=====================================================
Explanation:
Assume the polynomial we want to find is in the form Ax^2+Bx+C
The goal is to find the values of A, B, and C.
We start with 3x^2+4x-1, then we subtract off Ax^2+Bx+C. Set this equal to 1 and we get:
(3x^2+4x-1) - (Ax^2+Bx+C) = 1
3x^2+4x-1 -Ax^2-Bx-C = 0x^2 + 0x + 1
(3x^2-Ax^2) + (4x-Bx) + (-1-C) = 0x^2 + 0x + 1
(3-A)x^2 + (4-B)x + (-1-C) = 0x^2 + 0x + 1
From here we equate the coefficients of the x^2 terms together and we see that 3-A = 0 which leads to A = 3.
Do the same for the x terms to get 4-B = 0 leading to B = 4
Finally, we have -1-C = 1 lead to C = -2
The polynomial Ax^2+Bx+C becomes 3x^2+4x-2
-------------------
Checking the answer:
(3x^2+4x-1) - (Ax^2+Bx+C)
(3x^2+4x-1) - (3x^2+4x-2)
3x^2+4x-1 - 3x^2-4x+2
(3x^2-3x^2) + (4x-4x) + (-1+2)
0x^2 + 0x + 1
0 + 0 + 1
1
We get a difference of 1, so the answer is confirmed.
PLEASE HELPPP I REALLY NEED IT I DONT UNDERSTAND PART C PLEASE SOMEONE EXPLAIN TO ME AND I WILL GIVE BRAINLEST THANK YOU SM!!!! PLEASE I REALLY DONT UNDERSTAND
Answer:
Step-by-step explanation:
12 miles is the ride distance
the guy is able to travel at 6 yard per second
Question C asks how many minutes will the trip take
first we have to convert miles to yards....
there are 1760 yards in one mile
12*1760= the total distance to be traveled.. in yards..
21,120 yards
Next we'll figure out the time to travel that distance.. but we're give a rate of travel in seconds... 6 yards every second
so divide the total yards by the seconds.. that are take to travel every second.. in on second he goes 6 yards. so divide the total yards by 6 for each second of travel
21,120 / 6 = 3520 seconds to go 12 miles or the 21,120 yards.. it's the same distance in different units
then.. b/c the question is asking for minutes divide the 3,520 seconds by 60.. b/c that's how many seconds are in one minute
3,520 / 60 = 58.6666666666666 minutes or 58 minutes and 2/3 of one minute.... make sense?
I need help please!!!!!!
Answer:
uuuhh...
Step-by-step explanation:
What is the value of Line GJ?
a
10
b
30
c
1
50
Answer:
10
Step-by-step explanation:
How many candles did Cassie sell?
Answer:
it is 25
Step-by-step explanation:
The two boxes shown are cuboids.
Work out how many of the smaller boxes you would need to completely fill the larger one.
Answer:
250 smaller cuboids
Step-by-step explanation:
Given
Small and Big cuboids
Required
Number of smaller cuboids in the big one
To do this, we calculate the volume of both cuboids.
[tex]Volume = Length * Width * Height[/tex]
For the small cuboid
[tex]V_1 = 10cm * 3cm * 4cm[/tex]
[tex]V_1 = 120cm^3[/tex]
For the big cuboid
[tex]V_2 = 50cm * 30cm * 20cm[/tex]
[tex]V_2 = 30000cm^3[/tex]
The number of small in big is then calculated by diving the volumes
[tex]Number = \frac{V_2}{V_1}[/tex]
[tex]Number = \frac{30000cm^3}{120cm^3}[/tex]
[tex]Number = \frac{30000}{120}[/tex]
[tex]Number = 250[/tex]
Hence, there are 250 small cuboids in the large one
divide 3/4 divided ny 2/5
Answer:
1.875
Step-by-step explanation:
I used a calculator
Answer:
1.36
Step-by-step explanation:
Judy wants to buy juice boxes at the lowest unit rate. Which is the best
buy?
(A) a single juice box for $1.00
(B) a package of 3 juice boxes for $3.00
(C) package of 6 juice boxes for $5.46
(D) a package of 10 juice boxes for $9.20
Answer:
i think it is d, the pack of 10
Step-by-step explanation:
every juice box is 1 dollar, so the pack of 6, has one box at 46 cents, and the box of 10, has one box at the price of 20 cent
buying a 6 pack, and 4 one packs, will give you ten, but a bit more expensive. hope it helped!
Find the equation of the line perpendicular to y = -4x + 3 that also interacts the point (8,1)
Answer:
The answer is "[tex]y = \frac{1}{4}(x-4)[/tex]".
Step-by-step explanation:
Given:
[tex]Line = y= -4x+3 \\ \\point= (8,1)[/tex]
The formula for the standard Equation of a line:
[tex]\to y= mx +c[/tex]
compare the above line value:
[tex]m= -4\\\\c= 3[/tex]
When a line is perpendicular so, the m value is: [tex]= \frac{1}{4}[/tex]
[tex]\to m_1 \times \m_2 = -1\\\\\to -4 \times m_2= -1\\\\\to m_2 = \frac{-1}{-4}\\\\\to m_2= \frac{1}{4}[/tex]
Line equation when one point and m is given:
[tex]\to (y-y_1) = m (x- x_1)\\\\\to (y-1) = \frac{1}{4}(x- 8)\\\\\to 4y-4 = x- 8\\\\\to 4y = x-8+4\\\\\to 4y = x-4\\\\\to y = \frac{1}{4}(x-4)\\[/tex]
Which statement about conduction is true?
1.Conduction uses electromagnetic waves.
2.Conduction transfers energy from one particle to another.
3.Conduction produces currents in a heated pot of water.
Answer:
statement 2, conduction is the transfer of heat through direct contact
Help!!! Find the length of X
Answer:
x=6.5
Hope my answer is helpful to you
Denis is looking to buy a new car. He can take a loan out for $12,000 with an interest rate of 4% for 5 years. How much would his loan cost in total, including interest?
Gill had less money than Roddy had
After Roddy spent 40% of his money,
he had $14 less than Gill. How much
money did Gill initially have?
Answer:
50
Step-by-step explanation:
Answer: the answer is 50
Step-by-step explanation:
98. What is the sum of the first 27 terms in the arithmetic series 25 +19+13 + ...?
Answer:
sum of the first 27 terms = -1431
Step-by-step explanation:
arithmetic series sum of the first n terms formula:[tex] s_{n} = \frac{n}{2} (2a + (n - 1)d)[/tex]
n = 27 terms
first term, a = 25
common difference, d = 19 - 25 = -6
substitute the values into the formula
[tex] s_{27} = \frac{27}{2} (2(25) + (27 - 1)( - 6))[/tex]
[tex] s_{27} = 13.5(50 + 26( - 6))[/tex]
[tex] s_{27} = 13.5(50 - 156)[/tex]
[tex] s_{27} = 13.5( - 106)[/tex]
[tex]s_{27} = - 1431[/tex]
Quinten ordered dinner from Domino’s. The cost was $27.45. He wants to give the driver a 15% tip. What is the total that Quinten will spend?
Answer:
The correct answer would be 4.11
Please help me with question 5
Answer:
Third choice, 3/20
Step-by-step explanation:
Add all the numbers on the right side of the chart together:
16 + 12 + 22 + 15 + 26 + 9 = 100
So they're rolled the dice 100 times, and of that, they got a 4 fifteen times. So it's 15/100, simplify that equation and it's 3/20
Simplifying an equation means making an equation have smaller numbers if possible. For this question 15 and 100 can both be divided by 5, it is also the biggest number they can both be divided by, so u divide both by 5 and it's 3 and 20, making it 3/20
Winter math packet
Answer:
32. C
34.C
36. 2
Answer:
32. C, 34. C, 35. C, 36. 2 miles
Step-by-step explanation:
32. C because you can see the ratio is 7:1. There is only one answer that has a ratio of 7:1 which is C
34. C because the ratio of batches of cookies to cooking oil is [tex]1:\frac{2}{3}[/tex] since you want 4 batches of cookies, multiply 4 by [tex]\frac{2}{3}[/tex] to get C
35. C because the ratio of butter to sauce is [tex]\frac{2}{3}:2\frac{1}{2}[/tex] multiply [tex]\frac{2}{3}[/tex] by 4 to get C
36. 2 miles because the ratio of miles to hours is [tex]\frac{1}{2} :\frac{1}{4}[/tex] multiply [tex]\frac{1}{2}[/tex] by 4 to get 2 miles
5. Which term best describes the outcome of flipping a coin as either heads or tails?
Answer:
It is a fifty v fifty chance so it can be either depends on the height you throw or which side you throw it at
Step-by-step explanation:
Carl is boarding a plane. He has 222 checked bags of equal weight and a backpack that weighs 4 Write an equation to determine the weight, w of each of Carl's checked bags
Answer: 2w + 4 = 35
Step-by-step explanation:
Carl's two checked bags and his one backpack together weigh 35kg.
Carl's two checked bags have equal weight so both their weight can be denoted as 2w.
Equation is;
2w + 4 = 35
If you were to solve;
2w + 4 = 35
2w = 35 - 4
w = 31/2
w = 15.5kg
Determine the DOMAIN and RANGE from the graph
Given:
The graph of a function.
To find:
The domain and range of the function.
Solution:
We have, the graph of a function and we need to find the domain and range of the function.
We know that, domain is the set of input values (x-values) and range is the set of output values (y-values).
From the given graph it is clear that function is defined for all values of x except x=0 because as x tends to 0 the function tends to negative or positive infinite. So, domain can be any real number except 0.
[tex]Domain=R-\{0\}[/tex]
[tex]Domain=(-\infty,0)\cup (0,\infty)[/tex]
From the given graph it is clear that the value of function can be any real number except y=0. So, range can be any real number except 0.
[tex]Range=R-\{0\}[/tex]
[tex]Range=(-\infty,0)\cup (0,\infty)[/tex]
Therefore, the correct option is B.
Can you help me out with this question pls
What is the solution to the system below?
-4x + 5y = 27
x - 6y = -2
Answer:
(x,y)=(-8,-1)
Step-by-step explanation:
(2) rearrange
x=-2+6y
-4(-2+6y)+5y=27
8-24y+5y=27
8-19y=27
-19y=19
y=-1
x=-2+6(-1)
x=-2-6
x=-8
Hope this helps :)
PLEASE ANSWER!!
20. Carpenters use the term pitch to describe the slope of a
roof. For example, a roof with a pitch of 1/4
means the
roof has 1 foot of vertical rise for every 4 feet of
horizontal distance. The figure below shows a 13-foot-
long roof with 5 feet of vertical rise and x feet of
horizontal distance. What is the pitch of this roof?
F. 1/6
G. 58
H. 5/12
J. 5/14
K. 5/18
Answer:
5/12
Step-by-step explanation:
The pitch of the roof is 5/12.
Option H is the correct answer.
What is the Pythagorean theorem?Pythagorean theorem states that for a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
We can apply this theorem only in a right triangle.
Example:
The hypotenuse side of a triangle with the two sides as 4 cm and 3 cm.
Hypotenuse side = √(4² + 3²) = √(16 + 9) = √25 = 5 cm
We have,
We know that the pitch of a roof is defined as the ratio of the vertical rise to the horizontal distance, and is typically expressed as a fraction.
In this case, we are given that the roof is 13 feet long, with 5 feet of vertical rise and x feet of horizontal distance.
Therefore,
The pitch of the roof.
Pitch = vertical rise / horizontal distance
Pitch = 5 / x
We don't know the value of x, but we can use the fact that the roof is 13 feet long to solve it.
Since the horizontal distance and vertical rise form the legs of a right triangle, we can use the Pythagorean theorem to find the value of x.
x² + 5² = 13²
x² + 25 = 169
x² = 144
x = 12
Now,
Pitch = 5 / x
= 5 / 12
Therefore,
The pitch of the roof is 5/12.
Learn more about the Pythagorean theorem here:
https://brainly.com/question/14930619
#SPJ2
if 25% of a sum is Rs 2500. what is the 20% of the sum?
Answer:
25/100x=2500
x=250000/25
x= 10000
20/100×10000=y
2000
through: (-4, -3) and (-3, -2)
Answer: x + 1
Hope this helps :)
Answer:
x+1
Step-by-step explanation:
I hope you have a merry christmas!
) Find the distance between the boll
-owing pairs of points
i) (2, 3) and (41)
[I took this from the internet, but hope it helps!]
Answer plz I will give correct answer as brainliest
Answer:
It is a triangle
Step-by-step explanation:
This is called Triangle Inequality. We can use its theorem to identify whether these three sides work or not. The Theorem states, "the sum of the smallest lengths of any two sides must be greater than or equal to the length of the remaining side." If we look at the sides, 11,4,7, we can conclude that these are applicable sides for a triangle because the sum of the two smallest lengths, 4 and 7, are the same value as 11. Therefore, these measurements are a triangle.
5. Twice the sum of a number and -38 amounts to 20. (Hint: needs parentheses)
6. Alex sold his used lawn tractor and accessories for $210. If he received twice as much money for the lawn
tractor as he did for the accessories, find how much money he received for the lawn tractor. Write an
equation. Then solve the equation.
7. The cost of a television with remote control is $649. This amount is $125 more than the cost without remote
control. Find the cost of the television without remote control. Write and equation. Then solve the
equation.
Answer:
5Twice the sum of a number and -38 amounts to 20. (Hint: needs parentheses)
6. Alex sold his used lawn tractor and accessories for $210. If he received twice as much money for the lawn
tractor as he did for the accessories, find how much money he received for the lawn tractor. Write an
equation. Then solve the equation.
7. The cost of a television with remote control is $649. This amount is $125 more than the cost without remote
control. Find the cost of the television without remote control. Write and equation. Then solve the
equation.
The values from the given situations are required.
The number is 48.
Cost of lawn tractor is $140.
Cost of TV without remote is $387.
Let [tex]x[/tex] be the number
[tex]2(x+(-38))=20\\\Rightarrow x-38=\dfrac{20}{2}\\\Rightarrow x=10+38\\\Rightarrow x=48[/tex]
The number is 48.
[tex]x[/tex] = Cost of lawn tractor
[tex]y[/tex] = Cost of accessories
Cost of lawn tractor is twice of the accessories
[tex]x=2y[/tex]
Total cost of lawn tractor and accessories is $210
[tex]x+y=210\\\Rightarrow 2y+y=210\\\Rightarrow y=\dfrac{210}{3}\\\Rightarrow y=70[/tex]
Cost of lawn tractor is [tex]x=2y=2\times 70=140[/tex]
[tex]x[/tex] = Cost of TV
[tex]y[/tex] = Cost of remote
Cost of TV and remote is $649
Cost is $125 more than the cost without remote control
[tex]x+y=649[/tex]
[tex]x-y=125[/tex]
Adding the equations we get
[tex]2x=649+125\\\Rightarrow x=\dfrac{649+125}{2}\\\Rightarrow x=387[/tex]
Learn more:
https://brainly.com/question/15125547?referrer=searchResults
A student is standing 20 feet away from the base of a tree. He looks to the top of the tree at a 50 degree angle of elevation. His eyes are 5 feet above the ground. Using cos 50= .64, what is the height of the tree to the nearest foot?
Answer:
23.84 feet
Step-by-step explanation:
Solving this question above, we using Trigonometric function tangent = Opposite/Adjacent
Opposite side + h = Height of the tree
We are told that:
A student is standing 20 feet away from the base of a tree. He looks to the top of the tree at a 50 degree angle of elevation. His eyes are 5 feet above the ground.
20 feet = Adjacent side = Distance form the tree
tan 50 = (h+5)/20
Cross Multiply
h + 5 = 20 × tan50
h = 20tan50 - 5
h= 18.835071852
h =18.84
Therefore the height of the tree is calculated as:
18.84+5 feet
=23.84 feet
Answer:
24 feet
Step-by-step explanation:
EZ
The area of a square is 36cm what is the length of one side?
Answer:
6cm
Step-by-step explanation:
The area of a square is s^2, where s is the length of one side.
s^2 = 36cm^2
s = [tex]\sqrt{36\\}[/tex]cm
s = 6cm
Answer:
Step-by-step explanation:
Area of square = 36 cm²
Side² = 36
Take square root,
√side² = √36 = √6*6
side = 6 cm
Consider quadrilateral ABCD and point in the figure below.
Graph r(135 degrees,E) (ABCD). Which graph (next page) shows the pre-image ABCD and the image A'B'C'D'?
Answer: Its A
Step-by-step explanation: I just took this test plz mark brainlist