Answers
Answer:
a) [tex]f(x) = x + 3[/tex]
b) [tex]f(x) = -x - 5[/tex]
c) [tex]f(x) = 2x + 6[/tex]
Step-by-step explanation:
To determine the equation of a straight line, we need two things:
1. two known points (coordinates) on the line, used to calculate the gradient
2. the y-intercept of the line (the y-coordinate of the point at which the line crosses the y-axis)
Then we can use the equation:
[tex]\boxed {f(x) = ax + q}[/tex]
where a is the gradient and q is the y-intercept, to determine the equation of the line.
a) known points: (0, 3), (-4, -1)
y-intercept: 3
gradient = [tex]\frac{y_2 - y_1}{x_2 - x_1}[/tex]
⇒ [tex]\frac{3 - (-1)}{0 - (-4)}[/tex]
⇒ [tex]\bf 1[/tex]
∴ a = 1 , q = 3
∴ equation:
[tex]{f(x) = ax + q}[/tex]
[tex]f(x) = 1x + 3[/tex]
⇒ [tex]\bf f(x) = x + 3[/tex]
b) known points: (-7, 2) , (0, -5)
y-intercept = -5
gradient = [tex]\frac{2 - (-5)}{-7 - 0}[/tex]
⇒ [tex]\bf -1[/tex]
∴ equation:
[tex]f(x) = -1x + (-5)[/tex]
⇒ [tex]\bf f(x) = -x - 5[/tex]
c) known points: (-3, 0), (0, 6)
y-intercept = 6
gradient = [tex]\frac{6 - 0}{0 - (-3)}[/tex]
⇒ [tex]\bf 2[/tex]
∴ equation:
[tex]\bf f(x) = 2x + 6[/tex]
Related Questions
Given two points (-3, 1) and (4, -1) are on a line. Write an equation in slope-
intercept form of the line.
y=____x+____
Answers
Answer:
y=-2/7x+1/7
Step-by-step explanation:
Find the slope first
-1-1/4+3
-2/7
m=-2/7
y=-2/7x+b
1=-2/7(-3)+b
b=1/7
probar por medio de induccion
Answers
Answer:
Wt
Step-by-step explanation:
ayudaa para mañana !!
Answers
Answer:
ok bueno dejamr haber que ago
Answer:
2/5 > 1/3
9/20 > 13/30
17/12 < 22/15
Step-by-step explanation:
Encuentra un denominador común. por ejemplo, 2/5 y 1/3 tienen un denominador común de 15. 2/5 se convierte en 6/15 y 1/3 se convierte en 5/15. 6 es mayor que 5. ¡Espero que esto ayude y buena suerte!
1. A house cost $112,000 in 2010. By the year 2015, the house had a value of $132,000. What was the growth rate as a percent for that 5-year period?
Pls help
A. 6.48%
B. 3.34%
C. 5.23%
D. 2.15%
Answers
Answer:
The growth rate for the period was of 17.86%.
Step-by-step explanation:
To find the growth rate as a percent, we multiply the change by 100, and divide by the initial value.
A house cost $112,000 in 2010. By the year 2015, the house had a value of $132,000.
Change: 132 - 112 = 20
Initial value: 112
Growth rate as a percent:
20*100/112 = 17.86%
The growth rate for the period was of 17.86%.
Answer:b
Step-by-step explanation:
It's math,I'll send u a picture!
Answers
Answer:
suree.
Step-by-step explanation:
Hellllllllppppp meeeee
Answers
Answer:
x=18°
Step-by-step explanation:
5x-18=4x
subtract 4x from both sides
x-18=0
add 18 to both sides
x=18°
I need help with this question
Answers
Answer:
2,540 miles
Step-by-step explanation:
The computation of the fewer miles is given below;
For Space explorer B
= 15,000 miles ÷ 5 hours
= 3,000 miles per hour
For space explorer A
y = 4,600 x
That means in one hour it covered 460 miles
So, the fewer miles would be
= 3,000 - 460
= 2,540 miles
The area of Ms. Anderson’s office floor measures 120
square feet. She puts down a carpet that covers 40%
of the floor. What is the area of Ms. Anderson’s floor not covered by the carpet?
Answers
Answer:
72 square feet not covered
Step-by-step explanation:
100%-40% = 60%
60% of 120 = 0.6x120 = 72
Answer:
72
Step-by-step explanation:
because i know
What generalization can you make about the following equations: 7 divided by 1/4 = 28. 7 x 4 = 28. quick pls. ✌️I'll make you brainliest if you can help
Answers
Answer:
I guess its because they have the same outcome
The function f(x)=2000(1.05)^(x) models a population of butterflies after x years. What will the population be in 7 years? plz help quick
Answers
Answer:
About 2,800.
Step-by-step explanation:
2,000(1.05)^x
x =7.
2,000(1.05)^7
find 1.05 to the power of 7, which is 1.4071....
then times 1.4071... by 2,000. You will get 2,814.2 - or about 2,800.
The population of butterflies after 7 years will be approximately 2814 butterflies.
What is an exponential function?An exponential function is defined as a function whose value is a constant raised to the power of an argument is called an exponential function.
The formula f(x) = 2000(1.05)ˣ can be used to model the population of butterflies after x years, where x is a non-negative integer.
Here, the initial population is 2000.
To find the population of butterflies after 7 years, we can substitute x = 7 into the given function and evaluate:
f(7) = 2000(1.05)⁷
Using a calculator, we get:
f(7) ≈ 2814
Therefore, the population of butterflies after 7 years will be approximately 2814 butterflies.
Learn more about exponential function here:
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The carnival also offers two magic shows. The morning show is only 20 minutes and it costs $3.75. For the afternoon show, it is 35 minutes and costs $5.25. Which show would give you more for your money?
Answers
Answer:
35 minutes
Step-by-step explanation:
The carnival offers two magic shows
The morning show is for 20 mintes at $3.75
= 3.75/20
= 0.1875
The afternoon show is for 35 minutes at $5.25
= 5.25/35
= 0.15
Hence you pay a lesser amount for 35 minutes
30. Which reason justifies the statement below?
A. Definition of Congruence
B. Angle Addition Postulate
C. Supplement Theorem
D. Definition of Vertical Angles
Answers
Yw
The correct reason for the statement ∠1 ≅ ∠2 will be;
⇒ Definition of Vertical Angles.
Option D is true.
What is Vertical angles?
When the two lines are crosses to each other at a point then the vertical angles are formed.
Given that;
∠1 and ∠2 are formed between two lines which crosses at a point.
Now,
The two lines are vertical lines which passes through a point and ∠1 and ∠2 are formed between them.
So, By definition of Vertical Angles;
∠1 ≅ ∠2
Therefore,
The correct reason for the statement ∠1 ≅ ∠2 will be;
⇒ Definition of Vertical Angles.
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The sum of two numbers is 15. Twice the large
number plus 4 times the smaller number is 24.
Find the large number.
Answers
2x+4y=24
2x+4(15-x)=24
2x+60-4x=24
-2x=-36
x=18
the larger number is 18
Find the quotient. Answer as a decimal.
–6 ÷ 1
1
3
3
1
Answers
Answer:
≈ -0.0005
Step-by-step explanation:
HELP
In a fruit basket there are 9 bananas, 4 apples, and 3 plums. Fill in the blanks- The ratio of bananas to apples is ___:___
Answers
Answer:
9:4
Step-by-step explanation:
Jill collected honey from 9 different beehives, and recorded the amount collected, in gallons, from each hive in the line plot shown:
She wants to write the value of each point marked on the number line above (Points A-D) in gallons. What is the value of A using fractions?
My brother needs help I don't remember this devilish stuff
Answers
Answer:
A= 6/8 gallons
The rain gauge after a week showed that there were ten inches of rain. Every day the rain evaporated two inches but one more inch of rain was added. By what day was the rain gauge free of water?
A. day 11
B. day 10
C. day 8
D. day 7
Answers
Answer:
10 days to free water from rain gauge
Use the rectangle below to answer both part 1 and part 2
X+5
Part 1: Write an equation to find the value of x, if the area of the rectangle is 48 in?
Equation:
Part 2: What is the value of x, if the area of the retangle is 48 in2? Solve your equation from part 1.
X =
Blank 1:
Blank 2:
Answers
Answer:
i believe the equation is x = 48 ÷ 4 - 5
and x = 7
Step-by-step explanation:
you will need to take the are devided by width, because area is length times width. then subtract 5.
48÷4=12
12-5=7
Your uncle is 2 years older than 3 times your age.
You are x years old. Write an expression to describe your uncles age.
It would be a lot helpful if you could answer this! :D
Answers
you are x
three times is 3x
2 years older is 3x + 2
Answer:
3x+2
Step-by-step explanation:
3 times x plus 2 since he's 2 years older than that
For each statement, write what would be assumed and what would be proven in a proof by contrapositive of the statement. Then write what would be assumed and what would be proven in a proof by contradiction of the statement.
a. If x and y are a pair of consecutive integers, then x and y have opposite parity.
b. For all integers n, if n² is odd, then n is also odd.
Answers
Answer:
a)
Given Statement - If x and y are a pair of consecutive integers, then x and y have opposite parity.
Proof by Contrapositive:
Assumed statement: Suppose that integers x and y do not have opposite parity.
Proven Statement: x and y are not a pair of consecutive integers.
Proof -
x = 2u₁ , y = 2u₂
Then
(x, x+1) = (2u₁ , 2u₁ + 1) = (Even, odd)
If y = 2u₁ + 1
Not possible
⇒x and y are not a pair of consecutive integers.
Hence proved.
Proof by Contradiction:
Assumed statement: Suppose x and y are not a pair of consecutive integers.
Proven Statement: Suppose x and y do not have opposite parity.
Proof -
If x and y are not a pair of consecutive integers.
⇒ either x and y are odd or even
If x and y are odd
⇒x and y have same parity
Contradiction
If x and y are even
⇒x and y have same parity
Contradiction
(b)
Proof by Contrapositive:
Assumed statement: Let n be an integer such that n is not odd (i.e. n is an even integer)
Proven Statement: n² is not odd (i.e n² is even)
Proof -
Let n is even
⇒n = 2m
⇒n² = (2m)² = 4m²
⇒n² is even
Hence proved.
Proof by Contradiction:
Assumed statement: Let n be an integer such that n² be odd.
Proven Statement: suppose that n is not odd (i.e n is even)
Proof -
Let n² is odd
⇒n² is even
⇒n² = 2m
⇒2 | n²
⇒2 | n
⇒n = 2x
⇒ n is even
Contradiction
x+y+x=22
a+a+x=28
y+2y+2a=38
2y*x*2a=?
there are no 0, negative number, or fractions
solve for all variables
Answers
y = 6
a = 10
? = 1920
x + y + x = 22
8 + 6 + 8 = 22
a + a + x = 28
10 + 10 + 8 = 28
y + 2y + 2a = 38
6 + 2(6) + 2(10) = 38
2y * x * 2a =
2(6) * 8 * 2(10) = 1920
If 5 hours is 25% of the time a trip will take, how long will it take?
Answers
Answer:
20 hours
Step-by-step explanation:
Answer:
20
Step-by-step explanation:
We know that 25% is 1/4 of the time. So 5 hours would be multiplied by 4, which is the reciprocal of 1/4.
5 x 4 = 20, so that's your answer. I hope I helped :)
Identify the pattern for the following sequence. Find the next three terms in the sequence.
-15, -11, -7, -3,
a. Subtract 4; -7, -11, -15
b. Add 4; 2, 6, 10
C. Subtract 4: 1,5, 9
d. Add 4; 1,5,9
Answers
Answer:
d. add 4; 1, 5, 9
Step-by-step explanation:
to get from -15 to -11, they had to add 4, and so on.
-3+4= 1
1+4= 5
etc.
3^3
or 3 x 3 x 3.
4^7
( 7 x 7 x 7 x 7)
and
5^6
Answers
Answer:
3^3= 27
4^7= 16384
5^6=3125
write a real-world problem given the equation 2/3x = 12. Then solve the equation.
Answers
Answer:
You want to buy long pieces of paper at Dollar Tree for 66 cents. You have $12. How many long pieces of paper can you buy
Step-by-step explanation:
Solve for y.
25 = y2
y =
or
Answers
Answer:
y=5 or y=−5 it does not matter either one
Step-by-step explanation:
25=y2
Step 1: Subtract y^2 from both sides.
25−y2=y2−y2
−y2+25=0
Step 2: Subtract 25 from both sides.
−y2+25−25=0−25
−y2=−25
Step 3: Divide both sides by -1.
−y2
−1
=
−25
−1
y2=25
Step 4: Take square root.
y=±√25
y=5 or y=−5
Answer:
Let's solve your equation step-by-step.
25 = [tex]y^{2}[/tex]
Step 1: Subtract y^2 from both sides.
25 − [tex]y^{2}[/tex] = [tex]y^{2}[/tex] − [tex]y^{2}[/tex]
−[tex]y^{2}[/tex]+ 25 = 0
Step 2: Subtract 25 from both sides.
−[tex]y^{2}[/tex]+ 25 − 25 = 0 − 25
−[tex]y^{2}[/tex] = − 25
Step 3: Divide both sides by -1.
[tex]y^{2}[/tex] / −1 = −25 / −1
[tex]y^{2}[/tex] =25
Step 4: Take square root.
y = ± √25
y = 5 or y = −5
Answer:
y = 5 or y = −5
Hope it helps
Please mark me as the brainliest
Thank you
The day after the day after tomorrow is four days before Monday. What day is it today?
Answers
In a study published in the American Psychological Association's Journal of Personality and Social Psychology, 227 college students were asked to rate their level of aggression and indicate their level of exposure to video game violence. The study found that students who reported playing more violent video games engaged in more aggressive behavior. Which of the following conclusions can you make on the basis of this study?
a. There is no relationship between violent video games and aggression.
b. Nonviolent video games make students less aggressive.
c. Playing violent video games is associated with more aggressive behavior.
d. Violent video games make students more aggressive.
Answers
Answer:
c. Playing violent video games is associated with more aggressive behavior.
Step-by-step explanation:
This question is solved interpreting the text.
The study found that students who reported playing more violent video games engaged in more aggressive behavior.
The conclusion that it leads is that violent video games is associated with more agressive behavior. Keyword is associated, and the correct answer is given by option c.
The conclusion that can you make on the basis of this study is: c. Playing violent video games is associated with more aggressive behavior.
What is a Conclusion?A conclusion refers to the final understanding that can be reached on a matter based on the findings in the study.
The findings from this study indicate that students who were exposed to violent video games had the tendency of becoming more aggressive.
So, we can conclude that violent video games is associated with aggressive behavior.
Learn more about conclusions from studies here:
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Lightening Energy Drink has 15.2 calories per fluid ounce. If Jeremy drinks two 12 ounce of Lightening Energy Drinks, then how much calories Dias he consume? Must show work
Answers
Answer:
15.2*12=182.4
Step-by-step explanation:
Please help with this area assignment
Answers
Answer:
375
Step-by-step explanation:
15 times 25 equals 375