--212x21 4 Kuta Software - Infinite Algebra 2 Graphing Absolute Value Equations Graph each equation. 1) y=x-11 De 36 2) -\ x41

Answer:

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This gives us:

Answer:

[tex](x,y,z)=\left(\; \boxed{-1,7,-4} \; \right)\quad \textsf{(smaller $x$-value)}[/tex]

[tex](x,y,z)=\left(\; \boxed{1,-1,4} \; \right)\quad \textsf{(larger $x$-value)}[/tex]

Step-by-step explanation:

Given system of equations:

[tex]\begin{cases}x^2+z^2=17\\\;4x+y=3\\\;\;\;y+z=3\end{cases}[/tex]

To solve by the method of substitution, first rearrange the third equation to make y the subject:

[tex]\implies y=3-z[/tex]

Substitute this into the second equation and solve for z:

[tex]\begin{aligned}\implies 4x+(3-z)&=3\\3-z&=3-4x\\-z&=-4x\\z&=4x\end{aligned}[/tex]

Substitute the found expression for z into the first equation and solve for x:

[tex]\begin{aligned}\implies x^2+(4x)^2&=17\\x^2+16x^2&=17\\17x^2&=17\\x^2&=1\\x&=\pm1\end{aligned}[/tex]

Substitute the found values of x into the second equation and solve for y:

[tex]\begin{aligned}\implies x=-1 \implies 4(-1)+y&=3\\-4+y&=3\\y&=7\end{aligned}[/tex]

[tex]\begin{aligned}\implies x=1 \implies 4(1)+y&=3\\4+y&=3\\y&=-1\end{aligned}[/tex]

Substitute the found values of x into the derived expression for z and solve for z:

[tex]\begin{aligned}\implies x=-1 \implies z&=4(-1)\\z&=-4\end{aligned}[/tex]

[tex]\begin{aligned}\implies x=1 \implies z&=4(1)\\z&=4\end{aligned}[/tex]

Therefore, the solutions are:

[tex](x,y,z)=\left(\; \boxed{-1,7,-4} \; \right)\quad \textsf{(smaller $x$-value)}[/tex]

[tex](x,y,z)=\left(\; \boxed{1,-1,4} \; \right)\quad \textsf{(larger $x$-value)}[/tex]

Answer:

[tex]x - 3 = 13 \\ \\ x = 13 + 3 \\ \\ x = 16[/tex]

-3 goes to other side and changes into +3

The circumference of a circle is given by the formula:

Where d is the diameter of the circle.

If the circumference is 109.9 ft, we have:

So the diameter of the garden is 35 feet.

Background:

• Domain,: a set of all possible values of the independent variable (,x,, in this case).

• Range,: a set of all possible values of the dependent variable (,y,, in this case), after substituting the domain.

Based on the arrows of the function, we can conclude that those extend to infinity (negative and positive).

Also, based on the coordinates of the vertex given we can see that the first value of y is 4.

Answer:

• Domain

• Range

SOLUTION

We want to find the figure in which lines perpendicular to l are drawn through points A, B, C, and D

The correct figure will be the one in which a vertical line is drawn across each of points A, B, C and D.

Looking at this, we can see that the correct answer is the first option

Answer:

a

Step-by-step explanation:

Recall that:

and that the domain of a rational function consists of all real numbers such that the denominator is different from zero.

If f(x)=5x+3 and g(x)=4x-5 we get that:

The domain of the above rational function is:

Answer: Last option.

The standard deviation of a binomial distribution with n trials and a probability of success of p is given by the formula:

From the problem, we identify:

Then:

Okay, here we have this:

Considering the provided information, and that we must identify which of the provided options allow us to determine that the two triangles are similar, we obtain the following:

As the angle-angle similarity says that if two angles of one triangle are congruent with two angles of another triangle, then the triangles are similar.

Finally, we see that the only option that satisfies this statement is option D, since it indicates that two angles of the triangles are congruent. Therefore the correct option is D.

the lines that cross the centroid are divided into 2 by this the short line corresponds to 1/3 of the complete line and the long line corresponds to 2/3 of the complete line

so KH is 1/3 of DH

if KH=12, then

the value of DH is 36

A

Since AB in perpendicular to CD and bisects mThis can be written as

but

then

pluggin the value of the angle m[tex]\begin{gathered} 130+2m<\text{DOP}=180 \\ 2m<\text{DOP}=180-130 \\ m<\text{DOP}=\frac{50}{2} \\ m<\text{DOP}=25 \end{gathered}[/tex]Therefore the angle m

B

As we mentioned above the angle mthen m

Using equation (1) of part to find the angle m[tex]\begin{gathered} m<\text{MOP}+38+38=180 \\ m<\text{MOP}=180-76 \\ m<\text{MOP}=104 \end{gathered}[/tex]therefore the angle m

Given:

In 2010 the population was 5800.

2012 the population had dropped to 4,600.

Let 't=0' be the year 2010.

P(t) represents the year population of the town t years after 2010.

Slope of a function P(t) is

Population of town t years after 2010.

Population in the year 2016 that is t=6

Population in the year 2016 is 2200

By definition, consider that natural numbers are all numbers from 1 to infinity. Whole numbers are the same natutal numbers plus zero. Integers are all numbers from minus infinity to infinity and rational are all number with finite decimals, and periodic infinite decimals.

Then, based on the previous description, the diagram which correctly shows the subsets of rational numbers is:

diagram F.

ANSWER

EXPLANATION

The surface area of the box (rectangular prism) is:

where L = length; W = width; H= height

Therefore, we have that the surface area of the box is:

The volume of the box is:

Therefore, the volume of the box is:

(2,3) (4,6) (6,9) (8,12) is the set of ordered pair lie on the function that is direct proportion.

Direct proportion is mathematical comparison between two variable

when one increase also increase the other or one decrease also decreases the other then , they are direct proportion.

In direct proportion , the ratio of these variable remains same no matter what.

The following are the set of ordered pair,

a. (2,6) (4,8) (6,10) (8,12)

calculating ratio,

[tex]\frac{2}{6} = \frac{1}{3} \neq \frac{4}{8} = \frac{1}{2}[/tex]

Ratio is changing so, ordered pair are not direct proportion

b. (2,2) (4,2) (6,2) (8,2)

ratios = [tex]\frac{2}{2} =1 \neq \frac {4}{2} = 2[/tex]

Ratio is different

c. (2,1) (4,3) (6,5) (8,7)

Ratio is different , the ordered set is not direct proportion

d. (2,3) (4,6) (6,9) (8,12)

ratios = [tex]\frac{2}{3}=\frac{4}{6}[/tex]

Ratios are same in entire ordered set

Hence , (2,3) (4,6) (6,9) (8,12) is a direct proportion.

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We must calculate the weighted average as follows:

Therefore, the average speed is 85.68 km/h

to solve this we need to translate into math terms, so

Step 1

a) let d represents the number of dimes

let n represents the number of nickles

so

re write the expressions

The number of nickels is three more than seven times the number of dimes in other words you have to add 7 to seven times the number of dimes to obtain the number of nickles

hence

therefore , the expression for the number of nickles is

I hope this helps you

Let us assume the numbers are x and y.

The first part of the question can be written as

and the second part can be written as

From equation 1, we can get a value for y as

Substitute for y in equation 3 into equation 2:

Expanding and solving, we get

Next, we substitute for the value of x into equation 3:

Therefore, the two numbers are 114 and 86

Solve e from the equation by substraction 96 to both sides of the equal sign:

The value of  sector KL is 52

If JM and KN are two diamters of the circle,

then they intersect at the center

The sector JK and NM are equal

Thus,

The sector JN and KM are also equal

sector KM = sector KL + sector LM

Sector JN = Sector KM

sector JN = sector KL + sector LM

125 =  6x + 4 + 8x + 9

125 = 14x + 13

14x = 125 - 13

14x = 112

x = 8

sector KL = 6x + 4

= 6(8) + 4 = 48 + 4 = 52

Therefore, the sector KL is 52

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The slope formula for 2 points is

where

By substituting these values into the slope formula, we get

therefore, the slope is 4.

Given:

The point A(5, 7).

To given transformation is (x-5, -y+2).

So,

The new point is,

Therefore, the coordinate for A' after the given transformation has occured is A'(0,-5).

Answer:

D is correct.

Step-by-step explanation:

Let x be the lowest score. Then x + 40 is the highest score.

[tex]x + x + 40 = 152[/tex]

[tex]2x + 40 = 152[/tex]

[tex]2x = 112[/tex]

[tex]x = 56[/tex]

[tex]x + 40 = 96[/tex]

Lowest score is 56, highest score is 96.

First We will put the number of toys per day in simple form:

Then, to know how many toys will be made in 9 days, let's multiply the number of toys per day by the given number of days:

Now We will put the number in scientific notation:

In order to calculate how much will be owed, we can use the formula below for interest compounded continuously:

Where A is the final amount after t years, P is the initial amount and r is the interest rate.

So, using P = 1300, r = 0.04 and t = 6, we have:

Therefore the amount owed after 6 years is $1652.62.

Given the radical equation:

Squaring both sides to eliminate the root.

Factor the equation to find the roots:

we will check ( q = 1 and q = 9 ) by substitution into the given equation:

When q = 1

So, ( q = 1 ) is an extraneous solution.

When q = 9

So, ( q = 9 ) is the solution of the given equation.

So, the answer will be:

The extraneous solution to the radical equation is 1

Step 1

Plot the graph of f(x)

Step 2

The function of g(x) suggests that f(x);

Thus, the graph of g(x) will look like this;

Answer;

Given:

The height equation is,

Explanation:

For maximum/minimum of a function, the first derivative of function is 0.

Differentiate the function with respect to x.

For maximum and minimum,

So rocket reach it maximum height after 4.5 seconds of launch.

Substitute 4.5 for t in the equation to determine the maximum reached by rocket.

So maximum height of rocket is 330 feet.

The expression 4sr²(2rs + 3s)  is not completely factored.

An algebraic expression consists of unknown variables, numbers and arithmetic operators.

In other words, an expression or algebraic expression is any mathematical statement which consists of numbers, variables and an arithmetic operation between them.

An expression is completely factored when no further factoring is possible.

Therefore, let's check if the expression is completely factored.

4sr²(2rs + 3s)

The expression still have a common factor which is s. This means its not completely factored.

The complete factorisation is as follows;

4sr²(2rs + 3s) = 4s²r²(2r + 3)

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Explanation

The area under a curve between two points can be found by doing a definite integral between the two points

Step 1

a) set the intergral

hence

Step 2

evaluate

let ; numbers of intervals

therefore, the area is

I hope this helps you

To divide, subtract exponents to same base variables.

Multiply exponents of exponents

x= 6

y= 18