Select all the equations that have {4} as its solution set.
Responses

79−3x=12x+19

7−x=12x


x2+3=10x−21


5 + 2x = 3x + 3

SELECT ALL, THIS IS MULTIPLE CHOICE.

Answer: 56 minutes

Step-by-step explanation:

7 = 7, 14, 28, 35, 42, 49, 56

8 = 8, 16, 24, 32, 40, 48, 56

7 and 8 have 56 in common so it would take them 56 minutes

The solutions to these system of equations are given as follows:

1. x = 1, y = 7.

2. x = 0.5, y = 2.

3. x = 6, y = -2.

4. x = 3, y = 3.

A system of equations is a set of equations involving multiple variables that are related, and then operations are made to solve these equations and identify the numeric value of each variable in the context of a problem.

For item 1, it is already stated that the solution for x is x = 1, hence the solution for y is obtained as follows:

y = 2(1) + 5 = 7.

For item 2, we are given two equations for y, hence the solution for x is obtained as follows:

2x + 1 = 6x - 1

4x = 2

x = 2/4

x = 0.5.

Hence the solution for y is:

y = 2(0.5) + 1 = 1 + 1 = 2.

For item 3, from the second equation, we have that:

y = 4 - x.

Then the solution for x will be of:

2(x - 7) = 4 - x

2x - 14 = 4 - x

3x = 18

x = 18/3

x = 6.

The solution for y is:

y = 4 - 6 = -2.

For item 4, from the first equation, we have that:

y = 3x - 6.

Then, replacing on the second equation, the solution for x is obtained as follows:

x + 3(3x - 6) = 12

x + 9x - 18 = 12

10x = 30

x = 3.

Then the solution for y is:

y = 3x - 6 = 3(3) - 6 = 9 - 6 = 3.

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The surface area of the largest size sphere that can fit in this box is 400π

What is the surface area of the sphere?

The surface area of a sphere is the space that the sphere's outer surface occupies. A sphere is a circle in three dimensions. A circle is a two-dimensional (2D) shape, whereas a sphere is a three-dimensional (3D) shape, which is the difference between the two.

Here, we have

The diameter of the biggest sphere will be equal to the side of the sphere.

radius = 20/2

​ = 10

The surface area of the sphere = 4πr²

=4π(10)²

= 400π

Hence, the surface area of the largest size sphere that can fit in this box is 400π.

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The conversion of the measurement of 65 lb will be 29483.5 g.

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.

In this case, we need to convert 65 lb to g

It should be noted that we have to multiply the weight value by 453.5

Therefore, it should be noted that 65 lb will be:

= 65 x 453.5

= 29483.5 g.

Therefore, it should be noted that the conversion of the measurement of 65 lb will be 29483.5 g.

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Answer:

B

Step-by-step explanation:

if x = 0 ; y = 3

if x = -7 ; y = 0

A 0 + 7(3) = 21

0 + 21 = 21

21 = 21 (ok)

3(-7) + 0 = 21

-21 = 21 (false)

B

0 + 21 = 21

21 = 21 (ok)

(-3)(-7) + 0 = 21

21 = 21 (ok)

Answer:

1). True

2). x = 16.4 m^2

3). A = 24, h = 4

4). A = 18.39

5). 162

Step-by-step explanation:

I took this quiz on K12 and got everything correct! Brainliest welcome! :)

The probability that the proportion of no-shows in a sample of 789 ticketed passengers would differ from the population proportion by less than 3% is 0.9968

The probability is calculated using z score, this is used to determine the amount of standard deviations a sample, X is from the mean

The z score is given by the formula

z = (X - μ) / σ

Definition of variables

mean, μ  = p = 9% = 0.09

sample size, n = 789

standard deviation, σ

= √{(p(1 - p)) / n}

= √{(0.09(1 - 0.09)) / 789}

= √{(0.09 * 0.91) / 789}

= 0.0102

The probability

differ from the population proportion by less than 3%

|X - 0.09| < 0.03

X < 0.12 OR X > 0.06

0.06 < X < 0.12

P(z < 0.12) - P(z < 0.06 )

z score for z < 0.06

z = (0.06 - 0.09) / 0.0102

= -2.9412

p value for z < -2.9412 = 0.0016

z score for z < 0.12

z = (0.12 - 0.09) / 0.0102

=  2.9412

p value for z < 2.9412 = 0.9984

The probability required = 0.9984 - 0.0016 = 0.9968

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The simple interest is 2112.5 and the maturity value is 21,612.5

In the given question,

We have to find the simple interest and maturity value.

The given principal amount (P)= 19,500

The interest rate (r)= 6 1/2%

We write the interest in improper fraction. We can write it as 6 multiple with 2 then adding the result of multiplication with 1.

So the simplest form (r)=13/2%

Time = 20 months.

Now converting the months into years.

As we know that in one year have 12 months.

So the Time = 20/12

Time (T)= 5/3

The formula of simple interest is

I = P*R*T/100

Now putting the value

I = 19,500*(13/2)*(5/3)/100

Simplifying

I = 19,500*13*5/100*2*3

I = 1,267,500/600

I = 2112.5

Hence, the simple interest is 2112.5.

Now finding the maturity value(MV).

MV=P+I

MV=19,500+2112.5

MV=21,612.5

Hence, the maturity value is 21,612.5

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After factorization we get the two terms ( w - 3 ) ( w + 2 )

And the values of  A and B as 3 and 2 respectively .

That is A = 3 and B = 2.

The given expression is w² - w - 6.

This question can be calculated easily by middle term split

First step is to multiply the first and the last term

which will give us - 6

thus now we have to look for two number which when either added or subtracted will give us - 1

Thus we can write it as :

w² - 3 w + 2 w - 6

Now take the terms which are common

and we will get

w ( w - 3 ) + 2 ( w - 3 )

( w - 3 ) ( w + 2 )

Thus if we compare it with (w - A) (w + B)

we will get the values of A and B as

3 and 2 respectively .

That is A = 3 and B = 2

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The simplified value of (2x - 4)² is 4x² - 16x + 16.

First, let us understand the algebraic identities;

Algebraic identities are equations in which the left hand side of the equation is identically equal to the right hand side of the equation.

Some of the identities are:

We are given (2x - 4)².

Use the identity (a - b)² = a² - 2ab + b² to expand to the given expression.

So, a = 2x and b = 4.

Put it into the identity, we will get;

Therefore,

(2x - 4)² = (2x)² - 2 * 2x * 4 + (4)² = 4x² - 16x + 16

Thus, the simplified value of (2x - 4)² is 4x² - 16x + 16.

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The length of wall in real life is 4 feet.

Given that on an architect's blueprint, 1 inch corresponds to 4 feet.

In this architect's plan, a wall represented by a line 1 inches long on the blue print.

So, the length of wall in real life is = 4 feet.

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Answer:

4ft

Step-by-step explanation:

If 1 inch corresponds to 4 ft on the blueprint. The ratio is 1 inch on the blue print for every 4 ft in real life.

Answer:

Step-by-step explanation:

The numbers matched with its divisibility numbers is

for 60 the divisibility numbers are 2,3,5,10 .

for 48 the divisibility numbers are 2,3    and

for 81 the divisibility numbers are 3,9 .

In the question ,

three numbers are given as 60 , 48 and 81

we need to match them with their , respective divisibility numbers that are given in the option  

For the first number 60 ,

we see that 60 is divisible by 2 , 3 , 5 and 10 because

30*2 [tex]=[/tex] 60  , 3*20 [tex]=[/tex] 60 , 5*12 [tex]=[/tex] 60 and 10*6 [tex]=[/tex]60 ,

So, for 60 the divisibility numbers are 2,3,5,10

that is option(c)

For the second number 48 ,

we see that 48 is divisible by 2 and 3  because

2*24 [tex]=[/tex] 48 , 3*16 [tex]=[/tex] 48 ,

So , for 48 the divisibility numbers are 2,3

that is option(b)

For the third number 81

we see that 81 is divisible by 3 and 9  because

3*27 [tex]=[/tex] 81 , 9*9 [tex]=[/tex] 81

So , for 81 the divisibility numbers are 3 an 9

that is option(a)

Therefore , The numbers matched with its divisibility numbers is

for 60 the divisibility numbers are 2,3,5,10 .

for 48 the divisibility numbers are 2,3    and

for 81 the divisibility numbers are 3,9 .

The given question is incomplete , the complete question is

Match the numbers 60 , 48 and 81  with its divisibility numbers

(a) 3,9

(b) 2,3

(c) 2,3,5,10

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Answer: C

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The standard form of polynomial is x^2 + 9x - 1/10

To write the equation in standard form, look at the degree of highest term and then rewrite the equation in decreasing order of degree i.e. from highest to lowest.

The given polynomial is

⇒ x^2 + 9x - 1/10

The standard form of the polynomial is

⇒ x^2 + 9x - 1/10

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Answer:

Step-by-step explanation:

The answer would be 1.82448

The two possible solutions of the given quadratic equation are -

x =  +√6 +5 and x =  -√6 +5

For the given question;

(x - 5)² - 6 = 0

Bring constant on other side.

(x - 5)² = 6

Taking square root both side.

√ (x - 5)² = √6

(x - 5) = ±√6

Separate the constant and variables.

x =  ±√6 +5

There are two possible solution.

x =  +√6 +5 and x =  -√6 +5

Thus, the two possible solutions of the given quadratic equation are -

x =  +√6 +5 and x =  -√6 +5.

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Distance is the total length covered by an object.

Displacement is the distance between the final point and the initial point.

The distance of the helicopter's flight is 150 m

The displacement of the helicopter's flight is zero.

Displacement is the distance between the final point and the initial point.

We have,

A helicopter lifts 75m vertically into the air and then comes back down to the ground.

Distance is the total length covered by an object.

Distance of the helicopter's flight.

= 75m + 75m

= 150 m

Displacement of the helicopter's flight.

= Final point - Initial point

= 0 - 0

= 0  

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The equation of the transformation of the exponential function y = 2ˣ in the form y = A·2ˣ + k, obtained from the simultaneous found using the points on the graph is y = (-2)·2ˣ + 3

An exponential equation is an equation that has exponents that consists of variables.

The given equation is y = 2ˣ

The equation for the transformation is; y = A·2ˣ + k

The points on the graphs are;

(0, 1), (1, -1) and (2, -5)

Plugging the x and y-values to find the value A and k gives  the following simultaneous equations;

When x = 0, y = 1, therefore;

1 = A·2⁰ + k = A + k

1 = A + k...(1)

When x = 1, y = -1, which gives;

-1 = A·2¹ + k

-1 = 2·A + k...(2)

Subtracting equation (1) from equation (2) gives;

-1 - 1 = 2·A - A + k - k

-2 = A

1 = A + k, therefore;

1 = -2 + k

k = 2 + 1 = 3

k = 3

Which gives;

y = -2·2ˣ + 3 = 3 - 2·2ˣ

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Based on the number of people present, the total number of combinations of Chairperson and Vice Chairperson is 240 combinations.

In order for us to find out the total possible combinations, we will use the formula as:

Total possible combinations = Number of possible chairpersons * Number of possible vice chairpersons

We are given that;

Number of possible chairpersons = 16

Number of possible vice chairpersons = 15 (This is because a chairperson is chosen first and leaves 15 people.)

Thus, we can say that;

Total possible combinations = 16 * 15

Total possible combinations = 240 combinations

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Answer:

yes

Step-by-step explanation:

because 4

Answer:

Step-by-step explanation:

average rate of change

[tex]=\frac{25-(-10)}{9-2} \\=\frac{35}{7}\\=5[/tex]

Answer:6/13/3

Step-by-step explanation:look at how the year’s difference are

Answer: -2 isn’t a whole number and -1.2 isn’t a integer.

a) $149911.84 can be afforded

b) $39600 is the total money you will pay the loan company

c) $246088.16 is the interested amount

Calculation

Given,

d=$1100

N= 30 years

r = 8% or 0.08

a) Loan amount that can be afforded

[tex]=\frac{d[1- (1+\frac{r}{k})^{-Nk} }{\frac{0.08}{12} }[/tex]

[tex]=\frac{1100[1- (1+\frac{0.08}{12})^{-30*12} }{\frac{0.08}{12} }[/tex]

= $149911.84

b) Total money you pay = d×N×k

=1100×30×12

=$39600

c) Interest paid = Total money paid – loan amount

⇒39600–14911.84 = $246088.16

Hence,

a) $149911.84 can be afforded

b) $39600 is the total money you will pay the loan company

c) $246088.16 is the interested amount

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Answer:

yes, if the labor takes 150 minutes (or 2h 30 minutes)

Step-by-step explanation:

m + 350 = 2m + 200

2m - m = 350 - 200

m = 150

Using the given table, the y-values are 36, 54, 81, 121.5, and 182.25.

We are given a table. Mathematical tables are collections of numbers that represent the outcome of a computation with varied arguments. The table has two columns and five rows. The first column shows the x-values. The second column shows the f(x) values. We know that y = f(x). So, the second column shows the y-values. The y-value is the vertical value in a pair of coordinates. It denotes how high or low the point is. In an ordered pair of coordinates, the y-coordinate is always written second (x, y). The five rows show the data points with corresponding x-values and y-values.

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The number of mainland countries is 20 and the number of island countries is 5 countries that Willy visited.

Let the number of mainland be represented by m

Let the number of island be represented by x.

This will be illustrated as:.

m + x = 25 .... i

2m + 5x = 65 .... ii

From equation i, m = 25 - x.

Put this into equation ii

2m + 5x = 65

2(25 - x) + 5x = 65

50 - 2x + 5x = 65

3x = 65 - 50

3x = 15

Divide

x = 15 / 3

x = 5

Island countries = 5

Since m + x = 25

m = 25 - 5 = 20

Mainland countries = 20

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