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3 years ago

What is the greatest common factor of the terms 14c-2dand 42c3d ?

Mathematics

1 answer:

AlekseyPX3 years ago

7 0

That would be 14c^2d

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Consider the function f(x) = x² – 3x – 4 and complete parts (a) through (C). (a) Find f(a+h); f(a+h)-f(a) (b) Find (c) Find the

Artist 52 [7]

Answer:

(a)

$f(a+h)=a^{2} +2ah+h^{2} -3a-3h-4$

(b)

$f(a+h)-f(a)=2ah+h^{2} -3h$

(c)

$\frac{df(a+h)}{dx} \left \{ { \atop {a=7}} \right. =2h+11$

Step-by-step explanation:

(a)

Simply evaluate (a+h) in the function:

$f(a+h)=(a+h)^{2} -3(a+h)-4=a^{2} +2ah+h^{2} -3a-3h-4$

(b)

Evaluate (a) in the function:

$f(a)=a^{2} -3a-4$

Using the previous answers lets calculate f(a+h)-f(a)

$f(a+h)-f(a)=a^{2} +2ah+h^{2} -3a-3h-4-(a^{2} -3a-4)=2ah+h^{2} -3h$

$\frac{df(a+h)}{dx} \left \{ { \atop {a=7}} \right. =2a+2h-3=2(7)+2h-3=2h+14-3=2h+11$

7 0

3 years ago

Francis works at Carlos Bakery and is making cookie trays. She has 48 chocolate chip cookies, 64 rainbow cookies, and 120 oatmea

amm1812

The number of cookies and trays are illustrations of greatest common factors.

The number of trays is 8
6 chocolate chips, 8 rainbows and 15 oatmeal cookies would fit each tray

The given parameters are:

$\mathbf{Chocolate\ chip=48}$

$\mathbf{Rainbow=64}$

$\mathbf{Oatmeal=120}$

<u>(a) The number of trays</u>

To do this, we simply calculate the greatest common factor of 48, 64 and 120

Factorize the numbers, as follows:

$\mathbf{48 = 2 \times 2 \times 2 \times 2 \times 3}$

$\mathbf{64 = 2 \times 2 \times 2 \times 2 \times 2 \times 2}$

$\mathbf{120 = 2 \times 2 \times 2 \times 3 \times 5}$

So, the GCF is:

$\mathbf{GCF= 2 \times 2 \times 2}$

$\mathbf{GCF= 8}$

Hence, the number of tray is 8

<u>(b) The number of each type of cookie</u>

We have

$\mathbf{Chocolate\ chip=48}$

$\mathbf{Rainbow=64}$

$\mathbf{Oatmeal=120}$

Divide each cookie by the number of trays

So, we have:

$\mathbf{Chocolate\ chip = \frac{48}{8} = 6}$

$\mathbf{Rainbow = \frac{64}{8} = 8}$

$\mathbf{Oatmeal = \frac{150}{8} = 15}$

Hence, 6 chocolate chips, 8 rainbows and 15 oatmeal cookies would fit each tray

Read more about greatest common factors at:

brainly.com/question/11221202

4 0

2 years ago

Can u guys help me with this problem

netineya [11]

Answer:

$-0.7$ or $-\frac{7}{10}$

Step-by-step explanation:

$-0.75-(-\frac{2}{5})+0.4+(-\frac{3}{4})$

The opposite of $-\frac{2}{5}$ is $\frac{2}{5}$

$-0.75 + \frac{2}{5} +0.4 - \frac{3}{4}$

Convert decimal number −0.75 to fraction $-\frac{75}{100}$ .

Reduce the fraction $-\frac{75}{100}$ to lowest terms by extracting and canceling out 25.

$-\frac{3}{4} + \frac{2}{5}+0.4-\frac{3}{4}$

Least common multiple of 4 and 5 is 20. Convert $-\frac{3}{4}$ and $\frac{2}{5}$ to fractions with denominator 20.

$-\frac{15}{20}+ \frac{8}{20} +0.4 - \frac{3}{4}$

Since $-\frac{15}{20}$ and $\frac{8}{20}$ have the same denominator, add them by adding their numerators.

$\frac{-15 +8}{20} +0.4-\frac{3}{4}$

Add -15 and 8 to get -7

$-\frac{7}{20}+0.4-\frac{3}{4}$

Convert decimal number 0.4 to fraction $\frac{4}{10}$ . Reduce the fraction $\frac{4}{10}$ to lowest terms by extracting and canceling out 2.

$-\frac{7}{20}+\frac{2}{5}-\frac{3}{4}$

Least common multiple of 20 and 5 is 20. Convert $-\frac{7}{20}$ and $\frac{2}{5}$ to fractions with denominator 20.

$-\frac{7}{20}+\frac{8}{20}-\frac{3}{4}$

Since $-\frac{7}{20}$ and $\frac{8}{20}$ have the same denominator, add them by adding their numerators.

$20-7+8-\frac{3}{4}$

Add -7 and 8 to get 1.

$\frac{1}{20}-\frac{3}{4}$

Least common multiple of 20 and 4 is 20. Convert $\frac{1}{20}$ and $\frac{3}{4}$ to fractions with denominator 20.

$\frac{1}{20}-\frac{15}{20}$

Since $\frac{1}{20}$ and $\frac{15}{20}$ have the same denominator, subtract them by subtracting their numerators.

$\frac{1}{20}-15$

Subtract 15 from 1 to get -14.

$20-14$

Reduce the fraction $-\frac{14}{20}$ to lowest terms by extracting and canceling out 2.

$-\frac{7}{10}$ or $-0.7$

Hope this helps! Brainliest would be much appreciated! Have a great day! :)

8 0

2 years ago

The dimensions of a triangular prism are shown.

Serhud [2]

9514 1404 393

Answer:

B. 32 square inches

Step-by-step explanation:

Each of the two triangular faces has an area of ...

A = (1/2)bh = (1//2)(6 in)(4 in) = 12 in²

The lateral surface area is the product of the prism height (0.5 in) and the perimeter of the base.

LA = (0.5 in)(5 in +5 in + 6 in) = 8 in²

So, the total area is the area of the two base and the lateral area:

SA = 2A +LA

SA = 2(12 in²) +8 in² = 32 in²

The surface area of the prism is 32 square inches.

7 0

3 years ago

Read 2 more answers

NEED HELP IMMEDIATELY Which expression is equivalent to one over four n − 16?

Gemiola [76]

B. 1/4(n - 64)

Multiplying n and -64 by 1/4 leaves you with 1/4n - 16, the original equation.

5 0

3 years ago