Answer:
13 1/6 years old
Step-by-step explanation:
10 9/12 + 2 5/12 = 12 14/12 simplifies to 13 2/12 or 13 1/6
Rationalise the equation :
[tex] \frac{y ^{2} }{ \sqrt{x^{2} + y {}^{2} } + x} [/tex]
Answer:
[tex]\sqrt{x^2+y^2}-x[/tex]
Step-by-step explanation:
[tex]\textsf{Mulitply by}\quad\dfrac{\sqrt{x^2+y^2}-x}{\sqrt{x^2+y^2}-x}:[/tex]
[tex]\implies \dfrac{y^2}{\sqrt{x^2+y^2}+x} \times \dfrac{\sqrt{x^2+y^2}-x}{\sqrt{x^2+y^2}-x}[/tex]
[tex]\implies \dfrac{y^2(\sqrt{x^2+y^2}-x)}{(\sqrt{x^2+y^2}+x)(\sqrt{x^2+y^2}-x)}[/tex]
[tex]\implies \dfrac{y^2(\sqrt{x^2+y^2}-x)}{(\sqrt{x^2+y^2})^2-x^2}[/tex]
[tex]\implies \dfrac{y^2(\sqrt{x^2+y^2}-x)}{x^2+y^2-x^2}[/tex]
[tex]\implies \dfrac{y^2(\sqrt{x^2+y^2}-x)}{y^2}[/tex]
[tex]\textsf{Cancel the common factor}\:y^2:[/tex]
[tex]\implies \sqrt{x^2+y^2}-x[/tex]
Rationalising the denominator of the given fraction means we need to multiply both the numerator and the denominator of the fraction by the conjugate of the expression in the denominator. For example:
[tex]\;\longrightarrow\dfrac{1}{a+b}[/tex]
Here the conjugate of denominator of the expression is a - b. So we need to multiply both the numerator and denominator with the fraction.
[tex]\;\longrightarrow \dfrac{1}{a+b} \times \dfrac{a-b}{a-b}[/tex]
Hence, this is what the rationalization means.
Elucidation:We have been given and equation and we have been asked to rationalise the equation.
The conjugate of the denominator of the given equation is √(x² + y²) - x. Therefore;
[tex]\implies \dfrac{y^2}{\sqrt{x^2+y^2}+x} \times \dfrac{\sqrt{x^2+y^2}-x}{\sqrt{x^2+y^2}-x}[/tex]
[tex]\implies \dfrac{y^2(\sqrt{x^2+y^2}-x)}{(\sqrt{x^2+y^2}+x)(\sqrt{x^2+y^2}-x)}[/tex]
[tex]\implies \dfrac{y^2(\sqrt{x^2+y^2}-x)}{(\sqrt{x^2+y^2})^2-x^2}[/tex]
[tex]\implies \dfrac{y^2(\sqrt{x^2+y^2}-x)}{x^2+y^2-x^2}[/tex]
[tex]\implies \dfrac{y^2(\sqrt{x^2+y^2}-x)}{y^2}[/tex]
[tex]\implies \boxed{\sqrt{x^2+y^2}}[/tex]
Hence, this is our required solution for this question.
Directions: Simplify and write in standard form, letting f(x) = x2 + 2x + 1, g(x) = 3 - 2x,
h(x) = 2x2, and k(x) = x +4.
k(h(x))
Answer:
2x² + 4
Step-by-step explanation:
Check out the attached photo
The rectangular prism below has a total surface area of 158 in^2. Use the net below to determine the missing dimension, x
A. 6 in
B. 8 in
C. 12in
D. 10 in
Answer:
b
Step-by-step explanation:
What is the end behavior of the function f of x equals 3 times the cube root of x?
As x → –∞, f(x) → –∞, and as x → ∞, f(x) → ∞
As x → –∞, f(x) → ∞, and as x → ∞, f(x) → –∞
As x → –∞, f(x) → 0, and as x → ∞, f(x) → 0
As x → 0, f(x) → –∞, and as x → ∞, f(x) → 0
[tex]f(x) = 3 \sqrt[3]{x} [/tex]
[tex]lim f(x) = 3 \sqrt[3]{ - \infty } = - \infty \\ x = > - \infty [/tex]
[tex]limf(x) = 3 \sqrt[3]{ \infty } = \infty \\ x = > \infty [/tex]
Answer:
As x → –∞, f(x) → –∞, and as x → ∞, f(x) → ∞.
Step-by-step explanation:
I got it right on the test.
Convert 0.54. to a decimal In base 3
Answer:
what does a this mean? .54 is a decimal
[tex]5 = \frac{x}{3} + 2[/tex]
step by step please.
Answer:
9
Step-by-step explanation:
Given equation:
[tex]5 = \dfrac{x}{3} + 2[/tex]
To determine the solution (x) of the equation, we need to isolate it. To do this, we can subtract 2 both sides of the equation.
[tex]\implies 5 - 2 = \dfrac{x}{3} + 2 - 2[/tex]
[tex]\implies 3 = \dfrac{x}{3}[/tex]
To further isolate "x", we can use cross multiplication.
[tex]\implies 3 \times 3 = x[/tex]
Finally, simplify the expression on the left-hand-side to obtain the value of x.
[tex]\implies \boxed{9 = x}[/tex]
The Hiking Club plans to go camping in a State park where the probability of rain on any given day is 17%. What is the probability that it will rain on at least four of the five days they are there? Round your answer to the nearest thousandth.
Answer: 30%
Explanation: Every day is 30%.
- Jackson
In an amphitheater, there are 20 seats in the front row, 23 seats in the second row, 26 seats in the third row, and so on, in an arithmetic sequenc A) Write an explicit formula to find an. The number of seats in the nº row.
B) The last row in the amphitheater has 83 seats in it. How many rows a seats are there?
C) Write an expression using sigma notation that represents the total number of seats in the amphitheater.
D) Evaluate this expression. How many total seats are there?
For the given arithmetic sequence we have:
A) [tex]A_n = 20 + (n - 1)*3[/tex]B) 22 rows.C) [tex]\sum_{n = 1\ to\ 22} (20 + (n - 1)*3)[/tex]D) There are 1,133 seats in total.How to write the formula for the sequence?
We know that we have 20 seats on the front row, and then we add 3 more on each row, so the formula will be:
[tex]A_n = 20 + (n - 1)*3[/tex]
This gives the number of seats on the n-th row.
B) The last row has 83 seats, then we need to solve:
[tex]A_n = 20 + (n - 1)*3 = 83\\\\(n - 1)*3 = 83 - 20 = 63\\\\n - 1 = 63/3 = 21\\\\n = 21 + 1 = 22[/tex]
So we conclude that there are 22 rows.
C) The total number of seats will be:
[tex]\sum_{n = 1\ to\ 22} (20 + (n - 1)*3)[/tex]
D) Instead of using the sum above (we should add 22 terms) we use the general formula for the sum of N terms in an arithmetic sequence:
[tex]S_N = (N/2)*(2A_1 + (N - 1)*d)[/tex]
In this case, we replace N by 22, and d is the common difference of the sequence, which we know is equal to 3, so we wil have:
[tex]S_{22} = (22/2)*(2*20+ (22 - 1)*3) = 11*(40 + 21*3) = 1,133[/tex]
There are 1,133 seats in total.
If you want to learn more about sequences, you can read:
https://brainly.com/question/7882626
Find the area of the parallelogram below, after the
purple triangle-sized hole was removed.
Answer:
142.5
Step-by-step explanation:
Area of a triangle = 1/2*a*h
1/2*9*3 = 13.5
Area of a parallelogram = a*h
12*13 = 156
156-13.5 = 142.5
what decimal part of $1 is 6 pennies
Choose all the common denominators for 1/9 and 1/2
Answer:
Common denominators of 9 and 2 are 18,36
Step-by-step explanation:
Can someone help me find the value of y and how to my got it
Explanation:
The tickmarks tell us that sides HG and FG are the same length. The triangle is isosceles. Directly from this, we know that the opposite angles F and H are congruent. Both are 4y-7 degrees.
Angle G is 90 degrees because of Thales' Theorem. This is because HF is the diameter of the circle. It's also the hypotenuse of the right triangle.
For any triangle, the three interior angles always add to 180 degrees.
F+G+H = 180
(4y-7) + (90) + (4y-7) = 180
8y + 76 = 180
8y = 180-76
8y = 104
y = 104/8
y = 13
Eli and Samantha work at a dry cleaners ironing shirts. Eli can iron 20 shirts per hour, and Samantha can iron 35 shirts per hour. Samantha worked 2 more hours than Eli and they ironed 400 shirts between them. Write a system of equations that could be used to determine the number of hours Eli worked and the number of hours Samantha worked. Define the variables that you use to write the system.
Answer:
Step-by-step explanation:
I did this before. I'm 14 :D
E-
y=20x
Eli ironed 2 more hours and got 400 shirts.
S-
y=35x
Let x be the number of shirts ironed.
400/20x = 20.
20-2=18.
That means she ironed 360 shirts prior.
If both of them were at the same speed of 18 by (let x represent). Then Samantha ironed 630 shirts while Eli ironed 360 shirts, but ironed 2 more hours which got him to get 400 shirts.
Please help! 23, 24, and 25
Answer:
please let's remove all the scamers on brainly, help me by not clicking on such scam links
A triangle has two sides of length 6 and 19. What is the largest possible whole-number length for the third side?
Answer: 18
Step-by-step explanation:
If 19 Is hypotenuse and 6 is one of the sides
i need this answerd ASAP ill give brainliest to whoever solves it first along with 3
40 points
Answer:
Below.
Step-by-step explanation:
Mean = (61+59+60+50+54+56+61+63)/8
= 464/8
= 58 degrees
Deviations:
61 - 58 = 3
59-58 = 1
60-58 = 2
50-58 = -8 = 8 (absolute value)
54-58= -4 = 4
56-58 = -2 = 2
61-58 = 3
63-58 = 6
MAD = (3+1+2+8+4+2+3+6) / 8
= 3.625
= 3.6 to the nearest tenth.
The difference of two numbers is 9 if the larger number is one more than twice the smaller number find the larger number
Answer:
17
Step-by-step explanation:
let the two numbers be X and Y
let larger number = Y
from the first statement
Y - X = 9 equation (1)
from the second statement
Y = 1+ 2X equation (2)
substitute equation (2) into (1)
1+2X-X = 9
1+X= 9
X = 9-1 = 8
X= 8
put X = 8 into equation (2)
Y= 1+2X
Y= 1+2(8)
Y= 1+16 = 17
larger number = 17.
A storage container measures 3 ft by 6 ft and is 5 ft high. What is the volume of this container in cubic yards?
Answer:
3 1/3 yd^3
Step-by-step explanation:
Volume of a rectangular prism: L*W*H
ft. = 1/3 yd.
3/3 = 1 yd.
6/3 = 2 yd.
5/3 = 1 2/3 yd.
1*2*1 2/3
=2* 1 2/3
=2 4/3
= 3 1/3 yd.^3
Find the value of x.
Step-by-step explanation:
9x+5x+71+139+92=540
14x+302=540
14x=540-302=238
x=238/14
x=17
Which is part of the process in the formation of hail pellets? They are tossed up and down in clouds. They lose layers of ice and grow smaller. They grow to less than 5 mm in diameter. They form ice crystals directly from water vapor.
Answer:
A. They are tossed up and down in clouds
Step-by-step explanation:
The solution is, D. They grow heavy and fall to the ground., is part of the process in the formation of hail pellets.
What is hail pellets?Graupel is also called snow pellets or soft hail, as the graupel particles are particularly fragile and generally disintegrate when handled. Sleet are small ice particles that form from the freezing of liquid water drops, such as raindrops.
here we have,
Hail is a form of precipitation when droplets of water freeze together in the cold upper reaches of the thunderstorms.
Thee chunks of that range from 5 to 15 cm can be round and jagged. Hail fall on the ground in a solid form they are often associated with tornadoes and certain parts of the world receive more hail than other parts do.
These frozen droplets of water when fall from the clouds get uplifted by wind and that adds another layer to them. The freezing occurs below the zero degrees at an altitude of 11,000 feet.
Mostly found in North America Nebraska, colorado and Wyoming states. and African regions in winter and South America in summer.
Varies in diameter from peas shape to size of a softball.
To learn more on hail pellets click:
https://brainly.com/question/13129574
#SPJ7
Polynomial? If so, is the
polynomial a monomial, binomial, or trinomial?
5/3m^2n^2p
Answer:
yes it is a polynomial. it is a monomial
Drag each model to show whether it is less than, equal to, or greater than 1/2.
Answer:
2/3=More
1/4=less
7/8=more
2/6=less
2/4=equal
Step-by-step explanation:
Look at each model that shows each fraction and also look at the denominators and the numerators of each fraction.
#1
2/3=4/61/2=3/6Greater than 1/2
#2
1/41/2=2/4Less than 1/2
#3
7/81/2=4/8Greater than 1/2
#4
2/61/2=3/6Less than 1/2
#5
2/4=1/2Equal to 1/2
FREE BRAINLIEST IF CORRECT: Write the following without the absolute value sign: |a^2| if a>0
Answer:
Step-by-step explanation:
When you square a number, whether it's positive or negative, the square is always positive. That is, a2 is positive whether a is positive or negative. Examples:
12 = 1 x 1 = 1
(-1)2 = (-1) x (-1) = 1
52 = 5 x 5 = 25
(-5)2 = (-5) x (-5) = 25
Since the answer is always positive, you don't need the absolute value signs: |a2| = a2.
hope this helps can i get brainly pls
Please help me solve this with steps
Answer:
x = 1.5 or 3/2
Step-by-step explanation:
First, expand the equation.
(2x - 3)² = 0
(2x - 3)(2x - 3) = 0
In similar equations, we would solve for both pairs of parenthesis. However, since the equations inside both are the same, we only need to solve for ONE of them, bringing one correct answer.
2x - 3 = 0
Add 3 to both sides.
2x = 3
Divide both sides by 2.
x = 3/2 or 1.5.
Step-by-step explanation:
Mark me brainliest please i really need itsolve the triangle.round to the nearest degree.
Answer:
30°, 60°
Step-by-step explanation: AB:BC:CA=√3:1:2
Abel ran more than 8 miles this week. which set of steps shows how to write an inequality that represents the number of miles abel ran? identify the variable as the number of miles. identify the inequality symbol as less than. identify the constant as 8 miles. write the inequality as m less-than 8. identify the variable as the number of miles. identify the inequality symbol as less than. identify the constant as negative 8 miles. write the inequality as m less-than negative 8. identify the variable as the number of miles. identify the inequality symbol as greater than. identify the constant as negative 8 miles. write the inequality as m greater-than negative 8. identify the variable as the number of miles, m. identify the inequality symbol as greater than. identify the constant as 8 miles. write the inequality as m greater-than 8.
The inequality that represents the scenario is x > 8
How to determine the inequality?From the question, we understand that:
Abel ran more than 8 miles this week
Let the number of miles be x.
The text "more than" means that we make use of the greater than inequality symbol
So, the inequality that determines the steps is:
x > 8
Read more about inequality at:
https://brainly.com/question/11234618
Answer:
m
Step-by-step explanation:
percent discount
A $98.00 power inverter is on sale for $78.40
Answer: 20%
Step-by-step explanation:
98 - 78.40 = $19.6
Discount is 19.6/98 = 0.2
Percentage = 0.2 × 100/ 1
Line A is perpendicular to Line B. If the slope of Line A is 2/5, what is the slope of Line B?
what are ordered pairs
Answer:a pair of elements a, b having the property that (a, b) = (u, v) if and only if a = u, b = v.
2. a) How many months is one
quarter of a year?
Answer:
3
Step-by-step explanation:
A quarter is equal to four and since 12 divided by 4 = 3, 3 months is a quarter of a year
Have a great day!