Write an algebraic expression for the following word phrase.
The quotient of and x

The value of the expression such that a and b are integers is 1/9

An exponential function is a mathematical function in the form y = ab^x

Given the indices expression

[tex]\frac{(9\frac{1}{2} )^b}{3^a}[/tex]

This can be simplified as:

[tex]=\frac{(3^{2*\frac{1}{2}} )^b}{3^a}\\=\frac{3^b}{3^a}[/tex]

According to the law of indices, the expression will becomes;

[tex]\frac{3^b}{3^a} =3^{b-a}[/tex]

Recall that a - b = 2, such that b - a = -2. Substitute into the result to have:

[tex]\frac{3^b}{3^a} =3^{b-a}\\3^{b-a}=3^{-2}\\3^{b-a}=1/9[/tex]

Hence the value of the expression such that a and b are integers is 1/9

Learn more on indices here: https://brainly.com/question/10339517

Answer:

A) 24;12;0;-12;-24 because the numbers are gradually going down and they go into the negatives which means they repeat the numbers in the beginning.

B)-36;-25;-16;-9;-4 i am uncertian on this one but i think im doing it right.

[tex]\textit{volume of a cylinder}\\\\ V=\pi r^2 h~~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ r=5.7\\ h=10 \end{cases}\implies \begin{array}{llll} V=\pi (5.7)^2(10)\implies V=324.9\pi \\\\\\ V\approx 1020.7 \end{array}[/tex]

Answer:

Step-by-step explanation:

-lukelaws

did i help?

Answer:

This is what it should look like. The slope is 0 and there are two points. (0,3) (1,3)

Answer:

1/2

Step-by-step explanation:

The slope is the rise over the run, also known as the change in y value over the change in x value

m = 2/4  =1/2

We know it is positive since it goes up from the left to the right

Answer:

The answer is A

Step-by-step explanation:

A pentagon is a polygon that has 5 sides and 5 vertices.

Answer:

Step-by-step explanation:

a.16×25×10×4

= 100 * 160

= 16,000

b,49×99​

= 49 * 100 - 49

= 4900 - 49

= 4,851.

Answer:

They both have a y intercept of 0

Step-by-step explanation:

Linear equations are written in the form y = mx + b. m is the slope and b is the y-intercept. It also states that they intersect at the origin, so they must have a y-intercept of 0.

Answer:

31.5

Step-by-step explanation:

bxh/2

so 9x7=63 and divided by 2 is 31.5

Answer:

31.5

Step-by-step explanation:

use the formula base times high divided by 2

9x7=63

63/2=31.5

Answer:

640 Bacteria

Step-by-step explanation:

First, find out how many times the population will double. Divide the number of minutes by how long it takes for the population to double.

812÷203=4

The population will double 4 times.

Now figure out what the population will be after it doubles 4 times. Multiply the population by 2 a total of 4 times.

402222=640

That calculation could also be written with exponents:

4024=640

After 812 minutes, the population will be 640 bacteria.

Answer:

y = 3x + 2

Step-by-step explanation:

The easiest way to do this, would be to substitute a point (e.g., (2,8)) into your equations to find the one that is true.

(2, 8)

y = 3x - 2

8 = 3(2) - 2

8 = 6 - 2

8 = 4

This statement is false

(2, 8)

y = 3x + 2

8 = 3(2) + 2

8 = 6 + 2

8 = 8

This statement is true

(2, 8)

y = 2x - 3

8 = 2(2) - 3

8 = 4 - 3

8 = 1

This statement is false

(2, 8)

y = 2x + 3

8 = 2(2) + 3

8 = 4 + 3

8 = 7

Therefore, b is the correct answer.

Hope this helps!

The relation that represents the pattern in the table of values is given as; y = 3x + 2

Let us first find the slope of the values from;

m = (y₂ - y₁)/(x₂ - x₁)

m = (8 - 5)/(2 - 1)

m = 3

Thus, the y-intercept is;

5 = 3(1) + c

c = 2

Thus, equation is;

y = 3x + 2

Read more about Linear Equation at; https://brainly.com/question/16834757

#SPJ5

Answer:

160

Step-by-step explanation:

FEJ angle is the large angle and the number in red shows how big it is. Remember the whole thing is 180 degrees.

Answer:

Divide both sides by 5.

Step-by-step explanation:

Divide both sides by same non-zero constant.

Answer:

[tex]\text{k = 4, 5, 6, 7, 8... and onwards}[/tex]

Step-by-step explanation:

The product of k/3 and 12 be greater than 12.

⇒ k/3 × 12 > 12

The first step in determining the possible values of "k" is to simplify the left-hand-side (L.H.S) of the inequality.

⇒ (12 × k)/3 > 12

⇒ (12 ÷ 3) × k > 12

⇒ (4) × k > 12

The next step in determining the possible values of "k" is to isolate the variable. To do this, we can divide 4 both sides.

⇒ [4 × k]/4 > 12/4

⇒ k > 12/4

⇒ k > 3

To satisfy the inequality, the value of k must be greater than 3. Thus, the values of k could be [tex]\text{4, 5, 6... }[/tex] and so on.

Answer:

centroid (2, 2.666666666...)

circumcenter (2, 1.75)

orthocenter (2, 2.5)

Step-by-step explanation:

the coordinates of the centroid of a triangle are

((x1 + x2 + x3)/3, (y1 + y2 + y3)/3)

so, we have

(-4 + 2 + 8)/3 = 6/3 = 2 = x

(0 + 8 + 0)/3 = 8/3 = y = 2.666666666...

the circumcenter is the crossing point of the lines going perpendicular through the midpoint of each side.

the orthocenter is the crossing point of the lines going perpendicular on each side through the opposing vertices (the heights of the triangle).

so, we need to calculate additionally the slopes of 2 sides and their midpoints before we can get these 2 centers. the third side would only confirm the result but not provide additional information.

A = (-4, 0), B = (2, 8), C = (8, 0)

midpoint D of AC = ((-4 + 8)/2, (0+0)/2) = (2, 0)

the slope of AC is

(y2 - y1)/(x2 - x1) = (0 - 0)/(8 - -4) = 0/12 = 0 (a flat line)

the slope of the perpendicular line is -1/slope of original line. which is -1/0 = -infinity.

but don't worry, that means it is a constant line x = ...

and since it has to go through the midpoint D, the perpendicular line is x = 2

midpoint E of BC = ((2+8)/2, (8+0)/2) = (5, 4)

the slope of BC is

(0-8)/(8-2) = -8/6 = -4/3

so, the slope of the perpendicular line is 3/4.

that line is then y = 3/4 x + b

it has to go through the midpoint E

4 = 3/4 × 5 + b = 15/4 + b

16 = 15 + 4b

4b = 1

b = 1/4

so, the full perpendicular line is

y = 3/4 x + 1/4

crossing both perpendicular lines is simply using the first in the second equation :

y = 3/4 × 2 + 1/4 = 6/4 + 1/4 = 7/4 = 1.75

for the orthocenter we can use the same slopes, but the lines go now through the opposing vertices instead through the side midpoints.

so, line 1 is going through B, which makes it also x = 2.

line 2 is going through A, so

0 = 3/4 × -4 + b

0 = -1 + b

b = 1

line 2 is then

y = 3/4 x + 1

crossing these 2 lines gives us

y = 3/4 × 2 + 1 = 6/4 + 4/4 = 10/4 = 5/2 = 2.5

Answer:

5 would be the midian

Step-by-step explanation:

You would need to add 0+2+4+6+8+10

Then count how many numbers there are (6)

Then put it in a fraction

30/6

Then divide and then you get 5

Answer:

21,67

Step-by-step explanation:

0+2+4+6+8+10 all divided by numbers in the set data[6]=21,67

[tex]~~~~~~~~~~~~\stackrel{\textit{payments at the end of the period}}{\textit{Future Value of an ordinary annuity}} \\\\ A=pymnt\left[ \cfrac{\left( 1+\frac{r}{n} \right)^{nt}-1}{\frac{r}{n}} \right] \\\\\\ ~~~~~~ \begin{cases} A=\textit{accumulated amount}\\ pymnt=\textit{periodic payments}\dotfill &279\\ r=rate\to 6\%\to \frac{6}{100}\dotfill &0.06\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{quarterly, thus four} \end{array}\dotfill &4\\ t=years\dotfill &22 \end{cases}[/tex]

[tex]A=279 \left[ \cfrac{\left( 1+\frac{0.06}{4} \right)^{4 \cdot 22}-1}{\frac{0.06}{4}} \right]\implies A=279\left[\cfrac{1.015^{88}~~ - ~~1}{0.015} \right] \\\\[-0.35em] ~\dotfill\\\\ ~\hfill A\approx 50348.47~\hfill[/tex]

i wanted to ask what exactly the question is

??

Answer:

100,00

Step-by-step explanation:

In order to find this, you would divide 450,000,000 by 4500. You would then get the final answer of 100,000. Hope this helps!

Explanation:

The volume formula ...

  V = BH

is a formula for the volume of a general prism whose cross sections parallel to the base all have area B. The distance between the parallel bases is represented by H.

__

To use this formula to find the volume of a tent, the area of the end of the tent would be substituted for B, and the length of the tent (distance between the ends) would be substituted for H.

An appropriate formula would need to be used for the end area.

Answer:

Step-by-step explanation:

To find the value of x, isolate it on one side of the equation.

First, add by -6 from both sides.

→ -6+x+-6=-4+6

Solve.

→ -4+6=2

x=2

I hope this helps you! Let me know if my answer is wrong or not.

Answer:

y = 29

Step-by-step explanation:

Since it is a vertical angle, both angles represented by the equations are equal. Meaning we can set them equal to each other and find y by simplifying.

4y-8 = 79+y

-79     -79

4y-87 = y

-4y       -4y

-87 = -3y

Divided by -3

29 = y

Answer:

the answer is x=15.....

Answer:

Step-by-step explanation:

(5x+30)=7x Subtract 7x from both sides. 5x+30−7x=0 Combine 5x and −7x to get −2x. −2x+30=0 Subtract 30 from both sides. Anything subtracted from zero gives its negation. −2x=−30 Divide both sides by −2. x= −2 −30 ​ Divide −30 by −2 to get 15.                 answer should be x=15

Answer:

Infinitely many solutions

Step-by-step explanation:

(1) ---- 6x - 4y = 9

(2)---- 12x - 8y = 18

If you multiply (1) by 2 → 12x - 8y = 18 --- (3)

and then when you compare (2) and (3), you'll find that you still can't find the value of X and Y therefore, there's infinitely many solutions

Answer:

Infinitely Many Solutions!!

Step-by-step explanation:

You need to do elimination method!!

This is because we need to top the equation to cancel out and become negative.  

6x−4y=9

12x−8y=18

You could do 6x and everything multiplied by -2. But 4y can do the same too!!

I rather do 4y x -2!

-12x+8y=-18

12x−8y=18

Everything cancels out!!

0=0

But 0 equals to 0 goes on forever so the answer is infinite solutions!!

**The reasoning behind the two other choices**

No solution would be like -3=0 which is not our case!!

One solution has something that goes into everything evenly!

Using the normal distribution, it is found that the value of x is of 3.585.

In a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

In this problem, the mean and the standard deviation are given, respectively, by [tex]\mu = 2.5, \sigma = 0.5[/tex].

The value of x is the 100 - 1.5 = 98.5th percentile, which is X when Z = 2.17, hence:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]2.17 = \frac{X - 2.5}{0.5}[/tex]

[tex]X - 2.5 = 0.5(2.17)[/tex]

[tex]X = 3.585[/tex]

Hence the value of x is of 3.585.

More can be learned about the normal distribution at https://brainly.com/question/24663213