- student claims that there is no solution to the system of inequalities shown.
y≥x² + 3
y< x + 1
2
PART A (2 POINTS): Explain a method for proving that the student's claim is correct.
peaker notes

The graph of the first linear equation:

y = x + 3

Can be seen in the image at the end.

Let's graph the first line, which is:

y = x + 3.

To graph it, we need to find two points on the line, to find these, we can evaluate the linear equation in two values of x.

Using x = 0 we get:

y = 0 + 3

y = 3

So we have the point (0, 3).

Using x = 1, we get:

y = 1 + 3

y = 4

So we have the point (1, 4)

Now we can graph these two points on the same coordinate axis and connect them with a line. Like in the example below.

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The value illustrated shows that x is -55 units to the left of 0.

From the given statement we have the value of x is negative. Therefore, we need the complete statement about x being positive.

Therefore we have to put an alternate sign to the given statement we get -x is 55 units to the right of 0.

Negation to the given statement about x is -(-x) is -(55) units to the left of 0. The statement will be that x is -55 units to the left of 0.

By using  the drop-down menus to complete the given statement about x is -55 units to the left of 0.

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The sum of two hundred even numbers in the sequence from 0 to 398 is 39800

To find the sum of two hundred even numbers from 0 to 398, we can use the formula of sum of an arithmetic progression.

[tex]S_n = \frac{n}{2}[2a(n-1)]d[/tex]

The number of terms given here is 200, the first term is 0 and the common difference is 2

Substituting the values into the equation

[tex]S_n = \frac{n}{2}[2a+(n-1)]d\\S_n = \frac{200}{2}[2*0+(200-1)*2\\S_n = 100(0+199)*2\\S_n = 39800[/tex]

The sum of two hundred even numbers from 0 to 398 is 39800

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Answer: false

Step-by-step explanation:

Use 1/4 cup per square foot

-4, -1/2, 3, 13/2, 10,… represents an arithmetic sequence.

An arithmetic sequence progresses with a common difference which is the difference of consecutive terms.

So for each of the number sequences, we will try to check if the consecutive terms has a common difference.

A) 32, 16, 8, 4, 2,...

16-32 = -16

8-16 = -8

4-8 = -4

2-4 = -2

As the differences of consecutive terms are not same, this sequence is not an arithmetic sequence.

B)5, 10, 20, 40, 80,...

10-5 = 5

20-10 = 10

40-20 = 20

80-40 = 40

Here also the differences of consecutive terms are not same, this sequence is not an arithmetic sequence.

C) -4, -1/2, 3, 13/2, 10,…

-1/2- -4 = 7/2

3- -1/2 = 7/2

13/2-3 = 7/2

10-13/2 = 7/2

This sequence has a common difference and hence is an arithmetic sequence.

D) 4, 8/3, 16/9, 32/27, 64/81,…

8/3-4 = -4/3

16/9-8/3 = -8/9

32/27-16/9 = -16/27

64/81-32/27 = -32/81

Here also the differences of consecutive terms are not same, this sequence is not an arithmetic sequence.

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Answer:

His gain is 3.50$ which is also 50% of 7

Step-by-step explanation:

for next time so you dont gotta waste points all you have to do is go 10.50 -7.00 =3.50 and then just ask go ogle if you are able what percentage is 3.50 of 7.00 because 7.00$ is what he had to pay for so he is making a 50% gain

Answer:

-6

Step-by-step explanation:

-3x = 18

divide both sides by -3

18 ÷ -3 = -6

Answer:660 in

Step-by-step explanation: Just add 6 sides, 9 ft= 108 in, + 2 in = 110, 110x6 = 660

write an equation of the line in slope intercept format (-3,3) (0,-1)​

the equation of the line is

y=mx+b

so

step 1

Find the slope

m=(-1-3)/(0+3)

m=-4/3

step 2

Find the equation

we have

m=-4/3

b=-1 ----> is given

substitute

Answer

8:28 Hope this helps.

Hello!

Let's solve:

   [tex]\text{Write down the equation}\\\dfrac{6\dfrac{2}{3} }{\dfrac{1}{5} } \\\\\\\text{Convert the nominator, a mixed partial fraction to an improper fraction}\\\dfrac{\dfrac{20}{3} }{\dfrac{1}{5} } \\\\\\\text{When dividing by a fraction, flip the fraction over and multiply its reciprocal}\\\dfrac{20}{3} *\dfrac{5}{1} = \dfrac{100}{3} \\\\\\\text{Convert the improper fraction back mixed partial fraction}\\\dfrac{100}{3} =33\dfrac{1}{3}[/tex]

Answer: [tex]\dfrac{100}{3} \text{ or }33\dfrac{1}{3}[/tex]

Hope that helps!

Answer:

u = 14

Step-by-step explanation:

2u - 17 = 11

add 17 to both sides:

2u - 17 + 17 = 11  + 17

2u = 28

divide both sides by 2:

2u/2 = 28/2

u = 14

Answer: Last Digit Method: If the last digit in 6095 is 0, 2, 4, 6, or 8, then 6095 is divisible by 2. The last digit in 6095 is 5, thus 6095 is not divisible by 2.

Step-by-step explanation:

Answer:

m/4 = 3x - 30

Step-by-step explanation:

Hello!

Let's subtract the second equation from the first equation:

Now, solve for m.

Multiply both sides by 12 to get rid of the denominators

Plug in 12x - 120 for m in m/4

The value of m/4 is 3x - 30.

Answer:

y = -1/3 x + 1/3

Step-by-step explanation:

In the picture.

The Solution:

Given the fractions below:

We are asked to find the sum of the above two fractions.

The Lowest Common Multiple (LCM) of 5 and 10 is 10

Thus, the correct answer is

The area of the square with a side length of 13 units is 169 square units.

A square is simply a regular quadrilateral having all four sides and angles equal.

The area of a square is expressed as;

A = a²

Where a is the side length.

Given the data in the question;

To determine the area of the square, plug the given value into the area of square formula and solve for A.

A = a²

A = ( 13 )²

Area A = 169 square units.

Therefore, the area of the square is 169 square units.

Option D) is the correct answer.

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V'(t) = -250(1-(1/40)t)

If we know the time, we can plug in the value for "t" in the above derivative and find how much water drained for the given point of t.

Given:

V =2000( 1- (1/40)t)^2   , where 0≤t≤40.

Here we have to find the derivative with respect to "t"

We have to use the chain rule to find the derivative.

V'(t) = 2 (2000)(1- (1/40)t)d/dt(1- (1/40)t)

V'(t) = 2(2000)(1-(1/40)t(-1/40)

When we simplify the above, we get

V'(t) = -250(1-(1/40)t)

If we know the time, we can plug in the value for "t" and find how much water drained for the given point of t.

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Answer:

w is -3

Step-by-step explanation:

A line with a perpendicular slope with have a slope that is the negative inverse of the reference line.  If the reference line is -(2/3), the perpendicular line will have a slope of (3/2).

The line formed by ab:  y = (3/2)x + b

We have one given point on line ab with one coordinate known, (3,4), so let's use it to find b:

y = (3/2)x + b

4 = (3/2)*3 + b for (3,4)

4 = (9/2) + b

b = 4 - (9/2)

b = - 0.5

The equation is y = (3/2)x - 0.5

The slope of (3/2) is equal to the Rise/Run of two points on the line:  (3,4) and (w,-5):

    Rise = (4 - (-5)) = 9

    Run = (3 - w)

Slope =  9/(3-w)

(3/2) =  9/(3-w)

(3/2)(3-w) =  9

(9/2) - (3/2)w = 9

9 - 3w = 18

-3w = 9

w = -3

Point b is (-3, -5)

See attached graph.

The actual height of the building is 739.2 feet.

Given the height of a building estimated by Charlie is 924 feet.

His father said that there is 20% error in the estimation.

we should determine 20% of the estimated height.

⇒ height = 924 feet

⇒ error = 20%

⇒ 924 × 20/100

⇒ 924/5

= 184.8 feet

Subtract the error in height with the height given.

⇒ estimated height - error in height

⇒ 924 - 184.8

= 739.2 feet.

hence the actual height is 739.2 feet.

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Answer:

f(-2) = -8

Step-by-step explanation:

We are given a function:

[tex]f(x)=2x-4[/tex]

We are told to find f(-2).

First, substitute -2 as x in f(x):

[tex]f(x) = 2x-4\\\\f(-2) = 2x-4[/tex]

Then, substitute -2 as x in the equation itself:

[tex]f(-2) = 2(-2) - 4[/tex]

Then, simplify by multiplying 2(-2):

[tex]f(-2) = 2(-2) - 4\\\\f(-2) = -4 - 4[/tex]

Finally, simplify by performing the final arithmetic:

[tex]f(-2) = -4 - 4\\\\f(-2) = -8[/tex]

Therefore, f(-2) = -8.

Answer:

c

Step-by-step explanation:

c

Answer:

I think its 180

Step-by-step explanation:

The percentage increase in the cost of the airline tickets is 38%.

Percentage is the fraction of a number out of hundred. The sign that is used to represent percentages is %. Percentage is a measure of frequency. In order to convert a value to a percentage, multiply the value by 100.

in order to determine the percentage increase, multiply the fraction of the change in price and the initial price by 100.

Percentage increase = (change in price / initial price)  100

Change in price = new price - initial price = $310 - $225 = $85

Initial price = $225

($85 / $225) x 100 = 38%

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Carlita has $25.17 in her checking account.

A deposit account held at a bank or other financial institution is known as a transaction account.

The amount of money in her checking account = -$ 15

She earned $87.99

Now money in her checking account = -15+87.99 = $ 72.99

She paid her phone bill worth $47.82

money in her checking account = $ ( 72.99 - 47.82 ) = $25.17

Therefore she has $25.17 in her checking account.

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Answer:

7(u+2)=42

7u+14=42

-14 -14

7u=28

u=4

Mr musa since the servant to the market to buy orange is 15 naira the servants have eaten three oranges on the way ,mr musa a 25 cover orange more than the market price. Hence 12 be number of oranges mr musa received.

Two or more expressions with an equal sign is called as equation.

Let market price be M

(M+0.25)x=15

Oranges brought=15M

Servent ate 15M-3=x

15M=x+3

Divide both sides by 15.

M=(x+3)/15

((x+3)/15+1/4)x=15

Calculate the LCM and solve

(4x+12+15)x/60=15

Apply cross multiplication

4x²+27x=900

4x²+27x-900=0

By solving it we get x=12

Hence 12  be number of oranges mr musa received.

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Answer: -27

Step-by-step explanation: -3 raised to the power of 3 is written (-3) 3 = -27. Note that in this case the answer is the same for both -3 3 and (-3) 3 however they are still calculated differently. -3 3 = -1 * 3 * 3 * 3 = (-3) 3 = -3 * -3 * -3 = -27. For 0 raised to the 0 power the answer is 1 however this is considered a definition and not an actual calculation.

The probability that a randomly selected student in the class test scored marks which is less than 82 is 0.9192

It is given that in a test, the scores for an exam normally distributed has a mean of 75 and a standard deviation of 5. We have been asked to find the probability that a randomly selected student scored less than 82.

From the question we have,

Mean = 75

Standard deviation (SD)  = 5

Therefore, the probability that a randomly chosen student has a score of less than 82 is represented as:

(P) Probability ( X < 82) = P { Z < [tex]\frac{82-75}{5}[/tex] }

                = P {Z < 7/5}

                = P {Z <1.4}

                = Area from - ∞ to  1.4

                = 0.9192

From the z table the area under the normal curve that corresponds to  1.4 is  0.9192

Hence the required probability of that a randomly selected student scored less than 82 is 0.9192

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