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Match the function with its inverse.


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Answer:

there is no picture for me to answer on

Answer:

Option C is correct.

Step-by-step explanation:

y = x^2+4x+5

We need to find the vertex of the above equation.

The above equation represents the parabola.

The slope of parabola can be found by taking derivative of the given equation

dy/dx = 2x+4

The slope of the parabola at the vertex is zero SO,

2x+4 = 0

2x = -4

x = -4/2

x = -2

Putting value of x =-2 to find the value of y

y = x^2+4x+5

y =(-2)^2+4(-2)+5

y = 4-8+5

y =9-8

y = 1

So, the vertex is (-2,1)

Option C is correct.

Answer:

[tex]\large\boxed{\left(\dfrac{7}{2},\ \dfrac{27}{2}\right)}[/tex]

Step-by-step explanation:

The formula of a midpoint of a segment AB with endpoints at A(x₁, y₁) and B(x₂, y₂):

[tex]M_{AB}\left(\dfrac{x_1+x_2}{2},\ \dfrac{y_1+y_2}{2}\right)[/tex]

We have the points (-3, 9) and (10, 18).

Substitute:

[tex]M(x,\ y)\\\\x=\dfrac{-3+10}{2}=\dfrac{7}{2}\\\\y=\dfrac{9+18}{2}=\dfrac{27}{2}[/tex]

The point slope of the line that passes through the points (-7, 2) and having a slope of 5 is y - 2 = 5 (x + 7).

Slope of a line is the ratio of the change in y coordinates to the change in the x coordinates of two points given.

Given that,

Slope of a line = 5

A point on the line = (-7, 2)

Point slope of a line having a slope of m and passing through a point (x', y') is,

y - y' = m(x - x')

Substituting the given slope and point,

y - 2 = 5 (x - -7)

y - 2 = 5 (x + 7)

Hence the required form of the line is y - 2 = 5 (x + 7).

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Answer:

Step-by-step explanation:

No, the heights of the cones are not the same, so Cavalieri’s principle does not apply.

Answer:

15.733kg

Step-by-step explanation:

33.2 - 21.4 = 11.8

3/4 of the bucket empty is 11.8kg.

11.8 divided by 3 is 3.933. 3.933 x 4 is 15.733

Step-by-step explanation:

y~x

y=kx

where

y=2,x=4

2=k*4

k=2/4

k=0.5//

find y when x =32

then

y=32*0.5

y=16//

[tex]\bf \qquad \qquad \textit{direct proportional variation} \\\\ \textit{\underline{y} varies directly with \underline{x}}\qquad \qquad y=kx\impliedby \begin{array}{llll} k=constant\ of\\ \qquad variation \end{array} \\\\[-0.35em] \rule{34em}{0.25pt}[/tex]

[tex]\bf \textit{we also know that } \begin{cases} y=2\\ x=4 \end{cases}\implies 2=k(4)\implies \cfrac{2}{4}=k\implies \cfrac{1}{2}=k \\\\\\ therefore\qquad \boxed{y=\cfrac{1}{2}x} \\\\\\ \textit{when x = 32, what's \underline{y}?}\qquad y=\cfrac{1}{2}(32)\implies y=16[/tex]

Answer:

B. 4⁄5

Step-by-step explanation:

 7 1⁄5

– 6 2⁄5

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

We need to borrow from the 7  since 1/5 is less than 2/5

7 becomes 6 and the one becomes 5/5

 6  5/5+1⁄5

– 6 2⁄5

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

Combining the fraction

 6  6⁄5

– 6 2⁄5

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

      4/5

Answer: $126.50

$230×.45= $103.5

$230-$103.5=126.50

Answer:

126.50

Step-by-step explanation:

If he spent 45% of the money, he still has 100% -45% = 55%

He will still he have 55% of his money

230* 55%

Changing to decimal form

230*.55

126.50

Answer:

2x^2+3

Step-by-step explanation:

(3x^2 + 2x+4) - (x^2 +2x+1)

I'm going to rewrite this using distributive propery and without parenthesis:

3x^2 + 2x + 4 - x^2 - 2x - 1

Now I'm going to pair up any like terms by use of the commutative property.

3x^2 - x^2 + 2x - 2x + 4 - 1

Now simplify:

2x^2 + 0 +3

2x^2+3

Answer:

The final value of subtraction is 2x² + 3

Step-by-step explanation:

It is given that (3x² + 2x + 4) - ( x² + 2x + 1)

To find the value of subtraction

(3x² + 2x + 4) - ( x² + 2x + 1) =  (3x² + 2x + 4 -  x² - 2x - 1)

 = 3x² - x² + 2x - 2x + 4 - 1

 = 2x² + 0 +3

 = 2x² + 3

Therefore the final value of subtraction is 2x² + 3

Step-by-step explanation:

The slope-intercept form of an equation of a line:

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

m - slope

b - y-intercept

[tex]61)\ m=3,\ b=-2\\\\\boxed{y=3x-2}\\\\62)\ m=\dfrac{4}{5},\ b=4\\\\\boxed{y=\dfrac{4}{5}x+4}\\\\63)\ m=-\dfrac{7}{4},\ b=-3\\\\\boxed{y=-\dfrac{7}{4}x-3}\\\\64)\ m=-\dfrac{3}{4},\ b=-2\\\\\boxed{y=-\dfrac{3}{4}x-2}[/tex]

Answer:

[tex]y=5x[/tex]

Step-by-step explanation:

we know that

A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form [tex]y/x=k[/tex] or [tex]y=kx[/tex]

In a proportional relationship the constant of proportionality k is equal to the slope m of the line and the line passes through the origin

we have

For x=0, y=0 -----> the line passes through the origin

For x=1, y=5 ----> [tex]k=y/x=5/1=5[/tex]

For x=2, y=10 ----> [tex]k=y/x=10/2=5[/tex]

For x=3, y=15 ----> [tex]k=y/x=15/3=5[/tex]

so

The constant of proportionality is k=5

The table represent a direct variation

The equation is equal to [tex]y=kx[/tex]

substitute the value of k

[tex]y=5x[/tex]

Answer:

So I did most of you table for you:

First blank:4

Second blank:-4

Third blank:-8

Fourth blank: Left to you: Just plug in 6 into 1/2x^2-5x+4 (I will check)

Fifth blank: Left to you: Just plug in 8 into 1/2x^2-5x+4 (I will check)

The graph is D.

Step-by-step explanation:

So they have a table to fill in and they tell you in the first row what they want you to plug in

So the table is asking us to answer this:

What is h(0),h(2),h(4),h(6), and h(8).

h(0) means to replace x with 0 in [tex]\frac{1}{2} x^2-5x+4[/tex].

[tex]\frac{1}{2}(0)^2-5(0)+4[/tex]

[tex]0-0+4[/tex]

[tex]0+4[/tex]

[tex]4[/tex]

So the first blank is 4 since h(0)=4.

h(2) means to replace x with 2 in [tex]\frac{1}{2} x^2-5x+4[/tex].

[tex]\frac{1}{2} (2)^2-5(2)+4[/tex]

[tex]\frac{1}{2} (4)-10+4[/tex]

[tex]2-10+4[/tex]

[tex]-8+4[/tex]

[tex]-4[/tex]

So the second blank is -4 since h(2)=-4.

h(4) means to replace x with 4 in [tex]\frac{1}{2} x^2-5x+4[/tex].

[tex]\frac{1}{2}(4)^2-5(4)+4[/tex]

[tex]\frac{1}{2}(16)-20+4[/tex]

[tex]8-20+4[/tex]

[tex]-12+4[/tex]

[tex]-8[/tex]

So the third blank is -8 since h(4)=-8

Maybe you can try the last 2 blanks in the table part. That is try computing h(6) and h(8). I will check it for you.

Now the points I have so far are (0,4) from the h(0)=4, (2,-4) from the h(2)=-4, and (4,-8) from the h(4)=-8.

I'm looking for a graph that goes through these points (0,4) , (2,-4) , and (4,-8).

By the way the only graphs that are worth looking at is C and D because they are open up.  I know my curve for h(x)=1/2x^2-5x+4 should be a parabola open up because 1/2 is positive and 1/2 is the coefficient of x^2.

So Graph C has y-intercept (0,10) not (0,4) so Graph C is not right.

Graph D has y-intercept (0,4).  It also goes through (2,-4) and (4,-8).  

I don't know if you notice but the x-axis and y-axis are going up by two's in each graph.

On a horizontal number line, -6 is located to the (left) of -4. So, -6 is (less than) 4.

Answer:

On a horizontal number line, -6 is located to the (left) of -4. So, -6 is (less than) 4.

Step-by-step explanation:

The domain of the function in the mapping given is: A. {x | x = -5, -3, 1, 2, 6}.

The domain of a function includes all the possible values of x (input) in a function.

The corresponding set of y-values (output) is the range of the function.

The set of x-values in the mapping are, -5, -3, 1, 2, 6.

Therefore, the domain of the function in the mapping given is: A. {x | x = -5, -3, 1, 2, 6}.

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Answer:

[tex]11\ aces[/tex]

Step-by-step explanation:

we know that

Pamela on average serves an ace 44% of the time

That means ----> Pamela serves 44 aces every 100 serves

Using proportion

Let

x -----> the number of aces

[tex]\frac{44}{100}=\frac{x}{25}\\ \\x=44*25/100\\ \\x= 11\ aces[/tex]

Simple form of equation 3x – 5 + 23x – 9 = 26x-14

Linear Equation in One Variable is an equation that has a variable and the exponent number is one.

Can be stated in the form:

[tex] \large {\boxed {\bold {ax = b}} [/tex]

or

ax + b = c, where a, b, and c are constants, x is a variable

Whereas Linear Equation in two Variable is a linear equation that has 2 variables and the exponent is one

Can be stated in the form:

[tex] \large {\boxed {\bold {ax + bx = c}}} [/tex]

x, y = variable

There are several ways to solve an equation

• Add / Subtract / divide / multiply the same value on both sides

• Combine like terms

• Factoring

• Expanding

Like terms are terms whose variables and their exponents are the same.

You can combine and add terms

The algebraic form of 3x - 5 + 23x - 9 is a Linear Equation in One Variable, can be simplified:

• 1. Combine like terms

(3x + 23x) + (-5 - 9)

• 2. Add like terms:

26x -14

an algebraic expression

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[tex]\(3x - 5 + 23x - 9\)[/tex] simplifies to [tex]\(26x - 14\).[/tex]

To simplify the expression [tex]\(3x - 5 + 23x - 9\)[/tex], we can combine like terms

[tex]\[3x - 5 + 23x - 9 = (3x + 23x) + (-5 - 9)\][/tex]

[tex]\[= 26x - 14\][/tex]

[tex]\bf ~~~~~~ \textit{Simple Interest Earned Amount} \\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & \$5000\\ P=\textit{original amount deposited}\dotfill&\$2000\\ r=rate\to r\%\to \frac{r}{100}\\ t=years\dotfill &3 \end{cases} \\\\\\ 5000=2000(1+r3)\implies \cfrac{5000}{2000}=1+3r\implies \cfrac{5}{2}=1+3r \\\\\\ 5=2+6r\implies 3=6r\implies \cfrac{3}{6}=r\implies 0.5=r\implies \stackrel{\textit{converting to percent}}{0.5\cdot 100\implies 50\%}[/tex]

Answer:

The correct answer is third option

They are not congruent, because only one pair of corresponding sides is congruent.

Step-by-step explanation:

From the figure we can see that, two isosceles  triangles.

ΔFGH and ΔFJH

We get FG = GH and FJ = HJ

And side FH is common for both the triangles.

We can not say these two triangles are congruent.

Therefor the  correct answer is third option

They are not congruent, because only one pair of corresponding sides is congruent.

Final answer:

The congruency between Triangle FGH and Triangle FJH can be considered through Desargues's theorem, which relates congruency to parallel sides and intersecting vertex connections, and similarity can also be established by the AAA theorem, which involves congruent corresponding angles.

Explanation:

To determine whether Triangle FGH is congruent to Triangle FJH, one would need to employ the principles of Desargues's theorem, which states that if two triangles have their corresponding vertices connected by lines that meet at a point, and if the corresponding sides of the triangles are parallel, then the triangles are congruent. The information given suggests multiple instances where triangles are similar or congruent based on the congruency of angles or parallelism of lines, as dictated by the aforementioned theorem. For example, in the triangles ABC and FCE mentioned, the similarity is confirmed via the Angle Angle Angle (AAA theorem) because all corresponding angles of the triangles are congruent, which is a direct consequence of the vertical angles property and the alternate interior angles property. This similarity implies that there's a proportionality between the sides of the triangles, which could be a stepping stone in proving the congruency between Triangle FGH and Triangle FJH if similar conditions apply.

Answer:

[tex]\large\boxed{f(x)=6x^3+2x}[/tex]

Step-by-step explanation:

[tex]\text{If}\ f(-x)=f(x)\ \text{then}\ f(x)\ \text{is an even function.}\\\\\text{If}\ f(-x)=-f(x)\ \text{then}\ f(x)\ \text{is an odd function.}[/tex]

======================================================

[tex]f(x)=3x^2+x\\\\f(-x)=3(-x)^2+(-x)=3x^2-x\\\\f(-x)\neq f(x)\ \wedge\ f(-x)\neq-f(x)\\\\============================\\\\f(x)=4x^3+7\\\\f(-x)=4(-x)^3+7=-4x^3+7\\\\f(-x)\neq f(x)\ \wedge\ f(-x)\neq-f(x)\\\\============================\\\\f(x)=5x^2+9\\\\f(-x)=5(-x)^2+9=5x^2+9\\\\f(-x)=f(x)-\text{It's an even function}\\\\============================\\\\f(x)=6x^3+2x\\\\f(-x)=6(-x)^3+2(-x)=-6x^3-2x=-(6x^3+2x)\\\\f(-x)=-f(x)-\text{It's an odd function.}[/tex]

The function F(x)= 3x²+x is an odd function, option A is correct.

A relation is a function if it has only One y-value for each x-value.

To determine whether a function is odd or not, we need to check if f(-x) = -f(x) for all x in the domain of the function.

Let's check the function

F(x) = 3x²+ x

F(-x) = 3(-x)² + (-x) = 3x²- x

-f(x) = -(3x² + x) = -3x² - x

Since F(-x) = -f(x), this function is odd.

The other functions are even as they satisfy f(-x)=f(x)

Hence, the function F(x)= 3x²+x is an odd function, option A is correct.

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Answer:

[tex]-y=-2x+8\\y=2x-8[/tex]

Step-by-step explanation:

To solve, first subtract 2x from both sides.

[tex]2x-y=8\\-y=-2x+8[/tex]

You appear to want the solution for -y, so I've included it. Given that you also want the solution for y, divide both sides by -1.

[tex]-y=-2x+8\\y=2x-8[/tex]

Answer:

- y = 8 - 2x

Step-by-step explanation:

2x - y = 8

Subtracting 2x on both sides,

=> 2x - 2x - y = 8 - 2x

=> - y = 8 - 2x  

Answer:

h < 14

Step-by-step explanation:

2h +8 > 3h - 6

2h - 3h >  - 6 - 8

-h > -14  (multiply both sides by -1; remember to flip the inequality sign!)

h < 14

Answer:

[tex]Q_1=2[/tex]

[tex]Q_3=6[/tex]

Step-by-step explanation:

Notice that we already have the data sorted from least to greatest.

Now to find Q1 and Q3 we can use the following formulas

For a set of data ordered from least to greatest of the form [tex]X_1, X_2, ..., X_n[/tex]

Where n is the total number of data

[tex]Q_1=X_{\frac{1}{4}(n+1)}[/tex]

In this case [tex]n=10[/tex]

So:

[tex]Q_1=X_{\frac{1}{4}(10+1)}[/tex]

[tex]Q_1=X_{2.75}[/tex]

Round the nearest whole and get:

[tex]Q_1=X_{3}[/tex]

[tex]Q_1=3[/tex]

For Q3 we have:

[tex]Q_3=X_{\frac{3}{4}(n+1)}[/tex]

[tex]Q_3=X_{\frac{3}{4}(10+1)}[/tex]

[tex]Q_3=X_{8.25}[/tex]

Round the nearest whole and get:

[tex]Q_3=X_{8}[/tex]

[tex]Q_3=6[/tex]

Answer:

Q1: 2.5

Q3: 6

Step-by-step explanation:

The median area is 3 and 4.

The lower quartile is 3+2=5 5/2 2.5

The upper quartile is 6+6= 12 12/2 6

Answer:

(5x + 7y)(25x² - 35xy + 49y²)

Step-by-step explanation:

125x³ + 343y³ ← is a sum of cubes and factors in general as

a³ + b³ = (a + b)(a² - ab + b² )

125x³ = (5x)³ ⇒ a = 5x

343y³ = (7y)³ ⇒ b = 7y

125x³ + 343y³

= (5x + 7y)((5x)² - (5x × 7y) + (7y)²)

= (5x + 7y)(25x² - 35xy + 49y²) ← in factored form

Answer:

112

Step-by-step explanation:

3(7-3) = 3 x 4 = 12

12^2 = 144

144 -4(6+2)

144-4(8)

144-32

112

[tex]\bf \stackrel{\mathbb{P~E~M~D~A~S}}{3(7-3)^2-4(6+2)}\implies 3(\stackrel{\downarrow }{4})^2-4(\stackrel{\downarrow }{8})\implies 3(\stackrel{\downarrow }{16})-4(8) \\\\\\ \stackrel{\downarrow }{48}-4(8)\implies 48-\stackrel{\downarrow }{32}\implies 16[/tex]

Answer:

[tex]8(2x^2 + x + 4)[/tex]

Step-by-step explanation:

Given:

We'd factor out 8:

[tex]8(2x^2 + x + 4)[/tex]

Our answer would be [tex]8(2x^2 + x + 4)[/tex]

The completely factored form of the expression 16x2 + 8x + 32 is 8(2x2 + x + 4), after factoring out the greatest common factor, 8.

The question asks for the completely factored form of the expression 16x2 + 8x + 32. To factor this expression completely, we look for a common factor in all the terms. Observing the coefficients (16, 8, and 32), we recognize that 8 is the greatest common factor (GCF). Factoring out the GCF, we get:

8(2x2 + x + 4).

This expression cannot be factored further since the quadratic inside the parentheses does not factor neatly over the integers. Thus, the completely factored form of 16x2 + 8x + 32 is 8(2x2 + x + 4).

Answer:

c.

Step-by-step explanation:

the most that can be factored out is -1.5,

-1.5 * w = -1.5w

-1.5 * -5 = 7.5

-1.5w + 7.5, so it's

-1.5(w-5)

Answer:

x = 8

Step-by-step explanation:

log₅ (10x − 1) = log₅ (9x + 7)

10x − 1 = 9x + 7

x = 8

The set of ordered pairs that defines a function is:  {(1,3),(5,2),(6,9),(1,12),(10,2)} (last option).

A set of ordered pairs that defines a function will have exactly one y-value that assigned to every x-value. In essence, it means none of its x-values can have two corresponding y-value.

All the sets of ordered pairs have exactly one y-value that corresponds to each of its x-value except {(1,3),(5,2),(6,9),(1,12),(10,2)}, which have two different y-values that corresponds to the x-value of 1.

Therefore, the set that doesn't define a function is:  {(1,3),(5,2),(6,9),(1,12),(10,2)} (last option).

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A set of ordered pairs defines a function if each element of the domain is mapped to a single, unique value in the range. Set D does not define a function because it contains two distinct ordered pairs with the same first element, (1,3) and (1,12).

A set of ordered pairs defines a function if each element of the domain is mapped to a single, unique value in the range. Looking at the given sets of ordered pairs, we can determine which ones define a function by checking if there are any repeated first elements in the pairs. If there are repeated first elements, then the set does not define a function.

Out of these sets, Set D does not define a function because it contains two distinct ordered pairs with the same first element, (1,3) and (1,12).