that is most dense will be at the bottom of the liquid.

The liquid that is least dense will be at the top of the liquid.

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Answer:

B

Step-by-step explanation:

1.(5x^3)(xy^4 -2x^3y)

2.5x^4y^4 -10x^6y

A crossover design is a reiterated assessments design in which each experimental unit (patient) receives various treatments at different time periods, i.e., the patients switch from one therapy to another during the trial.

The crossover design has the benefit of each subject acting as his or her own control, and it requires a lesser number of patients than parallel-group trials.

There are various drawbacks. For example, crossover designs often last longer than parallel-group research.

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Answer:

117 degrees

Step-by-step explanation:

The degree of the polynomial, x⁵+1-3x⁴+3x⁹-2x, is: 9.

What is the Degree of a Polynomial?

The degree of a polynomial is determined by the monomial with the highest degree.

Given the polynomial, x⁵+1-3x⁴+3x⁹-2x, the monomial with the highest degree is 3x⁹.

Therefore, the degree of the polynomial given is: 9.

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Answer:

[tex]f(x) = a(x^2+4)(x-3)^2[/tex]

Step-by-step explanation:

So I'm assuming it means that one of the zeros is at x=3 with a multiplicity of 2 and it has an imaginary solution of 4i. Anyways, imaginary solutions come in conjugate pairs meaning if you have a complex solution of [tex]a-bi[/tex] there is another complex solution which is the conjugate of that which is [tex]a+bi[/tex] but since the imaginary solution is 4i, the complex number is just [tex]0+4i[/tex] so the conjugate is [tex]0-4i[/tex] or [tex]-4i[/tex]. So since you have x=3 as a zero that can be represented as [tex](x-3)^2[/tex] since 3 would make it 0 and it has a multiplicity of 2. As for the other factors, you won't just have ([tex](x-4i)(x+4i)[/tex], you'll have a factor that is set up in a way that the solutions are: [tex]x=\pm\sqrt{-4}[/tex]. That means it'll be a quadratic. So it'll be in the form [tex]x^2+b[/tex]. Since you're moving b to the other side and it's negative. that means it has to be positive and since the value is 4, you'll have the factor [tex](x^2+4)[/tex] which when set equal to zero has the solutions sqrt(-4). So this gives you the equation

[tex]f(x) = a(x^2+4)(x-3)^2[/tex]

Answer:

5621 years

Step-by-step explanation:

Plug everything in first.

[tex]N=N_0e^{-kt}\\\\\implies 0.57 = e^{-0.0001t}\\\\\implies\ln \left(0.57\right)=-0.0001t\\\\t=-\frac{\ln \left(0.57\right)}{0.0001}[/tex]

Round to closest amount of years = 5621 years

Answer:

30 square yards

Step-by-step explanation:

You can calculate the area of a triangle by using the formula: [tex]A = \frac{1}{2}bh[/tex], where b=base, and h=height, and since you have both values you can easily calculate the area by plugging the values in

Plug Values Into Equation:

[tex]A = \frac{1}{2}(15)(4)[/tex]

Multiply 15 and 4

[tex]A=\frac{1}{2}(60)[/tex]

Multiply by 1/2 (or technically divide by 2)

[tex]A = 30[/tex]

Answer:

The answer is 30yd²

Step-by-step explanation:

A=hb b/2

=4·15/2

=30yd²