Answer:
c. ( 5, 3)
Step-by-step explanation:
6x-27=4x-17
6x-27-4x=4x-17-4x
2x-27=-17
2x-27+27=-17+27
2x=10
x=10/2
x=5
y=6(5)-27
y=30-27
y=3
Tom drinks 8oz of water for every 3 miles he bikes after 21 miles how much water did he drink
Answer:
he drinks 56oz of water
Step-by-step explanation:
divide 21 by 3 that would equal seven than multiply it by 8 which is 56
Answer:
57 ounces
Step-by-step explanation:
[tex]\frac{3 miles}{8oz water}[/tex] × 7 = [tex]\frac{21miles}{56ozwater}[/tex]
5. What is the solution to the system? *
Captionless Image
6. Explain what your solution means in terms of the scenario. *
Answer:
This is what I came up with
5. (6,32)
6. That means that when six kites are order it would be the same cost from each company
Step-by-step explanation:
The solution y = 3x + 12 represents a linear relationship between two variables in the given scenario, with an initial cost of $12 and an additional cost of $3 for each unit increase in the independent variable "x." The interpretation of this relationship depends on the specific context of the problem.
The given system of equations can be written in slope-intercept form, which is in the form y = mx + b, where "m" represents the slope of the line, and "b" represents the y-intercept. In this context, the system is as follows:
4 = 3m + b
12 = b
We can solve this system to find the values of "m" and "b."
First, we already know that b = 12 from the second equation.
Now, substitute this value into the first equation:
4 = 3m + 12
Next, isolate "3m" by subtracting 12 from both sides of the equation:
3m = 4 - 12
3m = -8
Finally, divide both sides by 3 to solve for "m":
m = -8/3
So, we have found that m = -8/3 and b = 12.
Now, let's interpret the solution in the context of the scenario:
The equation y = 3x + 12 represents the relationship between "x" (which could represent a quantity like time or another variable) and "y" (which could represent a cost, height, or another quantity). In this specific case, it seems like the equation describes a linear relationship between two variables.
In terms of the scenario, it could mean that there is an initial cost of $12 (the y-intercept) and an additional cost of $3 for each unit increase in "x." This interpretation depends on the context of the problem. For example, if "x" represents the number of items purchased, then $12 could be an initial fee, and $3 could be the cost per item.
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The question probable may be:
find the system to the solution you have to put in into slope intersecpt form so y=mx+b
so 4=m(3)+b
12=b
y=3x+12 Explain what your solution means in terms of the scenario. *
Is the ratio 3:4 the same as 4:5
Answer:
No the ratio 3:4 is not equal to 4:5
Step-by-step explanation:
3:4 = 3/4 and 4:5 = 4/5
3/4 is equal to 0.75 and 4/5 is equal to 0.8
0.75 [tex]\neq[/tex] 0.8
therefore, 3:4 [tex]\neq[/tex] 4:5
Hope this helps!
What is the measure of all angles. HELP ASAP! Will someone answer this for me like right now. Thanks
Answer:
∠ ABC = ∠ DBE = 65°
∠ ABD = ∠ CBE = 115°
Step-by-step explanation:
See the diagram attached to this question.
Now, ∠ ABC and ∠ DBE are two vertically opposite angles.
So, 3x + 38 = 5x + 20
⇒ 2x = 18
⇒ x = 9
So, ∠ ABC = ∠ DBE = 3(9) + 38 = 65° (Answer)
Again, ∠ ABC and ∠ ABD are supplementary angles.
Then, ∠ ABC + ∠ ABD = 180°
⇒ ∠ ABD = 180° - 65° = 115°
And ∠ ABD = ∠ CBE {Vertically opposite angles}
So, ∠ ABD = ∠ CBE = 115° (Answer)
the ratio of girls to boys in a gym class is 1 to 2 if there are 30 students in the class how many girls are in the class?
Answer:
10 Girls
Step-by-step explanation:
This shows that there is twice as many boys in the gym class than girls.
Step 1: Determine what the ratio relates to the amount
1:2 -> 10:20
10 Girls
20 Boys
Answer:
The enswer is corect because is the biggest then girls to boys
Step-by-step explanation:
How do I do this????????????
Answer:
10 rows with the set of 100 blocks is what she will make
Step-by-step explanation:
Where
First row is 1
Second row is 3
Third row is 5
This shows that the blocks are set in an oddly fashion
Meaning each row has a odd number of blocks
Therefore from
1 block- row 1
3 blocks- row2
5 blocks- row 3
7 blocks - row 4
9 blocks- row 5
11 blocks - row 6
13 blocks- row 7
15 blocks - row 8
17 blocks- row 9
19 blocks - row 10
Add of the blocks it amounts to 100 blocks
Meaning the triangular will be at the 10th row when she has use 100 blocks
The measures of the angles of triangle RST are in the ratio 2:4:9. What are the measures of the angles ?
Measures of the angles are 24°, 48° and 108°
Step-by-step explanation:
Step 1: Given ratio = 2:4:9. Sum of angles of triangle = 180°Let angles be 2x, 4x and 9x.
⇒ 2x + 4x + 9x = 180
⇒ 15x = 180
⇒ x = 180/15 = 12
Step 2: Find angles.2x = 24°, 4x = 48° and 9x = 108°
Which of the following are necessary when proving that the diagonals of a
rectangle are congruent? Check all that apply.
o A. Opposite sides are congruent.
O
B. All obtuse angles are congruent.
O
C. Opposite sides are perpendicular.
O
D. All right angles are congruent.
Answer:look
Step-by-step explanation:
The diagonals of a rectangle exist congruent the necessary conditions are
A. Opposite sides are congruent.
C. Opposite sides are perpendicular.
How to verify that the diagonals of a rectangle are congruent?A quadrilateral exists named a rectangle if the opposite sides exist congruent and parallel to each other. All interior angles exist as right angles and are congruent.
To verify that the diagonals of a rectangle exist congruent the necessary conditions are:
1. Opposite sides of a rectangle exist congruent.
2. All right angles exist congruent.
Therefore, the correct answer is options A and C.
A. Opposite sides are congruent.
C. Opposite sides are perpendicular.
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14 divied by 3/8 equals
Answer:
37 1/3
Step-by-step explanation:
14 divided by 3/8=
14*8/3=
37 1/3
Justin wanted to wrap his moms birthday present shaped like a rectangular prism with pretty paper. The box is 2.1 feet long, 2.7 feet wide, And 3.2 feet high. What is the total surface area of the box?
Answer:
42.06 ft²
Step-by-step explanation:
2 sides = 2(2.7 ft × 3.2 ft) = 2 × 8.64 ft² = 17.28 ft²
Front + back = 2(2.1 ft × 3.2 ft) = 2 × 6.72 ft² = 13.44 ft²
Top + bottom = 2(2.1 ft × 2.7 ft) = 2 × 5.67 ft² = 11.34 ft²
Total area = 42.06 ft²
Which statements are true? Check all that apply. StartRoot 1.8 EndRoot < 1.8 StartRoot 1.8 EndRoot greater-than 1 StartRoot 1.8 EndRoot less-than StartRoot 1.9 EndRoot 1.3 less-than StartRoot 1.8 EndRoot less-than 1.4 StartRoot 1.9 EndRoot + StartRoot 1.8 EndRoot greater-than 2 StartRoot 1.9 EndRoot minus StartRoot 1.8 EndRoot greater-than 0.1
The first, second, third, and fifth statements are true, but the fourth and sixth statements are false. The responses are based on evaluating the square root calculations.
Explanation:The statements we are analyzing are related to the square root of 1.8 (√1.8). Let's work through them:
√1.8 less than 1.8: This statement is true because the square root of a positive number less than its actual number.√1.8 greater than 1: This is true. Since √1.8 is approximately 1.34, which is greater than 1.√1.8 less than √1.9: This is true. Since the larger the number, the larger its square root will be.1.3 less than √1.8 less than 1.4: This is false. As previously stated, √1.8 is approximately 1.34, so it's not less than 1.3 nor greater than 1.4.√1.9 + √1.8 greater than 2: This is true. √1.9 is approximately 1.38 and √1.8 is 1.34. Adding these values exceeds 2.√1.9 − √1.8 greater than 0.1: This is false. The difference between √1.9 and √1.8 is less than 0.1.Learn more about Square Root Comparisons here:https://brainly.com/question/30877013
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Find the area of the region bounded by the line y=3x−6 and line y=−2x+8. a) the x-axis.
Answer:
[tex]\displaystyle A = \frac{12}{5}[/tex]
General Formulas and Concepts:
Math
Number LinePre-Algebra
Order of Operations: BPEMDAS
BracketsParenthesisExponentsMultiplicationDivisionAdditionSubtractionLeft to RightEquality Properties
Multiplication Property of EqualityDivision Property of EqualityAddition Property of EqualitySubtraction Property of EqualityAlgebra I
Terms/CoefficientsFactoringCoordinates (x, y)Solving systems of equations using substitution/eliminationSolving systems of equations by graphingFunction NotationInterval NotationCalculus
Integration
Integration Property [Addition/Subtraction]: [tex]\displaystyle \int {[f(x) \pm g(x)]} \, dx = \int {f(x)} \, dx \pm \int {g(x)} \, dx[/tex]
Integration Property [Multiplied Constant]: [tex]\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx[/tex]
Integration Property [Splitting Integral]: [tex]\displaystyle \int\limits^c_a {f(x)} \, dx = \int\limits^b_a {f(x)} \, dx + \int\limits^c_b {f(x)} \, dx[/tex]
Integration Rule [Reverse Power Rule]: [tex]\displaystyle \int {x^n} \, dx = \frac{x^{n + 1}}{n + 1} + C[/tex]
Integration Rule [Fundamental Theorem of Calculus 1]: [tex]\displaystyle \int\limits^b_a {f(x)} \, dx = F(b) - F(a)[/tex]
Area of a Region Formula: [tex]\displaystyle A = \int\limits^b_a {[f(x) - g(x)]} \, dx[/tex]
f(x) is always top functiong(x) is always bottom function"Top minus Bottom"Step-by-step explanation:
Step 1: Define
Identify bounded region. See attached graph.
y = 3x - 6
y = -2x + 8
Bounded by x-axis and between those 2 lines (already pre-determined; taking an integral always takes it to the x-axis).
Step 2: Analyze Graph
See attached graph.
Looking at our systems of equations on the graph, we see that our limits of integration is from x = 2 to x = 4.
We don't have a continuous top function through the interval [2, 4] (it switches from y = 3x - 6 to y = -2x + 8), so we need to split it into 2 integrals to find the total area.
We can either use the graph and identify the intersection point, which is x = 2.8, or we can solve it algebraically (systems of equations - substitution method):
Substitute in y: 3x - 6 = -2x + 8[Addition Property of Equality] Add 2x on both sides: 5x - 6 = 8[Addition Property of Equality] Add 6 on both sides: 5x = 14[Division Property of Equality] Divide 5 on both sides: x = 14/5Our 2 intervals would be [2, 14/5] and [14/5, 4] for their respective integrals.
Step 3: Find Area
Our top functions are the linear lines y = 3x - 6 and y = -2x + 8 and our continuous bottom function is the x-axis (x = 0).
We can redefine the linear lines as f₁(x) = 3x - 6, f₂(x) = -2x + 8, and g(x) = 0.
Integration
[Area of a Region Formula] Rewrite/Redefine [Int Prop SI]: [tex]\displaystyle A = \int\limits^b_a {[f_1(x) - g(x)]} \, dx + \int\limits^c_b {[f_2(x) - g(x)]} \, dx[/tex][Area of a Region Formula] Substitute in variables: [tex]\displaystyle A = \int\limits^{\frac{14}{5}}_2 {[(3x - 6) - 0]} \, dx + \int\limits^4_{\frac{14}{5}} {[(-2x + 8) - 0]} \, dx[/tex][Integrals] Simplify Integrands: [tex]\displaystyle A = \int\limits^{\frac{14}{5}}_2 {[3x - 6]} \, dx + \int\limits^4_{\frac{14}{5}} {[-2x + 8]} \, dx[/tex][Integrals - Algebra] Factor: [tex]\displaystyle A = \int\limits^{\frac{14}{5}}_2 {[3(x - 2)]} \, dx + \int\limits^4_{\frac{14}{5}} {[-2(x - 4)]} \, dx[/tex][Integrals] Simplify [Int Prop MC]: [tex]\displaystyle A = 3 \int\limits^{\frac{14}{5}}_2 {[x - 2]} \, dx - 2 \int\limits^4_{\frac{14}{5}} {[x - 4]} \, dx[/tex][Integrals] Integrate [Int Rule RPR]: [tex]\displaystyle A = 3(\frac{x^2}{2} - 2x) \bigg| \limits^{\frac{14}{5}}_2 - 2(\frac{x^2}{2} - 4x) \bigg| \limits^4_{\frac{14}{5}}[/tex][Integrals] Evaluate [Int Rule FTC 1]: [tex]\displaystyle A = 3(\frac{8}{25}) - 2(\frac{-18}{25})[/tex][Expression] Multiply: [tex]\displaystyle A = \frac{24}{25} + \frac{36}{25}[/tex][Expression] Add: [tex]\displaystyle A = \frac{12}{5}[/tex]We have found the area bounded by the x-axis and linear lines y = 3x - 6 and y = -2x + 8.
Topic: Calculus BC
Unit: Area between 2 Curves, Volume, Arc Length, Surface Area
Chapter 7 (College Textbook - Calculus 10e)
Hope this helped!
Answer:
A = 12/5 units
Step-by-step explanation:
USING ALGEBRA:
We can find the intersection point between these two lines;
y = 3x - 6y = -2x + 8Set these two equations equal to each other.
3x - 6 = -2x + 8Add 2x to both sides of the equation.
5x - 6 = 8Add 6 to both sides of the equation.
5x = 14Divide both sides of the equation by 5.
x = 14/5Find the y-value where these points intersect by plugging this x-value back into either equation.
y = 3(14/5) - 6Multiply and simplify.
y = 42/5 - 6Multiply 6 by (5/5) to get common denominators.
y = 42/5 - 30/5Subtract and simplify.
y = 12/5These two lines intersect at the point 12/5. This is the height of the triangle formed by these two lines and the x-axis.
Now let's find the roots of these equations (where they touch the x-axis) so we can determine the base of the triangle.
Set both equations equal to 0.
(I) 0 = 3x - 6Add 6 both sides of the equation.
6 = 3xDivide both sides of the equation by 3.
x = 2Set the second equation equal to 0.
(II) 0 = -2x + 8Add 2x to both sides of the equation.
2x = 8Divide both sides of the equation by 2.
x = 4The base of the triangle is from (2,0) to (4,0), making it a length of 2 units.
The height of the triangle is 12/5 units.
Formula for the Area of a Triangle:
A = 1/2bhSubstitute 2 for b and 14/5 for h.
A = (1/2) · (2) · (12/5)Multiply and simplify.
A = 12/5The area of the region bounded by the lines y = 3x - 6 and y = -2x + 8 between the x-axis is 12/5 units.
The ratio of people to books in a classroom is 10:4 what is the unit rate of people per book
Answer:
Unit rate of people per book = 2.5
Step by step explanation:
Given:
Number of peoples = [tex]10[/tex]
Number of books = [tex]4[/tex]
Their ratios = [tex]10 : 4[/tex]
We have to find the unit rate of people per book.
To find out the unit rate of people per book we have to divide the total number of peoples by the total number of books.
Or
For this we will follow the unitary method:
For [tex]4[/tex] book there are [tex]10[/tex] persons.
For [tex]1[/tex] book there will be [tex]\frac{10}{4}[/tex] persons.
So,
The numeric value = [tex]\frac{10}{4}[/tex]
= [tex]2.5[/tex]
There are 2.5 people per book and that it also the unit rate of people per book.
rachel spent $3.60 for stamps to mail packages. Some were 30-cent stamps and the rest were 20-cent stamps. The number of 20-cent stamps was 2 less than the number of 30-cent stamps. How many stamps of each kind did rachel buy?
Rachel bought six 20-cent stamps and eight 30-cent stamps.
Step-by-step explanation:
Given,
Amount spent on stamps = $3.60 = 3.60*100 = 360 cents
Let,
x = 20 cent stamps
y = 30 cent stamps
According to given statement;
20x+30y=360 Eqn 1
x = y-2 Eqn 2
Putting value of x from Eqn 2 in Eqn 1
[tex]20(y-2)+30y=360\\20y-40+30y=360\\50y=360+40\\50y=400[/tex]
Dividing both sides by 50
[tex]\frac{50y}{50}=\frac{400}{50}\\y=8[/tex]
Putting y=8 in Eqn 2
[tex]x=8-2\\x=6[/tex]
Rachel bought six 20-cent stamps and eight 30-cent stamps.
Keywords: linear equation, substitution method
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Final answer:
Rachel bought 8 thirty-cent stamps and 6 twenty-cent stamps. We solved a system of equations representing the cost of the stamps and their quantity relationship to determine the numbers.
Explanation:
Rachel spent $3.60 for stamps to mail packages, buying 30-cent stamps and 20-cent stamps. The number of 20-cent stamps was 2 less than the number of 30-cent stamps. To solve this, we can use a system of equations to represent the total cost and the relationship between the number of stamps:
Let x be the number of 30-cent stamps.
Let y be the number of 20-cent stamps.
Based on the information given:
0.30x + 0.20y = 3.60 (Total cost equation)
y = x - 2 (Relationship between the stamps)
We substitute the second equation into the first equation:
0.30x + 0.20(x - 2) = 3.60
0.30x + 0.20x - 0.40 = 3.60
0.50x = 4.00
x = 8
Now we solve for y using the second equation:
y = 8 - 2
y = 6
So Rachel bought 8 thirty-cent stamps and 6 twenty-cent stamps.
Bally manufacturing sent intel corporation an invoice for machinery with a $15,200 list price. Bally dated the invoice August 14 with 5/10 EOM terms. Intel receives a 40% trade discount. Intel pays the invoice on August 27. What does Intel pay Bally?
Answer:
9120
Step-by-step explanation:
What is the value of y?
Enter your answer in the box.
Answer:64
Step-by-step explanation:
Add 79 with 37 an you will get 116 you need to know the total angle for a triangle is 180 so 180 minus 116 is 64
The measure of the angle y for the triangle is 64°.
What is the angle of a triangle?The triangle is a shape having three sides and the sum of the angles of the triangle is always equal to 180°.
Here in the given triangle, the two angles are 79° and 37°. The measure of the unknown angle y° will be calculated as:-
y + 79 + 37 = 180
Now solve for the value of angle y below,
y = ( 180 - 79 - 37 )
y = 64°
Therefore, the measure of the angle y for the triangle is 64°.
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If a figure was dilated using a scale factor of 2/3, the first step in mapping it back
onto itself is to dilate the new figure with a scale factor of ?
2/3
2
3
3/2
Answer:3/2
Step-by-step explanation:
2/3 of a year is how many months
Answer:8
Step-by-step explanation:
There are 12 months in a year if you divide by 3 you get 4 and whatever you do to the numerator you have to do the denominator vice versa so you would multiply by four and get eight so it would be eight months
Answer:
2/3 of a year is 8 months
Step-by-step explanation:
When Carrie mows a lawn, she charges a flat fee of $5 plus an hourly rate, R. Carrie worked 2 hours at her last job. She charged a total of $20.00 for all lawns she mowed. Which equation represents what Carrie charged as an hourly rate?
A. 5 + r = 20
B. 5 + 2r = 20
C. 5r + 2 = 20
D. 20 + 2r = 5
Answer:
option B.) 5 + 2r = 20 is correct
Step-by-step explanation:
Carrie mows a lawn, she charges a flat fee of $5 plus an hourly rate, r.
The amount Carrie earns for mowing lawns for t number or hours
= 5 + rt
Carrie worked for 2 hours and charged a total of $20.
Therefore we can write
20 = 5 + r [tex]\times[/tex] 2 [tex]\Rightarrow[/tex] 20 = 5 + 2r
Therefore option B.) 5 + 2r = 20 is correct
What Is 6 divided by 2/6?
Can you explain step by step please
Answer:
18Step-by-step explanation:
[tex]\frac{6}{\frac{2}{6} } =6*\frac{6}{2} =6*3=18[/tex]
Answer:
18
Step-by-step explanation:
6/(2/3)
Turn 6 into a fraction first.
(6/1) / (2/6)
(6/1) x (6/2)
36/2
18
What is the rate of change of the function described in the table?
the average rate of change of the function over the interval [tex]\(10 < x < 15\)[/tex] is [tex]\( -\frac{6}{5} \)[/tex].
To find the average rate of change of the function over the interval (10 < x < 15), we use the formula:
[tex]\[ \text{Average Rate of Change} = \frac{\text{Change in } f(x)}{\text{Change in } x} \][/tex]
We can calculate the change in [tex]\(f(x)\)[/tex] by subtracting the function values at the end and start of the interval, and the change in x by subtracting the end and start values of x.
Given the function values:
- [tex]\(f(10) = 30\)[/tex]
- [tex]\(f(15) = 24\)[/tex]
And the interval [tex]\(10 < x < 15\)[/tex], the change in [tex]\(f(x)\) is \(f(15) - f(10) = 24 - 30 = -6\)[/tex].
The change in x is [tex]\(15 - 10 = 5\)[/tex].
Now, we plug these values into the formula for the average rate of change:
[tex]\[ \text{Average Rate of Change} = \frac{-6}{5} \][/tex]
So, the average rate of change of the function over the interval [tex]\(10 < x < 15\)[/tex] is [tex]\( -\frac{6}{5} \)[/tex].
The complete Question is given below:
Given the function defined in the table below, find the average rate of change, in simplest form, of the function over the interval 10 < x < 15
x | f(0)
0 | 42
5 | 36
10 | 30
15 | 24
20 | 18
25 | 12
Find the value of 49/ 50 ÷ 7/ 6 using any method. Type your answer as a fraction in simplest form.
To divide fractions, multiply the first fraction by the reciprocal of the second fraction. Simplify the resulting fraction.
Explanation:To divide fractions, we need to multiply the first fraction by the reciprocal of the second fraction. So, the reciprocal of 7/6 is 6/7. Therefore, 49/50 ÷ 7/6 = 49/50 x 6/7. When we multiply the numerators (49 x 6) and the denominators (50 x 7), we get 294/350. This fraction can be simplified by dividing both the numerator and denominator by their greatest common divisor, which is 14. Therefore, 294/350 simplifies to 21/25.
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Can you show the work for (4x-4)(x-4)
Answer:
4x² - 20x + 16
Step-by-step explanation:
Given
(4x - 4)(x - 4)
Each term in the second factor is multiplied by each term in the first factor, that is
4x(x - 4) - 4(x - 4) ← distribute both parenthesis
= 4x² - 16x - 4x + 16 ← collect like terms
= 4x² - 20x + 16
1. How far does the tip of a 12 cm
long minute hand on a clock move
in 45 minutes?
Answer:
Therefore the tip of the minute hand on the clock moves 56.57 cm in 45 minutes.Step-by-step explanation:
Using this formula to find the length of the arc
Arc length = [tex]2\pi r (\frac{\theta}{360} )[/tex]
Here [tex]\theta = \frac{360}{60}\times 45[/tex] [for 45 minutes]
[tex]=270^\circ[/tex]
Radius(r) = length of the minute hand = 12 cm
The length of the arc is = [tex]2\pi \times 12\times \frac{270}{360}[/tex]
= 56.57 cm
Therefore the tip of the minute hand on the clock moves 56.57 cm in 45 minutes.
What is nine - fifteenths minus two - sixths
Answer: four-fifteenths or [tex]\frac{4}{15}[/tex]
Step-by-step explanation:
What is written with words is mathematically expressed as:
[tex]\frac{9}{15}-\frac{2}{6}[/tex]
We can simplify both fractions, by dividing the numerator and denominator of the first by 3 and dividing the numerator and denominator of the second by 2:
[tex]\frac{9}{15}=\frac{3}{5}[/tex]
[tex]\frac{2}{6}=\frac{1}{3}[/tex]
Then:
[tex]\frac{3}{5}-\frac{1}{3}[/tex]
Calculating the least common multiple (l.c.m) in the denominator as [tex]15[/tex]:
[tex]\frac{9-5}{15}=\frac{4}{15}[/tex] This is the result: four-fifteenths
Me Matthews purchases 22 boxes of pencils for 5 fourth grade classes. Each box contains 45 pencils. How many pencils will each class receive?
Answer: 198 pencils per class
Explanation:
22 boxes * 45 pencils = 990 pencils
990 pencils / 5 classes = 198 pencils per class
Answer: 198 pencils per class
Explanation:
22 boxes * 45 pencils = 990 pencils
990 pencils / 5 classes = 198 pencils per class
.
How many solutions does the following system have?
y=2x-12
y=3x+12
The system has one solution
Step-by-step explanation:
Let us revise the type of the solutions of a system of equations
One solution if the coefficients of x or/and y are different in the simplest form of the two equationsInfinite many solutions if the coefficients of x , y and the numerical terms are equal in the simplest form of the two equationsNo solution if the coefficients of x and y are equal and the numerical terms are different in the simplest form of the two equationsThe system of equations is:
y = 2x - 12 ⇒ (1)
y = 3x + 12 ⇒ (2)
∵ The equations are in its simplest form
∵ The coefficients of x in the two equations are different
- That is the 1st case above
∴ The system has one solution
Let us prove that by solving the system
To solve the system of equations equate (1) and (2) to find x
∵ 3x + 12 = 2x - 12
- Subtract 2x from both sides
∴ x + 12 = -12
- Subtract -12 from both sides
∴ x = -24
- Substitute the value of x in equation (1) or (2) to find y
∵ y = 3(-24) + 12
∴ y = -72 + 12
∴ y = -60
∴ The solution of the system is (-24 , -60)
The system has one solution
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Match each function with its inverse function.
Answer:
check the photo.
Step-by-step explanation:
The inverse of the function
f(x) = ax + b is g(x) = (x/a) - (b/a)
(learn it by heart)
complete the equation of the line through (-8, 8) and (1, -10)
Answer:
[tex]y=-2x-8[/tex]
Step-by-step explanation:
Let [tex]y=mx+c[/tex] be the equation of this line.
The points must satisfy this equation.
When x=-8, and y=8, we get:
[tex]8=-8m+c....(1)[/tex]
When x=1, and y=-10, we get:
[tex]-10=m+c...(2)[/tex]
Subtract equation (1) from equation (2) to get:
[tex]m--8m=-10-8[/tex]
9m=-18
m=-2
We put m=-2 in equation to get (2)
-10=-2+c
c=-10+2
c=-8
Therefore the equation is:
y=-2x-8
on the last friday in may, one fourth of the 280 students in a school were away on a field trip how many students were on the field trip