The equation of perpendicular line is [tex]$y=-\frac{11}{6} x+\frac{43}{6}[/tex].
What is the equation of a Straight Line ?The equation of the straight line is represented by
y = mx + c
where m is the slope , and c is the intercept on y axis.
Calculate the slope m of BC using the slope formula
[tex]$m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$[/tex]
with [tex]$\left(\mathrm{x}_{1}, \mathrm{y}_{1}\right)=\mathrm{B}(8,4)$[/tex] and [tex]$\left(\mathrm{x}_{2}, \mathrm{y}_{2}\right)=\mathrm{C}(-3,-2)$[/tex]
[tex]$m_{B C}=\frac{-2-4}{-3-8}=\frac{6}{11}[/tex]
Given a line with slope m then the slope of a line perpendicular to it is
[tex]$m_{\text {perpendicular }}=-\frac{1}{m}=-\frac{1}{\frac{-6}{11}}=-\frac{11}{6}$[/tex], then
[tex]$y=-\frac{11}{6} x+c[/tex] is the partial equation
To find c substitute A(3,8) into the partial equation
[tex]$9=-\frac{-11}{6}+C[/tex]
[tex]$-\left(-\frac{11}{6}\right)+C=9$$[/tex]
Apply rule -(-a)=a
[tex]$\frac{11}{6}+C=9$$[/tex]
Subtract [tex]$\frac{11}{6}$[/tex] from both sides
[tex]$\frac{11}{6}+C-\frac{11}{6}=9-\frac{11}{6}$$[/tex]
Simplify
[tex]$C=\frac{43}{6}$$[/tex]
[tex]$y=-\frac{11}{6} x+\frac{43}{6}[/tex] be the equation of perpendicular line.
Therefore, the value of c = 43/6.
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(3,-3), m=-2
y=
What does y equal?
Answer:
-9
Step-by-step explanation:
y=-2(3)-3
4% improvement of 82
solution for what is 4% of 82:
4 percent 82*=
(4:100)*82=
(4*82):100=
328:28=3.28
Step-by-step explanation:
Step 1: our output value is 82
Step 2: it represent the unknown value with x
Step3: from stop one above ,82=100%.
Step4: Similarly. x=4%
Step5: this results in a pair of simple equations
82 equals 100% (1).
x=4%(2).
Step6: by dividing equation 1 by equation 2 and noting that both the rhs right hand side of both equations have the same unit (%) we have unit
Please help！With steps and explanation
9514 1404 393
Answer:
dy/dx = (2 -x)/40.005Step-by-step explanation:
(a) Solving the x-equation for u gives ...
u = (x -1)/4
Differentiating both equations with respect to u, we have ...
dy/du = 1 -4u
dx/du = 4
Then dy/dx is ...
dy/dx = (dy/du)/(dx/du) = (1 -4u)/4
Substituting for u gives ...
dy/dx = (1 -4(x -1)/4)/4
dy/dx = (2 -x)/4
__
(b) The approximate change in y is ...
∆y ≈ (dy/dx)(∆x)
For ∆x = 2.98 -3.00 = -0.02, and x=3, the approximate change is ...
∆y ≈ (2 -3)/4(-0.02)
∆y ≈ 0.005
solve and show steps :
9514 1404 393
Answer:
-(5√7 +9√35)/380
Step-by-step explanation:
The denominator is made rational by multiplying numerator and denominator by the conjugate of the denominator.
[tex]\dfrac{\sqrt{7}}{5-9\sqrt{5}}=\dfrac{\sqrt{7}}{5-9\sqrt{5}}\cdot\dfrac{5+9\sqrt{5}}{5+9\sqrt{5}}=\dfrac{5\sqrt{7}+9\sqrt{35}}{5^2-9^2\cdot5}=\boxed{-\dfrac{5\sqrt{7}+9\sqrt{35}}{380}}[/tex]
_____
Additional comment
This process takes advantage of the factoring of the difference of squares:
a² -b² = (a -b)(a +b)
The method is used to eliminate complex numbers and square roots from denominators.
How long will it take a train to travel 50 km at an average speed of 40m/s? Give your answer in minutes and seconds.
Answer:
20.8
if i'm wrong i'm rlly rlly sorry!!
Use the point and the slope to graph each line. Write the equation of the line.
The line passes through point (4,0) and has slope 0.5.
Answer:
y=0.5x-4.5
Step-by-step explanation:
y=mx+b
Use the information provided to find b
0=0.5(4)+b
-2=b
Therefore, the equation goes down to...
y= 0.5x-2
Step-by-step explanation:
using the formula
m = y -y1/ x - x1
0.5 = y -0/x-4 (0.5 = 1/2)
1/2 = y/x -4
2y = x -4
divide both sides by 2
y = 1/2 ( x -4)
y = 1/2x - 2
y -1/2x = -2
A club plans to spend no more than 85% of the $1,200.00 in its activity budget to buy as many
radio-controlled helicopters as possible. The price of a helicopter is $110.99 plus sales tax of
6%. What is the greatest number of helicopters the club can buy?
Sales tax on helicopter
[tex]\sf\longmapsto 0.6(110.99)=6.65[/tex]
Cost of one helicopter
[tex]\sf\longmapsto 110.99+6.65=117.64[/tex]
Now
85% of 1200.00:-[tex]\sf\longmapsto 0.85(1200)= 1020[/tex]
Total helicopters:-
[tex]\sf\longmapsto 1020/117.64\approx 9[/tex]
What is 80% of 34? I’ve been struggling with percents
Answer:
27.2
Step-by-step explanation:
34x.80=27.2
Answer:
27.2 is the 80 % of 34, so if 34 is the whole then mutiply by .8
Find the solution(s) of the system of equations.
y = –x2 + 2
y = x2 + 4x + 4
You find one quarter, two dimes, and two nickels.
a. Write the dollar amount as a decimal.
Answer:
$0.55
Step-by-step explanation:
1 quarter is 25 cents
2 dimes is a total of 20 cents
2 nickels is a total of 10 cents
if you add all of it up 25+20+10 you get 55 cents but u need it in dollar amount so it would but $0.55 since u have less than a dollar.
The function f is defined by f (x)=x²+4.
Find f (3a).
Maximize P=6x+11y using simplex where
4x+y is less than/equal to 8
x+4y is less than/equal to 12
and x is greater than/equal to 0 , y is greater than/equal to 0
9514 1404 393
Answer:
(x, y, P) = (4/3, 8/3, 112/3)
Step-by-step explanation:
In standard form, the constraints are all "less than or equal to", the variables are all non-negative, and the objective is maximization. This problem is presented in standard form.
4x +y ≤ 8
x +4y ≤ 12
x ≥ 0; y ≥ 0
maximize P = 6x +11y
__
Now we add the slack variables to make the constraints be "equal to". These have a coefficient of +1, and they, too, are non-negative. Here, we'll use s and t as the slack variables.
4x +y +s = 8
x +4y +t = 12
These equations, together with the objective function, are combined in a matrix-like "tableau" in which each row is the set of coefficients in one of the equations. Here, the columns represent x, y, s, t, P and the constants. The equation for the objective function is negated so we're trying to minimize that, as well.
[tex]\begin{array}{ccccc|c}4&1&1&0&0&8\\1&4&0&1&0&12\\-6&-11&0&0&1&0\end{array}[/tex]
Find the column with the most negative value on the bottom row. (Column 2) Divide the rightmost column by this column and find the smallest quotient. Here, the quotients are 8/1 = 8, and 12/4 = 3. The smallest is 3. This identifies the 4 in column 2, row 2 as the "pivot."
Now, row operations are performed to make the pivot be 1 and other values in the pivot column be zero. This gives a new tableau. For example, the new values in row 1 are ...
4 -1/4, 1 -4/4, 1 -0/4, 0 -1/4, 0 -0/4, 8 -12/4
The new tableau is ...
[tex]\begin{array}{ccccc|c}15/4&0&1&-1/4&0&5\\1/4&1&0&1/4&0&3\\-13/4&0&0&11/4&1&33\end{array}[/tex]
Now, the most negative number on the bottom row is in column 1, and the smallest quotient of column 6 and column 1 is in row 1. This makes 15/4 the "pivot". After the required row operations, the next tableau is ...
[tex]\begin{array}{ccccc|c}1&0&4/15&-1/15&0&4/3\\0&1&-1/15&4/15&0&8/3\\0&0&13/15&38/15&1&112/3\end{array}[/tex]
All values in the last row are non-negative, so we are finished. The rightmost column tells us the values of x, y, P that are the solution to the problem
(x, y, P) = (4/3, 8/3, 112/3)
__
The graphical solution confirms the Simplex solution.
Help me with maths .
Answer:
Step-by-step explanation:
m x n / p + (-n) =5 X 8 / -2 + (-8) =-20-8=-28
There are two solutions, for a quadratic equation that represents the relation between distance and
time.
One of the solutions is positive and the other is negative.
If the values are associated with time, then we will choose
A the positive and the negative
solutions.
B the positive solution.
C neither the positive nor the.
D the negative solution.
Answer:
B. The Positive Solution
Step-by-step explanation:
Because Time is a positive quantity
PLEASE HELP!!!!!
will mark brainliest!!!!!
Answer:
y=8x+3
Step-by-step explanation:
to check plug the numbers to the equation and you will that it is right
Answer:
f(x) = 8x + 3
Explanation:
I knew f(x) = mx +b is the formula for a linear equation and that when x = 0,
f(x) = b
So, when x = 0 in the table, f(x) = 3 and therefore b = 3
Now we can plug in f(x) = 11 and x =1 into f(x) = mx+b along with our b value
11 = m(1) + 3
solving for m we get m = 8 which finishes our unknowns
f(x) = mx + b
f(x) = 8x + 3
3 apples for $0.59 unit rate
Answer:
around .20 per apple
Step-by-step explanation:
The product of three integers is -40. What could the three integers be?
Explain your thinking.
Answer:
10, 4, -1
Step-by-step explanation:
10×4=40
40×-1=-40
-40=-40
The three integers could be 8, -5, and 1.
What are integers?A number without a decimal or fractional element is known as an integer, which can be both positive and negative, including zero.
Given that, the product of three integers is -40.
Since the product is negative, there should be at least one negative number.
The three numbers can be 8, -5, and 1.
8 × (-5) ×1 = -40
Hence, the three integers could be 8, -5, and 1.
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Sales Revue • Total sales revenue was $120 million in Quarter 1 • Total sales revenue in Quarter 2 decreased by $10 million compared to Quarter 1. • Sales revenue in the East was $78 million in Quarter 1. • Sales revole in the West increased by $46 million from Quarter 1 to Quarter 2. Question Arrange the sales revenue lo 000.0001) by Quirtor und the percentages in the East and West regions
The required revenue table categorized by Quarter (Qrt1 and Qrt 2) and Region (East and West) is :
____________Sale Revenue _____________
_______ Qrt 1 ___ Qrt1 %___ Qrt 2 ____ Qrt2 %
East ___ $78 _____65% ____$22 ______ 20%
West___ $42 _____ 35%____$88 ______ 80%
Sales Revenue ; Quarter 1 = $120 million Sale Revenue ; Quarter 2 = $120 - $10 = $110 millionQuarter 1 :
East = $78 million East percentage = (78/120) × 100% = 65%West = 120 - 78 = $42 million West percentage = 100% - 65% = 35%Quarter 2 :
West = $42 + $46 = $88 million West percentage = (88/110) × 100% = 80%East = $110 - $88 = $22 million East percentage = 100% - 80% = 20%Therefore, The distribution table which displays the revenue of the comp may is given above.
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7/2(-4-2/3g)=
Pleas help meeeeeeudkxi
Answer:
-14g-84/6
Step-by-step explanation:
multiply the numbers
7/2 (-4-1 · 2/3g)
7/2(-4-2/3g)
combine multiplied terms into a signle fraction
7/2(-4-2/3g)
7/2(-4+-2g/3)
find common denominator
7/2(-4+-2g/3)
7/2(3(-4)/3+-2g/3)
combine fractions with common denominator
7/2(3(-4)/3+-2g/3)
7/2(3(-4)-2g/3)
multiply the numbers
7/2(3(-4)-2g/3)
7/2(-12-2g/3)
rearrange terms
7/2(-12-2g/3)
7/2(-2g-12/3)
combine multiplied terms into a single fraction
7/2 · -2g-12/3
7(-2g-12)/2 · 3
distribute
7(-2g-12)/2 · 3
-14g-84/2 · 3
multiply the numbers
-14-84/2 · 3
-14g-84/6
Topics: Precalculus, Matrix
What number is 30% of 20? for 10 points and brainlist
Answer:
6
Step-by-step explanation:
20*.3=6.
30 percent turns into .3
Mason is turning 5 years old next Saturday. He has picked sidewalk chalk and a helium balloon to give to each of his friends who come to his party. His dad
has a coupon for $10 off of any purchase over $25 at the party supply store. If sidewalk chalk cost $3.29 and balloons cost $1 each, how much did his dad pay
for the favors for 10 of Mason's friends and 1 of each for Mason as well?
Mason's dad paid $36.19 for the chalk and the balloons
Mason's dad paid $47.19 for the chalk and balloons,
Mason's dad paid $37.19 for the chalk and balloons.
Mason's dad paid $26.19 for the chalk and the balloons.
Tytoth
012
NEXT
SAVE & EXIT
BI
614 PM
10/24/2021
Answer:
dad paid 37.19
Step-by-step explanation:
Find the least common multiple of 15x^2 and 6x.
Answer:
30x^2
Step-by-step explanation:
The least common multiple (LCM) of two or more non-zero whole numbers is the smallest whole number that is divisible by each of those numbers. In other words, the LCM is the smallest number that all of the numbers divide into evenly.
what desmal is inbetween 1/2 and 3/4
Answer:
1/2 = 0.5
3/4 = 0.75
Step-by-step explanation:
1,400,000
Would that be 1.4 x 10^5 or 1.4 x 10^6
Answer:
1.4 x 10^6
Step-by-step explanation:
Cual es la simplificación de 72/64
9/8
Step-by-step explanation:
divides 72 por 8 que es 9, y 64 dividido entre 8 es 8 dando te 9/8.
(7 pts) A school has 400 feet of fencing to build a set of 3 athletic fields as shown below. What dimensions
should they use to build the largest possible athletic complex? Include appropriate units with your answer.
х
Answer:
Step-by-step explanation:
the side lengths are (400 - 4x)/2 = 200 - 2x
A = x(200 - 2x)
A = 200x - 2x²
Maximum area will occur when the derivative is set to zero.
dA/dx = 200 - 4x
0 = 200 - 4x
x = 200/4 = 50 ft
each field will be 50 x 33⅓ ft.
total area will be 5000 ft²
Which is not very big for a sports complex. I've owned houses with more floor space than that.
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Investment account starting balance of $7400 in one year it had increased by 7.5%. How much is this in dollars
Answer:
7955
Step-by-step explanation:
(1 point)
7. The students in Mr. Collin's class used a surveyor's measuring device to find the angle from
their location to the top of a building. They also measured their distance from the bottom of the
building. The diagram shows the angle measure and the distance.
Building
To the nearest foot, what is the height of the building?
A. 239 ft
B. 154 ft
C. 67 ft
D. 33 ft
slope 1/4 y intercept-5
slope int form: y=1/4x-5