Select all the expressions which have 3 as the greatest common factor of the terms.
b + 3 + 6c
27n + 66p
38 – 9j + 6k
12x + 75y + 21
–32 – 24z

Answer:

288

Step-by-step explanation:

please review the attachment for step by step soluation

Given:

LCM(a,b) = 90 and GCD(a,b) = 3.

b is three more than a.

To find:

The values of a and b.

Solution:

We have,

LCM(a,b) = 90

GCD(a,b) = HCF(a,b) = 3

According to the question,

[tex]b=a+3[/tex]

If a and b are two positive integers, then

[tex]a\times b=HCF(a,b)\times LCM(a,b)[/tex]

[tex]a\times (a+3)=3\times 90[/tex]

[tex]a^2+3a=270[/tex]

[tex]a^2+3a-270=0[/tex]

Splitting the middle terms, we get

[tex]a^2+18a-15a-270=0[/tex]

[tex]a(a+18)-15(a+18)=0[/tex]

[tex](a+18)(a-15)=0[/tex]

Using zero product property, we get

[tex]a+18=0[/tex] and [tex]a-15=0[/tex]

[tex]a=-18[/tex] and [tex]a=15[/tex]

a is a positive integer so it cannot be negative. So, a=15.

Now,

[tex]b=a+3[/tex]

[tex]b=15+3[/tex]

[tex]b=18[/tex]

Therefore, the value of a is 15 and the value of b is 18.

Answer:

[tex]\displaystyle (-\infty, -\frac{1}{6})[/tex]

Step-by-Step explanation:

We have the function:

[tex]\displaystyle y=\int_{1}^{x}\frac{1}{3+t+3t^2}\, dt[/tex]

And we want to find the interval for which y is concave upwards.

Therefore, we will need to find the second derivative of y, find its inflection points (where y''=0), and test for values.

So, let's take the derivative of both sides with respect to x. So:

[tex]\displaystyle y^\prime=\frac{d}{dx}\Bigg[\int_{1}^{x}\frac{1}{3+t+3t^2}\, dt\Bigg][/tex]

By the Fundamental Theorem of Calculus:

[tex]\displaystyle y^\prime=\frac{1}{3+x+3x^2}[/tex]

So, we will take the derivative again. Hence:

[tex]\displaystyle y^\prime^\prime=\frac{d}{dx}\Big[\frac{1}{3+x+3x^2}\Big]=\frac{d}{dx}\Big[(3+x+3x^2)^{-1}\Big][/tex]

We will use the chain rule. Let:

[tex]\displaystyle u=x^{-1}\text{ and } v=3+x+3x^2[/tex]

Differentiate:

[tex]\displaystyle y^\prime^\prime=-(3+x+3x^2)^{-2}(1+6x)[/tex]

Rewrite:

[tex]\displaystyle y^\prime^\prime=-\frac{6x+1}{(3+x+3x^2)^2}[/tex]

So, points of inflection, where the concavity changes, is whenever the second derivative is 0 or undefined.

We can see that the second derivative will never be undefined since the denominator can never equal 0.

So, our only possible inflection points are when it's equal to 0. Hence:

[tex]\displaystyle 0=-\frac{6x+1}{(3+x+3x^2)^2}[/tex]

Multiplying both sides by the denominator gives:

[tex]0=-(6x+1)[/tex]

Then it follows that:

[tex]\displaystyle x=-\frac{1}{6}[/tex]

So, our only possible point of inflection is at x=-1/6.

We will test for values less than and greater than this inflection point.

Testing for x=-1, we see that:

[tex]\displaystyle y^\prime^\prime=-\frac{6(-1)+1}{3+(-1)+3(-1)^2}=1>0[/tex]

Since the result is positive, y is concave up for all values less than -1/6.

And testing for x=0, we see that:

[tex]\displaystyle y^\prime^\prime=-\frac{6(0)+1}{3+(0)+3(0)^2}=-\frac{1}{3}[/tex]

Since the result is negative, y is concave down for all values greater than -1/6.

Therefore, the interval for which y is concave up is:

[tex]\displaystyle (-\infty, -\frac{1}{6})[/tex]

Note that we use parentheses instead of brackets since at exactly x=-1/6, our graph is neither concave up nor concave down.

Answer:

x<3

Step-by-step explanation:

2x<6
/     /

2    2

x<3

Answer:

The average daily maximum temperature is

26.56 °C higher than the average daily minimum temperature

Step-by-step explanation:

Here, we simply want to calculate how higher is the average daily maximum temperature to average daily minimum temperature

We simply proceed to subtract the two

Mathematically, that will be;

21.85 - (-4.7)

= 21.85 + 4.7

= 26.56 °C

The unknown number will be equal to 64.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that the cube of the product of 8 and the number is 512. The unknown number will be calculated as,

8 x = 512

x = 512 / 8

x = 64

The number which is the product of 8 will be equal to 64.

The complete question is given below.

The cube of the product of 8 and the number is 512. What is the number?

To know more about an expression follow

https://brainly.com/question/1713767

#SPJ2

Answer:

In Step 2.

Step-by-step explanation:

They should have distributed the 2 to the x and 1 instead of subtracting it.

Answer:

one that looks like triangle

Step-by-step explanation:

Answer:

x-83=70

x = 70 + 83

x= 153

Answer: use mahthway it hels

Step-by-step explanation:

Answer:

0.443 hours

Step-by-step explanation:

time = total distance / mph

time = 50 / 112.9094

time ≈ 0.443 hours

Answer:

0.443 hours

Explanation:

Given following:

Formula:

[tex]\sf time \ taken = \dfrac{distance}{speed}[/tex]

Substitute values to find time taken:

[tex]\sf \rightarrow time = \dfrac{50}{112.9094 }[/tex]

evaluate

[tex]\sf \rightarrow time = 0.4428329262[/tex]

rounded to nearest thousandth

[tex]\sf \rightarrow time = 0.443[/tex]

Answer:

It is A or D but mostly A is correct.

Step-by-step explanation:

give brainliest

Heres the answer welcome btw

Answer:

1: 2 and $3.072

Step-by-step explanation:

According to the question, the data provided is as follows

10 half gallons

For this she paid $15.36

Based on the above information,

The ratio in fractional form is

= 1 ÷ 2

= 1 : 2

And, the cost of gasoline per gallon is

Since  half of 10 gallons is 5

And, the amount paid is $15.36

So, the cost of gasoline per gallon is

= $15.36 ÷ 5

= $3.072

Step-by-step explanation:

Answer:

17.5 hours

Step-by-step explanation:

divide 15 by 3 to get 5,

multiply 5 by the amount of hours it takes to draw 3 illustrations so 5 x 3.5, the answer is 17.5

Answer:

Volume of cylinder is: Volume=1808.64 ft³

Step-by-step explanation:

Height of cylinder = 9 ft

Base diameter of cylinder = 16 ft

We need to find volume of cylinder .

The formula used is: [tex]Volume=\pi r^2h[/tex]

We need radius:

The radius = diameter/2 = 16/2 = 8 ft

Putting values and finding volume of cylinder

[tex]Volume=\pi r^2h[/tex]

[tex]Volume=3.14\times (8)^2\times (9) \\Volume=3.14\times 64\times (9) \\Volume=1808.64 \: ft^3[/tex]

So, Volume of cylinder is: Volume=1808.64 ft³

Answer:

3/4

Step-by-step explanation:

21/16 ÷ 7/4

21/16 × 4/7

3/4

Answer:

8:20

Step-by-step explanation:

8+20=28 and all that has happened is the ratio got bigger.

Answer: infinite

Step-by-step explanation: since they have the same slope and y interscept it is a coincident line and has infinite solutions

y= 4-x

y= 4-x

Answer:

infinitely many

Step-by-step explanation:

when you simplify, you get the following two equations:

y=-x+4

y=-x+4

those two equations are the same, therefore it is many

Answer:

y-100

x-250

Step-by-step explanation:

because the lines are insecting the other lines on that line

Answer: About 16 snaps

Step-by-step explanation:

In a box and whisker plot, the rightmost line in the "box" of the plot is the third quartile, which represents the 75th percentile.

In this graph, although it is difficult to pinpoint the EXACT number of snaps sent, the 75th percentile would be marked at about 16 snaps.

Answer:

Domain: -3 ≤ x ≤ 3

Range: -2 ≤ y ≤ 4

General Formulas and Concepts:

Algebra I

Step-by-step explanation:

According to the graph, our x-values span from -3 to 3. Since both are closed dot, they are inclusive in the domain:

[-3, 3] or -3 ≤ x ≤ 3

According to the graph, our y-values span from -2 to 4. Since both are closed dot, they are inclusive in the range:

[-2, 4] or -2 ≤ y ≤ 4

[tex]\frac{x}{2}-\frac{2}{x+1}=1[/tex]

We have 2 denominators that we need to get rid of. Whenever there are the denominators, all we have to do is multiply all whole equation with the denominators.

Our denominators are both 2 and x+1. Therefore, we multiply the whole equation by 2(x+1)

[tex]\frac{x}{2}[2(x+1)]-\frac{2}{x+1}[2(x+1)] = 1[2(x+1)][/tex]

Then shorten the fractions.

[tex]\frac{x}{2}[2(x+1)]-\frac{2}{x+1}[2(x+1)] = 1[2(x+1)]\\x(x+1)-2(2)=1(2x+2)[/tex]

Distribute in all.

[tex]x^2+x-4=2x+2[/tex]

We should get like this. Because the polynomial is 2-degree, I'd suggest you to move all terms to one place. Therefore, moving 2x+2 to another side and subtract.

[tex]x^2+x-4-2x-2=0\\x^2-x-6=0\\[/tex]

We are almost there. All we have to do is, solving for x by factoring. (Although there are more than just factoring but factoring this polynomial is faster.)

[tex](x-3)(x+2)=0\\x=3,-2[/tex]

Thus, the answer is x = 3, -2

Answer:

Top one

Step-by-step explanation:

It is more appropriate to measure the speck of dust using millimeters because that is most similar to the scale of the speck's size.

Answer: I believe it's 13 > 5x or 5x+13. . But I'm not completely sure.