3(x+2)+7 equivalent expression

For the quadratic equation:

x^2 + 7x = 8x + 12

The two solutions are:

x = 4

x = -3

I'm only solving the first question, as it is how the guidelines say.

Here we have the quadratic equation:

x^2 + 7x = 8x + 12

First, we can rewrite this equation as:

x^2 + 7x - 8x - 12 = 0

x^2 - x - 12 = 0.

Using Quadratic formula we can see that the solutions (or zeros of the quadratic) are:

x = (1 ± √(  (-1)^2 - 4*1*-12))/(2*1)

x = (1 ± 7)/2

Then the two solutions are:

x = (1 + 7)/2 = 4

x = (1 - 7)/2 = -3

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Answer: C, x = -16

Step-by-step explanation:

1. Distribute

7x-2(x+1)=6x+14

7x-2x-2=6x+14

2. Combine like terms

7x-2x-2=6x+14

5x-2=6x+14

3. Add 2 to both sides

5x-2+2=6x+14+2

4. Simplify

Add the numbers

5x=6x+16

5. Subtract 6x from both sides

5x-6x=6x+16-6x

6. Simplify

Combine like terms

-x=16

7. Divide both sides by the same factor

-x/-1=16/-1

8. Simplify

Cancel terms that are in both the numerator and denominator

Divide the numbers

Answer:

3x(x+6)

=(3x)(x+6)

=(3x)(x)+(3x)(6)

=3x2+18x

Step-by-step explanation:

Answer: -21x^3 + 28x^2 y

Answer:

1) Conditional

If a month begins with letter M, then it has 31 days.

2) Converse

If a month has 31 days, then it begins with letter M.

3) Inverse

If a month does not begin with the letter M, then it does not have 31 days.

4) Contrapositive

  If a month does not have 31 days, then it does not begin with the letter M.

Step-by-step explanation:

1) Conditional

If a month begins with letter M, then it has 31 days.

2) Converse

If a month has 31 days, then it begins with letter M.

3) Inverse

If a month does not begin with the letter M, then it does not have 31 days.

4) Contrapositive

  If a month does not have 31 days, then it does not begin with the letter M.

Conditional statement states the original statement. If 'p' , then 'q'

Converse statement switch positions in the original if --then statement. If 'q', then 'p'

Inverse statement states the opposite of the original statement. If not 'p', then not 'q'.

Contrapositive if not 'q' , then not 'q'.

The situation in which the binomial distribution can be approximated to the normal distribution is given by:

(b) a nurse instructs an adult patient to take his resting pulse 10 times over the next few days. a resting pulse requires resting for at least 10 minutes before taking the pulse. the random variable ???? is the number of measurements that are less than 100 beats per minute.

The formula for the probability of x successes is:

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

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

The parameters are given by:

The binomial distribution can be approximated to the normal distribution if there are at least 10 failures and 10 successes on the experiment, that is:

np ≥ 10, n(1 - p) ≥ 10.

Meaning that a large number of trials is usually required for the approximation.

In the context of this problem, to achieve the large number of trials needed for the approximation, multiple days are needed to take the observations, hence option b is correct.

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Answer:

y = x(2.50)+3.25

Step-by-step explanation:

y (total cost )= x (miles rode) * 2.50 (cost per mile) + 3.25 (initial cost)

Answer:

y=1.34x-3.22

Step-by-step explanation:

y=mx+b

find m/ gradient:

[tex]m = \frac{-3.94 - 2.4}{-4.75 - 0}[/tex]

∴[tex]m=1.34[/tex]

find b/ y-intercept:

sub (2.4,0)

0= 1.34 (2.4) +b

b=0-3.216

b= -3.216

∴ b=-3.22(2.d.p)

linear equation:

∴1.34x-3.22

Answer:

-3(-1) + 4 = 3 + 4 = 7

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

-3(1) + 4 = -3 + 4 = 1

-3(2) + 4 = -6 + 4 = -2

In the picture there is a prism with measures. The surface area of prism is 156.

Given that,

In the picture there is a prism with measures.

We have to find the surface area of prism.

The surface area of prism=(2×base area)+(Base perimeter×height)

The base is trapezoid

So, the area of trapezoid is (a+b)/2×h

=(6+12)/2×4

=18/2×4

=9×4

=36

Here base area we got is 36.

Now, we find the perimeter of trapezoid is a+b+c+d

=6+12+5+5

=18+10

=28

Here, base perimeter we got is 28.

Now surface area of prism is

=(2×36)+(28×3)

=72+84

=156

Therefore, the surface area of prism is 156.

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The compound interest of $182.60 will not be enough to pay for the award.

So, annual interest will be sufficient to serve the award:

(Refer to the compound chart given below)

Therefore, the compound interest of $182.60 will not be enough to pay for the award.

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Answer: Sorry for the late answer, I was already answering it by the time someone else answered

Step-by-step explanation:

Since two angles on a straight line add up to 180, I used the angles given to find the adjacent angles to it by subtracting those angles from 180. Then, since the angles of a triangle add up to 180, I used the angles I just solved for to find the angle that is adjacent to n. I did the same thing I did to the first two angles by subtracting it from 180 to find n, which was 69 degrees

The distance of art store from Ella's house is  2/3 miles or 0.67 miles.

It is a question of time, speed and distance.

It is given in the question that Ella walks to the art store at 2mph, but returns home at 4 mph.

Also, the total time taken by Ella to cover the journey is 1/2 an hour.

We have to find the distance of art store from Ella's house.

Let the distance from Ella's house to art store be d miles.

We know that,

Speed = distance/time

Time = distance/speed

Hence, we can write,

time = d/2  (walking to the art store from from)

Also,

time = d/4  (walking to home from the art store)

Hence,

d/2 + d/4 = 1/2

3d/4 = 1/2

d = 2/3 miles or 0.67 miles.

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Answer: 51

Step-by-step explanation:

Answer:

0.41

Step-by-step explanation:

correct value of x will 9 if Maggie corrected her mistake.

When the greatest power of the variable is consistently 1, an equation is considered to be linear. A one-degree equation is another name for it. The typical form of a linear equation with one variable is Ax + B = 0. The variables x and A in this situation are variables, whereas B is a constant.

Applying the parallel line theorem

alternate angles are always equal -

therefore ,

 4x + 2 = 7x - 25

27 = 3x

x = 9

so , the correct value of x will be 9 if maggie corrected her mistake

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Based on the fact that the two numbers multiply to 2,400 and add up to -16, the numbers are undefined.

Assume that one of the numbers is x and the other number is y, the system of equations to represent this is given that the two numbers add up to -16 and multiplying to 2,400:
x + y = -16

xy = 2,400

Expressing y in terms of x :

xy = 2,400

y = 2,400 / x

Solving for x gives:

x + y = -16

x + (2,400 / x) = -16

x = 0

y = 0

The problem given in the question is wrong because the results of x and y are undefined.

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Using Venn diagram, if a student is chosen randomly, (a) the probability that he or she is not in any of the language classes is 0.5, (b) the probability that he or she is taking exactly one language class is 0.32, and (c) if 2 students are chosen randomly, the probability that at least 1 is taking a language class is 0.753.

Venn diagram is a diagram used to present the relationship between sets in a logical form. (See attached image)

Let A = students in the Spanish class = 28

B = students in the French class = 26

C = students in the German class = 16

Hence, the probability of each class is:

P(A) = 28/100 = 0.28

P(B) = 26/100 = 0.26

P(C) = 16/100 = 0.16

P(A ∩ B) = 12/100 = 0.12

P(B ∩ C) = 6/100 = 0.06

P(A ∩ C) = 4/100 = 0.04

P(A ∩ B ∩ C) = 2/100 = 0.02

(a) P(not A, B, C) = 1 - P(A ∪ B ∪ C)

P(not A, B, C) = 1 - [P(A) + P(B) + P(C) - P(A ∩ B) - P(B ∩ C) - P(A ∩ C) + P(A ∩ B ∩ C)]

P(not A, B, C) = 1 - (0.28 + 0.26 + 0.16 - 0.12 - 0.06 - 0.04 + 0.02)

P(not A, B, C) = 1 - 0.5

P(not A, B, C) = 0.5

(b) P(A, B, C only) = P(A only) + P(B only) + P(c only)

P(A, B, C only) = [P(A) - P(A ∩ B) - P(A ∩ C) + P(A ∩ B ∩ C)] + [P(B) - P(A ∩ B) - P(B ∩ C) + P(A ∩ B ∩ C)] + [P(C) - P(B ∩ C) - P(A ∩ C) + P(A ∩ B ∩ C)]

P(A, B, C only) = (0.28 - 0.12 - 0.04 + 0.02) + (0.26 - 0.12 - 0.06 + 0.02) + (0.16 - 0.06 - 0.04 + 0.02)

P(A, B, C only) = 0.14 + 0.10 + 0.08

P(A, B, C only) = 0.32

(c) P = 1 - (50/100 x 49/99)

P = 1 - (49/198)

P = 149/198

P = 0.753

To complete the problem, here are the questions:

(a) If a student is chosen randomly, what is the probability that he or she is not in any of the language classes?

(b) If a student is chosen randomly, what is the probability that he or she is taking exactly one language class?

(c) If 2 students are chosen randomly, what is the probability that at least 1 is taking a language class?

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The simplified value of (3⁴)⁻¹ is 1/(3⁴) , which means one over three raised to the fourth power , the correct option is (a) .

In the question ,

the expression is given as (3⁴)⁻¹ ,

the rule of law of exponents states that a⁻ⁿ = 1/aⁿ .

Using the above mentioned law of indices , the expression  (3⁴)⁻¹ can be written as ,

(3⁴)⁻¹ = 3⁻⁴ = 1/3⁴

which can be expressed in words as one over three raised to the fourth power .

Therefore , the simplified value of (3⁴)⁻¹ is 1/(3⁴) , which means one over three raised to the fourth power , the correct option is (a) .

The given question is incomplete , the complete question is

The Simplified value of (3⁴)⁻¹ is

(a) one over three raised to the fourth power

(b) one over three raised to the power of negative four

(c) −3 to the power of 4

(d) 3 to the power of 3

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Clay and Jason are 600 feet far apart.

When an object goes above the surface, the altitude is measured as +ve and when an object goes below the surface, the altitude is measured as -ve.

Since Clay is flying a helicopter at an altitude of 400 feet in the air,

The Value of altitude of Clay = +400

Since, Jason is diving 200 feet below the surface,

The Value of altitude of Jason = -200

The the distance between Clay and Jason = (The Value of altitude of Clay) - (The Value of altitude of Jason)

= +400 - (-200)

= 400 + 200

= 600 feet

Therefore, the distance between Clay and Jason is 600 feet.

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Answer:

As a fraction: 3/50

It cannot be turned into a mixed number

If the balance were growing according to the exponential function, the balance owed on your credit card after 9 months is equal to $1,502.02.

In Mathematics, an exponential function simply refers to a mathematical function whose values are generated by a constant that is raised to the power of an argument.

From the information provided, an exponential function that models or represents the rate at which the balance owed on your credit card triples is given by:

f(x) = 500(1 + 0.13)^x

Where:

After 9 months, the balance owed on your credit card would be calculated by substituting the value of x with 9 as follows:

Balance owed,  f(x) = 500(1 + 0.13)^9

Balance owed, f(x) = 500(1.13)^9

Balance owed, f(x) = 500 × 3.0040419380

Balance owed, f(x) = $1,502.02.

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Complete Question:

Growing linearly, the balance owed on your credit card triples from $500 to $1500 in 9 months. If the balance were growing according to the exponential function f(x) = 500(1 + 0.13)^x, where x represents the number of months, what would the balance be after 9 months? Round your answer to the nearest cent.

Answer:

$1502.02

Step-by-step explanation:

f(x)=500(1+0.13)^x

f(9) = 500(1.13)^9

f(9) = 500(3.004041938)

f(9) = 1502.02

Answer: $1502.02

answer = a

formula; a(1 + r)^x

a = the initial amount - 7.71  [answer cannot be b or d]

! i think it's a as the decay factor is < 1, therefore, 100-.933333

Answer:

b

Step-by-step explanation:

Mang Efren's present age is 30 years.

Let's assume the present age of Mang Efren's son is x years.

Mang Efren is presently 5 times as old as his son.

So, Mang Efren's present age = 5x years

Four years ago,

Mang Efren's son's age = x - 4 years.

Mang Efren's age = 5x - 4 years

According to the question, four years ago, the product of their ages was 52.

From this information, we will create an equation.

(x - 4)(5x - 4) = 52

5x² - 4x - 20x + 16 = 52

5x² - 24x + 16 - 52 = 0

5x² - 24x - 36 = 0

Solving the quadratic equation to obtain the value of x,

5x² - 30x + 6x - 36 = 0

5x(x -6) + 6(x - 6) = 0

(5x - 6)(x - 6) = 0

x = 6

So, Mang Efren's present age is 5 × 6 = 30 years.

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By using the concept of uniform rectilinear motion, the distance surplus of the average race car is equal to 3 / 4 miles. (Right choice: A)

In accordance with the statement, both the average consumer car and the average race car travel at constant speed (v), in miles per hour. The distance traveled by the vehicle (s), in miles, is equal to the product of the speed and time (t), in hours. The distance surplus (s'), in miles, done by the average race car is determined by the following expression:

s' = (v' - v) · t

Where:

Please notice that a hour equal 3600 seconds. If we know that v' = 210 mi / h, v = 120 mi / h and t = 30 / 3600 h, then the distance surplus of the average race car is:

s' = (210 - 120) · (30 / 3600)

s' = 3 / 4 mi

The distance surplus of the average race car is equal to 3 / 4 miles.

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Answer:

8800000 or 88x 10^5

Step-by-step explanation:

4x2200000=8800000

Answer:

seven and a half hours

Step-by-step explanation:

aa