Answer:
f(x) = 7 . x=1 .
Maria earns an hourly wage of $10. She drew the following graph to show the relation of her income as a function of the hours she works. How did she modify the function y = x to create her graph?
Hey i need help finding the orthocenter for the following points, please show the steps you used. thanks
(-3, 0.5)
(3,3)
(2,-1)
9514 1404 393
Answer:
(81/43, -31/43) ≈ (1.884, -0.7209)
Step-by-step explanation:
The orthocenter is the intersection point of the altitudes of the triangle. Since this is not a right triangle, you need to find the equations of the altitude lines, then find where those intersect.
If we call the points A, B, C in the order given, the attached figure shows the altitude lines from B perpendicular to AC, and from C perpendicular to AB.
We can find the equation of the perpendicular line using the form ...
∆x·x +∆y·y = c
where ∆x and ∆y are the differences in coordinates between the points on the "side" and the value of constant 'c' is determined by evaluating the expression using x and y as the coordinates of the opposite vertex.
__
For line AC, we have ...
(∆x, ∆y) = C - A = (2, -1) -(-3, 0.5) = (2+3, -1-0.5) = (5, -1.5)
Then the equation of the first altitude line is ...
5x -1.5y = 6(3) -1.5(3) = 10.5
Multiplying by 2 puts this in standard form:
10x -3y = 21
__
For line AB, we have ...
(∆x, ∆y) = B - A = (3, 3) -(-3, 0.5) = (3+3, 3-0.5) = (6, 2.5)
Then the equation of the second altitude line is ...
6x +2.5y = 6(2) +2.5(-1) = 9.5
Multiplying by 2 puts this in standard form:
12x +5y = 19
__
Then the orthocenter is the solution to the system of equations ...
10x -3y -21 = 0
12x +5y -19 = 0
This set of equations can be solved a number of ways. One is the "cross-multiplication" method.
1/(10·5 -12·(-3)) = x/(-3·(-19) -5·(-21)) = y/(-21(12) -(-19)(10))
x = 162/86 = 81/43
y = -62/86 = -31/43
The orthocenter is (81/43, -31/43) ≈ (1.884, -0.7209).
_____
Additional comment
The "cross multiply method" is based on cross products when the equations are written in standard form:
ax +by +c = 0
dx +ey +g = 0
Usually, the coefficients are written in two rows of four, with the first column repeated at the end:
a b c a
d e g d
Then cross products are formed, where diagonal down is positive and diagonal up is subtracted from that:
p1 = (ae -db), p2 = (bg -ec), p3 = (cd -ga)
These give the solution to the equations when put in the form ...
1/p1 = x/p2 = y/p3 ⇒ x = p2/p1 and y = p3/p1
If you look at videos of this "cross multiply method," they will put the 1/p1 at the end of the string of equalities, and they will use the coefficients in the order starting with b instead of a. I find the arrangement here easier to remember, so less likely to get confused.
Further comment
You can, of course, find the slopes of the lines, and their opposite reciprocals, then use a point-slope form or some other method for writing the equations of the altitude lines. The solution to the equations can proceed by substitution or elimination. No doubt these methods are somewhat familiar. The method used here tries to get to the answer much more quickly with a lot less writing. (Unfortunately, it takes a bit of writing to explain it all.)
Here's a fun question:
Pewdiepie has 4 heart attacks from G-fuel in October and 6 heart attacks from G-fuel in November. How many heart attacks did Pewdiepie have in total?
Answer:
10. I feel bad for him.
Step-by-step explanation:
WHAT IS FRICTION BETWEEN????? NEED ANSWERS ASAP
Answer:
Friction is a force between two surfaces that are sliding, or trying to slide, across each other.
Step-by-step explanation:
For example, when you try to push a book along the floor, friction makes this difficult.
Answer:
Friction is the force that opposes motion between any surfaces that are in contact. There are four types of friction: static, sliding, rolling, and fluid friction. Static, sliding, and rolling friction occur between solid surfaces. Fluid friction occurs in liquids and gases.
Step-by-step explanation:
Which equation matches the story: Elena spends $17 and buys a $3 book and a bookmark for each of her 5 cousins. How much does each bookmark cost?
3(x+5)=17
3x+5=17
5(x+3)=17
5x+3=17
Answer:
$2.80
Step-by-step explanation:
17-3=14
14 divided by 5=
2.8
Add 0 since it's about money.
$2.80
The two triangles formed by the flagpole and the man shown below are similar.
What is the height of the flagpole?
57 feet
51 feet
8.5 feet
42.5 feet
joke 1. 2 hunters were out in the woods right while they were following fresh tracks from a big elk one of the hunters drop to the ground and his eyes roll backwards so the other hunter whips out his phone and calls the hospital "I THINK MY FRIEND IS DEAD!" he told the doctor the doctor told him " Calm down let's make sure he's dead. so there is a moment of silence the you here a big pop the hunter says "NOW WHAT!" (he shot his friend)
joke 2. I wanted to be a democrat for halloween but i could not stick my head far enough up my a/s/s to be one.
brainliest for being funny?
3(x + 7)
plz heeelp
who ever helps gets 5 points
Answer:
3x + 21
Step-by-step explanation:
3(x+7)
3 * x + 3 * 7
3x + 21
HOPE THIS HELPS
PLZZ MARK BRAINLIEST
Answer:
3x + 21
Step-by-step explanation:
3(x + 7)
3(x + 21)
3x + 21
What type of correlation is the graph below?
a
No correlation
b
Negative
c
Quadratic correlation
d
Positive
Answer:
C I think
Step-by-step explanation:
Write a quadratic function whose graph has the given characteristics.
x-intercepts: (4, –1)
point: (1, –2)
Answer:
here you go
Step-by-step explanation:
Which expression is equivalent to 4^6 ⋅ 4^−8?
A.) 1/4^2
B.) 1/4^14
C.) 4^2
D.) 4^14
(PS. Don't answer this just for the points, please put some effort into this, yes i know im the on seeking others help, but i tried i didn't understand so came here.)
The critical points of a rational inequality are x = –4 and x = 2. Which set of points can be tested to find a complete solution to the inequality?
Answer:
-2
Step-by-step explanation:
Answer:
-2
Step-by-step explanation:
Wesley subscribes to a telecommunication company’s movie package.The plan includes a basic monthly charge of $40 and an additional charge of $1.50 for every movie ordered. 2a) Write an equation for the total charge for a month, C, in terms of the number of movies, m, Wesley orders per month. This is a required question 2b) If Wesley ordered 4 movies one month, what was his total charge for the month?
Answer:
46
Step-by-step explanation:
So, the plan
monthly =40 + 1.50x
and he orders 4 movies in a month your problem to solve now looks like this
1 month = 40+1.50x4
Then, 1 month= 40 + 6
1 month= 46
Plzzzz answer quick i need this badly
Answer:
What u need
Step-by-step explanation:
Answer:
what do you need help with?
Step-by-step explanation:
help help help help help
Answer:
C
Step-by-step explanation:
Step 1. Add the fractions
One way you can solve this problem is by adding the fractions
1/4 + 1/6 + 5/12
1(3)/4(3) + 1(2)/6(2) + 5/12
3/12 + 2/12 +5/12
10/12
2. Multiply by 48
10/12 * 48( to find the amount of cupcakes)
40
3. Subtract
Now that we know the total number of cupcakes excluding the lemon is 40, we can do 48 - 40 , which is 8 cupcakes or C
Answer:
C. 8
Step-by-step explanation:
1/4 = 12
1/6 = 8
5/12 = 20
12+8+20=40
48-40 = 8
Helen is typing a report and is using two different sizes of fonts, as shown below. What is the ratio of the height of a letter typed using font I to the height of a letter typed using font II?
2/9
1/3
3
9
WILL RECIEVE BRAINLIST
Answer: 2/9
Step-by-step explanation:
What are the slope and the y-intercept of the line that represents plant A's height in inches in terms of the number of weeks? (Hint: The formula
for slope is slope = rise/run, and the y-intercept is the y-coordinate when x = 0.)
Answer:
Plant A is y=2x+6
Step-by-step explanation:
Slope: 2
Y-intercept: 6
how many dimes equal the value of 6 quarters.show you step
Answer:
the answer to this complicated problem is 25
Answer:
15 dimes
Step-by-step explanation:
6 quarters= $1.50
$1.50 divided by 10 cents= 15 dimes
A market sells blueberries for $3 per pint. The first day, the market sold a total of $35 worth of blueberries. The second day, the market sold a total of $47 worth of blueberries. And the third day, the market sold a total of $57 worth of blueberries. Estimate how many pints the market sold over the three days.
Answer:Around 50 pints
Step-by-step explanation:
$35=$40
$47=$50
$57=$60
$40+$50+$60=$150/3=50
16 is what percent of 96?
Answer:
15.36%
Step-by-step explanation:
Find the value of the variable that makes the equation true 3x-11=-2x+19
Answer:
x = 6
Step-by-step explanation:
Given
3x - 11 = - 2x + 19 ( add 2x to both sides )
5x - 11 = 19 ( add 11 to both sides )
5x = 30 ( divide both sides by 5 )
x = 6
Maura runs 5 miles in 1.25 hours.How many miles could she run in 5 hours?
I NEED HELP!!
Answer:
15
Step-by-step explanation:
Find the values of x and y by writing two equations and solving the system of equations.
Answer:
y=2 x=5
Step-by-step explanation:
3x-2y=11
2x-3y=4
you multiply both equations to cancel one variable out. in this case you multiply the first equation by 2 and the second by -3
6x-4y=22
+ -6x-9y=12
--------------------------
0x+5y=10
y=2
you plug that in either equation
3x-2(2)=11
3x-4=11
3x=15
x=5
Solve -4b + 2 = 18.
b =
Answer:
b = -4
Step-by-step explanation:
your equation: -4b + 2 = 18
subtract 2 from both sides: -4b = 16
divide both sides by -4 to isolate the variable: b = -4
Answer:
b= -4b=18-2
=16
b=16+(-4)
=12
Solving equations with like terms -8 -3y + 2y =32
Answer:
y= -40
Step-by-step explanation:
To find the inverse of f(x) = 2x – 1, Patel begins by replacing f(x) with y. He then switches x and y. What is the next step?
A.Solve the equation for x.
B.Subtract 1 from both sides of the equation.
C.Solve the equation for y.
D.Replace y with f–1(x).
it a
Answer:
Step-by-step explanation:
C. Solve for y
I really need help!!!
if f(x)=x^2+4x-5, find f(-4)
Answer:
−5
Step-by-step explanation:
By substituting the value of x in f(x) with -4,
(-4)^2+4(-4)-5
=16+(−16)−5
=0−5
=-5
Your welcome :D
BRAINLIST!!
The Kims drove 450 miles in each direction to Grandmother's house and back again. If their
car gets 25 miles per gallon and their cost for gasoline was $3.25 per gallon for the trip to
Grandmother's house, but $3.50 per gallon for the return trip, how much more money did they
spend for gasoline returning from Grandmother's house than they spent going to Grandmother's?
A) $2.25
B) $4.50
C) $6.25
D) $9.00
2^4 - 7^3 – 15^2 = 0
Answer:
False
Step-by-step explanation:
(y - 6) = -4(x + 3) in slope intercept form
Answer:
y=-4x-6
Step-by-step explanation:
use the formula y=mx+b
oh btw i just posted a question so please maybe help with it???
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[tex]y - 6 = - 4(x + 3)[/tex]
[tex]y - 6 = - 4x - 12[/tex]
Add sides 6
[tex]y - 6 + 6 = - 4x - 12 + 6[/tex]
[tex]y = - 4x - 6[/tex]
This is the slope-intercept form.
Done...
♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️
Write an equation of the line that passes through the given point and is parallel to
the given line.
10. (14, 3); 2y - x - 8
Answer:
y = x - 23
Step-by-step explanation: