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3 years ago

Find the GCF of 48 and 42

Mathematics

2 answers:

Alika [10]3 years ago

6 0

Answer:

6 is the GCF

Step-by-step explanation:

<u>Definition of GCF: The largest number that divides two or more numbers evenly. </u>

<u />

Factors of 48 = 1 , 2 , 3 , 4 , 6 , 8 , 12 , 16 , 24 , 48

Factors of 42 = 1, 2, 3, 6, 7, 14, 21, 42

Answer: 6 is the GCF

ivann1987 [24]3 years ago

3 0

Answer:

The gcf of 42 and 48 can be obtained like this:

The factors of 42 are 42, 21, 14, 7, 6, 3, 2, 1.

The factors of 48 are 48, 24, 16, 12, 8, 6, 4, 3, 2, 1.

The common factors of 42 and 48 are 6, 3, 2, 1, intersecting the two sets above.

In the intersection factors of 42 ∩ factors of 48 the greatest element is 6.

Therefore, the greatest common factor of 42 and 48 is 6.

Taking the above into account you also know how to find all the common factors of 42 and 48, not just the greatest.

Hope I helped

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How do I do numbers 12 to 14?

NARA [144]

Answer:

12. 1 second, 35 ft; 2 seconds, 32 ft

13. (t, y) = (1.4 seconds, 37.6 feet)

14. 37.6 ft; the vertex is the highest point

Step-by-step explanation:

12. You have properly answered question 12.

After 1 second, the height is 35 feet; after 2 seconds, it is 32 feet.

13. My method of choice is to plot the graph on a graphing calculator and let it show me the coordinates of the vertex when I highlight that point. (See attached.) The vertex is ...

(t, y) = (1.4, 37.6)

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3 years ago

Use the given information to find the exact value of the trigonometric function

eimsori [14]

$\begin{gathered} \csc \theta=-\frac{6}{5} \\ \tan \theta>0 \\ \cos \frac{\theta}{2}=\text{?} \end{gathered}$

Half Angle Formula

$\cos \frac{\theta}{2}=\pm\sqrt[\square]{\frac{1+\cos\theta}{2}}$ $\tan \theta>0\text{ and csc}\theta\text{ is negative in the third quadrant}$ $\begin{gathered} \csc \theta=-\frac{6}{5}=\frac{r}{y} \\ x^2+y^2=r^2 \\ x=\pm\sqrt[\square]{r^2-y^2} \\ x=\pm\sqrt[\square]{6^2-(-5)^2} \\ x=\pm\sqrt[\square]{36-25} \\ x=\pm\sqrt[\square]{11} \\ \text{x is negative since the angle is on the 3rd quadrant} \end{gathered}$ $\begin{gathered} \cos \theta=\frac{x}{r}=\frac{-\sqrt[\square]{11}}{6} \\ \cos \frac{\theta}{2}=\pm\sqrt[\square]{\frac{1+\cos\theta}{2}} \\ \cos \frac{\theta}{2}is\text{ also negative in the 3rd quadrant} \\ \cos \frac{\theta}{2}=-\sqrt[\square]{\frac{1+\frac{-\sqrt[\square]{11}}{6}}{2}} \\ \cos \frac{\theta}{2}=-\sqrt[\square]{\frac{\frac{6-\sqrt[\square]{11}}{6}}{2}} \\ \cos \frac{\theta}{2}=-\sqrt[\square]{\frac{6-\sqrt[\square]{11}}{12}} \\ \\ \end{gathered}$

Answer:

$\cos \frac{\theta}{2}=-\sqrt[\square]{\frac{6-\sqrt[\square]{11}}{12}}$

Checking:

$\begin{gathered} \frac{\theta}{2}=\cos ^{-1}(-\sqrt[\square]{\frac{6-\sqrt[\square]{11}}{12}}) \\ \frac{\theta}{2}=118.22^{\circ} \\ \theta=236.44^{\circ}\text{ (3rd quadrant)} \end{gathered}$

Also,

$\csc \theta=\frac{1}{\sin\theta}=\frac{1}{\sin (236.44)}=-\frac{6}{5}\text{ QED}$

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3 years ago

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yarga [219]

Answer:

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Step-by-step explanation:

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If an object is translated, it maintains its shape and size as well as the length of its sides and angles, only the location changes.

If polygon LMNP with ∠M of 50° is translated 5 units right and 4 units down to a new point, M' has the same angle measure. Hence ∠M' = 50°

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Alex777 [14]

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Read 2 more answers

Find the GCF of 48 and 42​

Find the GCF of 48 and 42