: Consider the distance from the school to the coffee shop and the
distance from the library to the coffee shop. Draw their respective
line segments in the above graph. If the school is relocated in a
way that it is collinear to the coffee shop and the library, and the
distance to the coffee shop is preserved, then the point
representing the school will partition the line segment from the
coffee shop to the library in a x: y ratio. What are the values of x
and y?
Answers
Answer:
x = 7 and y = 1
Step-by-step explanation:
Coordinates of Coffee shop = (12, 16)
Coordinates of Library = (16, 8)
School has been shifted to the new position so that distance of school is preserved from the coffee shop.
Coordinates of the new position of school = (15, 10)
Ratio in which distance between coffee shop and library is divided by the location of school is x : y.
If a segment having extreme ends [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] is divided into two parts by point (x, y) in the ratio of m : n,
x = [tex]\frac{mx_2+nx_1}{m+n}[/tex]
y = [tex]\frac{my_2+ny_1}{m+n}[/tex]
From the points given in the picture,
15 = [tex]\frac{16x+8y}{x+y}[/tex]
15x + 15y = 16x + 8y
15y - 8y = 16x - 15x
7y = x
[tex]\frac{x}{y}=\frac{7}{1}[/tex]
Therefore, x = 7 and y = 1 will be the answer.
Related Questions
If f(3) = 3(x+5+2, what is f(a+ 2)?
Answers
Solution:
f(3) = 3(x + 5 + 2)
f(3) = 3(3 + 5 + 2)
f(3) = 3(10)
f(3) = 30
Substitute 30 for a:
f(30 + 2)
f(32)
Best of Luck!
Solve the inequality for x.
8x-30< -5 (4- 2x)
_
Answers
Answer:
x > _ -5
Step-by-step explanation:
If you have any questions about the way I solved it, don't hesitate to ask me in the comments below =)
76, 84, 93, 67, 82, 87, and 76. what is the mean
Answers
Answer:
81
Step-by-step explanation:
First, add all the numbers:
[tex]76+84+93+67+82+87+76=565[/tex]
Second, divide by the amount of numbers(count the amount of numbers that are there.):
[tex]\frac{565}{7} = 80.714285.....[/tex]
Third, round your answer to the nearest whole number:
[tex]80.714285...(estimated)= 81[/tex]
Answer:
The mean is 84.7777777777778
Step-by-step explanation:
Jessie kristen and kendell all went shopping together and bought shirts. Kristen bought a shirt that cost $8.50. Jessie shirt cost $12.75. If there total bill was $39.45 how much did kendall's shirt cost?
Answers
Answer:
Kendall's shirt cost 18.20
Step-by-step explanation:
12.75+8.50=21.25
39.45-21.25=18.20
Find the equation of the line. Use exact numbers.
Answers
Answer:
[see below]
Step-by-step explanation:
Using two points on the line:
(0,3) (2,0)
Find the slope of the line:
[tex]m=\frac{rise}{run}=\frac{0-3}{2-0}=\frac{-3}{2}=-\frac{3}{2}[/tex]
The slope of the line is [tex]-\frac{3}{2}[/tex].
The y-intercept is (0,3).
The line equation should be: [tex]y=-\frac{3}{2}x+3[/tex].
Hope this helps.
Answer:
[tex]y=-\frac{3}{2}x+3[/tex]
Step-by-step explanation:
We can find an equation for the line by using the slope of the line and the y-intercept.
We can see that the y-intercept of of the line is 3.
To find the slope of the line, we can use the slope formula. The slope formula is:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
where (x₁, y₁) and (x₂, y₂) are points on the line. To find the slope of the line, I will use the x-intercept, which is (2, 0), for (x₂, y₂) and y-intercept, which is (0, 3), for (x₁, y₁).
[tex]m=\frac{0-3}{2-0}=\frac{-3}{2}=-\frac{3}{2}[/tex]
So now we know the y-intercept and the slope, so lets plug it into the slope-intercept form equation. This gives us:
[tex]y=-\frac{3}{2}x+3[/tex]
So the equation of the line would be [tex]y=-\frac{3}{2}x+3[/tex].
I hope you find my answer helpful.
25 POINTS!!! Under a dilation centered at the origin, the vertex, (2, 3), of a polygon is moved to the point (−8, −12) . What is the scale factor of the dilation? Enter your answer in simplified form in the box.
Answers
325
Step-by-step explanation:
(x+8)2+(y+12)2=235The scale factor of the point will be ( 1 / 4).
What is a scale factor?The scale factor is defined as the proportion of the new image's size to that of the previous image. Dilation is the process of increasing the size of an object while maintaining its shape. Depending on the scale factor, the object's size can be increased or decreased.
Given that under a dilation centered at the origin, the vertex, (2, 3), of a polygon is moved to the point (−8, −12).
The scale factor will be calculated as below:-
Scale factor = ( 2 / 8 ) = ( 1 / 4 )
Therefore, the scale factor of the point will be ( 1 / 4).
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If a leaf fell 140 meters in 4 minutes how many meters did it travel per minute?
Answers
Answer:
The leaf travels 35 meters per minute
Step-by-step explanation:
Given:
Distance = 140 meters
Time = 4 minutes
Speed = distance / time
Speed in meter per minute
Distance in meter
Time in minutes
Speed = distance / time
= 140 meters / 4 minutes
= 35 meters per minutes
Therefore,
The leaf travels 35 meters per minute
It takes 1 minute to bake 7 cookies. How many
cookies could you bake in 2 minutes? Assume the
relationship is directly proportional.
cookies
Answer
Answers
Answer:
Step-by-step explanation:
so the problem is 7 cookies in 1 minutes which is 7 x1 but if we want to know how many we have in 2 minutes we would have to multiply by 2 not 1. so we do 7x2 which is 14. 14 cookies in 2 minutes
Help please, click the other pictures to see the answer choices. #1 is the first blank #2 is the second blank answer choices.
Answers
Answer:
"Side-Angle-Side" and "can be proven congruent"
Step-by-step explanation:
It is SAS because you are given that two of the sides and one angle are congruent, meaning that you can use SAS to prove that the two triangles are congruent.
Brooke and Lamont ran a half marathon, Brooke finished in 1 hour 45
minutes. Lamont finished in 115 minutes. Who had the faster time?
Answers
Answer: brooke had the faster time
Step-by-step explanation:
This is because if you convert 1 hour 45 into minutes it would be stated as 105 minutes and if you do 115 - 105 you are left with 10 which the bigger number is the fastest so it would be brooke the reason I subtracted was to see if they were not similar. Hope this helps :)
Brooke was the fastest because 115 minutes is very close to 2 hours. Therefore Lamont took longer.
what is the angle JKM???
Answers
Answer:
176°
Step-by-step explanation:
Since, KR bisects angle JKM, so, measure of angle JKM will be twice of the measure of angle RKM.
[tex]m\angle JKM = 2\times m\angle RKM \\ m\angle JKM = 2\times 88 \degree \\ \huge \red{ \boxed{ m\angle JKM = 176 \degree}}[/tex]
Which of the following identifies when food is most susceptible to bacteria and microorganism growth?
fall
winter
spring
summer
Answers
summer the food is most susceptible to bacteria and microorganism growth because of heat
What is Microbiology?Microbiology is the scientific study of microorganisms, those being unicellular, multicellular, or acellular.
Susceptibility is a term used when microbe such as bacteria and fungi are unable to grow in the presence of one or more antimicrobial drugs.
Susceptibility testing is performed on bacteria or fungi causing an individual's infection after they have been recovered in a culture of the specimen.
In summer the food is most susceptible to bacteria and microorganism growth because of heat where as in the winter and fall the bacteria wont grow easily.
Hence, summer the food is most susceptible to bacteria and microorganism growth because of heat
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Alexis bakes 90 identical pizzas. Each pizza is cut either into 8 small slices or 6 large slices. There are 5 small slices for for every 3 large slices. How many of the 90 pizzas are cut into small slices?
Answers
Answer:
50
Step-by-step explanation:
Let x represent the number of pizzas cut into small slices. Then the ratio of small to large slices is ...
[tex]\dfrac{8x}{6(90-x)}=\dfrac{5}{3}\\\\8x=10(90-x)\quad\text{multiply by $6(90-x)$}\\\\18x=900\quad\text{add $10x$}\\\\x=50\quad\text{divide by 18}[/tex]
50 of the 90 pizzas were cut into small slices.
_____
Check
The 50 pizzas cut into 8 small slices each results in 400 small slices. The 40 pizzas cut into 6 large slices each results in 240 large slices. The ratio of small slices to large slices is 400 : 240 = 5 : 3.
-|-5 + 3 - 2| + 2 The answer is supposed to be six.
Answers
Step by Step:
-|-5+3-2|+2
-|-4|+2
-4+2
=-2
Help ASAP!!!
Convert 2 gallons into pints (1 gallon=4 quarts, and 1 quart=2 pints).
Answers
2 Gallons = 16 Pints
How to put 634 in scientific form
Answers
Answer:
6.34 × 10²
Step-by-step explanation:
Calculating scientific notation for a positive integer is simple, as it always follows this notation: a x 10b.
Step 1
To find a, take the number and move a decimal place to the right one position.
Original Number: 634
New Number: 6.34
Step 2
Now, to find b, count how many places to the right of the decimal.
New Number: 6 . 3 4
Decimal Count: 1 2
There are 2 places to the right of the decimal place.
Step 3
Building upon what we know above, we can now reconstruct the number into scientific notation.
Remember, the notation is: a x 10b
a = 6.34
b = 2
Now the whole thing:
6.34 x 10²
Step 4
Check your work:
10² = 100 x 6.34 = 634
Answer:
6.34 x 10^2
Step-by-step explanation:
Move the decimal place to the left 2 positions
Calculate the area of a circle with radius 1.6m
Answers
Answer:
A≈8.04m² is the answer
Find the value of x will mark BRAINLYList
Answers
Answer:
25 degrees
Step-by-step explanation:
56+99=155
180-155=25
25 degrees
Johnny's rare book collection contains 40 books he donates 15% of his books to the National Library sells 1/4 of his books to a rare dealer and sell for books on Amazon how many books were made in Johnny's book collection
Answers
Answer:
20 books
Step-by-step explanation:
Fractions and all that.
Which rule best describes the following pattern? 8, 4, 10, 6, 12, 8, 14, ...
Answers
-4+6
or it could be written out as
n-4+6=x
Is 13/1 rational or irrational?
Answers
Answer:
It is rational number not irrational number
Find the mistake in the following : 3 x ( 4 + 2 ) = 12 + 2
Answers
Answer: The mistake is improper use of distribution property.
Step-by-step explanation:
It is given that [tex]3\times (4+2)=12+2[/tex].
We need to find the mistake.
The given expression is
[tex]3\times (4+2)[/tex]
Using distribution property, we get
[tex]3\times (4)+3\times(2)[/tex]
[tex]12+6[/tex]
So, [tex]3\times (4+2)=12+6[/tex].
In the given calculation the 3 is not distributed properly because 3 is not multiplied with 2.
Therefore, the mistake is improper use of distribution property.
Two parallel lines were cut by a transversal. Which of the following
scenarios is NOT a possible result?
1 point
a pair of same side interior angles with measures of 65 and 115°
a pair of alternate exterior angles with measures of 130 and 50°
a pair of supplementary angles with measures of 110' and 70°
a pair of corresponding angles with measures of 40° and 40°
Send me a copy of my responses.
Submit
Answers
Answer:
B. a pair of alternate exterior angles with measures of 130° and 50°
Step-by-step explanation:
Alternate exterior angles formed when two parallel lines are cut across by the same transversal line, are said to be congruent.
Therefore, a pair of alternate exterior angles cannot have different angle measures of 130° and 50°. Rather, both alternate exterior angles should be of equal measure of degree.
All other scenarios are possible result except option B: "a pair of alternate exterior angles with measures of 130° and 50°".
Option B is correct. "A pair of alternate exterior angles with measures 130 and 50degrees".
If two lines are cut by a transversal, line geometry is formed.
The following angles are formed by the transversal;
alternate interior and exterior anglesupplementary angles (sums up to 180degrees)pair of corresponding anglespair of vertically opposite angles (from intersection of two lines that formed X)Note that alternate exterior angles are obtuse angles (greater than 90 degrees). This statement falsifies the second option which says that "a pair of alternate exterior angles with measures 130 and 50degrees. 50 degrees" is an acute angle not obtuse.
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The graph of f(x) is shown below.
For each point (a,b) on the graph of y = f(x), the point ( 3a - 1, b/2) is plotted to form the graph of another function y = g(x). For example, (0,2) lies on the graph of y = f(x), so (3 * 0 - 1, 2/2) = (-1,1) lies on the graph of y = g(x).
(a) Plot the graph of y = g(x). Include the diagram in your solution.
(b) Express g(x) in terms of f(x).
(c) Describe the transformations that you would apply to the graph of y = f(x) to obtain the graph of y = g(x). For example, one transformation might be to stretch the graph horizontally by a factor of 5
Answers
(a) I have attached the graph.
(b) The function g(x) is given by g(x) = f(2x + 2)/3. You can work this out algebraically. You can also work this out by using the graph of the function.
(c) We can obtain the graph of y = g(x) from the graph of y = f(x) through the following transformations:
* stretch horizontally by a factor of 2
* stretch vertically by a factor of 3
* shift downwards by 2 units
When might you need to measure an object’s radius?
Answers
Answer:
Finding the circumference?
Write an equation
Jason is attending the Indiana State Fair, where the
admission is $10.00. It costs $5.50 for each ride.
a
1
Answers
Answer:
y= $5.50x+$10.00
Step-by-step explanation:
Admission is $10. Depending on how many rides you're going ride is how much you multiply $5.50 by.
The square root of 53
falls between ____
and _____
but it's closest to _____
(*Your answers must be between -20 and 20)
Answers
Answer:
Falls between 7 and 8
Step-by-step explanation:
Square root of 53 is 7.28
Answer:
7.280109
Step-by-step explanation:
The square root of 53 is 7.28
Jamal has $35 to spend at the mall. If pairs of shorts are $9.99, how many can he buy?
Answers
$35 / $9.99 = 3.5 pairs of shorts
We have to round down because you cannot buy half a pair of shorts
The correct answer is 3 pairs of shorts.
Answer: he can buy 3 pairs
Step-by-step explanation: $9.99 x 3 = $29.97 | $9.99 x 4 = $39.96
A family spent $93 at a carnival. They spent $18 on tickets to the carnival and $36 on food.They spent the rest of the money on games. Write and solve an equation representing how much money, in dollars, the family spent on games.
Answers
Answer:
$93-$18-$36=$39
$39
Step-by-step explanation:
Answer:
18 + 36 + 39 = 93 The family spent $39 on games.
Step-by-step explanation:
18 + 36 + g = 93
I'm using "g" to substitute the number of money they spent on games. To find what that is, you simply add 18 and 36.
18 + 36 = 54
So we know they used 54 dollars on tickets and food. Now we can take that away from the total amount spent.
93- 54 = 39
Here we can tell that the amount the family spent on games was 39 dollars. Or in other words, g = 39
Hope that helps and have a great day!
How many solutions does this system have? 2x−3y+z=5 2x−3y+z=−2 −4x+6y−2z=10 Explain your answer in terms of intersecting planes.
Answers
Answer:
5 because once you evaluate your functions and simplify your equations you get all 5 solutions.
Step-by-step explanation:
