write the rational expressions as equivalent rational expressions with the lowest common denominator
1. The equivalent rational expression with the lowest common denominator of [tex]\frac{2}{3d^{2} + 14d^{2} - 5 }[/tex] is [tex]\frac{2}{(d+5)(3d-1)}[/tex]
2. The equivalent rational expression with the lowest common denominator of [tex]\frac{3d}{3d^{2} - 22d + 7}[/tex] is [tex]\frac{3d}{(d-7)(3d-1)}[/tex]
1.
[tex]\frac{2}{3d^{2} + 14d^{2} - 5 }[/tex]
Let factorise the denominator below
3d² + 14d - 5
-15 and 14
Two numbers we can multiply to get -15 and add to get 14 are 15 and -1.
Therefore,
3d²- d + 15d - 5
d(3d - 1) + 5(3d - 1)
(d+5)(3d-1)
Therefore, the equivalent rational expression with the lowest common denominator will be
[tex]\frac{2}{(d+5)(3d-1)}[/tex]
2.
[tex]\frac{3d}{3d^{2} - 22d + 7}[/tex]
Factorise the denominator
3d²- 22d+7
3d²- d - 21d + 7
d(3d - 1) - 7(3d - 1)
(d - 7)(3d - 1)
Therefore, the equivalent rational expression with the lowest common denominator will be
[tex]\frac{3d}{(d-7)(3d-1)}[/tex]
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help on this please
Answer:
Opening: Opens upwards
Axis of Symmetry: -7/2
Vertex: (-7/2, -81/4)
X - intercepts: (1, 0) and (-8, 0)
Y - intercept: (0, -8)
Step-by-step explanation:
Opening: 'a' is greater than zero
Axis of Symmetry:
[tex]\frac{-7}{2(1)} =\frac{-7}{2}[/tex]
Vertex:
[tex]y= (\frac{-7}{2})^{2} +7(\frac{-7}{2}) -8\\y= (\frac{49}{4}) +(\frac{-49}{2}) -8\\y= \frac{49}{4} +\frac{-98}{4} -8\\y=\frac{-49}{4}-8\\y = \frac{-81}{4}[/tex]
X - intercepts:
(x-1)(x+8)
x = 1 and x = -8
Y - intercept: (0, -8)
[tex]y= 0^{2} +7(0) -8\\\\y= -8\\[/tex]
Find the surface area and the volume of the prism .
Answer:
[tex]14 + 4 + 5.5 + 3 + 5.5 {?}^{2} [/tex]
Answer:
Step-by-step explanation:
We have 2 congruent large prisms and one small one.
Volume of a large one= 2*2*14 = 56 cm^3.
Volume of smaller one = 4*3*2 = 24 cm^3.
So volume of the whole prism
= 2*56 + 24
= 136 cm^3.
Surface area of a large one = 3*2*14 + 2*2*5.5 + 2*2*2 = 114
Surface Area of smaller one = 4*3*2 + 2*2*4 = 40
So surface area of the whole prism
= 2 * 114 + 40
= 268 cm^2.
solve pls brainliest
Answer:
7.5 < 7.5061 < 7.56 < 9.213
Step-by-step explanation:
solve pls brainliest
Answer:
a. 9m/s × 27s = 243m
b. -6°C/3hrs = -2°C/hr
Identify the axis of symmetry of the parabola.
What would be the right answer?
Answer:
x=-3, That is the x value of the vertex, and it is a vertical parabola.
Need help with a math question
First: Find out their decimal form.
- 2 1/6 as a decimal is 2.16
7/3 as a decimal
To get 7/3 converted to decimal, you simply divide 7 by 3. Don't worry. You don't need to get the calculator out, because we did this for you.
7/3 as a decimal is:
2.333333333
According to the laws of physics, the weights of objects on the Earth are proportional to their weights on the Moon. A boy who weighs 66 lb on Earth weighs 10.92 lb on the Moon. How much will a man who weighs 185 lb on Earth weigh on the Moon? Round your answer to the nearest tenth.
A man who weighs 185 lb on Earth weighs 30.8 lb on the Moon
Two variables are said to be directly proportional if as one variable increases/decreases, the other variables does the same by the same amount.
Let y represent the weight of object on earth and x represent the weight of object on the moon.
y ∝ x
y = kx
When y = 66, x = 10.92, hence:
66 = 10.92k
k = 6
When y = 185 lb:
185 = 6x
x = 30.8 lb
A man who weighs 185 lb on Earth weighs 30.8 lb on the Moon
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Answer:
30.8lb
Step-by-step explanation:
The test statistic of
z=1.00
is obtained when testing the claim that
p>0.7.
a. Identify the hypothesis test as being two-tailed, left-tailed, or right-tailed.
b. Find the P-value.
c. Using a significance level of
α=0.10,
should we reject
H0
or should we fail to reject
H0?
This is a two tailed, right tailed or left tailed test?
A tune-up automotive facility marks up its
parts by 45%. Suppose that the facility
charges its customers $2.03 for each spark
plug it sells. What is the facility's cost for each
spark plug?
Answer: $1.40
Work Shown:
x = cost before markup
1.45x = cost after the 45% markup
1.45x = 2.03
x = (2.03)/(1.45)
x = 1.40
Does any one the the answer
Answer:
18 Square Feet
Step-by-step explanation:
ABC is 3 times larger then DEF so you multiply 6 by 3 which gives you 18. Let me know if I'm wrong.
Answer:
18 square feet
Step-by-step explanation:
Because the area of ADEF =6 sq ft
And you have 12ft in A and B
in order to start a small business a student takes out a simple interest loan for $8,000 for 6 months at a rate of 6.25%, how much interest must the student pay and find the future value of the loan round to the nearest cent as needed
Answer:
The student must pay 4247.5 - 4000 = 247.50 dollars in interest
Step-by-step explanation:
ERIOD
DATE
NAME
4. Priya bought these items at the grocery store. Find each unit price.
a. 12 eggs for $3. How much is the cost per egg?
b. 3 pounds of peanuts for $7.50. How much is the cost per pound?
c. 4 rolls of toilet paper for $2. How much is the cost per roll?
d. 10 apples for $3.50. How much is the cost per apple?
Answer:
A 3.00/12=.25 ea
B 7.50/3=2.50/1lb
C 2.00/4=.50ea
S 3.50/10=.35/ea
Here you go! Hope it helps.
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Thank you -= Miss Hawaii
A small city gets its water supply from three sources: two wells and a small upland reservoir. The well supplies require pumping, and so are more expensive. Reservoir water flows directly to the town by gravity. The town needs a total of 20 mgd (million gallons per day) of water. The cost of water is zero if obtained from the reservoir, $60/million gallons if from Well-field 1, and $30/million gallons if from Well-field 2. The reservoir can deliver 9 mgd; Well-field 1 has a capacity of 25 mgd, and Well-field 2 has a capacity of 3 mgd. (Hint: use the Lagrange multipliers for the last three questions. You can check your answers using Excel solver)
a) Formulate this problem in terms of an objective function and constraint(s).
b) Solve the problem by hand using the Lagrange Multipliers, and find the minimum total cost combination of flows from each source, and minimum total cost.
c) How much, annually, should the city be willing to pay to expand the capacity of the reservoir, Well-field 1, and Well-field 2
d) If the city decided to conserve water and the demand decreased from 20 to 19.5 mgd, how much would the city benefit from this conservation?
e) If you had a chance to expand the capacity of reservoir, Well-field 1, or Well-field 2 reservoir, Well-field 1, and Well-field 2 What would be the new cost? which one(y) would you prefer to increase, why?
Answer: A small city gets its water supply from three sources: two wells and a small upland reservoir. The well supplies require pumping, and so are more expensive. Reservoir water flows directly to the town by gravity. The town needs a total of 20 mgd (million gallons per day) of water. The cost of water is zero if obtained from the reservoir, $60/million gallons if from Well-field 1, and $30/million gallons if from Well-field 2. The reservoir can deliver 9 mgd; Well-field 1 has a capacity of 25 mgd, and Well-field 2 has a capacity of 3 mgd. (Hint: use the Lagrange multipliers for the last three questions. You can check your answers using Excel solver)
a) Formulate this problem in terms of an objective function and constraint(s).
b) Solve the problem by hand using the Lagrange Multipliers, and find the minimum total cost combination of flows from each source, and minimum total cost.
c) How much, annually, should the city be willing to pay to expand the capacity of the reservoir, Well-field 1, and Well-field 2
d) If the city decided to conserve water and the demand decreased from 20 to 19.5 mgd, how much would the city benefit from this conservation?
e) If you had a chance to expand the capacity of reservoir, Well-field 1, or Well-field 2 reservoir, Well-field 1, and Well-field 2 What would be the new cost? which one(y) would you prefer to increase, why?
Step-by-step explanation: A small city gets its water supply from three sources: two wells and a small upland reservoir. The well supplies require pumping, and so are more expensive. Reservoir water flows directly to the town by gravity. The town needs a total of 20 mgd (million gallons per day) of water. The cost of water is zero if obtained from the reservoir, $60/million gallons if from Well-field 1, and $30/million gallons if from Well-field 2. The reservoir can deliver 9 mgd; Well-field 1 has a capacity of 25 mgd, and Well-field 2 has a capacity of 3 mgd. (Hint: use the Lagrange multipliers for the last three questions. You can check your answers using Excel solver)
a) Formulate this problem in terms of an objective function and constraint(s).
b) Solve the problem by hand using the Lagrange Multipliers, and find the minimum total cost combination of flows from each source, and minimum total cost.
c) How much, annually, should the city be willing to pay to expand the capacity of the reservoir, Well-field 1, and Well-field 2
d) If the city decided to conserve water and the demand decreased from 20 to 19.5 mgd, how much would the city benefit from this conservation?
e) If you had a chance to expand the capacity of reservoir, Well-field 1, or Well-field 2 reservoir, Well-field 1, and Well-field 2 What would be the new cost? which one(y) would you prefer to increase, why?
Carlos has earned more than $260 selling magazines subscriptions. Each subscription
was sold for $12. How many did Carlos sell?
Answer:
21.6 magazines
Step-by-step explanation:
260/12=21.6
Change 3/2 3.14 to degree measure
A. 180 degrees
B. 90 degrees
C. 270 degrees
D. 360 degrees
Answer:
option b
hope ut is help full
The graph of a proportional relationship passes through the point (5, 2) .
What is the constant of proportionality of the relationship?
5
2
25
I don't know.
Well, 5 is like the point where it is, and 2 is the constant of proportionality.
Answer:
0.4
Step-by-step explanation:
2= slope *5 ,slope = 0.4
2w + y = 6
a. Find y if w = -4
b. Find y if w = 10
Answer:
a. Find y if w = -4 --- y = 14
b. Find y if w = 10 --- y = -14
Step-by-step explanation:
This is all about substitution!! For question a, we need to substitute "w" with "-4" ...
2 (-4) + y = 6
We know that a positive time a negative equals a negative...so 2 · -4 is -8.
-8 + y = 6
Now let's add 8 on both sides to isolate the variable...which equals to
y = 14
Onto question b...We substitute w with 10.
2 (10) + y = 6
= 20 + y = 6
Subtract 20 from both sides to isolate "y"
y = -14
Hope this helpsss :D
Fill in the table using this function rule.
y=30-4x
X
y
1
3
5
6
a
Answer:
26
18
10
6
hope this will help u
Someone pls help- am struggling.
500 = 400 + 50s. Therefore, Bart can buy 2 pairs of shoes.
=============================================================
Explanation:
s = number of pairs of shoes
50s = amount spent on shoes ($50 per pair)
50s+400 = total amount spent on shoes and uniforms
That expression is the same as 400+50s because we can add numbers in any order we want. Set this equal to the $500 he started with to get the equation 500 = 400 + 50s
We have enough info to determine the answer must be choice B
We can stop here if you wanted.
----------
Let's solve that equation for s
500 = 400 + 50s
400 + 50s = 500
50s = 500-400 .... subtract 400 from both sides
50s = 100
s = 100/50 .... divide both sides by 50
s = 2
This means he can buy 2 pairs of shoes.
Buying the shoes only will cost 50s = 50*2 = 100 dollars, which on top of the $400 for the uniforms, leads to a grand total of 400+50s = 400+100 = 500 dollars. This helps confirm we have the correct value for s.
Footlocker and Footaction are each having a sell on all of the latest name brand shoes. At Footlocker, you can get 2 pairs of Nikes for $69.98. At Footaction you can get 3 pair of shoes for $99.99
Answer:
I'm not sure what this is asking but footaction is cheaper
Step-by-step explanation:
footlocker the shoes (single pair) is 69.98/2 or 34.99
footaction is 99.99/3 or 33.33
Please Help! I will give you a lot of points and the brainiest!
A married man filing separably with a taxable income of $130,000. Compute the tax owned (look at chart)
--PLEASE show work
First, find the tax rate for a person whose taxable income is $130,000. By looking at the table, you can see the tax rate is 33%. To find the total tax, multiply 33% by $130,000.
[tex]0.33 \times 130000 = 42900[/tex]
Thus, the tax this person has to pay is $42,900.
What is the value of x in the equation x - y = 30, when y = 15?
-
04
O 8
O 80
O 200
[tex]\huge\text{Hey there!}[/tex]
[tex]\large\text{Equation: }[/tex]
[tex]\rm{x - y = 30}[/tex]
[tex]\large\text{Solving: }[/tex]
[tex]\rm{x - y = 30}[/tex]
[tex]\rm{\rightarrow x - 15 = 30}[/tex]
[tex]\large\text{Add \boxed{15} to both sides:}[/tex]
[tex]\rm{x - 15 + 15 = 30 + 15}[/tex]
[tex]\large\text{Simplify it:}[/tex]
[tex]\rm{x = 30 + 15}[/tex]
[tex]\rm{x = 45}[/tex]
[tex]\large\text{Therefore, your answer should be:}[/tex]
[tex]\huge\boxed{\mathsf x \frak{ = 45}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
what is the answer to 28.2 divided by 2
Answer:
14.1
Step-by-step explanation:
Solve the equation for x. *x-3x+5 = 20 X + X =
Answer:
5
Step-by-step explanation:
Help with Algebra 2, forgot how to do it
Answer:
[tex]f(x) = 3 \: \: \: \: for \: \: \: \: - 6 < x < 1 \\ f(x) = - x \: \: \: \: for \: \: \: \: 1 < x < 6[/tex]
Express your answer in scientific notation. 0.00045 – 2.5-10-5
Answer:
17.49955
Step-by-step explanation:
Hope this helps
Which choice is the correct graph of [x1 < 5?
A 4
B
C
D
E
-
F
5
A. Graph A
O B. Graph B
C. Graph
ОО ОООО
O D. Graph D
O E. Graph E
OF. Graph F
Answer:
B
Step-by-step explanation:
Da"B"a"B"y
2 B so
"B" graph "B"
↑that explains it
Determine whether the equation is a linear equation in two variables. 5y = x - 5
Answer:
Yes
Step-by-step explanation:
start with 5y=x-5
divide both sides by 5 to get:
y= x/5 - 1
since a linear equation is represented by y=mx+b, and this can be represented in that form, this is a linear equation.
Which kind of triangle is showing
Answer:
it's an scalene triangle
having all the sides and angels different from each other
Step-by-step explanation:
brainliest plz