What is the LCM of xy(x + 1) and x(x + 2)?


A.x2(x + 3)


B.x2(x + 1)(x + 2)


C.xy(x + 1)(x + 2)


D.xy(x + 3)

You simply need to mulotiply those two numbers

Then u get 126!

Easy Peasy

When you graph the two functions given, the graph B) shift 1 unit to the right.

Graph the two functions, see attached pictures:

~Rise Above the Ordinary

Let x = 1st positive integer

Let x + 1 = 2nd positive integer

As give, their sum of squares is 841

[tex]x^{2}+(x+1)^{2}=841[/tex]

[tex]x^{2}+x^{2}+2x+1=841[/tex]

[tex]2x^{2}+2x+1=841[/tex]

[tex]2x^{2}+2x-840=0[/tex]

factor 2 out, [tex]x^{2}+x-420=0[/tex]

[tex]x^{2}+21x-20x-420=0[/tex]

[tex]x(x+21)-20(x+21)=0[/tex]

(x+21)(x-20)

This gives, x=20 and =-21 (neglect the negative value)

So, x = 20

x+1 = 21

So, the two numbers are : 20 and 21

Answer:Juan live 384 miles from the mountains.

Step-by-step explanation:

Let x be the speed  of Juan for trip to the mountains

Time taken by Juan to reach the mountains=8 hours

then distance traveled by Juan for trip to mountain= speed × time=8x..........(1)

Time taken by Juan to reach the home= 6 hours

Speed increased by 16 miles per hour ∴ the resultant speed to reach the home by Juan =x+16

then distance traveled by Juan to reach the home =speed × time

= (x+16)6......................(2)

Now distance is same in both the case (1) and (2),we get

8x= (x+16)6

⇒8x=6x+96..............(by solving brackets)

⇒2x=96..............(subtracting 6x from both sides )

⇒x=48....................(dividing 2 from both sides)

Putting this value in (1) ,we get

Distance traveled by Juan for trip to mountain =8×48=384 miles.

∴ Juan live 384 miles from the mountains.

By using the rate and time of journey, it is determined that Juan lives 384 miles away from the mountains.

This question is about calculating the distance based on the rate and time of travel. Let's denote the distance to the mountains as 'D'. According to the question, Juan drove to the mountains and it took 8 hours. On his way home, there was no traffic and he was able to travel at a faster rate, which took 6 hours.

Let's denote the speed to the mountains as 'S', therefore his speed back was 'S + 16' (16 miles per hour faster). From the formula speed = distance/time (D = S*T), we know that the distance to and from the mountains remained the same, so we can set up the following equation to solve for the unknown distance D:

8S = 6(S + 16)

Solving for 'S' we get 48 mph. We can substitute S=48 into the first equation to get D = 8S = 8*48 = 384 miles. So, Juan lives 384 miles away from the mountains.

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The remainder when dividing 23870 by 38 is 16.

To find the remainder when dividing 23870 by 38, you divide the larger number (the dividend) by the smaller number (the divisor). If the division operation does not produce a whole number, the 'left over' digits are considered the remainder. When you divide 23870 by 38, the quotient (or the answer) is 628, and the remainder is 16. Therefore, 16 is the remainder when 23870 is divided by 38.

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Answer:

336.49 calories.

Step-by-step explanation:

if;                      87.4 calories  = 1 serving of cherries

so;                  how much calories  =  3.85 serving of cherries

hence:

           3.85 seving * 87.4 calories / 1 serving

the answer is

               336.49 calories

Answer:

The distance is 55 units.

Step-by-step explanation:

Think of the bottom left corner of the rectangles, the shared vertex, as the origin of a coordinate plane. The positive x-axis is the lower 108-unit long horizontal side, and the positive y-axis is the left vertical 98-unit long side. The bottom left vertex is (0, 0). The center of the small rectangle is at (10, 16). The center of the large rectangle is at (54, 49). Now use the distance formula to find the distance between those two points.

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

[tex] d = \sqrt{(54 - 10)^2 + (49 - 16)^2} [/tex]

[tex] d = \sqrt{44^2 + 33^2} [/tex]

[tex] d = \sqrt{1936 + 1089} [/tex]

[tex] d = \sqrt{3025} [/tex]

[tex] d = 55 [/tex]

The correct answer would be -21.63 and +21.63

h(t) is a linear function with a slope of -15.

Answer:

B

Step-by-step explanation:

P = 10 + x + 2x + 7

= (10 + 7) + (x + 2x)

= 17 + 3x

Therefore, the perimeter is 17 + 3x feet.

Answer:7x+12

Step-by-step explanation:

Answer: {-10, +10}

Step-by-step explanation: A common mistake in this problem would be to say that if x² = 100, x must equal 10.

Remember however that before you do anything else you must set the equation equal to 0.

So our first step is to subtract 100 from both sides to get x² - 100 = 0. Next, factor the left side to get (x + 10)(x - 10) = 0.

So either x + 10 = 0 or x - 10 = 0.

Solving for x in each equation, we have x = -10 or x = +10.

So our answer is not just 10, it's -10 or +10.

I have also attached my work in the image provided.

The correct answer is A. 11

Answer:  y  ≤ 8

Solution:

Step 1: Rearrange the equation so that all the like terms are on one side

5y + 16 ≤ 56  

= 5y ≤ 56 - 16                      constants on one side and variable on the other

= 5y ≤ 40

= y  ≤ 8

Hope the solution helps to understand the question!

Tip: Remember that if the inequality is multiplied by a negative sign the inequality sign flips.

To round off to 10, the difference should range from 5 to 14. If the difference between two numbers is from 5 to 14, they all are rounded to 10.

Example:

[tex]18-9=9[/tex] (near to 10)

[tex]26-15=11[/tex]

[tex]46-39=7[/tex]

[tex]50-42=8[/tex]

If Julia rounded to the nearest ten to estimate the difference between two numbers. The estimated difference was 10. (18,9)(25,14), (36,22) and (45, 38) are few pairs of numbers she might have subtracted.

A number system is defined as a system of writing to express numbers.

The difference should range from 5 to 14.

Difference in math is the result of one of the important mathematical operations, which is obtained by subtracting two numbers

To round off to 10.

If the range of difference between two numbers is from 5 to 14. Then those numbers are rounded to ten.

Let us consider some pairs of numbers whose difference is rounded to ten.

18-9=9

25-14=11

36-22=14

45-38=7

Hence (18,9)(25,14), (36,22) and (45, 38) are few pairs of numbers she might have subtracted.

To learn more on Number system click:

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Answer:

$ 548.59

Step-by-step explanation:

The complete solution is given in attachment below.

1. When you rotate a figure counterclockwise, is that a positive rotation or a negative rotation? It is a positive rotation. Positive rotations are counterclockwise or anti-clockwise.

2. Rotating from the x-axis to the y-axis is a rotation of how many degrees? it is generally 180 degrees. To rotate a figure 180 degrees, we apply the rule (x, y) → (-x, -y).

i dont really know about 2. but i think for 1. is it is a negative rotation if you spin it like that.

A

to calculate the slope m , use the ' gradient formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (1, 3) and (x₂, y₂ ) = (5, 4)

m = [tex]\frac{4 - 3}{5 - 1}[/tex] = [tex]\frac{1}{4}[/tex] → A

13  By the factor theorem, if the function is divisible by x - 3 then f(3) = 0. So we have:-

2(3)^3 + k(3)^2 + 7(3) - 3 = 0

9k = 3 - 21 - 54 = -72

k =  -72/9 =  -8 answer

14.   Similarly ,   f(-4) = 0 , so we have:-

(-4)^3 + 9(-4)^2 + k(-4) - 12 = 0

-64 + 144 - 4k - 12 = 0

4k = -64 + 144 - 12 = 68

k = 68/4

k = 17   answer

Answer : C

A. (5 + 3) × 2 = 16

Here we have 5 +3 . there is a + sign in between.  so it does not comes under Associative property of multiplication

B. 5 × (3 + 2) = 25

We have 3 + 2 . there is a + sign in between.  so it does not comes under Associative property of multiplication

C. 5 × (3 × 2) = 30

we have 5 times 3 times 2.  so it comes under Associative property of multiplication

D. 2 + (4 × 7) = 30

We have  2 + . there is a + sign in between.  so it does not comes under Associative property of multiplication

The sum of the first four terms of the series would be c. -102

Answer:

43:76  

Step-by-step explanation:

Answer:

A. 12

Step-by-step explanation:

i= use complicated conjugate to search out definite quantity of 8 + 12i

i = 12i

i= twelve × ei 90°

i = twelve × (cos 90° + i sin 90°)

r = |i| = twelve

The absolute value of the complex number 8 + 12i is found by squaring the real part, squaring the imaginary part, adding these two results, and then taking the square root. This results in the square root of 208.

The absolute value of a complex number a + bi is calculated through the formula sqrt(a² + b²). So, to find the absolute value of the complex number 8 + 12i, we substitute a with 8 and b with 12. We can perform the calculations as follows:

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The cost of renting 2 snowmobiles for 5 hours would be $75, as you double the cost for one snowmobile, which is $37.50.

The cost for renting one snowmobile for 5 hours is

$37.50

. If you want to rent 2 snowmobiles for the same amount of time, you simply need to double the cost. In mathematics, this is a simple multiplication operation. So,

2 x $37.50 = $75

. Therefore, the cost of renting 2 snowmobiles for 5 hours would be

$75

.

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3 miles per day * 365 days = 1095

1095-1000=95

The answer is B. 95 miles more.

Answer:

60

Step-by-step explanation:

Answer:

60 dollars.

Step-by-step explanation:

Markup is nothing but the difference between the selling price of a good or service and its cost. It is expressed as a percentage above the cost. In short, we can say that  it is the added price over the total cost of the good or service that provides the seller with a profit.

Original price = 50 dollars

ADD: 20% on original price = Markup price = 50(20/100) = 10 dollars

Hence Sales price = 50+10 = 60 dollars

Answer:

b on edge

Step-by-step explanation:

The dimensions of the rectangle are 3 inches by 12 inches. This conclusion is achieved by using the supplied information that the rectangle is four times as long as it is wide, and the area is 36 square inches.

The problem is describing a rectangle whose length is four times its width and has an area of 36 square inches. The formula for the area of a rectangle is length x width. Given the rectangle is four times as long as it is wide, we can represent the width as 'w' and the length as '4w'. Therefore, the calculation would look as follows: 4w * w = 36. Solving this equation we get w^2=9, so w=3. Consequently, the length would be 4*3=12. Therefore, the dimensions of the rectangle are 3 inches by 12 inches.

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y=20,000-.10x

with x being the number of years

Answer:

[tex]y=\$20,000\cdot (0.90)^x[/tex]

Step-by-step explanation:

We have been given that Kelly bought a new car for $20,000. The car depreciates at a rate of 10% per year. We are asked to write an equation to model the car's value.

Since car's value depreciates by 10% per year, so value of car is depreciating exponentially.

We know that an exponential decay function is in form [tex]y=a\cdot (1-r)^x[/tex], where

a = Initial value,

r = Decay rate in decimal form.

Let us convert 10% into decimal form as:

[tex]10\%=\frac{10}{100}=0.10[/tex]

Upon substituting our given values in decay formula, we will get:

[tex]y=\$20,000\cdot (1-0.10)^x[/tex]

[tex]y=\$20,000\cdot (0.90)^x[/tex]

Therefore, our required equation would be [tex]y=\$20,000\cdot (0.90)^x[/tex].