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3 years ago

Factor 3^5 + 12^4 − 36^3

Mathematics

2 answers:

Troyanec [42]3 years ago

8 0

Answer:

-39501

Step-by-step explanation:

3^5 + 12^4 − 36^3 can be rewritten with 3^3 as a factor showing up one or more times in each term:

(3^3)(3^2) + 3^4*4^4 - (6^2)^3 or:

(3^3)(3^2) + (3^3)*3*256 - (6^6) or:

same same - 3^6*2^6

Factoring out 3^3, we get:

(3^3)(3^2) + 3*256 - 3^3*64) or

(3^3){9 + 256 -1728} or

3^3{-1463}, oe

-39501

Crazy boy [7]3 years ago

7 0

Find the greatest common factor among the bases, which is 3. Now find the lowest power that they can all go in to, that’s also 3. So we’re factoring our a 3^3 to get :

3^3[(1^2) + (4^1) + (12)]

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How many whole numbers leave a remainder of 2 when divided into 56, and a remainder of 1 when divided into 28? a.) 0 b.) 2 c.) 3

meriva

56 would have a remainder of 2 using multiples of 3

56/3 = 18 remainder 2

56/6 = 9 remainder 2

56/9 = 6 remainder 2

56/18 = 3 remainder 2

56/27 = 2 remainder 2

Now divide 28 by the above numbers to see which ones have 1 as a remainder:

28/3 = 9 remainder 1

28/6 = 4 remainder 4

28/9 = 3 remainder 1

28/18 = 1 remainder 10

28/27 = 1 remainder 1

There are 3 numbers that will work.

Answer: c. 3

4 0

2 years ago

Solve by completing the square: x^2 + 3x - 9 = 0

tekilochka [14]

Answer:

Step-by-step explanation:

x^2 + 3x - 9 =0

By comparing with the equation ax^2+bx+c = 0,

we get,

a = 1, b=3, c = -9

we know the formula for x is,

x = (-b±√(b^2 - 4ac))/2a

x = (-3±√45)/2

x = (-3±3√5)/2

x = (-3+3√5)/2, (-3-3√5)/2

6 0

3 years ago

Read 2 more answers

A rectangle has length 72 cm and width 56 cm. The other rectangle has the same area as this one, but its width is 21 cm. What is

katovenus [111]

Answer:

The constant of variation is 4032

Step-by-step explanation:

Given:

Let a rectangle (say A) has length of rectangle(l)= 72 cm and width of rectangle(w) = 56 cm.

Area of rectangle is multiply its length by its width.

Then,

area of rectangle (A) = $l \times w$ = $72 \times 56$ = 4,032 square cm.

It is given that the other rectangle B has the same area as the rectangle A.

Then, the area of rectangle (B) = area of rectangle (A) = 4,032 square cm. .......[1]

First find the length of rectangle B:

Given: width of the rectangle B is 21 cm

then, by definition

Area of rectangle B = $l \times w$ = $l \times 21$

From [1];

4032 = $l \times 21$

Divide 21 both sides we get;

$l =\frac{4032}{21} = 192$ cm

therefore, the length of rectangle B is 192 cm

To find the constant variation:

if y varies inversely as x

i.e, $y \propto \frac{1}{x}$

⇒ $y = \frac{k}{x}$ where k is the constant variation.

or k = xy

As area of rectangle is multiply its length by width.

This is the inversely variation.

as: $l \propto \frac{1}{w}$

or $l = \frac{A}{w}$ where A is the constant of variation

Since, the area (A) of both the rectangles are constant.

therefore, the constant of variation is, 4032

5 0

3 years ago

Suppose that in a random selection of 100 colored candies, 24% of them are blue. The candy company claims that the percentage

LuckyWell [14K]

Answer:

We conclude that the percentage of blue candies is equal to 23% at 0.01 significance level.

Step-by-step explanation:

We are given that in a random selection of 100 colored candies, 24% of them are blue.

The candy company claims that the percentage of blue candies is equal to 23%.

Let p = percentage of blue candies.

So, Null Hypothesis, $H_0$ : p = 23% {means that the percentage of blue candies is equal to 23%}

Alternate Hypothesis, $H_A$ : p $\neq$ 23% {means that the percentage of blue candies is different from 23%}

The test statistics that would be used here One-sample z proportion test statistics;

T.S. = $\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n}} }$ ~ N(0,1)

where, $\hat p$ = sample proportion of blue colored candies = 24%

n = sample of colored candies = 100

So, test statistics = $\frac{0.24-0.23}{\sqrt{\frac{0.24(1-0.24)}{100}} }$

= 0.234

The value of z test statistics is 0.234.

Now, at 0.01 significance level the z table gives critical values of -2.5758 and 2.5758 for two-tailed test.

Since our test statistics lies within the range of critical values of z, so we have insufficient evidence to reject our null hypothesis as it will not fall in the rejection region due to which we fail to reject our null hypothesis.

Therefore, we conclude that the percentage of blue candies is equal to 23%.

6 0

3 years ago

What are the solutions to the equation (x – 6)(x + 8) = 0?

Ghella [55]

Answer:

x₁ = 6 and x₂ = 8

Step-by-step explanation:

See the picture below

8 0

3 years ago