Answers
Let -4x - 15y = 17 be known as equation 1 and -x + y = -13 as equation 2.
To solve the system of equations, we need to determine the value of the "x" and "y" variables. Let us start by determining the value of the y variable.
Note: Since the second equation looks easier to solve for y (in my opinion), I will determine the value of y in the second equation.
This can be done by isolating y on one side of the equation.
Equation 2: [tex]\bold{-x + y = -13}[/tex]
Add "x" on both sides of the equation:
[tex]\implies -x + y = -13[/tex]
[tex]\implies -x + y + x = -13 + x[/tex]
[tex]\implies y = -13 + x[/tex]
Therefore, the value of y is -13 + x. Let us substitute the value of y, obtained from equation 2, into equation 1 to determine the value of x.
Equation 1: [tex]\bold{-4x - 15y = 17}[/tex]
Substitute the value of y in the equation:
[tex]\implies 4x - 15y = 17[/tex]
[tex]\implies -4x - 15(-13 + x) = 17[/tex]
Simplify the distributive property:
[tex]\implies -4x - 15(-13 + x) = 17[/tex]
[tex]\implies -4x + (195 - 15x) = 17[/tex]
[tex]\implies -4x + 195 - 15x = 17[/tex]
Combine like terms on both sides:
[tex]\implies -4x + 195 - 15x = 17[/tex]
[tex]\implies -19x + 195 = 17[/tex]
Subtract 195 on both sides of the equation:
[tex]\implies -19x + 195 = 17[/tex]
[tex]\implies -19x + 195 - 195 = 17 - 195[/tex]
[tex]\implies -19x = -178[/tex]
Divide -19 on both sides of the equation:
[tex]\implies -19x = -178[/tex]
[tex]\implies \dfrac{-19x}{-19} = \dfrac{-178}{-19}[/tex]
[tex]\implies \bold{x = \dfrac{178}{19} }[/tex]
Now, substitute the value of x in -13 + x to determine the value of y. Once determined, we can put the solution in (x, y) form.
[tex]\implies y = -13 + x[/tex]
[tex]\implies y = -13 + \dfrac{178}{19}[/tex]
[tex]\implies y = \dfrac{-247}{19} + \dfrac{178}{19}[/tex]
[tex]\implies \bold{y = \dfrac{-69}{19} }[/tex]
∴ Solution ⇒ (x, y) ⇒ (178/19, -69/19)
Therefore, the solution to the following system of equations is (178/19, -69/19)
Learn more about system of equations: https://brainly.com/question/13024262
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Answer:
There would be 42 girls and 18 boys.
Step-by-step explanation:
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WILL GIVE BRAINLYEST
Make an inequality in standard fom with two variables and explain a real world
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Explain how you would graph the inequality
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Answer:
The graph of an inequality in two variables is the set of points that represents all solutions to the inequality. A linear inequality divides the coordinate plane into two halves by a boundary line where one half represents the solutions of the inequality. The boundary line is dashed for > and < and solid for ≤ and ≥.
Step-by-step explanation:
What is the area in square feet?
Answers
Answer:
426 square feet
Step-by-step explanation:
First, find the angle of each shape separately.
Area of a triangle = 1/2 base times height
1/2(9x8)
1/2(72) = 36
Area of a rectangle = base times height.
26 x 15 = 390
Now, add the numbers together to get the total area. 390+36=426
Answer:
426 square feet
Step-by-step explanation:
-First find the area of the rectangle:
26 x 15 = 390
-Next, find the area of the triangle on top:
9 x 8/2 = 36
-Finally, add the two to get the full area of the figure:
390 + 36 = 426
Answer: 426 square feet
Hope this helps! :)
Casey wants to buy a gym membership. One gym has a $176 joining fee and costs $29 per month. Another gym has no joining fee and costs $51 per month.
Part 1 out of 2
In how many months will both gym memberships cost the same? What will that cost be?
Answers
Answer:
8 months for cost to be same, cost will be $408
Step-by-step explanation:
x = months
176 + 29x = 0 + 51x
176 = 22x
8 = x
176 + (29*8) = 408
0 + (51*8) = 408
Given the function f(x) = -x2– 7x + 18, determine the average rate of change
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Answer: 4
Step-by-step explanation:
If there are 2.54 centimeters in an inch and 12 inches in a foot, how many centimeters in 3 feet
Answers
Answer:
91.44
Step-by-step explanation:
Answer:
3 ft = 91.44 cm
Step-by-step explanation:
We want to convert 3 ft to cm.
So we need a conversion factor.
Multiplying 3 ft by (12 in / 1 ft results in 36 in (this is equivalent to 3 ft).
Next, we convert 36 in to cm:
36 in 2.54 cm
-------- * ------------- = 91.44 cm
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A model of a skyscraper uses the scale of 2 inches = 45 feet. If the actual skyscraper is 992 feet tall, how tall is the model?
Answers
Answer:
44.08 or 44.1
Step-by-step explanation:
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Answer:
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Step-by-step explanation:
Answer:
D, Divide both sides by -4.6
Step-by-step explanation:
You want to get the x and the regular integers on separate sides of the equals sign, so you divide the -4.6 to get the x on its own side of the equals sign. That's the first step to solving the equation.
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Answer:
1=3 given
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Step-by-step explanation:
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Step-by-step explanation:
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Step-by-step explanation:
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A jewelry box contains 13 gold earrings, 10 silver earrings and 12 titanium
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Answers
Answer:
The probability is 406/625
Step-by-step explanation:
If they are of different materials, we have the following combinations of selection;
(gold and silver) or ( silver and titanium) or (gold and titanium )
The number of earrings present is 13 + 10 + 12 = 25
Probability of selecting a gold earring is 13/25
Probability of a silver is 10/25
Probability of a titanium is 12/25
Substituting these into the probabilities, we have;
(13/25 * 10/25) + (10/25 * 12/25) + (13/25 * 12/25)
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Answers
Answer:
D
Step-by-step explanation:
We know that MRT = 133 which means that is the total. Angle MRN and NRT are what makes the total angle which is 133. To find what each angle is individually, we can add them both together.
(2g - 2) + (4q - 9) = 133
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6q = 144
q = 24
Best of Luck!
D. (2g - 2)+(4g -9) = 133
Because,
Given, angle MRT = 133°
and MRN = 2g - 2 °
and NRT = 4g - 9°
and MRT = MRN + NRT .........(equation (i))
Placing values in equation (i) we get,
133° = (2g - 2)° + (4g - 9)°
=> 133 = (2g - 2) + (4g - 9)
=> (2g - 2) + (4g - 9) = 133
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Answer:
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Step-by-step explanation:
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A boy weighs x pounds. His younger sister weighs 53 pounds less than him. His father weighs four times as much as his sister. A simplified expression that represents the fathers weight (in pounds) is (blank -blank)
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Answer:
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Step-by-step explanation:
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What is 10/8 written as a decimal?
Answers
Answer:
10/8= 1.25
Step-by-step explanation:
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What are decimal numbers?The decimal numbers can only be expressed as fractions since they contain a fractional component. The accepted method for representing both integer and non-integer numbers is the decimal numeral system. There are 10 single-digit numbers in the decimal system:
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On simplifying , we get
The value of n in the decimal equivalence is given by dividing the number 10 by 8
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To learn more about decimal numbers click :
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Answer:
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Answer:
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Step-by-step explanation:
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A.
100
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Answer:
D
Step-by-step explanation:
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Answer:
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Step-by-step explanation:
Answer:
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Liza and Kelly rode their bikes everyday for five days. They each rode the same distance everyday. Lisa rode 60 miles in all and Kelly rode 25 miles in all. How many more miles per day did Lisa ride than Kelly?
Answers
Answer:
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Step-by-step explanation:
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g(x) = -4x2 + 4x – 2
What is the maximum or minimum step by step
Answers
We want the maximun or minimum of [tex]g(x)=-4x^2+4x-2[/tex]
Firstly, notice that we have a leading coefficient of -4, wich means our parabola is concave down. Thus, our function will have a maximum.
To find what is the maximum, let's firstly find on wich value of x it happens. We'll start by taking the first derivative of the function:
[tex]g'(x)=-8x+4[/tex]
To find the extremes of the function, we just need to find where the derivative equals zero. Setting g'(x)=0 we have
[tex]0 = -8x+4\\8x=4\\x=\frac{1}{2}[/tex]
So we found that the x coordinate of the maximum is x=1/2. To find the y coordinate we just need to substitute the value of x into the original function.
[tex]g(1/2)=-4(1/2)^2+4(1/2)-2\\g(1/2)=-1+2-2\\g(1/2) = -1[/tex]
Therefore, the maximum point [tex]M[/tex] of the function is
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Glad to help! Wish you great studies.
If you found this helpful consider giving this answer brainliest ;)
It has a fixed cost of $62,150. If the selling price per unit is $9.50 and the variable cost per unit is $6.25, the breakeven point is
Answers
Answer:
Break-even point = $19,123 (Approx)
Step-by-step explanation:
Given:
Fixed cost = $62,150
Selling price = $9.50
Variable cost = $6.25
Find:
Break-even point
Computation:
Break-even point = Fixed cost / [Selling price - Variable cost]
Break-even point = 62150/[9.50-6.25]
Break-even point = 62150/3.25
Break-even point = $19,123 (Approx)