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2 years ago

Use prime factorization to find the GCF of 10, 45

Mathematics

1 answer:

Taya2010 [7]2 years ago

7 0

Answer:

Step-by-step explanation:

$10=2\cdot\boxed{5}\\\\45=3\cdot3\cdot\boxed{5}\\\\GCF(10,\ 45)=\boxed{5}$

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What is 5 times a number ,r, decreased by seven

Lapatulllka [165]

Answer:

5n - 7 < 23

Step-by-step explanation:

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2 years ago

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Rachael is placing a protective cover on a glass case. The case is a cube, and the perimeter of one cube face is 56 inches.

Dmitry_Shevchenko [17]

Answer:

336

Step-by-step explanation:

We know that a cube has 6 faces which means we can use this equation:

56 x 6 = 336

336 square inches is the answer.

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2 years ago

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A car can travel 374 kilometers on 34 liters of gasoline. How far can it travel on 35 liters?

vovangra [49]

Answer:

385 kilometers

Step-by-step explanation:

Divide 374 by 34 to get the unit price

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2 years ago

1) Suppose f(x) = x2 and g(x) = |x|. Then the composites (fog)(x) = |x|2 = x2 and (gof)(x) = |x2| = x2 are both differentiable a

Rufina [12.5K]

Answer:

This contradict of the chain rule.

Step-by-step explanation:

The given functions are

$f(x)=x^2$

$g(x)=|x|$

It is given that,

$(f\circ g)(x)=|x|^2=x^2$

$(g\circ f)(x)=|x^2|=x^2$

According to chin rule,

$(f\circ g)(c)=f(g(c))=f'(g(c)g'(c)$

It means, $(f\circ g)(c)$ is differentiable if f(g(c)) and g(c) is differentiable at x=c.

Here g(x) is not differentiable at x=0 but both compositions are differentiable, which is a contradiction of the chain rule

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2 years ago

What is the length of AC?<br><br><br> 3 ft<br><br> 4 ft<br><br> 9 ft<br><br> 18 ft

iragen [17]

Answer: The length of AC is 18 ft.

Step-by-step explanation:

By the given diagram,

AM = MB and CN = NB

M and N are the mid points of the sides AB and CB respectively,

Thus, by the mid point theorem,

MN ║ AC,

By the alternative interior angle theorem,

∠BMN ≅ ∠BAC

∠BNM ≅ ∠BCA

Thus, by AA similarity postulate,

ΔBMN ≅ ΔBAC

By the property of similar triangles,

$\frac{BM}{BA}=\frac{MN}{AC}$

$\frac{BM}{BM+MA}=\frac{MN}{AC}$

$\frac{4}{4+4}=\frac{9}{AC}$

$\frac{4}{8}=\frac{9}{AC}$

$4AC=72\implies AC = 18\text{ ft}$

Thus, The length of AC is 18 ft.

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3 years ago

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