What is the point of intersection when the system of equations below is graphed on the coordinate plane?



(1, –3)
(–1, 3)
(1, 3)
(–1, –3)

To calculate the distance between two points:

We apply the following formula:

d = √(x₂ - x₁)² + (y₂ - y₁)²

The points are:

We substitute data and solve:

[tex]\bf{d=\sqrt{(6-(-3))^2+(-8-8(-8))^2 } }\\ \\ \bf{ d=\sqrt{9^2+0^2}=\sqrt{81+0} }\\ \\ \bf{d=\sqrt{81}=9 }[/tex]

The distance between the points (−3,− 8), (6, – 8) is 9.

on solving the equation, we have therefore the value of x from the given equation comes out to be 13.5

An equation is a formula in mathematics that joins two statements with the equal symbol = to represent equality. The definition of an equation in algebra is a mathematical statement proving the equality of two mathematical expressions. In the equation 3x + 5 = 14, for instance, the terms 3x + 5 and 14 are separated by an equal sign. The link between two phrases on either side of a letter is expressed mathematically. There is often only one variable, which is also the symbol. instance: 2x - 4 Equals 2.

equation given is 3(x+2)=7x-48

value of x

[tex]3(x+2)=7x-48\\ 3x+6=7x-48\\7x-48-3x-6=0\\ 4x-54=0\\ 4x=54\\ x=54/4\\ x=13.5\\[/tex]

value of x from the given equation comes out to be 13.5

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let the third side be b then use the pythagoras theorem

The new model {A} for the total number of new green tea and fruit juice sales can be written as {A} = 9t^4 + 3t² + 105 .

What is expression ?

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.

Any mathematical statement that includes numbers, variables, and an arithmetic operation between them is known as an expression or algebraic expression. In the phrase 4m + 5, for instance, the terms 4m and 5 are separated from the variable m by the arithmetic sign +.

An algebraic expression is made up of a number of variables, constants, and mathematical operations. We are aware that variables have a wide range of values and no set value. They can be multiplied, divided, added, subtracted, and other mathematical operations since they are numbers. as in 3x Plus 4.

Given is that during a 20-year period, G and I can be modeled by the following equation (where t is the time in years) :

G = 6t^4+ 3t³ – 2t² + 5t + 60

I = 3t^4 - 3t³ + 5t² - 5t + 45

where {G} is the number (in billions) of new green tea sales and {I} be the number in billions of new fruit juice sales.

A new model {A} for the total number of new green tea and fruit juice sales can be written as -

{A} = {G} + {I}

{A} = 6t^4+ 3t³ – 2t² + 5t + 60 + 3t^4 - 3t³ + 5t² - 5t + 45

{A} = 9t^4 + 3t² + 105

Therefore, the new model {A} for the total number of new green tea and fruit juice sales can be written as {A} = 9t^4 + 3t² + 105

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The correct representations of the inequality are

-6x + 15 < 10 - 5x

A number line from negative 3 to 3 in increments of 1. An open circle is at 5 and a bold line starts at 5 and is pointing to the right.

From the question, we are to determine the correct representations of the inequality

From the given information,

The given inequality is

-3(2x - 5) < 5(2 - x)

To determine the correct representations, we would proceed to solve the inequality

Solving the inequality

-3(2x - 5) < 5(2 - x)

-6x + 15 < 10 - 5x

This is one of the representations of the inequality

Then,

Collect like terms

-6x + 15 < 10 - 5x

-6x + 5x < 10 - 15

-x < -5

Multiply through by -1

x > 5

If the solution is represented on a number line, we would have a number line from negative 3 to 3 with an increments of 1 and an open circle at 5 and a bold line starts at 5 and is pointing to the right.

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Answer:

54

Step-by-step explanation:

ratio is 7:9

7=42

9=?

9×42÷7

Therefore , the solution of the given problem of angles comes out to be equation :  x+ y =85°.

'

In Euclidean geometry, an angle is a shape that is made up of two rays, known as the tone's flanks, that meet at a midpoint known as such angle's vertex. Two rays may combine to form an angle there in plane where they are positioned. When two planes collide, an angular is also generated. They are referred to as dihedral angles. An angle in plane geometry is the possible configuration of two rays of lines that share a termination. The origin of the English term "angle" is the Latin phrase "angulus," which meaning "horn." The vertex is the point in which the two vectors, also known as that of the faces of the angle, converge.

Here,

Given :

Let two angles be x and y  is

=> x+ y =85°

So, the equation is represented as  x+ y =85°.

Therefore , the solution of the given problem of angle comes out to be equation :  x+ y =85°.

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Answer:

If we assume she runs around it once and since they tell us its a square: 27x4=108

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

When calculating the surface area of a 3D shape, it is important to remember to include the area of all the components that make up the shape.

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Using formula of midpoint of a line, the coordinate of the midpoint is (-3, 0)

The midpoint of a line is a point that is equidistant from both endpoints of the line. It can be found by taking the average of the x-coordinates of the two endpoints, and then taking the average of the y-coordinates of the two endpoints. For example, if the two endpoints of a line are (x₁, y₁) and (x₂, y₂), then the midpoint of the line is:

Midpoint = ((x₁ + x₂) / 2, (y₁ + y₂) / 2)

The formula of midpoint of a line is given as;

M(x, y) = (x₂ + x₁) / 2, (y₂ + y₁) / 2

Substituting the values into the formula;

M(x, y) = (-7 + 1) / 2, (-5 + 5) / 2

M(x , y) = -6/2, 0/2

M(x, y) = -3, 0

The coordinate of midpoint is (-3, 0)

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The ratio 81:108 can be simplified to 9:13. To find the simplest form of the ratio, you can divide both numbers by the greatest common factor. The greatest common factor of 81 and 108 is 9, so you can divide both numbers by 9 to get the simplified ratio of 9:13.

Therefore , as a result, x = 53 and y = 10 are the answers to the trigonometry problem that was presented.

Trigonometry is the discipline of mathematics that studies correlations between angles and sides of triangles. Trigonometry is present in all of geometry because every ahead and move form may indeed be resolved to a set of triangles. Amazingly intricate connections exist between geometry and other areas of mathematics, particularly arithmetic, real or abstract, infinite series, arithmetic, and infinite series.

Here,

Sin 30 = Opposing Side/High

1/2 = 5 / y

y = 5 / (1/2)

y = 10

Cos 30 = Adjustment Side/ Hyp

√3/2 = x/y

√3/2 = x/10

x = 10√3 / 2

x = 5√3

In light of this, the given fractional problem's answer is

x = 5√3 and y = 10.

Therefore , as a result, x = 53 and y = 10 are the answers to the trigonometry problem that was presented.

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280 AND 245 RS  the company GAIN,20% OFF it is 280 rs and 30% off it is 245 rs

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The number of months Mark can have the phone is given by the equation

A = 11.4 months

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the number of months be represented as = A

Now , the equation is

Now , the total amount with Mark = $ 146.43

The initial amount for the smartphone = $ 33

The amount per month for 2GB is = $ 9.95

So , the amount for A months = $ 9.95 ( A )

So , the equation will be

Initial amount for the smartphone + the amount for A months = total amount with Mark

Substituting the values in the equation , we get

33 + 9.95 ( A ) = 146.43   be equation (1)

On simplifying the equation , we get

Subtracting 33 on both sides of the equation , we get

9.95 ( A ) = 113.43

Divide by 9.95 on both sides of the equation , we get

A = 11.4 months

Therefore , the value of A is 11.4 months

Hence , the number of months is 11.4 months

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Answer:

Step-by-step explanation:

Its A

The answer is 2.50. This, 250% in deciaml form is 2.50, in improper fraction form is 52 and as a mixed number it is 2 12. 2 1 2.

Answer: I'm sorry if it's wrong I'm pretty sure it's ≥ if not I'm sorry

Step-by-step explanation:

Answer:

a. A' (-3, -1) B' (3, 2) C' (6, 0); b. A' (-1, -3) B' (1, 6) C' (2, 0); c. A' (-2, -3) B' (2, 6) C' (2, 0)

Step-by-step explanation:

Solutions for graph a, b and c are attached.

a. (x, y) to (3x, y)

A' (-3, -1) B' (3, 2) C' (6, 0)

b. (x, y) to (x, 3y)

A' (-1, -3) B' (1, 6) C' (2, 0)

c. (x, y) to (2x, 3y)

A' (-2, -3) B' (2, 6) C' (2, 0)

REMEMBER: Connect the lines to make the triangles for each graph BEFORE submitting.

Answer:  19/400

Step-by-step explanation:

4.75% = 4.75/100 (in fractions)

          = 475/10000 (multiply by 100 for both the numerator and denominator)

           = 19 / 400 (divide by 25 for both the numerator and denominator)

How do I know it is 25 for the last step?

Obtain the highest common factor of 475 and 10000. The highest common factor of these two numbers is 25.

Answer: 2.403 × 10^3 atoms

Step-by-step explanation:

10^13 x 6.02 = 6.02^23 and 6.02^23 x 4 = 2,403 turned into 2.403 x 10^3 atoms.

Jahnay is making 6.5 cakes from the given ingredients.

The division in mathematics is one kind of operation. In this process, we split the expressions or numbers into the same number of parts.

Given:

Recipe: Makes 1 Cake =  120 g sugar + 130 g butter + 260 g flour + 3 eggs.

Jahnay is following this recipe to make cakes.

Jahnay uses 780 g of butter.

To find the number of cakes:

Use division operation,

780 ÷ 120,

= 780/120

= 78/12

= 6.5

Therefore, Jahnay makes 6.5 cakes.

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Answer: 2.25 grams

Step-by-step explanation:

In this problem, we are given the ratio of grams to weight. Since we are trying to find how many grams to give to a person with a specific weight, we can use proportions to solve.

[tex]\frac{150mg}{5kg} =\frac{x}{75kg}[/tex]               [cross multiply]

[tex]11250=5x[/tex]                  [divide both sides by 5]

[tex]x=2250mg[/tex]

We are almost done with the problem. The problem is asking for grams, not mg, so we can use unit conversions to change that.

[tex]\frac{1000mg}{1g}=\frac{2250mg}{y}[/tex]          [cross multiply]

[tex]1000y=2250[/tex]               [divide both sides by 1000]

[tex]y=2.25[/tex]

Therefore, we need to give 2.25 grams.

Answer:

2.66

Step-by-step explanation:

Answer:

2.66

Step-by-step explanation:

look at first at tenths for the biggest no .if there is a tie proceed to hundredths for biggest no and so on

Answer: y=20-2x

Step-by-step explanation:

The pound of cement used based on the information will be C. 2 pounds.

A fraction simply means a piece of a whole. In this situation, the number is represented as a quotient such that the numerator and denominator are split. In this situation, in a simple fraction, the numerator as well as the denominator are both integers.

In this case, for each pound of sand, he uses 1 2/3 pounds of gravel and for each pound of gravel, he uses 2/5 pound of cement.

The pound of cement used will be:

Gravel = 1 2/3 × 3

= 5 pounds

Cement used will be:

= 2/5 × 5.

= 2 pounds.

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Answer:

[tex](\frac{5}{3} ;\frac{4}{3} ).[/tex]

Step-by-step explanation:

[tex]\left \{ {{x+y=3} \atop {\frac{y+2}{2} =x}} \right. \ = > \ \left \{ {{x+y=3} \atop {y+2=2x}} \right. \ = > \ \left \{ {{x+y=3} \atop {2x-y=2}} \right. \ = > \ \left \{ {{x=\frac{5}{3} } \atop {y=\frac{4}{3} }} \right.[/tex]

Answer:

Question is not clear

Step-by-step explanation:

The number of yards of rope she can make for the step is 3 yards

From the question, we have the following parameters that can be used in our computation:

Yards of rope per step = 1/2 yards per step

Total number of steps = 6 steps

The number of yards of rope she can make for the step can then be calculated using the following equation

The number of yards of rope = Total number of steps * Yards of rope per step

Substitute the known values in the above equation, so, we have the following representation

The number of yards of rope = 1/2 * 6

Evaluate

The number of yards of rope = 3

Hence, the number of yards of rope is 3

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Complete question

Judi is making a rope ladder. she uses 1/2 yard of rope for each step. how many steps can she make with 6 yards of rope?