Answer:
[tex]y = -\frac{1}{4}x - 2[/tex]
Step-by-step explanation:
i'm not sure if you're trying to find the equation of the line ?? but i'll assume that's the case and find the slope-intercept form equation of the line.
slope intercept form is [tex]y = mx + b[/tex], where [tex]m[/tex] is the slope and [tex]b[/tex] is the y-intercept. since the slope is already identified, you can plug in [tex]-\frac{1}{4}[/tex] for [tex]m[/tex].
[tex]y = mx + b[/tex] ⇒ [tex]y = -\frac{1}{4}x+b[/tex]plug in the [tex]x[/tex] and [tex]y[/tex] values from the coordinate pair that passes through the line, which is (-4, -1). you can start with either [tex]x[/tex] or [tex]y[/tex], but i'm going to start with [tex]x[/tex].
first, plug in [tex]-4[/tex] for [tex]x[/tex].
[tex]y = -\frac{1}{4}x+b[/tex] ⇒ [tex]y = -\frac{1}{4}(-4)+b[/tex]now plug in [tex]-1[/tex] for [tex]y[/tex].
[tex]y = -\frac{1}{4}(-4)+b[/tex] ⇒ [tex]-1 = -\frac{1}{4}(-4)+b[/tex]after plugging in all of the given values, the equation is now [tex]-1 = -\frac{1}{4}(-4)+b[/tex], in which you need to solve for [tex]b[/tex].
now it's time to solve! begin by multiplying [tex]-\frac{1}{4}(-4)[/tex] in order to simplify the right side of the equation.
[tex]-\frac{1}{4}(-4) = 1[/tex]you now have [tex]-1 = 1 + b[/tex]. subtract 1 from both sides of the equation. on the right side, it cancels itself out, leaving you with [tex]b[/tex]. on the left side of the equation, you now have [tex]-1 - 1[/tex], which equals [tex]-2[/tex].
therefore [tex]-2 = b[/tex], or [tex]b = -2[/tex].
now that you've solved for your [tex]b[/tex] value, plug it into your initial slope-intercept form equation!
[tex]y = -\frac{1}{4}x + b[/tex] ⇒ [tex]y = -\frac{1}{4}x - 2[/tex]if you want to check to make sure that the values are correct, plug (-4, -1) into your completed slope-intercept form equation. as you did in the beginning, plug in [tex]-4[/tex] for [tex]x[/tex] and [tex]-1[/tex] for [tex]y[/tex].
[tex]y = -\frac{1}{4}x - 2[/tex] ⇒ [tex]-1 = -\frac{1}{4}(-4) - 2[/tex]begin simplifying by multiplying [tex]-\frac{1}{4}(-4)[/tex].
[tex]-1 = -\frac{1}{4}(-4) - 2[/tex] ⇒ [tex]-1 = 1 - 2[/tex]subtract [tex]1 - 2[/tex].
[tex]-1 = 1 - 2[/tex] ⇒ [tex]-1 = -1[/tex]since both sides of the equation are equal, that means your [tex]b[/tex] value of [tex]-2[/tex] is correct because it makes the equation true!
aaaand there you go! i hope this helps. have a great day! <3
In which quadrant, or on which axis, does the terminal side of angle 540° lie?
Your answer:
A. Q II
B. QIII
C. Quadrantal angle / positive x-axis
D. Quadrantal angle / negative x-axis
In triangle ABC, the measure of C is 90°,
AC=24, and BC=10. What is the value of sin
A?
Answer:
Sin A = 0.38462
Step-by-step explanation:
From the trigonometric function,
Sin A = [tex]\frac{Opposite}{Hypotenuse}[/tex] ................... 1
So that, applying the Pythagoras theorem to determine the value of hypotenuse,
[tex]/Hyp/^{2}[/tex] = [tex]/Opp/^{2}[/tex] + [tex]/Adj/^{2}[/tex]
= [tex]24^{2}[/tex] + [tex]10^{2}[/tex]
= 576 + 100
[tex]/Hyp/^{2}[/tex] = 676
Hyp = [tex]\sqrt{676}[/tex]
= 26
The hypotenuse of the triangle is 26.
Thus, from equation 1;
Sin A = [tex]\frac{10}{26}[/tex]
Sin A = 0.38462
Quadrilateral MNPQ is shown.
Trapezoid M N P Q is divided into 4 triangles by N Q and M P, which intersect at point R inside the trapezoid. N P is parallel to M Q and M N is congruent to Q P. Angle N M P is 30 degrees and angle P M Q is 32 degrees. Segment Q R equals 4.1.
If MP = 5.9, what is RN?
(Round your answer to the nearest tenth. Write NA if there is not enough information given.)
Answer:4.1
Step-by-step explanation:
In the Quadrilateral MNPQ, if MP = 5.9, then RN = 1.8.
What is a trapezoid?An open, flat object with four straight sides and one set of parallel sides is referred to as a trapezoid or trapezium. A trapezium's non-parallel sides are referred to as the legs, while its parallel sides are referred to as the bases.
Given:
Quadrilateral MNPQ is shown.
Trapezoid MNPQ is divided into 4 triangles by NQ and MP.
MQ is parallel to NP.
That means, MQ and NP always at the equal distance.
MN ≅ QP
So,
MP = QN
Now,
QN = QR + RN and QR = 4.1:
MP = QN
5.9 = 4.1 + RN
Then RN = 5.9 - 4.1 = 1.8
Therefore, the value of RN is 1.8.
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Ill give brainliest,
The fastest train on Earth, the TGV from France can travel at faster speeds than most any other train. During a test, the train travel 800 miles in 2.5 hours. What is its speed?
Answer:
The fastest car on Earth, a British-made Thrust SSC, would win every ... The fastest train on Earth, the TGV from France, can travel at faster speeds than trains in the United States. During a speed test, the train traveled 800 miles in 2.5 hours. What is its ... Based on this speed.
Step-by-step explanation:
The speed of the train is 320 miles per hour.
What is speed?Speed is the ratio of the given distance and time.
It shows how fast an object is moving at a given time.
The formula is Distance / Time.
We can find the distance or time when the required values is given using this formula.
We have,
The speed of the TGV train can be calculated using the formula:
Speed = distance/time
where distance is given in miles and time is given in hours.
In this case,
The distance traveled by train is 800 miles, and the time taken to travel this distance is 2.5 hours.
Substituting these values into the formula, we get:
Speed = 800 miles / 2.5 hours
Simplifying the expression on the right-hand side, we get.
Speed = 320 miles per hour
Therefore,
The speed is 320 miles per hour.
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Does anyone know if im correct on this!?!?
Answer:
You are correct.
Step-by-step explanation:
The steps indicate clear method for the final answer.
Answer:
you are correct
Step-by-step explanation:
the points (3,48) and 5,768) lie on the graph of an exponential function. write the equation in exponential form. Must explain or I'll report! answer asap!
Answer:
y = 3/4*4ˣStep-by-step explanation:
The function is:
y = abˣSubstitute the values from the given points and solve for b:
48 = ab³768 = ab⁵Divide the second equation by the first one:
768/48 = ab⁵/ab³b² = 16b = 4Find a using the first equation:
48 = a*4³a = 48/64a = 3/4The function is:
y = 3/4*4ˣA certain population has 1,000 people in it. Which of the following numbers would be an appropriate number for a
random sample?
O 10
200
O 1,000
0900
Answer:
10
Step-by-step explanation:
The equations 3x-2y=-14 and 3x+y=-11 are plotted on the same set of axes. what are the coordinates of a point that's common to both equations? how do you know?
Answer:
14
Step-by-step explanation:
Answer:
(-4, 1)
Step-by-step explanation:
Solve it as a system of equations:
[tex]3x-2y=-14\\3x+y=-11[/tex]
subtract the two equations
[tex]-3y = -3[/tex]
divide both sides by -3
[tex]y=1[/tex]
Plug this into the equation 3x + y = -11 to solve for x
[tex]3x + 1 = -11\\[/tex]
subtract 1 from both sides
[tex]3x = -12[/tex]
divide both sides by 3
[tex]x = -4[/tex]
So the answer is (-4, 1)
What is the positive solution to this equation?
4x²+12x=135
Answer:
4.5
Step-by-step explanation:
Fireworks are set off from a hill 80 feet above the Mississippi. The outer
shells will fall after exploding at its maximum height. The firework's height
about the surface of the river is given by the function h(t) = -16t^2 + 64t +
80. What is the height of the rocket after 1.5 seconds?
Answer:
752 ft
Step-by-step explanation:
Assuming t represents time, and the time we are trying to find is how high the rockets go after 1.5 seconds, we must take the equation and put 1.5 in wherever t occurs, this looks like:
-16(1.5)²+64(1.5)+80
solving this, we get:
-24²+96+80
576+96+80
752
Simplify the following expression. 3(2x + 7)
Answer:
6x+21
Step-by-step explanation:
3(2x+7)
3 multiply both 2x and 7
6x+21
hope it's helpful ❤❤❤❤❤
THANK YOU.
the school nurse is packing first aid kits. the ratio of bandages to gloves is 9:2. if she has 48 gloves, how many bandages will she need to make it complete kits
A. 216
B. 11
C. 3
D.96
Answer:
A
Step-by-step explanation:
48*9 =432
432/2=216
There are 780 registered voters in Cloud County. In the last election, 40% of the registered voters actually voted. How many people in Cloud County voted in the last election?
What is the solution to this inequality?
-9x – 15 < 3
O > -2
O I < 2
Or<-2
O > 2
Answer:
x>-2
Step-by-step explanation:
-9x-15<3
•Move the constant to the right
9x<3+15
•calculate
-9x<18
•Divide both sides
Pls help! I think this is do today.
Donovan has 5 times as many red fish as he does blue fish and half as many gray fish as blue fish. How many total fish (F) does Donovan hav
x=20 is the solution to 4=x-16
Answer:
True
Step-by-step explanation:
So let's put this question into one equation.
x - 16 = 4 if x = 20
Well, this is a true statement. If we were to replace x with 20. We would see that the equation makes sense.
20 - 16 = 4
20 minus 16 does indeed equal 4.
Please help me ASAP I need this done please! (Giving brainliest)
Answer:
Step-by-step explanation:
a 2x-2+6x+10=120
b x=14
c l=47 w=13
pls answer this one
By prime factorisation method factorize 400 and find the sum of prime numbers involved.
Step-by-step explanation:
PLS MARK ME AS BRAIN LIST ANSWER
Expand & simplify
(2x + 6)2
Answer: 4x+12
Step-by-step explanation:
The distributive property states that a(b+c) = ab+ac.
Thus, simply do 2*2x+2*6 = 4x+12
Hope it helps <3 :D
there are n counters in a bag. 4 of the counters are red and the rest are blue. Ross takes a counter from the bag at random and does not replace it. he then takes another counter at random from the bag. the probability Ross takes two blue counters is 1/3. find the value of n
Answer: n = 10.
Step-by-step explanation:
In the bag, we have n counters.
4 of the counters are red.
the rest are blue, then we have:
(n - 4) blue counters.
Now, the probability that Ross takes a blue counter from the bag is equal to the quotient between the number of blue counters (n - 4) and the total number of counters, n
Then the probability is:
p1 = (n - 4)/n
Now he draws another, and it must be blue again, then we can calculate the probability in the same way as above, but he already take a blue counter, so the number of blue counters is (n - 5) and the total number of counters is (n - 1)
The probability of this event is:
p2 = (n - 5)/(n - 1)
The joint probability (the probability that Ross takes two blue counters) is equal to the product of the individual probabilities, and we know that this is equal to 1/3, then we have the equation:
1/3 = ( (n - 4)/n)*((n - 5)/(n - 1))
Now let's solve this for n.
n*(n - 1)/3 = (n - 4)*(n - 5)
(n^2 - n)/3 = n^2 - 4*n - 5*n + 20
n^2 - n = 3*(n^2 - 9*n + 20)
n^2 - n = 3*n^2 - 27*n + 60
0 = (3*n^2 - n^2) - 27*n + n + 60
0 = 2*n^2 - 26*n + 60
The two solutions of this equation can be found with Bhaskara's equation:
[tex]n = \frac{-(-26) +- \sqrt{(-26)^2 - 4*2*60} }{2*2} = \frac{26+- 14}{4}[/tex]
Then the two solutions are:
n = (26 - 14)/4 = 3
This is not an option, because we know for sure that we have 4 red counters, then this option can be discarded.
The other solution is:
n = (26 + 14)/4 = 40/4 = 10
Then we have n = 10, 10 counters in total.
What is the area of this trapezoid?
Help! I need this please!
A phone usually sells for $245. It is now on sale for 10% off the original price. What is the new sale price for the phone?
Answer:
$220.50
Step-by-step explanation:
245.00×10%=24.50
245.00-24.50=220.50
Answer:
$24.50
Step-by-step explanation:
MATH HELP!! ASAP!!! MARKING BRIAINLIEST!!
Answer:
18 meters.
Step-by-step explanation:
The ratio is 1cm:2m, so for every centimeter, you multiply it by 2 and convert it to meters. So, 9 cm time 2 equals 18 and then add meters, so 18 meters.
(hope this helps :P)
Do you links of a rectangle is for X +7 and the width is three if the area of the rectangle is 129 square units what is the value of X
Answer:
x = 36
Step-by-step explanation:
Length of a rectangle, x+7
Width = 3
Area of the rectangle, A = 129 units²
The area of a rectangle is given by :
A = lb
So,
[tex](x+7)\times 3=129\\\\(x+7)=43\\\\x=43-7\\\\x=36[/tex]
So, the value of x is equal to 36.
A construction company is fencing the triangular plot shown. 50 it What is the exact length of fencing that the company will need?
A.50 + 50√2 Ft
B.100 + 50√2ft
C .50√2 ft
D. 150√2 ft
Answer:
b
Step-by-step explanation:
the awnser was c for me on my test but i guess it and got it right.
24 kilograms turned into pounds
Answer:
52.91 pounds
Step-by-step explanation:
Help with this pleaseeeeee!!!!!!!
Answer:
60
Step-by-step explanation:
V=Base area*height
V=((5*8)/2)*3
V=(40/2)*3
V=20*3
V=60
Challenge A gold mine has two elevators, one for equipment and another for the miners. The
equipment elevator descends 6 feet per second. The elevator for the miners descends 13 feet per
second. One day, the equipment elevator begins to descend. After 32 seconds, the elevator for the
miners begins to descend. What is the position of each elevator relative to the surface after
another 12 seconds? At that time, which elevator is deeper?
The nosition of thn
in
Answer:
.
Step-by-step explanation:
Solve x2 + 10x = 24 by completing the square. What is the solution set of the equation? Show your work.
Answer:
32.6193819
Step-by-step explanation:
calulater never lies XD
Answer:
The answer should be: x=2,-12
which on your answer should backwards: {-12,2}
Step-by-step explanation: