Solve the following system of equations by substitution. Show all steps.
f (x) = -x^{2} + 2x +3
g (x) = -2x + 3
Answers
Answer:
Given system of equations:
[tex]\begin{cases}f(x)=-x^2+2x+3\\g(x)=-2x+3\end{cases}[/tex]
To solve by substitution, equate the equations and solve for x:
[tex]\begin{aligned}f(x) & = g(x)\\\implies -x^2+2x+3 & = -2x+3\\-x^2+4x & = 0\\x^2-4x & = 0\\x(x-4) & = 0\\\implies x & = 0\\\implies x-4 & = 0 \implies x=4\end{aligned}[/tex]
Therefore, the x-values of the solution are [tex]x = 0[/tex] and [tex]x = 4[/tex].
To find the y-values of the solution, substitute the found values of x into the functions:
[tex]f(0)=-(0)^2+2(0)+3=3[/tex]
[tex]g(0)=-2(0)+3=3[/tex]
[tex]f(4)=-(4)^2+2(4)+3=-5[/tex]
[tex]g(4)=-2(4)+3=-5[/tex]
Therefore, the solutions to the given system of equations are:
[tex](0, 3)[/tex] and [tex](4, -5)[/tex]
Related Questions
These tables represent a quadratic function with a vertex at (6, 8). Which is the average rate of change for the interval from x = 13 to x = 14?
Answers
The average rate of a function is 81 if a quadratic function with a vertex at (6, 8).
What is a function?It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
We have:
Quadratic function with a vertex at (6, 8).
It is required to find the average rate of the function:
Here the data table is not given, so we are assuming the value of a function:
At x = 13 is 196
f(13) = 144
At x = 14 is 225
f(14) = 225
The average rate of a function:
= [f(14) - f(13)]/(14 - 13)
= [225 - 144]/(1)
= 81
Thus, the average rate of a function is 81 if a quadratic function with a vertex at (6, 8).
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how do u turn decimals into fractions
Answers
Answer:
place the decimal number over its place value
Step-by-step explanation:
For example in 0.4 the four is in the tenths place, so we place 4 over 10 like 4/10
Answer:
Step-by-step explanation:
Decimal to fraction: Write the decimal number with denominator 1Now , multiply the numerator and the denominator by 10 for every number after the decimal point.SimplifyExample:
4.52
[tex]4.52 =\dfrac{4.52}{1}[/tex]
In 4.52, there are two decimal places. So multiply the numerator and denominator by 100
[tex]\dfrac{4.52*100}{1*100}=\dfrac{452}{100}=\dfrac{452 \div 4}{100 \div 4}=\dfrac{113}{25}[/tex]
7x + 2y = −12
3x + 4y = −24
Answers
Answer:
x= 0 , y= 6
Step-by-step explanation:
multiplying 1st equation by 2 and subracting equation 2nd from 1st
14x + 4y = -24
- ( 3x + 4y) = - (-24)
11x = 0
so, x=0
keep x=0 in equation 2nd
3*0 + 4y = -24
y = -24 / 4
so , y = 6
Y’all pls help I’m gunna cry
Answers
First Quartile = 57
Third Quartile = 62
i need help with the area only for 7 8 and 9
Answers
We will get the areas of each one of the given triangles:
7) A = 12.69 mm²
8) A = 19.21 in²
9) A = 16.81 yd²
How to get the area of the given triangles?
7) First, we have an equilateral triangle, where all the sides measure 5.4mm
For an equilateral triangle of side length S, the area is:
[tex]A = \frac{\sqrt{3} }{4}S^2[/tex]
In this case, S = 5.4 mm, replacing we get:
[tex]A = \frac{\sqrt{3} }{4}(5.4mm)^2 = 12.62 mm^2[/tex]
8) Now we have two equal sides and one different. The general area of a triangle of base B and height H is:
A = B*H/2.
In this case, the base measures 3.4 in.
To get the height, let's divide the triangle into two right triangles, such that one cathetus is 3.4in/2 = 1.7 in.
The hypotenuse measures 5.9 in
And the other cathetus is the height of the triangle.
Then, by using the Pythagorean theorem, we see that the height is:
[tex]H = \sqrt{(5.9 in)^2 - (1.7in)^2} = 5.65 in[/tex]
Then the area of this triangle is:
[tex]A = (3.4 in)*(5.65 in)/2 = 19.21 in^2[/tex]
9) Here the base measures 8.2 yds, and the height 4.1 yds, so the area is just:
[tex]A = (4.1 yd)*(8.2 yd)/2 = 16.81 yd^2[/tex]
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Given that the measure of ∠x is 66°, and the measure of ∠y is 66°, find the measure of ∠z
Answers
Answer:
48
Step-by-step explanation:
66*2=132
180-132=48
Hope this helps!
If not, I am sorry.
what types of angles are in these quadrilaterals iready level d
Answers
Based on the quadrilaterals given, the types of angles that we see are Acute and Obtuse.
Which angles are shown in these quadrilaterals?Acute angles are those that are less than 90° and these are shown in the trapezium quadrilateral.
Obtuse angles are higher than 90° and so are drawn outwards as seen in the parallelogram.
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2. Draw a diagram to show that 5(x + 2) = 5x + 10.
Answers
Step-by-step explanation:
5(x+2)
1. Distributive property
2. Multiply
(5*x) + (5*2)
(5x)+(10)
Remove parenthesis
5x+10 ;
Therefore, 5(x+2) = 5x+10
Hopefully this helps! :3
How many lines of symmetry does this figure have?
1
2
4
3
Answers
The number of lines of symmetry for the given figure will be 4.
What is symmetry?Symmetry is described in geometry as a balanced and proportionate likeness between two halves of an object.
As we know that similarity is defined as when the image is divided into two halves and one portion is completely overlapped by the other.
So in the given figure, the figure can be divided into two halves by drawing four lines along with the arrows and along with the corners. In all cases, the two halves overlap with the other.
Therefore the number of lines of symmetry for the given figure will be 4.
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Marcella bought a 300 pack of candied chocolates. she randomly picked out 30 candies. the results
were 8 green, 11 blue, 6 yellow, and 5 brown. how many of each color do you think is in the bag
Answers
Answer:
there are 75 colors of each candy
Step-by-step explanation:
300÷4=75
What method can be used?
Answers
Answer:
'''
Step-by-step explanation:
Solve the system of equations.
Answers
Answer:
The answer is the third bullet. (number 3)
Describe how you would simplify the given expression.
(20x^5y^2/5x^-3y^7)^-3
Answers
Answer:
hope you can understand
what is the solution to the equation 1/5n=3
a n=8
b n=15
c n=25
d n=125
Answers
Answer:
[tex]\huge\boxed{\sf n = 15}[/tex]
Step-by-step explanation:
Given Equation:[tex]\displaystyle \frac{1}{5} n = 3\\\\Multiply \ 5 \ to \ both \ sides\\\\n = 3 \times 5\\\\n = 15\\\\\rule[225]{225}{2}[/tex]
The average cost of tuition plus room and board for a small private liberal arts college is reported to be $9,500 per term, but a financial administrator believes that the average cost is higher. a study conducted using 350 small liberal arts colleges showed that the average cost per term is $9,845. the population standard deviation is $1,200. let α = 0.05. what is the p-value for this test?
Answers
Factorize the following perfectly:
1) 9x^4-16y^439
2) 64x^4+y^4
Answers
Answer:
neither can be factored any further but if it is (9x^4) - (16y^4) it can be factored down to ((3x^2)+(4y^2)) ((3x^2)+(4y^2))
Step-by-step explanation:
13 - r < 82
PLA I NEED THIS
Answers
Answer:
r > -69
Step-by-step explanation:
13 - r < 82
subtract 13 from both sides
13 - r - 13 < 82 - 13
- r < 69
to flip the inequality sign, multiply both side by -1 to make r positive:
- r (-1) < 69 (-1)
r > -69
[tex]\rule{50}{1}\large\textsf{\textbf{\underline{Question:-}}}\rule{50}{1}[/tex]
13-r<82
[tex]\rule{50}{1}\large\blue\textsf{\textbf{\underline{Answer and how to solve:-}}}\rule{50}{1}[/tex]
First of all, we need to isolate r (get r by itself). What I Mean by that is
We need to get r by itself on one side of the inequality.
So it should look something like this:-
r<___
So r is all by itself.
How will we get r by itself? Well, First of all, we need to subtract 13 on both sides:-
[tex]\longmapsto\bf{-r < 82-13[/tex]
Simplifying,
[tex]\longmapsto\bf{-r < 69}[/tex]
Now, is r by itself? Nopes, There's also a minus sign next to it , which indicates that r is multiplied by -1.
So we do the opposite operation and divide both sides by -1:-
(watch what happens)
[tex]\longmapsto\bf{r > -69}[/tex]
The inequality sign changed from "less than" to "greater than".
This happened because we divided by a negative number on both sides.
Good luck with your studies. [tex]\ddot\smile[/tex]#TogetherWeGoFar
[tex]\rule{300}{1}[/tex]
Which of the following best describes /JKL?
32°
L
K
Answers
The best statement that describes the angle JKL is inscribed angle.
What is an inscribed angle?An inscribed angle in a circle is formed by two chords that have a common end point on the circle. The chord JK and LK intersect in the circle.
The angle ∠JKL is not an obtuse angle because it's less than 90 degrees.
The angle ∠JKL is not a vertical angle because it's not vertically opposite any angle.
The angle ∠JKL is not a central angle because it was not from from the centre of the circle.
The angle is an inscribed angle because it was formed by the intersection of two chords in the circle.
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1. The area of a rectangular carpet is X² + X - 2. HINT: Area = length X breadth
a). if X is a whole number, use factorization to find the length and the breadth of the carpet in terms of X.
b). if X = 2 m, find the actual dimensions of the carpet.
c). it costs R50 per square metre to make such this carpet. how much will it cost to manufacture 5 carpets?
Answers
Answer:
a) Length= (x+2) and breadth=(x-1) b) 4 m^2 c) R1000
Answer:
answers in photo / +explanation
Step-by-step explanation:
a)
length: x+2
width/breadth: x-1
b)
length: 4m
width/breadth: 1m
area: 4m²
c)
R1000
the diagram is not drawn to scale!!
pls
Answers
Answer:
135°
Step-by-step explanation:
That triangle in the corner is an right angle isosceles triangle as that line the midpoint of both sides :
the base angle of this triangle (x) will be :
180 = 90 + 2x
90 = 2x
x= 45
Angles on a straight line add up to 180. So to work out a :
180 = 45 + a
135 = a
Hope this helped and brainliest please
Which of the expressions are equivalent to the one below? (5x1)-7
Answers
Answer:
-2
Step-by-step explanation:
[tex](5 \times 1) - 7 \\ 5 - 7 \\ - 2[/tex]
An elevator began in the 9th floor. It went down 7 floors. Then, it went up 4 floors. On which floor did it stop?
Answers
Answer: Hope this helps you!
6th floor
Step-by-step explanation:
If it starts on the 9th floor and goes down 7 floors that is:
9 (9 floors) + -7 (down 7 floors)
which is also equal to 9-7
9-7 = 2
Next, we need to go up by 4 floors starting with 2, 2+4
2+4 = 6
Brainliest?
The area of a newspaper page (opened up) is about 640.98 square inches. Determine the length and width of the page if its length is about 1.25 times its width.
The width of the page is ___ inches.
Answers
.✎let's answer it :3
question ⇩
✎ The area of a newspaper page (opened up) is about 640.98 square inches. Determine the length and width of the page if its length is about 1.25 times its width.
The area of a newspaper page (opened up) is about 640.98 square inches. Determine the length and width of the page if its length is about 1.25 times its width.The width of the page is ___ inches.
answer ➡ 1.24 incheshope it helps
correct me if I am wrong
by #galadohannadivine29how do we solve this I need a quick answer please :)
Answers
Sorry don't no the answer
sorry if I kwon the answer
I telling u the answer
Explanation: Key word, boundary. Meaning its perimeter of the field. Find the perimeter then multiply by 3. inches
A brand of cereal had 1.2 milligrams of iron per serving. Then they changed their recipe so they had 1.8 mg of iron per serving.
Answers
Using it's concept, it is found that the percent increase in the amount of iron per serving was of 50%.
What is the percentage increase of a value?It is given by the increase divided by the initial value, and subtracted by 100%.
In this problem:
The initial value is of 1.2 mg.The increase was of 1.8 mg - 1.2 mg = 0.6 mg.Hence the percent increase is given by:
P = 0.6/1.2 x 100% = 50%.
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Need help with the question
Answers
Answer:
y = 3
Step-by-step explanation:
given that y varies directly with x then the equation relating them is
y = kx ← k is the constant of variation
to find k use the condition y = 57 when x = 19 , then
57 = 19k ( divide both sides by 19 )
3 = k
y = 3x ← equation of variation
when x = 1 , then
y = 3 × 1 = 3
Question
What expression represents the area of the square?
Answers
(3x-2)^2
squares area is 2 times its side length, since all the sides are the same. if the side length is 3x-2, take its second power
The area of a square is the product of the length of each side with itself. That is, Area A = s x s where s is the length of each side of the square.
In a recent study on world happiness, participants were asked to evaluate their current lives on a scale from 0 to 10, where 0 represents the worst possible life and 10 represents the best possible life. The mean response was 5.4, with a standard deviation of 2.3.
(a) What response represents the 86th percentile? (Round to two decimal places as needed).
(b) What response represents the 55th percentile? (Round to two decimal places as needed).
(c) What response represents the first quartile? (Round to two decimal places as needed).
Answers
The response that represents the 86th percentile is 7.884
The response that represents the 55th percentile is 5.69
The response that represents the first percentile 3.85
How to solve for the 86th percentilemean = 5.4
sd = 2.3
p(X>x) = 0.86
find the value of z using the NORMSINV function in excel with a probability of 0.86
z = 1.080
x = mean + sd*z
= 5.4 + 2.3 * 1.080
= 7.88
How to solve for the 55th percentilemean = 5.4
sd = 2.3
p(X>x) = 0.55
find the value of z using the NORMSINV function in excel with a probability of 0.55
z = 0.1257
x = mean + sd*z
= 5.4 + 2.3 * 0.1257
= 5.69
c. The first quartile is 25%
z = -0.6745
5.4 + 2.3 * -0.6745
= 5.4-1.551
= 3.85
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PLS HELP NEED THIS ASAP
Answers
The probability that the dog that's selected will weigh less than 30 pounds will be 55%.
How to calculate probability?From the information given, it was stated that 45% of the dogs weigh more than 30 pounds. Therefore, the probability that the dog that's selected will weigh less than 30 pounds will be:
= 1 - 45%
= 55%
The probability that it weighs more than 30 pound given that it has long fur will be 27%.
The events are independent since the occurence of one doesn't affect the other one.
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-8x - 5y = 12
8x - y = 12