Solve.
y = x – 8
2x + 3y = 1
Use the substitution method.​

Answer:

no

Step-by-step explanation:

Let's plug in -2 for x.

8 - 2 (-2) <12

8 + 4 < 12

12 < 12

Since this is a false statement, -2 is not a solution to the inequality.

Answer: No

Step-by-step explanation: To determine whether x = -2 is a solution to the inequality, substitute a -2 in for r.

So we have 8 - 2(-2) < 12.

Notice that I used parentheses.

This is a great habit to get into when

substituting numbers in for variables.

So we have 8 - (-4) which can be changed to 8 + (+4) or +12.

Since 12 is not less than 12, -2 is not a solution.

The first two pieces are the same, let each of those equal x, so you have x + x = 2x

The 3rd piece is the sum of the first two + 4, so this would be 2x + 4

Now you have 2x + 2x + 4 = 100 cm

Combine like terms:

4x +4 = 100

Subtract 4 from both sides

4x = 96

Divide both sides by 4

X = 24

First piece is 24 cm

Second piece is 24 cm

Third piece is 52 cm

Answer:

4: 3

Step-by-step explanation:

In this case, we have that there is a relationship between width and height, which is 16: 9, which means that any screen that has the same ratio would be an identical screen.

How would we do this? it must either be raised to a power or rationalized on both sides of the ratio.

If we raise to a power, it would give very large dimensions for an HDTV, therefore, it is best to remove the square root on both sides, since it has more common values for a TV.

[tex]\sqrt{16} :\sqrt{9}[/tex]

4: 3

Therefore, a 4: 3 screen is a good choice for an HDTV with the same ratio.

Answer:

Ideiidididid

Step-by-step explanation:

Cici

Answer:

  11.5%

Step-by-step explanation:

Put the given numbers in the formula and do the arithmetic.

  r = 1 - (6000/26000)^(1/12) = 1 -(3/13)^(1/12) ≈ 1 -0.88498 ≈ 11.5%

The company used a depreciation rate of 11.5%.

Answer: 59

Step-by-step explanation:

On 15th day Kyle will do 59 crunches.

An equation is a statement that consists of algebraic expressions equated with other algebraic expressions by an equal sign.

The crunches Kyle did on Day 1 are 3

The rate by which he is increasing per day is 4 crunches/per day

let t represent the number of days

Let the number of crunches on t day be y

Then the equation formed will be

y = 3 + 4(t-1)

On 15th day, he will do

y = 3+ (15-1) *4

y = 3+56

y = 59

Therefore, on 15th day Kyle will do 59 crunches.

To know more about Equation

https://brainly.com/question/10413253

#SPJ2

Answer:

a) 72

b) 9

c) 9

d) 54

Step-by-step explanation:

a) 12 * 6 = 72

b) 3 * 6 = 18. 18 ÷ 2 = 9

c) 3 * 6 = 18. 18 ÷ 2 = 9

d) 72 - 18 = 54

Answer: 10 questions.

Step-by-step explanation:

The optimal aproach would be divide the total range in half, for example, she can ask:

Is the number equal or greater than 500?

if he answers no, now she knows that the numer is in the range 1 to 499

if he says yes, she can know that the number is in the range 500 to 1000.

Now, suppose that the answer is yes.

Now she can ask if the number is equal or greater than 750.

Now we have two possible sets. (500, 749) and (750 , 1000).

Now we can divide those sets again, depending on the answer.

suppose we got the set of (750, 1000)

we can divide it into two sets and so on.

So, we have 999 options and we want to divide it by 2 until we reach to 1., the number of divisions by 2 is the number of times that she asked a question.

999/2^n ≤ 1.

we must find the smaller n that keeps the above inequality true.

999 ≤ 2^n

knowing that 2^10 = 1024.

999/1024 = 1024

So in the worst case, she should ask 10 questions.

Answer:

Matched pairs design

Step-by-step explanation:

A matched pair design can be used in a case where the same people are being measured in before-and-after comparison. The same set of people are measured for the amount of sleep each night before the administration of the drugs and after the drug administration and this is used to test for a difference.

Answer:

Step-by-step explanation:

-6x^2 + x -3 + 2x + 4

________________________

x^2 + 9

-6x^2 + 3x + 1

__________

  x^2 + 9

the solution is the first one

Answer:

D.[tex]\frac{-6x^{2}-x-7 }{x^{2}+9}[/tex]

Step-by-step explanation:

since the [tex]x^{2}+9=x^{2} +9[/tex] you just have to add [tex]\frac{-6x^{2}+x-3-2x-4 }{x^{2}+9 }[/tex] so the answer will be: [tex]\frac{-6x^{2}-x-7 }{x^{2}+9 }[/tex]

Answer:

domain is [-6,6] or -6 ≤ x ≤6

Step-by-step explanation:

domain is x value of given function

dark circle means that that number is included in domain

Answer:

d) 3 feet by 4 feet

Step-by-step explanation:

Volume of the prism = 48 feet³

Height if the prism = 4 feet

To determine the possible values of the length and width of the prism let's divide the volume by the height.

So 48/4 = 12

So we'll be looking for a product of two numbers to give us 12

And it's between 12 and 1, 4 and 3 , and 6 and 2.

We have only 4 and 3 in the option.

Answer:

$3360

Step-by-step explanation:

First you have to do 20 times 2 to find out how many new seats there are.

Then you have to multiple that number by the cost to get the cost of all the new seats.

I hope this helped ;)

Answer:

A. p(x) = 19x - 15

Step-by-step explanation:

→Set it up, like so:

[tex](25x)-(6x+15)[/tex]

[tex]25x - 6x-15[/tex]

→Add like terms (25x and -6x):

[tex]19x - 15[/tex]

Divide total bags by total hours:

30 bags / 3 hours = 10 bags per hour

Answer:

76

Step-by-step explanation:

The sum of the angles of a triangle add to 180

40+ 3x+10 + 2x+20 = 180

Combine like terms

70 + 5x = 180

Subtract 70

70+5x-70 =180-70

5x = 110

Divide by 5

5x/5 = 110/5

x = 22

We want to find BCA

BCA = 3x+10

        = 3(22)+10

        = 66+10

         =76

Answer:

76

Step-by-step explanation:

The sum of the angles of a triangle add to 180

3x+10 + 2x+20 = 140

5x+30=140

-30       -30

5x=110

x=22

3*22=66+10=76

Answer:

13 cm

Step-by-step explanation:

To find the answer, you can use the formula to calculate the volume of a cone and isolate the height:

V= πr^2[tex]\frac{h}{3}[/tex]

V= volume= 218 cubic centimeters

π= 3.14

r= radius= 4 cm

h=height

218= 3.14*4^2*[tex]\frac{h}{3}[/tex]

218*3=3.14*16*h

654=50.24*h

h=654/50.24

h=13

According to this, the height of the container is 13 cm.

Answer:

The student got 16 problem correct

Step-by-step explanation:

Take the number of problems and multiply by the percent correct

20 * 80%

20 *.80

16

The student got 16 problem correct

Answer: The student got 16 problem correct.

Step-by-step explanation: To solve this problem, you first want to take the number of problems that are on the math test and multiply that by the percent the student got correct.

So we have 20 × 80%

Now write 80% as a decimal to get .80.

So we have 20 × .80 which is equal to 16.

So the student got 16 problems correct

and 4 problems incorrect on their test.

Answer:

Esther made the right option which gives her maximum value at the end of 3 years than Vida and Clair.

Step-by-step explanation:

The life is all about making the right choices. Esther has made a decision to collect GH¢1000 now. To calculate future value of Esther choice at the end of 3 year we will use formula below,

FV = PV [tex](1 + r)^{t}[/tex]

discount factor at year 3 t 10% is 0.751

FV = 1000 (0.751) / (1.1)3

FV = GH¢2487.

Vidha choose to collect GH¢3000 at end of 3 year, the present value of GH¢3000 at 10% discount rate will be;

PV = FV [tex](1 + r)^{-t}[/tex]

PV = 3000 (0.751)

PV = GH¢2253.

Clair is indifferent from the choices given but this is also not a smart choice.

Esther has made the right choice among the three women and she gets maximum value of GH¢2487.

Answer: A=12, B=2, C=11

Step-by-step explanation:

With the given problem, you would first expand the numerator.

[tex]\frac{x^1^5y^3z^1^2}{x^3yz}[/tex]. Then you can simply from there. You can subtract the exponents. [tex]x^1^2y^2x^1^1[/tex]

Answer:

This, polynomial has order 7.

Step-by-step explanation:

Given the polynomial

P(x) = 3 – 2x2 + 5x5 – 7x7

[tex]P(x) = 3 - 2x^2+ 5x^5 - 7x^7[/tex]

Order for any polynomial is highest exponential value for variables . The exponent for polynomial is also called as degree.

Hence in terms of degree, the term in polynomial which has  the highest degree . That degree is the order of the polynomial.

For example ,

in [tex]x^5 + x^8 + x^9[/tex]

here we see that variable x has highest power of 9. Thus, order of the given equation is 9.

Similarly for the polynomial given we see that

in the polynomial [tex]P(x) = 3 - 2x^2+ 5x^5 - 7x^7[/tex]

x has three power 2, 5 and 7 .

As 7 is the highest power of P(x) = 3 - 2x^2+ 5x^5 - 7x^7

This, polynomial has order 7.

Answer:

a) [tex] P(X \geq 1) = 1-P(X<1) = 1-P(X=0)[/tex]

[tex]P(X=0)=(9C0)(0.99)^0 (1-0.99)^{9-0}=1x10^{-18}[/tex]

And replacing we got:

[tex] P(X \geq 1) =1 -1x10^{-18} \approx 1[/tex]

b) [tex]P(X=7)=(9C7)(0.99)^7 (1-0.99)^{9-7}=0.003355[/tex]

[tex]P(X=8)=(9C8)(0.99)^8 (1-0.99)^{9-8}=0.083047[/tex]

[tex]P(X=9)=(9C9)(0.99)^9 (1-0.99)^{9-9}=0.913517[/tex]

And adding we got:

[tex] P(X \geq 7) = 0.003355+0.083047+0.913517 =0.99992[/tex]

c) [tex] P(X \leq 8) =1 -P(X>8) = 1-P(X=9)[/tex]

[tex]P(X=9)=(9C9)(0.99)^9 (1-0.99)^{9-9}=0.913517[/tex]

And replacing we got:

[tex] P(X \leq 8)= 1-0.913517=0.086483[/tex]

Step-by-step explanation:

Let X the random variable of interest "numebr of times that an alarm is triggered", on this case we now that:

[tex]X \sim Binom(n=9, p=0.99)[/tex]

The probability mass function for the Binomial distribution is given as:

[tex]P(X)=(nCx)(p)^x (1-p)^{n-x}[/tex]

Where (nCx) means combinatory and it's given by this formula:

[tex]nCx=\frac{n!}{(n-x)! x!}[/tex]

Part a

We want to find this probability:

[tex] P(X \geq 1) = 1-P(X<1) = 1-P(X=0)[/tex]

[tex]P(X=0)=(9C0)(0.99)^0 (1-0.99)^{9-0}=1x10^{-18}[/tex]

And replacing we got:

[tex] P(X \geq 1) =1 -1x10^{-18} \approx 1[/tex]

Part b

[tex] P(X \geq 7)= P(X=7) +P(X=8)+ P(X=9) [/tex]

[tex]P(X=7)=(9C7)(0.99)^7 (1-0.99)^{9-7}=0.003355[/tex]

[tex]P(X=8)=(9C8)(0.99)^8 (1-0.99)^{9-8}=0.083047[/tex]

[tex]P(X=9)=(9C9)(0.99)^9 (1-0.99)^{9-9}=0.913517[/tex]

And adding we got:

[tex] P(X \geq 7) = 0.003355+0.083047+0.913517 =0.99992[/tex]

Part c

[tex] P(X \leq 8) =1 -P(X>8) = 1-P(X=9)[/tex]

[tex]P(X=9)=(9C9)(0.99)^9 (1-0.99)^{9-9}=0.913517[/tex]

And replacing we got:

[tex] P(X \leq 8)= 1-0.913517=0.086483[/tex]

Answer:

1/12

Step-by-step explanation:

dice has 6 sides so the prob of getting 4 is 1/6

coin has 2 sides  so the prob of getting tails is 1/2

Probability of getting both tails and a four simultaneously is = 1/2×1/6=1/12.

hope this helped!

Please mark as Brainliest!

Answer:

1/12

Step-by-step explanation:

The probability of get a 4 in a die is 1/6 because a die has the following numbers 1,2,3,4,5,6 ; we see each number occurs just once hence; 1/6 is the probability.

The probability of getting a tail is 1/2 because there are one tail and one head in a 2 side face coin.

Hence getting a tail and a four is ;

1/6 × 1/2 = 1/12

Answer:

x = 98

Step-by-step explanation:

The exterior angle is equal to the sum of the opposite interior angles

x + 24 = 122

Subtract 24 form each side

x+24-24 =122-24

x =98

Answer:

[tex] x = 98 \: \: degrees \\ [/tex]

Step-by-step explanation:

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

[tex]24 + x = 122 \\ x = 122 - 24 \\ x = 98 \: \: degrees[/tex]

hope this helps

brainliest appreciated

good luck! have a nice day!

Answer:

For this case we know that the fixed cost is $36.50 and the variable cost is 17% of the total amount of money customers spend, let's asusme that this variable is x. And we can create a model like this one:

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

Where y represent the income and x the the total amount of money customers would need to spend. For this case the value for b = 36.50 and the slope m would be 0.17 since if we convert the % into a fraction we got 0.17. So then the best option is:

[tex] 150 = 36.5 +0.17x[/tex]

D. 150 = 36.50 + 0.17x

Step-by-step explanation:

For this case we know that the fixed cost is $36.50 and the variable cost is 17% of the total amount of money customers spend, let's asusme that this variable is x. And we can create a model like this one:

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

Where y represent the income and x the the total amount of money customers would need to spend. For this case the value for b = 36.50 and the slope would be 0.17 since if we convert the % into a fraction we got 0.17. So then the best option is:

[tex] 150 = 36.5 +0.17x[/tex]

D. 150 = 36.50 + 0.17x

Answer:

Step-by-step explanation:

We would determine the volume of the

pyramid-like paperweight. Formula for volume is expressed as

Volume = mass/density

From the information given,

mass = 400g

Density = 1.61g/cm³

Volume = 400/1.61 = 248.45cm³

The formula for determining the volume of a pyramid us expressed as

Volume = 1/3 × base area × height

From the information given,

Base area = 120 cm²

Volume = 248.45cm³

Therefore,

248.45 = 1/3 × 120 × height

248.45 = 40 × height

height = 248.45/40 = 6.2 cm

Answer:

[tex] \hat p =\frac{14}{250}= 0.056[/tex]

And for this case that represent the 5.6% of the homeless persons who are veterans

Step-by-step explanation:

We know that in a survey of 250 homeless persons 14 were veterans. We can find the estimated proportion of homeless persons who are veterans with the following formula:

[tex] \hat p =\frac{X}{n}[/tex]

The last one is an unbiased estimator of the true population proportion p

And replacing the info given we got:

[tex] \hat p =\frac{14}{250}= 0.056[/tex]

And for this case that represent the 5.6% of the homeless persons who are veterans

Answer:

degree 1

Step-by-step explanation:

The trapezoidal rule is exact when the second derivative is zero.  This occurs when the polynomial is degree one or less

Answer:  c) 3 x 5

Step-by-step explanation:

When multiplying matrices of dimension m x n, the "inside" values MUST be the same. The dimension of their product is the "outside" values.

P = 3 x 4

Q =      4 x 5

The "inside" values are both 4 so the product can be found.

The "outside" values are 3 & 5 so the dimension of the product is 3 x 5.

If the problem was flipped to: find QP, we would get the following:

Q = 4 x 5

P =        3 x 4

the "inside" values of 3 & 5 are not the same so the product does not exist.

Answer:

Since there is no change in the height value over that time, the slope is 0

Answer:

3/5

Step-by-step explanation:

(3/5) · (1/2) over (3/5) · (1/2) + (2/5) · (1/2)

= 3/5