Answer:
Step-by-step explanation:
Perpendicular means that the slopes of the "old" line and the "new" line are opposite reciprocals; bisector means that the "new" line goes directly through the center of the "old" line. This perpendicular bisector, then, will go directly through the center of the "old" line, cutting it directly in half and leaving in its wake a 90 degree angle. To write this equation, then, of the perpendicular bisector, we need the slope of the old line and the midpoint of the old line. Let's work on the midpoint first:
[tex]M=(\frac{3+6}{2},\frac{5-7}{2})\\M=(\frac{9}{2},\frac{-2}{2})\\M=(\frac{9}{2},-1)[/tex] So the "new" line will go through this point.
Onto the slope:
[tex]m=\frac{-7-5}{6-3}\\m=\frac{-12}{3}[/tex]so the slope is
m = -4. That means that the perpendicular slope is
[tex]m=\frac{1}{4}[/tex] Now we're ready to write the equation:
[tex]y-5=\frac{1}{4}(x-3)[/tex] and
[tex]y-5=\frac{1}{4}x-\frac{3}{4}\\y=\frac{1}{4}x-\frac{3}{4}+\frac{20}{4}[/tex] and finally,
[tex]y=\frac{1}{4}x+\frac{17}{4}[/tex]
Answer:
Step-by-step explanation:
A(3, 5) ; B(6,-7)
Let's find the slope of AB = [tex]\dfrac{y_{2}-y_{1}}{x_{2}-x_{1}}\\[/tex]
[tex]=\dfrac{-7-5}{6-3}\\\\=\dfrac{-12}{3}\\\\= - 4[/tex]
m = -4
Slope of the perpendicular line to AB = -1/m = [tex]\dfrac{-1}{-4}=\dfrac{1}{4}[/tex]
The perpendicular line of AB is bisector also. So, it goes through the midpoint of AB
Midpoint of AB = [tex](\dfrac{x_{1}+x_{2}}{2}, \dfrac{y_{2}-y_{1}}{2})[/tex]
[tex]=(\dfrac{3+6}{2},\dfrac{5+(-7)}{2})\\\\=(\dfrac{9}{2},\dfrac{-2}{2})\\\\=(\dfrac{9}{2},-1)[/tex]
Equation of require perpendicular line: y - y1 = m (x -x1)
[tex](x_{1},y_{1})= (\dfrac{9}{2},-1)\\ \\m =\dfrac{1}{4}\\\\y-[-1]=\dfrac{1}{4}(x-\dfrac{9}{2})\\\\y+1=\dfrac{1}{4}x-\dfrac{1}{4}*\dfrac{9}{2}\\\\y=\dfrac{1}{4}x-\dfrac{9}{8}-1\\\\y=\dfrac{1}{4}x-\dfrac{9}{8}-\dfrac{8}{8}\\\\y=\dfrac{1}{4}x-\dfrac{17}{8}[/tex]
How many people can Liam buy lunch for
Answer:
At most, Liam can only buy lunch for 6 people.
Step-by-step explanation:
It isn't going to be a decimal answer because there can't be half of a person
All you have to do is divide 50 by 8 and round down because you don't want to spend more than 50 dollars.
Writing it mathematically, it would be:
p [tex]\leq[/tex] 6
I have gymnastics practice very 3 days and tennis practice every 8 days. How many days will it take for me to have BOTH gymnastics and tennis practice on the same day?
Answer:
24 days
Step-by-step explanation:
Find LCM, or least common multiple
List out all the multiples of 3:
3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, ...
Now 8:
8, 16, 24, 32, 40, 48, 56, 63, 72, 80, 88...
LCM is 24, because they both hit 24 first.
If my answer is incorrect, pls correct me!
If you like my answer and explanation, mark me as brainliest!
-Chetan K
Explanation:
This is because 24 is the LCM (lowest common multiple) of 8 and 3.
We multiply the given values to get 8*3 = 24. This trick only works if the original two numbers have no common factors other than 1.
We can verify that 24 is indeed the LCM by listing out the multiples
multiples of 8 are: 8, 16, 24, 32, 40, ...multiples of 3 are: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, ...We see that 24 is found in both lists and it's the smallest such item. The next common item would be 48, which is a multiple of 24. In other words, every 24 days, your two practices will line up on the same day.
create a problem using radios of for your guardian/parent or friends solve. write both of your problems and Solutions in your Journal
Answer:
The following,... and uh I don't have a journal ;->
Step-by-step explanation:
You and your 10 friends each have 121 books that you will be bringing to a Best Book Barrage book exchange. Once everyone arrives you count a total of books. Assuming everyone brings the same amount of books how many people came to the exchange?
Answer: 8,228
pls help, and explain. I will give brainliest
Answer:
Nicole should take 13 1/8 cups of snack mix.
Step-by-step explanation:
If a serving size is 7/8 and Nicole wants to take 15 serving sizes (15 7/8's), then we must multiply 7/8 by 15:
15 × 7/8
Write 15 over 1 (15 = 15/1) to make the calculations easier:
15/1 × 7/8
Multiply the numerators and denominators separately:
15 × 7 / 1 × 8
105 / 8
Instructions don't say you have to do this but I will convert this improper fraction into a mixed number:
105/8 = 13 1/8
Which polynomial correctly combines the like terms and puts the given polynomial in standard form?
one-thirdx + 8x4 – two-thirdsx2 – x
8x4 – one-thirdx2 – x
8x4 + two-thirdsx2 + two-thirdsx
8x4 – two-thirdsx2 – two-thirdsx
8x4 – two-thirdsx2 – x
Answer:
C
Step-by-step explanation:
Please someone tell me the answer of these questions
Answer:
VERTICALLY OPP ANGLES
Step-by-step explanation:
The perimeter of a rectangle is 18cm . if the length is (x+2), find it's width.
Answer:
W = 7 - x
Step-by-step explanation:
The perimeter is P= 2L + 2×W , where L is the length and W is the width.
If L = (x+2) , replacing L with the expression x+2 we have
P= 2×(X+2) + 2W ⇔ 18 = 2x + 4 + 2W ⇔ 2W =18 - 2x - 4 ⇔ 2W = 14 - 2x
⇔ W = 7 - x
Grace bought a property valued at $200,00.00 and 20% down and a mortgage amortized over 10 years. She makes equal payments due at the end of every months. Interest on the mortgage is 4% compounded semi-annually and the mortgage is renewable after five years. a) What is the size of each monthly payment? b) What is the outstanding principal at the end of the five-year term? c) What is the cost of the mortgage for the first five years?
Answer:
Size of each monthly payment = $161.69 per month
Step-by-step explanation:
Given:
Value of property = $20,000
Downpayment = 20%
Number of payment = 12 x 10 = 120
Interest rate = 4% = 4% / 12 = 0.33 %
Computation:
Loan balance = 20,000 - 20%
Loan balance = $16,000
A] Size of each monthly payment [In Excel]
Size of each monthly payment = PMT(0.33%,120,16000,0)
Size of each monthly payment = $161.69 per month
Match function with its corresponding graph
Answer:
Step-by-step explanation:
We can see that there are roots at (-2,0) and (-1,0)
also, the root at (-2,0) should bounce right off
and the root at (-1,0) should go through
With all that being said it has to be B
The point B (-2, 1) has been transformed to B' (-5, -3). The transformation is described as
A T (-3,-4)
B R x=2
C T (-3,-2)
D D3
Answer:
Option A: T(-3, -4)
Step-by-step explanation:
For a general point (x, y), if we apply the transformation:
T(a, b)
at that point, the new point that we will get is:
T(a,b)[ (x, y) ] = (x + a, y + b)
Notice that if w take the difference between the new point (x + a, y + b) and the original point (x, y)
we get:
(x + a, y + b) - (x, y) = (x + a - x, y + b y) = (a, b)
These are x-value and y-value that describe our transformation T(a, b).
Then if we know that the original point is B (-2, 1)
and the transformed point is B'( -5, -3)
We can just take the difference to get:
(-5, -3) - (-2, 1) = (-5 - (-2), -3 - 1) = (-5 + 2, -4) = (-3, -4)
Then the transformation applied is:
T(-3, -4)
The correct option is A.
A garden is rectangular with a width of 8 feet and a length of 10 feet. If it is surrounded by a walkway 2 feet wide, how many square feet of area does the walkway cover?
Answer:
The rea of walk way is 32 ft^2.
Step-by-step explanation:
width, w = 8 feet
length, L = 10 feet
width of walkway, d = 2 feet
length of outer, L' = 10 + 2 + 2 = 14 feet
Area of outer, A' = L' x w = 14 x 8 = 112 ft^2
Area of inner, A = L x w = 10 x 8 = 80 ft^2
The area of walkway = A' - A = 112 - 80 = 32 ft^2
The rea of walk way is 32 ft^2.
At a particular restaurant, each slider has 225 calories and each chicken wing has 70 calories. A combination meal with sliders and chicken wings has a total of 7 sliders and chicken wings altogether and contains 1110 calories. Write a system of equations that could be used to determine the number of sliders in the combination meal and the number of chicken wings in the combination meal. Define the variables that you use to write the system.
Answer:
X+y=7
Step-by-step explanation:
i remember doing something like this but mines had the word onion rings .
Consider circles 7 through 12. If circle 7 is at 45°, what is the radian measure of each of these circles in relation to the main circle? Explain how you know these values.
Answer: Hello your question lacks vital information attached below is the vital information
Along with the image below, Use your knowledge of the unit circle and radian measure of angles to answer the following questions. [Note: When the questions ask you to consider circles and their angle in relation to the main circle, the question is referring to the location of the center of each circle.]
answer:
Circle 7 = π / 4
Circle 8 = 7π / 12
Circle 9 = 11 π / 12
Circle 10 = 5π / 4
Circle 11 = 19π / 12
Circle 12 = 23π / 12
Step-by-step explanation:
Given that 45° = π/4.
∴ All the six(6) circles ( 7 through 12 ) are separated by : 60° = π/3
The Radian measure of the remaining circles through 12 :
Circle 8 = π/3 + π /4 = 7π / 12
Circle 9 = π/4 + 2 π/3 = 11 π / 12
Circle 10 = 5π / 4
Circle 11 = 19π / 12
Circle 12 = 23π / 12
Reason : All the six(6) circles ( 7 through 12 ) are separated by : 60° = π/3
Find the medians of the following sets of data.
I) 23, 17, 36, 47, 42
Answer:
36 is the median of give data
For this exponential function,
what is the output value (y),
when the input value (x) is 3?
y = 10.5x.
(3, [?])
Replace x with 3 and solve:
10 x 5^3
Simplify:
10 x 125 = 1250
Answer: y = 1250
(3 , 1250)
Step-by-step explanation:I got it right on my test.
-1/2 divided by 1/19
Answer:
-19/2 or
-9 1/2
Step-by-step explanation:
-1/2 ÷ 1/19
Copy dot flip
-1/2 * 19/1
-19/2
-9 1/2
(06.01)A scatter plot is shown:
A scatter plot is shown. Data points are located at 1 and 8, 2 and 7.8, 3 and 7.4, 4 and 6.5, 5 and 5.4, 6 and 4.5, 7 and 3.1, 8 and 2, 9 and 1.
ASAP:
What type of association does the graph show between x and y?
Linear positive association
Nonlinear positive association
Linear negative association
Nonlinear negative association
Answer:
Step-by-step explanation:
If you plot those coordinates in your calculator in the stat plot function under "stat", you will see that the dots are almost but not quite in a straight line going from upper left to lower right. This indicates a strong negative linear association, third choice down.
Answer:
D. Nonlinear Negative Association
Step-by-step explanation:
9. Find the remainder when the polynomial: p(x) = x⁴ + 2x³- 3x² + x - 1 is divided by (x - 2)
pls it's urgent
Answer:
answer is 21..............
Explanation:
p(x) = x⁴ + 2x³- 3x² + x - 1
Factor of p(x)
x-2=0
x=2
Then by using synthetic division
What's 672 divided by 32
Find all solutions to the equation
in the interval [0, 21). Enter the
solutions in increasing order.
Answer:
0,1,2,3,4,5,6.......19,20
Step-by-step explanation:
in this interval 0 is included and 21 is not included. So starting from 0 up to 20, all are the solutions
(b) A shopkeeper gives 20% discount on the marked price of a television set. The VAT amount at the rate of 13% is Rs. 2,600. Find the marked price and the amount of discount.
Answer:
6.3
Step-by-step explanation:
i had the same question for school
Rihanna works in a coffee shop approximately nine miles from her apartment She bikes every day from her apartment to the coffee shop and then back to her apartment in the evening. However, on her way to work, she always stops halfway through to meet her best friend at a park. If the distance from apartment to the park is (5x +2) miles and the trip from the park to the coffee shop is (25x -8) miles long, then what is the value of x?
Answer:
x = 0.5
Step-by-step explanation:
When we add up the distance between the apartment and park with the distance between the park and the coffee shop, the total will equal nine miles.
Our equation will look like this:
(5x + 2) + (25x - 8) = 9
Add up the like terms
5x + 2 + 25x - 8 = 9
30x - 6 = 9
Add 6 to both sides
30x - 6 = 9
+ 6 + 6
30x = 15
Divide both sides by the coefficient, 30, to isolate the variable, x
30x/30 = 15/30
x = 15/30
Reduce
x = 1/2
A walker has travelled 9 km along a trail. If he has completed 80% of the trail, how much further does he still have to go?
Answer:
2.25 km to go
Step-by-step explanation:
In order to get this answer, you have to figure out how many km 10% is, 0.1125. Then multiply that by the remaining 20% because he already finished 80% of the trail. So, 0.1125 x 20 = 2.25.
Hope this helps! :)
Suppose that d varies jointly with r and t, and d = 110 when r = 55 and t = 2. Find r when d = 40 and t = 3.
Answer:
r = 13.33
Step-by-step explanation:
d = k*r*t
Where,
k = constant of proportionality
d = 110 when r = 55 and t = 2
d = k*r*t
110 = k * 55 * 2
110 = 110k
k = 110/110
k = 1
Find r when d = 40 and t = 3
d = k*r*t
40 = 1 * r * 3
40 = 3r
r = 40/3
= 13.333333333333
Approximately,
r = 13.33
32
Two forces one is 10N and other is 6N act on a body The directions are unknown the resultant force on the body is
a. between 4 and 16N
b. more than 6N I
c. more than 1ON
d between 6 and 16N
If Forces are acting on opposite direction
[tex]\\ \rm\hookrightarrow F_{net}=F_2-F_1[/tex]
[tex]\\ \rm\hookrightarrow F_{net}=10-6[/tex]
[tex]\\ \rm\hookrightarrow F_{net}=4N[/tex]
If both acting on same direction
[tex]\\ \rm\hookrightarrow F_{net}=F_1+F_2[/tex]
[tex]\\ \rm\hookrightarrow F_{net}=10+6[/tex]
[tex]\\ \rm\hookrightarrow F_{net}=16N[/tex]
Hence
[tex]\boxed{\sf 4N\leqslant F_{net}\leqslant 16N}[/tex]
Can someone help me on this please
y=8200(0.96)^x growth or decay find
Answer:
This would be a .04 or 4% decay.....
for every "time unit" (x in this case) you will be multiplying
the amount by .96 ... in other words if you started with one dollar
the results would be 96 cents... after two "time" steps you would have
only 92 cents (.96 *.96)
Step-by-step explanation:
can i get some help solving this
Answer:
A =147 cm^2
Step-by-step explanation:
A = pi r^2
The radius is 7 and let pi = 3
A = 3*7^2
A = 3*49
A =147
Helpo pleasssse
On my hw I have a parabola that opens down with its vertex at (-3,-6)......
For the range would I say that {yER | y > -6} OR {yER | y < -6} ????
I'm just confused from the negative numbers
Answer: The range is [tex]\{y \in \mathbb{R}\ | \ y \le -6\}[/tex]
Explanation:
The parabola opens down, forming a "frowny face" in a way (just without the eyes). Or you can think of it as a hill or mountain. This means that the vertex (-3,-6) is at the top of that mountain. It's the highest point of that parabola.
The range is the set of all possible y values. We see that y = -6 is the largest it can get. So y = -6 or y is smaller than this. We would then write [tex]y \le -6[/tex] to describe all the possible y values.
Therefore, the range is [tex]\{y \in \mathbb{R}\ | \ y \le -6\}[/tex]
This translates to "y is a real number such that y is -6 or smaller".
So the second answer you wrote is close, but you forgot the "or equal to" portion of the inequality sign.
See below for a visual example of what's going on.
A. -5x+4y=-20
B. -5x-4y=-20
C. -5x+4y=0
D. 5x+4y=-20
