Write and then evaluate an expression for the following number line.

Answer:

  $700 for a chair and a table

Step-by-step explanation:

Let t and c represent the price of a table and a chair, respectively. The given relations are ...

  10c = 4t

  15c +2t = $4000

Divide the first equation by 2 and substitute for 2t:

  5c = 2t

  15c +5c = $4000

  20c = $4000

  c = $200

  t = 5c/2 = 5($200)/2 = $500

The total price of a chair and a table is ...

  $200 +500 = $700 . . . . price of a chair and a table

y=3/4x+1/4

I hope this helped :)

Answer:

Step-by-step explanation:

two points on the line are (-3,-2) and (5,4)

slope=(4-(-2))/(5-(-3)=(4+2)/(5+3)=6/8=3/4

eq. of line is

y+2=3/4(x+3)

4y+8=3x+9

4y=3x+9-8

4y=3x+1

y=3/4 x+1/4

Answer:

10.5

Step-by-step explanation:

Hope I helped please mark brainliest if I did and thanks! <3

[tex]W = \displaystyle \int^{5}_{2} F(x) ~ dx\\\\\\= \displaystyle \int^{5}_{2} \left(12x^2 +7\right) ~dx\\\\\\= 12\displaystyle \int^{5}_{2} x^2 ~dx + \displaystyle \int^{5}_{2} 7~ dx\\\\\\=12 \left[\dfrac{x^3}3 \right]^{5}_{2} + 7\left[x\right]^{5}_{2}\\\\\\=4(5^3-2^3) + 7(5-2) = 468 + 21 = 489~ J[/tex]

Answer:

3(x+1)

Step-by-step explanation:

Answer:

10

Step-by-step explanation:

13 pieses - 3 pieces = 10 pieces that are eaten

Answer:

10

Step-by-step explanation:

Answer:

D or answer choice 4

Step-by-step explanation:

Answer:

D. is your answer

Answer:

c=38

Step-by-step explanation:

Answer:

c = 38

Step-by-step explanation:

Answer:

Step-by-step explanation:

as the chart is broken into steps with the same precision we're looking for. Just choose the one where height is closest to zero or 0.6 s

To do it mathematically

The equation is

h = 2 - ½gt²

to find g, plug in a time and height

0.236 = 2 - ½g(0.6²)

g = 9.8 m/s

check another one just to be sure

1.559 = 2 - ½(9.8)0.3²

1.559 = 1.559

now plug in zero elevation with an unknown time

0 = 2 - ½(9.8)(t²)

-2 = - ½(9.8)(t²)

t² = 4/9.8

t = 0.6388765...

t = 0.6 s

The time it takes for the penny to hit the ground is about 0.6 seconds.

Option B is the correct answer.

The equation of a line is given by:

y = mx + c

where m is the slope of the line and c is the y-intercept.

Example:

The slope of the line y = 2x + 3 is 2.

The slope of a line that passes through (1, 2) and (2, 3) is 1.

We have,

To determine the time it takes for the penny to hit the ground, we need to find the point where the height of the penny is equal to zero.

Looking at the table,

We can see that the height of the penny is negative when t = 0.7 and becomes more negative for larger values of t.

So the penny must hit the ground between t = 0.6 and t = 0.7 seconds.

Now,

We can use linear interpolation to estimate the time at which the height of the penny is zero by finding the equation of the line that passes through the two points closest to zero on the table, namely (0.6, 0.775) and (0.7, -0.401).

So,

The slope of the line passing through these points.

= (change in height) / (change in time)

= (-0.401 - 0.775) / (0.7 - 0.6)

= -1.176

The equation of the line passing through these points.

y - 0.775 = -1.176(x - 0.6)

Simplifying

y = -1.176x + 1.438

Setting y to zero and solving for x.

0 = -1.176x + 1.438

x = 1.438 / 1.176

x ≈ 1.22

Therefore,

To the nearest tenth of a second, the time it takes for the penny to hit the ground is about 0.6 seconds.

Learn more about equation of a line here:

https://brainly.com/question/23087740

#SPJ7

Answer:

16 I guess.

Step-by-step explanation:

lolololololol?

9514 1404 393

Answer:

  x = -2

Step-by-step explanation:

Multiply both sides of the equation by -1.

  (-1)(2) = (-1)(-x)

  -2 = x

The value of x that makes the equation true is x = -2.

Answer A is correct.

Step-by-step explanation:

Negative one is less than one.

Step-by-step explanation:

each child gets a certain amount of items costing the specified price by item.

so, we need to multiply the number of children with the number of items with the price per item to get the total cost.

500×3×3.5 for pencils = 5,250

500×5×7.5 for notebooks = 18,750

500×1×21.75 for crayons = 10,875

500×2×9.26 for pad paper = 9,260

total 44,135

since we have only 1,200 available in the existing fund, we need a new one to cover the remaining

44,135 - 1,200 = 42,935

Answer:

  A) 1: exponential; 2: linear

  B) 1: f(x) = 45000·0.9^x; 2: f(x) = -3000x+45000

  C) The difference is significant. 1: $11,348; 2: $6,000

Step-by-step explanation:

The values for Car 1 have a common ratio of 40500/45000 = 0.9. An exponential function is used to describe a sequence where the terms have a common ratio.

The values for Car 2 have a common difference of 42000-45000 = -3000. A linear function is used to describe a sequence where the terms have a common difference.

__

An exponential function can be written as ...

  f(x) = (initial value)·(common ratio)^x

A linear function can be written as ...

  f(x) = (common difference)x + (initial value)

The functions are ...

  Car 1: f(x) = 45000·0.9^x

  Car 2: f(x) = -3000x +45000

___

The formulas for the different car values after 13 years give ...

 Car 1: f(13) = 45000·0.9^13 ≈ 11,348

  Car 2: f(13) = -3000(13) +45000 = 6,000

The value of Car 1 will be almost double the value of Car 2 after 13 years. Yes the difference in value is significant.

"Find all real solutions of" basically means solve for x. You're looking for the real numbers x such that the given equation is satisfied. "Zeros" is synonymous with "solutions".

It looks like the first equation is

3x³ + x² - 38x + 24 = 0

It's not immediately obvious whether this can be factorized, so we first carry out the rational zero test to see if there are any rational solutions. *If* this equation has any rational solutions, then they must take the form of (divisor of 24)/(divisor of 3). That is, take any divisor of the constant coefficient and divide it by any divisor of the leading term's coefficient.

We have

• divisors of 24 : ±1, ±2, ±3, ±4, ±6, ±8, ±12, ±24

• divisors of 3 : ±1, ±3

Sadly, there are 64 possible roots to test, but we only need one to make the rest of the problem easier.

• Let x = +1 / +1 = 1. Then plugging x = 1 into the equation gives

3•1³ + 1² - 38•1 + 24 = -10 ≠ 0

so x = 1 is *not* a solution

• Let x = +2 / +1 = 2. If x = 2, then

3•2³ + 2² - 38•2 + 24 = -24 ≠ 0

so x = 2 is *not* a solution.

• Let x = +3 / +1 = 3. If x = 3, then

3•3³ + 3² - 38•3 + 24 = 0

so x = 3 is a solution.

By the remainder theorem, this means that x - 3 divides 3x³ + x² - 38x + 24. Using long or synthetic division,

(3x³ + x² - 38x + 24) / (x - 3) = 3x² + 10x - 8

so that

3x³ + x² - 38x + 24 = 0

is the same as

(x - 3) (3x² + 10x - 8) = 0

We factorize the remaining quadratic to get

3x² + 10x - 8 = (3x - 2) (x + 4)

and so the original equation is equivalent to

(x - 3) (3x - 2) (x + 4) = 0

Solve for x :

x - 3 = 0   or   3x - 2 = 0   or   x + 4 = 0

x = 3   or   x = 2/3   or   x = -4

The other equations can be solved similarly, though some of the others you included are much simpler.

For the second problem (note that you left out an exponent), we solve the equation

x³ - 2x² - 23x + 60 = 0

Again, not immediately obvious how to factorize this. But using the rational root test, we have

• divisors of 60 : ±1, ±2, ±3, ±4, ±5, ±6, ±10, ±12, ±15, ±20, ±30, ±60

• divisors of 1 : ±1

If you follow the same steps as before, you'll find the first rational solution with x = 3. So x - 3 divides x³ - 2x² - 23x + 60, and long division gives

(x³ - 2x² - 23x + 60) / (x - 3) = x² + x - 20

and the resulting quadratic is easily factored,

x² + x - 20 = (x - 4) (x + 5)

So, we have

x³ - 2x² - 23x + 60 = (x - 3) (x - 4) (x + 5) = 0

which means

x - 3 = 0   or   x - 4 = 0   or   x + 5 = 0

x = 3   or   x = 4   or   x = -5

For the third problem, we can factor by grouping.

x³ - 4x² - x + 4 = 0

x² (x - 4) - (x - 4) = 0

(x² - 1) (x - 4) = 0

(x - 1) (x + 1) (x - 4) = 0

Then

x - 1 = 0   or   x + 1 = 0   or   x - 4 = 0

x = 1   or   x = -1   or   x = 4

For the fourth problem, we use the rational root test again, but twice this time.

x⁴ - 6x³ + 7x² + 6x - 8 = 0

• divisors of -8 : ±1, ±2, ±4, ±8

• divisors of 1 : ±1

We find that x = 1 and x = 2 are both rational roots, so both x - 1 and x - 2 divide x⁴ - 6x³ + 7x² + 6x - 8. By long division,

(x⁴ - 6x³ + 7x² + 6x - 8) / ((x - 1) (x - 2)) = x² - 3x - 4

and factoring this gives

x² - 3x - 4 = (x + 1) (x - 4)

So, we have

x⁴ - 6x³ + 7x² + 6x - 8 = (x - 1) (x - 2) (x + 1) (x - 4) = 0

which means

x - 1 = 0   or   x - 2 = 0   or   x + 1 = 0   or   x - 4 = 0

x = 1   or   x = 2   or   x = -1   or   x = 4

For the last problem,

x⁴ + 4x³ + 7x² + 16x + 12 = 0

we use the rational root test again.

• divisors of 12 : ±1, ±2, ±3, ±4, ±6, ±12

• divisors of 1 : ±1

We find that both x = -1 and x = -3 are rational solutions, and dividing gives

(x⁴ + 4x³ + 7x² + 16x + 12) / ((x + 1) (x + 3)) = x² + 4

which we cannot factorize further over the real numbers. So we end up with

x⁴ + 4x³ + 7x² + 16x + 12 = (x + 1) (x + 3) (x² + 4) = 0

so that

x + 1 = 0   or   x + 3 = 0   or   x² + 4 = 0

x = -1   or   x = -3

(We omit the third equation here because it has no real solution since x² + 4 ≥ 4 for all real x.)

Answer:

Step-by-step explanation:

Say the class has 20 students

20(1/4) = 5 play instruments

5(2/5) = 2 speak a second language

2 / 20 = 1/10

Answer:

(3*5)+(19*3)

Step-by-step explanation:

both numbers GCF is 3.

(3*5)=15

(19*3)=57

15+57=72

Hope that helps

Answer:

A is the cheapest deal.

Step-by-step explanation:

find unit rate; cost / quantity

20.20 / 10 = $2.02 per gallon

26.04 / 12 = $2.17 per gallon

28.24 / 24 = $2.01 per gallon

30.45 / 25 = $2.03 per gallon

Using the probability table, it is found that:

Item a:

To find the probabilities involving the total cost, we have to add the variables X and Y from the table, then:

[tex]P(X = 30) = P(X = 15|Y = 15) = 0.2[/tex]

[tex]P(X = 35) = P(X = 15|Y = 20) + P(X = 20|Y = 15) = 0.15 + 0.15 = 0.3[/tex]

[tex]P(X = 40) = P(X = 15|Y = 25) + P(X = 20|Y = 20) + P(X = 25|Y = 15) = 0.05 + 0.15 + 0.05 = 0.25[/tex]

[tex]P(X = 45) = P(X = 20|Y = 25) + P(X = 25|Y = 20) = 0.1 + 0.1 = 0.2[/tex]

[tex]P(X = 50) = P(X = 25|Y = 25) = 0.05[/tex]

The probability involving values of 45 or more is:

[tex]P(X \geq 45) = P(X = 45) + P(X = 50) = 0.2 + 0.05 = 0.25[/tex]

0.25 = 25% probability that this couple spends 45 dollars or more.

Item b:

For a discrete distribution, the expected value is the sum of each outcome multiplied by it's respective probability, hence, involving the 10% discount for prices above $45:

[tex]E(X) = 0.2(30) + 0.3(35) + 0.25(40) + 0.9[0.2(45) + 0.05(50)] = 36.85[/tex]

The expected amount the couple actually has to pay is $36.85

A similar problem is given at https://brainly.com/question/25782059

Answer:

y = 8x + 12

Step-by-step explanation:

y = (2x + 3)4

Distribute the 4 to the 2x  and 3

y = 8x + 12

^ Expanded form

Answer:

$6,000

Step-by-step explanation:

$6,000 Because miles younger than 50

Answer:

25/15

Step-by-step explanation: