Answers
Whole part = 2
Fractional part = 59/396
======================================================
Work Shown:
3 & 3/5 = 3 + 3/5
3 & 3/5 = 15/5 + 3/5
3 & 3/5 = 18/5
--------------------
4 & 8/9 = 4 + 8/9
4 & 8/9 = 36/9 + 8/9
4 & 8/9 = 44/9
--------------------
Now apply the rule that 1/(A/B) = B/A. We apply the reciprocal to the fraction A/B to get B/A
That means something like 1/(18/5) becomes 5/18
Also, 1 over (44/9) becomes 9/44
1 over (3/5) becomes 5/3
-------------------
We now have the following:
(5/18) + (9/44) + (5/3)
We'll come back to this later. But first need the LCD, which means we need the LCM of the denominators.
Write out the prime factorization of each denominator
18 = 2*3*344 = 2*2*113 = 1*3The unique prime factors are: 2, 3, 11
We have 2 occur at most twice, so 2^2 is part of the LCM.We have 3 occur at most twice, so 3^2 is part of the LCMWe have 11 occur at most 1 time, so 11^1 is part of the LCMThe LCM is 2^2*3^3*11^1 = 1188, which is also the LCD
-------------------
We need to get each fraction to have the LCD
5/18 = (5/18)*(66/66) = 330/1188
9/44 = (9/44)*(27/27) = 243/1188
5/3 = (5/3)*(396/396) = 1980/1188
We can now add the fractions like so
(5/18) + (9/44) + (5/3)
(330/1188) + (243/1188) + (1980/1188)
(330+243+1980)/1188
2553/1188
-------------------
We're almost done. We just need to convert to a mixed number, aka mixed fraction
Using a calculator or long division, you should find that
2553/1188 = 2.1489898989899
approximately. Focus just on the stuff to the left of the decimal point. That's the whole part of the answer.
We can then say: 2553-1188*2 = 177
This forms the numerator of the fractional part. The denominator stays at the LCD 1188
That forms the fraction 177/1188. Divide both parts of that fraction by 3 to fully reduce it. You should get to 59/396
-------------------
So that's how we end up with the mixed number 2 & 59/396
Related Questions
Use the data in the table to complete the sentence. x y –2 7 –1 6 0 5 1 4 The function has an average rate of change of __________.
Answers
Answer: To find the average rate of change, evaluate the function at the given points.
Evaluate the difference of the function at the given points.
Divide the difference of the function at the given points with the difference of the given points.
Step-by-step explanation:
The Average of rate is -1.
Everytime it goes up by one the y goes down by 1 so it would be -1.
The average rate of change of the function in the table given is: -1.
What is Average Rate of Chnge of a Function?Average rate of change of a function = change in y / change in x = rise/run.
Given the table representing a function, and using two set of ordered pairs, (-2, 7) and (0, 5):
Average rate of change of the function = (7 - 5)/(-2 - 0)
Average rate of change of the function = 2/-2
Average rate of change of the function = -1.
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The measure of central angle MNL is π radians, and the measure of the entire circle is 2π radians.
The ratio of the measure of the central angle to the entire circle measure is
Answers
Answer:
1 : 2
Step-by-step explanation:
π / 2π = 1/2
1 : 2
what two numbers add up to 55 and multiply to -375
Answers
Answer:
-6.13406 and 61.13406
Step-by-step explanation:
x + y = 55
x × y = -375
y = 55 - x
x × (55 - x) = -375
55x -x² = -375
x² - 55x - 375 = 0
solution of a quadratic equation :
x = (-b ± sqrt(b² - 4ac))/(2a)
a=1
b=-55
c=-375
x = (55 ± sqrt(55² + 4×375))/2 = (55 ± sqrt(4525))/2 =
= (55 ± sqrt(25 × 181))/2 = (5×11 ± 5×sqrt(181))/2 =
= 5/2 × (11 ± sqrt(181)) =
= 61.13406... or -6.13406...
y = 55 - 5/2×(11 ± sqrt(181)) = 55/2 ± 5/2×sqrt(181) =
= -6.13406... or 61.13406...
There is a bag with only red marbles and blue marbles. The probability of randomly choosing a red marble is 1 /9 . There are 63 marbles in total in the bag and each is equally likely to be chosen. Work out how many red marbles there must be.
Answers
Answer: 7 red marbles.
Step-by-step explanation:
Since we are given the information that there are only red marbles and blue marbles in the bag and that the probability of randomly choosing a red marble is 1 /9 while there are 63 marbles in total.
Then the number of red marbles will be:
= 1/9 × 63
= 7
There are 7 red marbles
The number if blue marbles will be:
= 63 - 7
= 56 blue marbles
APB is parallel to CTRD. PQRT is a quadrilateral. work out the size of the angle marked x you must show your working
Answers
Answer: X would be 84 degrees.
Step-by-step explanation: APB is a straight angle, which adds up to 180 degrees. TPQ is 90 degrees, and QPB is 32 degrees, so 180-90-32=58. APT is 58 degrees. APT and PTR are alternate interior angles, therefore they have the same angle measure. So PTR is also 58 degrees. A quadrilateral adds up to 360 degrees, so add up the three known angles in the quadrilateral, 58+90+128, which gives you 276 degrees. 360-276=84 degrees, therefore X would be 84 degrees.
A general formula for a parabola is y2=4px.
What is the value of p in the equation y2=−4x?
P=−4
P=−1
P=1
P=4
Answers
Answer:
P = -1
Step-by-step explanation:
-1 x 4 = -4
The solution is : p= -1, is the value of p in the equation y^2=−4x.
What is equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign. In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal.
here, we have,
Explanation:
We have been given parabola along positive side of x-axis with equation
y² = 4px
and, y² = -4x
after equating the values of y² we will get
4px =-4x
Divide each term by x on both left hand side and right hand side we will get
4p= -4
Now, divide each term by 4 on both left hand side and right hand side we will get the final result p=-1
Hence, The solution is : p= -1, is the value of p in the equation y^2=−4x.
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Given 15=3(2x+4)−3
Prove x=1
Complete the proof. Provide reasons for 1-6 below. Make sure to number your answers.
Answers
we start with the inside of the para thesis so multiply 2•1 which gives us 2 and we add 4 which gives us 6
now we have 15=3(6)-3
we multiply the 3 and 6 and we get 18
Now we have 15=18-3 so we subtract 18-3 and we get 15
15=15 is the product
The value of x in the expression 15 = 3(2x + 4) - 3 is 1.
What is expression?A number, a variable, or a combination of numbers and variables and operation symbols is called expression.
According to the given question.
We have an expression
[tex]15 = 3(2x+ 4) -3[/tex]
Solve the above expression for x.
Step 1: open the parentheses
[tex]15 = 3(2x + 4) -3[/tex]
⇒ [tex]15 = 6x + 12 -3[/tex]
Step 2: simplify the above expression.
[tex]15 = 6x + 9[/tex]
Step 3: subtract 9 to the both the sides
[tex]15 - 9 = 6x + 9 -9[/tex]
⇒[tex]6 = 6x[/tex]
Step 4: Divide both the sides by 4
⇒ [tex]\frac{6}{6} =\frac{6x}{6}[/tex]
⇒ [tex]x = 1[/tex]
Hence, we proved that x = 1 for the above expression.
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The graph below shows the solution to which system of inequalities?
Answers
Answer:
A
Step-by-step explanation:
During a sale, a store offered 35% discount on a particular couch that was originally priced at $390. After the sale, the discount price of the camera was increased by 35%. What was the price of the couch after this increase? Round to the nearest cent.
Answers
Answer:
$342.23
Step-by-step explanation:
35/100 x $390 = $136.50
Price of couch after 35% discount
= $390 - $136.50
= $253.50
35/100 x $253.50 = $88.725
Price of couch after the 35% increase
= $253.50 + $88.725
= $342.225
= $342.23 (round off to nearest cents)
What is the angular velocity of a point that rotates through
radians in 24 second
What’s the answer?
Answers
Answer:
Option A
Step-by-step explanation:
Angular velocity of an object is defined by,
Angular velocity (w) = [tex]\frac{\triangle \theta}{\triangle t}[/tex]
Here, Δθ = Change in angle of rotation
Δt = Duration or time
In this question Δθ = [tex]\frac{7\pi }{2}[/tex] radians and Δt = 24 seconds
Therefore, angular velocity = [tex]\frac{\frac{7\pi }{2} }{24}[/tex]
= [tex]\frac{7\pi }{48}[/tex] radians per second
Option A is the answer.
Two large parallel metal plates carry opposite charges. They are separated by 85mm. The work done by the field is 6x10-3J and its field exerts on a particle with charge +8µC. Calculate the surface charge density on each plate.
Answers
Answer:
The surface charge density is [tex]7.8\times10^{-8} C/m^2[/tex].
Step-by-step explanation:
separation, d = 85 mm
Work, W = 6 x 10^-3 J
charge , Q = 8µC
The potential difference is given by
W = q V
[tex]V=\frac{6\times 10^{-3}}{8\times 10^{-6}}=750 V[/tex]
Let the charge on he capacitor is q.
[tex]q = CV\\\\q = \frac{\varepsilon oA}{d}\times V\\\\\frac{q}{A} = \frac{8.85\times 10^{-12}\times750}{0.085} =7.8\times10^{-8} C/m^2[/tex]
tion 9 of 10
10 Points
Two sides of a triangle have lengths 4 and 8. Which of the Two sides of the triangle have lengths of 4 and 8. Which of the following can NOT be the length of the third side?
A. 7
B. 4
C. 5
D. 6
Answers
Answer:
B. 4
Step-by-step explanation:
the sum of two sides of a triangle should be longer than one other side
Are lines l & k parallel?
Answers
Answer:
yes both lines have a slope of 2, so they are parallel.
Step-by-step explanation:
Sam bought a computer and printer for ₹ 1,15,499. The cost of the computer was ₹ 85,789. What was the cost of the printer?
₹ 29,710
₹ 2,01,228
₹9,73,389
Answers
Answer:
₹29,710
Step-by-step explanation:
We minus ₹ 85,789 from ₹ 1,15,499 to get ₹ 29,710
Which relationship has a zero slope?
Answers
Answer:
b has zero slop mark me as a brilliant
Help please!
Brainliest + 20 points
Answers
Answer:
im not sure but pls gimme brainlyist bc im a dum dum
Step-by-step explanation:
What is the value of x in the diagram?
Answers
Answer:
x=5
Step-by-step explanation:
Since this is a right triangle, we can use the pythagorean theorem
a^2 + b^2 = c^2
x^2+ ( 2x+2)^2 = (2x+3)^2
FOIL the squared terms
x^2 +(4x^2 + 4x+4x+4) = 4x^2 + 6x+6x +9
Combine like terms
5x^2+8x +4 = 4x^2 +12x +9
Subtract 4x^2 +12x +9 from each side
5x^2+8x +4 -4x^2 -12x -9= 4x^2 +12x +9-4x^2 -12x -9
x^2 -4x -5 =0
Factor
(x-5) (x+1) = 0
Using the zero product property
x=5 x=-1
But x cannot be negative or we would have negative length
x=5
A pyramid with a triangular base has a volume of 50cm³. If the base and the height of the triangular base are 5cm and 8cm respectively, find the height of the pyramid ?
Answers
Answer:
h = 7.5 cm
Step-by-step explanation:
Firstly, we find the area of the triangular base
Mathematically, we have the area of a triangle as;
A = 1/2 * b * h
A = 1/2 * 5 * 8 = 20 cm^2
Mathematically, we have the formula as;
V= 1/3 * A * h
A is base area and h is height
50 = 1/3 * 20 * h
20h = 3 * 50
20h = 150
h = 150/20
h = 7.5 cm
Sin0=12/37 find tan0
Answers
Answer:
[tex] \large{ \tt{❃ \: EXPLANATION}} : [/tex]
We're provide - Sin θ = [tex] \frac{12}{37} [/tex] which means 12 is the perpendicular & 37 is the hypotenuse [ Since Sin θ = [tex] \tt{ \frac{p}{h}} [/tex] ] . We're asked to find out tan θ ].[tex] \large{ \tt{❁ \: USING \: PYTHAGORAS \: THEOREM}} : [/tex]
[tex] \large{ \tt{❊ \: {h}^{2} = {p}^{2} + {b}^{2} }}[/tex]
[tex] \large{ \tt{⇢ {p}^{2} + {b}^{2} = {h}^{2} }}[/tex]
[tex] \large{ \tt{⇢ \: {b}^{2} = {h}^{2} - {p}^{2} }}[/tex]
[tex] \large{ \tt{⇢ \: {b}^{2} = {37}^{2} - {12}^{2} }}[/tex]
[tex] \large{ \tt{⇢ \: {b}^{2} = 1369 - 144}}[/tex]
[tex] \large{ \tt{ ⇢{b}^{2} = 1225}}[/tex]
[tex] \large{ \tt{⇢ \: b = \sqrt{1225}}} [/tex]
[tex] \large{ \tt{⇢ \: b = 35 \: \text {units}}}[/tex]
Now , We know - Tan θ= [tex] \tt{ \frac{perpendicular}{base} }[/tex]. Just plug the values :[tex] \large{ \tt{➝ \: Tan \: \theta = \frac{p}{b} = \boxed{ \tt{ \frac{12}{35} }}}}[/tex]
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(HELP FAST TIMED)Which polynomial is prime x^3+3x^3+2x+6
Answers
Answer:
the third one
Step-by-step explanation:
A polynomial with integer coefficients that cannot be factored into polynomials of lower degree.
the third one is the answer
I NEED HELP PLZ it is very much appreciated
Answers
Answer:
C
Step-by-step explanation:
average, average, average
if there is one dot to the right that is far away and 3 dots to the left that are close to the like, estimated distance of the right dot would be 3 and the total distance sum of each dot to the left is 3, so the line would be between the 1 right dot and 3 left dots
Answer:
D
Step-by-step explanation:
D has three dots near to the line
E)
The parallelogram WXYZ belwo is a rhombus. Find the measure of
angles 1, 2, 3, 4 and 5 given that angle WZY is 60°
w
2
3
1
4
Answer:
60
Answers
Answer:
1. 60°
2. 60°
3. 30°
4. 30°
5. 30°
Step-by-step explanation:
to find angleXYZ suntract 180 from 60
angle ZWX=120°
Angle WXY=60°
The diagnals divide the inteesections in half
Which statement is necessarily true if is an altitude to the hypotenuse of right ? A. ≅ B. C. D. ∠BAC ≅ ∠BDC
Answers
Answer:
Step-by-step explanation:
Find C. See the image below
Answers
Answer:
55 degrees
Step-by-step explanation:
First, we can use Thales' Theorem to determine that because AC is along the circle's diameter, angle B (the angle opposite to that side) is a right angle.
Next, we know that an inscribed angle with its vertex on the circle, formed by two intersecting chords (A in this case) is equal to 1/2 of its intercepted arc, so angle A = 70/2=35
We can then use the fact that a triangle adds up to 180 degrees here to get
35+90+C=180
C=55 degrees
Topic: Modeling exponential functions
Kathy plans to purchase a car that depreciates
(loses value) at a rate of 14% per year. The initial
cost of the car is $21,000. Which equation
represents the value, v, of the car after 3 years?
1) v = 21,000(0.14)
2) v = 21,000(0.86)
3) v= 21,000(1.14)
4) v= 21,000(0.86)(3)
Answers
Answer:
Step-by-step explanation:
The standard form equation for this type of problem is
[tex]y=a(b)^x[/tex] where a is the initial value, b is the rate of depreciation, and x is the number of years in question. Because the value of the car is going down, b can also be written as (1 - r) where r is the rate of depreciation. For us, then, the equation will look like this:
[tex]y=a(1-r)^x[/tex] and filling in:
[tex]y=21000(1-.14)^3[/tex] which in simplified form is
[tex]y=21000(.86)^3[/tex] which I'm assuming is how choice 4 should look.
Yashoda and Ingrid shared a sum of money in the ratio 3:2, respectively. Ingrid
received $1200. What was Yashoda's share?
Answers
Answer:
Yashoda got 1800
Step-by-step explanation:
Yashoda : Ingrid
3 : 2
Ingrid got 1200
Divide this by 2
1200/2 = 600
Multiply each side by 600
Yashoda : Ingrid
3*600 : 2*600
1800 : 1200
Yashoda got 1800
Please please help me
Answers
Answer:
may be the answer is 1000.not sure.
Answer:
answer is c 1600
hope it helps
PLEASE HELP - WILL MARK BRAINLIEST w/ explanation (see attachment)
Answers
Answer:
∠ DOC = 26°
Step-by-step explanation:
The secant- secant angle DOC is half the difference of the intercepted arcs, that is
∠ DOC = [tex]\frac{1}{2}[/tex] (AB - CD) = [tex]\frac{1}{2}[/tex] (82 - 30)° = 0.5 × 52° = 26°
hey guys ... just want to make this answer sure... subtract 2x²+3x+6 from 3x²+5x+7=? A)x²+2x+1 or
B)x²+8x+13
Answers
Answer:
answer is A
Step-by-step explanation:
Answer:
A
Step-by-step explanation:
3x² + 5x + 7 - (2x² + 3x + 6) ← distribute terms in parenthesis by - 1
= 3x² + 5x + 7 - 2x² - 3x - 6 ← collect like terms
= x² + 2x + 1 → A
Does this graph represent a function? Why or why not?
Answers
Answer:
B yes, because it pases the vertical line test