Write
31/3 as a whole or mixed number in simplest form

Answer:

Yes you are right.

The answer is .45 or 45/100 which reduces to 9/20.

Step-by-step explanation:

[tex]\frac{4x}{15}=\frac{3}{25}[/tex]

Your first step is to cross multiply:

[tex]15(3)=25(4x)[/tex]

Simplify both sides:

[tex]45=100x[/tex]  You got this! You go!

Divide both sides by 100:

[tex]\frac{45}{100}=x[/tex]

You wrote 45/100 as .45 which is correct!

Nice.

Answer:

x = 12.25

Step-by-step explanation:

Given

x - 3(x - 7) = 4(x - 7) - 2x ← distribute parenthesis on both sides

x - 3x + 21 = 4x - 28 - 2x ← simplify both sides

- 2x + 21 = 2x - 28 ( subtract 2x from both sides )

- 4x + 21 = - 28 ( subtract 21 from both sides )

- 4x = - 49 ( divide both sides by - 4 )

x = [tex]\frac{49}{4}[/tex] = 12.25

Answer: x=12.25

Step-by-step explanation: First, multiply the numbers into the parentheses. You will get:

X -3x +21 = 4x -28 -2x

Combine like terms.

-2x +21 =2x -28

Isolate x by adding 2x to each side.

21 =4x -28

Add 28 to each side to get x by itself.

49=4x

Divide by 4.

X =12.25

For this case we must subtract:

[tex]2- \frac {5} {8} =\\\frac {8 * 2-5} {8} =\\\frac {16-5} {8} =\\\frac {11} {8}[/tex]

Thus, you have [tex]\frac {11} {8}[/tex]of string, after you have cut[tex]\frac {5} {8}[/tex] of it.

If we convert to a mixed number we have to:

[tex]\frac {11} {8} = 1 \frac {3} {8}[/tex]

Answer:

He has [tex]1 \frac {3} {8}[/tex] of string.

Step-by-step explanation:

In a standard deck of 52 cards, there are 2 red aces, 2 red Queens, and 13 spades.  That leaves 35 cards for everything else.

For the game to be fair, the cost must equal the expected value.  The expected value is the sum of each outcome times its probability.

C = (12) (13/52) + (20) (2/52) + (38) (2/52) + (0) (35/52)

C = 68/13

C ≈ 5.2308

Answer:

The lectures cost is $7.33 per hour

Step-by-step explanation:

* Lets explain how to solve the problem

- For the level 3 course the examination hours cost twice as much

 as workshop hours

- The workshop hours cost twice as much as lecture hours

- There are examination hours , workshop hours and lecture hours

- There are 3 hr for examination, 24 hr for workshops and 12 hr

  for lectures

* Let the cost of the lecture hours is $x per hour

∴ The cost of the lecture hours is x per hour

∵ The cost of workshop hours is twice the cost of lecture hours

∴ The cost of the workshop hours is 2(x) = 2x per hour

∵ The cost of examination hours is twice the cost of workshop hours

∵ The cost of the workshop hours is 2x

∴ The cost of examination hours is 2(2x) = 4x per hour

- The cost of the level 3 is the sum of the costs of the lecture hours,

  workshop hours and examination hours

∵ There is 12 hours for lectures

∵ There is 24 hours for workshops

∵ There is 3 hours for examination

∵ The total cost of level 3 = 12(x) + 24(2x) + 3(4x)

∴ The total cost of level 3 = 12 x + 48 x + 12 x

∵ The total cost of level 3 = $528

∴ 12 x + 48 x + 12 x = 528

∴ 72 x = 528 ⇒ divide both sides by 72

∴ x = 7.33

∵ x is the cost of the lecture hours per hour

∴ The lectures cost is $7.33 per hour

Answer:

f=31

Step-by-step explanation:

35-f=4

-35   -35

-f=-31

*-1  *-1

f=31

[tex]\large \textnormal{F=31}[/tex], is the correct answer.

[tex]\large \textnormal{First, subtract by 35 from both sides of the equation.}[/tex]

[tex]\displaystyle 35-f-35=4-35[/tex]

[tex]\large \textnormal{Solve.}[/tex]

[tex]\displaystyle -f=-31[/tex]

[tex]\large \textnormal{Then you divide by -1 from both sides of the equation.}[/tex]

[tex]\displaystyle \frac{-f}{-1}=\frac{-31}{-1}[/tex]

[tex]\large \textnormal{Solve to find the answer.}[/tex]

[tex]\displaystyle -31\div-1=31[/tex]

[tex]\large \boxed{f=31}\checkmark[/tex]

Hope this helps!

Answer:

f(n + 1) = f(n) + 2

Step-by-step explanation:

A recursive formula gives any term in the sequence from the previous term.

the n th term of an arithmetic sequence is

f(n) = f(1) + (n - 1)d ← d is the common difference

Given

f(1) = 6 and

f(4) = 12, then

f(1) + 3d = 12, that is

6 + 3d = 12 ( subtract 6 from both sides )

3d = 6 ( divide both sides by 3 )

d = 2

To obtain a term in the sequence add 2 to the previous term, hence

f(n + 1) = f(n) + 2 ← recursive formula

Answer:

c

Step-by-step explanation:

its c

Answer:

The graph has a minimum.

Step-by-step explanation:

The top answer choice would also be a genuine statement if that negative symbol was removed from outside the 4. Second, whenever A is positive, the parabola opens up with a minimum value.

If you are ever in need of assistance, do not hesitate to let me know by subscribing to my channel [USERNAME: MATHEMATICS WIZARD], and as always, I am joyous to assist anyone at any time.

Answer:

2

Step-by-step explanation:

Angela has a marbles.

Brian has twice as many as Angela, so Brain has 2a.

Caden has three times as many as Brain, so Caden has 3(2a)=6a.

Daryl has five times the number of marbles as Caden, so Daryl has 5(6a)=30a.

We are given that these 4 people together have 78 marbles.

Angela's + Brain's + Caden's + Daryl's =78

  a          +    2a      +   6a        + 30a      =78

Combine the like terms:

39a=78

Divide both sides by 39:

  a=78/39

   a=2

Answer: y=-ax(x-500)(x-1000)^2

Step-by-step explanation:

The behavior of the x-intercept of a graph is given by the multiplicity of the zero

The required polynomial for the coaster is, y = -a·x·(x - 500)·(x - 1000)²

Reason:

The question relates to the introduction of characteristics to the graph of a polynomial through knowledge of the effect of parameters of a polynomial

Known parameter:

Parent function is, y = a·x·(x - 1000)

The polynomial crosses the x-axis when (x - 500) is a factor of the polynomial, therefore, we have;

y = a·x·(x - 500)·(x - 1000)

Given that the graph is to initially rise, the leading coefficient is negative, therefore, we have;

y = -a·x·(x - 500)·(x - 1000)

For the polynomial to come in smoothly to stop at y = 0, when x = 1,000 we have that a turning point of the polynomial will be located at x = 1,000, this is given by introduction of a bump on the x-axis at x = 1,000 with a factor of (x - 1,000)²

Therefore, the required polynomial is y = -a·x·(x - 500)·(x - 1000)²

The height of the above polynomial is progressively smaller as x tends towards 1,000, given that the factors, (x - 500), and (x - 1,000), becomes smaller.

Learn more about the graph of polynomial functions here:

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Answer:

A

Step-by-step explanation:

Calculate the midpoint using the midpoint formula

[ 0.5(x₁ + x₂ ), 0.5(y₁ + y₂ ) ]

with (x₁, y₁ ) = (- 1, 5) and (x₂, y₂ ) = (5, 5)

midpoint = [ 0.5(- 1 + 5), 0.5(5 + 5) ]

              = [ 0.5(4), 0.5(10) ] = (2, 5 ) → A

Answer:

The answer would be A 2,5

Step-by-step explanation:

Answer:

(12,1.625)

Step-by-step explanation:

According to the given statement:

Cost of gas per gallon = $6

Cost of diesel per gallon = $8

Cost of x gallon gas  = 6x

Cost of y gallon diesel = 8y

You have at most $85 to spend on fuel

Therefore the equation we get is:

6x+8y≤85

You must purchase at least 12 gallons of gas for your car

x≥12

Plot the graph and you get possible solutions:

(12,1.625)..

Angle BCA

Step-by-step explanation:

You can see this due to the angle having the name amount of congruent angle marks.

Answer:

TRUE

Step-by-step explanation:

Answer:

The pairs are (13,15) and (-15,-13).

Step-by-step explanation:

If n is an odd integer, the very next odd integer will be n+2.

n+1 is even (so we aren't using this number)

The sum of the squares of (n) and (n+2) is 394.

This means

(n)^2+(n+2)^2=394

n^2+(n+2)(n+2)=394

n^2+n^2+4n+4=394               since (a+b)(a+b)=a^2+2ab+b^2

Combine like terms:

2n^2+4n+4=394

Subtract 394 on both sides:

2n^2+4n-390=0

Divide both sides by 2:

n^2+2n-195=0

Now we need to find two numbers that multiply to be -195 and add up to be 2.

15 and -13 since 15(-13)=-195 and 15+(-13)=2

So the factored form is

(n+15)(n-13)=0

This means we have n+15=0 and n-13=0 to solve.

n+15=0

Subtract 15 on both sides:

n=-15

n-13=0

Add 13 on both sides:

n=13

So if n=13 , then n+2=15.

If n=-15, then n+2=-13.

Let's check both results

(n,n+2)=(13,15)

13^2+15^2=169+225=394.  So (13,15) looks good!

(n,n+2)=(-15,-13)

(-15)^2+(-13)^2=225+169=394.  So (-15,-13) looks good!

Answer:

The GCF of both the terms is 8....

Step-by-step explanation:

Given:

What is the greatest common factor of 8x and 40y.

The GCF of 8x and 40y is 8.

We will use the method of prime factorization to find the greatest common factor.

The prime factorization of 8x is:

8x = 2*2*2*x

The prime factorization of 40y is:

40y = 2*2*2*5*y

Therefore the common factors in both the terms are 2*2*2 which becomes 8

Thus the GCF of both the terms is 8....

Answer:

8

Step-by-step explanation:

Answer:

X     Y

1       5

4/5   4

2/5   2

Step-by-step explanation:

y=5x

We we know y we need to solve for x

X Y

  5

  4

  2

Let y =5

5 = 5x

Divide by 5

5/5 =5x/5

1=x

Let y =4

4 = 5x

Divide by 5

4/5 =5x/5

4/5=x

Let y =2

2 = 5x

Divide by 5

2/5 =5x/5

2/5=x

X     Y

1       5

4/5   4

2/5   2

Answer:

x=0.8 if y=4, x=0.4 if y=2

Step-by-step explanation:

Rearrange the equation to get:

5x= 4 and

5x= 2

Divide equations by 5 to get:

x=0.8

x=0.4

Answer:

4 ≤ x

4

●→

Step-by-step explanation:

There is no illustration, it looks something like this.

[tex]\bf ~\hspace{7em}\textit{negative exponents} \\\\ a^{-n} \implies \cfrac{1}{a^n} ~\hspace{4.5em} a^n\implies \cfrac{1}{a^{-n}} ~\hspace{4.5em} \cfrac{a^n}{a^m}\implies a^na^{-m}\implies a^{n-m} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \cfrac{a^3b^{-4}}{a^2b^3a^{-5}}\implies \cfrac{a^3}{1}\cdot b^{-4}\cdot \cfrac{1}{a^2}\cdot \cfrac{1}{b^3}\cdot \cfrac{1}{a^{-5}}\implies a^3\cdot b^{-4}\cdot a^{-2}\cdot b^{-3}\cdot a^5 \\\\\\ a^3a^5a^{-2}b^{-4}b^{-3}\implies a^{3+5-2}b^{-4-3}\implies a^6b^{-7}[/tex]

Answer:

Step-by-step explanation:

write this expression : f(x) = a(x-h)²+k

when  the axis of symmetry is the line  : x =h and the vertex A(h,k)

y=2x²+4x-3

y = 2(x²+2x - 3/2)

y=2((x²+2x+1) -1 -3/2)

y = 2((x+1)² - 5/2)

y = 2(x+1)² -5.....vertex form      x= -1 the axis of symmetry  and A(-1,-5)the vertex

Answer:

The equation of the axis of symmetry is x = -1.

The  coordinates of the vertex are (-1, -5).

Step-by-step explanation:

y = 2x^2 + 4x - 3

y = 2(x^2 + 2x) - 3

y = 2[ (x + 1)^2 - 1] - 3

y = 2(x + 1)^2  - 5.

The equation of the axis of symmetry is x = -1.

The  coordinates of the vertex are (-1, -5)

Answer:

Triangle APB is an isosceles triangle ⇒ 3rd answer

Step-by-step explanation:

* Lets explain the how to solve the problem

- ABCD is a square

∴ AB = BC = CD = AD

∴ m∠A = m∠∠B = m∠C = m∠D = 90°

- DPC is equilateral triangle

∴ DP = PC = DC

∴ m∠DPC = m∠PCD = m∠CDP = 60°

- In the Δs APD , BPC

∵ AD = BC ⇒ sides of the square

∵ PD = PC ⇒ sides of equilateral triangle

∵ m∠ADB = m∠BCP = 30° (90° - 60° = 30) ⇒ including angles

∴ Δs APD , BPC are congregant ⇒ SAS

- From congruent

∴ AP = BP

∴ Triangle APB is an isosceles triangle

Answer:

C:  Two dimensions

Step-by-step explanation:

Yes:  a plane has two dimensions; think of a plane as being defined by the x- and y-axes, which intersect at a point in the plane.

A plane have two dimensions.

A plane is a flat, two-dimensional surface that prolongs infinitely far. A plane is a two-dimensional analogue that could consist of a point, a line and three-dimensional space.

A plane is a flat, two-dimensional surface that extends indefinitely. It has two dimensions because every point in the plane can be described by a linear combination of two independent vectors.

Hence, a plane have two dimensions.

Find out more information about plane here:

https://brainly.com/question/17515776

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Answer:

-13x^4+2x^3+8x^2-5x

Step-by-step explanation:

(3x^2-5x-7x^4)-(-2x^3+6x^4-5x^2)

= 3x^2-5x-7x^4+2x^3-6x^4+5x^2

= -13x^4+2x^3+8x^2-5x

Answer:

-x(13x³ - 2x² - 8x + 5)

Step-by-step explanation:

1. Distribute the negative to the numbers inside the parenthesis. Remember that two negatives multiplied will make a positive, and a negative and a positive will become a negative.

3x² - 5x - 7x^4 + 2x³ - 6x^4 +  5x²

2. Combine like terms. Remember that only numbers with the same number and exponents can be combined.

3x² - 5x - 7x^4 + 2x³ - 6x^4 +  5x²

                        ↓

   8x² - 5x - 7x^4 + 2x³ - 6x^4

                        ↓

        8x² - 5x - 13x^4 + 2x³

3. Rewrite the answer in descending order of powers.

-13x^4 + 2x³ + 8x² - 5x

4. Simplify The equation. The terms all have x in common, so we will take that out first. The smallest amount of x's any term has is one (-5x only has one x), so the most we can take out is one x. We will do this by lowering the power of every x by one.

x(-13x³ + 2x² + 8x - 5)

5. Since 13 and 5 are prime and do not go into 2 or 8 we will not be simplifying the coefficients. However, the last thing we can do is take out a negative.

-x(13x³ - 2x² - 8x + 5)

Answer:

It is C. Multiply each side by negative one over five , subtract 25 from each side.

Hope this helped you! :3

Answer:

D;Multiply each side by −5, add 25 to each side

Step-by-step explanation:

-1/5 (x − 25) = 7

To solve this equation, we will first multiply both-side of the equation by -5

-5 × -1/5(x-25) =7 × 5

(At the left-hand side of this equation, the  5 we multiplied will cancel the 5 at the denominator, leaving us with just '1' since negative multiply by negative is positive), Hence our equation becomes;

(x - 25) = 35

x - 25 = 35

Then the next thing to do is to add 25 to both-side of the equation in other to get the value of your x

x -25 + 25 = 35 + 25

x=60

Therefore,  option D is the correct sequence of operation to follow to enable you solve the equation.

Check the picture below.

Answer:

Either A or B.

Step-by-step explanation:

When shifting to the left you are adding to x.

Example: x^2 shifted to the left by 3. (x+3)^2

For this case we have that, by definition of horizontal translation of functions we have to:

We assume h> 0:

To graph[tex]y = f (x-h),[/tex] the graph moves, h units to the right.

To graph[tex]y = f (x + h)[/tex], the graph moves, h units to the left.

If we have the following function:

[tex]f (x) = x ^ 2 + 3x + 2[/tex]and move 2 units to the left, then:

[tex]f (x + 2) = g (x) = (x + 2) ^ 2 + 3 (x + 2) +2[/tex]

ANswer:

Option B

166

27 + 42 + 21 + 76 = 166

Answer:

x = -1255

Step-by-step explanation:

336+x/5=85

Subtract 336 from each side

336-336 +x/5=85-336

x/5 =-251

Multiply each side by 5

x/5 * 5 = -251 *5

x = -1255

Answer:

Step-by-step explanation:

The slope-intercept form of an equation of a line:

[tex]y=mx+b[/tex]

m - slope

b - y-intercept

========================================

Let

[tex]k:y=m_1x+b_1\\\\l:y=m_2x+b_2\\\\l\ \perp\ k\iff m_1m_2=-1\to m_2=-\dfrac{1}{m_1}\\\\l\ \parallel\ k\iff m_1=m_2[/tex]

========================================

We have the equation of a line in a general form (Ax + By + C = 0)

Convert it to the slope-intercept form:

[tex]4x+7y+3=0[/tex]             subtract 7y from both sides

[tex]4x+3=-7y[/tex]         divide both sides by (-7)

[tex]-\dfrac{4}{7}x-\dfrac{3}{7}=y\to m_1=-\dfrac{4}{7}[/tex]

Therefore

[tex]m_2=-\dfrac{1}{-\frac{4}{7}}=\dfrac{7}{4}[/tex]

We have the equation:

[tex]y=\dfrac{7}{4}x+b[/tex]

Put the coordinates of the point (-2, 1) to the equation, and solve for b :

[tex]1=\dfrac{7}{4}(-2)+b[/tex]

[tex]1=-\dfrac{7}{2}+b[/tex]     multiply both sides by 2

[tex]2=-7+2b[/tex]           add 7 to both sides

[tex]9=2b[/tex]            divide both sides by 2

[te]x\dfrac{9}{2}=b\to b=\dfrac{9}{2}[/tex]

Finally:

[tex]y=\dfrac{7}{4}x+\dfrac{9}{2}[/tex] - slope-intercept form

Convert to the general form:

[tex]y=\dfrac{7}{4}x+\dfrac{9}{2}[/tex]         multiply both sides by 4

[tex]4y=7x+18[/tex]      subtract 4y from both sides

[tex]0=7x-4y+18[/tex]

Answer:

[tex](d + 8m)^2[/tex]

Step-by-step explanation:

[tex]d^2 + 16dm + 64 m^2  = (d + 8m)^2[/tex]

d^2 + 16dm + 64m^2

64m^2 + 16dm + d^2

Note: This polynomial is already in lowest terms. It cannot be factored. Are you sure that you posted the entire, correct problem?