Which represents the solution(s) of the system of equations, y = x2 – 6x 8 and y = –x 4? Determine the solution set by graphing. (1, 3) only (2, 0) and (4, 0) (1, 3) and (4, 0) no solutions.
Answers
The solution of the considered system of equation is represented by: Option C: (1,3) and (4,0)
What is a solution to a system of equations?For a solution to be solution to a system, it must satisfy all the equations of that system, and as all points satisfying an equation are in their graphs, so solution to a system is the intersection of all its equation at single point(as we need common point, which is going to be intersection of course)(this can be one or many, or sometimes none)
For the considered case, the system of equations given to us is:
[tex]y = x^2 - 6x + 8\\y = -x + 4[/tex]
Plotting both's graph and finding the common points on both's graph, we get the common points as:
(1,3) and (4,0)
These points satisfy both the equations simultaneously.
Therefore, the solution of the considered system of equation is represented by: Option C: (1,3) and (4,0)
Learn more about solutions to a system of equations here:
https://brainly.com/question/2825832
Answer:
c is correct
Step-by-step explanation:
Related Questions
find the value of x plz plz plz
Answers
Answer:
X=28
Step-by-step explanation:
Answer:
28
Step-by-step explanation:
A triangle always has 180° so that means 40° (2x+9)° and another angle add up to 180°.
We can find out two angles in order to find out the third, one of them is 40° the other is 180°-105° because there are 180° on a line.
you get 75.
75°+40°=115°
180°-115°=65°
2x+9=65°
Make x the subject of the formula:
2x=56
(take away 9)
x=28
(divide both sides by 2)
Jim is 50% as tall as a ladder. The ladder is 12 feet tall. How tall is Jim?
Answers
Answer:
Jim is 6ft tall
Step-by-step explanation:
This ladder is 12 feet tall. And Jim is half of it (Fifty %) So, Therefore Jim is 6ft tall
50% of (multiplied by) 12 feet equals 6 feet
A (x) = x ^ 4-2022x ^ 3-2022x ^ 2-2022x-2022
A (2023)?
Answers
Answer:
1
Step-by-step explanation:
Through simply substituting your value into everywhere there is an 'x', you can get your answer.
[tex]A(2023)=(2023)^4-2022(2023)^3-2022(2023)^2-2022(2023)-2022\\A(2023)=1[/tex]
I need help on this problem ASAP !!! :)
Answers
Answer:
[tex]\displaystyle 8,9[/tex]
Step-by-step explanation:
Deduct one from nine to get eight, then use the Pythagorean Theorem:
[tex]\displaystyle a^2 + b^2 = c^2 \\ \\ 8^2 + 4^2 = x^2 \hookrightarrow 64 + 16 = x^2 \hookrightarrow \sqrt{80} = \sqrt{x^2}; 4\sqrt{5}\:[or\:8,94427191...] = x \\ \\ \boxed{8,9 \approx x}[/tex]
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What does How much did each candy bar cost?
Add
Subtract
Divide
Multiply
Answers
Answer:
One candy bar cost $4.02
Step-by-step explanation:
14.19 - 5.79 = 8.4 (total candy bar cost)
8.4 / 2 = 4.2 cost of one candy bar
Answer:
4.2
Step-by-step explanation:
14.18-5.79 = 8.4
8.4/2 = 4.2
Weldon bought a pair of hiking boots that cost $64.00 before tax. If a 7.5% tax is added to Weldon's total, how much did he spend in total on the hiking boots? Round to the nearest cent, if necessary.
Answers
Answer:
68.80
Step-by-step explanation:
64 x (7.5% +1)
64 x 1.075 = 68.80
Find the equation of the hyperbola if y=2x−5 and y=−2x+3 are the asymptotes, and it is known that one of the vertices is on the y-axis.
Answers
Answer:
(x-2)^2/4 - (y+1)^2/16 = 1
Step-by-step explanation:
The first thing you want to do is find the center of the hyperbola. Since you have the two equations of the asymptotes, their intersection must be what you want. setting 2x - 5 equal to -2x + 3, you get that x = 2, meaning that 2 is the x-coord of your center. Plugging this value of x into the equations, you get that y = -1. Now that you have your center, you have the information that one of the vertices is on the y-axis. Since the distance from the center to the vertice must be a straight line, you know for sure that this hyperbola is a horizontal one (a vertical one would not have a vertice on the y-axis given this center). Knowing this, you have the equation form (x-2)^2/a^2 - (y+1)^2/b^2 = 1. I got a little confused here, but remember that you now know the center and the equations of the asymptotes. y = 2x - 5 is equal to 2(x - 2) - 1. The form of the asymptotes of a horizontal hyperbola is b/a(x-h) + k, which means that b/a must be equal to 2. This also means that 2a = b, and 4a^2 = b^2. Now you can substitute b^2 for 4a^2, leaving you with the equation (x-2)^2/a^2 - (y+1)^2/ 4a^2 = 1. Remember that vertice on the y-axis? Since it must be at the same y-coordinate (since you know that it must be a horizontal line from the center to the vertice), you know the vertice has to be (0, -1). You can plug these values into the previous equation, which gives you (0 - 2)^2 / a^2 - 0 = 1. This leaves you with 4/a^2 = 1, which means that a must be 2. Since you already know that b is 2a, b must be equal to 4. Plugging those values into the equation, you get your final answer, (x-2)^2/4 - (y+1)^2/16 = 1.
PLEASE HELP!!! I REALLY NEED THIS
Answers
Answer:
The length of the third side is √73
Step-by-step explanation:
To find the third side, we use the Pythagorean Theorem: a² + b² = c²
a² and b² are the two smaller sides
c² is the longest side
The two shortest sides are 4√2 and ?
The longest side is 9
a² = 4√2²
b² = ?
c² = 9²
Now we put together the equation:
4(√2)² + b² = 9²
The square of √2 is 2
4 × 2 + b² = 9²
Multiply 4 and 2 to get 8
8 + b² = 9²
Calculate 9 to the power of 2 and get 81
8 + b² = 81
Subtract 8 from both sides
8 + b² - 8 = 81 - 8
Subtract 8 from 81 to get 73
b² = 73
Take the square root of both sides of the equation
√b² = √73
Simplify
b = √73
Length of third side: √73
Answer in decimal form: 8.5440037453175311678716483262397
Which statement best describes a graph of paired points that form a proportional relationship? A straight line can be drawn through all of the the points but the line does not pass through the origin. A straight line can be drawn through all the points and the lines passes through the point where x = 0 and y = 0. A straight line can be drawn through all the points and the line passes through the point (3, 0). A straight line cannot be drawn through all the points and the line passes through the origin.
Answers
Answer:
a straight line can be drawn through all the points and the lines passes through the point where x = 0 and y = 0 (the origin).
Step-by-step explanation:
in a proportional relationship, one variable is always a constant value times the other. That constant "a" is know as the "constant of proportionality".
y = ax
and as you can easily see, that implies if x = 0, then y = 0.
therefore, the given answer is correct.
For a function f(x), the difference quotient is 21x2 + 21xh + 7h2 + 2. Which statement describes how to determine the average rate of change of f(x) from x = –3 to x = 2? Substitute –3 for x and 2 for h in the difference quotient. Substitute –3 for x and 5 for h in the difference quotient. Substitute 2 for x and –3 for h in the difference quotient. Substitute 2 for x and –5 for h in the difference quotient.
Answers
Answer:
Substitute –3 for x and 5 for h in the difference quotient.
Step-by-step explanation:
The difference quotient for the function f(x) is 21x² + 21xh + 7h² + 2. Now, we know that the difference quotient equal f(x + h) - f(x) = 21x² + 21xh + 7h² + 2. The change in x is h = x₂ - x₁. So, if x changes from x = -3 to x = 2, where x₁ = -3 and x₂ = 2, h = x₂ - x₁ = 2 - (-3) = 2 + 3 = 5.
So to find the average rate of change of f(x) from x = -3 to x = 2, we substitute x = -3 and h = 5 into the difference equation f(x + h) - f(x) = 21x² + 21xh + 7h² + 2. Since, x starts at x = -3 and increases by 5 units to x = 2.
Answer:
(on edge) B. Substitute –3 for x and 5 for h in the difference quotient.
Step-by-step explanation:
I am thinking of a number, I multiply it by 12 and subtract 194, I get the same answer if I multiply by 5 and subtract 12
Answers
26 x 12 - 194 =118
26 x 5 - 12 = 118
The bottom of a ladder must be placed 4.6 feet away
from a wall for the safety of the person climbing the
ladder. The ladder is 15.2 feet long. How high up does
the ladder reach?
Answers
Answer:
2.44ftStep-by-step explanation:
In this problem, we are going to use Pythagoras theorem to solve for the height
given
x= 4.6 ft
hypothenus=15.2
y=?
we know that
hyp^2=x^2+y^2
15.2=4.6^2+y^2
15.2-4.6^2=y^2
15.2-21.16=y^2
5.96=y^2
√5.96=y
y=2.44ft
the height of the ladder is 2.44ft
John and kim shared $2400 dollars in the ratio 2:6.What is kim's share ?
Answers
Answer:
she has $1,800
Step-by-step explanation:
to solve we divide 2,400 by 8, which is the total amount of the 2 together. then we get 300 per share, and so we multiply that by kim's 6. to check, we can do 2(300)+6(200) which gives us our origional value of 2,400.
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What is an equation of the line that passes through the points (4,-2) and (8,3)
Answers
Answer:
I think its y=mx
Step-by-step explanation:
not sure :)
What is 3500/9 simplified?
Answers
Hey there!
Let's simplify
[tex]\bold{\displaystyle\frac{3500}{9} }}[/tex]
Is there any way we can simplify this fraction?
No. 3500 and 9 do not have any common factors.
This fraction is already in its simplest form.
However, [tex]\bold{\displaystyle\frac{3500}{9} }[/tex] is an improper fraction.
An improper fraction is a fraction where the numerator (top) is greater than its denominator.
You can easily remember where the denominator is by remembering this:
The Denominator is Down
The nice thing about improper fractions is that you can simplify them... A little.
Hey! How can we simplify a fraction that's already in its simplest form?!
If the fraction is improper, then we can just write it as a mixed number.
A mixed number is a number with both a whole number and a fraction.
Let's write this fraction as a mixed number.
First, how many times does 9 go into 3,500? (evenly)
388 times
Now, take 388 and multiply it times 9:
3,492
Subtract:
3,500-3,492=8
That's our numerator.
Therefore, the mixed fraction is
[tex]\bold{388\displaystyle\frac{8}{9} }[/tex]
We can easily check if this is correct by multiplying 388 times 9 and adding 8.
See? We ended up with 3,500.
Hence, 3500/9 simplified is
[tex]\boxed{\boxed{\bold{388\frac{8}{9} }}}[/tex]
Hope everything is clear.
Let me know if you have any queries; if you do, please comment.
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[tex]\rule{200}{2}[/tex]
A rectangle's length, f(x), is 2 more than three times a unit length, x, and its width, g(x), is twice the unit length, x. Combine functions f(x) and g(x) to get h(x). Which is h(x) written in the simplest form? H(x) = 5x + 2 h(x) = 6x + 2 h(x) = 6x2 + 2 h(x) = 6x2 + 4x
Answers
Answer:
[tex]h(x)=6x^2+4x[/tex]
Step-by-step explanation:
As the rectangle's length, f(x), is 2 more than three times a unit length, x, so,
f(x)=3x+2
As the rectangle's width, g(x), is twice the unit length, x, so,
g(x)=2x.
The length and width of the rectangle are related to the area and the perimeter of the rectangle. So, the length, f(x), and the width, g(x), can be combined to give the area or perimeter, h(x).
So, h(x) might be the area or the perimeter of the rectangle.
If h(x) is the area, then
[tex]h(x)=f(x) \times g(x)[/tex] [as area=lenght x width]
[tex]\Rightarrow h(x)=(3x+2)\times 2x[/tex]
[tex]\Rightarrow h(x)=6x^2+4x[/tex] (this is in the given options)
If h(x) is the perimeter, then
[tex]h(x)=2\{f(x) + g(x)\}[/tex] [as perimeter=2(lenght + width)]
[tex]\Rightarrow h(x)=2\{(3x+2)+ 2x\}[/tex]
[tex]\Rightarrow h(x)=2(5x+2)[/tex]
[tex]\Rightarrow h(x)=10x+4[/tex] (not in the given options)
So, from the given options [tex]h(x)=6x^2+4x[/tex] is correct.
Answer:
h(x) = 6x^2 + 4x
Step-by-step explanation:
Got it right on lesson.
We have a circle with origin O, diameter AD and AB||CB. Prove AB=CD.
Answers
Answer:
draw a start to D to A and to B
then put some period to O
Step-by-step explanation:
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Tritium is a radioactive isotope of hydrogen that decays by about 5% per year. A large bottle of water that contained 856,000 tritium atoms remained undisturbed for 13 years. How much tritium does the bottle contain now?
Answers
Answer: if you’re rounding to the nearest whole number it’s
439,421
Step-by-step explanation:
The number of tritium atoms that the bottle contains now is; 439,384.8 atoms.
How much tritium does the bottle contain now?It follows from the task content that;
The large bottle of water that contained 856,000 tritium atoms remained undisturbed for 13 years.On this note, the number of atoms remaining is;
N = 856,000 × (0.95)¹³
N = 856,000 × 0.5133
N = 439,384.8 atoms
Read more on radioactive decay;
https://brainly.com/question/1383030
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PLEASE ANSWER QUICK Angles which share a common ray and common vertex, but no interior points are called:
Group of answer choices
Opposite angles
Adjacent angles
Vertical angles
Interior angles
Answers
how do u find the constant RATIO of the exponential curve
Answers
Answer:
We call base 2 the constant ratio. In fact, for any exponential function with the form f(x)=abx f ( x ) = a b x , b is the constant ratio of the function. This means that as the input increases by 1, the output value will be the product of the base and the previous output, regardless of the value of a.
Step-by-step explanation:
Notice from the table that:
the output values are positive for all values of x
as x increases, the output values increase without bound
as x decreases, the output values grow smaller, approaching zero
The graph below shows the exponential growth function
f(x)=2x
- sinx
dy/dx = ?
cosx or -cosx?
Answers
Step-by-step explanation:
y=-sinx
dy/dx = d(-sinx)/dt= -cosx
hope it helps
Answer:
[tex]y = - \sin(x) \\ \frac{dy}{dx} = - \frac{d}{dx} ( \sin(x) ) \\ \boxed{ \frac{dy}{dx} = - \cos(x) }[/tex]
dy/dx = -cos(x) is the right answer.Evan measured a house and made a scale drawing. The scale of the drawing was 3 centimeters = 7 meters. What is the scale factor of the drawing? Simplify your answer and write it as a fraction.
Answers
what is the value of X in the equation 3X -1/9 Y equals 18 Y equals 17
Answers
Answer:
5.70
Step-by-step explanation:
18y=17 then y=17/18
3x-1/9y=18y
3x-1/9×17/18=18×17/18
x=2771/486
x=5.70
Least common denonminator of 9 over 10 and 4 over 5
Answers
Answer:10!
Step-by-step explanation: Rewriting input as fractions if necessary: 9/10, 4/5 For the denominators (10, 5) the least common multiple (LCM) is 10. LCM (10, 5)Therefore, the least common denominator (LCD) is 10. Calculations to rewrite the original inputs as equivalent fractions with the LCD: 9/10=9/10×1/1=9/104/5=4/5×2/2=8
f(x)=2x^3-7x^2-10x+24
•use factor theorem to show that (x+2) is a factor of f(x)
f(x)=2x^3-7x^2-5x+4
•find the remainder using synthetic division when f(x) is divided by (x-1)
•use factor theorem to show that (x+1) is a factor of f(x)
Answers
Answer:
Solved in the diagram
Needs to be 20characters long
Steve spent 1/4 of his monthly salary for rent and 1/7 of his monthly salary for his utility bill. If $867 was left, what was his monthly salary?
Answers
Answer:x=(45/31)*1426=$2070. ANSWER
20% of that is $414
1/9 of that is $230
They add to $644
What is left is $1426.
Step-by-step explanation:
Answer:1428
Step-by-step explanation:
x−1128x
=867
(1−1128)x
=867
Factor out x.
1728x
=867
Simplify.
x
=1428
Solve for x.
Classify: d + 53
a. variable expression
b. numerical expression
Answers
Answer:
a variable expression
Step-by-step explanation:
because it consists unknown variable d
which is the equation of a parabola with vertex (0,0) that opens to the left and has a focal width of 12? please select the best answer from the choices provided
Answers
Answer:
Mention any Two study routes(courses or program) that higher education could offer.
hmm i get it very well then thanks alot
Answers
Answer:
B. 1002
Step-by-step explanation:
0.o :P XD :V
Which statements are true when solving x^2=81
Answers
Answer:
d.) the only solution is 9.
Step-by-step explanation:
The only way to solve this equation is to get the square root:
x^2 = 81
[tex]\sqrt{x^2}[/tex] = [tex]\sqrt{81}[/tex]
x = 9
The square root of 81 is 9 and the square root of x^2 is just x.
Please mark me the brainliest!?!
Answer:nahh , had that question & i picked "D" but it said its E & A.
Step-by-step explanation: