Where do the following graphs intersect? Show how you can find the intersection point algebraically.
1) y-2x=3
2) y-3= x^2
Answers
y-2x = 3
y-2x+2x = 3+2x
y = 2x+3
Plug that into equation (2)
y - 3 = x^2
2x+3 - 3 = x^2
2x = x^2
Get everything to one side
2x = x^2
2x-2x = x^2-2x
0 = x^2-2x
x^2-2x = 0
Now factor and use the zero product property to find the solutions for x
x^2-2x = 0
x(x-2) = 0
x = 0 or x-2 = 0
x = 0 or x = 2
If x = 0, then y is...
y = 2x+3
y = 2(0)+3
y = 3
So (x,y) = (0,3) is one solution of the system. This is one point where the graphs intersect.
If x = 2, then y is...
y = 2x+3
y = 2(2)+3
y = 4+3
y = 7
So (x,y) = (2,7) is another solution to the system. This is another point where the graphs intersect.
See the attached image for a visual. The two curves cross at point A and point B
A = (0,3)
B = (2,7)
Related Questions
solve for y. 8x+y=15
Answers
y = 15 - 8x
8x = 15 + -1y
x = 1.875 + -0.125y
x = 1.875 + -0.125y
Help with geometry...
Answers
[tex]\bf \textit{distance between 2 points}\\ \quad \\ \begin{array}{lllll} &x_1&y_1&x_2&y_2\\ % (a,b) A&({{ 1}}\quad ,&{{ 2}})\quad % (c,d) G&({{ -4}}\quad ,&{{ 2}})\\ B&({{ 2}}\quad ,&{{ 3}})\quad % (c,d) H&({{ -3}}\quad ,&{{ 3}})\\ C&({{ 3}}\quad ,&{{ 1}})\quad % (c,d) G&({{ -2}}\quad ,&{{ 1}}) \end{array}\qquad % distance value d = \sqrt{({{ x_2}}-{{ x_1}})^2 + ({{ y_2}}-{{ y_1}})^2}\\\\[/tex]
[tex]\bf -------------------------------\\\\ AG=\sqrt{(-4-1)^2+(2-2)^2} \\\\\\ BH=\sqrt{(-3-2)^2+(3-3)^2} \\\\\\ CG=\sqrt{(-2-3)^2+(1-1)^2}[/tex]
and doing the distances from ABC to DEF
[tex]\bf \textit{distance between 2 points}\\ \quad \\ \begin{array}{lllll} &x_1&y_1&x_2&y_2\\ % (a,b) A&({{ 1}}\quad ,&{{ 2}})\quad % (c,d) D&({{ 1}}\quad ,&{{ -1}})\\ B&({{ 2}}\quad ,&{{ 3}})\quad % (c,d) E&({{ 2}}\quad ,&{{ 0}})\\ C&({{ 3}}\quad ,&{{ 1}})\quad % (c,d) F&({{ 3}}\quad ,&{{ -2}}) \end{array}\qquad % distance value d = \sqrt{({{ x_2}}-{{ x_1}})^2 + ({{ y_2}}-{{ y_1}})^2}[/tex]
[tex]\bf -------------------------------\\\\ AD=\sqrt{(1-1)^2+(-1-2)^2} \\\\\\ BE=\sqrt{(2-2)^2+(0-3)^2} \\\\\\ CF=\sqrt{(3-3)^2+(-2-1)^2}[/tex]
now... the ABC to JKL... surely you'd know how to do... the same way, just use the distance formula
A hypothesis is only tentative: to make sure it's valid, you have to ___________.
Answers
Which choices are real numbers? Check all that apply.
A. (-131072)^1/7
B. (-531441)^1/12
C. (-1024)^1/5
D. (-256)^1/8
Answers
[tex] \sqrt{x} [/tex]
That can be written as
x^(1/2)
...and when you take an even root of a negative number, there is no real answer. (2 is an even number).
Looking at the answer choices here, we can see that B and D use even roots, so they will give non-real answers.
So, A and C are the answer choices to select.
The real numbers are:
A. [tex]\((-131072)^{1/7}\)[/tex]
C. [tex]\((-1024)^{1/5}\)[/tex]
These have odd roots, resulting in real numbers.
To determine which of the given expressions are real numbers, we need to check if the roots of negative numbers are defined within the set of real numbers.
A. [tex]\((-131072)^{1/7}\)[/tex]
The expression [tex]\((-131072)^{1/7}\)[/tex] is the 7th root of [tex]\(-131072\)[/tex]. Since 7 is an odd number, the 7th root of a negative number is defined and is a real number.
So, [tex]\((-131072)^{1/7}\)[/tex] is a real number.
B. [tex]\((-531441)^{1/12}\)[/tex]
The expression [tex]\((-531441)^{1/12}\)[/tex] is the 12th root of [tex]\(-531441\)[/tex]. Since 12 is an even number, the 12th root of a negative number is not defined within the set of real numbers.
So, [tex]\((-531441)^{1/12}\)[/tex] is not a real number.
C. [tex]\((-1024)^{1/5}\)[/tex]
The expression [tex]\((-1024)^{1/5}\)[/tex] is the 5th root of [tex]\(-1024\)[/tex]. Since 5 is an odd number, the 5th root of a negative number is defined and is a real number.
So, [tex]\((-1024)^{1/5}\)[/tex] is a real number.
D. [tex]\((-256)^{1/8}\)[/tex]
The expression [tex]\((-256)^{1/8}\)[/tex] is the 8th root of [tex]\(-256\)[/tex]. Since 8 is an even number, the 8th root of a negative number is not defined within the set of real numbers.
So, [tex]\((-256)^{1/8}\)[/tex] is not a real number.
Summary:
- A. [tex]\((-131072)^{1/7}\)[/tex] is a real number.
- B. [tex]\((-531441)^{1/12}\)[/tex] is not a real number.
- C. [tex]\((-1024)^{1/5}\)[/tex] is a real number.
- D. [tex]\((-256)^{1/8}\)[/tex] is not a real number.
Find AB if AP and HQ are altitudes and ΔABC ~ ΔHGI
Answers
so, "x" is either 7 or 3, but the segment HQ is larger then 3, thus it cannot be 3
what's the segment AB? well, 10 - x.
Write the sum using summation notation, assuming the suggested pattern continues. -9 - 3 + 3 + 9 + ... + 81
Answers
Honestly I believe this is correct:
∑ 15 at the top, n =0 (-9+6n)
how to factor 6x^2+5x+1
Answers
Write the equation of a circle with center (-2,3) and a radius of 4. Show all work to receive credit.
Answers
(x-a)^2+(y-b)^2=r^2
where:
(a,b) is the center of the circle
given that the center of our circle is (-2,3) with the radius of 4, the equation will be:
(x+2)^2+(y-3)^2=4^2
expanding the above we get:
x^2+4x+4+y^2-6y+9=16
this can be simplified to be:
x^2+4x+y^2-6y=16-13
x^2+y^2+4x-6y=3
Question 6 jessica drive 380 miles using 14 gallons of gas. at this rate, how many gallons of gas would she need to drive 418 miles
Answers
Factor out the largest possible term.
12x^5-4x^2+16x^3= ?
(Please include steps if you can)
Answers
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Work Shown:
The GCF of the coefficients 12,-4,16 is 4
The GCF of the variable terms is x^2 since this is the smallest variable term that is found in each of x^5, x^2 and x^3
Overall, the GCF is 4x^2.
Factor each term in terms of the GCF
12x^5 = (12)*(x^5)
12x^5 = (4*3)*(x^3*x^2)
12x^5 = (4x^2)*(3x^3) <--- call this equation (1)
-------------
4x^2 = (4x^2)*(1) <--- call this equation (2)
-------------
16x^3 = (4*4)*(x^2*x)
16x^3 = (4x^2)*(4x) <--- call this equation (3)
-------------
Using those individual factorizations, we can apply the distributive property to factor out the GCF
12x^5 - 4x^2 + 16x^3
(4x^2)*(3x^3) - 4x^2 + 16x^3 ... substitute equation (1)
(4x^2)*(3x^3) - (4x^2)*(1) + 16x^3 ... substitute equation (2)
(4x^2)*(3x^3) - (4x^2)*(1) + (4x^2)*(4x) ... substitute equation (3)
4x^2*(3x^3 - 1 + 4x) ... use the distributive property
Therefore, 12x^5 - 4x^2 + 16x^3 factors to 4x^2*(3x^3 - 1 + 4x)
This means, 12x^5 - 4x^2 + 16x^3 = 4x^2*(3x^3 - 1 + 4x) is a true equation for all real numbers x.
Mario and Luigi want to purchase some extra controllers for their friends.each controller costs 29.99. Use an algebraic expression to describe how much they spend in total,before sales tax,based on purchasing the console(299.00)the number of games(59.99 each) and the number of extra controllers
Answers
A diner asked its customers, 'Did you cook dinner last night?' The results on the survey are shown in the table below: Male Female Cooked dinner 305 279 Did not cook dinner 152 459 What is the probability that one of the customers chosen from this survey was a female and cooked dinner? 0.23 0.38 0.47 0.61
Answers
Answer:
0.23
Step-by-step explanation:
ΔZAP has coordinates Z (−1, 5), A (1, 3), and P (−2, 4). A translation maps point Z to Z' (1, 1). Find the coordinates of A' and P' under this translation.
Answers
To solve this problem, we should first identify the number of units that point Z was translated. The number of units of movement of point Z should be similar to the number of units of movement of points A and P.
Let us say that the movement is Δx and Δy for horizontal and vertical translations respectively.
From Z to Z’:
Δx = 1 – (-1) = 2
Δy = 1 - 5 = - 4
Therefore the translation is in the form of (x + 2 , y – 4). Points A and P then becomes:
A’ = (1 + 2 , 3 – 4)
A’ = (3, -1)
P’ = (-2 + 2, 4 – 4)
P’ = (0, 0)
Answers:
A’ = (3, -1)
P’ = (0, 0)
Answer:
Step-by-step explanation:
lets be honest whos reading this when theres an expert answer
Which equation illustrates the additive inverse property?Select one of the options below as your answer:A. c + d = d + cB. c × d = d × cC. -c + (-c) = 0D. d + (-d) = 0
Answers
The correct option is A
c + d = d + c
I hope that helps!
so answer is
d + (-d) = 0 (last choice)
What is the answer??
Answers
hope this helps!
In how many ways can 50 cards be chosen from a standard deck of 52 cards?
Answers
The number of ways you can draw 50 cards from 52 is 52*51*50*49*48*47*...4*3 (it ends in 3).
,
But the number of ways that those 50 cards form the same set repeats is 50! = 50*49*49*47*....3*2*1
So, the answer is (52*51*50*49*48*....*3) / (50*49*48*...*3*2*1) = (52*51) / 2 = 1,326.
Note that you obtain that same result when you use the formula for combinations of 50 cards taken from a set of 52 cards:
C(52,50) = 52! / [(50)! (52-50)!] = (52*51*50!) / [50! * 2!] = (52*51) / (2) = 1,326.
Answer: 1,326
Solve log 1/100 = log(10^x+2)
A.) x= 0
B.) x= -2
C.) x= -4
D.) x= 4
Answers
HELP PLEASE! GIVING BRAINLIEST ANSWER. (TRIGONOMETRY)
What is the rate of change from x = 0 to x = pi over 2?
8 over pi
pi over 8
-8 over pi
-pi over 8
Answers
The correct option is A )[tex]\frac{8}{\pi }[/tex]
To find the rate of change of a function from x = 0 to x = \\frac{\\pi}{2}, we need to apply the concept of the average rate of change.
This is essentially the change in the function's value divided by the change in x. Assume the function we are analyzing is y = f(x).
Step-by-Step Solution:
Identify the interval: [tex][0, \frac{\pi}{2}].[/tex]Calculate the function values at the endpoints: f(0) and[tex]f{\frac{\pi}{2})[/tex].Calculate the average rate of change using the formula:Average Rate of Change =[tex]\frac{f(\frac{\pi}{2}) - f(0)}{\frac{\pi}{2} - 0}[/tex]
When x = 0, f( x ) = - 4,
When x = π / 2, f( x ) = 0
Average Rate of Change =[tex]\frac{0- (-4)}{\frac{\pi}{2} - 0}[/tex]
Average Rate of Change =[tex]\frac{8}{\pi }[/tex]
The correct option is A )[tex]\frac{8}{\pi }[/tex]
Find the complete perimeter of the sector that intercepts arc AC.
Round to the nearest hundredth.
Answers
Calculate for the circumference of the circle with the equation,
C = 2πr
where C is circumference and r is radius. Substitute the known value for r,
C = 2π(7) = 43.98
Then, multiply the obtained value by the ratio of the angle intercepted and the whole revolution.
Arc = 43.98 x (45°/360°)
Arc = 5.5
The whole perimeter of the sector includes the arc and 2 radii. Hence, the equation for the whole perimeter is,
Perimeter = Arc + 2r
Substituting the values,
Perimeter = (5.5) + 2(7)
Perimeter = 19.50
ANSWER: 19.50 units
State whether the given measurements determine zero, one, or two triangles. b = 84°, b = 28, c = 25
Answers
Using the cosine formula:
SinB/b = SinC/c
Sin84°/28 = SinC/25
SinC = (Sin84°)(28)/25
C = 62.6° 0r 117.4°
When B = 84°, it is not possible for C = 117.4°
so, angles of triangles did not exceed 180°
it means there is only one triangle
0=2x+3(3x-4)-(-x+14)
Fraction answer need help!!!
Answers
Follow BEDMAS
0=2x+9x-12-(-x+14)
0=2x+9x-12+x-14
Add like terms
0=11x-12+x-14
0=12x-12-14
0=12x-26
Flip the eqaution
12x-26=0
Move -26 across the equal sign
12x=0+26
12x=26
x=26/12
x=13/6
Hope this helps! A thanks/brainiest answer would be appreciated :)
What conjecture can you make about the sum of the first 30 odd numbers
Answers
The sum of the first 30 odd numbers is equal to the square of 30. To find the sum, we can use a formula for the sum of an arithmetic series. Plugging in the values, we get a sum of 900.
Explanation:Conjecture: The sum of the first 30 odd numbers is equal to the square of the 30. To prove this conjecture, we can use a formula for the sum of an arithmetic series which is given by: S = n/2(2a + (n-1) d), where S is the sum of the series, n is the number of terms, a is the first term, and d is the common difference. In this case, the first term a is 1, the common difference d is 2 (since we are adding odd numbers), and the number of terms n is 30. Plugging in the values, we have: S = 30/2(2(1) + (30-1)2) = 15(2 + 58) = 900. Thus, the sum of the first 30 odd numbers is 900, which is equal to the square of 30.
Learn more about conjecture here:https://brainly.com/question/33833070
#SPJ2
How long does it take to drive 160 miles at 70mph?
Answers
time=[Distance]/[Speed]
Distance=160 miles
Time=70 mph
thus;
time=160/70
=2 2/7 hours
Final answer:
To calculate the travel time to drive 160 miles at 70mph, use the formula Time = Distance ÷ Speed. The result is approximately 2.2857 hours, or about 2 hours and 17 minutes.
Explanation:
To calculate how long it takes to drive 160 miles at a constant speed of 70 miles per hour (mph), you can use the basic formula for time, which is Time = Distance ÷ Speed.
Distance to be traveled is 160 miles.
Speed of travel is 70 mph.
By plugging the numbers into the formula, we get:
Time = 160 miles ÷ 70 mph = 2.2857 hours.
To convert this time into minutes, we multiply by 60 (the number of minutes in an hour), so:
2.2857 hours × 60 minutes/hour = 137.1428 minutes, which is approximately 2 hours and 17 minutes.
The perimeter of a square is in p inches. Write expressions, in terms of p, for the length of the side of the square and the area of the square.
Answers
if the side length is p then the perimiter (distance around) is 4 times the length of the side or 4 times p or 4p
the area is side times side but since all sides are equal length, side^2 is the aera
perimiter=4p
area=p²
Bob is driving along a straight and level road toward a mountain. At some point on his trip, he measures the angle of elevation to the top of the mountain and finds it to be 21°44'. Find the height of the mountain to the nearest foot if Bob is 13,428.7 feet from the center of the mountain at the base.
A. 5453 ft
B. 5353 ft
C. 53,534 ft
D. 535,342 ft
Answers
h = 13428.7 * tan 21 44
Height = 5353 feet
Answer:
Option B is the correct answer.
Step-by-step explanation:
The arrangement is given in the below figure.
We have height of the mountain = x
We also have
[tex]tan(21^044')=\frac{x}{13428.7}\\x=5352.98ft[/tex]
Height of the mountain to the nearest foot = 5353 ft
Option B is the correct answer.
(07.03 LC)
The steps below show the incomplete solution to find the value of p for the equation 4p − 2p + 4 = −1 + 21:
Step 1: 4p − 2p + 4 = −1 + 21
Step 2: 4p − 2p + 4 = 20
Step 3: 2p + 4 = 20
Which of these is most likely the next step?
2p = 5
2p = 8
2p = 16
2p = 24
Answers
First they combined like terms on one side.
Step 2: 4p − 2p + 4 = 20
Then they combined like terms on the other side.
Step 3: 2p + 4 = 20
Now you have to subtract 4 from both sides.
Step 4: 2p = 16
So the answer is C. 2p = 16
2p+4=20
-4=-4
2p = 16
When a researcher needs to compare means for a variable grouped into two categories based on some less-than interval variable, an _ in appropriate?
Answers
When a researcher needs to compare means for a variable grouped into two
categories based on some less-than interval variable, a t-test is appropriate.
To add, The analysis of two populations means through the use of
statistical examination is called a t-test. Small sample sizes commonly
use a t-test with two
samples. What statisticians call as test statistics are
identified as t-values. A systematized value that is calculated from sample
data during a hypothesis test is called a test statistic. The procedure that
calculates the test statistic compares your data to what is expected under the null
hypothesis.
You already have an experience with the basic principles behind a t-test if you’ve
tried to communicated with a distracted teenager.
There is a state soccer tournament with 128 teams competing for 1st place. Each week, half of the teams get eliminated. How many teams remain after 6 weeks?
A.
16
B.
8
C.
4
D.
2
Answers
Week 0 (start; initial): 128 TEAMS
Week 1: 64 teams
Week 2: 32 teams
Week 3: 16 teams
Week 4: 8 teams
Week 5: 4 teams
Week 6: 2 teams
You can also solve for this using a common ratio.
[tex]A_0 = 128[/tex]
[tex]A_1 = A_0(0.5) = 128(0.5)[/tex]
[tex]A_2 = A_1(0.5) = 128(0.5)^{2}[/tex]
[tex]A_3 = A_2(0.5) = 128(0.5)^{3}[/tex]
[tex]A_n = 128(0.5)^{n}[/tex]
[tex]A_6 = 128(0.5)^{6} = 2[/tex]
Thus, after 6 weeks, there will only be 2 teams left.
B is the midpoint of AC, D is the midpoint of CE. BD=10, and AE =2x. Find the length of CE if CD =3x
Answers
Since B is midpoint of AC and D is midpoint of CE, therefore, BD is parallel to AE and BD = 0.5 AE
AE = 2 BD = 2 x 10 = 2x
Therefore, x= 10
D is the midpoint of CE and CD = 3x, therefore CE = 6x where x = 10
Based on this, CE = 6 x 10 = 60 units of length
Add 43.688 + 127.859?
Answers
43.688
+127.859
________
171.547