For which values of x is the expression undefined

[tex]\begin{array}{lcccl} &\stackrel{solution}{gallons}&\stackrel{\textit{\% of }}{amount}&\stackrel{\textit{gallons of }}{pure~alcohol}\\ \cline{2-4}&\\ \textit{25\% solution}&x&0.25&0.25x\\ \textit{5\% solution}&y&0.05&0.05y\\ \cline{2-4}&\\ mixture&20&0.08&1.6 \end{array}~\hfill \begin{cases} ~\hfill x + y &= 20\\\\ 0.25x+0.05y&=1.6 \end{cases} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\stackrel{\textit{using the 1st equation}}{x+y=20\implies \underline{y = 20-x}} \\\\\\ \stackrel{\textit{substituting on the 2nd equation}}{0.25x~~ + ~~0.05(\underline{20-x})~~ = ~~1.6}\implies 0.25x+1-0.05x=1.6 \\\\\\ 0.20x+1=1.6\implies 0.2x=0.6\implies x=\cfrac{0.6}{0.2}\implies \boxed{x=3}[/tex]

The height of the toy is an illustration of the height function

The given parameters are:

The function of the height is calculated as:

h(t) = -16t² + Vot + H

This gives

h(t) = -16t² + 200t + 50

Hence, the velocity function is h(t) = -16t² + 200t + 50

In (a), we have:

h(t) = -16t² + 200t + 50

Differentiate

h'(t) = -32t + 200

Set to 0

-32t + 200 = 0

Subtract 200 from both sides

-32t = -200

Divide both sides by -32

t = 6.25

Substitute 6.25 for t in h(t)

h(6.25) = -16 *6.25² + 200 * 6.25 + 50

h(6.25) = 675

Hence, the time to reach the maximum height is 6.25 seconds and the maximum height is 675 feet

This is represented as

h(t) >300

So, we have:

-16t² + 200t + 50 > 300

Subtract 300 from both sides

-16t² + 200t - 250 > 0

Using a graphical calculator, we have:

t = 11.09s and t = 1.41 s

Hence, the rocket will be at a height more than 300 at 11.09s and 1.41 s

This means that

h(t) = 0

So, we have:

-16t² + 200t + 50 = 0

Using a graphical calculator, we have:

t = 12.75

Hence, the rocket will hit the ground at 12.75s

Read more about height function at:

https://brainly.com/question/12446886

Answer: question 1 equals 31 Over 8 or 3.875 .

question 2 equals 425 over 24 .

question 3 equals 41 over 6 or 6.83333333

question 4 equals 55 Over 14

Step-by-step explanation: hope it helps you .

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Explanation:

Refer to the figure below.

Focus on triangle ABF. Angle AFB = 40 is marked in red. Angle BAF = 90 is marked in blue. The missing angle is 180-90-40 = 50 which is angle ABF.

Inscribed angle ABF = 50 doubles to arc AC since this inscribed angle subtends the arc in question. I'm using the inscribed angle theorem.

arc AC = 2*(angle ABF) = 2*50 = 100 degrees

Note: We don't need the fact that angle AGD = 86

Using proportions, it is found that her discount is of $0.29664.

A proportion is a fraction of a total amount.

In this problem, the total amount she spent on gas is given by:

T = $45.23 + $102.34 + $13.67 + $34.56 + $48.72 + $52.12 = $296.64.

Considering that she receives ten cents off per gallon on gas for every $100 she spends, we apply the proportion to find that her discount is given by:

[tex]D = 0.1 \times \frac{296.64}{100} = 0.29664[/tex]

Her discount is of $0.29664.

More can be learned about proportions at https://brainly.com/question/24372153

Answer:

The

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section

It's difficult to access

It's also really

sen-

sitive

to what you could type.

The value of x, y and z from the system of equation are -1, -8 and 5 respectively.

Data;

To solve this problem, we have to solve the system of equation using substitution method.

From equation (iii)

[tex]2z = 10\\z = 5[/tex]

let us substitute the value of z into equation (ii)

[tex]-3y + 7z = 59\\z = 5\\-3y + 7(5) = 59\\-3y + 35 = 59\\-3y = 59 - 35\\-3y = 24\\y = -8[/tex]

Let's substitute the value of x and y into equation (i)

[tex]-2x + 6y + 3z = -31\\y = -8, z = 5\\-2x + 6(-8) + 3(5) = -31\\-2x - 48 + 15 = -31\\-2x - 33 = -31\\-2x = -31 + 33\\-2x = 2\\x = -1[/tex]

From the calculation above, the value of x, y and z are -1, -8 and 5 respectively.

Learn more on system of equations here;

https://brainly.com/question/14323743

Answer:

B. megalopolis

Step-by-step explanation:

Hope it helps you in your learning process.

Answer:

The slope of the line is -1

Step-by-step explanation:

You need to use the slope formula

Slope Formula: y2 - y1 / x2 - x1

**The numbers represent subscripts but the subscripts aren't on computers**

Your Coordinate Points:

(7, -3) and (3, -7)

Do -7 - (-3) / 3-7

First, do -7 - (-3)

The negatives cancel to an addition problem.

-7 + 3

Now do -7 + 3. This is a subtraction problem that should be negative.

-7 + 3 = -4

Next, do 3 - 7

That should be 4

-4/4 is what we have right now.

Do -4 divided by 4 which has to contain a negative.

That is simply -1.

The slope of the line is -1

Answer:

B 5

Step-by-step explanation:

it is the same ratio as the red

Answer:

Step-by-step explanation:

Let the Beth's score is x.

The average is 80.

Solve the following equation:

Beth's score was 75

[tex]\textit{arc's length}\\\\ s=r\theta ~~ \begin{cases} r=radius\\ \theta =\stackrel{radians}{angle}\\[-0.5em] \hrulefill\\ \theta =2\\ s=99 \end{cases}\implies 99 = r(2)\implies \cfrac{99}{2}=r\implies 49.5=r[/tex]

f(x+1)

Answer:

48

Step-by-step explanation:

180 is the whole thing

So add 25 and 107 to make 132, then 180-132

Answer:

p = 1.26

Step-by-step explanation:

We know that the total weight (p) is going to be split equally (divided) by 3.

We also know that divided weight will be equal to 0.42 pounds.

p / 3 = 0.42

To solve:

multiply both sides by 3 to cancel the division by 3

p = 1.26

To test this you could divide 1.26 by 3 again to get 0.42

Explanation:

The N stands for Pi so when you type in the answers to Khan Academy use the Pi symbol when theres an N! These are the common questions and common radius Khan Academy gives when they ask to find the radius of the circle.

Answers:

For 4 - 267.95  

For 1/4 - 1/48n  

For 1 - 4/3n    

For 9 - 972n

For 7 - 1372/3n

For 6 - 288n

For 3 - 36n

For 10 - 4000/3n

For 8 - 2048/3n

For 1/2 - 1/6n

For 5 - 500/3n

For 2 - 33.49

Step-by-step explanation:

I did the go math so all of these rights and the majority of the answers are the questions Khan Academy will ask you to find the radius of the circle.

Answer:

find the common factor in the given algebraic expressions 4 (x-y) , 6(y-x)

Answer:

57mm

Step-by-step explanation:

Length of missing side= perimeter- known lengths

= 152mm- (30+20+45)mm

= (152 - 95)mm

= 57mm

Answer:

4:7

Step-by-step explanation:

4:7 is the same as 4/7

Answer:

$25.40

Step-by-step explanation:

Find the unit price. So what you do is just divide 304.80 by 12 to get the price of one which comes out to be $25.40

Answer:

Step-by-step explanation:

a.

[tex]2^3*2^{-3}=2^0\\b.\\\frac{2^3}{2^5} =2^{-2}\\c.\\2^{-3}*5^{-3}=10^{-3}[/tex]

Answer:

Rational

Step-by-step explanation:

5.74 is the same as 5.74 over 1. In other words, 5.74 can be written with a numerator and denominator, like this:

 5.74  =  5.74/1

5.74 x 100/ 1 x 100

You can multiply the numerator and denominator of any fraction by the same number and keep the value of the fraction the same. Here we will multiply the numerator and denominator by 100 to get rid of the decimal point.

5.74 × 100/ 1 × 100

When we calculate the numerator and the denominator above, we get this fraction:

574/100

The fraction above is the same as 5.74. Furthermore, the numerator and the denominator of the fraction above are integers. Therefore, we can conclude that the answer to "Is 5.74 a rational number?" is yes.

Answer:

Step-by-step explanation:

y - 9 = -2(x + 5)

y - 9 = -2x - 10

y = -2x - 1

In a trapezoid, the segment at the midpoint is the average of the other two bases.

In other words: YZ = (QR + TS) / 2

5x + 1 = ( (2x + 7) + 19 ) / 2

2(5x + 1) = 2x + 26

10x + 2 = 2x + 26

8x = 24

x = 3

YZ = 5x + 1

YZ = 5(3) + 1

YZ = 15 + 1

YZ = 16

Hope this helps!

Answer:

C) $0.28 per packet

Step-by-step explanation:

I divided them to find how much each packet costs

Each pack of watermelon costs $0.76
Each pack of tomato seed packet costs 0.48

Subtract and you have your answer!

0.76 - 0.48 = 0.28

Answer:

1 hour=55 miles

Step-by-step explanation:

Answer:

55 mph

Step-by-step explanation:

605 miles/11 hours

605/11 mph

55 mph

Hope this helps!

Answer:

[tex]x=20\\\\m\angle B = 92^{\circ}\\\\m\angle C = 40^{\circ}[/tex]

Step by step explanation:

[tex]~~~m\angle A +m\anglee B + m\angle C =180^{\circ}\\\\\implies 48+6x-28+2x = 180\\\\\implies 8x +20 = 180\\\\\implies 8x = 180 -20 = 160\\\\\implies x = \dfrac{160}8=20\\\\\\m\angle B = (6x -28)^{\circ} = (6\cdot 20 -28)^{\circ}=92^{\circ}\\\\m\angle C = (2x)^{\circ} = (2\cdot 20)^{\circ}=40^{\circ}[/tex]

This is one single number just a bit under 175 thousand. Delete the comma if needed.

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

Work Shown:

x = number of total doctors

24.7% of x = number of female doctors

0.247x = 43200

x = 43200/(0.247)

x = 174,898.785425101 approximately

x = 174,899 when rounding to the nearest whole number

f(x) = (2x³ + 1 + x²)/(x² + 9) as a sum of two functions g(x) and h(x), where g is an odd function and h is an even function is f(x) = 2x³/(x² + 9)  + (1 + x²)/(x² + 9).

To answer the questions, we need to know what functions are

A function is a mathematical expression that shows the relationship between two variables.

Since f(x) = (2x³ + 1 + x²)/(x² + 9).

Its odd part g(x) = [f(x) - f(-x)]/2

So, g(x) =  [f(x) - f(-x)]/2

= [(2x³ + 1 + x²)/(x² + 9) - (2(-x)³ + 1 + (-x)²)/((-x)² + 9)]/2

= [(2x³ + 1 + x²)/(x² + 9) - (-2x³ + 1 + x²)/(x² + 9)]/2  

= (2x³ + 1 + x² + 2x³ - 1 - x²)/2(x² + 9)  

= 4x³/2(x² + 9)  

g(x) = 2x³/(x² + 9)  

Its even part h(x) = [f(x) + f(-x)]/2

So, h(x) =  [f(x) + f(-x)]/2

= [(2x³ + 1 + x²)/(x² + 9) + (2(-x)³ + 1 + (-x)²)/((-x)² + 9)]/2

= [(2x³ + 1 + x²)/(x² + 9) + (-2x³ + 1 + x²)/(x² + 9)]/2  

= (2x³ + 1 + x² - 2x³ + 1 + x²)/2(x² + 9)  

= 2(1 + x²)/2(x² + 9)  

h(x) = (1 + x²)/(x² + 9)

So, f(x) = g(x) + h(x)

f(x) = 2x³/(x² + 9)  + (1 + x²)/(x² + 9)  

So, f(x) = (2x³ + 1 + x²)/(x² + 9) as a sum of two functions g(x) and h(x), where g is an odd function and h is an even function is f(x) = 2x³/(x² + 9)  + (1 + x²)/(x² + 9).

Learn more about odd and even functions here:

https://brainly.com/question/26322830

Answer:

[tex]g(x)=\frac{2x^{3} }{x^{2} -9}[/tex]

[tex]h(x)=\frac{x^{2}+1 }{x^{2} -9}[/tex]

Step-by-step explanation:

'x² - 9' is an even.

Break up the numerator into odd an even parts to get your answer.

'2x³' is odd and 'x² + 1' is even.

[tex]g(x)=\frac{2x^{3} }{x^{2} -9}[/tex]

[tex]h(x)=\frac{x^{2}+1 }{x^{2} -9}[/tex]