For the piecewise Function below, which of the following statments is true? Someone please help me

x + x+6 +x+12+x+18+ x+24 = 930

5x + 90 = 930

5x = 930 - 60

5x = 870

x = 174 (which is the smallest consec multiple of 6)

174 is answer.

Given that sum of 5 consecutive multiples of 6 is 930

To find the smallest multiple

The consecutive multiples of 6 would be of the form

6(k-2), 6(k-1), 6k, 6(k+1), 6(k+2) for some natural number k.

The sum would be

6(k-2)+ 6(k-1)+ 6k+ 6(k+1)+ 6(k+2)= 6(5k) = 930

Divide by 30

k = 930/30 = 31

Smallest number = 6(k-2) = 6(31-2)

= 6(29) = 174

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

Verify:

174+180+186+192+198 = 930

Hence verified

[tex]\overline{NP}\ ||\ \overline{AB}\\\\\overline{JI}\ ||\ \overline{PN}[/tex]

-2(x + 9)  = -8

Distributive property.

-2x - 18 = -8

Add 18 to both sides.

-2x = 10

Divide both sides by -2.

x = -5

Answer:

Part 1) Option C. Same side interior angles

Part 2) Option A. [tex](3x+4)+(2x+11)=180\°[/tex]

Part 3) Option B. [tex]m<5=77\°[/tex]

Step-by-step explanation:

Part 1) we know that

If p and q are parallel

then

m<3 and m<5 are consecutive interior angles or Same side interior angles

and

[tex]m<3+m<5=180\°[/tex]

Part 2) we know that

[tex]m<3+m<5=180\°[/tex] -----> by consecutive interior angles (supplementary angles)

we have that

[tex]m<3=(3x+4)[/tex]

[tex]m<5=(2x+11)[/tex]

so

substitute

[tex](3x+4)+(2x+11)=180\°[/tex]

Part 3) Find the measure of angle 5

we know that

[tex](3x+4)+(2x+11)=180\°[/tex]

Solve for x

[tex]5x+15\°=180\°[/tex]

[tex]5x=180\°-15\°[/tex]

[tex]x=165\°/5\°=33\°[/tex]

[tex]m<5=(2x+11)[/tex]

substitute the value of x

[tex]m<5=(2(33)+11)=77\°[/tex]

Answer: C, A, B

Step-by-step explanation:

Answer:

A) y=mx+b

Step-by-step explanation:

The slope-intercept form is simply the way of writing the equation of a line so that the slope (steepness) and y-intercept (where the line crosses the vertical y-axis) are immediately apparent. Often, this form is called y = mx + b form.

Henrieta's work is incorrect. The correct answer is 0.04.

No, Henrieta's work is not correct. To divide 0.80 by 20, we need to divide the numerator (0.80) by the denominator (20).

Dividing 0.80 by 20, we get 0.04.

Therefore, the correct answer is 0.04.

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Answer,

- 1 1/4

Hope this helps :-)

[tex]6\cdot32=6(30+2)=(6)(30)+(6)(2)=180+12=192\\\\7\cdot29=7(30-1)=(7)(30)-(7)(1)=210-7=203[/tex]

Answer:

Step-by-step explanation:

Answer:

2 student who want to jump are measured

You would first try to round the numbers to the nearest 10 and then multiply for a reasonable estimate. In other words, 40x70=2800

Answer:

3

Step-by-step explanation:

Its the number immediately before x

Answer:

What is the coefficient in the expression 3x13+4?

               3/13

Step-by-step explanation:

Since one piece is four time the length x, we can represent that as 4x.

Thus making the equation:

4x+x=275

5x=275

x=55

4(55)=220

220+55=275

So, the length of the longer piece is 220 inches, and the length of the shorter piece is 55 inches.

In order to find the length of the shorter piece of pipe, we can set up and solve the equation x + 4x = 275. When simplified, we get 5x = 275, and by dividing both sides of the equation by 5, we find that x = 55. This tells us that the length of the shorter piece is 55 inches.

To solve this problem, let's denote the shorter piece as x. Because the other piece is four times the length of the shorter one, it can be denoted as 4x. We know that these two pieces put together make the total length of the initial pipe, which is 275 inches. Therefore, we can set up the equation: x + 4x = 275.

Simplifying this equation, we get 5x = 275. To get the value of x, we need to divide both sides of this equation by 5, resulting in x = 55. Hence, the length of the shorter piece is 55 inches.

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3 3/4 miles as a decimal is 3.75 miles. He rode for one hour. Average speed within an interval is (distance made) / (interval duration). So the average speed = 3.75 miles / 1 hour, or 3.75 mph.

2 11/32 / 1 1/2 = 25/16 hope this helps you

Answer:

$82.5

Step-by-step explanation:

We can calculate it with a direct rule of 3. As it has a 30% off, the remaining price is the 70% and we want to know how much is the 100%

[tex]70\% -\!\!\!-\!\!\!- \$57.75\\ 100\% -\!\!\!-\!\!\!- \$ x[/tex]

We use the formula of the direct rule of 3:

[tex]x = \frac {100/100*57.75}{70/100} \\ \\ x = \frac {57.75}{70/100}\\ x = 57.75 * 100/70[/tex]

x = 82.5

The original price of the stereo was $82.5

The original price of the stereo is 82.5

Since the car stereo system was on sale for 30% off, this means that it was sold for 100% - 30% = 70% of the original price.

Let the original price be represented by x

Therefore, 70% of x will be 57.75

70/100 × x = 57.75

0.7 × x = 57.75

0.7x = 57.75

Divide both side by 0.7

0.7x/0.7 = 57.75/0.7

x = 82.5

The original price of the stereo is 82.5

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If a page costs 3.50 and there are 500 pages, all you have to do to get your answer is multiply these 2 numbers,

The answer is 1750

The question is asking for a decimal number between 200 and 300 with '7' in the thousandths place and '2' in the hundredths place. One possible answer is 250.027, but other variations exist based on the whole number part as long as it is between 200 and 300.

The student's question is asking for a specific decimal number between 200 and 300. The conditions set are that the number should have '7' in the thousandths place, and '2' in the hundredths place. Since there are no conditions for the other places, these digits could be any whole number.

One possible answer could be 250.027. We have '2' in the hundredths place (right after the decimal point), '7' in the thousandths place (two spots after the decimal point), and the whole number part is between 200 and 300. Other possibilities exist too, like 267.327 or 280.217.

This question could relate to a topic like Place Value Decomposition where students learn to read, write, and understand the value of each digit in a decimal number.

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Hey there!!

Given equation :

... 5n + 30 - 17n - ( -12n )

... 5n + 30 -17n + 12n

... 5n + 30 - 5n

... 30

The answer is 30...

Hope my answer helps!!

Solving for n, we find that n equals 3.5 or 7/2.

Simplify the equation by removing the parentheses,
5n + 30 - 17n - (-12)

5n + 30 - 17n + 12.

5n - 17n =30 + 12.

-12n + 42 = 0.

-12n = -42.

n = 42 / 12.

n = 7 / 2 or n = 3.5.

y = 3x + 21  that's the answer

Answer: Option B. exponential decay

Solution:

If initially the number of competitors is n

If the number of round is "r" and the number of competitors after "r" rounds is N(r)

1) After the first round (r=1), the number of competitors is:

N(r)=N(1) = n * 50% = n * 50/100 →N(r)=N(1)=n*0.5=n*0.5^1

2) After the second round (r=2), the number of competitors is:

N(r)=N(2) = N(1) * 50% = (0.5 n)*(50/100)=(0.5n)*(0.5)→N(r)=N(2)=n*0.5^2

3) After the third round (r=3), the number of competitors is:

N(r)=N(3)=N(2)*50%=(n*0.5^2)*(50/100)=(n*0.5^2)*(0.5)→N(r)=N(3)=n*0.5^3

Then:

For r=1→N(r)=N(1)=n*0.5^1

For r=2→N(r)=N(2)=n*0.5^2

For r=3→N(r)=N(3)=n*0.5^3

In general: N(r)=n*0.5^r

This is an exponential function because the independent variable "r" is in the exponent, and because the number of competitors (funcion N(r) )decrease with the number of rounds the type of relationship most appropiately models this situation is an exponential decay

The reduction by 50% of competitors each round in a chess tournament is modeled by an exponential decay relationship, not a linear decrease, as it depends on the current number of competitors.

The chess tournament with the number of competitors decreasing by 50% each round is best modeled by a exponential decay relationship. This is because with each round, the number of competitors is halved, which is a rate that depends on the current number of competitors. (A) linear decrease would imply a constant decrease irrespective of the current number of competitors, which is not the case here.

Exponential relationships can be represented by mathematical functions where the rate of change is proportional to the current value. In contrast to exponential growth, where the quantity increases at a rate proportional to its current value, exponential decay describes a situation where the quantity is reduced by a certain factor over equal successive periods.

1) The solution of expression is, x = - 6

2) The solution is, - 26

We have to give that,

1) An expression is,

3x - 6 = 7x + 18

2) An expression,

65 - 4² (10 - 2) + 37

Now, Simplify the expressions as,

1) 3x - 6 = 7x + 18

Add 6 on both sides,

3x - 6 + 6 = 7x + 18 + 6

3x = 7x + 24

Subtract 7x on both sides,

3x - 7x = 24

- 4x = 24

Divide both sides by - 4,

x = - 24/4

x = - 6

Hence, Solution is, x = - 6

2) 65 - 4² (10 - 2) + 37

Apply the BODMAS rule,

65 - 16 (8) + 37

65 - 128 + 37

65 + 37 - 128

102 - 128

- 26

Therefore, the Solution is, - 26

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g(x):

flip f(x) over x-axist and next translate 2 units down.

Look at the picture.

Translations

y = f (x) + m up m units

y = f (x) - m down m units

y = f (x + m) left m units

y = f (x - m) right m units

Stretches/Shrinks

y = n · f (x) stretch vertically by a factor of n

y = 1/n · f (x) shrink vertically by a factor of m (stretch by 1/n)

y = f (1/n x) stretch horizonally by a factor of n

y = f (nx) shrink horizontally by a factor of n (stretch by 1/n)

Reflections

y = - f (x) reflect over x-axis (over line y = 0)

y = f (- x) reflect over y-axis (over line x = 0)

x = f (y) reflect over line y = x

3/5(30) = 18.

60% of the days in April it rained.

It rained 18 days in April.

Best of luck.

60% of it rained cause 3/5 is equaled to 60% so 18 Yeah.

15 and 45 becuase bith 3 and 8 can go into them.

Answer:

175 %

Step-by-step explanation:

7/4 = (7/4)* 100

= 700 / 4

=  175 %

The answer is 175% I think

Answer-

The coordinates of the solution to the system of equations is (4, -3)

Solution-

According to the graph the equations are,

[tex]y=-\frac{1}{2}x-1\\\\y=\frac{1}{4}x-4[/tex]

We can get the coordinates of the solution to the system of equations, by substitution.

[tex]\Rightarrow y=\frac{1}{4}x-4[/tex]

Putting the value of y in first equation,

[tex]\Rightarrow \frac{1}{4}x-4=-\frac{1}{2}x-1[/tex]

[tex]\Rightarrow \frac{1}{4}x+\frac{1}{2}x=-1+4[/tex]

[tex]\Rightarrow \frac{3}{4}x=3[/tex]

[tex]\Rightarrow x=3\times \frac{4}{3}[/tex]

[tex]\Rightarrow x=4[/tex]

Putting the value of x in the first equation,

[tex]y=-\frac{1}{2}\times 4-1=-2-1=-3[/tex]

Therefore, the coordinates of the solution to the system of equations is (4, -3)