A positive integer is 4 less than another. If 3 times the reciprocal of the smaller integer is subtracted from the reciprocal of the larger integer, then the result is −67. Find all pairs of integers that satisfy this condition.
Answer:
(0.0147, 4.0147) and (-4.04, 0.04)
Step-by-step explanation:
Let the smaller number be x
Let the larger number be y
If a positive integer is 4 less than another, then;
x = y - 4 ...1
If 3 times the reciprocal of the smaller integer is subtracted from the reciprocal of the larger integer and result is -67, then;
1/y - 3(1/x) = -67
1/y -3/x = -67 ...2
Substitute 1 into 2
1/y - 3/y-4 = -67
y-4-3y/y(y-4) = -67
-4-2y = -67(y^2-4y)
- 4-2y = -67y^2 +268y
-67y^2 +268y+2y + 4 = 0
-67y^2 +270y + 4 =0
67y^2 -270y - 4 = 0
Factorize
-270±√270² - 4(-4)(67)/2(67)
= -270±√72,900+1072/134
= -270±271.97/134
= -270 -271.97/134 and -270 +271.97/134
= -541.97/134 and 1.97/134
x = 0.0147 and -4.04
y = x+4
y = 0.0147+4
y = 4.0147
If x = -4.04
y = -4.04 + 4
y = 0.04
Hence the pair of values are (0.0147, 4.0147) and (-4.04, 0.04)
Howard buys 5 suits a year when he earns $70,000. When his income increases to $200,000, he buys 15 suits a year. Based on this
information, suits are considered to be
a complementary good.
an inferior good.
a neutral good.
a normal good.
a substitute good.
Answer:
a complementary good
Step-by-step explanation:
Howard spends $70,000 per year on 5 suits. When his income reaches $200,000, he purchases 15 suits per year. Suits are classified as a normal good based on this information.
What is meant by Normal Good?A normal good is one that sees an increase in demand due to an increase in consumer income. In other words, an increase in wages leads to an increase in demand for ordinary goods, whereas a decrease in wages or layoffs leads to a decrease in demand. In economics, an inferior good is one whose demand falls when consumer income rises (or rises when consumer income falls), as opposed to normal goods, which experience the opposite effect. Normal goods are those whose demand increases as consumer income rises. Normal goods are those for which the relationship between consumer income and quantity demanded is positive. In other words, the income effect is positive while the substitution effect is negative.To learn more about normal good, refer to:
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How many solutions does the nonlinear system of equations graphed below
have?
Answer:
One. The point at which the parabola and the line intersect.
Find the greatest common factor of the following monomials 34c^5 and 26c^4 and 2c^6
Answer:
63c^5
Step-by-step explanation:
which statement best explains how Italian society was affected by the Renaissance?
italian society entered a new era of artistic and academic achievement
Please help, this is due in 30 minutes
Answer:
i think the first one maybe... not so sure
Answer:
Should be B and D
Step-by-step explanation:
You plug in the first number before the comma, and if it equals the second number after the comma then the point 'satisfies the equation'.
(2/5)p=14
Mike sold y boxes of cookies for $5 each. He made at least $200.
What’s the least amount of boxes of cookies he sold?
Answer: 1 =5$
200$=40
Step-by-step explanation:
Answer:
40 boxes
Step-by-step explanation:
200 = 5x
x = 40
what is 4.5609+3.098
Answer:
7.6589
Step-by-step explanation:
find the area of the kite please. image included!!!
For what value of y does 125=(1/25)^(y-1)?
Answer:
y = -1/2 is the answer to 125=(1/25)^(y-1)
A construction company pours concrete at a constant rate to make a sidewalk. There are 1,054 cubic feet of concrete available, and 6.2 cubic feet of concrete is poured each minute. The equation below shows the total volume, in cubic feet, of concrete remaining minutes after the construction company begins to pour the concrete.
Answer:
Step-by-step explanation:picture of problem please
25% of 275 is 68.85
Answer:
Step-by-step explanation:
no its not
its 68.75
5 11/12 + 3 9/12? Step by step
Answer:
Simplified: 9 2/3
Step-by-step explanation:
Convert the mixed numbers into improper fractions
To do this, multiply the denominator by the whole number and add the numerator: (denominator × whole number + numerator)/denoninator
First fraction:
5 11/12
(12 × 5 + 11)/12
(60 + 11)/12
71/12
Next fraction:
3 9/12
(12 × 3 + 9)/12
(36 + 9)/12
45/12
Substitute these fractions in the original problem now:
71/12 + 45/12
Add the numerators only. The denominators stay the same.
(71 + 45)/12
116/12
Now that the calculations are done, convert this back into a whole number
How many times does 12 fit into 116 equally? If you answered 9 times, then you are correct. This 9 will sit as the whole number in the fraction
12 × 9 = 108
This doesn't equal 116 perfectly so we must find the left over
116 - 108 = 8 left over (which is used as the numerator)
9 8/12
If your class or problem asks that you simplify your answer, then look at both the numerator and denominator to determine any common factors within them
8 and 12 both have common factors of 2 and 4
Since 4 is the bigger number, divide both 8 and 12 by 4 to simplify your answer
9 2/3
Caroline saves money in an arithmetic sequence: $350 the first year, another $550
the second, and so on. How much money does she save after 31 years?
What are the solutions to the quadric equation x^2-16=0
Answer:
x=4, x=-4
Step-by-step explanation:
x^2-16=0
Add 16 to both sides;
x^2-16+16=0+16
Simplify;
x^2=16
x=[tex]\sqrt{16}[/tex], x[tex]-\sqrt{16}[/tex]
[tex]\sqrt{16}[/tex]
=4
factor the number;16
[tex]\sqrt{4^2}[/tex]
=[tex]\sqrt{4}[/tex]
-[tex]\sqrt{16}[/tex]
Factor the number 16;
[tex]\sqrt{4^2}[/tex]
=-4
True or false: As long as its argument is restricted to [0,2pi] the polar form of a complex number is not unique.
Some say its true, some say its false. I'm sure one of the answers I looked at is correct, but some teachers probably purposefully left a one star
Answer:
true
Step-by-step explanation:
i think
HELP OKEAEE HELPE PELASE
Answer:
The y-intercept is 4
Step-by-step explanation:
Pls help...................
I have 6 yard of ribbon i want to make ornaments that use 1/4 yard each how many ornaments can I make
Answer:
24
Step-by-step explanation:
It take 4 to make one yard and you need six yards soo..
6 x 4 = 24
Answer:
24 ornaments
Step-by-step explanation:
[tex]\frac{1}{4} = 25%[/tex]%
6 yards x 0.25 = 1.5 yards
[tex]\frac{6}{0.25} = 24[/tex] ornaments
to check:
24 ornaments x 0.25 yards each = 6 yards in total
I NEED AN ANSWER WITHIN LIKE 10 MINUTES-
Which expression is equivalent to -2 1/4 over -2 2/3
A. 9/4 Divided by 3/2
B. -9/4 divided by (-2/3)
C. -9/4 divided by 2/3
D. 9/4 divided by (-3/2)
Answer:
I think the option B is the answer -9/4 divided by (-2/3)
I hope this might help u
evaluate 11P4 and 9C5
What is 21/1 divided by 1/4
Answer:
84
Step-by-step explanation:
To divide two fractions we turn the second fraction upside down and multiply two fractions
21/1 ÷ 1/4 ➡ 21/1 × 4/1 = 84/1
This can be written as 84
The map of a trail is shown below. Find the value of x.
16+23=39
180-39=151
Answer:
151
s i g h
y o u w i l l g e t 5 0 p o i n t s .
Answer:
d=4
Step-by-step explanation:
because 6x4=24
-6x4=-24
Find the lateral surface area of the following prism: 5 cm 4 cm 5 cm 8 cm 6 cm LSA = [?] cm2 Enter
Answer:
Step-by-step explanation:
I was using 6×8 rectangle as a base of the triangular prism (as shows on the picture.
Let use the definition of a triangular prism and LSA = (5 + 5 + 6) × 8 = 128 cm²
The lateral surface area of the triangular prism is 128 square cm.
What is triangular prism?A triangular Prism is a pentahedron. It is a 3-D shape with two identical faces in the shape of a triangle connected by three rectangular faces. The edges and vertices of the bases are joined with each other via three rectangular sides.
For the given situation,
The sides of the triangle are 5 cm, 6 cm, 5 cm.
The length of the prism = 8 cm
The formula for lateral surface area of triangular prism is
[tex]LSA=(perimeter)(length)[/tex]
On substituting the above values,
⇒ [tex]LSA=(5+6+5)(8)[/tex]
⇒ [tex]LSA=(16)(8)\\[/tex]
⇒ [tex]LSA=128[/tex]
Hence we can conclude that the lateral surface area of the triangular prism is 128 square cm.
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How many times can 45 go into 7,200?
Answer:
160
Step-by-step explanation:
divided 7200 by 45 to get 160
Which expression is equivalent to −3 2/3
Answer:
The answer is -3 - 2/3
Step-by-step explanation:
Just subtract
40°
50°
Х
x = __ degrees
Step-by-step explanation:
you just do 180 - 90 = 90 degree is x value
Answer:
x should equal 90.
Step-by-step explanation:
x is the sum of those two interior angles. 50 + 40 equals 90.
help i need the answers by tomorrow
8 inch radius:
area: 200.96
circum: 50.25
12 yd rad:
area: 452.16
circum:75.36
20 ft dia:
area: 314
circum:62.8
36 dia:
area:1017.36
circum: 113.04
Which expression is not equivalent to 2/3 x4
Answer:
I don't know I need the answer choices
Step-by-step explanation: