The sum of the reciprocals of the first four consecutive positive integers is greater than two. What is the least number of consecutive positive integers necessary to make the sum of the reciprocals greater than three?
The least number of consecutive positive integer that is required to make the sum of the reciprocals greater than three is 7.
What is an integer?An integer is simply a number that is not a fraction.
The first four consecutive positive integers are:
1, 2, 3 , 4.
Their reciprocals are:
1/1, 1/2, 1/3, 1/4; and
The sum of them are greater than 2; that is
1/1 + 1/2 + 1/3 + 1/4 = 2.08333333333 > 2
to make the expression >3
We would require the following integers
1/1 + 1/2 + 1/3 + 1/4+ (1/5) + (1/6) + (1/7) + (1/8)+ (1/9) + (1/10) + (1/11) = 3.01987734488
Thus, the additional consecutive reciprocal integers that is required to make the sum of the reciprocal of the fist four greater than 3 is 7.
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A plant grows at a constant rate . daniel records the height of the plant each week . the unit reat is meausred in inches per week . what is the constant of proportionality ?
By the consideration of direct proportionality, the constant of proportionality for the height of the plant is equal to 3 inches per week.
How to find a constant of proportionality in direct proportional equation
Let x and y the number of weeks and the height of the plant, respectively. Given the consideration of direct proportionality, the height of the plant inasmuch as the number of weeks increases. Then, the constant of proportionality (in inches per week) is found by dividing the height of the plant by the number of the respective week:
k = 18 inches /6 weeks = 15 inches /5 weeks = 12 inches/4 weeks = 3 inches/week
By the consideration of direct proportionality, the constant of proportionality for the height of the plant is equal to 3 inches per week.
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Answer:
x=20
Step-by-step explanation:
The angles are 'Co-interior Angles', they make a C shape and add up to 180 degrees
so 4x +5x =9x
9x=180
x=20
4x=80
5x=100
The average monthly temperature of a city can be modeled by a
cosine graph. Melissa has been living in Phoenix, Arizona, where the
average annual temperature is 75°F. She would like to move, and live
in a location where the average annual temperature is 62°F. When
examining the graphs of the average monthly temperatures for
various locations, Melissa should focus on the
The average monthly temperature of a city can be modeled by a cosine graph, Melissa should focus on the Midline. This is further explained below.
What is Melissa's focus on the Midline.?Generally, The average temperature would be indicated somewhere along the curve, most likely near the middle.
In conclusion, Melissa should concentrate on the Midline, which can be used to model the average monthly temperature of a city.
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please solve this question
Step-by-step explanation:
please give this answer brainlist answer
There are two approaches to solving the equation -3x + 10 = 4x - 20
Subtract 4x from both sides. OR Add 3x to both sides.
–7x + 10 = –20 OR 10 = 7x – 20
Solve the equation using both approaches.
The perimeter of a rectangle is 32 inches. The length is 1 foot, what is the width of the rectangle in inches?
Answer:
15
Step-by-step explanation:
divide the perimeter by two and minus 1
Answer: 15ft
Step-by-step explanation:
Start off by drawing a rectangle with the given information. Since it is a rectangle we know that the opposite side is also 1. So subtract 2 from 32 to get 30. Divide this by 2 and you will get your width of your rectangle. Hope this helps!
Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used.
Using the properties of integer exponents, match each expression with its equivalent expression.
From the power rules, the matching of each expression with its equivalent expression is:
[tex]5^{-3}=\frac{1}{125}[/tex]
[tex]-5^{-3}=-\frac{1}{125}[/tex]
[tex](-5^{-3})^{-1}=-125[/tex]
[tex](-5^{-3})^{0}=1[/tex]
Power RulesThere are different power rules, see some them:
1. Negative exponent. For this rule when you have a negative exponent, you need to invert the number, i.e, the power base is converted to the denominator. After that, you should solve the power with a positive exponent. See the examples:
[tex]4^{-3}=\frac{1}{4^3} =\frac{1}{64} \\ \\ {\frac{4}{6} }^{-2}=( {\frac{6}{4} })^{2}=\frac{36}{16}[/tex]
2. Power. For this rule, you should repeat the base and multiply the exponents. See the example, [tex](2^{2})^3=2^6=64[/tex].
3. Zero Exponent. When you have an exponent equals to zero, the result must be 1. See the example, [tex]2^0=1[/tex].
From this for your question, you have:
[tex]5^{-3}=\frac{1}{5^3}=\frac{1}{125}[/tex][tex]-5^{-3}=-\frac{1}{5^3}=-\frac{1}{125}[/tex][tex](-5^{-3})^{-1}=(-5)^{3}=-125[/tex][tex](-5^{-3})^{0}=(-5)^{0}=1[/tex]Read more about power rules here:
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Im kinda stuck i no like this type of math help please
Answer:
EAD
Step-by-step explanation:
Please help me with this question
I tried to use the law of cosine but the numbers I get are in decimal places and are too small for the angles.
Answer:
y = √119 ≈ 10.909θ ≈ 65.376°α ≈ 24.624°sin(θ) = (√119)/12 ≈ 0.909059cos(θ) = 5/12 ≈ 0.416667tan(θ) = (√119)/5 ≈ 2.181742csc(θ) = (12√119)/119 ≈ 1.100038sec(θ) = 2.4cot(θ) = (5√119)/119 ≈ 0.458349Step-by-step explanation:
You can use the Law of Cosines after you find y or θ. Using the given information, you can apply the Pythagorean theorem, the Law of Sines, or the definition of the cosine trig function.
The mnemonic SOH CAH TOA is intended to remind you of the relations between sides and angles in a right triangle. It tells you ...
Sin = Opposite/Hypotenuse
Cos = Adjacent/Hypotenuse
Find yThe Pythagorean theorem relates the measures of the sides. It tells you ...
y² +5² = 12²
y = √(144 -25) = √119
Find anglesThe trig relations above tell you ...
sin(α) = 5/12 ⇒ α = arcsin(5/12) ≈ 24.624°
cos(θ) = 5/12 ⇒ θ = arccos(5/12) ≈ 65.376°
Of course, once you find one of the angles, you can find the other. The sum of the two acute angles in a right triangle is 90°.
Find trig functionsUsing the definitions above for the trig functions, you have ...
sin(θ) = y/12 = (√119)/12
cos(θ) = 5/12
tan(θ) = y/5 = (√119)/5
Using trig identities, you have ...
csc(θ) = 1/sin(θ) = 12/√119 = (12√119)/119
sec(θ) = 1/cos(θ) = 12/5 = 2.4
cot(θ) = 1/tan(θ) = 5/√119 = (5√119)/119
_____
Additional comment
The attached calculator screen shot shows you the angle θ on the first line, and the value of y on the second line. The csc, sec, and cot are shown on the third line. You will notice the angle mode (DEG) is seen in the lower left corner. If the calculator angle mode is set to radians, you will see the angles as relatively small radian values: θ ≈ 1.141, α ≈ 0.4298.
We have shown both exact values and decimal values you can round to the desired precision.
Edgar runs 8/9 of a mile each day. what is the total distance that edgar runs in a 5-day week?
The distance that edgar runs in a 5-day week will be 4.45 miles.
What is the distance?Distance is defined as the length between the two points it can be represented in mm,cm, meters,km, and miles.
Given that:-
Edgar runs 8/9 of a mile each day. what is the total distance that Edgar runs in a 5-day week?
The total distance will be calculated as:-
D = [tex]\dfrac{8}{9}[/tex] x 5
D = 4.45 miles
Therefore the distance that edgar runs in a 5-day week will be 4.45 miles.
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IMPORTANT, PLEASE HELP QUICKLY! 15 POINTS
Explain how to factor the expression q(x)=9x2−24x+16 to the expression q(x)=(3x−4)2 . You may show your work. Be sure to include a detailed explanation of your steps.
Answer:
Given function:
[tex]q(x)=9x^2-24x+16[/tex]
To factor a quadratic in the form [tex]ax^2+bx+c[/tex], find two numbers that multiply to [tex]ac[/tex] and sum to [tex]b[/tex]:
[tex]ac=9 \cdot 16=144[/tex]
Two numbers that multiply to 144 and sum to -24 are: -12 and -12
Rewrite [tex]b[/tex] as the sum of these two numbers:
[tex]\implies q(x)=9x^2-12x-12x+16[/tex]
Factorize the first two terms and the last two terms separately:
[tex]\implies q(x)=3x(3x-4)-4(3x-4)[/tex]
Factor out the common term [tex](3x-4)[/tex]:
[tex]\implies q(x)=(3x-4)(3x-4)[/tex]
Therefore:
[tex]\implies q(x)=(3x-4)^2[/tex]
Does this graph represent a function? Why or why not?
Answer:
the answer is D
Step-by-step explanation:
I'm not good at explaining but, it is because the line is not touching more than 1 point on the graph. Basically making it pass the vertical line test, therefore making the answer D.
Good luck, hope this helps !!!
20 POINTS TO THE FIRST RIGHT ANSWER!!!! PLS HELP
A sculptor is planning to order a rectangular block of composite stone to sculpt a lion. The sculptor anticipates that the lion will be 5 feet long, about 2 feet wide and at the tallest part of the lion's body, have a height of 3.5 feet. The composite stone weighs 40 pounds per cubic foot. To the nearest cubic foot, estimate the weight of the smallest rectangular block that the sculptor must purchase in order to create his statue.
The weight of the smallest rectangular block is ____
pounds.
The weight of the smallest rectangular block is 1400 pounds.
What is density?The density refers to the heaviness of an object. It is the ratio of mass to volume.
Then we have
Density = Mass / Volume
A sculptor is planning to order a rectangular block of composite stone to sculpt a lion.
The sculptor anticipates that the lion will be 5 feet long, about 2 feet wide and at the tallest part of the lion's body, have a height of 3.5 feet.
The composite stone weighs 40 pounds per cubic foot.
To the nearest cubic foot, estimate the weight of the smallest rectangular block that the sculptor must purchase in order to create his statue.
Then the weight of the smallest rectangular block will be
Mass = density x volume
The volume will be
V = 5 x 2 x 3.5
V = 35 cubic feet
Then the weight will be
Mass = 40 x 35
Mass = 1400 pounds
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Which triangles in the diagram are congruent?
70°
triangle 1
70°
triangle 3
OA triangle 1 and triangle 2
OB. triangle 1, triangle 2, and triangle 3
OC. triangle 1 and triangle 3
OD. triangle 1, triangle 3, and triangle 4
70°
triangle 2
#
triangle 4
Submit Test
Rea
Answer:
its e
Step-by-step explanation:
because e is is referring to savvy
In which direction must the graph of f(x) = x be shifted to produce the graph of g(x) = x − 6?
Answer:
f(x) must be shifted 6 units down in order to produce the graph of g(x).
A proportional relationship between the number of pounds of cabbage (x) and the price in dollars (y) is graphed, and the ordered pair (5, 2) is on the graphed line.
Part A: What is the price of 1 pound of cabbage? Show your work.
Part B: What does the ordered pair (10, 4) on the graph represent? Explain in words.
Answer:
Part A - 2/5 of a dollar
Part B - It shows that 10 pounds of cabbage cost $4
Step-by-step explanation:
If 5 pounds cost $2 then 1 pound costs 2/5 of a dollar.
(10,4) - 10 is the x-axis which is pounds and 4 is the y-axis which is $. So 10 pounds cost $4.
what is the factored form of x^3 - 729
Answer:
(x - 9)(x^2 + 18x + 81).
Step-by-step explanation:
Use the difference of cubes factorization, which claims that a^3 - b^3 = (a - b)(a^2 + ab + b^2)
x^3 - 729 = (x - 9)(x^2 + 18x + 81)
Answer:[tex](x-9) (x^{2} +9x + 81)[/tex]
Step-by-step explanation:
please help me with these or just the first one even ty
Answer:
-3+15-75+375
=12-75+375
=-63+375
=302
n=8
302÷8 = 37
Which equation represents the line that passes through the point (-2.4, -7.1) and has a slope of -5.3
Multiplying Monomials and Binomials:16x(x+24)
Select all the functions that show an inverse variation...
a) y=6x
b) y=3/x
c) y=1/3x
d) y= -.07x
e) y= 2/x+4
f) xy=-3
PLEASE HELP ILL MARK BRAINLEST
Which quadratic equation is equivalent to (x-4)2-(x-4) - 6 = 0?
Answer:
x=4
Step-by-step explanation:
2x-8-x+4-6=0
or,2x-x-8+4=0
or,x-4=0
or,x=0+4
•°•x=4
ans
Answer:
x = 2 or 7
Step-by-step explanation:
(x-4)² - (x-4) - 6 = 0
x²-8x+16-x+4 -6 = 0
x²-9x+14 = 0
(x-2)(x-7) = 0
∴x = 2 or 7
If f(x) = 2x² - 5 and g(x) = 3x + 3, find (f- g)(x).
OA. 3x-2x2 - 2
OB. 2x²-3x-8
OC.-²2²-8
OD. 2x²-3x-2
(f- g)(x) = 2x²-3x -8 , Option B is the correct answer.
What is a Function ?A function is a mathematical statement that derives relation between two variables.
Two functions are given in the question
f(x) = 2x² - 5
g(x) = 3x + 3
(f- g)(x) = ?
(f- g)(x) = (2x² - 5 - (3x + 3))
(f- g)(x) = 2x²-3x -8
Therefore Option B is the correct answer.
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3. (3, 5) and (k, 9), slope = 1/2
Linear relationships unit 3 lesson 10 grade 8 openuprespurces
Answer:
k = 11, if I understand the question.
Step-by-step explanation:
Please rephrase the question if my interpretation is incorrect. (BTW, isn't (k,9) a dog?)
======================
I'll assume that we want to find the value of k as given by the equation of a line that has a slope of (1/2).
Let's determine if we can establish an equation with what we know:
1. It goes through point (3,5), and
2. It has a slope of (1/2)
We'll look for a line with the form y=mx+b, where m is the slope and b is the y-intercept (the value of y when x=0).
From (2) we know y = (1/2)x + b.
We can find b by using the one known point that lies on the line (3,5). Use y = (1/2)x + b, insert the point (3,5), and solve for b:
y = (1/2)x + b
5 = (1/2)(3) + b
5 = 1.5 + b
b = 3.5
The line is y = (1/2)x + 3.5.
Now use the point (k,9):
y = (1/2)x + 3.5
9 = (1/2)k + 3.5
(1/2)k = 5.5
k = 11
The point is (11,9) so k = 9
See the attached graph.
A software company wants to get an idea of their customers' level of satisfaction with their software. To do so, they included a phone number on the packaging of their most recent software release, with the message, "If you have any concerns with the product, please call this number." Based on the overwhelmingly negative response they received from these calls, the company decided to stop selling the product.
What could be wrong with their decision?
A.
The phone system screened out certain positive comments because of a malfunction.
B.
The release of the software coincided with the spread of a virus which affected the performance of the program.
C.
The note on the package only told customers to call in the event that they had a concern, which could bias the results negatively.
D.
The customers were misinformed about the purpose of the program.
Answer:
C. The note on the package only told customers to call in the event that they had a concern, which could bias the results negatively.
Explanation:
Since customers were only told to call if they had concerns, all of the calls were about concerns or problems that they were having - meaning all of the calls were negative. However, they were never informed to call if they were happy or content with the product, meaning they were never informed of the people who had positive comments, only negative.
find the length of AD
The length of AD is 5 units. so, option A is the correct answer.
What is the Pythagoras theorem?The Pythagoras theorem states that the square of the longest side must be equal to the sum of the square of the other two sides in a right-angle triangle.
The length of DC is given as 13 units.
The length of AC is given as 12 units. We can see that angle D is a right angle, so the triangle will be a right-angle triangle.
by Pythagoras theorem;
[tex]DC ^2 = AD^2 + AC^2\\\\13^2 = AD^2 + 12^2\\\\AD^2 = 169 - 144\\\\AD^2 = 25\\\\AD = 5[/tex]
Hence, the length of AD is 5 units. so, option A is the correct answer.
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Two linear equations are shown.
C
654321₁
4
66
y=1/3x+2
y=4/3x-5
What is the solution to the system of equations?
O (7.4)
0 (7.33)
O
0 (8)
O
O (9.7)
Answer: Option (2)
Step-by-step explanation:
Setting the equations equal to each other,
[tex]\frac{1}{3}x+2=\frac{4}{3}x-5\\\\7=x[/tex]
If x=7, then [tex]y=\frac{7}{3}+2=\frac{13}{3}[/tex]
pe-intercept Equatic
Question 4 of 10
If f(x) = 5x - 12, what is f(2)?
Answer:
f(2) = 2
Step-by-step explanation:
Given function:
f(x) = 5x - 12
To Find:
f(2)
Solution:
Well,it is absolutely clear from the problem,that x = 2.So just substitute 2 in x's place on the function,then simplify using PEMDAS.
[tex]f(x) = 5x - 12[/tex]
[tex]f(2) = 5(2)- 12[/tex]
[tex]f(2) = 10 - 12[/tex]
[tex]\boxed{f(2) = - 2}[/tex]
Hence,f(2) is equal to -2.
How do you solve this?
Step-by-step explanation:
to "solve" this I need an equation.
this whole expression must be equal to something.
without that I can only try to simplify the expression.
remember that
a/b / c/d = ad / bc
so, here we have
3a/(((a²/x) - 1)(a/x - 1)) = 3a/(a³/x² - a²/x - a/x + 1) =
= 3a/(a³/x² - a²/x - a/x - a/a) =
= 3a/((a²/x² - a/x - 1/x - 1/a)×a) = 3/(a²/x² - a/x - 1/x - 1/a)
