[tex]\\ \sf\longmapsto \frac{5}{ \sqrt{7} - \sqrt{3} } + \frac{1}{ \sqrt{7} + \sqrt{3} } \\ \\ \sf\longmapsto \frac{5( \sqrt{7} + \sqrt{3} ) + 1 (\sqrt{7} - \sqrt{3} )}{( \sqrt{7} - \sqrt{3} )( \sqrt{7} + \sqrt{3} )} \\ \\ \sf\longmapsto \frac{5 \sqrt{7} + 5 \sqrt{3} + \sqrt{7} - \sqrt{3} }{( { \sqrt{7} )}^{2} - ( \sqrt{3}) {}^{2} } \\ \\ \sf\longmapsto \frac{5 \sqrt{7} + \sqrt{7} + 5 \sqrt{3} - \sqrt{3} }{7 - 3} \\ \\ \sf\longmapsto \frac{6 \sqrt{7} + 4 \sqrt{3} }{4} [/tex]
Carter buys a one-gallon bottle of juice for $23.04. What is the unit rate of the cost of the juice per fluid ounce?
1 gallon
=
1 gallon=
4 quarts
4 quarts
1 quart
=
1 quart=
2 pints
2 pints
1 pint
=
1 pint=
2 cups
2 cups
1 cup
=
1 cup=
8 fluid ounces
8 fluid ounces
Before you try that problem, answer the question below.
How many fluid ounces of juice did Carter buy?
1 gallon = 4 quarts
4 quarts = 8 pints
8 pints = 16 cups
16 cups = 128 fluid ounces
He bought 128 ounces
Find x. Round your answer to the nearest tenth of a degree.
Answer:
x = 55.8
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
cos theta = adj / hypotenuse
cos x = 9/16
Taking the inverse cos of each side
cos^-1 (cos x) = cos^-1 (9/16)
x=55.77113
To the nearest tenth
x = 55.8
Answer:
Relative to x, the side of 16 is the hypotenuse, and the side of 9 is adjacent.
So we think, what trigonometric property relates hypotenuse and adjacent sides of a right triangle?
SOH CAH TOA
We can use the COSINE function to solve in this case, as we have both the ADJACENT SIDE (A) and the HYPOTENUSE (H).
Cosine = Adjacent/Hypotenuse
Cosine (x) = 9/16
Angle x = 55.8 degrees.
Let me know if this helps!
The table below shows some inputs and outputs of the invertible function f with domain all real numbers.
Answer:
f^-1 (-15) = -6
f^-1(4) + f(9) = 0
Step-by-step explanation:
f^-1 (-15) =
Look where the output is -15 and find the x value ( x=-6)
Since where are using the inverse function, the input becomes the output and the output and the output becomes the input
f^-1 (-15) = -6
f^-1 (4) = -11 (inverse function)
f(9) = 11 ( regular function)
f^-1(4) + f(9) = -11+11 = 0
accountancy
So i have to make trial balance and im kinda confused with 'interest'. So which side did it go to? Credit or debit? It didn't state the interest as received or expense/paid. someone told me to look at the bank but hey i need more explanation T^T
muscle max gym charges a $30 fee to join plus $2 each day that you go workout. Capital cross-fit charges $10 to join and $4 each day you use the gym. After how many days of workouts would the two gyms have cost you the same amount of money?
Set up equations for each gym.
multiply daily cost by number of days(x) and add the fee:
Muscle max: 2x + 30
Capital: 4x + 10
Now set them
Equal to each other and solve for x:
2x + 30 = 4x + 10
Subtract 2x from both sides :
30 = 2x + 10
Subtract 10 from both sides :
20 = 2x
Divide both sides by 2:
X = 10
It will take 10 days
Find the surface area of the figure round your answer to the nearest tenth if necessary
Answer:
.kpokojj8nvchrfhuthuvu9jeuvh
Step-by-step explanation:
j8tguhrhfgzhedh8ugh8euweuhujdhhruehf hhcufe7fhd fu y in my as 08ygrt8hthts8hewhrs8h8h8
Write an equation for the graph below in terms of x
Answer:
x = -2
Step-by-step explanation:
the line goes through -2 on the x-axis
the line also goes through -3 on the y-axis
five brothers of 4, 9, 11, 13 and 16 years respectively, receive an inheritance of 1,500,000, the will stipulated that that amount must be shared by the heirs so that, placed the shares in a bank, they would result in equal capitalized amounts, when each one reached 21, could raise his share. Knowing that the bank charges an interest rate of 9% per year, what is the amount of each share?
9514 1404 393
Answer:
Youngest to oldest:
160,406.86246,805.83293,230.01348,386.58451,170.72Step-by-step explanation:
At 9% interest per year, the present value of 1 at age 20 is ...
p(a) = 1.09^(a-20)
Adding the present values for the different ages, we get a total of about 2.35528984846. Dividing the inheritance by that amount gives the multiplier for each of the present value numbers. The result is the list of shares shown above. At age 20, each brother will inherit about 636,864.29.
__
Additional comment
This is the sort of question that suggests the use of a graphing calculator or spreadsheet for doing the tedious number crunching.
(We assume the bank pays 9% per year, rather than charges 9% per year.)
HELPP plz don't send a file whats the answer and explanation plz if you can
Answer:
5/0 is not a rational number
Step-by-step explanation:
you cant divide by 0
PLEASE HELP!!!
Find the equation of the line with an x intercept of 4 and a y intercept of -1.5
Answer:
y = 4x - 1.5
Step-by-step explanation:
The slope intercept form of a line is
y = mx+b where m is the slope and b is the y intercept
y = 4x - 1.5
Factors and rewrite the expression 25x-15
Answer:
5(5x-3)
Step-by-step explanation:
The common factor in this expression is 5 so divide 5 to all the values
25/5=5
-15/5= -3
Put these values into parenthesis and leave the 5 on the left side and out of the parenthesis
5(5x-3)
Answer:
5(5x - 3)
Step-by-step explanation:
The greatest common factor here is 5. Divide each term by 5 and simplify.
25x/5 = 5x
15/5 = 3
Therefore, the answer is 5(5x - 3).
Please help explanation if possible
Answer:
18.84 feet. let me know if you have ay other questions.
Step-by-step explanation:
The way to find the formula for circumference is kinda complicated so it is best to ust memorize the formula, which is 2πr. or 2 times pi times the radius.
Your problem gives you the formula, but instead of 2 and r in it you have d, which is the diameter.
The diameter of the circle is 2 times the radius, so that's why it is replaced.
the radius is the distance from the center fo the circle to one edge, and the diameter is the distance through the circle passing through its center. so it's the center to one end plus the center to another end. or r+r which is also 2r.
So d = 2r, so in this problem d =6 feet.
So now the formula πd = 3.14*6 feet = 18.84 feet
The productivity of a country is given by f(x, y) = 600x^2/3 y^1/3, where x and y are the amount of labor and capital.
a) Compute the marginal productivities of labor and capital when x = 125 and y = 64.
b) Use part (a) to determine the approximate effect on productivity of increasing capital from 64 to 66 units, while keeping labor fixed at 125 units.
c) What would be the approximate effect of decreasing labor from 125 to 124 units while keeping capital fixed at 64 units?
(5, 4)
11-5-2)
16.nat's the slope-intercept form of the equation of the line graphed in this figure?
O A. y = 5/3x + 1
O B.y=-3x + 1
O C. y = 3x + 1
O D.y = -5/3X - 1
Answer:
The answer is B. y=3/5x+14. (08.02 MC)
Factor completely 2x3 + 10x2 + 14x + 70. (5 points)
(2x^2 + 14)(x + 5)
(x^2 + 7)(2x + 10)
2(x^3 + 5x2 + 7x + 35)
2[(x^2 + 7)(x + 5)]
Answer:
2[(x^2 + 7)(x + 5)]
Step-by-step explanation:
Note that the ratio of the first and second terms is the same as that between the third and fourth terms. So this cubic will factor by grouping, but first we can separate out the common scalar factor 2...
2x3+10x2+14x+70=
2(x3+5x2+7x+35)
2((x3+5x2)+(7x+35))
2(x2(x+5)+7(x+5))
2(x2+7)(x+5)
Answer:
The answer is D. 2[(x2 + 7)(x + 5)]
Step-by-step explanation:
Give example to verify if the given statement is true or false
1) if two numbers are co-primes , at least one of them should be prime number.
Answer:
no
Step-by-step explanation:
if two numbers are co-prime that is not necessary that one of them must be a prime number
After how many years, to the nearest whole year, will an investment of $100,000 compounded quarterly at 4% be worth
$213,022?
Provide your answer below:
9514 1404 393
Answer:
19 years
Step-by-step explanation:
The compound interest formula tells you the future value of principal P invested at annual rate r compounded n times per year for t years is ...
A = P(1 +r/n)^(nt)
Solving for t, we get ...
t = log(A/P)/(n·log(1 +r/n))
Using the given values, we find t to be ...
t = log(2.13022)/(4·log(1 +0.04/4)) ≈ 19.000
The investment will be worth $213,022 after 19 years.
Question 6 of 10
The domain of a function f(x) is x = 0, and the range is ys -1. What are the
domain and range of its inverse function, '(x)?
Answer: y = 0 and x = -1
A fruit company delivers its fruit in two types of boxes: large and small. A delivery of 7 large boxes and 9 small boxes has a total weight of 192
kilograms. A delivery of 5 large boxes and 3 small boxes has a total weight of 114 kilograms. How much does each type of box weigh?
please help me
find x
9514 1404 393
Answer:
x = 6√2
Step-by-step explanation:
The side ratios in an isosceles right triangle are ...
1 : 1 : √2
These will be the same as ...
x : x : 12
so, ...
x = 12/√2
x = 6√2
In performing a one-way ANOVA, ________ measures the variability of the observed values around their respective means by summing the squared differences between each observed value of the response and its corresponding treatment mean.
Answer: SS Error
Step-by-step explanation:
The SS Error refers to the sum of the squares of the deviations of the observations, from their mean. It is simply the total variance from the observations on the study.
In performing a one-way ANOVA, the SS Error measures the variability of the observed values around their respective means and this is done through the summation of the squared differences between each observed value of the response and its corresponding treatment mean.
Người ta chiếu xạ liều 3000 Rơn ghen vào một quần thể ruồi dấm ở thế hệ F1: Chiếu xạ 1000 con ruồi dấm không cho ăn đường thì có 80 con bị đột biến và chiếu xạ 1000 con ruồi dấm có cho ăn đường thì có 120 con bị đột biến. Cho ăn đường có ảnh hưởng đến tỉ lệ đột biến của ruồi giấm không, với mức ý nghĩa 5%? Giá trị kiểm định là
Answer:
gggggggggggggggggggggrrrrrrrrrrrttyuuiiiii
A popular beach erodes 4 inches per year on average.
An eroding beach.
A. How many years will it take for the coastline to erode one foot?
Answer:
3 years
Step-by-step explanation:
4 inches per year on average
1 foot = 12 inches
12 divided by 4 equals 3
therefore it is 3 years
Select the correct answers in the table.
Rachel enjoys exercising outdoors. Today she walked 5 2/3 miles in 2 2/3 hours. What is Rachel’s unit walking rate in miles per hour and in hours per mile?
Find the local linear approximation L(x) of the function f(x) = 5−x^2 at x = 2.
Use this to estimate f(2.1).
Answer:
L(x)=-4x+9
L(2.1)=0.6
Step-by-step explanation:
It's asking us to find the tangent line to curve f(x) = 5−x^2 at x = 2.
Theb use this to estimate f(2.1).
To find slope of tangent line, we must differentiate and then plug in 2 for x.
f'(x)=0-2x by constant and power rule.
f'(x)=-2x
So the slope of the tangent line is -2(2)=-4.
A point on this tangent line shared by the curve is at x=2. We can find it's corresponding y-value using f(x)=5-x^2.
f(2)=5-(2)^2
f(2)=5-4
f(2)=1
So let's rephrase the question a little.
What's the equation for a line with slope -4 and goes through point (2,1).
Point-slope form y-y1=m(x-x1) where m is slope and (x1,y1) is a point on the line.
Plug in our information: y-1=-4(x-2).
Distribute: y-1=-4x+8
Add 1 on both sides: y=-4x+9
Let's call this equation L(x), an expression to approximate value for f near x=2.
L(x)=-4x+9
Now the appropriation at x=2.1:
L(2.1)=-4(2.1)+9
L(2.1)=-8.4+9
L(2.1)=0.6
If we did plug in 2.1 into given function we get 5-(2.1)^2=0.59 . This is pretty close to our approximation above.
The half-life of a radioactive substance is 20 years. If you start with some amount of this substance, what fraction will remain in 180 years?
Answer:
1/512
Step-by-step explanation:
Let staring fraction = x
Half-life = 20 years ; this is the time taken for an element to decrease to half of its original size
Hence,
After 20 years - - - > x/2
After 40 years - - - - > x/2 ÷ 2 = x/2 * 1/2 = x /4
After 60 years - - - - > x/4 ÷ 2 = x/4 * 1/2 = x/8
After 80 years - - - - -> x/8 ÷ 2 = x/8 * 1/2 = x / 16
After 100 years - - - > x/16 * 1/2 = x/32
After 120 years - - - - > x/32 * 1/2 = x/64
After 140 years - - - - -> x / 64 * 1/2 = x / 128
After 160 years - - - - - > x / 128 * 1/2 = x/256
After 180 years - - - - > x/256 * 1/2 = x / 512
Hence, the fraction after 180 years = 1/512
Dad is twice as old as Junior. Gramps is twice as old as Dad. The sum of the three ages is 140. How old is Gramps?
Answer:
80
Step-by-step explanation:
We can start of with Junior's age. Then if dad is twice as old as Junior, then we add 2 parts and get 3 parts. Then Gramps is twice as old as Dad so we add 4 parts and get 7 parts. Now we divided 140 by 7. We get 20. This is Junior's age. By looking at that, we know Dad is 40, and Gramps is 80.
Gramps is 80 years old.
Hi! I'm happy to help!
We can say that Junior is x years old. This would mean that Dad is 2x years old, and Gramps is 4x years old. All together, their age is 7x. We can write an equation to solve.
7x=140
Divide both sides by 7 to find out x.
x=20
This means that Junior is 20 years old. Dad is double that, so he is 40 years old. And Gramps is double that so he is 80 years old.
To check our answer we can add all of them together.
20+40+80
140
This means that Gramps is 80 years old.
I hope this was helpful, keep learning! :D
What is the order of rotational symmetry for the figure?
A. 3
B. 2
C. 4 or more
D. 1
9514 1404 393
Answer:
C. 4 or more
Step-by-step explanation:
Rotating the figure in increments of 90° will give the same figure. There are 4 such rotations in a full turn. The order of rotational symmetry is 4.
When a 0.42 tax was added to the price of a ticket, the total bill come to $7.03. Describe the above situation as a linear equation.
Answer:
P = 7.03 - 0.42T
Step-by-step explanation:
Let the price of a ticket be P.
Let the ticket be T.
A linear equation can be defined as an algebraic equation that's typically written for two (2) independent variables, in which each of them has an exponent of one (1) and they make a straight line when plotted on a graph.
Given the following data;
Tax = 0.42
Total bill = $7.03
Translating the word problem into an algebraic expression, we have;
0.42T + P = 7.03
P = 7.03 - 0.42T
Ms. Lowder has 2 children, one in first grade and one in fifth grade. Both children need paper for school. Paper costs $2.29 per pack. If the first grader needs 2 packs of paper and the fifth grader needs 6 packs of paper, how much money will Ms. Lowder spend on paper?
the answer is she spend $18.32
