Each graph shows a relation. The first and second numbers of each ordered pair in the relation are members of the set of real numbers. In each case, find the domain and range and determine whether the relation is a function.

Answer:

The first table

Step-by-step explanation:

If you create a fraction x/y, you will see all of the answers reduce down to -1/4. The other tables don't reduce to the same values.

Answer:

(3,2)

Step-by-step explanation:

Setting up equation so we can use substitution method

x - y = 1 , x + 3y = 9

step 1 set first equation equal to x by adding y to both sides so we can use the substitution method to solve the system of equations.

x = y + 1 , x + 3y = 9

now we can plug in ( or substitute hence substitution method ) the first equation into the second

Solving for y using the substitution method

x + 3y = 9

plug in x = y + 1

y + 1 + 3y = 9

combine like terms

4y + 1 = 9

subtract 1 from both sides

4y = 8

divide both sides by 4

y = 2

Now to find the value of x we plug in the value of y into one of the equations and solve for x.

Solving for x

x - y = 1

y = 2

x - 2 = 1

add 2 to both sides

x = 3

The solution would be (3,2)

Answer:

x = 3 and y = 2 or (3,2) in coordinate form

Step-by-step explanation:

Given:

[tex]\displaystyle \large{\begin{cases} x-y=1 \\ x+3y=9 \end{cases}}[/tex]

Solve by elimination of x-terms by multiplying either one of equations with -1:

For this, I choose to multiply -1 in first equation:

[tex]\displaystyle \large{\begin{cases} -1(x-y=1) \\ x+3y=9 \end{cases}}\\\displaystyle \large{\begin{cases} -x+y=-1 \\ x+3y=9 \end{cases}}[/tex]

Then add both equations:

[tex]\displaystyle \large{-x+x+y+3y=-1+9}\\\displaystyle \large{4y=8}[/tex]

Divide both sides:

[tex]\displaystyle \large{\dfrac{4y}{4} = \dfrac{8}{4}}\\\displaystyle \large{y=2}[/tex]

Next, substitute y = 2 in one of equations to solve for x:

For this, I choose to substitute y = 2 in the first equation:

[tex]\displaystyle \large{x-y=1}[/tex]

Substitute y = 2 in:

[tex]\displaystyle \large{x-2=1}[/tex]

Add both sides by 2:

[tex]\displaystyle \large{x-2+2=1+2}\\\displaystyle \large{x=3}[/tex]

Hence, the solution is x = 3 and y = 2 or you can write as in coordinate form (3,2)

__________________________________________________________

First method is elimination method, I’ll demonstrate another method which is by using matrices to find the solutions.

Given:

[tex]\displaystyle \large{\begin{cases} x-y=1 \\ x+3y=9 \end{cases}}[/tex]

Write the system of equations in matrices form:

[tex]\displaystyle \large{\left[\begin{array}{ccc}1&-1\\1&3\end{array}\right] \left[\begin{array}{ccc}x\\y\end{array}\right] =\left[\begin{array}{ccc}1\\9\end{array}\right]}[/tex]

Let:

[tex]\displaystyle \large{A=\left[\begin{array}{ccc}1&-1\\1&3\end{array}\right] }\\\displaystyle \large{X=\left[\begin{array}{ccc}x\\y\end{array}\right] \\\displaystyle \large{B = \left[\begin{array}{ccc}1\\9\end{array}\right] }[/tex]

From [tex]\displaystyle \large{AX=B \to X=A^{-1}B}[/tex] where:

[tex]\displaystyle \large{A^{-1}=\dfrac{1}{\det A} \left[\begin{array}{ccc}d&-b\\-c&a\end{array}\right] = \dfrac{1}{ad-bc} \left[\begin{array}{ccc}d&-b\\-c&a\end{array}\right] }[/tex]

Find [tex]\displaystyle \large{\det A}[/tex]:

[tex]\displaystyle \large{\det A = ad-bc = 3+1=4}[/tex]

Therefore:

[tex]\displaystyle \large{A^{-1} = \dfrac{1}{4}\left[\begin{array}{ccc}3&1\\-1&1\end{array}\right]}\\\therefore \displaystyle \large{X = \dfrac{1}{4}\left[\begin{array}{ccc}3&1\\-1&1\end{array}\right] \left[\begin{array}{ccc}1\\9\end{array}\right]}[/tex]

Evaluate the matrices:

[tex]\displaystyle \large{X= \dfrac{1}{4}\left[\begin{array}{ccc}3(1)+1(9)\\-1(1)+1(9)\end{array}\right] }\\\displaystyle \large{X= \dfrac{1}{4}\left[\begin{array}{ccc}3+9\\-1+9\end{array}\right] }\\\displaystyle \large{X= \dfrac{1}{4}\left[\begin{array}{ccc}12\\8\end{array}\right]}\\\displaystyle \large{X= \left[\begin{array}{ccc}3\\2\end{array}\right] }\\\therefore \displaystyle \large{\left[\begin{array}{ccc}x\\y\end{array}\right] = \left[\begin{array}{ccc}3\\2\end{array}\right]}[/tex]

Therefore, the solution is x = 3 and y = 2

Answer: D

Step-by-step explanation:

Answer:

12

Step-by-step explanation:

End points of [tex]\overline{RS}[/tex] are:

[tex]R (4, \:-8)\implies x_1 = 4,\: y_1=-8[/tex]

[tex]S (25, \:-1)\implies x_2 = 25,\: y_2=-1[/tex]

Point T divides [tex]\overline{RS}[/tex] in the ratio 4 : 3

[tex]\implies m = 4,\: n= 3[/tex]

Now, by section formula:

[tex]T=\bigg(\frac{mx_2+nx_1}{m+n},\:\:\frac{my_2+ny_1}{m+n}\bigg)[/tex]

Plugging in the values of [tex]x_1 ,\: y_1, \:x_2,\: y_2\:\&\: m, \: n[/tex] in the above formula, we find:

[tex]T=\bigg(\frac{4(25)+3(4)}{4+3},\:\:\frac{4(-1)+3(-8)}{4+3}\bigg)[/tex]

[tex]\implies T=\bigg(\frac{100+12}{7},\:\:\frac{-4-24}{7}\bigg)[/tex]

[tex]\implies T=\bigg(\frac{112}{7},\:\:\frac{-28}{7}\bigg)[/tex]

[tex]\implies T=(16,\:\:-4)[/tex]

Sum of the coordinates of T = 16 + (-4) = 16 - 4 = 12

Step-by-step explanation:

it is a combination of a cone and half a sphere.

the volume of a cone is

ground area × height / 3

the ground area is a circle, so we have

pi×r²×h/3

in our case

pi×(10/2)²×12/3 = pi×5²×4 = pi×25×4 = 100pi

the volume of a sphere is

4/3 × pi×r³

and half a sphere is then

4/3 / 2 × pi×r³ = 4/6 × pi×r³ = 2/3 × pi×r³

in our case

2/3 × pi×5³ =2/3 × pi×125 = 250/3 × pi

together we get

100pi + 250/3 × pi = 300/3 × pi + 250/3 × pi =

= 550/3 × pi = 575.9586532... cm³ ≈ 576 cm³

if we use 3.14 for pi we get

575.6666666... cm³ ≈ 576 cm³

Answer:

82

Step-by-step explanation:

because diagonals are equal in quadrilater

The circumference of the smaller circle is C =  2*pi*x/3.

We have given that radius ob measures x units

circumference of the circle is given by,

[tex]C = 2\times \pi \times R[/tex]

where pi = 3.14

R= radius

we have two circles, A and B, where B is the larger circle and A is the smaller circle.

We know that,The circumference of B is 3 times the circumference of A.

The radius of circle B is OB = x

The radius of circle A is OA

We want to find an expression of OA.

The circumference of circle B is given by

[tex]C(B) = 2\times \piOB = 2\times pi\times x[/tex]

The circumference of circle A  is given by

[tex]C(A) = 2\times\pi\times OA[/tex]

we know that the circumference of circle B is 3 times the circumference of circle A,

[tex]C(B) = 3\times C(A)[/tex]

replacing the equations for the circumferences

[tex]2\times\pi\times x = 3\times (2\times pi\times OA)[/tex]

We have divide both sides by [tex]2\pi[/tex]we get:

[tex]x = 3\times OA[/tex]

Now we want to solve this for OA, then we need to isolate it,

[tex]x/3 = OA[/tex]

We can conclude that the radius of the smaller circle is equal to x/3.

Then the circumference of circle A is

[tex]C(A) = 2\times pi\times x/3[/tex]

To learn more about the circumference of the circle visit:

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Answer:

c

Step-by-step explanation:

Answer:

4250

Step-by-step explanation:

0.13 = 13%

1000×0.13=130
130×25= 3250 + 1000 = 4250

What I did:

You have to turn the percent to a decimal first

Then multiply the decimal by the first investment amount (1000)

then multiply that by the years that you have before retirement
You add that amount plus the 1000 you have started with

Answer:

  19

Step-by-step explanation:

The triangle inequality tells you the possible values of x are ...

  24 -10 < x < 24 +10

  14 < x < 34

There are 19 integer values of x in this range.

Answer:

Step-by-step explanation:

Domain is x-values the graph can have

  x = [-3,22]

range is the y values the graph includes

   range-=  [-3,+2]

Answer:

(Sorry if this answer is not correct, if it is or is not, please tell me in the comments!)

232.777778 feet squared (feel free to round the answer)

Step-by-step explanation:

The formula on how to find the volume is:

(the area of the floor) x (the height of the room) = 2025 cubic feet

We already know the height, so we need to plug it in.

(the area of the floor) x 9 feet = 2095 cubic feet

To get the area of the floor, we need to divide 2095 by 9.

So, the area of the floor is exactly 232.777778 feet squared.

Answer:

225 ft²

Step-by-step explanation:

Formula

Solving :

Answer:

n=5

Step-by-step explanation:

So I'm not sure how to write the equation, but i do know that each term has five added from the previous one, hope that help a little bit!

Answer:

I think it's B.

Step-by-step explanation:

Answer:

rhetorical stage, syncopated stage, symbolic stage

Step-by-step explanation:

The line of best fit of the traffic study is a line through a scatterplot of data points which shows the relationship between the points.

Your information is incomplete as the table isn't given. Therefore, an overview will be given.

The least square methods is used by statisticians to arrive at the geometric equation for the line. A straight line will simply result from a simple regression of two or more independent variables.

A regression that has to do with multiple related variables lead to a curved line. The line of best fit is an important output of regression analysis.

A regression that has two independent variables will have a formula with:

y = c + b1x1 + b2x2

where,

c = constant

b1 = first regression coefficient

x1 = first independent variable

b2 = second regression coefficient

x2 = second independent variable.

In conclusion, the line of best fit expresses the relationship in a scatterplot of the data points.

Learn more about line of best fit on:

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Answer:

x = 1/2

Step-by-step explanation:

28x + 1 = 32x - 1 <== subtract 28x from both sides

-28x      -28x

1 = 4x - 1 <== add 1 to both sides

+ 1      + 1

2 = 4x <== divide both sides by 4 to isolate the variable

/4   /4

1/2 = x

Hope this helps!

[tex] \Large{\boxed{\sf x = \dfrac{1}{2} }} [/tex]

[tex] \\ [/tex]

Given equation:

[tex] \sf 28x + 1 = 32x - 1 [/tex]

[tex] \\ [/tex]

Subtract 28x from each side :

[tex] \sf 28x + 1 - 28x = 32x - 1 - 28x \\ \\ \sf 1 = 4x - 1 [/tex]

[tex] \\ [/tex]

Add 1 to both sides:

[tex] \sf 1 + 1 = 4x \\ \\ \sf 2 = 4x [/tex]

[tex] \\ [/tex]

Divide both sides by 4:

[tex] \sf \dfrac{2}{4} = \dfrac{4x}{4} \\ \\ \\ \boxed{\boxed{\sf x = \dfrac{1}{2} }} [/tex]

[tex] \\ \\ [/tex]

▪️Learn more about equations here:

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Answer:

Depends on the question or if it specifically says to.

Step-by-step explanation:

For finding the volume of cylinders and spheres use the pi symbol or just say "use 3.14 for pi"

Answer:

x = 24

Step-by-step explanation:

The formula for determining the sum of interior angles is:

[tex](n-2) * 180[/tex]

[tex]4 * 180 = 720[/tex]

Therefore to determine an equation for x, we must add up all the interior angle equations and set them equal to 720.

[tex](2x+3) +(3x+12) + (7x+14) + (9x+2) + (4x+8) + (3x+9) = 720\\28x + 48 = 720\\28x = 672\\x = 24[/tex]

The equation and answer above shows how to find x, which equals 24.

Answer:

i dont lnow the language sorry

Answer:

Ray.

Step-by-step explanation:

Lines have no endpoints, while rays have 1 endpoint (:

[tex]\qquad\qquad\huge\underline{{\sf Answer}}♨[/tex]

Since it's a Trapezoid with its non - parallel sides equal to one another,

[tex]\qquad \sf  \dashrightarrow \:\angle A + \angle P = 180[/tex]

[ By forming co - interior angle pair ]

[tex]\qquad \sf  \dashrightarrow \:\angle A +100 = 180[/tex]

[tex]\qquad \sf  \dashrightarrow \:\angle A = 180 - 100[/tex]

[tex]\qquad \sf  \dashrightarrow \:\angle A = 80 [/tex]

Now, similarly,

[tex]\qquad \sf  \dashrightarrow \:\angle A + \angle R = 180[/tex]

[tex]\qquad \sf  \dashrightarrow \: \angle R + 80 = 180[/tex]

[tex]\qquad \sf  \dashrightarrow \: \angle R = 100[/tex]

Similarly,

[tex]\qquad \sf  \dashrightarrow \angle K + \angle R = 180[/tex]

[tex]\qquad \sf  \dashrightarrow \angle K + 100 = 180[/tex]

[tex]\qquad \sf  \dashrightarrow \angle K = 80[/tex]

Consecutive angles are supplementary

Opposite angles are equal

Opposite angles are equal again

Answer:

[tex]\pi[/tex] is infinite. 3.14 only has three numbers.

Step-by-step explanation:

so [tex]\pi[/tex] multiplied by any number (except 0) will have infinite numbers

Answer:

See below ↓

Step-by-step explanation:

When multiplying a number by 3.14, which is the simplified version of pi, it will give a constant term. But, when multiplying by π, the actual value is equal to 22/7, and it is a non-terminating decimal. Therefore, when you multiply any number with 3.14, it will be slightly lesser than when you multiply with π.

Answer:

24 / 6 = ccc

Step-by-step explanation:

There is 24 oz of cheese total that will be split evenly (divided) into 6 parts.

Each part will equal one sandwich worth of cheese (ccc) on the other side of the equation.

This one is very simple to solve, you could just calculate 24/6 to get your answer. But I'll go through it using typical algebra you would use for a less simple equation.

To solve:

Multiply by 6 to cancel the division by 6 on the left side

24 = 6ccc

Divide by 6 to isolate ccc again

4 = ccc

So each sandwich would get 4oz of cheese.

he studied for 495 minutes. 165 minutes a day.

Answer: He studied for 315 minutes. Because he studied for 1hr and 45 mins (105 mins). Then you multiply this by 3 because it's been three days.

Hope this helps!

Answer:

  43°

Step-by-step explanation:

Triangle ADM is a right triangle with legs AD=4 cm and DM=√18 cm. The angle at M is the angle of interest. It can be found using the inverse tangent function.

  Tan = Opposite/Adjacent

  tan(∠AMD) = AD/MD = 4/√18

  ∠AMD = arctan(4/√18) ≈ 43.31°

The angle the plane makes is about 43°.

Answer:

the measure of the angle that the plane ABC makes with the base of the prism = 43 degree (to the nearest degree)

Step-by-step explanation:

We notice that the plane ABC and the base of the prism intersect along the line BC

And as the plane (ADM) is perpendicular to the line BC

then the angle between the plane ABC and the base of the prism is the angle AMD

Let θ be the measure of the angle AMD

[tex]\begin{aligned}\tan (\theta) &=\frac{A D}{M D} \\&=\frac{4}{\sqrt{18}}\end{aligned}[/tex]

[tex]\begin{aligned}\Rightarrow \theta &=\tan ^{-1}\left(\frac{4}{\sqrt{18}}\right) \\&=43,31385 \ldots\end{aligned}[/tex]

Answer:

The median is 8.1

Step-by-step explanation:

You add up all the numbers and divide it by how much numbers there are.

1) Add. 1 + 7+ 16 + 18 + 40 = 81

2) Count. There are 10 numbers.

3) Divide 81/10

4) 8.1

The median is 8.1

Answer:

Pythagorean Theorem used for finding the missing side length for a triangle the formula is a^2 + b^2 = c^2
a= base
b= height
c= the diagonal side a.k.a. hypotenuse

Answer:

u see the formula for the Pythagorean theorem is a^2 + b^2 = c^2 i hope this helps please mark as brainliest have a good day!!! :D Bye

Step-by-step explanation:

Answer: Yes

Step-by-step explanation:

If you were to use AAS, you could prove the third pair of angles congruent by using the fact that the sum of the measures of the angles of a triangle is 180 degrees, and since you have two of the angles, you can solve for the third pair of angles, which would be congruent.