All categories

3 years ago

Find the smallest square number that is divisible by each of the numbers 8, 9 and 10

Mathematics

2 answers:

Vsevolod [243]3 years ago

8 0

Answer:

Step-by-step explanation:

Find Least common denominator of 8, 9 & 10

8 = 2 * 2 * 2

9 = 3* 3

10 = 5*2

LCM = 2*2*2*3*3*5 = 8 * 9 * 5 = 360

To make 360 a perfect square,multiply by 10

360*10 = 3600 is a perfect square

vekshin13 years ago

7 0

Answer:

Step-by-step explanation:

Find the LCM of 8,9 and 10.

Prime Factorization to find LCM,

8 = 2 × 2 × 2

9 = 3 × 3

10 = 2 × 5

LCM ( 8 , 9 , 10 ) = 2 × 2 × 2 × 3 × 3 × 5 =360

But 360 is not square

Now we make the pairs complete by multiplying same numbers in prime factorization of LCM.

We need one 2 and one 5 to complete the pair.

We get, Least Square number = 2 × 2 × 2 × 2 × 3 × 3 × 5 × 5 = 3600

Hope this helps

good Luck

You might be interested in

Precal : Note: Triangle may not be drawn to scale. Suppose a = 3 and A = 15 degrees

drek231 [11]

Given:

In a right triangle at B,

$\begin{gathered} a=3 \\ A=15^{\circ} \end{gathered}$

To find:

The length of the sides b and c and angle B.

Explanation:

Using the trigonometric ratio,

$\begin{gathered} sinA=\frac{a}{c} \\ \sin15^{\circ}=\frac{3}{c} \\ c=\frac{3}{\sin15^{\circ}} \\ c=11.59 \\ c\approx11.6 \end{gathered}$

Using the trigonometric ratio,

$\begin{gathered} \tan A=\frac{a}{b} \\ \tan15^{\circ}=\frac{3}{b} \\ b=\frac{3}{\tan15^{\circ}} \\ b=11.19 \\ b\approx11.2 \end{gathered}$

Using the angle sum property,

The angle B becomes,

$\begin{gathered} 90+15+B=180 \\ B=180-90-15 \\ B=75^{\circ} \end{gathered}$

Final answer:

The values are,

$\begin{gathered} b=11.2 \\ c=11.6 \\ B=75^{\circ} \end{gathered}$

3 0

1 year ago

What is the slope of a line that is perpendicular to the line whose equation is 7x−3y=10?

Sonja [21]

Since this equation is already in standard form, there is no need to convert it. Standard form is Ax + By = C. In this equation, 7 = A, 3 = B, and 10 = C. From standard form, Ax + By = C equals negative A over B.

7x + 3y = 10

↓

$\displaystyle\ m= \frac{-7}{-3}$

Then you'd simplify.

$\displaystyle\ m=\frac{7}{3}$

The slope cannot be simplified any more, so this would be the final answer.

- Marlon Nunez

7 0

3 years ago

How many more vertices does a rectangular prism have, compared to triangular pyramid?

iVinArrow [24]

The answer is C it’s 5

4 0

3 years ago

Read 2 more answers

Find the sum of 12a + 7b, −6a − 9, and 14a − 12b.

Ivan

The answer is: [A]: " 20a − 5b − 9 " .
______________________________________
Explanation:
_______________________________________________
(12a + 7b) + (−6a − 9) + (14a − 12b) =

12a + 7b + 1(−6a − 9) + 1(14a − 12b) =

12a + 7b + (1*-6a) + (1*-9) + (1*14a) + (1* -12b) =

12a + 7b − 6a − 9 + 14a − 12b = ?

Combine the "like terms:

12a − 6a + 14a = 20a ;

7b − 12b = - 5b ;

and then we have "-9" ;
_____________________________________________________
So, write as: " 20a − 5b − 9 " ; which is: Answer choice: [A].
______________________________________________________

8 0

3 years ago

Read 2 more answers

For a medical study, a researcher wishes to select people in the middle 60% of the population based on blood pressure.

Finger [1]

Answer:

Lower limit: 113.28

Upper limit: 126.72

Step-by-step explanation:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

$\mu = 120, \sigma = 8$