The formula that expresses R as a function of M and S is R = (M - 2S)/2.
To write a formula that expresses R as a function of M and S, we will need to rearrange the equation M=2R+2S to solve for R.
First, we will subtract 2S from both sides of the equation to isolate the term with R on one side:
M - 2S = 2R
Next, we will divide both sides of the equation by 2 to solve for R:
(M - 2S)/2 = R
Finally, we can write the equation in function form, with R as the dependent variable and M and S as the independent variables:
R = (M - 2S)/2
Therefore, the formula that expresses R as a function of M and S is R = (M - 2S)/2.
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Can 1 of you guys explain this to me really good please.
Answer:
333 ft^2
Step-by-step explanation:
To find the area of the new dance floor, use the trapezoid area formula.
Area of a Trapezoid: [tex]\frac{(base 1+base 2)h}{2}[/tex]
[(18 1/2 + 18 1/2) · 18]/2 - Plug in values
(37x18)/2 - Simplify
333 ft^2 - Solve
QUESTION 5 How many ways are there to construct a 3-digit code if numbers can be repeated?
There are 1,000 ways to construct a 3-digit code if numbers can be repeated. This is because there are 10 possible numbers (0-9) for each digit, and since numbers can be repeated, each digit has 10 options. So the total number of ways to construct a 3-digit code is 10 × 10 × 10 = 1,000.
Here is a step-by-step explanation:
1. Start with the first digit. There are 10 possible numbers (0-9) that can be used for this digit.
2. Move on to the second digit. Again, there are 10 possible numbers (0-9) that can be used for this digit, since numbers can be repeated.
3. Finally, move on to the third digit. There are 10 possible numbers (0-9) that can be used for this digit, since numbers can be repeated.
4. Multiply the number of options for each digit together to get the total number of ways to construct a 3-digit code: 10 × 10 × 10 = 1,000.
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I really need the answers to these math equations
A correct 2-column proof include the following: B. table B.
What is a supplementary angle?In Mathematics, a supplementary angle simply refers to two (2) angles or arc whose sum is equal to 180 degrees.
Since line segment r is parallel to line segment s, the 2-column proof to justify that angle b and angle h are supplementary angles should be written as follows;
Statement Reasons_________________
r║s Given
∠b ≅ ∠c Vertical angles
∠c and ∠e are supplementary Same-side interior angles
∠e ≅ ∠h Vertical angles
∠b and ∠h are supplementary Substitution
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The Amador family pays $7.50 per thousand cubic feet of natural gas. The total cost, t, varies directly as the number of thousand cubic feet of natural gas, g, used.
The constant of proportionality for the Amador family is obtained as k = 7.50.
What is a COP?The ratio between two quantities that are directly proportional is the constant of proportionality. When two quantities grow and shrink at the same rate, they are directly proportional.
If the cost t varies directly with the number of thousand cubic feet of natural gas g used, we can write -
t = kg
where k is the constant of proportionality, which represents the cost per thousand cubic feet of natural gas.
Since the Amador family pays $7.50 per thousand cubic feet of natural gas, we have -
k = 7.50
Therefore, the equation relating the total cost t to the number of thousand cubic feet of natural gas g used is -
t = 7.50g
This means that for every thousand cubic feet of natural gas used, the cost is $7.50.
If the Amador family uses 10,000 cubic feet of natural gas, the total cost would be -
t = 7.50(10) = $75
If they use 20,000 cubic feet of natural gas, the total cost would be -
t = 7.50(20) = $150
Therefore, the COP value is k = 7.50.
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what is the answer to this question?
Answer:
Dude.....it's a CIRCLE!!
In order to gaph the ine whote equition iay=52x+2, begin by ploeing the port Fromi ins pointi ne miove wits up the rese) and insts to the righe che runl. Fa in each blopk so thut the reseinng statement is true. In order to arach the ine whose equason isy=52x+3, begn by plotting the point: From this point, we mere units up (ehe fise) and unis to the right (the run). In ceder to graph the ine whose eqaston isy=52x+3, begin by ploting the poun From this point, we move Units up (the risel and unis to the tight (the nun).
This is why we move 5 units up and 2 units to the right from the y-intercept to find another point on the line.
In order to graph the line whose equation is y=5/2x+2, we need to begin by plotting the point (0,2) on the graph. This is the y-intercept of the equation, which is where the line crosses the y-axis. From this point, we need to move 5 units up (the rise) and 2 units to the right (the run). This will give us another point on the line. We can then draw a straight line through these two points to graph the equation.
Similarly, to graph the line whose equation is y=5/2x+3, we need to begin by plotting the point (0,3) on the graph. This is the y-intercept of the equation, which is where the line crosses the y-axis. From this point, we need to move 5 units up (the rise) and 2 units to the right (the run). This will give us another point on the line. We can then draw a straight line through these two points to graph the equation.
In both cases, the slope of the line is 5/2, which is the coefficient of x in the equation. The slope tells us how much the line rises or falls for every unit it moves to the right. In this case, the line rises 5 units for every 2 units it moves to the right. This is why we move 5 units up and 2 units to the right from the y-intercept to find another point on the line.
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FAMILY The table below shows the predicted annual cost for middle income family to raise a child from birth until adulthood. Draw a scatter plot and describe what relationship exists within the data
you have too draw a scatter
Simplify: 27 − 3 exponent 3 + 4 x 2 exponent 2 − 6.
Answer:
10
Step-by-step explanation:
27-[tex]3x^{3}[/tex]+(4 x [tex]2x^{2}[/tex]) - 6
= 27 - 27 + (4 x 4) - 6
= 0 + 16 - 6
= 10
Answer: 10
Step-by-step explanation:
27 - 3^3 + 4 × 2^2 - 6
= 27 - 27 + 4 × 4 - 6 (since 3^3 = 27 and 2^2 = 4)
= 0 + 16 - 6= 10
Therefore, the simplified value of the expression is 10.
The volume of a cylinder is 12,566.4 cm cubed. The height of the cylinder is 8 cm.
a) Find the radius of the cylinder to the nearest tenth of a centimeter.
b) Find the area of the base of the cylinder to the nearest tenth of a centimeter.
c) Find the lateral area to the nearest tenth of a centimeter.
d) Find the surface area of the cylinder.
As a result of the cylinder's volume being 12,566.4 centimetres³ and its height being 8 cm, the surface area of the cylinder is approximately 942.5 cm².
what is volume ?
Volume in mathematics refers to how much room a three-dimensional object takes up. It is a way to quantify how much enclosed room there is overall in a solid figure. Depending on the shape of the item, a number of formulas can be used to calculate its volume. A rectangular prism's volume, for instance, can be calculated by multiplying its length, breadth, and height, whereas a cylinder's volume can be calculated by dividing its base area by its height. The system being used will determine the unit of measurement for volume, but typical units include cubic metres (m³) and cubic centimetres (cm³).
given
a) V = πr²h, where V is the volume, r is the radius, and h is the height, is the expression for a cylinder's volume. By rearranging the calculation, we can find r:
V/(h) = √12,566.4/(*8)) Equals r ≈ 10 centimetres (rounded to the closest tenth of a cm) (rounded to the nearest tenth of a cm)
Consequently, the cylinder's radius is roughly 10 centimetres.
b) The equation A = r² determines the area of a cylinder's base. Using the r number we just discovered, we have:
A = π(10)² ≈ 314.2 cm² (rounded to the closest tenth of a cm) (rounded to the nearest tenth of a cm)
Consequently, the cylinder's base has a surface area of about 314.2 cm².
c) The equation L = 2πrh, where r is the radius and h is the height, determines the lateral area of a cylinder. With the numbers from the problem substituted, we obtain:
L = 2π(10)(8) ≈ 502.7 cm² (rounded to the closest tenth of a cm) (rounded to the nearest tenth of a cm)
Consequently, the cylinder's side area is roughly 502.7 cm².
d) The equation S = 2πr² + 2πrh gives the surface area of a cylindrical. Using the r and h numbers we discovered earlier, we have:
S = 2π(10)² + 2π(10)(8) ≈ 942.5 cm² (rounded to the nearest tenth of a centimetre) (rounded to the nearest tenth of a cm)
As a result of the cylinder's volume being 12,566.4 centimetres³ and its height being 8 cm, the surface area of the cylinder is approximately 942.5 cm².
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Victor makes cinnamon waffles. His recipe calls for 3 teaspoons of cinnamon per 8 teaspoons of sugar. How many teaspoons of sugar are needed for 96 teaspoons of cinnamon?
Answer:
He needs 256 teaspoons of sugar.
Step-by-step explanation:
This one is really simple!
96/3 = 32, meaning that we multiplied the recipe by 32.
This means that your teaspoons of sugar must also be multiplied by 32, which 8x32=256!
please I need a solution
obtain the solution using the long division method
the vertices of a polygon are (1,2) (1,6) (7,6) (7,2) (5,0) (3,0) graph the polygon then find its area
Answer:
32 square units
Step-by-step explanation:
You want the area of a polygon with the vertices (1,2) (1,6) (7,6) (7,2) (5,0) (3,0).
CompositionThe graphed figure can be decomposed into a rectangle 4 units high and 6 units wide, together with a trapezoid with bases 6 and 2, and height 2.
FormulasThe area formulas for these parts are ...
A = HW . . . . area of a rectangle of height H and width W
A = 1/2(b1 +b2)h . . . . area of a trapezoid with bases b1, b2, and height h
ApplicationThe rectangle area is ...
A = (4)(6) = 24
The trapezoid area is ...
A = 1/2(6+2)(2) = 8
So, the total area of the polygon is ...
A = 24 +8 = 32 . . . . square units.
The area of the polygon is 32 square units.
Are these proportion yes or no?
1/3 , 7/21
2/5 , 40/16
48/9 , 16/3
1) The ratios 1/3 , 7/21 are in proportion.
2) The ratios 2/5 , 40/16 are not in proportion.
3) the ratios 48/9 , 16/3 are in proportion.
We know that two ratios are said to be in proportion when both the ratios are equivalent.
Consider 1/3 , 7/21
Here 7/21 = (7 × 1)/(7 × 3)
= 1/3
This means 1/3 = 7/21
Thus, the ratios 1/3 , 7/21 are in proportion.
Consider 48/9, 16/3
Here 48/9 = (16 × 3)/(3 × 3)
= 16/3
This means 48/9 = 16/3
Thus, the ratios 48/9, 16/3 are in proportion.
Now consider 2/5 , 40/16
Here 40/16 = (8 × 5)/(8 × 2)
= 5/2
This means 2/5 ≠ 5/2
Thus, the ratios 2/5 , 40/16 are not in proportion.
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Jerry is a judge. He hears
5
55 cases every
2
3
8
2
8
3
2, start fraction, 3, divided by, 8, end fraction hours. Jerry hears cases at a constant rate.
How many cases does he hear per hour?
The number of cases which Judge Jerry hears every hour is 2 2/19
What is a Fraction?An element of a whole or, more broadly, any number of equal pieces, is represented by a fraction.
When used in conversational English, a fraction indicates the number of components of a particular size, as in one-half, eight-fifths, and three-quarters.
How to calculate:
GIven that he tries 5 cases in 2 3/8 hours
The unit rate of cases per hour is calculated by dividing the number of cases by the number of hours.
5/(2 3/8) = 5/(19/8) = 5 * 8/19 = 40/19 = 2 2/19
Therefore, the number of cases which Judge Jerry hears every hour is 2 2/19
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William’s car uses 1 litre of fuel to travel 12km. How much fuel will be needed to travel
420km?
Answer:
420km/12km = 35
1×35l = 35lites
rate it 5 stars pls TANXX
Answer:
35 litres
Step-by-step explanation:
We can use a ratio to solve.
1 litre x litres
------------- = ----------------
12 km 420 km
Using cross products
1 * 420 = 12x
Divide each side by 12.
420/12 = x
35 =x
35 litres
PLSSSS HELP IF YOU TURLY KNOW THISSSS
Answer:
x = 5
Step-by-step explanation:
5x - 7 = 3x + 3
- 3x -3x
2x - 7 = 3
+7 +7
2x = 10
Divide 2 from both sides
x = 5
Answer: 10
Step-by-step explanation:
2x - 7 = 3
add 7 to both sides = 2x = 10
now to solve:
once u have 2x = 10
divide both sides by 2
x=5
Rewrite the quantity as an algebraic expression of \( x \) and state the domain on which the equivalence is valid. \[ \csc (\operatorname{arccot}(x))= \] Domain:
The algebraic expression of \(\csc (\operatorname{arccot}(x)) \) is \(\frac{x}{\sqrt{1+x^2}}\) and the domain on which the equivalence is valid is \((-\infty, 0) \cup (0, \infty)\).
The quantity \[ \csc (\operatorname{arccot}(x)) \] can be rewritten as an algebraic expression of \(x\) using the following steps:
1. Recall that \(\operatorname{arccot}(x) \) is the inverse function of \(\cot(x) \), which means that \(\cot(\operatorname{arccot}(x)) = x \).
2. Use the identity \(\cot(x) = \frac{1}{\tan(x)} \) to rewrite the expression as \[ \csc (\operatorname{arccot}(x)) = \csc \left( \arctan \left( \frac{1}{x} \right) \right) \]
3. Recall that \(\csc(x) = \frac{1}{\sin(x)} \) and use the identity \(\sin(\arctan(x)) = \frac{x}{\sqrt{1+x^2}} \) to rewrite the expression as \[ \csc (\operatorname{arccot}(x)) = \frac{\sqrt{1+\left( \frac{1}{x} \right)^2}}{\frac{1}{x}} = \frac{x}{\sqrt{1+x^2}} \]
Therefore, the algebraic expression of \(\csc (\operatorname{arccot}(x)) \) is \[ \frac{x}{\sqrt{1+x^2}} \]
The domain of this expression is all real numbers except \(x=0\), since division by zero is undefined. Therefore, the domain on which the equivalence is valid is \(x \neq 0\), or in interval notation, \((-\infty, 0) \cup (0, \infty)\).
In summary, the algebraic expression of \(\csc (\operatorname{arccot}(x)) \) is \(\frac{x}{\sqrt{1+x^2}}\) and the domain on which the equivalence is valid is \((-\infty, 0) \cup (0, \infty)\).
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Reference Library. 40. In a standard deck of 52 cards, what is the probability of drawing a King (4 cards ), a Queen ( 4 cards ), or a Jack ( 4 cards )?
The probability of drawing a King, Queen, or Jack from a standard deck of 52 cards is 3/13.
The probability of drawing a King, Queen, or Jack in a standard deck of 52 cards can be calculated by using the formula for the probability of an event happening: P(E) = number of favorable outcomes / total number of possible outcomes.
In this case, the number of favorable outcomes is the total number of Kings, Queens, and Jacks in the deck, which is 4 + 4 + 4 = 12. The total number of possible outcomes is the total number of cards in the deck, which is 52.
So, the probability of drawing a King, Queen, or Jack is:
P(E) = 12 / 52
Simplifying this fraction gives us:
P(E) = 3 / 13
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Is the equation, y = 9x + 3 a proportional or non-proportional linear relationship?
Using the given functions: f(x)=2x^(2)-5x-3,g(x)=x-3 and h(x)=2x+5, what is the product of (g*f)(x) ? 2x^(3)+11x^(2)+18x+9 2x^(3)-z^(2)-18x+9 2x^(3)-x^(2)-12x+9
Using the given functions, the product of (g*f)(x) is 2x³ - 11x² + 12x + 9.
A relation between a set of inputs having one output each is called a function. The product of (g*f)(x) can be found by multiplying the functions f(x) and g(x) together.
Since f(x) = 2x² - 5x - 3 and g(x) = x - 3, then the product of (g*f)(x) can be solved as follows:
(g*f)(x) = g(x)*f(x) = (x - 3)(2x² - 5x - 3)
Use the distributive property:
(g*f)(x) = 2x³ - 5x² - 3x - 6x² + 15x + 9 = 2x³ - 11x² + 12x + 9.
Therefore, the correct answer is 2x³ - 11x² + 12x + 9.
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Score on last try:
4.74
of 5 pts. See Details for more. You can retry this quest Round all ainsurers to 3 decintal places. The vertex of kis
The vertex of this function would be (-1, -8).
The question seems to be incomplete and there are some typos in it. However, I will try to provide a general answer based on the given information.
When finding the vertex of a function, you can use the formula -b/2a to find the x-coordinate of the vertex. Once you have the x-coordinate, you can plug it back into the original function to find the y-coordinate of the vertex.
For example, if the function is y = 2x^2 + 4x - 6, the formula for the x-coordinate of the vertex would be -4/(2*2) = -1. The y-coordinate of the vertex would be 2(-1)^2 + 4(-1) - 6 = -8.
So the vertex of this function would be (-1, -8).
Remember to Round all answers to 3 decimal places, as instructed in the question.
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Use the pair of functions to find f(g(x)) and g(f(x)). Simplify your answers.
f(x) = x²+1, g(x) = √x+5
f(g(x)) =
g(f(x)) =
The solutions of the given functions are:
f(g(x)) = x+10√x+26 and g(f(x)) = √(x²+6)
f(x) = x²+1, g(x) = √x+5 are given.
To find f(g(x)), we need to substitute g(x) into the function f(x):
f(g(x)) = f(√x+5) = (√x+5)²+1 = x+10√x+26
To find g(f(x)), we need to substitute f(x) into the function g(x):
g(f(x)) = g(x²+1) = √(x²+1+5) = √(x²+6)
Therefore, the simplified answers are:
f(g(x)) = x+10√x+26
g(f(x)) = √(x²+6)
Note: It is important to include the parentheses when substituting one function into another to ensure the correct order of operations.
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3x+4y=-30 2x-5y=72 find y
nvm sorry wrong answer
Answer:-12
Step-by-step explanation:
To solve for y, we can use the second equation to isolate x and substitute the result into the first equation:
2x - 5y = 72
2x = 5y + 72
x = (5y + 72)/2
Now we can substitute this expression for x into the first equation:
3x + 4y = -30
3((5y + 72)/2) + 4y = -30
Simplifying the left side:
(15/2)y + 108 + 4y = -30
Combining like terms:
(23/2)y = -138
Dividing both sides by (23/2):
y = -138 * 2/23
Simplifying:
y = -12
Therefore, the value of y that satisfies both equations is -12.
Help me solve this homework please
Hence Proved that the sum of two consecutive exponents of the number 5 is divisible by 30. and if two consecutive exponents are 5^n and 5^n+1, then their sum can be written as 5^n-1*30.
What is exponents?Exponentiation is a mathematical operation, written as aⁿ. An exponent refers to the number of times a number is multiplied by itself. For example, 2 to the 3rd (written like this: 23) means: 2 x 2 x 2 = 8. 23 is not the same as 2 x 3 = 6. Remember that a number raised to the power of 1 is itself.
here, we have,
Let suppose two consecutive exponents of 5 are :
5^n and 5^n+1,
Sum of these exponents is
5^n + 5^n+1
So we writes this expression as
5^n + 5^n*5
=5^n(1 + 5)
=5^n * 6
=5^n-1 * 30
So it will be divisible by 30 .
Hence Proved that the sum of two consecutive exponents of the number 5 is divisible by 30. and if two consecutive exponents are 5^n and 5^n+1, then their sum can be written as 5^n-1*30.
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-5i - 3 = -43
Answer and work shown
Answer:
i = 8
Step-by-step explanation:
To solve this equation, we need to isolate the variable i on one side of the equation.
-5i - 3 = -43
First, we add 3 to both sides of the equation:
-5i - 3 + 3 = -43 + 3
Simplifying the left side:
-5i = -40
Now we divide both sides by -5:
-5i / -5 = -40 / -5
Simplifying:
i = 8
Therefore, the solution to the equation -5i - 3 = -43 is i = 8.
A cube with edge length 8 is balanced on one of its vertices on a horizontal table such that the diagonal from this vertex through the interior of the cube to the farthest vertex is vertical. When the sun is directly above the top vertex, the shadow of the cube on the table is a regular hexagon. The area of this shadow can be written in the form a*
√b, where a and b are positive integers and b is not divisible by any perfect square larger than 1. What is the value of a + b?
The required value of a + b is 35.
The area of the shadow can be calculated by finding the area of the regular hexagon. The formula for the area of a regular hexagon is:
A = (3√3)/2 * s^2,
where s is the length of one side of the hexagon.
Since the cube is balanced on one of its vertices, the length of one side of the hexagon is equal to the length of one edge of the cube, which is 8. Therefore, the area of the shadow is A = (3√3)/2 * 8^2 = 64√3/2 = 32√3.
The value of a is 32 and the value of b is 3, so the value of a + b is 32 + 3 = 35. Therefore, the answer is 35.
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Calculate the range, variance, and standard deviation for the following samples. a. 32, 44, 30, 36, 47 b. 110, 6, 4, 99, 80, 3, 5, 10,1 c. 110, 6, 4, 40, 80, 40, 55, 1 a. The range is 17. (Type an integer or a decimal. Do not round.) The variance is 44.16 (Round to two decimal places as needed.)
The answers of range, variance, and standard deviation are:
a. Range = 17, Variance = 44.16, Standard deviation = 6.65
b. Range = 109, Variance = 1514.14, Standard deviation = 38.91
c. Range = 109, Variance = 1486.86, Standard deviation = 38.56
The range is the difference between the highest and lowest values in the sample. The variance is a measure of how spread out the values are from the mean, and the standard deviation is the square root of the variance.
For sample a:
Range = 47 - 30
=> 17
Variance =[tex][(32-37.8)^2 + (44-37.8)^2 + (30-37.8)^2 + (36-37.8)^2 + (47-37.8)^2] / (5-1)[/tex]
=> 44.16
Standard deviation = √44.16
=> 6.65
For sample b:
Range = 110 - 1
=> 109
Variance = [tex][(110-34.44)^2 + (6-34.44)^2 + (4-34.44)^2 + (99-34.44)^2 + (80-34.44)^2 + (3-34.44)^2 + (5-34.44)^2 + (10-34.44)^2 + (1-34.44)^2] / (9-1)[/tex]
=> 1514.14
Standard deviation = √1514.14
=> 38.91
For sample c:
Range = 110 - 1
=> 109
Variance = [tex][(110-42)^2 + (6-42)^2 + (4-42)^2 + (40-42)^2 + (80-42)^2 + (40-42)^2 + (55-42)^2 + (1-42)^2] / (8-1)[/tex] = 1486.86
Standard deviation = √1486.86
=> 38.56
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Find all values of c that will make the polynomial a perfect square trinomial. 225r^(2)-120r+c
The value of c that will make the polynomial a perfect square trinomial is 16.
To find the values of c that will make the polynomial a perfect square trinomial, we need to use the formula for a perfect square trinomial, which is:
[tex](a+b)^(2) = a^(2)+2ab+b^(2)[/tex]
In this case, we have:
[tex]225r^(2)-120r+c = (15r+b)^(2)[/tex]
Expanding the right side of the equation, we get:
[tex]225r^(2)-120r+c = 225r^(2)+30rb+b^(2)[/tex]
Comparing the coefficients of the terms, we can see that:
-120r = 30rb
b = -4
Now, substituting b back into the equation, we get:
[tex]c = b^(2) = (-4)^(2) = 16[/tex]
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Solve :-7x-6y=4
When x=-3y+8
This question has two parts. First, answer Part A. Then, answer Part B.
Part A
Select the graph that represents the system of equations.
y=−3x−13 y=2x+2
In answering the question above, the solution is As a result, (x,y) = is the system of equations' answer (-3,8).
What is equation?A mathematical equation links two statements and utilises the equals sign (=) to indicate equality. In algebra, an equation is a mathematical assertion that proves the equality of two mathematical expressions. For instance, in the equation 3x + 5 = 14, the equal sign separates the numbers by a gap. A mathematical formula may be used to determine how the two sentences on either side of a letter relate to one another. The logo and the particular piece of software are usually identical. like, for instance, 2x - 4 = 2.
The equations in the system are:
[tex]y = -3x - 13 \sy = 2x + 2[/tex]
We may put the two equations equal to one another and get x to solve this system:
-3x - 13 = 2x + 2
3x added to both sides results in:
-13 = 5x + 2
By taking 2 away from both sides, we arrive at:
-15 = 5x
When we multiply both sides by 5, we get:
x = -3
We may use either of the original equations to calculate y now that we know x:
y = -3(-3) - 13 = 8
As a result, (x,y) = is the system of equations' answer (-3,8).
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