JIMMMM! :)
Part A: Explain why the x-coordinates of the points where the graphs of the equations y = 2^x and y = 4^x−2 intersect are the solutions of the equation 2^x = 4^x−2. (4 points)
Part B: Make tables to find the solution to 2^x = 4^x−2. Take the integer values of x between −4 and 4. (4 points)
Part C: How can you solve the equation 2^x = 4^x−2 graphically? (2 points)
Answers
The x coordinates are the inputs of the functions f(x) = 2^x and g(x) = 4^(x-2)
If we have some input x that leads to f(x) = g(x), then this x value is a solution. It makes the equation f(x) = g(x) true. This is why the x coordinate of the intersection point of y = 2^x and y = 4^(x-2) is the solution.
-------------------------------------------------------------------------
Part B
See attached for the table. See figure 1.
This is how you get the results you see in the table
Plug x = -4 into f(x) to get:
f(x) = 2^x
f(-4) = 2^(-4)
f(-4) = 0.0625
Do the same for g(x):
g(x) = 4^(x-2)
g(-4) = 4^(-4-2)
g(-4) = 4^(-6)
g(-4) = 0.000244140625
-------------------
Plug x = -3 into f(x) to get:
f(x) = 2^x
f(-3) = 2^(-3)
f(-3) = 0.125
Do the same for g(x):
g(x) = 4^(x-2)
g(-3) = 4^(-3-2)
g(-3) = 4^(-5)
g(-3) = 0.0009765625
-------------------
Plug x = -2 into f(x) to get:
f(x) = 2^x
f(-2) = 2^(-2)
f(-2) = 0.25
Do the same for g(x):
g(x) = 4^(x-2)
g(-2) = 4^(-2-2)
g(-2) = 4^(-4)
g(-2) = 0.00390625
-------------------
Plug x = -1 into f(x) to get:
f(x) = 2^x
f(-1) = 2^(-1)
f(-1) = 0.5
Do the same for g(x):
g(x) = 4^(x-2)
g(-1) = 4^(-1-2)
g(-1) = 4^(-3)
g(-1) = 0.015625
-------------------
Plug x = 0 into f(x) to get:
f(x) = 2^x
f(0) = 2^(0)
f(0) = 1
Do the same for g(x):
g(x) = 4^(x-2)
g(0) = 4^(0-2)
g(0) = 4^(-2)
g(0) = 0.0625
-------------------
Plug x = 1 into f(x) to get:
f(x) = 2^x
f(1) = 2^(1)
f(1) = 2
Do the same for g(x):
g(x) = 4^(x-2)
g(1) = 4^(1-2)
g(1) = 4^(-1)
g(1) = 0.25
-------------------
Plug x = 2 into f(x) to get:
f(x) = 2^x
f(2) = 2^(2)
f(2) = 4
Do the same for g(x):
g(x) = 4^(x-2)
g(2) = 4^(2-2)
g(2) = 4^(0)
g(2) = 1
-------------------
Plug x = 3 into f(x) to get:
f(x) = 2^x
f(3) = 2^(3)
f(3) = 8
Do the same for g(x):
g(x) = 4^(x-2)
g(3) = 4^(3-2)
g(3) = 4^(1)
g(3) = 4
-------------------
Plug x = 4 into f(x) to get:
f(x) = 2^x
f(4) = 2^(4)
f(4) = 16
Do the same for g(x):
g(x) = 4^(x-2)
g(4) = 4^(4-2)
g(4) = 4^(2)
g(4) = 16
Note that since the input x = 4 leads to the same output (16) this makes x = 4 a solution.
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Part C
To solve graphically, you need to use the table in part B to draw a curve through the set of points. Then determine where the curves cross (if they cross at all). You may need to adjust the graph window if the intersection point is off the screen.
See figure 2 for the graph (attached as well). Point A in green is the intersection point.
A = (4,16)
so x = 4 is the solution to f(x) = g(x).
Part A: The point or points of intersection are the values of the variables which satisfy both equations at a particular point.
If [tex]y=2^x and y=4 ^{x-2} [/tex] and the solution of which will satisfy both equations. This idea of equating the two equations is something that you would have come across before, maybe without realizing it.
Consider this:
[tex]x^2 + 6x + 9=0 This can also be looked at as being the two equations: y=x^2 +6x+9 and y=0 [/tex]
So the points of intersection are the roots in this case and satisfy the equation:
[tex]x^2 + 6x +9=0 This explains why it will be the solution to: 2^x = 4 ^{x-2} , because this is the equation formed at the intersection.[/tex]
Part B:
You just put integer values between -4 and 4 in each equation and when the output is the same for both that is the solution.
[tex]2^ ^{-4} = 0.0625 , [/tex] and [tex]4 ^{-6} = 0.000244[/tex]
[tex]2 ^{-3} = 0.125, [/tex] [tex]4 ^{-5} =0.000977[/tex]
[tex]2 ^{-2} =0.25[/tex] and [tex]4 ^{-4} =0.003906[/tex]
[tex]2 ^{-1}= -0.5,[/tex] and [tex]4 ^{-3} =0.01563[/tex]
[tex]2^0 =1[/tex] , and [tex]4 ^{-2} =0.0625[/tex]
[tex]2^1 = 2 [/tex] and [tex]4 ^{-1} =0.25[/tex]
[tex]2^2 =4 [/tex] and [tex]4^0 =1[/tex]
[tex]2^3 =8[/tex] and [tex]4^1=4[/tex]
[tex]2^4 =16, [/tex] and [tex]4^2 = 16 [/tex] (This is the solution when x=4)
Part C:
To solve graphically you just plot the two equations [tex]=2^x[/tex] and [tex]y=4 ^{x-2} [/tex]
Together graph of [tex]y=2^x [/tex] and [tex]y=4 ^{x-2} [/tex]
The picture below is how the graph looks like.
Full Credit to my online calculator 'cause we don't have a graphing calculator here.
I hope I helped!
Related Questions
*PLEASE HELP* BRAINLIEST* A 10% discount is offered on a certain item that sells for $10.95. How much is the discount and what is the discounted sales price?
Amount of discount =
Discounted sales price =
Answers
The amount of discount is $1.095 and the discounted sales price is $9.855.
We need to calculate the amount of discount and then subtract it from the original sales price to find the discounted sales price.
First, we calculate the amount of discount. A 10% discount on an item selling for $10.95 means we need to find 10% of $10.95. To find 10% of a number, we can multiply the number by 0.10 (which is the decimal equivalent of 10%).
Amount of discount = 10% of $10.95
= 0.10 [tex]\times[/tex] $10.95
= $1.095
Now that we have the amount of discount, we can calculate the discounted sales price by subtracting the discount from the original sales price.
Discounted sales price = Original sales price - Amount of discount
= $10.95 - $1.095
= $9.855
Plz help with math. will reward.
Answers
2. A
3.A
4. I got -32, so i'm pretty sure all of my other answers are wrong because this time my answer isn't even in the choices.
I'm not even sure how to the rest, so instead, just find a helpful youtube video instead of seeking answers. I tried dude!
Which of the following shows the length of the third side, in inches, of the triangle below?
A right triangle is shown. One side of the triangle is labeled shown as 97 inches. The height of the triangle is labeled as 65 inches.
Square root of 32
72
Square root of 13634
16
Answers
97^2 = 65^2 +x^2
9409 = 4225 +x^2
9409 -4225 = 5184
Sqrt(5184) = 72
length of missing side = 72 inches
5. 7x + 2 + 4y Identify the terms
I'm sorry... I'm a dumb person and these confuse me the most
Answers
I hope that's what you were looking for
A meteor crater is 3000 feet in diameter. Approximate the distance around the crater use 3.14 for pi
Answers
The formula for circumference is pi x diameter.
C= pi x d
C= 3.14 x 3000
C= 9420 feet
the volume of the sphere is increased by 72.8%. what is the percentage increase in the radius?
Answers
Final answer:
The volume of a sphere increases by 72.8%, which after calculations, results in a 20% increase in the radius of the sphere.
Explanation:
The volume of a sphere is given by the formula V = (4/3)πr³, where r is the radius of the sphere. An increase in volume by 72.8% implies that the new volume V' is equal to 1.728 times the original volume V. To find the percentage increase in the radius, we use the relationship between volume and radius:
V' = (4/3)πr'^3, where r' is the new radius after increase. Since V' = 1.728V, we have:
1.728 (4/3)πr³ = (4/3)π[tex]r'^3[/tex]Therefore, [tex]r'^3[/tex] = 1.728r³.After taking the cube root of both sides, we obtain:
r' = ∛1.728 * r ≈ 1.200 * rThus, the new radius is approximately 120% of the original radius, which means there is a 20% increase in the radius.
Final answer:
To calculate the percentage increase in the radius of the sphere when the volume is increased by 72.8%, we can use the formula for volume and solve for the new radius in terms of the original radius. The percentage increase in radius is then calculated by comparing the new and original radius.
Explanation:
The volume of a sphere is given by the formula V = (4/3)πr³, where r is the radius of the sphere. If the volume of the sphere is increased by 72.8%, we can calculate the new volume by multiplying the original volume by 1 + 0.728. Let's denote the original radius as r1 and the new radius as r2.
The formula for volume can be written as V = (4/3)πr³. Substituting r1 and r2 into the formula, we get:
Original volume: V1 = (4/3)πr1³New volume: V2 = (4/3)πr2³Since the two volumes are related by the percentage increase (1 + 0.728), we can write the equation:
(1 + 0.728)V1 = V2
Now, let's solve for r2 in terms of r1:
(1 + 0.728)V1 = (4/3)πr2³
r2 = ([(1 + 0.728)V1] * (3/4π))^(1/3)
Finally, we can calculate the percentage increase in the radius by comparing r2 to r1:
Percentage increase in radius = (r2 - r1) / r1 × 100%
I have a math question
Answers
For
the first question; we have a problem dealing with translations.
Our goal is to translate
the word problem into an algebraic one. So our numbers are
60, 2, and 5. Our variable, or the letter holding the unknown
number's place
value, is
N.
The
problem states that 60 is MORE THAN the PRODUCT of 5 and N. Focus
on the words I bolded and capitalized. These are your key words that
tells you what operations
you need to use. Note that 'product' signals the operation of
multiplication (Since the answer you get from multiplying numbers is
called the 'product'.) and
'more than' signals the operation of addition (Because you are left
off with more than you originally had before adding).
Now
that we know that our algebraic expression contains multiplication,
addition, letter N and the numbers 2 and 5; we can start plugging the
numbers in.
60
= 2 (more than) + (product of) 5N. The answer for the first
attachment is
B.
_____________________________________________________________
All
we need to do for the AB problem (Question 25 on your material) is
solve AB.
Note
1: When a problem has no operation separating two letters or numbers,
this means multiplication.
Note
2: A and B are variables. Variables are letters that stand for and
hold the place of our unknown quantities. However, the values are not
unknown anymore given the fact that the question tells us that A= 42
and B = 2. Thus we substitute A with 42 and B with 2, then work from
there. 42 * 2 =84. Answer = A.
____________________________________________________________________
And
finally, for question 26, we use PEMDAS. P = parenthesis (), E =
exponent x^2, M/D = x or /, A/S means + or subtraction.
According to PEMDAS, we first solve what's parenthesis, which is 77 – 32. Using mental math, 77 – 32 = 45. ( 7 – 3 = 4 and 7 – 2 = 5.). 5/9 * 45 is what we have left. 5 divided by 9 =0.5555555555555556. 0.5555555555555556 * 45 = 25. Answer is D.
How many yards equals 765 inches?
Answers
1 yard = 3 feet
1 foot = 12 inches
so 36 inches = 1 yard
765 / 36 = 21.25 yards
i think of a number, multiply it by 3 and add 4 and i get 22
form an equation, using x for the unknown number and then solve it
Answers
B) x=6
How to solve the equation: subtract 4 from both sides. You’re left with 3x=18. What is 18 divided by 3?
The student's clues form the equation 3x + 4 = 22. When solved, this equation reveals that the original number x is 6.
Explanation:The student is creating an algebraic equation to find an unknown number. Starting with the clues given:
They think of a number (which we represent with x)Multiply the number by 3 (3x)Add 4 (3x + 4)The result is 22 (3x + 4 = 22)Now, we can solve this equation to find x:
Start by subtracting 4 from both sides of the equation (3x + 4 - 4 = 22 - 4)Simplify to get 3x = 18Then divide both sides by 3 (x = 18/3)This gives us x = 6 as the unknown numberLearn more about Algebra here:https://brainly.com/question/24875240
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If s = -5 and t = 3, find the value of s^2t.
225
75
30
-75
Answers
Then 25*t = 25*3 =75
Answer:
75
Step-by-step explanation:
Write down in the terms of n, an expression for the nth term of the following sequences:
a.) 23, 20, 17, 14, 11
b.) 36, 30 24, 18, 12
Answers
Problem 4 the measure of the largest angle of a triangle is 90◦ more than the measure of the smallest angle, and the measure of the remaining angle is 30◦ more than the measure of the smallest angle. find the measure of each angle. showyourwork in obtaining your answe
Answers
_________________________________________________________
Explanation:
________________________________________________________
Note: There are 3 (three) angles in any triangle (by definition).
By definition, all the angles in any triangle add up to 180° .
________________________________________________________
The problems asks us to find the measure of EACH angle of the triangle.
We can set up an equation; given the information in the problem; to solve for the measure of EACH of the 3 (THREE) angles in the triangle:
________________________________________________________
→ " x + (x + 90) + (x + 30) = 180 " ;
_____________________________________________
in which: "x" is the measure of one of the angles;
(specifically, the smallest angle) in the triangle;
"(x + 90)" is the measure of another one of the angles in the triangle;
"(x + 30)" is the measure of another one of the angles in the triangle;
___________________________________________________________
By solving for "x" in the equation; we can solve for the measures of all the angles in the triangle;
_________________________________________________
→ x + (x + 90) + (x + 30) = 180 ;
x + x + 90 + x + 30 = 180 ;
→ 3x + 120 = 180 ;
______________________________________
Subtract "120" from each side of the equation ;
3x + 120 − 120 = 180 − 120 ;
to get: 3x = 60 ;
________________________________
Now, divide EACH SIDE of the equation by "3" ; to isolate "x" on one side of the equation ; and to solve for "x" ;
3x = 60 ;
3x / 3 = 60 / 3 ;
x = 20 ;
_________________________________________
Now, we have the original equation:
__________________________________
x + (x + 90) + (x + 30) = 180 ;
in which: x = 20° {the smallest angle) ;
"(x + 90)" = "(20 + 90) = 110° ;
"(x + 30)" = "(20 + 30)" = 50° ;
__________________________________________________________
Answer: The measurements of the angles are: 110° ; 50° ; 20° .
__________________________________________________________
To check our work:
20 + 110 + 50 =? 180 ?? ; → 130 + 50 =? 180 ?? ; → Yes!
_____________________________________________________
If a solid has faces that consist of 2 equilateral triangles and 3 congruent rectangles, what type of solid is it?
A. regular hexagonal prism
B. right rectangular prism
C. right triangular prism
D. triangular pyramid
Answers
The following data show the number of questions different students of a class could answer in a quiz competition:
2, 4, 2, 5, 1, 4, 5, 7, 3, 5, 6, 2, 2, 5, 5, 5, 4, 6
The dot plot below was made to represent the data.
For which number is the data plotted incorrectly?
2 3 4 5
Answers
There is one 1....so the one dot over the 1 is correct
There are four 2's....so the 4 dots over the 2 is correct
There is one 3....so 1 dot over 3 is correct
There are three 4's...but u only have 2 dots over the 4 when there should be 3....so ur answer is going to be 4 <==
Answer:
Number 4 plot incorrectly represent on dot plot.
C is correct
Step-by-step explanation:
The following data show the number of questions different students of a class could answer in a quiz competition:
2, 4, 2, 5, 1, 4, 5, 7, 3, 5, 6, 2, 2, 5, 5, 5, 4, 6
We are given the dot plot of the data set.
Data : 1 2 3 4 5 6 7
Frequency : 1 4 1 3 6 2 1
We need to choose which data number plot incorrectly.
For 2: Number of dot should be 4, In graph also 4, 4=4 (True)
For 3: Number of dot should be 1, In graph also 1, 1=1 (True)
For 4: Number of dot should be 3, In graph also 2, 3≠2 (False)
For 5: Number of dot should be 6, In graph also 6, 6=6 (True)
Hence, number 4 plot incorrectly
Chad owns twice as many cds as carlin owns. if you add 6 to the number of cds chad owns and then divide by 7, you get the number of cds bryce owns. bryce owns 30 cds. how many cds does carlin own?
Answers
An equation is formed of two equal expressions. The number of CDs owned by Carlin is 102.
What is an equation?An equation is formed when two equal expressions are equated together with the help of an equal sign '='.
Given the following points:
Chad owns twice as many CDs as Carlin owns. if you add 6 to the number of CDs chad owns and then divide by 7, you get the number of CDs Bryce owns. Bryce owns 30 CDs.Let the variables represent the following numbers as shown,
CDs owned by Chad = M.Cds owned by Carlin = NCDs owned by Bryce = OThe number of CDs owned by Chad.
M = 2N ______(1)
The number of CDs owned by Carlin.
= N ________(2)
The number of CDs owned by Bryce.
O = (6+2N) / 7
And O = 30
30 = (6 + 2N) / 7 ________(3)
From (3), the value of N can be written as,
30 = (6 + 2N) / 7
Multiply both sides by 7
30 x 7 = 6 + 2N
210 = 6 + 2N
Subtract 6 on both sides.
210 - 6 = 6 + 2N - 6
204 = 2N
Divide both sides by 2.
102 = N
N = 102
Thus, the number of CDs owned by Carlin is 102.
Learn more about Equation here:
https://brainly.com/question/14686792
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The area of a round mat is 64 pi square inches. what is the diameter of the mat
Answers
64*pi = pi * radius^2
64 = radius^2
radius = 8 inches
Therefore the diameter is 16 inches.
1. What point is the image of (4,5) with a translation of right 2 and down 3?
2. Find B' in a reflection of Triangle ABC when A(3,6), B(-4,2), C(-1,-3) over the y axis.
3. Which axis is (0,7) on?
A. X axis
B. Y axis
Answers
4 + 2 = 6
so now it is (6,5)
Down 3, is for they y axis
5 - 3 = 2
so now it is (6,2) which is your answer
When reflected over the y axis, you will be changing your x, and vice versa.
for B(-4,2), it will become B(4,2) For A, it will go from (3,6) to (-3,6), etc.
3. (0,7), when graphed will be located on the y axis
hope this helps
original cost: 1.25; Markup %:80
Answers
To find out 80% of 1.25, you need to convert 80(%) to a decimal. You can do this by dividing 80 by 100.
80/100 = 0.8
Add this to the original cost.
1.25 + 0.8 = 2.05
Your total cost in the end would be $2.05
80/100=0.8
1.25x0.8=1
1.25+1=2.25
The new price would be $2.25
Hope this helps!
Solve this Multi-Step Equation: (Show your work)
-3(t + 5) + (4t + 2) = 8
Answers
2t-12=8
2t = 20
t = 10
What is the solution of the system of equations?
-3x-4y-3z=-7
2x-6y+2z=3
5x-2y+5z=9
Answers
Let's begin with eliminating the y's in equations 1 and 3, then in equations 2 and 3:
[tex]-3x-4y-3z=-7 [/tex] times -1⇒ [tex]3x+4y+3z=7 [/tex]
[tex]5x-2y+5z=9[/tex] times 2⇒ [tex]10x-4y+10z=18[/tex]
ADD the two equations: 13x + 13z = 25
[tex]2x-6y+2z=3[/tex] times -1⇒[tex]-2x+6y-2z=-3[/tex]
[tex]5x-2y+5z=9[/tex] times 3⇒ [tex]15x-6y+15z=27[/tex]
ADD the two equations: 13x+13z=24
Subtract the two resulting equations and you get 0 = 1 which is false so there is no solution for the system.
Answer:
Given equations have no solution
Step-by-step explanation:
Given -
Three set of equations -
[tex]-3x-4y-3z=-7\\2x-6y+2z=3\\5x-2y+5z=9[/tex]
We will now equate "x" in the first equation in terms of "y" and "Z" and put it in second equation -
[tex]-3x-4y-3z=-7\\x = \frac{1}{3} (-4y -3z+7)\\\frac{2}{3}(-4y -3z+7) -6y+2z=3\\-8.667 y = -1.667\\y = 0.192\\[/tex]
We will substitute the value of y in the under given equation-
[tex]x = \frac{1}{3} (-4y -3z+7)\\x = \frac{1}{3} (-4*0.192 -3z+7)\\x= 2.077-z[/tex]
substituting the derived values in last equation, we get -
[tex]5x-2y+5z=9\\5(2.077-z)-2(0.192)+5z=9\\10.385-5z-0.384+5z=9\\0=-1[/tex]
Hence, the given equations have no solution
Suppose an investment of $500 doubles in value every 15 years. How much is the investment after 30 years? 45 years?
Answers
2 questions
4. Each small square is 1 in². Which estimate best describes the area of this figure? (first image)
a. 10 in²
b. 15 in²
c. 20 in²
d. 35 in²
5. Which estimate best describes the area under the curve in square units? (second image)
a. 20 units²
b. 25 units²
c. 35 units²
d. 40 units²
Answers
Answer: here are the correct answers for the k12 test. Have a great day!!!
Step-by-step explanation:
Use the Remainder Theorem to determine if [tex]x-2[/tex] is a factor of the polynomial [tex]f(x)=3x^5-7x^3-11x^2+2[/tex].
Answers
Therefore it is not a factor.
Triangle XYZ is located at X (−2, 1), Y (−4, −3), and Z (0, −2). The triangle is then transformed using the rule (x−1, y+3) to form the image X'Y'Z'. What are the new coordinates of X', Y', and Z'?
Please Help Me
Answers
Which mathematical symbol would best fill in the blank to compare the two real numbers?
square root of 7 blank 14 over 5
<
>
=
≈
Answers
14 over 5 is rounded to 2.8
square root of 7 < 14 over 5
Answer: The correct option is (A) < .
Step-by-step explanation: We are given to select the correct mathematical symbol that would best fill in the blank to compare the following two real numbers :
[tex]\sqrt7~~~?~~~\dfrac{14}{5}.[/tex]
First , we need to find the values of both the real numbers in decimal form.
We have
[tex]\sqrt7=2.64575...,\\\\\dfrac{14}{5}=2.8.[/tex]
Since, [tex]2.64575<2.8,[/tex] so we get
[tex]\sqrt7<\dfrac{14}{5}.[/tex]
Thus, the correct mathematical symbol is <.
Option (A) is CORRECT.
Give an example of a linear equation perpendicular to y=5
Answers
Final answer:
A linear equation perpendicular to y=5 is a vertical line, expressed as x=c, where c is any real number. For instance, x=2 is perpendicular to y=5.
Explanation:
A linear equation perpendicular to y=5 would need to have an undefined slope, meaning it's a vertical line. Since y=5 is a horizontal line, a perpendicular line will have no slope value that we can put in terms of y=mx+b, where m represents the slope and b represents the y-intercept. Thus, the equation will be of the form x=c, where c is any real number. This represents a vertical line that crosses the x-axis at the point (c,0).
For example, the linear equation x=2 is perpendicular to y=5 and crosses the x-axis at the point (2,0).
Which are the solutions of the quadratic equation? x2 = –5x – 3 –5, 0 5, 0
Answers
Note that if x=0, both sides of the equation are equal to 0.
So x=0 is a solution.
For [tex]x\neq0[/tex], then we can divide both sides of the equation by x, and we get x=-5.
Thus, the solution set is {0, -5}.
Remark: another way to solve the equation is to take -5x to the left hand side:
[tex]\displaystyle{x^2+5x=0[/tex],
then we factorize x as
[tex]\displaystyle{x(x+5)=0[/tex].
Thus we see that x is either 0, or -5.
The solutions of the quadratic equation x² = -5x - 3 are [tex]\( x = \frac{-5 - \sqrt{13}}{2} \)[/tex] and [tex]\( x = \frac{-5 + \sqrt{13}}{2} \)[/tex].
To find the solutions of the quadratic equation x² = -5x - 3, first we rearrange it to the standard form:
x² + 5x + 3 = 0
We solve this using the quadratic formula, which is given by:
x = [tex]\frac{-b \pm \sqrt{b^2 - 4ac}}{2a}[/tex]
For our equation, a = 1, b = 5, and c = 3. Substituting these values in, we get:
x = [tex]\frac{-5 \pm \sqrt{5^2 - 4*1*3}}{2*1}[/tex]
x =[tex]\frac{-5 \pm \sqrt{25 - 12}}{2}\\[/tex]
x =[tex]\frac{-5 \pm \sqrt{13}}{2}[/tex]
Hence, the solutions are:
x = [tex]\frac{-5 - \sqrt{13}}{2}[/tex] and x = [tex]\frac{-5 + \sqrt{13}}{2}[/tex]
Complete question: Which are the solutions of the quadratic equation? x² = -5x - 3
-5, 0[tex]\frac{-5 - \sqrt{13}}{2}[/tex], [tex]\frac{-5 + \sqrt{13}}{2}[/tex][tex]\frac{5 - \sqrt{13}}{2}[/tex], [tex]\frac{5 + \sqrt{13}}{2}[/tex]5,0Find an equation of a line whose graph intersects the graph of the parabola y=x^2 at (a) two points, (b) one point, and (c) no point.
Answers
(b) y = 2x - 1
(c) y = 2x - 3
f(x)=2x + 1 and g(x) = -3x+4. Find f(x) + g(x)
Answers
(2x+1) + (-3x+4)
2x+1-3x-4
-x-3
Your answer is -x-3
What are the missing parts that correctly complete the proof?
Answers
3. AXP and AXQ ----------- Definition of perpendicular.
4. AXP=AXQ ------------- All right angles are congruent.
6. AXP=AXQ ------------ SAS congruence
7. AP=AQ -------------Corresponding parts of congruent triangles
Just took the test!!!!
The missing parts of the question is required.
The blanks are
2 Definition of bisector
3 Definition of perpendicular
4 [tex]\angle AXP=\angle AXQ[/tex]
6 SAS congruence postulate
7 Corresponding parts of congruent triangles
In the given figure.
Line AX is a perpendicular bisector of PQ.
This means [tex]PX\cong QX[/tex]
[tex]\angle AXP=\angle AXQ=90^{\circ}[/tex]
[tex]AX\cong AX[/tex] because it is the same side.
[tex]\triangle AXP\cong \triangle AXQ[/tex] because of the above three points SAS congruence.
[tex]AP\cong AQ[/tex] because they are corresponding parts of congruent triangles
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