Find the values of a, b, and c such that the equation y=ax2+bx+c has ordered pair solutions (1,16), (−1,−2), and (0,−1). To do so, substitute each ordered pair solution into the equation. Each time, the result is an equation in three unknowns, a, b, and c. Then solve the resulting system of three linear equations in three unknowns, a, b, and c.
Answers
Answer:
c = -1
b = 9
a = 8
Step-by-step explanation:
16 = a × 1² + b × 1 + c
-2 = a × (-1)² + b × (-1) + c
-1 = a × 0² + b × 0 + c .........-> -1 = c
16 = a + b + c
-2 = a - b + c
16 = a + b - 1
-2 = a - b - 1
a + b = 17
a - b = -1 .......-> a = b - 1 ........ a = 9 - 1 = 8
(b - 1) + b = 17
2b - 1 = 17
2b = 18 .......-> b = 18/2 = 9
Answer:
y = 8x² +9x -1
Step-by-step explanation:
The coefficients of the quadratic function can be found from three points by substituting the point values into the equation and solving for the coefficients.
The equation we want to find coefficients for is ...
y = ax² +bx +c
For point (1, 16), the equation is 16 = a(1²) +b(1) +c
For point (-1, -2), the equation is -2 = a(-1)² +b(-1) +c
For point (0, -1), the equation is -1 = a(0) +b(0) +c
__
The last of these equations gives a value for c (c=-1). Substituting that into the other two gives the equations in a and b as ...
a + b = 17
a - b = -1
Adding the two equations gives ...
2a = 16 ⇒ a = 8
Subtracting the second from the first gives ...
2b = 18 ⇒ b = 9
Then the desired quadratic equation is ...
y = 8x² +9x -1
Related Questions
Which statement about this sum is true? −5 2/5+5.3
Answers
Answer:
D.It is less than 0 because the addends have opposite signs and the positive addend is farther from zero.
Step-by-step explanation:
The given expression is :
When we subtract a larger number from a smaller number, we get a negative answer as mathematically we cannot subtract a larger number from smaller, so we subtract the numbers in standard format and out a negative sign in front of the answer.
Like this given expression will become : -519.70
Now, any negative number is smaller than zero.
Therefore, the correct answer is option D.
Fatima earns $150 in 4 hours. At this rate, how many hours will it take her to earn $675?
Answers
Answer:
$150 = 4 hours,
So, in a ratio, 4 : 150
=> 150 * 4.5 : 4 * 4.5
=> 675 : 18 hours
Therefore to earn $675 at the rate of $150 for 4 hours, Fatima will need to work for 18 hours to earn $675
If my answer helped, kindly mark me as the brainliest!!
Thank You!!
The slope of the line parallel to the given line is
A point on the line parallel to the given line, passing through (4,2) is
The slope of the line perpendicular to the given line is
A point on the line perpendicular to the given line, passing through (-4, 2), is
Answers
Answer: 1/2
0,4
-2
-2,-2
Step-by-step explanation: took the lesson
Evaluate the algebraic expression d - b when b = 3, d = 12, h = 2 and r = 7.
Answers
Answer:
Step-by-step explanation:
d-b
d=12
b=3
12-3
=9
hope dis helps
Question
A boat is travelling due south at a speed of 53 miles per hour. If the boat started off 29 miles directly west of the city
Johnstown, how fast (in radians per hour) is the angle opposite the southward path changing when the boat has travelled 23
miles? (Do not include units in your answer, and round to the nearest hundredth.)
Answers
I think this is the answer i sorry if i am wrong
Let f(x) = 3 * sqrt(x) + 7. Define g$to be the inverse of f.
What is the value of g(g(f(f(f(36)))))?
Answers
By using the definition of inverse functions, we will see that:
g(g(f(f(f(36))))) = f(36) = 25.
What are inverse functions?Two functions f(x) and g(x) are inverses if:
f( g(x) ) = x
g( f(x) ) = x
Then we can rewrite:
g(g(f(f(f(36)))))
First, we can see that:
g(f(f(f(36)))) = f(f(36))
Replacing that in our expression, we get:
g(g(f(f(f36))))) = g(f(f(36)))
And the above expression is equal to f(36), to be sure of that, let's replace:
u = f(36)
Then we can rewrite:
g(f(f(36))) = g(f(u))
And by definition, the above thing is equal to u:
g(f(u)) = u = f(36).
Finally, we conclude that:
g(g(f(f(f(36))))) = f(36) = 3*√36 + 7 = 3*6 + 7 = 25
If you want to learn more about inverse functions, you can read:
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Can someone help me with this problem.
Answers
Answer:
D, 14 units
Step-by-step explanation:
Both coordinates have -5, so we know that 8 and -6 are at the same line.
We find the absolute value...
So 8=8 and -6=6. Lastly, we add them from 0 and 8+6= 14.
ANSWER IS 14 UNITS!!
Complete the proof. Given LM¯¯¯¯¯¯¯¯¯≅JK¯¯¯¯¯¯¯¯, MJ¯¯¯¯¯¯¯¯≅KL¯¯¯¯¯¯¯¯ Prove △LMJ≅△JKL
Answers
Here is the proof :-
LM=JKMJ=KLSo
Adjacent angle is also equal
<LMJ=<JKLHence
∆LMJ=∆JKL(SAS)The dimensions of this figure are changed so that the new surface area is exactly 14 what it was originally. What is the new surface area? Enter your answer as a decimal in the box. ft² Complex solid composed of rectangular prisms in an L shape. The bottom face is labeled with a length of 9.8 ft. The height of the shorter side of the L shape is labeled 6.5 ft. The height between the shorter side and taller side of the L shape is labeled 8.1 ft. The length of the of the taller section of the L shape is labeled 10.6 ft and the width is labeled 4.3 ft.
Answers
Answer:
Step 1. Read the problem. Draw the figure and label it with the given information. .
Step 2. Identify what you are looking for. the measure of an angle
Step 3. Name. Choose a variable to represent it. Let x= the measure of an angle.
Step 4. Translate. m\angle A+m\angle B+m\angle C=180
Write the appropriate formula and substitution
X + 4.3 + 10.6- 8.1 \end{array}
Step 7. Answer the question. The measure of the third angle is 6.8ft
The new surface area is approximately 12264.56 ft².
What is a prism?A prism is a three-dimensional object.
There are triangular prism and rectangular prism.
We have,
To solve this problem, we first need to calculate the original surface area of the complex solid.
The complex solid is composed of two rectangular prisms, one with dimensions 9.8 ft × 6.5 ft × 8.1 ft and one with dimensions 10.6 ft × 4.3 ft × 6.5 ft.
The surface area of the first rectangular prism is:
2(9.8 × 6.5) + 2(9.8 × 8.1) + 2(6.5 × 8.1) = 464.82 ft²
The surface area of the second rectangular prism is:
2(10.6 × 4.3) + 2(10.6 × 6.5) + 2(4.3 × 6.5) = 411.22 ft²
So the total original surface area of the complex solid is:
464.82 + 411.22 = 876.04 ft²
Now we need to find the new surface area, which is exactly 14 times the original surface area.
Therefore, we can write:
New surface area = 14 × original surface area
New surface area = 14 × 876.04
New surface area ≈ 12264.56 ft²
Thus,
The new surface area is approximately 12264.56 ft².
Learn more about Prism here:
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what is the volume of 1.5ft , 3ft , 5ft
Answers
Answer:
22.5
Step-by-step explanation:
To find volume, you need to multiply all of the numbers together.
1.5 ft x 3 ft x 5 ft = 22.5
A linear function can be used to estimate the decrease in snowfall measured since 1920 the decrease in the annual snowfall has been an average of 0.24 in per year let X represent the number of years since 1920 when the measurements began and let y represent the annual snowfall the initial measurement in 1920 was 48.6 in using the average change and initial measurement which is the best estimate of the annual snowfall and the 78th year after records were kept round to the nearest hundredth of a 15.84 in B 27.72 in C 29.88 in D 67.32 in
Answers
Answer:
C- 29.88
Step-by-step explanation:
i did it on the edge test
James just moved to a new home. He made a graph showing the number of boxes in each room.
James moved 3 boxes from the living room to the bedroom.
After James moved those 3 boxes, which two rooms had the same number of boxes?
Choose 2 answers:
Choose 2 answers:
(Choice A)
A
Living room
(Choice B)
B
Kitchen
(Choice C)
C
Bathroom
(Choice D)
D
Bedroom
Answers
Answer:
B and D
Step-by-step explanation:
Kitchen and Bedroom will have same number f boxes after James moved 3 boxes from the living room to the bedroom.
The kitchen and the bedroom will have the same number of boxes
How to determine the rooms?The key on the graph implies that:
1 image represents 3 boxes
Using the above key, we have:
Living room = 9 boxesKitchen = 15 boxesBedroom = 12 boxesBathroom = 3 boxesWhen 3 boxes are moved from the living room to the bedroom, we have:
Living room = 6 boxesKitchen = 15 boxesBedroom = 15 boxesBathroom = 3 boxesHence, the kitchen and the bedroom will have the same number of boxes
Read more about charts at:
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Plss help mee
you need to show your work
At the school's fall bake sale, all of the pies were cut into 6 pieces, so each person who bought a piece bought 1/6 of a pie. Each slice of pie sold for $1.00. How much money did the school make if all eleven pies were sold? (In other words, find 11 divided by 1/6 .)
Answers
Answer:
66.00
Step-by-step explanation:
eleven pies have 6 slices each
Multiply 6 by 11 to get 66
66x1.00=66.00
please answer this question
Answers
As we know an identity that ;
[tex]{\boxed{\bf{\cos{(2\theta)}=2\cos^{2}(\theta)-1}}}[/tex]Setting, [tex]{\bf{{\theta}=\footnotesize \dfrac{\pi}{8}}}[/tex] will give us ;
[tex]{:\implies \quad \sf \cos \left(2\times \dfrac{\pi}{8}\right)=2\cos^{2}\left(\dfrac{\pi}{8}\right)-1}[/tex]
[tex]{:\implies \quad \sf 2\cos^{2}\left(\dfrac{\pi}{8}\right)=\dfrac{1}{\sqrt{2}}+1}[/tex]
[tex]{:\implies \quad \sf 2\cos^{2}\left(\dfrac{\pi}{8}\right)=\dfrac{1+\sqrt{2}}{\sqrt{2}}}[/tex]
[tex]{:\implies \quad \sf \cos^{2}\left(\dfrac{\pi}{8}\right)=\dfrac{1+\sqrt{2}}{2\sqrt{2}}}[/tex]
Rationalizing the denominator of RHS, will yield ;
[tex]{:\implies \quad \sf \cos^{2}\left(\dfrac{\pi}{8}\right)=\dfrac{1+\sqrt{2}}{2\sqrt{2}}\times \dfrac{2\sqrt{2}}{2\sqrt{2}}}[/tex]
[tex]{:\implies \quad \sf \cos^{2}\left(\dfrac{\pi}{8}\right)=\dfrac{2\sqrt{2}+4}{8}}[/tex]
[tex]{:\implies \quad \sf \cos^{2}\left(\dfrac{\pi}{8}\right)=\dfrac{2\sqrt{2}+4}{8}}[/tex]
[tex]{:\implies \quad \sf \cos \left(\dfrac{\pi}{8}\right)=\pm \sqrt{\dfrac{2\sqrt{2}+4}{8}}}[/tex]
Now, as we know that ;
[tex]{\boxed{\bf{\sin (2\theta)=2\sin (\theta)\cos (\theta)}}}[/tex]Now, setting the same [tex]{\bf{{\theta}=\footnotesize \dfrac{\pi}{8}}}[/tex]
[tex]{:\implies \quad \sf 2\sin \left(\dfrac{\pi}{8}\right)\cos \left(\dfrac{\pi}{8}\right)=\sin \left(2\times \dfrac{\pi}{8}\right)}[/tex]
[tex]{:\implies \quad \sf 2\sin \left(\dfrac{\pi}{8}\right)\cos \left(\dfrac{\pi}{8}\right)=\dfrac{1}{\sqrt{2}}}[/tex]
[tex]{:\implies \quad \sf \sin \left(\dfrac{\pi}{8}\right)\left(\pm \sqrt{\dfrac{2\sqrt{2}+4}{8}}\right)=\dfrac{1}{2\sqrt{2}}}[/tex]
[tex]{:\implies \quad \sf \sin \left(\dfrac{\pi}{8}\right)=\dfrac{\sqrt{8}}{2\sqrt{2}(\pm \sqrt{2\sqrt{2}+4})}}[/tex]
[tex]{:\implies \quad \sf \sin \left(\dfrac{\pi}{8}\right)=\pm \dfrac{1}{\sqrt{2\sqrt{2}+4}}}[/tex]
This is the required answer
−4y−4+(−3) .........................................................
Answers
Every cereal box has a gift inside, but you cannot tell from the outside what the gift is. The store manager assures you that 13 of the 62 boxes on the shelf have the secret decoder ring. The other 49 boxes on the shelf have a different gift inside. If you randomly select two boxes of cereal from the shelf to purchase, what is the probability that BOTH of them have the secret decoder ring?
Answers
Answer:
I'm pretty sure it is 7.4% or 0.074.
Step-by-step explanation:
Answer:
0.041 = 4.1%
Step-by-step explanation:
The probability the first box has a secret decoder ring is 13/62.
The probability the second box has a secret decoder ring is 12/61.
The probability of both is:
P = (13/62) (12/61)
P ≈ 0.041
Solve for Z please will give brainliest
Answers
Answer:
z=6
Step-by-step explanation:
32=12+4(z-1)=
32=12+4z-4
32=8+4z
24=4z
6=z
find the zeros of x^4-10x^3+35x^2-50x+24=0
Answers
Sorry my writing is so messy, but basically I found all possible zeros by finding the factors of 24:
(Positive or negative) 1,2,3,4,6,8,12,24
Then, using remainder theorem (when you plug potential zeros into the x values to see if the equation will equal zero) I found out that 1 made the equation equal zero, and therefore was a zero.
Then I used synthetic division to make the equation smaller (I also used 2 because I found out that it was a zero using remainder theorem, same as how I found out 1)
Once I divided it small enough to factor, I simply factored it to find the last 2 zeros
(I didn’t explain everything 100% bc I don’t know how much of this you have learned so if you want clarification on something let me know)
Answer:
x=1 or x=2 or x=3 or x=4
Step-by-step explanation:
x4−10x3+35x2−50x+24=0
Step 1: Factor left side of equation.
(x−1)(x−2)(x−3)(x−4)=0
Step 2: Set factors equal to 0.
x−1=0 or x−2=0 or x−3=0 or x−4=0
x=1 or x=2 or x=3 or x=4
What are the similarities and differences between translations, reflections, and rotations?
One paragraph or more ( 5 sentences) will reward for Brainly best description!
Answers
Answer:
There are four main types of transformations: translation, rotation, reflection and dilation. A translation moves the object without rotating it or changing its size. Reflection flips the object about a line of reflection. Rotation rotates a figure about a fixed point. Dilation changes the size of a figure without changing its essential shape. When you reflect a point across the x-axis, the x-coordinate remains the same, but the y-coordinate is transformed into its opposite. a negative angle of rotation turns the figure in a clockwise direction. Transformation can be done in a number of ways, including reflection, rotation, and translation. ~When you reflect a point across the x-axis, the x-coordinate remains the same, but the y-coordinate is transformed into its opposite. A negative angle of rotation turns the figure in a clockwise direction.
Step-by-step explanation:
solve for x x/-4=-1.11
Answers
Explain how this graph demonstrates how the equation y = mx can be derived from the two points (1, m) and (x, y).
Answers
The equation y = mx of the graph is a linear equation
The linear equation that demonstrates the relationship on the graph is y = mx
How to determine the equation from the graphThe points on the graph are given as:
(1, m) and (x, y)
Start by calculating the slope (M)
[tex]M = \frac{y_2 -y_1}{x_2 -x_1}[/tex]
So, we have:
[tex]M = \frac{y - m}{x - 1}[/tex]
The linear equation is then calculated as:
[tex]y = M(x - x_1) + y_1[/tex]
This gives
[tex]y = \frac{y - m}{x- 1}(x - 0) + 0[/tex]
[tex]y = \frac{y - m}{x- 1}(x)[/tex]
Cross multiply
[tex]yx-y = yx - mx[/tex]
Evaluate the common terms
[tex]-y =- mx[/tex]
Divide both sides by -1
y = mx
Hence, the equation of the graph is y = mx
Read more about linear equations at:
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1.10 apples for 3.50. How much is the cost for 70 apples
Answers
Answer:
$0.31.
Step-by-step explanation:
If 1.10 apples cost $3.50, we should divide to find the rate per apple.
1.10/3.5 ≈ 0.31
0.31 is the aproximatley answer, since there is no clear answer (at least not from my work). 0.31*70=21.70
The cost of 70 apples are 0.31.
Given an equilateral triangle with side lengths 18 cm. What is the height of the triangle?
O 18 cm
O 9 cm
o 93 cm
O 183 cm
Answers
Step-by-step explanation:
If you draw an altitude of the right triangle, you get that the legs are (18/2)=9 and the height (which I'll call x) and a hypotenuse of 18.
By the Pythagorean theorem,
[tex] {9}^{2} + {x}^{2} = {18}^{2} \\ 81 + {x}^{2} = 324 \\ {x}^{2} = 243 \\ x = \sqrt{243} = 9 \sqrt{3} [/tex]
I WILL GAVE BRAINLIEST
Answers
Answer:
x < -14
Step-by-step explanation:
Step 1: Subtract 6 from both sides.
[tex]-3x+6-6 > 48-6[/tex] [tex]-3x > 42[/tex]Step 2: Divide both sides by -3 and flip the inequality sign.
[tex]-3x/-3 > 42/-3[/tex] [tex]x < -14[/tex]Therefore, the answer is x < -14.
Isolate the variable by dividing each side by factors that don't contain the variable.
Inequality Form:
x<−14
Interval Notation:
(−∞,−14)
hope this helps
The health of employees is monitored by periodically weighing them in. A sample of 54 employees
has a mean weight of 183.9 lb. Assuming that o is known to be 121.2 lb, use a 0.10 significance level
to test the claim that the population mean of all such employees weights is less than 200 lb.
Traditional Method
I need to know how to do the Traditional way with a step by step because I am not understanding it at all.
Answers
Put a ✓ in the box if the figure has line symmetry and put an ✗ if it does not have line symmetry.
Answers
#1
Both vertical and horizontal#2
Both vertical and horizontal#3
Both vertical and horizontal#4
None#5
Vertical#6
Vertical#7
None#8
VerticalAnswer:
See below.
Step-by-step explanation:
#1) Audi symbol
Vertical (√)Horizontal (√)#2) Under Armour Logo
Vertical (√)Horizontal (√)#3) Chanel Logo
Vertical (√)Horizontal (√)#4) Red Logo
Vertical (X)Horizontal (X)#5) Mouse Logo
Vertical (√)Horizontal (X)#6) Android Bot
Vertical (√)Horizontal (X)#7) Nike logo
Vertical (X)Horizontal (X)#8) Spider
Vertical (√)Horizontal (X)-4x=2 what does x equal
Answers
Answer:
-0.5
Step-by-step explanation:
-4x=2
2/-4= -0.5
x= -0.5
-4x/-4= 2/-4
1x= -1/2
which fractions equal three? need help ASAP.
Answers
Answer:
anything that has a numerator three times greater than its denominator. Examples: 3/1, 6/2, 9/3, 12/4, 15/5, so on.
Step-by-step explanation:
When simplifying, you divide both by the denominator and if it equals three, then the fraction is equal to three.
7% of 500 is use the percent formula A=PB A is percent of B
Answers
9514 1404 393
Answer:
35
Step-by-step explanation:
A = PB
A = (7%)(500) = 0.07×500 = 35
35 is 7% of 500
_____
You can think of the % symbol as being a shorthand way to write /100. That is, ...
7% = 7/100 = "seven hundredths" = 0.07
A 24-inch diameter pizza is cut into eight slices. What is the area of one slice?
Answers
Answer:
Area of a slice = Area of the pizza ÷ 8
Therefore the area of the pizza equals:
AreaPizza = π r^2 ( r = diameter ÷ 2)
= π 6^2
= 113.097
AreaSlice = AreaPizza ÷ 8
= 113.097 ÷ 8
= 14.137 inches squared
To the nearest square inch, each slice is 14 inches squared.
Step-by-step explanation:
Hope this helps.