Which equation represents a proportional relationship? A) y = 3x 4 B) y = 3 4x C) y = 3x 4 + 1 D) y = 3 4x + 1

Answer:

Power: (1/5)^3, 2^6

Expanded: 5x5, 6x6x6, 3x3x3/4, 2x2x2x2x2x2

How to say it: 5 raised to the 2nd power, 6 raised to the 3rd power, 3 raised to the 3rd power over 4

Value: 25, 216, 1/125, 9/4, 64

Step-by-step explanation:

Answer:

(x-2)/(2x+8)

Step-by-step explanation:

The first step to solve this expression is to use a² - 2a b + b² = (a - b)² to factor the expression

Factor out 2 from the expression

Write 2x as a difference

Factor out x from the expression

Factor out -2 from the expression

Factor out x + 4 from the expression

Reduce the fraction with x - 2

Finally,, distribute 2 through the parenthesis to find your answer

This means that the correct answer to your question is (x-2)/(2x+8)

Answer:

 x + 6

-----------      for all x EXCEPT x = -6

  x + 2

Step-by-step explanation:

Note that the numerator, x^2 + 12 x + 36, factors into (x + 6)^2, and that

the denominator factors into (x + 6)(x - 2).

Thus, the given expression reduces to:

  (x + 6)(x + 6)

-----------------------

  (x + 6)(x + 2)

and can be reduced to:

 x + 6

-----------         This is true for all x EXCEPT x = -6.  At x = -6, the expression

  x + 2            is not defined.

Answer:

She skates at 0.5 miles per hour :) hope it helped

Answer:

see explanation

Step-by-step explanation:

Since the figures are similar then the ratio of corresponding sides are equal, that is

[tex]\frac{8}{x}[/tex] = [tex]\frac{18}{6}[/tex] ( cross- multiply )

18x = 48 ( divide both sides by 18 )

x = [tex]\frac{48}{18}[/tex] = [tex]\frac{8}{3}[/tex]

AND

[tex]\frac{5}{y}[/tex] = [tex]\frac{18}{6}[/tex] ( cross- multiply )

18y = 30 ( divide both sides by 18 )

y = [tex]\frac{30}{18}[/tex] = [tex]\frac{5}{3}[/tex]

Answer:

2x-1 x -3x1=-9?

Step-by-step explanation:

This might be the right answer unless it is multiple choice

Answer:

Step-by-step explanation:

n - 4, n - 2, n, n + 2, n + 4 - five odd consecutive integers

The equation:

(n - 4) + (n - 2) + n + (n + 2) + (n + 4) = 295         combine like terms

(n + n + n + n + n) + (-4 - 2 + 2 + 4) = 295

5n = 295        divide both sides by 5

n = 59

the scale factor is .25

6×.25=1.5

Answer:

-3.2171798824

Step-by-step explanation:

Answer:

slope = [tex]\frac{5}{2}[/tex]

Step-by-step explanation:

Select any 2 ordered pairs from the given table, the use the slope formula to calculate the slope m

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (2, 5) and (x₂, y₂ ) = (4, 10) ← 2 ordered pairs from table

m = [tex]\frac{10-5}{4-2}[/tex] = [tex]\frac{5}{2}[/tex]

Answer:

The weight of the three blades together is [tex]134\ g[/tex]

Step-by-step explanation:

step 1

Find the area of the circle

The area of the circle is equal to

[tex]A=\pi r^{2}[/tex]

we have

[tex]r=4\ in[/tex]

assume

[tex]\pi=3.14[/tex]

substitute

[tex]A=(3.14)(4)^{2}[/tex]

[tex]A=50.24\ in^{2}[/tex]

step 2

Find the area of the 3 blades

we know that

The area of the 3 blades represent a central angle of 60 degrees, so

its a 1/6 of the area of complete circle

[tex]A=50.24/6=8.37\ in^{2}[/tex]

step 3

Find the weight of the three blades together to the nearest gram

[tex](8.37\ in^{2})*(16\ g/in^{2})=134\ g[/tex]

C. 226.87 in 2

Using the area of a circle formula

A=πr2

Answer:

226.87 in^2

Step-by-step explanation:

Formula

Area = pi*r^2

r = d/2

Givens

pi = 3.15

d = 17 inches.

Solution

r = d/2

r = 17/2

r = 8.5

Area = pi*r^2

Area = 3.14 * 8.5^2

227.87 in^2

Answer:

[tex]-\frac{2}{8} >-\frac{2}{3}[/tex]

Step-by-step explanation:

To compare fractions is useful to express the fractions as decimals and compare the values of the decimals first.

Using a calculator we can find that [tex]-\frac{2}{3} =-0.66666...[/tex] and [tex]-\frac{2}{8} =-0.25[/tex].

Now, remember that wen comparing negative numbers the smallest number is the greater one; this is because the closest a negative number is to zero the greatest is value.

-0.66666... and -0.25 are both negative. Since -0.25 is smaller (closer to zero), -0.25 is bigger than -0.66666... In other words, -0.25 > -0.66666...

We know that [tex]-\frac{2}{3} =-0.66666...[/tex] and [tex]-\frac{2}{8} =-0.25[/tex], so we can get back to our original fractions:

[tex]-\frac{2}{8} >-\frac{2}{3}[/tex]

We can conclude that [tex]-\frac{2}{8}[/tex] is greater than [tex]-\frac{2}{3}[/tex]

Answer:

[tex]f^{-1}(x) = log_{12}(y)[/tex]

Step-by-step explanation:

We have the following function

y = 12^x, and we need to find the inverse function.

To find the inverse function we should solve the equation for "x". To do so, first, we need to:

1. Take the logarithm in both sides of the equation:

lg_12 (y) = log _12 (12^x)

(Please read lg_12 as: "Logarithm with base 12")

From property of logarithm, we know that lg (a^b) = b*log(a)

Then:

lg_12 (y) = x*log _12 (12)

We also know that log _12 (12) = 1

Then:

x = log_12(y).

Then, the inverse of: y= 12^x is:

[tex]f^{-1}(x) = log_{12}(y)[/tex]

Answer:

B 2 2/3

Step-by-step explanation:

Triangles ADB and CDB are similar. Therefore similar parts can form a proportion.

AD/DB = DB/DC

AD = ?

DB = 4

DC = 6

x/4 = 4/6    Cross multiply

6x = 16

6x/6 = 16/6

x = 2 4/6 or x = 2 2/3

It's B

ANSWER

[tex]AD =2 \frac{2}{3}[/tex]

EXPLANATION

According the Altitude Theorem, the height of the triangle is equal to the geometric mean of the two segment it creates on the hypotenuse.

This implies that:

[tex] {4}^{2} =6 AD[/tex]

[tex]16 = 6 AD[/tex]

Divide both sides by 6.

[tex]AD = \frac{16}{6} [/tex]

Simplify

[tex]AD = \frac{8}{3} [/tex]

Change to mixed numbers

[tex]AD =2 \frac{2}{3} [/tex]

Answer:

Well in opinion, i think "rolling a standard number cube and getting an even number"

Answer:

Both events have the same likeliness of happening.

Step-by-step explanation:

A number cube has 6 numbers and 3 of them are even so the probability of rolling an even number is 3/6, which is 1/2. A coin has two sides, so the probability of flipping a coin heads up is 1/2. Rolling an even number on a number cube and flipping a coin heads up both have a 1/2 probability.

Answer:

Option d. [tex]f(x)=\$1,000(1+0.0355)^{x}[/tex]  

Step-by-step explanation:

we know that    

The compound interest formula is equal to  

[tex]A=P(1+\frac{r}{n})^{nt}[/tex]  

where  

A is the Final Investment Value  

P is the Principal amount of money to be invested  

r is the rate of interest  in decimal

t is Number of Time Periods  

n is the number of times interest is compounded per year

in this problem we have  

[tex]t=x\ years\\ P=\$1,000\\ r=0.0355\\n=1[/tex]  

substitute in the formula above  

[tex]A=\$1,000(1+\frac{0.0355}{1})^{1*x}[/tex]  

[tex]A=\$1,000(1+0.0355)^{x}[/tex]  

Convert to function notation

[tex]f(x)=\$1,000(1+0.0355)^{x}[/tex]  

Answer:

The answer is B

Inequalities help us to compare two unequal expressions. The correct option is A, (6+x)/15>(9/10).

Inequalities help us to compare two unequal expressions. Also, it helps us to compare the non-equal expressions so that an equation can be formed. It is mostly denoted by the symbol <, >, ≤, and ≥.

Given that Melinda will take 15 quizzes this semester. She would like to score a B or better on at least 90% of them.  Therefore, the ratio of the number of questions done to the total number of questions should be greater than 90%.

Also, given that Melinda has already gotten a b or better on 6 quizzes. Therefore, we can write the inequality as,

(6+x)/15 > 90%

(6+x)/15 > 90/100

(6+x)/15 > 9/10

Learn more about Inequality:

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Answer: There are 150 bars in a case, and 2 cases per day are used (or 300 bars), Thus, in 7 days you would use 7 x 2 or 14 cases, or 2100 bars.

Step-by-step explanation:

Answer:

14 cases of soap bars.

Step-by-step explanation:

In one case of soap bars there is = 150 bars

You use amount of soap bars per day = 300

You need to order to have enough for 7 days  = 300 × 7 = 2100 bars

150 bars ⇒ 1 case

2100 bars ⇒ [tex]\frac{2100}{150}[/tex] = 14 case

You need to order 14 case of soap bars for 7 days.

Subtract 1/3 from both sides

x/12 = 5/6 - 1/3

Simplify 5/6 - 1/3 to 1/2

x/12 = 1/2

Multiply both sides by 12

x = 12 × 12

Simplify 1/2 × 12 to 12/2

x = 12/2

Simplify 12/2 to 6

x = 6

Hi! The answer is c downloads per a day

Answer:

The correct answer is option A. 18x + 15

Step-by-step explanation:

It is given an expression in variable x,

5(4x + 3) - 2x

To simplify the given expression

5(4x + 3) - 2x = (5 * 4x) + (5 * 3) - 2x   (open the bracket)

  = 20x + 15 - 2x

  = 20x - 2x + 15

  = 18x + 15

Therefore the correct answer is 18x + 15

The correct option is option A.  18x + 15

6x + 9

Combine the like terms. 2x + 3x + x = 6x, and 9 just stays the same. This is as simple as the equation can get without knowing what 2x + 9 + 3x + x equals.

If 2x+9+3x+x= then 6x+9 will be x= 15

Answer:

  [tex]2a^{\frac{5}{2}}-4a^{-\frac{1}{2}}[/tex]

Step-by-step explanation:

It looks like you want to expand the expression ...

  [tex]\sqrt{a}\left(2a^2 -\dfrac{4}{a}\right)[/tex]

Use the distributive property and rules of exponents.

  [tex]=2a^{(\frac{1}{2}+2)}-4a^{(\frac{1}{2}-1)}\\\\=\boxed{2a^{\frac{5}{2}}-4a^{-\frac{1}{2}}}[/tex]

_____

The relevant rules of exponents are ...

  √a = a^(1/2)

  1/a = a^-1

  (a^b)(a^c) = a^(b+c)

To simplify the expression {x⁵}/{x²}, you subtract the exponents (5 - 2), resulting in x³, which is x cubed.

The given expression is {x⁵}/{x²}. To simplify this, we use the Division of Exponentials rule, which states that when dividing two expressions with the same base, you subtract the exponent of the denominator from the exponent of the numerator.

In this case, we subtract 2 from 5 (because the base is x and we have x to the power of 5 divided by x to the power of 2), giving us:

(x⁵⁻² which simplifies to (x³).

The simplified expression is therefore x cubed, or (x³).

Answer:

∠A = 58°

Step-by-step explanation:

The exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.

∠ACD is an exterior angle

∠A and ∠B are the opposite interior angles, thus

∠A + 80 = 138 ( subtract 80 from both sides )

∠A = 58°

ANSWER

[tex]Volume = 480.0{cm}^{3} [/tex]

EXPLANATION

The volume of the square pyramid is given by;

[tex]Volume = \frac{1}{3} {l}^{2} \times h[/tex]

Where l=12cm is the length of the square base and h=10cm is the height of the pyramid.

We substitute the values into the formula to get;

[tex]Volume = \frac{1}{3} \times {12}^{2} \times 10 {cm}^{3} [/tex]

This simplifies to,

[tex]Volume = \frac{1}{3} \times {12} \times 12\times 10 {cm}^{3} [/tex]

[tex]Volume = 4 \times 12\times 10 {cm}^{3} [/tex]

[tex]Volume = 480.0{cm}^{3} [/tex]

Third option is correct.

Answer:

The correct option is 3.

Step-by-step explanation:

The volume of a square pyramid is

[tex]V=\frac{1}{3}(\text{Base area})h[/tex]

[tex]V=\frac{1}{3}a^2h[/tex]                  .... (1)

Where, a is th side of base and h is the height of pyramid.

From the given figure it is clear that the height of the pyramid is 10 cm and the  length of base is 12 cm.

Substitute a=12 and h=10 in equation (1), to find the volume of the square pyramid.

[tex]V=\frac{1}{3}\times (12)^2\times (10)[/tex]

[tex]V=\frac{1}{3}\times (144)\times (10)[/tex]

[tex]V=(48)\times (10)[/tex]

[tex]V=480[/tex]

The volume of pyramid is 480 cm³. Therefore the correct option is 3.

The right answer is Function F.

Explanation:

f(x)=10(2)+2=22

g(x)= 2^(2)=4

h (x)=(2)^2+2 (2)+1=9

Answer:

A, Function f

Step-by-step explanation:

to see which function has the greatest output when x = 2, we simply plug in 2 into each function

f(2) = 10(2) + 2 ---> 20 + 2 = 22

f(2) = 22

g(2) = [tex]2^(2)[/tex] = 4

g(2) = 4

h(2) = (2)² + 2(2) + 1 ----> 4 + 4 + 1 = 9

h(2) = 9

comparing the functions, we see that the function with the largest output is f(x)

our answer is A, Function F

Answer:

see explanation

Step-by-step explanation:

Given

6x² + x - 1 = 0 ← in standard form

To factorise the quadratic

Consider the factors of the product of the x² term and the constant term which sum to give the coefficient of the x- term.

product = 6 × - 1 = - 6 and sum = + 1

The factors are + 3 and - 2

Use these factors to split the x- term

6x² + 3x - 2x - 1 = 0 ( factor the first/second and third/fourth terms )

3x(2x + 1) - 1(2x + 1) = 0 ← factor out (2x + 1) from each term

(2x + 1)(3x - 1) = 0

Equate each factor to zero and solve for x

2x + 1 = 0 ⇒ 2x = - 1 ⇒ x = - [tex]\frac{1}{2}[/tex]

3x - 1 = 0 ⇒ 3x = 1 ⇒ x = [tex]\frac{1}{3}[/tex]

Answer:

The graph would look like this

Step-by-step explanation:

The equation is less than so it is below the dotted line. The line is dotted becuase the answer is equal to anything on the line.

The graph will be a dashed line and the region below the line is hatched. Then the correct option is A.

The collection of all coordinates in the planar of the format [x, f(x)] that make up a variable function's graph.

The linear function is given below.

4y + 8 < -3x

The graph will be a dashed line and the region below the line is hatched.

Then the correct option is A.

The missing options are attached below.

More about the graph of the function link is given below.

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Answer:

[tex]\frac{1}{6}[/tex]

Step-by-step explanation:

P(tail ) = [tex]\frac{1}{2}[/tex]

numbers less than 3 are 1 and 2, hence

P(number < 3 ) =[tex]\frac{2}{6}[/tex] = [tex]\frac{1}{3}[/tex]

P(tail ) and P(number < 3 )

= [tex]\frac{1}{2}[/tex] × [tex]\frac{1}{3}[/tex] = [tex]\frac{1}{6}[/tex]

Answer:

35 cm

Step-by-step explanation:

To find the area of the bottom portion, you would use the formula for finding out a triangle (B*H*1/2) which is:

(4+4)*5.75*1/2=23

Then, for the top portion, one would find the area of the triangles on the sides (with two marks going through). Since along the middle is 8cm, and along the top is 4, we can see that there is 2cm on either side, so that is the length of the base of the triangle. To solve for the top triangles, you would do almost the same thing as the last one:

2*2*1/2=2

But since there's two identical triangles on either side, we can multiply that by two, which would bring it to 4.

That just leaves the rectangle that is left between the two triangles. To solve this, it's just B*H and luckily both of those are labeled for you already:

4*2=8  

Now, to find the total area, all you have to do is add up the areas of the different sections:

23+4+8=35 cm

Hope this helps!