What’s is the next number?
2,3,5,7,11,13,17

The x-coordinates of points P and Q, where lines y=2x+8 and y=2x-12 intersect the x-axis, are -4 and 6 respectively. Therefore, the distance between them, PQ, is 10 units.

The two given lines are y = 2x + 8 and y = 2x - 12. These lines intersect the x-axis when y = 0. Setting y=0 in these two equations, we find the x co-ordinates of the intersection points P and Q.

For y = 2x + 8, solving 2x + 8 = 0 gives x = -4. Hence, Point P is at (-4,0).

Similarly, for y = 2x - 12, solving 2x - 12 = 0 gives x = 6. Hence, Point Q is at (6,0).

The distance PQ can then be calculated using the distance formula: "PQ = |Q - P| = |6 - (-4)| = 10 units".

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Answer: Last option

{x| x>-3}

Step-by-step explanation:

We have the following inequality 3 (x + 2)> x

To solve the inequality, apply the following steps:

1) Apply distributive property

[tex]3 * x + 3 * 2> x\\\\3x + 6> x[/tex]

2) Subtract 6 on both sides of the inequality

[tex]3x +6 -6> x-6\\\\3x> x-6[/tex]

3) Subtract x on both sides of the inequality

[tex]3x-x> x-x-6\\\\2x> -6[/tex]

3) Divide by 2 both sides of the inequality

[tex]x> -3[/tex]

The solution is all numbers greater than -3

ANSWER

{x|x>- 3}

EXPLANATION

The given inequality is;

[tex]3(x+2) \: > \: x[/tex]

Expand the parenthesis to obtain,

[tex]3x+6>x[/tex]

Group like terms

[tex]3x-x \: > \: -6[/tex]

[tex]2x>-6[/tex]

Divide both sides by 2

[tex]x \: > \: - 3[/tex]

The correct choice is D.

Answer:  Apply the formula for the volume of a sphere.

Step-by-step explanation:

The volume of a sphere is  

4

π

r

3

3

We just need to insert  

r

=

2

c

m

into this to get the volume.

4

π

2

3

3

=

32

3

π

The exact volume is  

32

3

π

c

m

3

The approximate volume is  

33.5103217

Answer:

45 m

Step-by-step explanation:

The height at time of launch is at x = 0

Substitute x = 0 into f(x)

f(0) = - 5(0 + 1)(0 - 9) = - 5(1)(- 9) = 45 m

Answer with step-by-step explanation:

We are given the following two functions:

[tex]s(x) = 3x - 6[/tex]

[tex]t(x) = 6 - 3x[/tex]

We are to find the simplified formula and domain for [tex] v ( x ) = \frac { s ( x ) } { t ( x ) } [/tex] and [tex] w ( x ) = \frac { t ( x ) } { s ( x ) } [/tex].

[tex]\frac{3x-6}{6-3x}=\frac{3(x-2)}{3(2-x)}=\frac{x-2}{2-x}=\frac{x-2}{-(x-2))}=-1 [/tex]

So the domain for this function is (-∞, +∞) for v(x) = -1.

[tex]\frac{6-3x}{3x-6}=\frac{3(2-x)}{3(x-2)}=\frac{2-x}{x-2}=\frac{2-x}{-(-x+2)}=\frac{2-x}{-(2-x)}=-1[/tex]

The domain of this function is (-∞, +∞) for w(x)= -1

ANSWER

v(x)=-1

Domain: (-∞,2)U(2,+∞)

EXPLANATION

We have the given function

s(x) = 3x - 6 and t(x) = 6 - 3x.

We want to find the simplified formula and domain for

[tex]v(x) =( \frac{s}{t} )(x)[/tex]

[tex]v(x) = \frac{s(x)}{t(x)} [/tex]

[tex]v(x) = \frac{3x - 6}{6 - 3x} [/tex]

This function is defined if and only if

[tex]6 - 3x \ne0[/tex]

[tex]x \ne2[/tex]

Hence the domain is:

[tex]x \ne2[/tex]

We now simplify to obtain;

[tex]v(x) = \frac{ - (6 - 3x )}{6 - 3x} = - 1[/tex]

Answer:

D. The ocean has eroded the shoreline by carrying earth materials out to sea

Step-by-step explanation: I don't actually know why, I just did it on Study Island

Answer:

The ocean has eroded the shoreline by carrying earth materials out to sea.

Step-by-step explanation:

I had to do study island. Apparently, this answer was correct.

Answer:

So like terms are terms that have the same VARIABLE...

Step-by-step explanation:

So 2n + 3n is 5n and you can do that because they are like terms. you only need like terms for adding and subtracting

multiplying: 2n * 3n^2 = 6n^3

hope this helps!

Answer:

Base #2

Step-by-step explanation:

For this question, we need to find the base that's volume is a factor of 60.

Base #1 Volume = 7 * 3 or 21

21 is not a factor of 60, so it cannot be the base.

Base #2 Volume = 5 * 3 or 15

15 is a factor of 60, so it is the base.

Answer: I think it's base 4. Don't rely on me, 'cause I can't understand this right now.

It is D.) 237 and 2/3... glad I was able to help!

2852/12 is ———————> (A) 237

In solving the inequality, 3x+8/x-4 <= 0, we identify critical points and assign intervals based on them. The solution offers two possible scenarios: x is less than or equal to -8/3 or x is greater than 4.

The inequality 3x+8/x-4 =< 0 can be divided into two possible scenarios by clarifying the critical points. To solve this inequality, you first need to identify where the expression equals zero, that's where 3x+8=0 and x=4. Solving 3x+8=0 yields x=-8/3, which is the first

possible solution. Another critical point is where the denominator is zero, which is x=4.

Next, we need to check the signs of these intervals: (-inf, -8/3), (-8/3, 4) and (4, inf). Testing these intervals on the given inequality gives us the

solution that x is less than or equal to -8/3 or x is greater than 4 . Remember, x cannot be equal to 4 because it makes denominator zero in the origin expression which is undefined in mathematics.

Therefore, the correct solution is 'x less than or equal to -8/3 or x greater than 4'.

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To convert 3.2 feet to inches, multiply by the conversion factor of 12 inches per foot. The calculation 3.2 feet x 12 inches/1 foot results in 38.4 inches.

To convert 3.2 feet to inches, we use the following ratio: 1 foot = 12 inches. This is a standard conversion factor between feet and inches in the customary system of measurements.

First, set up the conversion like this:

Multiply the number of feet by the unit equivalence.

3.2 feet x 12 inches/1 foot = x inches.

Perform the multiplication to solve for x.

3.2 x 12 = 38.4 inches.

Therefore, 3.2 feet is equivalent to 38.4 inches. Remember, when converting from a larger unit to a smaller unit like feet to inches, you need to multiply by the conversion factor.

Answer:

$0.14

Step-by-step explanation:

Average it out. 1.68÷12=0.14

Answer:

$0.14

Step-by-step explanation:

1.68/12= 0.14

The likelihood of an event stating the 30% chance of snow means that, in 100 identical weather circumstances, we would predict it to snow during 30. This does not deliver any information on the quantity of snow.

The likelihood of an event given its probability represents the chance of that event taking place. When we say that there is a 30% chance of snow tomorrow, this means that out of every 100 similar weather scenarios, we would expect it to snow in 30 of them. Hence, the likelihood of it snowing tomorrow is 30%. It's important to understand that probability is a way to quantify the uncertainty associated with events predicted to occur, based on the known conditions.

Regarding the example, if we know that 'If it snows more than three inches, the schools are mandated to close.' and we see that 'The schools closed.' we can infer that 'It snowed more than three inches.' This however has no direct relation to the probability of snow tomorrow.

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Answer:

6 hours

Explaination

10/15=.66666667

.66666667*9=6 hours

You plug in f(x) into where x is within g(x) so you get G(f(x))=(X+6)^4

Answer:

[tex]\large\boxed{g(f(x))=(x+6)^4}[/tex]

Step-by-step explanation:

[tex]f(x)=x+6\\\\g(x)=x^4\\\\g(f(x))\to\text{put}\ x+6\ \text{to the equation of}\ g(x)\\\\g(f(x))=(x+6)^4[/tex]

My answer would be 8.. I may not be correct, but I tried. So, I placed the numbers from least to greatest and split it 1’s and 2’s VS 3’s and 4’s. I just added 1 plus 2 plus 2 and a half plus 2 and a half and got 8. I also added (3+3+3)+3 and a half plus 3

If you would like to show the questions to us, would be fine!

Multiply the side length by the number of sides to get the perimeter. The formula for finding the perimeter of a regular polygon is just the number of sides x the length of any side. Once you've multiplied those 2 numbers together, you've found the perimeter of the polygon

Final answer:

The perimeter of a polygon is calculated by adding together the lengths of all its sides. For regular polygons with equal side lengths, the perimeter is the side length multiplied by the number of sides. For irregular polygons, all unique side lengths must be measured and summed.

Explanation:

The perimeter of a polygon is the total length around the shape. It is calculated by summing the lengths of all its sides. For a regular polygon with all sides of equal length, like a square, if one side length is a, then the perimeter is simply 4a because there are four sides. In the case of irregular polygons, each individual side length must be measured and added together to find the total perimeter.

For instance, consider a rectangle with a length of l and a width of w; the perimeter would be 2l + 2w, because each opposite pair of sides are equal. The units used for the lengths will be the same units used for the perimeter, such as meters. Nonetheless, the calculation can become more complex with polygons of more sides. Each side must be accounted for precisely, and units must remain consistent.

Answer:

Option A) 0.02

Step-by-step explanation:

The probability p that one of the questions is correct is

[tex]P = \frac{1}{4}[/tex]

The number of questions that will answer (number of trials) is [tex]n = 3[/tex].

We want to find out the probability that [tex]x = 3[/tex] three questions will be answered correctly.

To calculate this probability we use the binomial formula:

[tex]P(x) = \frac{n!}{x!(n-x)!} p^x(1-p)^{n-x}[/tex]

Where

[tex]x=3\\n=3\\p=0.25[/tex]

Then:

[tex]P(x=3) = \frac{3!}{3!(3-3)!} 0.25^3(1-0.25)^{3-3}[/tex]

[tex]P(3) =0.25^3[/tex]

[tex]P(3) = 0.0156[/tex]

P(3) = 0.0156≈0.02

Answer:

Final answer is $12696.

Step-by-step explanation:

Given that initial amount P = $28000

Interest rate r = 5.8% = 0.058

Time = 1 year

Then future value is given by :

[tex]A=P\left(1+r\right)^t[/tex]

[tex]A=28000\left(1+0.058\right)^1=29624[/tex]

Similarly calculate future value for 2nd case:

Given that initial amount P = $16000

Interest rate r = 5.8% = 0.058

Time = 1 year

Then future value is given by :

[tex]A=P\left(1+\frac{r}{n}\right)^{n\left(t\right)}[/tex]

[tex]A=16000\left(1+0.058\right)^1=16928[/tex]

then difference = 29624 - 16928 = 12696

Hence final answer is $12696.

Answer:

$696.

Step-by-step explanation:

We are asked to find the amount of interest earned on $28,000 than $16,000 with APYs of 5.8% for a year.

We will use simple interest formula to solve our given problem.

[tex]I=Prt[/tex]

[tex]I[/tex] = Amount of interest,

P = Principal amount,

r = Interest rate in decimal form,

t = Time in years.

[tex]5.8\%=\frac{5.8}{100}=0.058[/tex]

Let us find difference of interests as:

[tex]\$28,000\times 0.058-\$16,000\times 0.058[/tex]

[tex](\$28,000-\$16,000)\times 0.058[/tex]

[tex](\$12,000)\times 0.058[/tex]

[tex]\$696[/tex]

Therefore, it will earn $696 more in interest.

Answer:

So we can write an equation to solve this:

12/100 = 36/x

And then we are going to solve for x

x(12/100) = 36

36 x (100/12) = 300

The total number of candy bars was 300

Jillian sold 12% of the class's candy bars, which amounts to 36 bars. To find the total, calculate what 1% would be by dividing 36 by 12, and then multiply by 100 to find that the class sold 300 candy bars in total.

The student is asking about a practical application of percentages in a real-world context, which is a common subject in middle school mathematics. To find the total number of candy bars sold by the class, we need to use the information that Jillian sold 12% of the total and that this amounted to 36 candy bars. The calculation is straightforward: if 12% equals 36, we want to find 100% (the total).

To do this, we set up a simple proportion: if 12% is 36, then 1% would be 36 divided by 12, which is 3 candy bars. Since we're looking for the total, we multiply the number of candy bars representing 1% (which is 3) by 100 to find that the class sold a total of 300 candy bars before taxes.

Step-by-Step Calculation:

Find 1% of the total by dividing 36 candy bars by 12%.

1% of the total = 36 candy bars / 12 = 3 candy bars.

Multiply the value of 1% by 100 to find the total amount.

Total candy bars = 3 candy bars × 100 = 300 candy bars.

Answer: 0.22

Step-by-step explanation:

Answer:Jason is not correct  as Jason changed the terms.

Step-by-step explanation:

Given the expression 34+5.6b+9.Jason used the commutative property to write the above expression changed to 9.0 + 56b + 3.4

We have to tell Jason work is correct or not.

Commutative property states that order does not matters but the terms remains same i.e a+b=b+aJason change the expression 34+5.6b+9 to 9.0 + 56b + 3.4here, Jason change the terms as well as order Jason is not correct  as Jason changed the terms.

In this situation of selling two properties for the same price but with different gain and loss percentages, the real estate agent does not break even but incurs an overall loss of 6.25%.

This is essentially a problem in profit and loss calculations in the domain of Mathematics. Since the selling price of both the sites is the same, the loss and gain percent will cancel out each other, resulting in no overall gain or loss. Here's why:

The total cost price is Rs. 14400 + Rs. 24000 = Rs. 38400 and the total selling price is Rs. 18000 + Rs. 18000 = Rs. 36000. So, the real estate agent has incurred an overall loss. To find the percentage of loss, use the formula face: [(Loss) / (Cost Price)] * 100 = [(Rs. 38400 - Rs. 36000) / Rs. 38400] * 100 = 6.25% loss.

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Answer:

19.4

Step-by-step explanation:

40^2=35^2+b^2

(Pythagorean Theorem)

b^2=375

b=19.4

Answer:

The expression is equivalent to x^2-17x-60 would be (x - 20)(x + 3)

Step-1 : Multiply the coefficient of the first term by the constant   1 • -60 = -60 

Step-2 : Find two factors of  -60  whose sum equals the coefficient of the middle term, which is   -17 .

-60+1= -59

-30+2= -28

-20+3= -17

Final (x + 3) • (x - 20)

Answer:

[tex]\large\boxed{4x+6y^3}[/tex]

Step-by-step explanation:

[tex]2x+x+x+2y\times3y\times y\\\\=(2x+x+x)+(2y\times3y\times y)\\\\=4x+(2\times3)(y\times y\times y)\\\\=4x+6y^3[/tex]

ANSWER

[tex]n=\frac{5}{6} [/tex]

EXPLANATION

The given equation is

[tex] \frac{4}{5}n =\frac{2}{3} [/tex]

We multiply both sides of the equation by:

[tex]\frac{5}{4}[/tex]

[tex] \frac{5}{4}\times \frac{4}{5}n =\frac{2}{3}\times\frac{5}{4} [/tex]

Multiply and cancel out common factors

This implies that:

[tex]n=\frac{5}{6}[/tex]

Option B is correct.

Answer:

x∈B

x∈A∪B

x∈A∪C

x∈A∩B

Step-by-step explanation:

As can be seen from the Venn diagram, x is the shaded portion between the intersection of 3 circles A, B and C.

hence x belong to b, and x belong to A union B, x belong to A union C and x belong to A intersection B !

Answer:

The following are correct:

B

C

D

E

F

Step-by-step explanation

Hello there!

Answer:

Triangle 2

Step-by-step explanation:

To determine which triangle has the bigger area, we would need to figure our the area of the triangles.

To solve for the area of the triangles, we would use the formula length × width × height or l × w × h

They gave us the information to the triangles in the question, so we would just solve.

Triangle 1: [tex]300 *400*500= 60,000,000[/tex]

Triangle 2: [tex]300*400*700=84,000,000[/tex]

When you finish solving, you would see that triangle 2 has the bigger area.

Triangle 2 would be the CORRECT answer because it has a bigger area than Triangle 1.

Triangle 2. Area is length x width x height

Answer:

upper left

Step-by-step explanation:

The generic equation for a circle centered at (h, k) with radius r is ...

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

Comparing that equation to the one you have, you can see that ...

-h = 0

-k = +3

r^2 = 9

Then you have (h, k) = (0, -3) and a radius of 3.

The circle has its center on the y-axis 3 units below the x-axis and just touches the x-axis. This is a description of the graph at upper left.