Answer:
[tex]y-1=\frac{1}{8}\left(x-7\right)[/tex] is the equation in point-slope form for the perpendicular bisector of the segment with endpoints B(6,9) and C(8,−7).
Step-by-step explanation:
The endpoints:
B(6,9)C(8,−7)Calculating the Midpoint M of BC:
[tex]\mathrm{Midpoint\:of\:}\left(x_1,\:y_1\right),\:\left(x_2,\:y_2\right):\quad \left(\frac{x_2+x_1}{2},\:\:\frac{y_2+y_1}{2}\right)[/tex]
[tex]\left(x_1,\:y_1\right)=\left(6,\:9\right),\:\left(x_2,\:y_2\right)=\left(8,\:-7\right)[/tex]
The Midpoint M of BC [tex]=\left(\frac{8+6}{2},\:\frac{-7+9}{2}\right)[/tex]
[tex]=\left(7,\:1\right)[/tex]
Calculating the slope of BC:
[tex]\mathrm{Slope\:between\:two\:points}:\quad \mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]\left(x_1,\:y_1\right)=\left(6,\:9\right),\:\left(x_2,\:y_2\right)=\left(8,\:-7\right)[/tex]
[tex]m=\frac{-7-9}{8-6}[/tex]
[tex]m=-8[/tex]
Given a line with slope [tex]m[/tex] then the slope of a
line perpendicular to it is:
[tex]m_{prependicular}=-\frac{1}{m}=-\frac{1}{-8}=\frac{1}{8}[/tex]
Equation of line using point-slope form
[tex]y-y_1=m\left(x-x_1\right)[/tex]
[tex]y-1=\frac{1}{8}\left(x-7\right)[/tex]
Therefore, [tex]y-1=\frac{1}{8}\left(x-7\right)[/tex] is the equation in point-slope form for the perpendicular bisector of the segment with endpoints B(6,9) and C(8,−7).
Your class is selling chocolates and caramel corn. Boxes of
chocolate sell for $6 each and bags of caramel corn sell for
$5 each. A total of 535 items were sold and $2889 was
raised. How many of each item was sold?
O 321 boxes of chocolate, 214 bags of caramel corn
o 214 boxes of chocolate, 321 bags of caramel corn
O 343 boxes of chocolate, 192 bags of caramel corn
0 211 boxes of chocolate, 324 bags of caramel corn
214 boxes of chocolate, 321 bags of caramel corn item was sold.
How many of each item was sold?Boxes of chocolate sell for $6 each and bags of caramel corn sell for
$5 each. A total of 535 items were sold and $2889 was
raised.
set of of chocolate was sold x boxes,
because a total of 535 items more sold .
so the caramel corn was sold (535 -x) bags,
and boxes of chocolate sell for $6 each , bags of caramel corn for each and $2889 was raised.
so 6 x+ 5.(535-x) = $2889.
6 x+ 5.535-x = $2889.
6 x+ 2675 - 5x = $2889.
6x - 5x =2889-265
x =214
so the caramel corn was sold 535-x =535-214 = 321
214 boxes of chocolate, 321 bags of caramel corn was sold.
To learn more about sold problems refer to:
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Caramel corn bags cost $5 apiece, while chocolate boxes cost $6 each. 535 products in total were sold, bringing in a total of $2889 then there exists 214 boxes of chocolate, 321 bags of caramel corn was sold.
How to estimate the value of x?Any one of the forms, including addition, subtraction, multiplication, and division, should be used for the algebraic expression. Bring the variable to the left side and the other values to the right side in order to find the value of x. To find the answer, simplify the values.
Let set of of chocolate was sold x boxes,
because a total of 535 items more sold .
so the caramel corn was sold (535 - x) bags, and boxes of chocolate sell for $6 each , bags of caramel corn for each and $2889 was raised.
From the given information, we get
6x + 5(535 - x) = $2889
simplifying the above equation, we get
6x + 5 × 535 - 5x = $2889
6x + 2675 - 5x = $2889
6x - 5x = 2889 - 265
x = 214
So the caramel corn was sold = 535 - x
Substitute the value of x in the above equation, we get
= 535 - 214
= 321
There exists 214 boxes of chocolate, 321 bags of caramel corn was sold.
Therefore, the correct answer is option b) 214 boxes of chocolate, 321 bags of caramel corn.
To learn more about the value of x refer to:
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Write a linear function f with f (4) = -3 and f(0) = -2.
f(x) =
Answer:
f(x)= -1/4x-2
Step-by-step explanation:
Slope= -1/4
y-intercept= -2
PLZ ANSWER!! ONLY IF YOU ARE CORRECT (SELECT ALL THAT APPLY)
Answer:A, C, and D
Step-by-step explanation:
in a survey of 300 adults 15% did not know how to ride a bike how many people do not know how to ride a bike
Answer:
45
Step-by-step explanation:
divide 300 by 100 then multiply it by 15 to find how many people makes 15% of 300
300 ÷ 100 = 3 ➡ 3×15 = 45
Sorry if I wasn’t specific on the list question but it’s like this pls help ASAP
Answer:
12 sugars and 24 flour
Step-by-step explanation:
if 4 x ( times ) 3 = 12,
8 x 3 = 24.
Answer:
Multiply by 3
Here is an equation that represents a function: 72x+12y=60.
Select all the different equations that describe the same function:
A.120y+720x=600
B.y=5-6x
C.2y+12x=10
D.y=5+6x
E.x=5/6-y/6
F.7x+2y=6
G.x=5/6+y/6
The equivalent equations to 72x+12y=60 are:
120y + 720x = 600y = 5 - 6xx = 5/6 - y/6Equivalent EquationsThe given equation is:
72x+12y=60
To find the equivalent equations, follow the steps below
Multiply the equation 72x+12y=60 by 10
10(72x) + 10(12y) = 10(60)
720x + 120y = 600
Divide the equation 72x+12y=60 by 12
(72x/12) + (12y/12) = 60/12
6x + y = 5
y = 5 - 6x
Divide the equation 72x+12y=60 by 72
(72x/72) + (12y/72) = 60/72
x + y/6 = 5/6
x = 5/6 - y/6
The equivalent equations to 72x+12y=60 are:
120y + 720x = 600y = 5 - 6xx = 5/6 - y/6Learn more on equivalent functions here: https://brainly.com/question/2972832
A collection of nickel and quarters is worth $4.65. There are 3 more nickels than quarters. How many coins are there in the collection?
Answer:
There are 15 quarters and 18 nickles
Step-by-step explanation:
The equations derived from this word problem are
5n + 25q = 465
and
3 + q = n
Fill (3 + q) into n in the first equation then solve. You get q = 15.
Then plug 15 into second equation (cause it's easier).
You get n = 18
At a pet store, 0.3 of the sales were for dog products, 1/10 of the sales were for cat products, and 3/5 of the sales were for other animal products. What fraction of the sales were for dog and cat products? Express your answer in simplest form
Answer:
4/10 combined. ❤️
Step-by-step explanation:
i hope this helped. You turn the .3 into a fraction. Say it aloud and it's 'three tenths." The cat products are 1/10 so you add 3/10+1/10=4/10 or 0.4.
What is the value of (1⅔ - ⅚) ÷ 2 5/12 *
ANSWER:
25/144
........................
What is 7.555 rounded to the nearest tenth
What is 7.555 to the nearest hundredth
Answer:
7.6
Step-by-step explanation:
what is the value of angle s
Answer:
54
Step-by-step explanation:
As we know s+19+(180-73)=180
so s+19=73
s=54
A pet store reports that 52% of their pets are female, 31% are puppies, and 27% are female puppies. What is the probability a randomly selected pet from the store is male?
Answer:
29% chance that it will be male
Let f(x) =3x^2-6x+2. Find f (2)
Answer:
f(2) = 3×2^2 - 6×2 + 2
= 12 - 12 + 2
= 2
Pamela bought 9 pounds of birdseed. What is the weight in ounces?
Answer:
9 pounds would be 144 ounces!
Step-by-step explanation:
1 times 9 is 9
so 16 times 9 is 144!
hope this helps you!
I need help with this question 2x<6
Step-by-step explanation:
2x=6
x=6
2
x=3 ans
hope it help u
A company's current stock price is $50.00 and its most recent dividend was $2.00 per share. Since analysts estimate the company will have a 5 percent growth rate, what is its expected return?
Answer:
Expected rate of return =7.1% (Approx.)
Step-by-step explanation:
Given:
Current stock price = $50
Divided d = $2
Growth rate g = 5 %
Find:
Expected rate of return
Computation:
Expected rate of return = D(1+g)/Current Price + g
Expected rate of return = [2(1+5%)/50] + 5%
Expected rate of return =7.1% (Approx.)
the operation * on the set R, of real numbers is defined by:
p * q =p3 + q3- 3pq; p,q€R
Is the operation * commutative in R?
Answer:
y=Mx+b
Step-by-step explanation:
Consider the right triangle below.
6x - 44
2x - 20
3x + 24
If the perimeter of the triangle is 224 cm, find the area of the triangle.
The area of the triangle is
cm
Answer:
Area = 1,344 cm²
Step-by-step explanation:
First, find the value of x and the numerical side length of all sides of the triangle before finding the area.
Thus:
Perimeter of a triangle = sum of all its side
Therefore,
(6x - 44) + (2x - 20) + (3x + 24) = 224
Solve for x
6x - 44 + 2x - 20 + 3x + 24 = 224
Add like terms
11x - 40 = 224
Add 40 to both sides
11x = 224 + 40
11x = 264
Divide both sides by 11
x = 24
Find the measurement of each side length by plugging in the value of x:
Hypotenuse = 6x - 44 = 6(24) - 44 = 100 cm
Height = 2x - 20 = 2(24) - 20 = 28 cm
Base = 3x + 24 = 3(24) + 24 = 96 cm
Find the area:
Area = ½×base×height
Plug in the values
= ½×96×28
Area = 1,344 cm²
1. Is this relation a function? Explain.
2. Is this relation linear? Explain.
Pls help this is due soon
yes its a function because it passes the vertical line test. Yes, it is linear because the slope is constant.
A. 3(x + 2) = 18
B. X + 2 = 18
Answer:
A. x=4
B. x=16
Step-by-step explanation:
A. multiply out: 3x+6=18
subtract 6 from both sides: 3x=12
divide both sides by 3: x=4
B. subtract 2 from both sides: x=16
HELP ME PLS IM STUCK HELLA AND ITS WRONG WHICH ONES RIGHT
Answer:
It is e = 3
Step-by-step explanation:
It is e = 3 and not e = -3 because 44e - 41 e = 3e, then you'd subtract 30 from both sides to get the 3e equal to something which is 9. then dividing both sides by 3 would give you e = 3
write a expression only using positive exponents
9c3/c -4
Answer:
ok sooo
Step-by-step explanation:
2x - 5 + - x - 2
If it takes you an hour to bike 20 miles, what is your unit rate?
Answer:
What units are you going by?
Step-by-step explanation:
Please helppp it’s confusing!!!
Answer:
First you'd look at PEMDAS (parenthesis, exponent, multiplication, division, addition, and subtraction( you'd look at them in this order to solve the equation properly.))
So there is a parenthesis, that would be the 3(2^0). ignore the three, because you're focusing on the parenthesis. Any number other than zero with an exponent of zero will always be one. leaving you with 3(1).
So by now you should know (depending on your level of mathematics, That a number beside a single number in a parenthesis is multiplication. so 3 times 1.
Knowing that any number, other than zero, multiplied by 1 is the number itself, The answer is 3
In short, 3(2^0) = 3
If Y (-7,-4) and (5,2), find the slope of a line perpendicular to YZ. Please help if you can
Answer:
-2
Step-by-step explanation:
The slop of YZ is 1/2. The slope perpendicular would be opposite, making it -2.
Answer:
- 2
Step-by-step explanation:
Calculate the slope m of YZ using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = Y(- 7, - 4) and (x₂, y₂ ) = Z(5, 2)
m = [tex]\frac{2+4}{5+7}[/tex] = [tex]\frac{6}{12}[/tex] = [tex]\frac{1}{2}[/tex]
Given a line with slope m then the slope of a line perpendicular to it is
[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{\frac{1}{2} }[/tex] = - 2
In rectangle ABCD, diagonals AC and BD intersect at E. If AE=3x-28 and DE=.5x+12, find the length of AC.
Given:
In rectangle ABCD, diagonals AC and BD intersect at E, AE=3x-28 and DE=.5x+12.
To find:
The length of AC.
Solution:
We know that, diagonals of a rectangle are equal and they bisect each other.
In rectangle ABCD, diagonals AC and BD intersect at E, so
[tex]AE=BE=CE=DE[/tex] ...(i)
Taking [tex]AE=DE[/tex], we get
[tex]3x-28=0.5x+12[/tex]
[tex]3x-0.5x=28+12[/tex]
[tex]2.5x=40[/tex]
Divide both sides by 2.5.
[tex]x=\dfrac{40}{2.5}[/tex]
[tex]x=16[/tex]
Now,
[tex]AE=3x-28[/tex]
[tex]AE=3(16)-28[/tex]
[tex]AE=48-28[/tex]
[tex]AE=20[/tex]
Using segment addition property,
[tex]AC=AE+CE[/tex]
[tex]AC=AE+AE[/tex] [Using (i)]
[tex]AC=20+20[/tex]
[tex]AC=40[/tex]
Therefore, the length of AC is 40 units.
On Roberto’s shelf he has 6 mystery books, 5 science fiction, 4 history and 3 adventure. Roberto will randomly choose 1 book to read. What is the probability that he will choose an adventure book?
Answer:
3/18, or simplified, he has a 1/6 chance of grabbing an adventure book.
Step-by-step explanation:
6 + 5 + 4 + 3 = 18. There's 3 adventure books, which makes it so that he has a 3/18 chance of it being an adventure book. How did I simplify? 18 ÷ 3 = 6, 3 ÷ 3 = 1.
What is another name for Plane P below?
A.
plane B
B.
plane n
C.
plane ABC
D.
plane BAD
Answer:
is. there. a. picture
Step-by-step explanation:
2. * DE is a midsegment of triangle ABC. Find the value of X.
Answer:
x = 8.5
Step-by-step explanation:
Based on the Midsegment theorem, the midsegment, DE is half the length of BC.
Given that BC = 17, therefore:
DE = ½*(17)
DE = 8.5.
x = DE = 8.5
Select all the statements that show correct reasoning for finding 15÷29. A Multiply 15 by 2, then divide by 9Multiply 15 by 2, then divide by 9 B Multiply 15 by 9, then divide by 2Multiply 15 by 9, then divide by 2 C Multiply 15 by 19, then multiply by 2Multiply 15 by 1 ninth, then multiply by 2 D Multiply 15 by 9, then multiply by 12
Answer:
None of the statements given in the options show the correct reasoning for finding 15÷ 29
Step-by-step explanation:
We are asked to find which of the statements below corresponds to: 15÷29.
15 ÷ 29 =
0.5172413793
= (10 + 5) ÷ 29
= (10 ÷ 29) + (5 ÷ 29)
= 0.5172413793
None of the statements given in the options show the correct reasoning for finding 15÷ 29