Answer:
(a) y = 1/4x - 4
(b) y = -4x + 17
Step-by-step explanation:
Slope-Intercept Form: y = mx + b
m - slope
b - y-intercept
(a)
Parallel lines have the same slope but different y-intercepts.
m = 1/4x
y = 1/4x + b
-2 = 1/4(8) + b
-2 = 2 + b
b = -4
y = 1/4x - 4
(b)
Perpendicular lines have the negative reciprocal slope.
m = -4
y = -4x + b
1 = -4(4) + b
1 = -16 + b
b = 17
y = -4x + 17
Answer:
(a) y = 1/4x - 4
(b) y = -4x + 17
Step-by-step explanation:
Slope-Intercept Form: y = mx + b
m - slope
b - y-intercept
Parallel lines have the same slope but different y-intercepts
Perpendicular lines have the negative reciprocal slope.
Two girls scout troops are completing a wilderness campout. Use the information to answer the questions. The Blue Tripp hikes 2/3 mile every 1/2 hour. The Yellow Troop hikes 3/4 mile every 1/3 hour. How long does it take each troop to walk 1 1/2 miles, 1/2 mile, and 3/4 mile?
Answer:
Kindly check explanation
Step-by-step explanation:
Given the following :
Blue tripp:
Hikes 2/3 miles every 1/2 hour
Yellow troop:
Hikes 3/4 miles every 1/3 hour
How long does it take each troop to walk 1 1/2 miles, 1/2 mile, and 3/4 mile?
To hike 1 1/2 miles
Blue troop:
2/3 miles = 1/2 hours
3/2 miles = x
2/3x = 3/4
x = 3/4 * 3/2
x = 9/8 = 1 1/8 hours
Yellow troop:
3/4 = 1/3 hours
3/2 = x
3/4x = 3/6
x = 3/6 * 4/3
x = 12/18 = 2/3 hours
To hike 1/2 mile :
Blue troop:
2/3 miles = 1/2 hours
1/2 miles = x
2/3x = 1/4
x = 1/4 * 3/2
x = 3/8 hours
Yellow troop:
3/4 = 1/3 hours
1/2 = x
3/4x = 1/6
x = 1/6 * 4/3
x = 4/18 = 2/9 hours
To hike 3/4 miles :
Blue troop:
2/3 miles = 1/2 hours
3/4 miles = x
2/3x = 3/8
x = 3/8 * 3/2
x = 9/16 hours
Yellow troop:
3/4 = 1/3 hours
3/4 = x
3/4x = 3/12
x = 1/4 * 4/3
x = 4/12
x = 1/3 hours
find c! please explain the steps and help me find the answer.
Answer:
34.78
Step-by-step explanation:
using cosine rule
AB^2 = CB^2 + AC^2 -2(CB × AC × COS C)
18^2 = 17^2 + 27^2 -2(27×17×COS C)
324= 289+729- 918COSC
324-289-789= -918COSC
-754= -918COSC
COS C = 754/918
COS C = 0.82135076253
C= arccos(0.82135076253)
C= 34.78(2 dp)
The ratio of art class to music class is 4:3. If there is 8 more students in art class, how many students are in music class
Answer:
9 students in music class.
Step-by-step explanation:
In art there are 4 and since there are 8 more 8 + 4 = 12. so there are 12 in Art.
4 x _ = 12. —> 4 x 3 = 12.
so we need to do the same for music class.
For music there are 3.
so we multiply by 3 like we did with the 4.
3 x 3 = _ —> 3 x 3 =9.
so there are 9 students in music class.
Serenity is moving and must rent a truck. There is an initial charge for the rental plus
a fee per mile driven. The total cost of renting the truck can be modeled by the
equation C = 50 +2.75m, where m is the number of miles driven. What is the y-
intercept of the equation and what is its interpretation in the context of the problem?
Answer:
The y-intercept of the equation is 50
Its interpretation in the context is " the initial charge for the rental "
Step-by-step explanation:
The linear relationship can be represented by the equation
y = a x + b, where
a is the slope ( the rate of change)b is the y-intercept (initial amount, or fixed amount, or the amount of y at x = 0)∵ Serenity is moving and must rent a truck
∵ There is an initial charge for the rental
∴ b represents the initial charge for the rental
∵ There is a fee per mile driven
∴ a represents the fee per mile driven
∵ The equation represents this situation is C = 50 + 2.75 m
∵ C is the total cost
∵ m is the number of miles driven
→ Compare it with the form of the equation above
∴ a = 2.75
∴ b = 50
∵ b is the y-intercept
∴ The y-intercept of the equation is 50
∵ b represents the initial charge for the rental
∴ The initial charge for the rental is $50
∴ Its interpretation in the context is " the initial charge for the rental "
A cone is shown below
What is the approximate volume of the cone?
A.
126 in.3
B.
377 in.3
C.
565 in.3
D.
1,131 in.3
Answer:
C.565 in.3 yeah maybe
Make a scatter plot of the data pairs, (year, revenue). Draw a trend line and write its equation. Predict the revenue of US theme parks in 2012. Someone help me please.
i think its 9.9 but if its not that its 8.7
The revenue of US theme parks in 2012 is 14.5 in dollars.
What is scatter plot?Scatter plots are used to observe and plot relationships between two numeric variables graphically with the help of dots. The dots in a scatter plot shows the values of individual data points.
From the given table, (1990, 5.7), (1992, 6.5), (1994, 7.0), (1996, 7.9), (1998, 8.7), (2000, 9.6), (2002, 9.9), (2004, 10.8), (2006, 11.5).
Using the coordinates (1990, 5.7) and (1992, 6.5), we get
Slope m=(6.5-5.7)/(1992-1990)
= 0.8/2
= 0.4
Substitute m=0.4 and (x, y)=(1990, 5.7) in y=mx+c, we get
5.7=0.4×1990+c
c=5.7-796
c=790.3
Substitute m=0.4 and c=-790.3 in y=mx+c, we get
y=0.4x-790.3
Substitute x=2012, we get
y=0.4×2012-790.3
y=804.8-790.3
y=14.5
Therefore, the revenue of US theme parks in 2012 is 14.5 in dollars.
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Bill wants to order new jerseys for his baseball team. He has found two different companies and needs to determine which one is the better deal for his team. PRINT IT sells jerseys for $21.0 each. TOP PRINT a onetime set up cost of $45.0 and jerseys for $18.0 each. A. Write a system of equations for this situation.
Answer:
[tex]Cost = 21.0j[/tex] --- PRINT IT
[tex]Cost = 45.0 +18.0j[/tex] --- TOP PRINT
Step-by-step explanation:
Given
Print IT & Top Print
Represent the number of jerseys with j.
For PRINT IT.
[tex]Cost=\$21.0[/tex] per jersey
For Top Print
[tex]Base\ Amount = \$45.0[/tex]
[tex]Cost = \$18.0[/tex] per jersey.
j jerseys with PRINT IT will cost: [tex]21.0 * j[/tex]
[tex]Cost = 21.0 * j[/tex]
[tex]Cost = 21.0j[/tex]
j jerseys with TOP PRINT will cost: [tex]45.0 +18.0 * j[/tex]
[tex]Cost = 45.0 +18.0j[/tex]
colby and jaquan are growing bacteria in an experiment in a laboratory. colby starts with 50 bacteria in his culture and the number of bacteria doubles every 2 hours. jaquan start with 80 of a different type of bacteria that doubles every 3 hours
Step-by-step explanation:
so, what is the question ?
all you are giving us here are some facts about what's going on. but what is the goal ? what do we need to find out ?
is it when the bacteria cultures have the same population ?
I assume that for my following answer :
"once every 2 hours" can be expressed by "x/2". with x being hours. so, instead of "x", which would mean "once every hour", we use "x/2".
"doubles (once) every 2 hours" is then
2×2×2×...×2 doubles on how many units of 2 hours we have.
this is
2^(x/2)
this is the factor we need to multiply with everything we want to behave that way (to double in size every 2 hours).
in our case here : 50 bacteria.
so, Colby's bacteria culture function is
c(x) = 50 × 2^(x/2)
similar for jaquan:
j(x) = 80 × 2^(x/3)
as his culture doubles every 3 hours.
now for the assumed question, when will both cultures have the same population ?
it is for that value of x that makes both function to deliver the same functional result.
50 × 2^(x/2) = 80 × 2^(x/3)
5 × 2^(x/2) = 8 × 2^(x/3)
now we use the log2 function on both sides and get
log2(5 × 2^(x/2)) = log2(8 × 2^(x/3))
remember the laws of logarithm. particularly
log(a×b) = log(a) + log(b)
and
loga(b) = logc(b)/logc(a)
log2(5) + log2(2^(x/2) = log2(8) + log2(2^(x/3)
log2(5) + x/2 = log2(8) + x/3 = 3 + x/3
3×log2(5) + 3x/2 = 9 + x
2×3×log2(5) + 3x = 2×9 + 2x
6×log2(5) + 3x = 18 + 2x
x = 18 - 6×log2(5) = 18 - 6×ln(5)/ln(2) = 4.068431431... hours
so, after a little bit more than 4 hours both bacteria cultures reach the exact same number of population : 204.8
which is, of course, only theoretical, as there cannot be "part bacteria" in the cultures.
now, we could calculate the x for when c(x) = 204, and the x for when c(x) = 205.
and then the same for j(x) and then see if or what overlap between these two x intervals there is.
during this overlap period both cultures will have the same (whole number) amount of bacteria.
but I think this is a topic for another question, as I am not even sure that I addressed the true original question.
Solve x + 3y = 9
3x − 3y = −13
Answer:
Answer:
x=-1
y=10/3
Step-by-step explanation:
You can solve the system of equations by applying the elimination method as following:
- Add both equations, then:
- Finally, you must substitute the value of x obtained into one the original equations and then you must solve fot y:
Solve the inequality
9-4r>5
[tex]9 - 4r > 5[/tex]
Plus sides 4r
[tex]9 - 4r + 4r > 5 + 4r[/tex]
[tex]9 > 4r + 5[/tex]
Subtract sides -5
[tex]9 - 5 > 4r + 5 - 5[/tex]
[tex]4 > 4r[/tex]
[tex]4r < 4[/tex]
Divided sides by 4
[tex] \frac{4}{4}r < \frac{4}{4} \\ [/tex]
[tex]r < 1[/tex]
_________________________________
Done♥️♥️♥️♥️♥️
Answer:
[tex]\boxed{\sf{r < 1}}[/tex]Step-by-step explanation:
[tex]\boxed{\underline{\text{SOLVING AN INEQUALITY}}}[/tex]
Given:
The inequality must be solved.
The process of solving an inequality consists of determining the values of the variable that make the statement true.
The definition of inequality is where one quantity is greater than or less than another.
Solutions:
9-4r>5First, subtract by 9 from both sides.
[tex]:\Longrightarrow \sf{9-4r-9 > 5-9}[/tex]
Solve.
5-9=-4
-4r>-4
Multiply by -1 from both sides.
[tex]\Longrightarrow: \sf{\left(-4r\right)\left(-1\right) < \left(-4\right)\left(-1\right)}[/tex]
Solve.
4r<4
Divide by 4 from both sides.
4r/4<4/4
Solve.
4/4=1
[tex]\Longrightarrow: \boxed{\sf{r < 1}}[/tex]
Therefore, the final answer is r<1.I hope this helps, let me know if you have any questions.
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8.55 l=_______ml ?
Help
Answer:
8550
Step-by-step explanation:
A rectangle is graphed on the coordinate grid.
Which represents the equation of the side that is parallel to side s?
a. y = negative x + 9
b. y = negative x minus 3
c. y = x + 9
d. y = x minus 3
Answer:
y= -x + 9 (or A)
Step-by-step explanation:
Edge
A restaurant sends customers in their loyalty program a coupon for a free birthday dessert. Suppose that 8\%8%8, percent of the children and 12\%12%12, percent of the adults redeem their coupons. The restaurant takes separate random samples of 100100100 children and 909090 adults from their loyalty program to see the difference between the sample proportions (\hat{p}_\text{C}-\hat{p}_\text{A})( p ^ C − p ^ A )left parenthesis, p, with, hat, on top, start subscript, start text, C, end text, end subscript, minus, p, with, hat, on top, start subscript, start text, A, end text, end subscript, right parenthesis. What will be the shape of the sampling distribution of \hat{p}_\text{C}-\hat{p}_\text{A} p ^ C − p ^ A p, with, hat, on top, start subscript, start text, C, end text, end subscript, minus, p, with, hat, on top, start subscript, start text, A, end text, end subscript, and why?
Using the Central Limit Theorem, it is found that the sampling distribution will be approximately normal, with mean of -0.04 and standard error of 0.0423.
What does the Central Limit Theorem state?It states that for a proportion p in a sample of size n, the sampling distribution of sample proportion is approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1 - p)}{n}}[/tex]It also states that when two variables are subtracted, the mean is the subtraction of the means, and the standard deviation is the square root of the sum of the variances.In this problem, for each sample, the mean and the standard error are given by:
[tex]p_C = 0.08, s_C = \sqrt{\frac{0.08(0.92)}{100}} = 0.0271[/tex]
[tex]p_A = 0.12, s_A = \sqrt{\frac{0.12(0.88)}{100}} = 0.0325[/tex]
Then, for the distribution of differences, we have that:
[tex]p = p_C - p_A = 0.08 - 0.12 = -0.04[/tex]
[tex]s = \sqrt{s_C^2 + s_A^2} = \sqrt{0.0271^2 + 0.0325^2} = 0.0423[/tex]
The sampling distribution will be approximately normal, with mean of -0.04 and standard error of 0.0423.
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HELP I WILL GIVE BRAINIEST I NEED HELP ASAP
Find the volume of the cylinder.
Find the volume of a cylinder with the same radius and double the height.
Answer:
923.63
Step-by-step explanation:
Answer:
v=3.14×r^2xh
v= 3.14 x 7^2x3
v = 461.58 in3
double the height
v=3.14 × 7^2 ×6
v= 923.6 in3
PLEASE HELP!!! Find the equation of this line. All three answers please!!!
Answer:
[tex]y=-\frac{3}{4}x+3[/tex]
Step-by-step explanation:
formula for the gradient is [tex]\frac{y_{2} -y_{1} }{x_{2} -x_{1}}[/tex]
we insert our intercepts to get [tex]\frac{0-3}{4-0}=\frac{-3}{4}[/tex]
and our y-intercept (where the line crosses the y-axis) is 3
Geometry help!!!!!!!
Answer:
[tex]\huge\boxed{\text{The polygons are NOT similar}}[/tex]
Step-by-step explanation:
Because triangle DBC has an angle of measure 49°, and triangle IHJ does not, the polygons are not similar.
Hope it helps :) and let me know if you want me to elaborate.
How is the right triangle formed? In other words, describe the lines that make leg “a” and leg “b” and the hypotenuse “c” of the right triangle.
Answer:
A right triangle consists of two legs and a hypotenuse. The two legs meet at a 90° angle and the hypotenuse is the longest side of the right triangleStep-by-step explanation:
n - Are x = 4 and y = 8 solutions of the equation: y = x² - 2x + 1? Circle: Yes or No
Answer:
No
Step-by-step explanation:
put 4 where x is and 8 where y is
y = x² - 2x + 1
does
8 = 4^2 -2(4) + 1
8 = 16 -8 + 1
8 = 9
Does 8 = 9 ?
No
Twice a number, decreased by 58 is less than 112
Answer:
x<85
Step-by-step explanation:
first we change the sentence in formula as the following
2x‒58<112
then we can solve easly
2x<112+58
2x<170
2x/2<170/2
x<85
i think this is clear &easy to understand .i hope it helps you
PLease help me!!!! (:
You' ll get brainliest!!!!
Answer:
The last one
Step-by-step explanation:
The last one is the only one in standard form.
A number cube is rolled in an experiment, and the frequency of each different roll is recorded. Image_8308 What is the experimental probability of getting a 4 or a 6?.
Using it's concept, it is found that the experimental probability of getting a 4 or a 6 is of 0.2833 = 28.33%.
What is a probability?A probability is given by the number of desired outcomes divided by the number of total outcomes.
For an experimental probability, these numbers of outcomes are taken from previous trials.
Researching the problem on the internet, it is found that the image gives that 13 + 11 + 9 + 8 + 10 + 9 = 60 trials, 8 + 9 = 17 resulted in a 4 or a 6, hence the probability is given by:
p = 17/60 = 0.2833.
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using the spinner above, what is the probability that you land on red or blue?
Answer:
75%
Step-by-step explanation:
red is 50 and the blue is 25
Help me plz pt2 sorry its the clearest pic I can get
Answer:
Step-by-step explanation:
TURKEY
The definition of congruence = yellow or number 2
If 2 lines are cut by a transversal such that same side interior angles are supplementary, then the lines are parallel = purple or number 6
Vertical angles are congruent = green or number 3
Given= orange or number 1
Definition of supplementary= blue or number 4
Substitution= red or number 5
I think those are the right answers for the turkey one. If it's not (but I'm pretty sure it is) But if it's not, then switch the yellow and green. Blue and red.
HAT
given=a||b orange number 1
vertical angles are congruent= green or number 2
definition of congruency= blue or number 3
definition of supplementary angles= yellow or number 4
If two parallel lines are cut by a transversal..... = purple or number 5
subsitution= red or number 6
Just saying, I might've done something wrong since it is late at night for me, but sorry just in advance. But I know for a fact that most of my answers are right
Simplify
I don’t get this subject
Answer: 3
You're going to multiply 3 by 2 which gives you 6. you then have 6 over 2. Next find a number that goes into both of them which is 2 in this case. So now you divide the top and bottom by 2, so now you have 3 because two divided by two is zero, that is as small as it gets.
Express as a sum
1) a-5
2) m-n
Express as a difference
1) 7+3
2) a+5
Answer:
I think it would be
Sums
1) a + -5
2) m + -n
Differences
1) 7 - -3
2) a - -5
Step-by-step explanation:
A triangle has two sides of length 11 and 12. What is the smallest possible whole-number length for the third side?
Answer: 2
To maximize the length of the third side, which I'll call x, it needs to be one of the two shorter sides.
So by the triangle inequality theorem, 11+x>12 meaning the minimum whole number value of x is 2.
what's the difference between partial variation and direct variation
Answer:
Direct Variation is a relation that is of the form y = mx.
and
Partial Variation is a relation that is of the form y=mx+b
Explanation:
This is a simple way to see the difference between them.
Hope This help you!
–3x + 5 = –3x + 10
A. 5/6
B. –5/6
C. no solution
D. identity
Answer:
No solution
Step-by-step explanation:
Select the correct answer from each drop-down menu. To find the average grades scored by students in science and math, the principal of a school sends a questionnaire to the top five students in each grade of the high school. Is the sample used by the principal random? Will a generalization from this sample be valid? The sample used by the principal is. A generalization made from this sample is.
Answer:
a) This is not a random sample
b) The generalization from this sample would not be valid
Step-by-step explanation:
No the sample is not random. If the questionnaire would had been send to any five students in a class irrespective of whether they are among the top five, then the sample could be referred as random sample.
The marks of top five students in any grade would give an average value that will be an outlier to the average of marks of all students with in a grade.
Hence, the generalization from this sample would not be valid
What is the approximate area of the shaded region under the standard normal curve below? Use the portion of the standard normal table given to help answer the question. A normal curve with a peak at 0 is shown. The area under the curve shaded is negative 2 to negative 1. Z Probability 0. 00 0. 5000 1. 00 0. 8413 2. 00 0. 9772 3. 00 0. 9987 0. 02 0. 14 0. 34 0. 84.
The area under the shaded region from 1 to 2 is 0.14
What will be the shaded region area?Probabilities actually define the percentage of the happening of an event
Here the shaded region shows the probability of the z-scores
The shaded region 1 to 2 is represented as:
[tex]P(1 < z < 2)[/tex]
By using the probability of z-score we can have
[tex]P(1 < z < 2)=P(z < 2)-P(z < 1)[/tex]
From the given standard normal table:
[tex]P(z < 2)=0.9772[/tex]
[tex]P(z < 1)=0.8413[/tex]
So, we have:
[tex]P(1 < z < 2)=0.9772-0.8413[/tex]
[tex]P(1 < z < 2)=0.1359[/tex]
The approximated value will be
[tex]P(1 < z < 2)=0.14[/tex]
Thus the area under the curve shaded is 1 to 2 is 0.14
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