1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Andreyy89
3 years ago
15

The gcf of two numbers less than or equal to 12 is 2. Their LCM is 20.What are the numbers?

Mathematics
1 answer:
bixtya [17]3 years ago
5 0

We know:

LCM(a,\ b)=\dfrac{ab}{GCF(a,\ b)}

We have

GCF(a,\ b)=2,\ LCM(a,\ b)=20,\ a\leq12,\ b\leq12

Substitute:

20=\dfrac{ab}{2}\qquad|\cdot2\\\\ab=40

40=1\cdot40=2\cdot20=4\cdot10=5\cdot8

Only 4 and 10 meet the requirements of the question.

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

40 and 1 NOT, because 40 > 12

20 and 2 NOT, because 20 > 12

5 and 8 NOT because GCF(5, 8) = 1

You might be interested in
A certain town never has two sunny days in a row. Each day is classified as being either sunny, cloudy (but dry), or rainy. If i
11111nata11111 [884]

Answer:

the proportion of days that are Sunny is 0.2

Step-by-step explanation:

Given the data in the question;

Using markov chain;

3 states; Sunny(1), Cloudy(2) and Rainy(3)

Now, based on given conditions, the transition matrix can be obtained in the following way;

\left[\begin{array}{ccc}0&0.5&0.5\\0.25&0.5&0.25\\0.25&0.25&0.5\end{array}\right]

so let the proportion of sunny, cloudy and rainy days be S, C and R respectively.

such that, from column 1

S = 0.25C + 0.25R   -------------let this be equation 1

from column 2

0.5C = 0.5S + 0.25R

divided through by 0.5

C = S + 0.5R ---------------------- let this be equation 2

now putting equation 2 into equation;

S = 0.25(S + 0.5R) + 0.25R

S = 0.25S + 0.125R + 0.25R

S - 0.25S = 0.375R

0.75S = 0.375R

S = 0.375R / 0.75

S = 0.5R

Therefore,

from equation 2; C = S + 0.5R

input S = 0.5R

C = 0.5R + 0.5R

C = R

Now, we know that, the sum of the three proportion should be equal to one;

so

S + C + R = 1

since C = R and S = 0.5R

we substitute

0.5R + R + R = 1

2.5R = 1

R = 1/2.5

R = 0.4

Hence, the proportion of days that are Rainy is 0.4

C = R

C = 0.4

Hence, the proportion of days that are Cloudy is 0.4

S = 0.5R

S = 0.5(0.4)

S = 0.2

Hence, the proportion of days that are Sunny is 0.2

8 0
3 years ago
Quadrilateral ABCD is similar to quadrilateral EFGH. Find the measure of side EF
garri49 [273]

Answer:

EF = 6.6

Step-by-step explanation:

Since ABCD is similar to EFGH, then EH is similar to AD. So, we can solve by first dividing 12 by 2 (EH by AD). The quotient of this is 6. This tells us that quadrilateral EFGH is 6 times larger than quadrilateral ABCD, since they are similar. So, with this and the measurement of AB (which is similar to EF), we can now solve for EF. We simply multiply 1.1 (the measurement of AB) by 6 (how many times larger EFGH is compared to ABCD). The product of this is 6.6, our final answer.

3 0
2 years ago
An equation that is true for every value of the variables is a(n)
Roman55 [17]
Identity, <span>For example, x + x = 2x is </span>true for every value<span> of x.</span>
5 0
3 years ago
Read 2 more answers
Use the fundamental theorem of calculus to find the area of the region between the graph of the function x^5 + 8x^4 + 2x^2 + 5x
BaLLatris [955]

Answer:

The area of the region is 25,351 units^2.

Step-by-step explanation:

The Fundamental Theorem of Calculus:<em> if </em>f<em> is a continuous function on </em>[a,b]<em>, then</em>

                                   \int_{a}^{b} f(x)dx = F(b) - F(a) = F(x) |  {_a^b}

where F is an antiderivative of f.

A function F is an antiderivative of the function f if

                                                    F^{'}(x)=f(x)

The theorem relates differential and integral calculus, and tells us how we can find the area under a curve using antidifferentiation.

To find the area of the region between the graph of the function x^5 + 8x^4 + 2x^2 + 5x + 15 and the x-axis on the interval [-6, 6] you must:

Apply the Fundamental Theorem of Calculus

\int _{-6}^6(x^5+8x^4+2x^2+5x+15)dx

\mathrm{Apply\:the\:Sum\:Rule}:\quad \int f\left(x\right)\pm g\left(x\right)dx=\int f\left(x\right)dx\pm \int g\left(x\right)dx\\\\\int _{-6}^6x^5dx+\int _{-6}^68x^4dx+\int _{-6}^62x^2dx+\int _{-6}^65xdx+\int _{-6}^615dx

\int _{-6}^6x^5dx=0\\\\\int _{-6}^68x^4dx=\frac{124416}{5}\\\\\int _{-6}^62x^2dx=288\\\\\int _{-6}^65xdx=0\\\\\int _{-6}^615dx=180\\\\0+\frac{124416}{5}+288+0+18\\\\\frac{126756}{5}\approx 25351.2

3 0
3 years ago
Tell me which statements belong in "agree" and disagree".
Delvig [45]

Answer:

Rig

Step-by-step explanation:

4 0
2 years ago
Other questions:
  • Solve and graph. c – 10 + 3c -2<br> B. C 3<br> D. C &lt; -2
    9·2 answers
  • 14÷7= ¿<br>A. 8<br>B.2<br>C.15<br>Helppppp
    12·2 answers
  • What is the value of 89 3/4
    15·2 answers
  • How could you use translations to draw a cube
    15·1 answer
  • Which of the following illustrates the truth value of the given conditional statement?
    15·1 answer
  • A rectangle and a chai go have the same area. If their bases are the same lengths, how do their Heights compare? Justify your an
    13·1 answer
  • A sector with an area of 26pie cm^2 has a radius of 6 cm. What is the central angle measure of the sector in radians?
    12·1 answer
  • isaac has 18 eggs. he is packing cartons with 1/3 of his eggs in each carton. which figure shows how the eggs are packed?
    8·1 answer
  • Write one way of representing the equation of the given line in point-slope form. Then rewrite the equation in slope-intercept f
    11·1 answer
  • Which statement about pentagon's and hexagons are true ​
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!