Find the domain the function graphed below. Express in interval notation.

Domain:

Answer:

x = 1

Step-by-step explanation:

The axis of symmetry for a vertically opening parabola is a vertical line with equation

x = h

where h is the value of the x- coordinate the line passes through.

The axis of symmetry passes through the vertex 1, 4 ) with x- coordinate 1

Hence equation of axis of symmetry is x = 1

Answer:

2

Step-by-step explanation:

To find the slope of a line given two points [tex](x_1,y_1) \text{ and } (x_2,y_2)[/tex] you could use the formula: [tex]\frac{y_2-y_1}{x_2-x_1} \text{ or even } \frac{y_1-y_2}{x_1-x_2}[/tex].

However, what I'm fixing to do is equivalent to that except I think easier to remember.

You line up the points vertically and subtract, then put 2nd difference over 1st difference.

Like this:

 ( 3  ,   4)

- ( 5  ,   8)

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

-2        -4

So the slope is -4/-2=4/2=2.

The slope is 2.

Answer:

$132,612.50

Step-by-step explanation:

We will use the present value - future value formula. WHich is:

[tex]FV=PV(1+r)^t[/tex]

Where

FV is the future value (amount)

PV is the present value (amount)

r is the rate of interest (per year)

t is the number of years

In the problem given, the present amount (PV) is 125,000. The rate of interest (r) is 3%, or 0.03. And the time frame is 2 years, or t = 2.

Plugging these info in the equation, we can get the future value as shown:

[tex]FV=PV(1+r)^t\\FV=125,000(1+0.03)^2\\FV=125,000(1.03)^2\\FV=132,612.5[/tex]

This is the future vallue of $125,000 3% in 2 years.

Answer: 70

Step-by-step explanation:

Solve the equation in the innermost parentheses first that means solving 4+1 =5

The next step would be subtracting 9 from five which gives you 4

Next multiply 3 to 4 which gives you 12

Then multiply 5 with 12 which equals 60

Now you have the equation 60+20/4*2

Solve the division and multiplication part of the equation first because of the rule pemdas which shows multiplication comes before addition

First divide 20/4 which gives you 5 then multiply with 2 which gives you ten

After dividing and multiplying you are left with the equation 60+10

The answer is 70

Answer:

First problem: Solving for g.

[tex]g=27^{\frac{1}{x-2}}[/tex]

Second problem: Solving for x.

[tex]x=\log_g(27)+2[/tex]

Third problem: Assuming g is 9 while solving for x.

[tex]x=3.5[/tex]

Step-by-step explanation:

First problem: Solving for g.

[tex]g^{x-2}=27[/tex]

Raise both sides by 1/(x-2).

[tex](g^{x-2})^{\frac{1}{x-2}}=27^{\frac{1}{x-2}}[/tex]

[tex]g^{1}=27^{\frac{1}{x-2}}[/tex]

[tex]g=27^{\frac{1}{x-2}}[/tex]

Second problem: Solving for x.

[tex]g^{x-2}=27[/tex]

x is in the exponent so we have to convert to logarithm form since we desire to solve for it:

[tex]\log_g(27)=x-2[/tex]

Add 2 on both sides:

[tex]\log_g(27)+2=x[/tex]

[tex]x=\log_g(27)+2[/tex]

Third problem: Assuming g is 9 while solving for x.

[tex]9^{x-2}=27[/tex]

I'm going to solve this in a different way than I did above but you could solve it exactly the way I did for x when 9 was g.

I'm going to write both 9 and 27 as 3 to some power.

9=3^2 while 27=3^3.

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

[tex]3^{2x-4}=3^3[/tex]

Since both bases are the same on both sides, we need the exponents to be the same:

[tex]2x-4=3[/tex]

Add 4 on both sides:

[tex]2x=7[/tex]

Divide both sides by 2:

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

[tex]x=3.5[/tex]

Now earlier for x in terms of g we got:

[tex]x=\log_g(27)+2[/tex]

I we input 9 in place of g and put it into our calculator or use some tricks without the calculator to compute we should get 3.5 as the answer like we did above when g was 9.

[tex]x=\log_9(27)+2[/tex]

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

[tex]x=1.5+2[/tex]

[tex]x=3.5[/tex]

Answer:

b + 15

Step-by-step explanation:

Let:

"boys" = b

"girls" = g = 15

Note that: "sum" = addition.

Combine:

b + 15 is your numerical expression of your question.

~

Answer:

1 to 15

Step-by-step explanation:

1 boy/ 15 girls

Answer:

(7, - 3 )

Step-by-step explanation:

Solve the 2 equations simultaneously to find intersection.

Given the equations of the sides

2x + 3y = 5 → (1)

3x + y = 18 → (2)

Multiplying (2) by - 3 and adding to (1) will eliminate the y- term

- 9x - 3y = - 54 → (3)

Add (1) and (3) term by term

(2x - 9x) + (3y - 3y) = (5 - 54) and simplifying gives

- 7x = - 49 ( divide both sides by - 7 )

x = 7

Substitute x = 7 into (1) or (2) for corresponding value of y

Substituting in (2)

21 + y = 18 ( subtract 21 from both sides )

y = - 3

Point of intersection = (7, - 3 )

Final Answer:

The coordinates of the intersection of the two lines are (x, y) = (7, -3).

Explanation:

To find the coordinates of the intersection of the two lines represented by the equations 2x + 3y = 5 and 3x + y = 18, we can solve this system of linear equations. Here's how to proceed step-by-step:
Step 1: Label the equations.
Let's call the first equation (1) and the second equation (2) for easy reference.
(1) 2x + 3y = 5
(2) 3x + y = 18
Step 2: Solve one of the equations for one of the variables.
Let's solve equation (2) for y:
y = 18 - 3x
Step 3: Substitute the expression for y in equation (1).
Now we substitute y in equation (1) with the expression we got from equation (2):
2x + 3(18 - 3x) = 5
Simplify the equation:
2x + 54 - 9x = 5
Combine like terms:
-7x + 54 = 5
Step 4: Simplify the equation for x.
Now we isolate x:
-7x = 5 - 54
-7x = -49
Divide both sides by -7 to find x:
x = -49 / -7
x = 7
Step 5: Substitute the value of x back into the equation for y.
We already have the expression for y from step 2 which was y = 18 - 3x. Now we substitute x = 7 into this expression to get y:
y = 18 - 3(7)
y = 18 - 21
y = -3
Step 6: State the coordinates of the intersection.
The coordinates of the intersection of the two lines are (x, y) = (7, -3).
Therefore, the vertex of the triangle at the intersection of the two graphs is at the point (7, -3).

Answer:

y = -3x+4

Step-by-step explanation:

Slope intercept form of a line is given by  y = mx + b

Where

m is the slope

b is the y intercept.

To find m, we need to take any arbitrary 2 points and see how many units up/down and how many units right/left we need to go from one to another. Basically change in y by change in x.

Let's take 2 arbitrary points: (0,4)  &  (2,-2)

So we need to go -6 units from y = 4 to y = -2. We need to go 2 units from x = 0 to x = 2.

Hence slope is change in y by change in x, which is -6/2 = -3

b is the y-interceept, the place where it cuts the y axis. Looking at the graph, it is at y = 4

Now we can write the equation as :

y = -3x+4

Answer:

Step-by-step explanation: Sorry no time gtg : / (if you really need it I'LL ANSWER TOMMOROW

Answer:  The required simplified expression is -6xy.

Step-by-step explanation: We are given to simplify the following rational expression :

[tex]E=-\dfrac{18x^2y}{3x}~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]

We will be using the following property of exponents :

[tex]\dfrac{z^a}{z^b}=z^{a-b}.[/tex]

From expression (i), we get

[tex]E\\\\\\=-\dfrac{18x^2y}{3x}\\\\\\=-\dfrac{18}{3}x^{2-1}y\\\\=-6xy.[/tex]

Thus, the required simplified expression is -6xy.

The slope of the line is the change in the Y values over the change in X values.

Using the given points (2,-5) and (-2,3)

The Y values are -5 and 3 and the X values are 2 and -2.

The slope = (3 - (-5)) / -2 - 2) = 8/-4 = -2

The slope is -2

Answer:

$840.08

Step-by-step explanation:

18.14% is the same as 0.1814. If we put the value of the sale as x that means that 0.1814x=152.39. Dividing both sides by 0.1814 you get x is approx. $840.08.

Answer: [tex]\$840.08[/tex]

Step-by-step explanation:

You need to analize the information provided:

- The comission on each sale made by the salesman is 18.14%.

- On a particular sale the salesman makes a comission of $152.39.

Then, the amount of the sale represents the 100%

Let be "x" the amount of that particular sale. You can use this procedure to calculate it:

[tex]x=\frac{(\$152.39)(100\%)}{18.14\%}\\\\x=\$840.08[/tex]

Answer:

The answer is B) Medical Research

Step-by-step explanation:

Medical research is something typically done by private companies.

Answer: B. Medical research.

Step-by-step explanation: Public Health Programs: the types of public health programs that address STIs are: Prevention education, testing and counseling, and diagnosis and treatment.

:)

Answer:

16

Step-by-step explanation:

You can choose

In total there are

[tex]2\cdot 2\cdot 4=16[/tex]

different outfits.

Another way to solve this problem is simply count all outfits:

Shirts [tex]Sh_1, \ Sh_2[/tex]

Pants [tex]P_1,\ P_2[/tex]

Shoes [tex]S_1, \ S_2,\ S_3,\ S_4[/tex]

All outfits

[tex]Sh_1P_1S_1, \\ Sh_1P_1S_2, \\ Sh_1P_1S_3, \\ Sh_1P_1S_4, \\ Sh_1P_2S_1, \\ Sh_1P_2S_2, \\ Sh_1P_2S_3, \\ Sh_1P_2S_4, \\ Sh_2P_1S_1, \\ Sh_2P_1S_2, \\ Sh_2P_1S_3, \\ Sh_2P_1S_4, \\ Sh_2P_2S_1, \\ Sh_2P_2S_2, \\ Sh_2P_2S_3, \\ Sh_2P_2S_4[/tex]

Step-by-step explanation:

let's Recall the properties of a parallelogram

1. the opposite sides of a parallelogram is congruent

AB=CD

8x-7=5x+2

8x-5x=7+2

3x=9

x=3

2. the consecutive angles are supplementary

angle A+angle D=180°

2y+50°+3y+40°=180°

5y+90°=180°

5y=90°

y=18

Answer:

The center is (5,0) and r=9.

Step-by-step explanation:

The standard form of a circle is [tex](x-h)^2+(y-k)^2[/tex] where (h,k) is the center and r is the radius.

On comparing your equation of

[tex](x - 5)^2 + (y-0)^2 = 9^2[/tex], we should see that h=5,k=0, and r=9.

The center is (5,0) and r=9.

Answer:

The center is at (5,0) and the radius is 9

Step-by-step explanation:

(x - 5)^2 + y^2 = 81.

An equation for a circle can be written in the form

(x-h)^2 + (y-k)^2 = r^2

Where (h,k) is the center and r is the radius

Rewriting the equation

(x - 5)^2 + y^2 = 81.

(x - 5)^2 + (y-0)^2 = 9^2

The center is at (5,0) and the radius is 9

The circumference of a circle with an area of 50.3 m² is 25.12 m.

For example;

For example;

In this case;

The Area of a circle = 50.3 m²

π = 3.14

But; Area of a circle = πr²

Therefore;

3.14r²= 50.3 m²

r² = 50.3/3.14

   =16.019

r = √16.019

 = 4.0023

 ≈ 4.00

But;

Circumference of a circle is given by 2πr

Thus;

Circumference = 2 × 3.14 × 4.00

                          = 25.12 m

Keywords; Perimeter, Area, Area of a circle, Circumference of a circle

Level: Middle school

Subject; Mathematics

Topic: Area and Perimeter

Sub-topic: Area and circumference of a circle

Hey there!

Isolate the y variable by subtracting 12x in both sides:

-4y = -12x - 8

To solve for y divide -4 in both sides

y = 3x + 2

Our answer would be y = 3x + 2

Answer:

y = 3x + 2

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Rearrange 12x - 4y = - 8 into this form

Subtract 12x from both sides

- 4y = - 12x - 8 ( divide all terms by - 4 )

y = 3x + 2 ← in slope- intercept form

Answer:

y = - [tex]\frac{1}{4}[/tex] x² + 3

Step-by-step explanation:

Any point (x, y) on the parabola is equidistant from the focus and directrix.

Using the distance formula

[tex]\sqrt{(x-0)^2+(y-2)^2}[/tex] = | y - 4 |, that is

[tex]\sqrt{x^2+(y-2)^2}[/tex] = | y - 4 |

Squaring both sides

x² + (y - 2)² = (y - 4)² ← distribute parenthesis

x² + y² - 4y + 4 = y² - 8y + 16 ( subtract y² - 8y  from both sides )

x² + 4y + 4 = 16 ( subtract x² + 4 from both sides )

4y = - x² + 12 ( divide both sides by 4 )

y = - [tex]\frac{1}{4}[/tex] x² + 3

Answer:

same as him took test right

Step-by-step explanation:

Answer:

The picture provided is the correct answer

Step-by-step explanation:

It needs to be greater than 4 or less than -4 in order for the absolute value to be greater than 7, so you're good.

Answer:

a) negative

Step-by-step explanation:

When you multiply a given negative number by a positive number, the result becomes smaller than the original.

For instance let [tex]-100[/tex] be the original number.

Multiply by 2.

The result is -200

We know [tex]-200\:<\:-100[/tex]

The correct answer is A.

Answer: a) negative

Step-by-step explanation:

-100x2=-200

-200 is negative.

Answer:

[tex]\large\boxed{\sqrt{170}}[/tex]

Step-by-step explanation:

The formula of a distance between two points:

[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

We have the points (9, 6) and (-4, 7). Substitute:

[tex]d=\sqrt{(-4-9)^2+(7-6)^2}=\sqrt{(-13)^2+1^2}=\sqrt{169+1}=\sqrt{170}[/tex]

The distance between the points (9,6) and (-4,7) can be found using the distance formula. By inputting the given coordinates into the formula, we find that the distance is √170 units.

The question is asking us to find the distance between two given points, (9,6) and (-4,7). In mathematics, this is commonly done using the distance formula: √[(x₂-x₁)² + (y₂-y₁)²]. Here, coordinates (x₁,y₁) are (9,6) and (x₂,y₂) are (-4,7).

Substituting these values into our formula, we have: Distance = √[(-4-9)² + (7-6)²] = √[(-13)² + 1²] = √[169 + 1] = √170.

Therefore, the distance between the points (9,6) and (-4,7) is √170 units.

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Answer:

The amount invested at 5.5% was $36,000 and the amount invested at 9% was $28,000

Step-by-step explanation:

we know that

The simple interest formula is equal to

[tex]I=P(rt)[/tex]

where

I is the Final Interest Value

P is the Principal amount of money to be invested

r is the rate of interest  

t is Number of Time Periods

Let

x -----> the amount invested at 5.5%

(64,000-x) -----> the amount invested at 9%

in this problem we have

[tex]t=1\ years\\I=\$4,500\\ P=\$64,000\\r1=0.055\\P1=\$x\\P2=\$64,000-\$x\\r2=0.09[/tex]

so

[tex]I=P1(r1t)+P2(r2t)[/tex]

substitute the given values

[tex]4,500=x(0.055*1)+(64,000-x)(0.09*1)[/tex]

[tex]4,500=0.055x+5,760-0.09x[/tex]

[tex]0.09x-0.055x=5760-4,500[/tex]

[tex]0.035x=1,260[/tex]

[tex]x=\$36,000[/tex]

[tex]64,000-x=64,000-36,000=\$28,000[/tex]

therefore

The amount invested at 5.5% was $36,000 and the amount invested at 9% was $28,000

Answer:

x1 = 2.79129, x2 = 1.79129

Step-by-step explanation:

x^2-5-x

x^2-5+x=0

x^2+x-5=0

-1+-square root od=f 1^2 - 4x1x(-5) / 2x1  = -1+- square root of 21 (add numbers together) / 2

then solve the formula with a plus sign instead of +- then and solve the formula with a - this time and you should get x1 = 2.79129, x2 = 1.79129, or -1 +square root of 21 (add numbers together) / 2 and -1 - square root of 21 (add numbers together) / 2

For this case we must solve the following equation:

[tex]x ^ 2 = 5-x[/tex]

By manipulating algebraically we have:

[tex]x ^ 2 + x-5 = 0[/tex]

The quadratic formula is given by:

[tex]x = \frac {-b \pm \sqrt {b ^ 2-4 (a) (c)}} {2a}[/tex]

We have to:

[tex]a = 1\\b = 1\\c = -5[/tex]

Substituting we have:

[tex]x = \frac {-1 \pm \sqrt {1 ^ 2-4 (1) (- 5)}} {2 (1)}\\x = \frac {-1 \pm \sqrt {1 + 20}} {2}\\x = \frac {-1 \pm \sqrt {21}} {2}[/tex]

So, we have two roots:

[tex]x_ {1} = \frac {-1+ \sqrt {21}} {2} = 1,7913\\x_ {2} = \frac {-1- \sqrt {21}} {2} = - 2.7913[/tex]

Answer:

[tex]x_ {1} = \frac {-1+ \sqrt {21}} {2}\\x_ {2} = \frac {-1- \sqrt {21}} {2}[/tex]

Answer:

30 each of 23% bars and 18 each of 79% bars

Step-by-step explanation:

If x is the number of 1 kg 23% copper bars, and y is the number of 1 kg 79% copper bars, then:

x + y = 48

0.23x + 0.79y = 0.44(48)

Substituting and solving:

0.23x + 0.79(48-x) = 0.44(48)

0.23x + 37.92 - 0.79x = 21.12

16.8 = 0.56x

x = 30

y = 48 - x

y = 18

You need 30 each of 23% bars and 18 each of 79% bars.

Answer:

See attachment

Step-by-step explanation:

The mapping for a dilation with a scale factor k, about the origin is given by:

[tex](x,y) \to \: (kx,ky)[/tex]

From the graph, the coordinates of B are (1,1) and the scale factor is k=4.

We substitute into the rule to get

[tex]B(1,1) \to \: B'(4,4)[/tex]

The image of point B is plotted on the graph in the attachment.

To find the image of point B under a dilation with a scale factor of 4 about the origin (0,0), multiply the coordinates of point B by 4.

To plot the image of point B under a dilation with a scale factor of 4 about the origin (0,0), we need to multiply the coordinates of point B by the scale factor. If point B is represented as (x,y), then the image of B would be (4x, 4y).

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Answer:

could it be letter H? please lmk

Answer:

3x² – 5x + 10

Step-by-step explanation:

(4x² – 2x + 8) - (x² + 3x - 2) =

Drop the first set of parentheses because it is unnecessary.

= 4x² – 2x + 8 - (x² + 3x - 2)

To get rid of the second set of parentheses, change every sign inside.

= 4x² – 2x + 8 - x² - 3x + 2

Now, combine like terms.

= 3x² – 5x + 10

Answer:

3x^2 -5x +10

Step-by-step explanation:

(4x² – 2x + 8) - (x² + 3x - 2)

Distribute the negative sign

(4x² – 2x + 8) - x² - 3x + 2

I like to line them up vertically

4x² – 2x + 8

-x² - 3x  + 2

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

3x^2 -5x +10

Answer:

A line that does not have an end to it.

Step-by-step explanation:

For example a line is forever, but if you put dots on the end, it will not be forever.

Answer:

A line segment is like a straight line, but has two dots on the edge of each end. A line segment has a starting and stopping point, which can help people tell the difference between other lines.

A line segment usually looks like this:

    \/   \/

 •----------•

Answer:

C. Reflection across the x-axis followed by the reflection across the y-axis.

Answer:

C

Step-by-step explanation: