A right triangle has one vertex on the graph of y = x^8, x>0, at (x, y), another at the origin, and the third on the positive y-axis at (0, y), as shown in the figure. Express the area A of the triangle as a function of x.
Answers
Answer:
Area = [tex]\frac{1}{2}x^{9}[/tex]
Step-by-step explanation:
From the graph attached,
Triangle given is a right triangle.
This triangle ha three vertices (0, y), (x, y) and (0, 0).
Therefore, measure of the base = x units
And measure of the height of the triangle = y units
Area of a triangle = [tex]\frac{1}{2}(\text{Base})(\text{Height})[/tex]
= [tex]\frac{1}{2}(x)(y)[/tex]
Since, y = [tex]x^{8}[/tex]
Therefore, Area of the triangle = [tex]\frac{1}{2}(x)(x)^8[/tex]
= [tex]\frac{1}{2}x^{9}[/tex]
Area of the given right triangle is [tex]\frac{1}{2}x^{9}[/tex] units².
Related Questions
Solve for x. 6x+11=3x-10
Answers
3x + 11 = -10
subtract 11 from both sides
3x = -1
divide both sides by 3
x = -1/3
In an AP with 18 terms the common difference is $-3$−3 . If the nth term is $-5$−5, what is its first term?
Answers
Answer:
46
Step-by-step explanation:
The n th term of an AP is
[tex]a_{n}[/tex] = a₁ + (n - 1)d
where a₁ is the first term and d the common difference
Here d = - 3 and [tex]a_{18}[/tex] = - 5 , thus
a₁ + (17 × - 3) = - 5
a₁ - 51 = - 5 ( add 51 to both sides )
a₁ = 46
Answer:
a = 46
Step-by-step explanation:
Refer to the attachment.
What is the value of x?
5 + 2/3x = -x + 20
Please explain:
Answers
The value of X is 9.
Solve for x by simplifying both sides of the equation, then isolating the variable.
Points A, B, and C are collinear. Point B is between A and C. BC=8x+709. AB=487+5x. AC=91. Find BC.
Answers
Answer:
BC = 29Step-by-step explanation:
Point B is between A and C and the points A, B, and C are collinear so:
AB + BC = AC
487 + 5x + 8x + 709 = 91
13x + 1196 = 91
- 1196 - 1196
13x = - 1105
÷13 ÷13
x = - 85
BC = 8x + 709 = 8(-85) + 709 = - 680 + 709 = 29
I will give brainliest and thank you to whoever helps/answers this
Answers
Answer:
0 0 6
0 6 0
6 0 0
Step-by-step explanation:
Simple place value
The midpoint of segment AB is (-2,5). The coordinates of point A are (-7,3). Find the coordinates of point B.
A)
(3,7)
B)
(3, 1)
09
(7,3)
D)
(-13, 1)
Answers
Answer:
A) (3,7)
Step-by-step explanation:
If the value of x goes from -7 to -2, that means to get the coordinate b you have to add 5 again, so the x value of coordinate B is 3. Then, if the value of y goes from 3 to 5 you have to add 2 to the y-value again to get 7. So the y value is 7. Meaning the final answer is (3,7)
Answer:
A) (3,7)
Step-by-step explanation:
if you graph the given points you see that point A from the mid point is 2 rise and 5 run. Count that same rise over run to find B. Look at graph for help.
6(1 + 5n) − 6n = 174
Answers
Answer:
N=7
Step-by-step explanation:
1. Distribute the 6 into the parentheses
6+30n-6n=174
2.combine like terms
6+24n=174
3. Subtract 6 on both sides
24n=168
4.now divide
24/24 cancels out 24/168 is what 7 soooo
n=7
What will be the coordinates of the upper-right vertex of
the next largest (fourth) square in the pattern?
(5,5)
(7,7)
(8,8)
(16, 16)
Answers
Answer:8,8
Step-by-step explanation:
Took the test on edge
Answer:
C. (8, 8)
Step-by-step explanation:
Edge 2022. ^
Pls help!!!!!!! Determine the lowest common denominator for each sum or difference.
X
7/6 + (-5/12)
Common Denominator: 10
Common Denominator: 12
Common Denominator: 24
X
13/24 + 7/12
3/2 - 4/5
x
1/8-5/3
x
-3/4+ (-2/3)
x
5- 7/10
Answers
Answer:
Common Denominator 10: 5-7/10 and 3/2-4/5
Common Denominator 12: -3/4 + (-2/3) and 7/6 + (-5/12)
Common Denominator 24: 1/8-5/3 and 13/24+7/12
Hopefully This Helps You :)
Answer:
Common Denominator 10: 5-7/10 and 3/2-4/5
Common Denominator 12: -3/4 + (-2/3) and 7/6 + (-5/12)
Common Denominator 24: 1/8-5/3 and 13/24+7/12
Step-by-step explanation:
At the fair the ratio of male to females was 8:6. If there are 112 people at the fair how many males are there?
Answers
Answer:
64
Step-by-step explanation:
Let the common multiplier of the given ratio be x.
Therefore,
Number of males = 8x
Number of females = 6x
[tex]8x + 6x = 112 \\ 14x = 112 \\ x = \frac{112}{14} \\ x = 8 \\ number \: of \: males = 8x = 8 \times 8 = 64 \\ [/tex]
Mathematics Diagnostic Assessment
14
Miller inventoried the batteries in his house. The two-way table below shows the data he collected.
AA
Total
29
18
AAA
11
14
Disposable
Rechargeable
Total
7
21
25
25
Ihs 50
Which correlation does the two-way table suggest?
A. The rechargeable batteries tend to be AAA.
B. None of the correlations listed are correct.
C. The rechargeable batteries tend to be AA.
D. The disposable batteries tend to be AAA.
tum. All rights reserved,
e here to search
o
Answers
Answer:
The rechargeable batteries tend to be AAA.
Step-by-step explanation:
Have a good day :)
Solve each literal equation for the given variable y=x+12;x
Answers
Answer:
Step-by-step explanation:
x + 12 = y
x = y - 12
Of Q is the midpoint od RP, Find the coordinates of R if P(9,-2) and Q (4,5)
Answers
Answer:
(-1,12)
Step-by-step explanation:
let R be(x,y)
Q(4,5)=midpoint
R(x,y)=(x1,y1)
p(9,-2)=(x2,y2)
now,
(4,5)= x1+x2/2 , y1+y2/2
(4,5)= x+9/2 , y-2/2
so,
x+9/2=4 y-2/2=5
x+9=8 y-2=10
x= -1 y=12
therefore, R(x,y)= (-1,12)
A cookie factory uses 4 1/4 bags of flour in each batch of cookies. The factory uses 8 1/2 bags of flour yesterday. How many batches of cookies did the factory make
Answers
Answer:
2
Step-by-step explanation:
4 1/4 bags of flour multiplied by 2 is 8 2/4 and that's equivalent to 8 1/2
Answer:
The answer is 2 Batches
Step-by-step explanation:
The answer is 2 because 4 1/4 multiplied by 2 is 8 2/4 or in a simplified version 8 1/2.
help please? i have no idea what i’m doing
Answers
1) Students in Jake's class were numbered in order from 1 to 24. Jake was asked to
choose classmates numbered with multiples of 5 to be in his group. Which
number could be the number of a classmate in his group?
>) 15
>) 16
() 21
>)7
Answers
Answer:
15
Step-by-step explanation:
15 is the only number with a multiple of 5.
The Number of classmates in his group is less than 21
What is an inequality?An inequality is an inequation separated by <,>≥,≤. the relationship between two values that are not equal is defined by inequalities. Inequality means not equal. Generally, if two values are not equal, we use “not equal symbol (≠)”. But to compare the values, whether it is less than or greater than, different inequalities are used.
Given here: Jake's class has 24 students and she is to choose a group which is a multiple of 5
Thus the possible multiples of 5 between 1 and 24 are
5,10,15,20
Therefore all these multiples are less than 21
Hence, The Number of classmates in his group is less than 21
Learn more about inequalities here:
https://brainly.com/question/28823603
#SPJ2
in grouped data each of the group is called?
Answers
Answer:
The class interval.
If a and bare negative, then a + b is also negative.
Answers
Step-by-step explanation:
Example: -2+-5
It can also be written as -2-5.
How I do these problems, I do 2+5, which is 7. Then I add a negative sign. So -2+-5 or -2-5 is equal to -7.
-a+-b can also be written as -a-b. So yes, if a and bare negative, then a + b is also negative.
hope it helps!
eric planted a seedling in his garden
Answers
Answer:
how is this a question......
f(x) = 3x ^ 2 + 2x + 10
Answers
Answer:
No x-intercept (zero)
f(0)=10
Step-by-step explanation:
Step-by-step
F(x) = 3x^2 + 2x + 10
To find x-intercept/zero, Substitute
F(x) = 0
0 = 3x^2 + 2x + 10
Swap the side of the equation
3x^2 + 2x + 10 = 0
Solve the quadratic equation
ax^2 +b+c = 0
X= -b+ b^2 -4 a c/ 2a
X= -2+ 2^2 -4 x 3 x 10/2x3
X= -2+ 4-4 x 3 x 10/ 2 x 3
-> x=-2+ 4-120/2 x 3 -> x=-2 4-120/6
X=-2+ -116/6
-> calculate the difference
X= -2+ -116/6
The square root of a negative
number dose not exit in the set of
Real numbers
No x-intercept/zero
PLEASE HELP MY BIRTHDAY WILL BE CANCELLED IF I DONT GET A GOOD GRADE ON THIS
Answers
Answer:
Option 4
Step-by-step explanation:
If the circle is filled in them it will be either ≤, ≥, ≈ .
One circle is open one is closed
if you saved 25 thousand dollars an hour, 40 hours per week for 2020 years, how much money do u have saved up ?!
Answers
Answer:
i dunno
Step-by-step explanation:
Evaluate the function f(x)=6x+2 at the given values of the independent variable and simplify.
a. f(8) b. f(x+6) c. f(−x)
. f(8)= (Simplify your answer.)
Answers
[tex]f(x) = 6x+2[/tex]
A.
To evaluate f(8), we substitute x with 8 in our expression.
[tex]f(8) = 6*8 + 2\\f(8) = 48 +2\\f(8) = 50[/tex]
Answer: f(8) = 50
B.
To evaluate f(x+6), we do the same but substitute x with x+6 instead.
[tex]f(x+6) = 6(x+6) + 2[/tex]
Expand the parenthesis by multiplying 6 with x and 6.
[tex]f(x+6) = 6x + 6*6 + 2\\f(x+6) = 6x+36+2\\f(x+6) = 6x+38[/tex]
Answer: f(x+6) = 6x + 38
C.
Again, we're doing the same thing, just substituting x with -x.
[tex]f(-x) = 6 * (-x) + 2\\ f(-x)=-6x+2[/tex]
Answer: f(-x) = -6x+2
Answer:
_____________________________________________
[tex] \longmapsto \: f(x) = 6x + 2[/tex]
_____________________________________________
A. [tex]f(8) = 6(8) + 2 = 48 + 2 = \boxed{ 50}✓[/tex]
_____________________________________________
B. [tex]f(x + 6) = 6(x + 6) + 2 \\ = 6x + 36 + 2 \\ = \boxed{ 6x + 38}✓[/tex]
_____________________________________________
C. [tex]f( - x) = 6( - x) + 2 = \boxed{ - 6x + 2}✓[/tex]
_____________________________________________
Juan is rappelling down a 495-foot cliff at a rate of 6 feet per second. Which equation would represent the height Juan is above the ground, H, after t seconds?
Answers
Answer:
The equation is H = 495 -6t
Step-by-step explanation:
Here, we want to write an equation that will represent the height Juan is above the ground, after t seconds.
The height we want to calculate is H. The initial height is 495 foot;
At the first second, the decrease in height will be 6 * 1, at the second 6 * 2 and thus at t seconds, the decrease in height will be 6 * t = 6t
Ask the height after t seconds will be;
H = 495 - 6t
Where t represents the time in seconds
Alex has 84 quarters and nickels worth a total of $17.80. Which equation can be used to find q, the number of quarters Alex has? 0.25q + 0.05(q – 84) = 17.80 0.05q + 0.25(84 – q) = 17.80 0.25(q – 84) + 0.05q = 17.80 0.05(84 – q) + 0.25q = 17.80
Answers
Answer:
D
Step-by-step explanation:
The equation can be used to find q is 0.05(84 - q) + 0.25q = 17.80 option (D) 0.05(84 - q) + 0.25q = 17.80 is correct.
What is a linear equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
We have:
Alex has 84 quarters and nickels worth a total of $17.80.
As we know,
1 nickel = 5 cents
1 dime = 10 cents
1 quarter = 25 cents
1 dollar = 100 cents
The amount that Alex = 84 quarters + $17.80
q = 84 quarters + $17.80
q is the number of quarters Alex has.
Remaining nickel value = 84 - q
In cents:
= 0.05(84 - q)
q in cents:
= 0.25q
0.05(84 - q) + 0.25q = 17.80
Thus, the equation can be used to find q is 0.05(84 - q) + 0.25q = 17.80 option (D) 0.05(84 - q) + 0.25q = 17.80 is correct.
Learn more about the linear equation here:
brainly.com/question/11897796
#SPJ5
What is the third multiple of 167?
Answers
167x 3=501
Brainliest?
Davis saved $1000 and then found a savings account that will give him 10% interest per year.
Represent the money in his account after n years.
1) Arithmetic or Geometric:
2) Common difference/ratio:
3) Recursive Formula:
4) Explicit Formula:
Answers
Answer:
1000x0.1=n
Step-by-step explanation:
first year he had 1000
second year they times the 1000 by .1 because thats ten percent
Twenty people are members of a local bowling club. Eight of them are men. What percentage of the
bowling team are women?
Answers
Answer:
60% of them are women 40% are men
Statements Reasons
Given: Z1 and 22 are supplements,
23 and 24 are supplements,
and 21 24.
Prove: 22 23
m21+ m2 = 180
mZ3+ m 24 = 180
21 and 22 are
.
2124
m21+ m2 2 = m 23+
m24
23 and 24 are supp
1
Statements
Reasons
3
2.
2
1
Assemble the proof by dragging tiles to
the Statements and Reasons columns.
Answers
got it correct edge 2021
The proof that m∠2 = m∠3 in the two column proof table is; shown in the various steps and concludes with subtraction property of equality
How to complete the two column proof?We are given;
∠1 and ∠2 are supplements
∠3 and ∠4 are supplements
∠1 ≅ ∠4
Now, since ∠1 and ∠2 are supplements, it means that;
m∠1 + m∠2 = 180° because of the definition of supplementary angles.
Since ∠3 and ∠4 are supplements, it means that;
m∠3 + m∠4 = 180° because of the definition of supplementary angles.
We are told that ∠1 ≅ ∠4
Thus;
m∠1 + m∠2 = m∠3 + m∠1 (Substitution property of equality)
Finally, we can reduce to get;
m∠2 = m∠3 (subtraction property of equality)
Read more about two column proof at; https://brainly.com/question/1788884
whats the answer to this problem 9x+10=2001-X
Answers
Answer: x=1991/10
Step-by-step explanation: Step 1: Simplify both sides of the equation.
9x+10=2001−x
9x+10=2001+−x
9x+10=−x+2001
Step 2: Add x to both sides.
9x+10+x=−x+2001+x
10x+10=2001
Step 3: Subtract 10 from both sides.
10x+10−10=2001−10
10x=1991
Step 4: Divide both sides by 10.
10x
10
=
1991
10
x=
1991
10
Answer:x=199.1
Step-by-step explanation: