Answer:
Step-by-step explanation:
1) slope = 3 ; y-intercept = 1
y = mx + b
y = 3x + 1
0 = 3x + 1 -y
-1 = 3x - y
ANS: 3x - y = -1
2) Passing through (0,2), slope = -4
y - y₁ = m(x -x₁)
y - 2 = -4(x - 0)
y - 2 = -4x
4x + y - 2 = 0
Ans: 4x + y = 2
3)Passing through (-1,3) and (1,1)
Slope = [tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
[tex]= \frac{1-3}{1-[-1]}\\\\= \frac{-2}{1+1}\\\\= \frac{-2}{2}\\\\= - 1[/tex]
m= -1 ; (-1 , 3)
y - y₁ = m(x -x₁)
y - 3 = (-1)(x - [-1] )
y -3 = (-1)(x +1 )
y - 3 = -x - 1
x + y -3 = -1
x +y = -1 + 3
Ans: x + y = 2
4) Passing through (1,3), slope = 1/2
y - y₁ = m(x -x₁)
[tex]y - 3 = \frac{1}{2}(x - 1)\\\\y - 3 = \frac{1}{2}x - \frac{1}{2}\\\\[/tex]
Multiply the equation by 2
[tex]2*y - 2*3 = 2*\frac{1}{2}x - 2*\frac{1}{2}\\\\2y - 6 = x - 1\\[/tex]
2y - 6 +1 = x
2y - 5 = x
-5 = x - 2y
Ans: x - 2y = -5
5) Passing through (1/2,1) and (4,2)
Slope = [tex]\frac{2-1}{4-\frac{1}{2}}[/tex]
[tex]= \frac{1}{\frac{7}{2}}\\\\= \frac{2}{7}[/tex]
m = 2/7 ; (4 , 2)
y - y₁ = m(x -x₁)
[tex]y - 2 = \frac{2}{7}(x - 4)\\\\7y - 7*2 = 7*\frac{2}{7}(x - 4)\\\\7y - 14 = 2(x -4)\\\\7y - 14 = 2x - 8\\\\[/tex]
7y - 14 + 8 = 2x
7y - 6 = 2x
Ans: 2x - 7y = -6
What is 10% of $10 what is 10% of $10
Answer:
$9
Step-by-step explanation:
This means the cost of the item to you is $9. You will pay $9 for a item with original price of $10 when discounted 10%. In this example, if you buy an item at $10 with 10% discount, you will pay 10 - 1 = 9 dollars.
A boat travels 8 miles north from point A to point B. Then it moves in the direction 5 40°W and reaches point Finally, it turns 5 40° E and
returns to point A
The total distance covered by the boat is going how many
miles.
A. 14.95
B. 18.44
C. 20.04
D. 25.88
Answer:
B, 18.44 miles
what is the value of the expression shown? 7 [(7 + 7) +7
Answer:
105
Step-by-step explanation:
7 (7x7) + 7 is the same as 7 x 14 + 7 so that would equal 105
JK=2x+5 and KL=3x-8 find JL
Answer:
Step-by-step explanation:
3x -8 = 2x + 5
x - 8 = 5
x = 13
3(13) - 8 + 2(13) + 5
39 - 8 + 26 + 5
31 + 31 = 62
6sacks of potatoes weigh 122.4 kg and 4 sacks of onions weigh 50 kg. What is the total amount of 1 sack of potatoes and 1 sack of onions
Answer: See explanation
Step-by-step explanation:
6 sacks of potatoes weigh 122.4 kg
1 sack would weigh 122.4 kg ÷ 6
122.4 ÷ 6 = 20.4
1 sack of potatoes weighs 20.4 kg
4 sacks of onions weigh 50 kg
1 sack would weigh 50 kg ÷ 4
50 ÷ 4 = 12.5
1 sack of onions weighs 12.5 kg
(40 points) !!!!!!!URGENT!!!!!! jack and jill both drive the same distance to the beach. by driving 15 mph faster than jack jill can get there in 3 hours while it takes jack 4 hours. how fast does each of them drive !!!!!!URGENT!!!!!
7 2/3
16 3/5
+ 8 1/2
______
8) 3(2x+1) = ?*
O 6x + 3
5x + 1
5x + 3
6x + 1
Answer:
6x + 3
General Formulas and Concepts:
Pre-Algebra
Distributive Property
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightStep-by-step explanation:
Step 1: Define
3(2x + 1)
Step 2: Expand
Distribute 3: 3(2x) + 3(1)Multiply: 6x + 3This year, Martin's income is 1 /4 greater than his income from last year. If s represents his income from last year, what is his income this year?
1/4s
Step-by-step explanation:
Multiply 1/4 with s
Answer:
1/4s
Step-by-step explanation:
x 1/4 by s
What would be the first step you do to solve the equation below?
2x - 4 = 12
The graph shows the number of songs downloaded after x hours.
What is the slope of the line?
(D is only marked bc I couldn’t unmark)
Step-by-step explanation:
For every 2 hours across, the line graph goes up by 15 songs.
Therefore the slope of the line is 15/2. (D)
read and analyze the problem below. Was the problem solved correctly? If not, explain the error and answer it correctly.
Solve:
2x - 8 + 3x + 2 = 4x + 10 + 3x - 6
student work:
2x - 8 + 3x + 2 = 4x + 10 + 3x - 6
5x - 6 = 7x + 16
-5x -5x
-6 = 2x + 16
-16 -16
-22 = 2x
2 2
-11 = x
PLEASE HELP ME!
Geometry i need help rn and could you tell me the name of this subject
Answer:
12Step-by-step explanation:
x is a midsegment of a given triangle as it connects the midpoints of the two sides.
Midsegment is parallel to the third side and equals to half of its measure:
x = 24/2 = 12help me plzzzz and tyyyy
Answer:
her language arts hw takes longer and it takes 2/9 hr longer
Step-by-step explanation:
first of all, 4/9 > 2/9
4/9-2/9=2/9
Which of the following would have a scale factor greater than one?
a) A Hot Wheels car
b) A picture of a skyscraper
c) A map of the world
d) A diagram of a plant cell
Answer:
NIO
Step-by-step explanation:
a
Leilany was on a treadmill and ran 1 mile in 9 minutes. How many minutes will it take her to run 3 miles?
Answer:
27
Step-by-step explanation:
1 mile took 9 min to run, so 3 miles will be:
3 x 9 =
27
Highschool level trigonometry!!! Need help knowing step by step how to find answer!
A ladder is 15 m long. The top of the ladder rests against the wall of a house, and the foot rests on level ground 2m from the wall. Draw a diagram to illustrate the situation. Calculate the angle between the ladder and the ground.
Answer:
[tex]\theta \approx 82.34^\circ[/tex]
Step-by-step explanation:
Please refer to the attached diagram. (Apologies if the shading or resolution is a bit off.)
So, we want to find θ.
Since we formed a right triangle, we can use right triangle ratios.
We know the measure of the adjacent side to θ and the hypotenuse.
Therefore, we will use the cosine ratio:
[tex]\displaystyle \cos(\theta)=\frac{\text{adjacent}}{\text{hypotenuse}}[/tex]
The adjacent side is 2 and the hypotenuse is 15. By substitution:
[tex]\displaystyle \cos(\theta)=\frac{2}{15}[/tex]
Now, we will take the inverse cosine of both sides. So:
[tex]\displaystyle \theta=\cos^{-1}\Big(\frac{2}{15}\Big)[/tex]
Use a calculator. Hence:
[tex]\theta \approx 82.34^\circ[/tex]
The angle between the ground and the ladder is about 82.34°.
Find the equation of the line shown.
Answer:
(0,5) will be linear equation
P= x/3 and x = 1/2 y. Write p in terms of y
Answer:
p = 1/2y - 3
Step-by-step explanation:
p=x/3 and x=1/2y [replace the "x" to solve]
p = (1/2y)/3
Find the first five terms for the following arithmetic sequence Tn=5n-6?
Answer:
The first five terms are -1,4,9,14 and 19.
Step-by-step explanation:
The arithmetic sequence is :
[tex]T_n=5n-6[/tex]
We need to find the first five terms of the sequence.
Put n = 1 for first term.
[tex]T_1=5(1)-6=-1[/tex]
Put n = 2 for second term.
[tex]T_2=5(2)-6=\\\\=10-6\\\\=4[/tex]
Put n = 3 for third term.
[tex]T_3=5(3)-6=\\\\=15-6\\\\=9[/tex]
Put n = 4 for fourth term.
[tex]T_4=5(4)-6=\\\\=20-6\\\\=14[/tex]
Put n = 5 for fifth term.
[tex]T_3=5(5)-6=\\\\=25-6\\\\=19[/tex]
Hence, the first five terms are -1,4,9,14 and 19.
Out of 50 bagels on a tray, 32 of them are cinnamon bagels. What percent of the bagels are cinnamon bagels?
Answer:
64 o/o
Step-by-step explanation: 50 times 2 is 100 and 32 x 2 is 64
The taxi and takeoff time for commercial jets is a random variable x with a mean of 8 minutes and a standard deviation of 2.8 minutes. Assume that the distribution of taxi and takeoff times is approximately normal. You may assume that the jets are lined up on a runway so that one taxies and takes off immediately after the other, and that they take off one at a time on a given runway.
A button hyperlink to the SALT program that reads: Use SALT.
(a) What is the probability that for 37 jets on a given runway, total taxi and takeoff time will be less than 320 minutes? (Round your answer to four decimal places.)
Incorrect: Your answer is incorrect.
(b) What is the probability that for 37 jets on a given runway, total taxi and takeoff time will be more than 275 minutes? (Round your answer to four decimal places.)
Incorrect: Your answer is incorrect.
(c) What is the probability that for 37 jets on a given runway, total taxi and takeoff time will be between 275 and 320 minutes? (Round your answer to four decimal places.)
Incorrect: Your answer is incorrect.
Need Help? Read It
Answer:
a) 0.9207 = 92.07% probability that for 37 jets on a given runway, total taxi and takeoff time will be less than 320 minutes
b) 0.8907 = 89.07% probability that for 37 jets on a given runway, total taxi and takeoff time will be more than 275 minutes
c) 0.8114 = 81.14% probability that for 37 jets on a given runway, total taxi and takeoff time will be between 275 and 320 minutes
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal probability distribution
When the distribution is normal, we use the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
For sum of n normally distributed variables, the mean is [tex]\mu*n[/tex] and the standard deviation is [tex]s = \sigma\sqrt{n}[/tex].
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
In this question, we have that:
For a single commercial jet:
[tex]\mu = 8, \sigma = 2.8[/tex]
For the 37 jets combined:
[tex]\mu = 37*8 = 296, s = 2.8\sqrt{37} = 17.03[/tex]
(a) What is the probability that for 37 jets on a given runway, total taxi and takeoff time will be less than 320 minutes?
This is the pvalue of Z when X = 320. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{320 - 296}{17.03}[/tex]
[tex]Z = 1.41[/tex]
[tex]Z = 1.41[/tex] has a pvalue of 0.9207
0.9207 = 92.07% probability that for 37 jets on a given runway, total taxi and takeoff time will be less than 320 minutes.
(b) What is the probability that for 37 jets on a given runway, total taxi and takeoff time will be more than 275 minutes?
This is 1 subtracted by the pvalue of Z when [tex]X = 275[/tex]. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{275 - 296}{17.03}[/tex]
[tex]Z = -1.23[/tex]
[tex]Z = -1.23[/tex] has a pvalue of 0.1093
1 - 0.1093 = 0.8907
0.8907 = 89.07% probability that for 37 jets on a given runway, total taxi and takeoff time will be more than 275 minutes.
(c) What is the probability that for 37 jets on a given runway, total taxi and takeoff time will be between 275 and 320 minutes?
This is the pvalue of Z when [tex]X = 320[/tex] subtracted by the pvalue of | when [tex]X = 275[/tex]
From a and b
0.9207 - 0.1093 = 0.8114
0.8114 = 81.14% probability that for 37 jets on a given runway, total taxi and takeoff time will be between 275 and 320 minutes
Can you help me with this question?
Answer:
Reason SAS postulate
Step-by-step explanation:
The two triangles must be congruent.
Reason: SAS postulate
PLEASE HELP ME 20 POINTS!!!!!!!!!!! In the plane shown in the figure below, lines land mare cut by the transversal line n. The eight angles at the
intersections of these lines are labeled. Which of the following statements, when it is true, CANNOT always be used
to prove that lines land mare parallel?
Answer:
Option (4)
Step-by-step explanation:
Since, lines l and m are the parallel lines and line 'n' is intersecting these parallel lines,
Option (1)
∠c ≅ ∠y
True.
[Corresponding interior angles]
Option (2)
∠a ≅ ∠w
True.
[Corresponding interior angles]
Option (3)
∠b ≅ ∠x
True.
[Corresponding interior angles]
Option (4)
∠b ≅ ∠z
False.
[Since, ∠b + ∠Z = 180°, consecutive exterior angles]
Option (5)
∠a ≅ ∠z
True.
[Alternate exterior angles]
Therefore, Option (4) will be the answer.
Which is the correct algebraic expression for each phrase?
2.5 times as many pages.
a. 2.5p
b. p+2.5
c. 2.5÷p
d. p-2.5
What is an equation in point-slope form of the line that passes through the point (6, −2) and has a slope of 3? A. y + 2 = 3(x − 6) B. y + 2 = −3(x − 4) C. y + 1 = 6(x − 4) D. y + 1 = −6(x + 4)
Answer:
answer A is correct because the formula of equation in point slope is
y-y1=m(x-x1)
where,(x1,y1)point is given that is (6,-2)
slope=m=3
equation in point-slope form of the line that passes through the point (6, −2) and has a slope of 3 is y + 2 = 3(x − 6)
What is Equation?statement of equality between two expressions consisting of variables and/or numbers.
As, equation line is:
y-y1=m(x-x1)
We have,
coordinates (6, −2) and slope=3
So,
y+2=3(x-6)
y+2=3x-18
y-3x= -20
Hence, equation in point-slope form of the line that passes through the point (6, −2) and has a slope of 3 is y+2=3(x-6).
Learn more about equation here:
https://brainly.com/question/21511618
#SPJ2
Identify the additive inverse and multiplicative inverse for the following number.
−3/4
Answer:
3/4 and - 4/3Step-by-step explanation:
Additive inverse ⇒ sum of numbers is zero:
-3/4 + x = 0x = 0 - (-3/4) = 3/4Multiplicative inverse ⇒ product of numbers is 1:
-3/4 * x = 1x = 1 ÷ (-3/4) = 1* ( - 4/3) = -4/3Step-by-step explanation:
the additive inverse and multiplicative inverse for the following number -3/4=-4/3
5x5:):):):):):):):):):):):)free
Answer:
25
Step-by-step explanation do 5 five times
What was the error made in this conversion?
A.)The 1 mile and 3,218 meters in Step 1 should be switched.
B.) The 1,609 meters and the 3,218 meters in Step 1 should be switched.
C.)The conversion factor should be added in Step 2 instead of being multiplied.
D.)The conversion factor should be divided in Step 2 instead of being multiplied.
Answer:
B.) The 1,609 meters and the 3,218 meters in Step 1 should be switched.Step-by-step explanation:
Step 1 is incorrect. It should be:
3218 meters x 1 mile / 1609 meters = 2 milesCorrect answer option is B
Juan bought fruit from the grocery store. The variables below define his purchase. Juan’s bananas cost half as much as apples. Which equations can be used to model his purchase? Select each correct equation. *
Answer:
[tex]B = \frac{1}{2}A[/tex]
[tex]A = 2B[/tex]
Step-by-step explanation:
Given
Represent apple with A and Banana with B
Required
Determine the relationship between A and B
From the question, we understand that:
B costs half as much as A
This can be represented as:
[tex]B = \frac{1}{2} * A[/tex]
[tex]B = \frac{1}{2}A[/tex]
Multiply both sides by 2
[tex]2*B = \frac{1}{2}A*2[/tex]
[tex]2B = A[/tex]
[tex]A = 2B[/tex]