Rewrite the following expression in standard form by finding common denominator and collecting like terms
Answers
The denominators of our fractions are 3, 6, and 9. 3 is already a prime, so we are going to let that one alone. 6 on the other hand is divisible by tow, so it can be decomposed into tow prime factors 2 and 3: [tex]6=(2)(3)[/tex].
9 is divisible by 3, so it can also be decomposed into tow prime factors 3 and 3: [tex]9=(3)(3)=3^{2} [/tex].
We have a common factor 3 in all our denominators, and among them the one raised to the highest power is [tex]3^{2} [/tex]. On the other hand we only have one non-common factor, 2. So, our common denominator will be:
[tex]common.denominator=(3^{2} )(2)=(9)(2)=18[/tex]
Now we know that the common denominator of our standard form fraction is 18, the only thing left is convert the denominators of each one of our fractions to 18 and simplify. To do that we are going to divide the common denominator by the denominator of each fraction, and then multiply the quotient by each one of the numerators:
[tex] \frac{2h}{3} - \frac{h}{9}+ \frac{h-4}{6} = \frac{(6)(2h)-(2)(h)+3(h-4)}{18} [/tex]
[tex] \frac{12h-2h+3h-12}{18} [/tex]
[tex] \frac{13h-12}{18} [/tex]
Answer: [tex] \frac{13h-12}{18} [/tex]
Related Questions
Marci is going to use tile to cover her terrace. How much tile does she need?
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The answer is 4*8+(16p/2)
32+8p
A=(32+8p)m^2
A=57.13 m^2 (to nearest hundredth of a m^2)
Hope this helps you>:)
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PLZ HELP I BEG U IT MAKE NO SENSE
Answers
Let ∠1, ∠2, and ∠3 have the following relationships.
∠1 and ∠2 are acute vertical angles.
∠3 is an obtuse angle adjacent to both ∠1 and ∠2.
What is the sum of the measure of ∠1 and the measure of ∠3?
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"The value of [tex]\angle1 +\angle3[/tex] lies between [tex]90^{\circ} < \angle1+\angle3< 180^{\circ}[/tex].
Given,[tex]\angle 1,\angle2, \angle3[/tex] have the following relationships.
[tex]\angle 1[/tex] and[tex]\angle2[/tex] are acute vertical angles. [tex]\angle 3[/tex] is an obtuse angle adjacent to both [tex]\angle 1[/tex] and [tex]\angle 2[/tex].We have to find the sum of measure of [tex]\angle1[/tex] and the measure of [tex]\angle3[/tex].
Angle sum property:We know that the angle sum property of triangle states that the sum of all angles of a triangle is equal to [tex]180 ^{\circ}[/tex].
[tex]\angle 1+\angle 2+\angle3= 180^ {\circ}[/tex]
[tex]\angle1+\angle3= 180-\angle2[/tex]
So, the value [tex]\angle1 and \angle3[/tex] is always greater than [tex]90{^\circ}[/tex] because [tex]\angle 3[/tex] is the obtuse angle and it is being added to [tex]\angle1[/tex],
so it is always greater than right angle and less than [tex]180^{\circ}[/tex].
Hence the value of [tex]\angle1 +\angle3[/tex] lies between [tex]90^{\circ} < \angle1+\angle3< 180^{\circ}[/tex].
For more details on angle sum property follow the link:
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Find the area of the figure shown in the diagram to the nearest hundredth.
A) 16.00 m2
B) 28.57 m2
C) 41.13 m2
D) 49.12 m2
Answers
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This figure is a composition of two quarter-circles and a square
Area of quarter circle = (1/4)*(area of circle)
Area of quarter circle = (1/4)*(pi*r^2)
Area of quarter circle = (1/4)*(pi*4^2)
Area of quarter circle = (1/4)*(pi*16)
Area of quarter circle = (1/4)*16*pi
Area of quarter circle = 4pi
There are two quarter circles, so the two circular areas add to 4pi+4pi = 8pi
Area of square = s*s = 4*4 = 16 square meters
Add the square area to the circular area: 8pi+16
Now use a calculator to find 8pi+16 = 41.1327412287183 which rounds to 41.13
using similarity solve for x. show all work
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First find h.
h²= 9 x 16
h²=144
Take square root.
h=12
Now to find x, we use Pythagorean theorem.
c²=a²+b²
Put values
x²=9²+12²
x²=81+144
x²=225
Take square root.
x=15
Answer: x=15
A stock investment went up 25% in 2006. Starting at this increased value, what percent would it have to go down in 2007 to be back to its original price at the beginning of 2006?
PS The answer is not 25%
Answers
It is 20%. Is that helpful at all?
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Which equation best represents a trend line for the scatter plot?
A. y=6/7x+50/7
B. y=−7/6x+55/6
C. y=7/6x+41/6
D. y=−6/7x+62/7
https://static.k12.com/nextgen_media/assets/8124601-NG_IMC_IT_03_NP037_32.png
(Copy and paste the URL into search bar to see graph)
Answers
General Idea:
We need to apply the below formula to find the trend line from the given x and y values.
[tex] (1)\; mean:\; \bar{x}\;=\;\frac{\sum x_i}{n}, \; \;\bar{y}\;=\;\frac{\sum y_i}{n}\\ \\ (2) \;trend\; line: \; y=A+Bx, \;B=\frac{S_{xy}}{S_{xx}}, \;\;A=\bar{y}-B\bar{x}\\ \\ Where:\\ \\ S_{xx}=\frac{\sum x_i^2}{n}-\bar{x}^2\\ \\S_{xy}=\frac{\sum x_iy_i}{n}-\bar{x} \cdot \bar{y} [/tex]
Applying the concept:
In the graph given the trend line passes through two points (1, 8) and (7, 1).
We need to make use of the two point formula to find the equation of trend line
[tex] m=\frac{y_2-y_1}{x_2-x_1} [/tex]
Substituting the points (1, 8) and (7, 1) in the above formula to find slope we get...
[tex] m = \frac{1-8}{7-1}=\frac{-7}{6} [/tex]
The point slope form of an equation which is used to write the equation of line when we know a point and slope is given below:
[tex] y-y_1=m(x-x_1) [/tex]
Substituting the values in the above formula we get ...
[tex] y-8=\frac{-7}{6}(x-1)\\Distributing \; -7/6\; in\; the\; right\; side\; of\; the\; equation \\ \\ y-8=\frac{-7}{6}x+\frac{7}{6}\\ Adding\; 8\; on\; both\; sides\\ \\ y-8+8=\frac{-7}{6} x+\frac{7}{6} +8\\ Combining \; like \; terms\\ \\ y=\frac{-7}{6}x+\frac{7}{6}+\frac{8 \cdot 6}{1 \cdot 6}\\ \\ y=\frac{-7}{6}x+\frac{7}{6}+\frac{48}{6}\\ \\ y=\frac{-7}{6} x+\frac{55}{6} [/tex]
Conclusion:
The equation best represents a trend line for the scatter plot is Option B.
B. y=−7/6x+55/6
are these two expressions equivalent when x=2? 7(8x+5) and 48x+35
Answers
The second expression equals 131.
So, no the expressions are not equivalent.
Answer:
7(8x+5) ≠48x+35 when x = 2.
That is; the two expressions are not equivalent when x = 2
Step-by-step explanation:
To solve this, we need to follow the steps below
We will substitute x = 2 in the first expression and simplify, then we will now substitute x =2 in the other expression and simplify, at the end of the simplification, we will compare the two expression to see if they are equal.
First lets open up the bracket, that is; 7(8x + 5)=56x + 35
Now substitute x = 2 in 56x + 35
56 x + 35 = 56(2) + 35 = 112 + 35 = 147
56 x + 35 = 147 when x = 2
Next is to substitute x = 2 in 48x + 35
48(2) + 35 =96 + 35 =131
The value of 48x + 35 = 131 when x =2
147 ≠ 131
Therefore the two expressions are not equivalent when x = 2
what is the additive inverse of the polynomial -6^3+4x ?
Answers
A. -5x3 + 4x2 - 6x - 9
B. -5x3 + 4x2 - 6x + 9
C. 5x3 - 4x2 + 6x - 9
D. -9 + 6x - 4x2 + 5x3
E. 9 - 6x - 4x2 + 5x3
Correct Answer: B
16 is what fractional part of 20
Answers
The number 16 is 4/5 fractional part of 20.
What is mean by Fraction?
A fraction is a part of whole number, and a way to split up a number into equal parts. Or, A number which is expressed as a quotient is called fraction. It can be written as the form of p : q, which is equivalent to p / q.
Let the fraction part of 16 = x
So, We can formulate;
⇒ 16 = x × 20
⇒ x = 16 / 20
⇒ x = 4/5
Thus, The number 16 is 4/5 fractional part of 20.
Learn more about the fraction visit:
https://brainly.com/question/5454147
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A scientist is working with 2 meters of gold wire. How long is the wire in millimeters? Be sure to include the correct unit in your answer. ( mm, cm, dm, m, km )
Answers
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2 meters(m) = 2000 millimeters (mm)
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Have a great day!
The correct answer is 2000 mm.
To convert the length of the gold wire from meters to millimeters, one must know the conversion factor between these two units. There are 1000 millimeters in 1 meter. Therefore, to convert 2 meters to millimeters, one multiplies the length in meters by 1000.
Calculation:
2 meters * 1000 millimeters/meter = 2000 millimeters
Thus, the length of the gold wire in millimeters is 2000 mm.
PLEASE HELP ME WITH THE REST OF THE QUESTIONS
Answers
omg delete thhis queston plz
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Answers
What is the volume of the rectangular pyramid?
A.
210 ft3
B.
105 ft3
C.
315 ft3
D.
21 ft3
Answers
l=9
w=5
h=7
9*5*7=315.
So with this problem, you must know the formula to figure it out.
The formula for a pyramid is: lwh/3 This merely stands for: length× width× height÷3
So for this rectangular pyramid, these are the measurements:
Length: 5 feet
Width: 9 feet
Height: 7 feet
So, we now insert the measurements into the formula.
5× 9× 7/3
Next, we multiply...
5×9×7= 315
Then, we divide...
315÷ 3= 105
Finally we have to add a label which would be "feet".
Answer: B) 105 ft3
How many solutions to the equation
5(x-3)-3x=8x-15-6x
A) no solution
B) excalty no solution
C) excalty two solution
D) infinitely many solutions
Answers
Since both sides equal, they are infinitely many solutions
D) infinitely many solutions
I believe he area is incorrect. So can somebody help me to figure out the area and arc length. PLEASE show your work. So I can understand :)
Answers
To find the arc length, you must use the formula: [tex] \frac{arc degree}{360} * 2 \pi r[/tex], then we plug in 80 as our arc degree and 1.3 as our radius, and we get: 1.81514242207
An investment of $900 is invested at a rate of 4%. The function that models this situation if f(t)=900(1+0.4^t) where does x represent time in years what is the rate of time in years. What is the rate of change of interval (3,10)
Answers
To find the rate of change of the interval (3,10) for the given function, you need to calculate the difference in the function values at those two time points and divide it by the difference in time. The rate of change of the interval (3,10) is: ((900(1 + 0.4^10)) - (900(1 + 0.4^3))) / (10 - 3)
Explanation:The given function f(t) = 900(1 + 0.4^t) models an investment of $900 at a rate of 4% over time, where t represents time in years. To find the rate of change of the interval (3,10), you need to find the difference in the function values at those two time points and divide it by the difference in time.
So, the rate of change of the interval (3,10) is:
((900(1 + 0.4^10)) - (900(1 + 0.4^3))) / (10 - 3)
What type of measurement would you use to describe the amount of water a pot can hold?
Answers
-gallons if it is a large pot
This means that the type of measurement that would be used is the measurement of the volume.
Some of these measurements are:
m^3 and cm^3
liters and milliliters
ounces
gallons
Hope this helps :)
Which division expression is equivalent to
Answers
(4 1 / 3) / (- 5 / 6)
= (4 x 3 / 3 + 1 / 3) / (- 5 / 6)
= (12 / 3 + 1 / 3) / (- 5 / 6)
= (13 / 3) / (- 5 / 6)
ANSWER = A
Answer:
the answer would be A
Step-by-step explanation:
I hope this is helpful
Helpppp!!! ASAP!!!!!!!!
Answers
A cone has a radius of 11 inches and a height of 4.5 inches.
What is the volume of the cone?
Use 3.14 for pi. Round to the nearest tenth.
A. 49.5 in³
B. 121.4 in³
C. 569.9 in³
D. 1024.4 in³
Answers
Answer:
Step-by-step explanation:
Volume = πr2h/3
radius of the cone is 11 inches
height of the cone is 4.5 inches
V= (3.14 *(121)*4.5)/3= 569.91 inches3
you are asked to determine if the two events "a randomly selected student has asthma" and "a randomly selected student has a household member who smokes" are independent. what probabilities could you calculate to answer this question?
Answers
event A = student has asthma
event B = at least one household member smokes
To find the probability of event A happening, we count the total number of people who have asthma out of the total in the survey. So we simply look at the "student has asthma" row and look at the "total" column. This value is 182. There are 182 people who have asthma. This is out of 937 (bottom right corner).
Divide the values: 182/937 = 0.194237
This value is approximate
So P(A) = 0.194237 approximately
The P means probability
P(A) = probability of event A happening
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Now compute P(B)
P(B) = 395/937
P(B) = 0.421558
Notice I'm dividing the total value in the "at least one member smokes" column over the grand total of 937
----------------------------------
Next we compute P(A and B) which is the probability both events occur at the same time.
P(A and B) = 113/937
P(A and B) = 0.120598
The 113 is the amount of people who have asthma AND have at least one household member that smokes (row1, column2)
----------------------------------
If events A and B were independent, then P(A)*P(B) should be equal to P(A and B)
Let's see if that is the case
P(A and B) = P(A)*P(B)
0.120598 = P(A)*P(B)
0.120598 = 0.194237*0.421558
0.120598 = 0.08188216
we get two different results so P(A and B) = P(A)*P(B) is not true
Therefore, A and B are not independent events. They are said to be dependent events.
Please help me i can’t do it thank you
Answers
30% of 20=6
85% of 100=85
90 of 200=180
25 of 28=7
45 of 80=36
.. % means /100
.. "of" means ×
2. 25% of 12 = 25/100×12 = (25×12)/100 = 300/100 = 3
3. 30% of 20 = 30/100×20 = (30×20)/100 = 6
The rest are worked the same way. Many calculators have a % function that will do this for you.
_____
Of course, you recognize that
.. 25% = 25/100 = 0.25
.. 30% = 30/100 = 0.30
This conversion of form is often described as "move the decimal point 2 places to the left to convert from a % to a decimal."
PLEASE ANSWER FAST!!!!
A rectangular prism has a length of 114 centimeters, a width of 4 centimeters, and a height of 314 centimeters. What is the volume of the prism? Enter your answer in the box as a simplified mixed number or a decimal.
Answers
This is the same thing as the last picture on my account,but I can’t fit the bottom part of the picture...can someone solve this for me?
Answers
B = 15
Hope this helps =)
It is about pattern matching. The only right triangle in the figure on the left has a long side of 15, a short side of 8, and a hypotenuse of 17.
The right triangle in the figure on the right has a hypotenuse of D (so D=17), a short side of C (so C=8). If you fold the figure, you find that B is the long leg of the right triangle (B=15).
All of the rectangular shapes in the figure on the left have width 4. All of the rectangular shapes in the figure on the right have width A (A=4).
The mapping you desire is
.. A = 4
.. B = 15
.. C = 8
.. D = 17
In the previous problem, how does the angle of depression from the top of the taller building relate to the angle of elevation from the top of the shorter building?
Answers
The angle of depresion from the top of the taller building and the angle of elevation from the top of the shorter building are alternate interior angles. Then, if the angle of depression of the taller building is 15° the angle of elevation of the shorter building is 15° too. To understand this, you should see the diagram attached.
In the diagram you can notice that both angles, of elevation and depression, have the same value.
Then, the answer is: The angle of depresion from the top of the taller building and the angle of elevation from the top of the shorter building are alternate interior angles.
Answer:A and D
Step-by-step explanation:
A nickel and a dime are flipped. what is the probability both coins will land tails up
Answers
There is 1/2 chance the nickel will land tails up, 1/2 chance the dime will land tails up.
1/2*1/2=1/4
Answer:
1/2
50%
Step-by-step explanation:
Help with this question please!!
Answers
= 2x * (4+5)
= 2x * 9
= 18x
ANSWER: 2x * (4 + 5)
Hope this helps! :)
ShoeShop is having a sale on flip-flops. The first 2 pairs cost $8.50 each plus each additional pair costs $3.75. Mrs. Tyler can spend a maximum of $34.75 on flip-flops for her family.
Which inequality can be used to find the number of flip-flops, p, that Mrs. Tyler can purchase from ShoeShop?
Answers
Answer:
3.75p+8.50<=34.75
Step-by-step explanation:
No matter what, if you get at least 2 pair of flip flops you will be spending $8.50 plus 3.75 per pair on each additional pair . If she has $34.75 to spend and cannot go over, the inequality sign will be less than or equal to. It is fine if she spends less than that and it's ok if she spends exactly that, but she cannot spend more than she has.
The inequality then would be this:
3.75p+8.50<=34.75....
Answer:
3.75p + 8.50 ≤ 34.75
Step-by-step explanation:
.
solve for k
j= k^2/4
Answers
4j=k^2
k=sqrt(4j) or (4j)^1/2
Answer:
k = +- 2sqrt(J)
Step-by-step explanation:
This is the correct answer, I just took the test and this is right!