which equations are equal to 1/4 (8x+56) =20

The numbers are 6 and -8

let

the first number = x

One of the number is 2 larger than another number .Therefore, the second number will be as follows;

Sum of there squares will be as follows:

Therefore,

x² + x² + 4x + 4 = 100

2x² + 4x + 4 - 100 = 0

2x² + 4x - 96 = 0

x + 2x - 48 = 0

let's find x

x - 6x + 8x - 48 = 0

x(x - 6) + 8(x - 6) = 0

(x - 6)(x + 8) = 0

x -6 = 0 and x + 8 = 0

x = 6 and x = -8

The numbers are 6 and -8.

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The two numbers are 7 and 4

Let the first number = x

let the second number = y

The sum of the numbers is 11, in algebra form x + y  = 11

The difference of the two numbers is 3, in algebra form, x - y = 3

To obtain the two unknown numbers, we solve the two equations;

from the first equation, x = 11 - y

substitute the value of x into the last equation;

(11 - y) - y = 3

11 - y - y = 3

11 - 2y = 3

2y = 11 - 3

2y = 8

y = 4

The value of x = 11 - 4 = 7

Thus, the two numbers are 7 and 4

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To find the product of two numbers with a sum of 11 and a difference of 3, solve the system of equations to find the numbers (7 and 4) and multiply them to get the product, which is 28.

To find the product of two numbers whose sum is 11 and whose difference is 3, we can let the two numbers be x and y, with x being the larger number. Therefore, we have two equations from the given information: x + y = 11 and x - y = 3.

Adding these two equations, we get:

Using x = 7 in the first equation, we have:

Now that we have both numbers, we can find their product:

The product of the two numbers is 28.

Answer:

Edge Checklist:

Find the third year’s salary by multiplying the second year’s salary by 1.05

Find the fourth year’s salary by multiplying the third year’s salary by 1.05.

Find the fifth year’s salary by multiplying the fourth year’s salary by 1.05.

The salaries form a geometric sequence because the athlete’s salary changes by a common ratio of 1.05 each year.

Answer:  the correct option is (C) f(0) = 6.

Step-by-step explanation:  We are given the function f(x) by the following set of ordered pairs :

{(1,0), (-10,2), (0,6), (3,17), (-2,-1)} .

We are to select the TRUE equation.

We know that

in the ordered pairs, the first element stands for the independent variable x and the second element stands for the dependent variable f(x).

So, the equations that comes from the given ordered pairs are

[tex]f(1)=0,~~f(-10)=2,~~f(0)=6,~~f(3)=17,~~f(-2)=-1.[/tex]

Thus, the only true equation is f(0) = 6.

Option (C) is CORRECT.

Without additional context or an image, we can't definitively determine which number the point A represents in your question.

The point A represents the number 0.1.

Points on a number line represent numbers. The numbers between 0 and 1 can be represented as decimals. The point A is located between 0 and 1, closer to 0, so it represents the number 0.1.

Therefore, the correct answer is option a. 0.1.

Unfortunately, without further context such as a diagram or graph, it's not possible to definitively identify which number Point A would represent. In a standard coordinate system, points are typically represented as pairs of numbers (x, y) which indicate their position on the grid. In a number line, each point corresponds to a specific number. Please provide additional details or an image to get a more accurate answer.

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The volume of Earth is about 49 times larger than the volume of the Moon, based on their provided radii.

To the nearest whole number, the volume of Earth is approximately 49 times larger than the volume of the Moon.

Given that the volumes of spheres are proportional to the cubes of their diameters, and using the radii provided (1079 miles for the Moon and 3959 miles for Earth), we can calculate the volume ratio:

Volume of Earth: [tex](3959)^3[/tex]

Volume of Moon: [tex](1079)^3[/tex]

Volume of Earth compared to the Moon,  = [tex](3959^3) / (1079^3)[/tex] ≈ 49.

There volume of the earth is 49 times larger.

The number sentences that solves the problem are;

B. (2 × 16) + (3 × 16) = 80
D. 16 × (2 + 3) = 80

To determine the number sentence, we have from the information given that;

Then, we can say that in each bag, there are;

= 3 + 2
= 5 objects

Now, in 16 of the goodies bag, the number of objects would be;

= 5 ×16

= 80 objects

Therefore, the sentences are in options B and D

Final answer:

To divide 660 grams in a 4:7 ratio, you first calculate the value of each part by dividing 660 grams by 11 (the sum of the ratio parts), resulting in 60 grams per part. Then multiply 60 grams by 4 to get 240 grams, and by 7 to get 420 grams, giving you two portions that comprise the ratio 4:7.

Explanation:

To divide 660 grams in the ratio 4:7, first add the two parts of the ratio together to find the total number of parts. This is 4 + 7 = 11 parts in total. The ratio indicates that for every 11 parts of the total weight, 4 parts should be in one portion and 7 parts in another. To find the weight of each part, divide the total weight (660 g) by the total number of parts (11).

660 g ÷ 11 = 60 g per part

Now, to get the weights for the two portions:

For the 4 parts: 60 g/part × 4 = 240 grams

For the 7 parts: 60 g/part × 7 = 420 grams

Thus, 660 grams divided in the ratio 4:7 of  gives two portions of 240 grams and 420 grams, respectively.

Answer:  √3 and √2 are irrational numbers;

                [tex]-\dfracP{1}{16}[/tex] and 0 are rational numbers.

Step-by-step explanation:  We are given to classify the following numbers as rational or irrational:

[tex]\sqrt{3},~~-\dfrac{1}{16},~~0,~~\sqrt{2}.[/tex]

Rational number:   The digits after the decimal are either repeating or terminating.

Irrational number:  The digits after the decimal are non-terminating and non-terminating.

(a) We have

[tex]\sqrt{3}=1.732050807568877~.~.~.[/tex]

Since the digits after the decimal are non-terminating and non-repeating, so √3 is an IRRATIONAL number.

(b) We have

[tex]-\dfrac{1}{16}=-0.0625.[/tex]

Since the digits after the decimal are terminating, so [tex]-\dfrac{1}{16}[/tex] is a RATIONAL number.

(c) We have

[tex]0=0.000.[/tex]

Since the digits after the decimal are  terminating, so [tex]0[/tex] is a RATIONAL number.

(d) We have

[tex]\sqrt{2}=1.414213562373095~.~.~.[/tex]

Since the digits after the decimal are non-terminating and non-repeating, so √2 is an IRRATIONAL number.

The point with the given coordinates (4 -2) is h.

Suppose we've two endpoints of a line segment as:

A(p,q), and B(m,n)

Then let the midpoint be M(x,y) on that line segment. Then, its coordinates are:

[tex]x = \dfrac{p+m}{2}[/tex]

and

[tex]y = \dfrac{q+n}{2}[/tex]

We are given that;

The graph of four points

Now,

One point is k with (-4,2)

One point is g with (2,4)

One point is h with (4,-2)

One point is j with (-2,-4)

Therefore, by the midpoint the answer will be h(4,-2).

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Final answer:

Triangles with two complementary angles must be right triangles. Since these angles add up to 90 degrees, the side between them is part of a right triangle. There can be many different right triangles that satisfy these conditions, but all must have a 90-degree angle. (Option D)

Explanation:

The question asks about the conditions that define a certain type of triangle. With two angles being complementary, they add up to 90 degrees. In geometry, a complementary pair of angles adds up to 90 degrees, which means that the two angles in question must be acute angles that add up to form a right angle. Therefore, the triangle with two complementary angles must be a right triangle.

Since the triangle can have many different dimensions for the other sides and angles while keeping the side between the complementary angles at 12 centimeters, we can infer that there are infinite variations of this triangle, each with different measures for the remaining side and angle. However, all those triangles must satisfy the condition of being right triangles.

Thus, the correct answer to this question is:

D. Exactly one triangle exists with the given conditions, and it must be a right triangle.