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
ockdown Learning Week 2 Higher
A and B are two cities.
b)
>
x В
واورأه
-os
D
Submit Answer
a) Measure the bearing of B from A.
AX
b) Measure the bearing of A from B.
Answers
Answer:
A) measure the bearing of A from B
F(x)=9(x-8) find f^-1(x)
Answers
Answer:
[tex]f^{-1}[/tex](x) = [tex]\frac{1}{9}[/tex] x + 8
Step-by-step explanation:
let y = f(x) and rearrange making x the subject, that is
y = 9(x - 8) ← divide both sides by 9
[tex]\frac{y}{9}[/tex] = x - 8 ( add 8 to both sides )
[tex]\frac{y}{9}[/tex] + 8 = x
Change y back into terms of x with x = [tex]f^{-1}[/tex](x) , thus
[tex]f^{-1}[/tex](x) = [tex]\frac{1}{9}[/tex] x + 8
Which of the following is a solution of x2 + 4x = -8?
O x = -2 - 21
O x = 2 + 21
O x = -4 + 41
O x = 4 - 41
Answers
Answer:
[tex]x=2i-2,\:x=-2i-2[/tex]
Step-by-step explanation:
[tex]x^2 + 4x = -8\\\\\mathrm{Solve\:by\:completing\:the\:square}\\\\\mathrm{Write\:equation\:in\:the\:form:\:\:}x^2+2ax+a^2=\left(x+a\right)^2\\\\\mathrm{Solve\:for\:}a,\:2ax=4x:\quad a=2\\\\\mathrm{Add\:}a^2=2^2\mathrm{\:to\:both\:sides}\\\\x^2+4x+2^2=-8+2^2\\\\\mathrm{Simplify\:}-8+2^2:\quad -4\\x^2+4x+2^2=-4\\\\\mathrm{Complete\:the\:square}\\\left(x+2\right)^2=-4\\\\\mathrm{For\:}f^2\left(x\right)=a\mathrm{\:the\:solutions\:are\:}f\left(x\right)=\sqrt{a},\:-\sqrt{a}\\[/tex]
[tex]\mathrm{Solve\:}\:x+2=\sqrt{-4}:\quad x=2i-2\\\\\mathrm{Solve\:}\:x+2=-\sqrt{-4}:\quad x=-2i-2\\\\x=2i-2,\:x=-2i-2\\[/tex]
Evaluate the expression for c = –0.3.
Write your answer as a decimal or whole number.
24c^2 =
Answers
Answer:
2.16
Step-by-step explanation:
c = -0.3
24c² =
plug in c
24(-0.3)²
solve for the exponent
24(0.09)
multiply
2.16
whats commutative property of multiplication.
Answers
Answer:
The commutative property is a math rule that says that the order in which we multiply numbers does not change the product.
Step-by-step explanation:
a) Calculate the area of a triangle that has base 8cm and height
6.5cm State units with your answer.
Answers
Answer:
26cm^2
Step-by-step explanation:
Base = 8cm
Height = 6.5cm
[tex]a = \frac{base \: cm \times heightcm}{2} [/tex]
Substitute values into the given equation
[tex]Area = \frac{8 \: cm \times 6.5 \: cm \: }{2} \\ = \frac{52 {cm}^{2} }{?} \\ = 26 \: {cm}^{2} [/tex]
What is the pattern ?
0, 1, 8, 27, 64,
Answers
Answer:
Step-by-step explanation:
1 (=1×1×1)
8 (=2×2×2)
27 (=3×3×3)
64 (=4×4×4)
Without using a calculator, choose the statement that best describes the value of {86}
Answers
Answer: my guess is 9
Answer:
there would be the 8 in the tens place and the 6 in the ones place
Step-by-step explanation:
you can see this in a place value chart
If m is the midpoint of ab find the coordinates of a if b(4,6) and m(1,2) A is pls help I need to know pls
Answers
Back Next
✓ Check
Question 1
Caroline said the absolute value of -25 is 25. Is she correct? Explain.
Answers
Answer:
lolllll
Step-by-step explanation:
Combine like terms fir the following expression: -3x+14-11+11x
Answers
Answer:
8x + 3
Step-by-step explanation:
In the expression -3x + 14 - 11 + 11x, we have two pairs of like terms that can be combined together:
-3x, 11x
14, -11
If we rewrite this expression with the like terms together, it would look like this:
-3x+11x + 14-11
To make the addition of -3x and 11x easier, we could switch their places in the expression to make it look like this:
11x-3x + 14-11
(Note: Even though we are switching the terms' places, the -3x still keeps its negative sign when you move it around.
11x-3x is 8x and 14-11 is 3.
Therefore, the expression -3x + 14 - 11 + 11x can be simplified by combining like terms into 8x + 3.
Which statement about rational numbers is true?
All rational numbers are fractions.
Rational numbers never have repeating decimals.
Some integers are not rational numbers.
All fractions containing integers are rational numbers.
Answers
Answer:
the true one is all fractions containing integers are rational numbers is true
Step-by-step explanation:
i think
Answer:
All fractions containing integers are rational numbers.
Step-by-step explanation:
The result of adding a complex number to its conjugate is “an integer/a pure imaginary number/a real number/a whole number” and the result of subtracting a complex number from its conjugate is “an integer/a real number/a pure imaginary number/a whole number”
Answers
Answer:
If Z is a complex number:
Z = a + b*i
where a and b are real numbers, and i is an imaginary number.
Then "a" is the real part.
"b*i" is the imaginary part.
The conjugate of Z is:
Zc = a - b*i
So the sign of the imaginary part changes.
Then:
Sum:
Z + Zc = (a + bi) + (a - bi) = 2*a + 0 = 2*a
and remember that a is a real number, then 2*a is also a real numer.
The correct answer is "A real number".
Difference:
Z - Zc = (a + bi) - (a - bi) = 2b*i
and this is a pure imaginary number, so here the correct answer is: "a pure imaginary number"
Answer: a pure imaginary number
explanation:
The sum of a complex number and its conjugate will always be two times the real part of that complex number.
Z=a+b*i
where a and b are real numbers, and i is an nonexistent number.
Then a is the real part.
"b*i" is the imaginary part.
The connection of Z is:
Zc = a - b*i
So the sign of the imaginary part changes.
Sum:
Z + Zc = (a + bi) + (a - bi) = 2*a + 0 = 2*a
and remember that a is a real number, then 2*a is also a real number.
The correct answer is "A real number".
Difference:
Z - Zc = (a + bi) - (a - bi) = 2b*i
The length of segment AB is 10 cm
If you draw a point halfway between A and B and label the point C, what is the
length of AC?
Answers
Answer:
Step-by-step explanation:
The distance between B and C is ... 10. M(7, 1), N(4, –1). eSolutions Manual - Powered by Cognero. Page 2 ... Find the coordinates of G if F(1, 3.5) is the midpoint of ... Find the distance between each pair of points. ... approximated by a straight line, estimate the length of ... relationship between AB and each segment if you.
True False: Complementary angles sometimes fom straight angles
Answers
Answer:
False
Step-by-step explanation:
Complementary angles form a right angle (L shape) and have a sum of 90 degrees. Supplementary angles form a straight line and have a sum of 180 degrees.
1)n/5=-10 How do we answer this question
Answers
Answer: Your answer will be [tex]\frac{-50}{5} =-10[/tex]
Step-by-step explanation: You will have
[tex](5)\frac{n}{5} =-10(5)[/tex] you will have to multiply 5 on both sides. So you will then simplify 5 and 5 to be left with n and multiply -10(5)=-50
So you get [tex]n=-50[/tex]
There is an attachment at the bottom help me please.
Answers
Answer:
Fourth option
Step-by-step explanation:
We know that A and B are rational numbers because they can be written as the quotient of two integers. Therefore, that eliminates the first and third options because they state that (at least) one of the numbers is irrational but we know that both are rational, hence, they are incorrect. The second option is incorrect because A · B = [tex]\frac{mn}{pq}[/tex], not [tex]\frac{mp + nq}{pq}[/tex], therefore, the correct answer is the fourth option.
HELP PLEASEEEE A dressmaker needs to cut 4-inch pieces of ribbon from rolls of ribbon that are 9 feet in length. How many 4-inch pieces can the dressmaker cut from 15 of these rolls of ribbon? How many inches of ribbon does the dressmaker have, in total?
Answers
Answer:
1620 peices
Step-by-step explanation:
9 ft = 9 x 12 (12 inches make 1 ft) = 108 x 15 rolls = 1620 inches
1620 inches divided by 4 inches = 405 peices
:)
Find the mode:
4,5, 4, 3, 5, 1, 6
Answers
Answer:
4 and 5Step-by-step explanation:
The mode in a given set of data is the number that appears the most.
4 appears twice
5 appears twice
3 appears once
1 appears once
6 appears once
How does the outlier affect the standard deviation in the following set of data?
9 9 10 10 12 15 16 16 17 17 17 20 23 28
5.32
Removing the outlier lowers the standard deviation by 1.09
No outlier
4.23
Answers
Answer:
Removing the outlier lowers the standard deviation by 1.09
Step-by-step explanation:
Find the standard deviation of the data WITHOUT the outlier first.
If you don't know how to do standard deviation, here are the steps:
1. Find the mean
2. Subtract the mean by the data set values
3. Square the differences
4. Add the squared numbers together and divide by the number of data set values
5. What you have now is the variance, and all you have to do now is square the variance and you have the standard deviation
Repeat this, but WITH the outlier this time.
Final step, just subtract the smaller number (answer you got from the data with the outlier) by the greater number (answer you got from the data without the outlier) and you have your answer: 1.09!
Josh wrote a whole number using the digits 8,4,7,2,9 and 0. Josh's number has a seven in the thousands and a 2 in the tens place. Josh's number is less then 500,000. Is Josh's number greater than 480,000?
Answers
Answer:
4 out of the 6 possible numbers Josh wrote were greater than 480,000, while 2 out of the 6 possible numbers are less than 480,000
Step-by-step explanation:
The given parameters are;
The number with which Josh wrote the whole number = 8, 4, 7, 2, 9, and 0
The number in the thousands of the whole number that Josh wrote = 7
The number in the tens of the whole number that Josh wrote = 2
The value of the whole number that Josh wrote < 500,000
Therefore, we have;
The possible numbers in the hundreds of thousands place = 4, and 2
Which gives the following possible combinations;
The number of ways of selecting the first number = 1 way, the number is 4 to make the value less than 500,000
The number of ways of selecting the second number = 3 ways
The number of ways of selecting the third number = 1 way, the number is 7
The number of ways of selecting the fourth number = 2 ways as there are only two numbers left after filling the second place digit
The number of ways of selecting the fifth number = 1 way, the number is 2
The number of ways of selecting the sixth number = 1 ways
The total number of possible number combinations = 3×2×1 = 6 possible numbers, which are;
487920 or 497820 or 407829 or 407928 or 487029 or 497028
Therefore, 2 out of the numbers are less than 480,000, the remaining 4 possible numbers are larger than 480,000.
Geography textbook has a width of 9 inches and a diagonal of 15 inches. What is the length of the
textbook?
Answers
Answer:
12 inches
Step-by-step explanation:
The Pythagorean's theorem states that a triangle's hypotenuse's length is equal to a^2+b^2=c^2.
9 is a, b is the length, and c is the 15.
9^2+b^2=225
225-81=144
The square root of 144 is 12, therefore 12 inches is the length.
Explain how to simplify the expression -98 - 31? Using the additive inverse.
Answers
Given:
The expression is -98 - 31.
To find:
The value of the given expression using the additive inverse.
Solution:
According to the additive inverse, for any number a,
[tex]a+(-a)=0[/tex]
Using additive inverse, we have
[tex]98+(-98)=0[/tex] ...(i)
[tex]31+(-31)=0[/tex] ...(ii)
Now, using (i) and (ii), we get
[tex]98+(-98)+31+(-31)=0[/tex]
[tex](98+31)+(-98-31)=0[/tex]
[tex]129+(-98-31)=0[/tex]
Subtracting 129 from both sides, we get
[tex]-98-31=-129[/tex]
Therefore, the value of given expression is -129.
4 to the second power is the same as 4 squared. True or false ?
Answers
Answer:
False.
Step-by-step explanation:
For which equations are in the solution for x the same number? 15 – х = -3
3
Answers
Answer:
Step-by-step explanation:
First equation:
15 - x = - 3
-x = - 3 - 15
-x = -18 (now negative signs on b.s cut eachother)
[x = 18]
Second equation :
15 - x = 3
-x = 3 - 15
- x = -12 ( now negative sign on b.s cut eachother)
[x = 12]
so x = 18 and x = 12 are not same
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.
WHAT IS |3x + 2| > 9
Answers
Answer:
Answer will be the 7/3<x>7/3
greastest common factor of 24 and 18
Answers
Answer: 6
Step-by-step explanation:
the biggest number that can go into both 24 and 18 evenly is 6. 24/6 is four, and 18/6 is three
HELP ME PLEASE ECPLAIN WHY
Answers
Answer:
A≈110.11
using formula 1/4[tex]\sqrt5(5+2\sqrt5)a2[/tex]
Step-by-step explanation:
please help!
4^x*5^y=20, 4^y*5^x=20^2, x+y=?
Answers
Answer:
x + y are either 2 or 4
Step-by-step explanation:
conclusion x + y = 2 OR 4