give the intersection points of y=x^5 and y=x^7
Step-by-step explanation:
that means both functions deliver the same result for the same x.
therefore
x⁵ = x⁷
one solution is of course, x = 0.
the other(s) we get for x<>0 by dividing both sides by x⁵ :
1 = x²
that means we have 2 more solutions (a quadratic equation has 2 solutions, a cubic equation has 3 solutions,...) :
x = 1
x = -1
so, the intersection points are
for x = 0, we get y = 0⁵ (or 0⁷) = 0
for x = 1, we get y = 1⁵ (or 1⁷) = 1
for x = -1, we get y = (-1)⁵ or (-1)⁷ = -1
(-1, -1)
(0, 0)
(1, 1)
The intersection points of the function y = x⁵ and y = x⁷ are (0, 0) , (1, 1) and (-1 , -1).
What is Intersection point?
The intersection point is the point at which the two lines are cuts to each other.
Given that;
The equations are,
⇒ y = x⁵
⇒ y = x⁷
Now, Solve for intersection point as;
The equations are,
⇒ y = x⁵
⇒ y = x⁷
Equate both equation to each other, we get;
⇒ x⁷ = x⁵
Subtract x⁵ both sides , we get;
⇒ x⁷ - x⁵ = x⁵ - x⁵
⇒ x⁷ - x⁵ = 0
⇒ x⁵ (x² - 1) = 0
This gives two conditions;
⇒ x⁵ = 0
or, ⇒ x² - 1 = 0
Solve both the equations as;
⇒ x⁵ = 0
⇒ x = 0
And, x² - 1 = 0
( x - 1 ) (x + 1) = 0
x = 1 or x = -1
Thus, The values of x are 0 , 1 and -1.
So, The intersection points are;
For x = 0; y = x⁵ = 0
For x = 1; y = x⁵ = 1
For x = -1; y = x⁵ = -1
Thus, The intersection points of the function y = x⁵ and y = x⁷ are (0, 0) , (1, 1) and (-1 , -1).
Learn more about the intersection point visit:
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divide $70 into the ratio of 2:7: 1
Answer:
$14:$49:$7
Step-by-step explanation:
To solve this question you first add the ratios.
So 2+7+1, which is 10. You then take this number and divide it by 70 to find 1 part. 70 divide by 10 is 7, which represents 1 part.
7 times by 2 is 14, 7 times by 7 is 49 and 7 times by 1 is 7.
Thus you get the ratio, $14:$49:$7.
And if you add 14+49+7, you get 70!
Pleaseee helpppp me!!!!!!!!!!!!!
Answer:
The graph is linear and increasing from x = -6 to x = -2.
The graph is nonlinear and decreasing from x = -2 to x = 0.
Step-by-step explanation:
Linear means it has a constant slope, or a constant rate of change. That makes a straight line on a graph. On the given graph, you can see the straight line increasing from x = -6 to x = -2.
Non-linear is just anything that isn't a constant slope, and makes a curve on a graph. On the given graph, the curve decreases from x = -2 until x = 0, where it reaches its lowest point and starts heading upwards again.
what is equivalent to |14-20|
Answer:
7/10
Step-by-step explanation:
9-3 divided by 1/3 +1
Answer:
9-3/ 1/3 +1= 1
Step-by-step explanation:
PEMDAS
-8, -11, -14, -17, -20, ...
Find the 30th term of this Arithmetic Sequence.
Answer:
-95
Step-by-step explanation:
formula in finding this is -3
Arithmetic Sequnce:
-8, -11, -14 ,-17,-20,-23,-26,-29,-32,-35,-38,-41,-44,-47,-50,-53,-56,-59,-62,-65,-68,-71,-74,-77,-80,-83,-86,-89,-92,-95.
Carry on learning
Step-by-step explanation:
arithmetic sequence means that every new term is created by adding a certain constant to the previous term.
clearly, we see here, this constant is -3.
and we start with -8.
a1 = -8
a2 = a1 - 3 = -8 - 3 = -11
a3 = a2 - 3 = a1 - 2×3 = -8 - 6 = -14
so, it becomes clear that
an = an-1 - 3 = a1 - (n-1)×3 = -8 - (n-1)×3
so,
a30 = -8 - 29×3 = -95
find the final amount when 10500 is invested at 9% simple interest for 4 years
Answer:
3780
Step-by-step explanation:
10500 x 9% x 4 divided by 100=3780
Calcula lo solicitado para una persona que gana un salario de $980.000 mensuales:
auxilio de transporte: $106.454
18 dias de trabajo: sueldo /30 * los dias que le quiero pagar
auxilio de transporte: aux tras/30* los dias que le quiero pagar
EPS: 4% sueldo
total a pagar:
ayudaaa porfa es para hoy mismo
Last year at a certain high school, there were 60 boys on the honor roll and 100 girls on the honor roll. This year, the number of boys on the honor roll increased by 10% and the number of girls on the honor roll increased by 25%. By what percentage did the total number of students on the honor roll increase? Round your answer to the nearest tenth (if necessary).
Answer:
19.3%
Step-by-step explanation:
There were 10% * 60 = 6 more boys, and 25% * 100 = 25 more girls, so in total 31 more students got on the honor roll. From 160 to 191, the percentage is 31/160 = 0.19375
0.19375 = 19.3%
Evaluate -24=(-6)-(-18).
Answer:
−24= 12
Step-by-step explanation:
Answer:
-2=1
Step-by-step explanation:
-24=(-6)-(-18)
-24=(-6)+18
-24=12
-24/12 = 12/12
-2=1
(2 negatives make a positive)
Find the median of the first 13 natural numbers
Answer
116.4k+ views
Hint: We will write the first ten odd natural numbers and then add them to find their sum. We will then substitute the values in the formula of arithmetic mean , a1+a2...+ann, where n is the number of terms and a1,a2,..an are n observations.
Complete step-by-step answer:
We have to find the arithmetic mean of first ten odd natural numbers .
Natural numbers are counting numbers and starts from 1.
Odd numbers are not multiples of 2.
The first ten odd natural numbers are 1,3,5,7,9,11,13,15,17,19.
Arithmetic mean is calculated by adding all the observations by the total number of observations.
Arithmetic mean is given by a1+a2...+ann, where n is the number of terms and a1,a2,..an are n observations.
Therefore, we will calculate the sum of the first ten odd natural numbers.
⇒1+3+5+7+9+11+13+15+17+19⇒100
Now, we will divide this by 10 as there are a total 10 numbers.
10010=10
Hence, the arithmetic mean of first ten odd natural numbers is 10.
Note: Arithmetic mean is also known as average or simply mean. Odd numbers are not divisible by 2. The sum of n odd natural numbers is also given by n2
Write a simplified expression for the perimeter of the triangle.
6x - 1, 5x + 6, 9
Perimeter : __ Units
Answer:
6973 t u 6hud3w. don't knoow
Answer:
the answer is 11x+14
Step-by-step explanation:
(h[tex]2[/tex] b[tex]\2[/tex])/2
Marlee has to find the point that divides the line segment between the points P(-6, 10) and R(2, -4) exactly in half. Marlee states: "the answer is M(-2, 3). Since a midpoint divides a line segment into 2 equal parts, I used the midpoint formula." Is this a logical argument?
Please choose one of these choices.:
A. Yes; using the midpoint formula will determine the middle point of a line segment.
B. No; she should have used the distance formula.
C. No; she should have used the quadratic formula.
D. No; she should have used the slope-intercept formula y = mx + b.
Answer:
A.
Step-by-step explanation:
If you use the points P(-6,10) and R(2,-4) and put them it the midpoint formula you would get (-2,3) therefore it would be logical to use it
The remainder obtained when x⁴ +15x³ +6x² - 12x + 3 is divided by (x+2) is____.
Answer:
-53
Step-by-step explanation:
(x+2)
x^4 = -2^4 = 16
15x^3 = 15* (-2)^3 = -120
6x^2 = 6(-2^2) = 24
12x = 12*(-2) = -24
substitute into equation:
x^4 + 15x^3 + 6x^2 - 12x + 3 = 16+ (-120) + 24 - (-24) + 3 = -53
Given Polynomial is x^4 +15x^3 +6x^2 - 12x +3
Divisor = x+2
We know that
Remainder Theorem:
Let P(x) be a polynomial of the degree is greater than or equal to 1 and (x-a) is another linear polynomial,If P(x) is divided by (x-a) then remainder is P(a).
So, P(x) is divided by (x+2) then the remainder is P(-2).
P(-2) =
⇛(-2)^4+15(-2)^3+6(-2)^2-12(-6)+3
⇛ 16+15(-8)+6(4)+72+3
⇛16-120+24+72+3
⇛ 67-120
⇛ -53
P(-2) = -53
Answer:- The remainder is -53.
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The remainder obtained when x^4 + 3x^2 - 2x + 2 is divided by (x + b) is the square of the remainder obtained when x^2 – 3 is divided by (x + b...
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help pls ! i need to do this and i cannot figure this out
Which fraction is equivalent to 9/12
=========================================================
Explanation:
Let's check to see if 9/12 is the same as 16/24.
Set them equal to one another, and then use cross multiplication like so
9/12 = 16/24
9*24 = 12*16
216 = 192
Both sides aren't the same value after simplifying everything. The third equation being false leads to the first equation being false as well.
Therefore, 9/12 is not the same as 16/24. We can rule out choice A.
-----------------------
Let's check choice B
9/12 = 15/20
9*20 = 12*15
180 = 180
We have a match, so 9/12 is the same as 15/20
Notice how:
9/12 = 0.7515/20 = 0.75Both fractions lead to the same exact terminating decimal, which is more evidence that the two fractions are equivalent.
Choice B is the final answer.
Find the next two numbers in the pattern -96, 48, -24, 12,...
[tex]▪▪▪▪▪▪▪▪▪▪▪▪▪ {\huge\mathfrak{Answer}}▪▪▪▪▪▪▪▪▪▪▪▪▪▪[/tex]
The given sequence is a geometric ~
let's find the common ratio (r) first ~
[tex] \dfrac{48}{ - 96} [/tex][tex] - \dfrac{1}{ 2} [/tex]And the first term (a1) of the sequence is ~ -96
let's find the 5th and 6th term.
The value of 5th term is ~
[tex]a_1{(r )}^{n - 1} [/tex][tex] - 96{ \bigg( - \dfrac{1}{2} \bigg) }^{5 - 1} [/tex][tex] - 96 { \bigg( - \dfrac{ 1}{2} \bigg) }^{4} [/tex][tex] - 96 \times \dfrac{1}{16} [/tex][tex] - 6[/tex]The value of 6th term is ~
[tex]a_1{(r )}^{n - 1} [/tex][tex]- 96{ \bigg( - \dfrac{1}{2} \bigg) }^{6 - 1} [/tex][tex]- 96{ \bigg( - \dfrac{1}{2} \bigg) }^{5 } [/tex][tex] - 96 \times - \dfrac{1}{32} [/tex][tex]3[/tex]Kristen and Marina are making prisms out of cardboard using the designs shown below.
Whose design uses more cardboard, and by how many square inches? Show how you determined your answer.
Answer:
kristen
Step-by-step explanation:
List the sides from shortest to longest in ABC. A 630 50° с B O A. AB,BC , AC о B. BC , AC , AB C. D. AC , BC, AB not enough information O
Help Please!
Answer:
A. AB, BC, AC
Step-by-step explanation:
The side lengths have the same order (smallest to largest) that their opposite angles have.
Angle B = 180° -50° -63° = 67°
The angles, smallest to largest, are C = 50°, A = 63°, B = 67°.
Their opposite sides (shortest to longest) are AB, BC, AC. (matches choice A)
which statement is correctly written as a conditional statement
Answer:
a shape has four sides,or it is a quadrilateral
It is normal for some newborn babies to lose weight in their first week of life. Baby Todd's birth weight was 10 pounds. One week after being born, he is 10% lighter. What is Todd's current weight? pounds Submit
Answer:
9 pounds
Step-by-step explanation:
100% - 10% = 90%
90% -> .9
[Solving] 10 * .9 = 9
Have a nice day!
I hope this is what you are looking for, but if not - comment! I will edit and update my answer accordingly. (ノ^∇^)
- Heather
Answer:
9 pounds
Step-by-step explanation:
10% of 10 pounds is 1 pound so baby Todd's current weight is 9 pounds.
The amount of oil it takes to cover the bottom of a frying pan.
Answer:
about 1 cup maybe less
Step-by-step explanation:
2. Kyle owes his sister 24. He gives his sister $15 that he earned mowing
lawns. Write and simplify an addition expression to find how much Kyle
still owes his sister. (leton 2)
ok so he is owing his sister 24 and he gives her 15
so 24-15=9
but as an addition expression it will be
x+15=24
x=24-15
x=9
3/4 ÷ 1/2 +1 ddgngadgaekyfyuktyjrthrgefwretrytjyktuli;obpnML"NKP?boliykujhtgrfedw
Answer:
5/2
Step-by-step explanation:
alternative = 2 1/2 , 2.5
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!9
Answer:
think its a
Step-by-step explanation:
the slope is 2/1 but both y int are different
Simplify 2y+4x=16x +6y
Can someone pls help me!
Answer:
x is -3
Step-by-step explanation:
Please help! I also don’t understand a). My friend did it for me when I wasn’t looking so if you could explain that too, that’s be great
Answer:
a) 45
b) No. AD and BC arent parallel.
Step-by-step explanation:
a)
3x + 2x + x + 90 = 360
6x = 270
x = 45
Hope you could understand.
If you have any query, feel free to ask.
three fifths of the children in a school are boys seven eighths of the girls in the school are right handed. What fractions of the children in the school are left handed girls?
Answer:
Step-by-step explanation:
Firstly, we need to get the fraction that are girls
What we have to do is to subtract the three-fifths from the total fraction of 1
Mathematically,that would be :
1- 3/5=2/5
We have it that seven-eigths of the girls are left-handed. This mean one-eight of the girls are left handed
To get the fraction of the school that are left handed, we multiply the fraction of girls by the fraction of left-handed girls
We have this as:
1/8 x 2/5=1/20
We have it that 1/20 of the children are left-handed girls
help will reward brainly
Answer: Positive but I might be wrong I haven't done slopes in a while
Step-by-step explanation: