Algebra > Linear equations > 188 - Set-up & solve equations (in context) > Quiz
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The sum of three consecutive odd numbers is 477. What is the 3rd number?

Answer:

c = 793/28 , d = -358/7

Step-by-step explanation:

Solve the following system:

{4 c + 2 d = 11 | (equation 1)

(7 d)/2 = -179 | (equation 2)

Multiply equation 2 by 2:

{4 c + 2 d = 11 | (equation 1)

0 c+7 d = -358 | (equation 2)

Divide equation 2 by 7:

{4 c + 2 d = 11 | (equation 1)

0 c+d = -358/7 | (equation 2)

Subtract 2 × (equation 2) from equation 1:

{4 c+0 d = 793/7 | (equation 1)

0 c+d = -358/7 | (equation 2)

Divide equation 1 by 4:

{c+0 d = 793/28 | (equation 1)

0 c+d = -358/7 | (equation 2)

Collect results:

Answer:  {c = 793/28 , d = -358/7

Answer:

the sign =3x

Step-by-step explanation:

you just need to do the step  

sign-2x+2x=x+2x

sign=3x

Answer:

Step-by-step explanation:

[tex]5k>22\qquad\text{divide both sides by 5}\\\\\dfrac{5k}{5}>\dfrac{22}{5}\\\\k>4\dfrac{2}{5}\to k>4.4\to k\in(4.4,\ \infty)[/tex]

Answer:

m=-44/5

Step-by-step explanation:

(7m+12)/8=(2m-1)/3

cross product

8(2m-1)=3(7m+12)

16m-8=21m+36

16m-21m-8=36

-5m-8=36

-5m=36+8

-5m=44

m=44/-5

m=-44/5

Answer:

30 ways

Step-by-step explanation:

The first medal can be awarded in 6 different ways since any of the runners could have it. Once the first medal is awarded, the second medal can only be given to any of the 5 runners available.

So there are 6x5=30 different ways to award the medals

There are 30 ways to award the medals to the winners

The given parameters are:

Runners = 6

Medals = 2

The first position can be awarded to any of the 6 runners, while the second position can be awarded to any of the remaining 5 runners

So, the number of ways is:

Ways = 6 * 5

Evaluate

Ways = 30

Hence, there are 30 ways to award the medals

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Answer:

700 dollars,

Step-by-step explanation:

what you do is divide 511 by 73 then multiply the number by 100

Answer:

2

Step-by-step explanation:

Conversion factor: 1/8

1) Cup = Fluid Ounce / 8

2) Cup = 32 / 8

3) Cup = 4

Answer:

2

There are 4 cups in a 32 fl oz carton, so she needs to get 2 more.

Answer:

There is no solution for x.

Step-by-step explanation:

We are given that [tex]\sin (\cos x) = 1[/tex] and we have to solve for x.

Let us assume that [tex]\cos x = \theta[/tex] then [tex]\sin \theta = 1[/tex] ........ (1)

Now, we know that for any value of x the value of cos x lies between 1 to - 1.

Hence, [tex]1 \geq  \cos x \geq  - 1[/tex]  for all x.

⇒ [tex]1 \geq  \theta \geq  - 1[/tex]

Now, for [tex]1 \geq  \theta \geq  - 1[/tex], the value of [tex]\sin \theta[/tex] can never be equal to 1.

Hence, there is no solution for x. (Answer)

Answer:

c

Step-by-step explanation:

turn the percent into a decimal and × by the number you get that number that the percent represents in the number add it to the number and you get the original price

The price which is highest is Option C)

After a 20% discount, the price was $170

What is Percentage?

A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, %

Given data ,

A)

After a 5 % discount , the price was $ 190

So , the percentage is calculated as

190 / 0.95 = $ 200

B)

After a 10 % discount , the price was $ 180

So , the percentage is calculated as

180 / 0.90 = $ 200

C)

After a 20 % discount , the price was $ 170

So , the percentage is calculated as

170 / 0.80 = $ 212.50

D)

After a 30 % discount , the price was $ 140

So , the percentage is calculated as

140 / 0.70 = $ 200

Therefore , the price $ 212.50 is the highest

Hence , the solution , after a 20% discount, the price was $170 is the highest

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Answer:

3x²

Step-by-step explanation:

[tex]\frac{d}{dx}[/tex](x³)

Apply the power rule: [tex]\frac{d}{dx}[/tex](x^a) = a * x^(a - 1):

3 * x^(3 - 1)

Simplify:

3x²

Answer:

f(x) = x³ - 4x² + x + 6

Step-by-step explanation:

The polynomial function f has zeros at -1, 2, and 3.

So, the least degree of the polynomial will be 3{As it has three roots}.

Then, if the function is of x variable then (x + 1), (x - 2) and (x - 3) will be the factors of the polynomial.

Therefore, we can write  

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

⇒ f(x) = (x + 1)(x² - 5x + 6)

⇒ f(x) = x³ - 5x² + 6x + x² - 5x + 6

⇒ f(x) = x³ - 4x² + x + 6  

Hence, this is the polynomial with least degree having rational coefficients and with leading coefficient of 1 and the zeroes -1, 2, 3. (Answer)

Answer:

A and B

Step-by-step explanation:

C) 9 7/8 - (- 2 4/5) - (- 1/2) =

= 9 7/8 + 2 4/5 + 1/2 (F)

D) - (- 9 7/8 + 2 4/5) - 1/2) =

= 9 7/8 - 2 4/5 - 1/2 (F)

E) 9 7/8 - (- 2 4/5 - 1/2) =

= - 7/8 + 2 4/5 + 1/2 (F)

Answer:

Step-by-step explanation:

Bc bhh

Answer:

0.8

Step-by-step explanation:

Of the 60 sneakers inspected, 48 were acceptable.  The experimental probability is therefore:

P = 48/60

P = 0.8

Answer:

Step-by-step explanation:

[tex]\dfrac{72}{12}=\dfrac{72:12}{12:12}=\dfrac{6}{1}=6:1[/tex]

Answer:

x-intercept is 2, y-intercept is 10.

Step-by-step explanation:

y=-5x+10

y=mx+b

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

m=-5 which means that the slope of this equation is -5.

And to find the y-intercept,

plug in x=0 into the equation and find out the value of y.

y=-5(0)+10=0+10=10

So the y-intercept is 10.

And to find the x-intercept,

plug in y=0 into the equation and find out the value of x.

0=-5x+10

-5x=0-10

-5x=-10

5x=10

x=10/5=2

So the x-intercept is 2.

Answer:Tueyndi

Step-by-step explanation:

Answer:1.6,9,14

Step-by-step explanation:

so x+6 input is x so you put the number in the input where the x is so 0+6=6,and 3+6=9 and so on.....

Answer:

They are known as terms in algebraic expression

Step-by-step explanation:

Answer:

Part a) [tex]\frac{1}{200}[/tex]

Part b) [tex]\frac{1}{450}[/tex]

Step-by-step explanation:

we know that

A reciprocal of a rational number  [tex]\frac{p}{q}[/tex]  is obtained by changing the numerator and denominator, so the numerator becomes the denominator and the denominator becomes the numerator obtaining  [tex]\frac{q}{p}[/tex]

Part a) we have

200

we know that

the given number can be expressed as [tex]\frac{200}{1}[/tex]

so

changing the numerator and denominator

The reciprocal is equal to [tex]\frac{1}{200}[/tex]

Part b) we have

450

we know that

the given number can be expressed as [tex]\frac{450}{1}[/tex]

so

changing the numerator and denominator

The reciprocal is equal to [tex]\frac{1}{450}[/tex]

Answer: x = 1.5

Step-by-step explanation:

5x - 2 = x + 4

Add 2 to each side

5x = x + 6

Subtract x from each side

4x = 6

Divide each side by 4

x = 1.5

Answer:

x = 3/2

Step-by-step explanation:

5x-2=x+4    (add 2 to both sides)

5x=x+4 + 2

5x=x+6  (subtract x from both sides)

5x - x = 6

4x = 6 (divide both sides by 4)

x = 6/4 = 3/2

Answer:

$116 for four months

Step-by-step explanation:

$29 • 4 = 116

The equivalent ratios are A and D.

Here's an explanation:

When you look at D, you see that 12 is a multiple of 6, and 16 is a multiple of 8. So you know that it looks like they're equivalent. Then you test it out, 12/2=6. 16/2=8. so 12:16 = 6:8. Eyeballing it first can save time sometimes.

Answer:

None

Step-by-step explanation:

A number's absolute value will always be positive

|9| = 9

|-9| = 9

Answer:

Step-by-step explanation:

none

Answer:

-0.5

Step-by-step explanation:

It looks like it's increasing by 0.5

Answer:-0.5

Step-by-step explanation:Say you were doing it in postive form half of 1 is 0.50 meaning you just add a negative sign

Answer:

6+10b

Step-by-step explanation:

Answer:

m∠y=72°

Step-by-step explanation:

The question is

Find the measure of angle y

step 1

Find the measure of angle x

see the attached figure to better understand the problem

we know that

m∠x=67° -----> by corresponding angles

step 2

Find the measure of angle y

we know that

(m∠x+m∠y)+42°=180° -----> because form a straight line

substitute the measure of angle x

67°+m∠y+42°=180

m∠y+108°=180

m∠y=180°-108°

m∠y=72°

Answer:

1.28

Step-by-step explanation:

I used calculator give me brainlist

Answer:

1.28

Step-by-step explanation:

so 32% is equal to .32 and you can imagine that the word "of" means x(as in multiply). Thus said .32 x 4 is 1.28

Answer:

Graph C) represents a function.

Step-by-step explanation:

Graph C) is the only graph that passes the vertical line test, a way to determine if a graph is a function. All other graphs do not pass the vertical line test. The vertical line test states that if a vertical line drawn intersects the graph of the relation more than once, then the relation is a NOT a function.

The function is indeed a relationship that has only one outcome for each input value (x-value) and output value (y-value). As a result, all functions could be regarded as relationships. However, not all relations are functions because not all of them satisfy the criterion, so each unique input generates just one output.

Therefore, the final answer is "Option C".

Learn more:

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If the unknown is the hypotenuse...

Following pyth. theorem,

x^2=11^2+19^2

x=21.95

If the unknown is a leg other than the hypotenuse...

Following pyth. theorem,

x^2=19^2-11^2

x=15.49