What is the justification for each step in the solution of the equation?

54+2x=5x−3(2+6x)

Select from the drop-down menus to correctly justify each step.

54+2x=5x−3(2+6x) Given

54+2x=5x−6−18x Choose....Addition property of equality, Distributive property, or multiplication Property of equality

54+2x=−13x−6 Combine like terms
54=−15x−6 Subtraction Property of Equality

60=−15x Choose......Addition property of equality, Distributive property, or multiplication Property of equality

−4=x choose........Addition property of equality, Distributive property or equality, or multiplication Property of equality

Answer:

0.03095

Step-by-step explanation:

         0.03095

200   6.19000

        -600

           1900

          -1800

             1000

            -1000

             0

Answer:

She will make a total commission of $1130+$325=$1445

Then 5% of $1445= $1445×5%=$72,75

To reduce a fraction, you divide the numerator and denominator by the same number.

This number is the greatest common divisor (GCD) of the numerator and denominator. By dividing both the numerator and denominator by their GCD, you simplify the fraction to its simplest form. The GCD is the largest number that evenly divides both the numerator and denominator without leaving a remainder.

Dividing by the GCD ensures that the fraction is expressed in its lowest terms, where the numerator and denominator have no common factors other than 1. This process eliminates any common factors and reduces the fraction to its simplest representation.

Therefore, To reduce a fraction, you divide the numerator and denominator by the same number. Option c is correct.

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Answer:

The area of the space that will be covered bricks is 4/15 ft^2

Step-by-step explanation:

Here, we are interested in calculating the area of the space that will be covered by bricks.

This can be obtained directly by finding the area of the rectangular shape;

Mathematically;

area of a rectangle = L * B

Since we have both measurements already;

Then the area of the space will be 3/5 * 4/9 = 12/45 = 4/15 ft^2

Answer: 4x√5

Simplify the radical by breaking the radicand up into a product of known factors, assuming positive real numbers.

Answer:

x = 9 ; y = 18

Step-by-step explanation:

This is a 30° 60° 90° triangle meaning the length of the big leg will be the value of the small leg times √3 and the hypotenuse will be double the length of the small leg.

Answer:

x = 9

y = 18

Step-by-step explanation:

tan(60) = 9 radical 3 / x

x = 9 radical 3 / tan(60)

x = 9

a² + b² = c²

9² + 9radical3² = c²

324 = c²

c = 18

y = 18

The area of the square is 144 \(cm^{2}\).

Let x be the side of the square. Then the length of the triangle is (x+4). Perimeter is the length of all sides of a geometric figure combined. For an equilateral triangle, it's equal to thrice the length of one side. For a square, it's four times the length of one side. The Perimeter of the Triangle is 3(x+4) & the Perimeter of the square is 4x.

We know, both these perimeters are equal. Hence,

4x = 3(x+4)

To further simplify the above equation.

4x = 3x + 12

x = 12

Hence, the length of one side of the square is 12 cm. The area of the square can be calculated as follows:

Area = \((side)^{2}\)

Area = 12 * 12

Area = 144 \(cm^{2}\)

Hence, the Area of the Square is 144 \(cm^{2}\)

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The line which has points (5,7),(-4,-2) is slanting upward.

Given that the line has points (5,7) and (-4,-2).

We are required to find whether the line is upward sloping, downward , horizontal or vertical.

The slope or gradient of a line is basically a number that describes both the direction and the steepness of the line.

Slope between two points \((x_{1} ,y_{1} ),(x_{2} ,y_{2} )\) is equal to \((y_{2} -y_{1}) /(x_{2} -x_{1} )\).

Slope between (5,7) and (-4,-2)=(-2-7)/(-4-5)

=-9/-9

=1

Because the slope is positive so it is an upward sloping line means the difference between the y coordinates and the difference between the x coordinates are equal.

Hence the line which has points (5,7),(-4,-2) is slanting upward.

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Answer:

d) y = (-3/4)(x - 3)^2 - 7

Step-by-step explanation:

The vertex form of a quadratic function is:

y = a(x - h)^2 + k

where (h, k) is the vertex of the parabola.

We are given that the vertex is (3, -7), so we can substitute these values into the equation:

y = a(x - 3)^2 - 7

Now we need to find the value of "a". We can use the fact that the function passes through the point (1, -10). Substituting these values into the equation gives us:

-10 = a(1 - 3)^2 - 7

Simplifying, we get:

-10 = 4a - 7

-3 = 4a

a = -3/4

Substituting this value of "a" into the equation, we get:

y = (-3/4)(x - 3)^2 - 7

Therefore, the quadratic function in vertex form that can be represented by the graph that has a vertex at (3, -7) and passes through the point (1, -10) is:

y = (-3/4)(x - 3)^2 - 7

1 Answer:

D

2 Answer:

B

Step-by-step explanation:

all we should do here is multiply both sides by -1 and switch the sign ≤ since we multiplied by a negative number

x is equal or greater than 3 so 3 is included

3 will be represented by a clored dot

so the graph is D

again multiply by -1 to get rid of the - signs and switch ≤ by ≥ since it's a negative number

x is equal or greater than -3  so -3 is included

the graph is b since there is a dot in -3

Answer:

g(x) = 12*x^2 + 8

Step-by-step explanation:

For a function f(x), a vertical stretch of scale factor k is defined as:

g(x) = k*f(x)

In this case, we know that f(x) = 3*x^2 + 2

And the function g(x) is the function f(x) vertically stretched by a factor of 4, then we have k = 4

and:

g(x) = 4*f(x)

Replacing by the actual function, we get

g(x) = 4*(3*x^2 + 2)

g(x) = 4*3*x^2 + 4*2

g(x) = 12*x^2 + 8

The correct option a. They are easier to buy and sell than other forms of investment, describes the relatively liquid.

A type of debt fund known as "liquid funds" mostly invests in higher financing instruments with 91-day maturities.

Thus,

Liquid assets are those that are challenging to buy, sell, or convert into cash.

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Answer:

The question is not clearly stated, but I can correctly infer that you wanted to ask the question below:

Out of 150 members, 120 took part, what is the percentage of the total that took part:

Answer:

80%

Step-by-step explanation:

The question is asking us to find what percentage of 150 is 120

Let the percentage of 150 that is 120 be x

x % of 150 = 120

x/100 × 150 = 120

0.01x × 150 = 120

0.01x = 120 ÷ 150 = 0.8

x = 0.8 ÷ 0.01 = 80

∴ 120 = 80% of 150

Answer:

The area is 45 inches

Step-by-step explanation:

L×W=A

Among the provided answer options, the closest value to -0.555 is -0.55, which is option c. Therefore, option c (-0.55) is the value of c that satisfies P(Z ? c) = 0.71.

The notation P(Z ? c) represents the probability that a standard normal random variable Z is less than or equal to c. To find the value of c that corresponds to P(Z ? c) = 0.71, we need to determine the Z-score associated with this probability.

Using a standard normal distribution table or a calculator, we can find that a Z-score of approximately 0.555 corresponds to a cumulative probability of 0.71. However, since we are looking for the value of c in P(Z ? c), we need to consider the opposite inequality.

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Step-by-step explanation:

if you did not make a mistake in the equation, then we have

-3x(x - 4) = -3x + 12

let's do the multiplication

-3x² + 12x = -3x + 12

and now let's combine all terms of the same type on one side of the equation to make it a "= 0" problem :

-3x² + 15x - 12 = 0

-x² + 5x - 4 = 0

this is a quadratic equation (because the highest exponent of the variable terms is "2" in x², so, things are squared or quadratic, hence the term "quadratic equation").

and it is one of the funny things in algebra :

am equation to the nth degree (that means the highest exponent of a variable term is n) has exactly n solutions (they might not be different, and they might not be members of R, but there are n solutions).

so, in our case, a quadratic equation has 2 solutions.

FYI - remember, the general solutions to such a quadratic equation

ax² + bx + c = 0

are

x = (-b ± sqrt(b² - 4ac))/(2a)

in our case

a = -1

b = 5

c = -4

x = (-5 ± sqrt(5² - 4×-1×-4))/(2×-1) =

= (-5 ± sqrt(25 - 16))/-2 = (-5 ± sqrt(9))/-2 =

= (-5 ± 3)/-2

x1 = (-5 + 3)/-2 = -2/-2 = 1

x2 = (-5 - 3)/-2 = -8/-2 = 4

so, our 2 solutions are x = 1 and x = 4.

Answer:

Step-by-step explanation:

First, expand the equation

-3x(x-4)=-3x+12

-3x^2+12+3x-12=0

-3x^2+15x-12=0

divide both sides by -3

x^2-5x+4

Solve by factoring

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

x=1, x=4

Answer:

The answer would be 10 cups

Step-by-step explanation:

The data includes a concave mirror with a radius of curvature of +31.5 cm and magnification of m = 3.40. The formula for magnification is m = v/u, and the focal length is f = r/2. Substituting the values, we get u = v/m, and using the mirror formula, the distance of the object from the mirror is 10.15 cm.

Given data: Radius of curvature of a concave mirror, r = +31.5 cm Magnification produced by the mirror, m = 3.40

We know that the formula for magnification is given by:

m = v/u where, v = the distance of the image from the mirror u = the distance of the object from the mirror We also know that the formula for the focal length of the mirror is given by :

f = r/2where,f = focal length of the mirror

Using the mirror formula:1/f = 1/v - 1/u

We know that a concave mirror has a positive focal length, so we can replace f with r/2.

We can now simplify the equation to get:1/(r/2) = 1/v - 1/u2/r = 1/v - 1/u

Also, from the given data, we have :m = v/u

Substituting the value of v/u in terms of m, we get: u/v = 1/m

So, u = v/m Substituting the value of u in terms of v/m in the previous equation, we get:2/r = 1/v - m/v Substituting the given values of r and m in the above equation, we get:2/31.5 = 1/v - 3.4/v Solving for v, we get: v = 22.6 cm Now that we know the distance of the image from the mirror, we can use the mirror formula to find the distance of the object from the mirror.1/f = 1/v - 1/u

Substituting the given values of r and v, we get:1/(31.5/2) = 1/22.6 - 1/u Solving for u, we get :u = 10.15 cm

Therefore, the distance of the mirror from the face is 10.15 cm. The units are centimeters (cm).Answer: 10.15 cm.

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Step-by-step explanation:

To create a frequency table for Sarita's data, we need to first count the number of times each value appears in the data set. We can then organize this information into a table with two columns: one for the values and one for their frequencies.

Here is the frequency table for Sarita's data:

Value Frequency

0 2

3 2

4 2

5 2

6 1

7 2

8 2

10 1

11 1

12 2

13 1

15 1

17 1

To create this table, we first counted the number of times each value appears in the data set. For example, the value 0 appears twice, so its frequency is 2. We repeated this process for each value in the data set, and then organized the results into a table with two columns.

Answer:

70

Step-by-step explanation:

the function 2x-5 = 135 and solving for x

42 inches divided by 1 gives the measurement 3 feet and 6 inches.

We have to find what number divides the number 42 inches to 3 feet and 6 inches.

We know that the conversion of measurement units,

1 foot = 12 inches

3 feet = 3 × 12 inches = 36 inches

3 feet 6 inch = 36 + 6 = 42 inches

So the required number divides 42 inches in to 42 inches itself.

Any number divided by 1 gives the same number.

So the required number is 1.

Hence the unknown number which divide 42 inches to 3 feet and 6 inches is 1.

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Step-by-step explanation:

Hey there!

The points of line AB are; (-1,-4) and (2,11).

Note:

~ Use double point formula.

\((y - y1) = \frac{y2 - y1}{x2 - x1} (x - x1)\)

~ Keep all values.

\((y + 4) = \frac{11 + 4}{2 + 1} (x + 1)\)

~ Simplify it.

\(y + 4 = \frac{15}{3} (x + 1)\)

\(y + 4 = 5x + 5\)

\(5x - y + 1 = 0\)

Therefore this is the equation of line AB.

Now, Finding the equation of line CD.

Given;

The points of line CD are; (1,1) and (4,10).

~ Using formula.

\((y - y1) = \frac{y2 - y1}{x2 - x1}(x - x1) \)

~ Keep all values.

\((y - 1) = \frac{10 - 1}{4 - 1} (x - 1)\)

~ Simplify it.

\(y - 1 = 3 x - 3\)

\(3x - y - 2 = 0\)

Therefore, 3x - y- 2 = 0 is the eqaution of line CD.

Use condition of parallel lines.

m1= m2

Slope of equation (i)

\(m1 = \frac{ - coeff. \: of \: x}{coeff \: of \: y} \)

\(m1 = \frac{ - 5}{ - 1} \)

Therefore, m1 = 5

Slope of second equation.

\(m2 = \frac{ - coeff \: .of \: x}{coeff \: .of \: y} \)

\(m2 = \frac{ - 3}{ - 1} \)

Therefore, m2 = 3.

Now, m1≠m2.

So, the lies are not parallel.

Check for perpendicular.

m1*m2= -1

3*5≠-1.

Therefore, they aren't perpendicular too.

So, they are neither.

Hope it helps...

Answer:

10:00

Step-by-step explanation:

4 hours from 6 is 10

Answer:

10:00 am or pm

Step-by-step explanation:

Answer:

interior angle because its at a side

Answer:

Step-by-step explanation:

total students = 27

students do not have a brother probability = 13/27

students do not have a sister probability = 12/27

= 4/9

Hope this is correct :)

The probability that a student is chosen randomly from the class does not have a sister is 0.375.

The probability that a student is chosen randomly from the class Has a brother is 0.208.

The probability that a student is chosen randomly from the class does not have a brother is 0.7916.

The probability that a student is chosen randomly from the class Has a sister is 0.625.

Probability is the branch of mathematics, which discusses the occurrence of a random experiment.

First, we need to calculate how many total students there are.

Once we have the total we have to divide the number in the category that we want by the total number of students to calculate the probability of randomly getting a student in that category.

Total Students = 3 + 12 + 2 + 7 = 24 students

The probability that a student is chosen randomly from the class does not have a sister is;

\(= \dfrac{2+7}{24}\\\\=\dfrac{9}{24}\\\\=0.375\)

The probability that a student is chosen randomly from the class Has a brother is;

\(= \dfrac{3+2}{24}\\\\=\dfrac{5}{24}\\\\= 0.208\)

The probability that a student is chosen randomly from the class does not have a brother is;

\(= \dfrac{7+12}{24}\\\\=\dfrac{19}{24}\\\\= 0.7916\)

The probability that a student is chosen randomly from the class Has a sister is;

\(= \dfrac{3+12}{24}\\\\=\dfrac{15}{24}\\\\= 0.625\)

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Answer:

No solution

Step-by-step explanation:

Answer:

the answer is 245

Step-by-step explanation:

Answer:

245

Step-by-step explanation: