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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Solve this question please
The expansion of the polynomial is given as:
[tex](5x^3+\frac{14}{3x^4})=15625x^{18}+87500x^{11} +\frac{612500}{3}x^3+\frac{6860000}{27x^3}+\frac{4802000}{27x^{10}}+\frac{5378280}{81x^{17}}+\frac{7529536}{729x^{24}}[/tex]
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
The expansion is given as:
[tex](5x^3+\frac{14}{3x^4})=15625x^{18}+87500x^{11} +\frac{612500}{3}x^3+\frac{6860000}{27x^3}+\frac{4802000}{27x^{10}}+\frac{5378280}{81x^{17}}+\frac{7529536}{729x^{24}}[/tex]
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Match the following reasons with the statements to complete the following proof.
In order to proof that ∠ ABC + m ∠DBE = 180° the correct proof is given as follows:
m ∠CBD - m ∠DBE - Given ∠ABC, ∠CBD are supplementary - Given by the definition of supplementary angels. m ∠ABC + m ∠CBD = 180° - this is is also based on exterior sides in opposite raysm ∠ABC + m ∠DBE = 180° because of the substituted angles.QEDWhat is a supplementary angle?Supplementary angles comprise of angles that are on a straight line and which must add up to 180°
It is right to state therefore, that ∠ABC, ∠CBD are supplementary angels.
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Figure A
Figure B
Figure A is rotated 180°, then reflected across the line.
Figure B is reflected across the line, then rotated 180°.
Which of the following shows the two figures after they are
transformed?
Answer:
The answer is c
Step-by-step explanation:
look at the picture carefully
What is equivalent? A B C OR D
please help
Answer:
[tex]8^{\frac{x}{3} }[/tex]
Step-by-step explanation:
CAN SOMEONE HELP ME PLS?????
You are correct, P(red) = P(green) = 0.25.
Point E,F,D are located on circle C
The measure of arc ED is 68 what is the Measure of angle EFD
The measure of the angle EFD will be 68 degrees. The correct answer is option B.
What is an angle?The angle is defined as the span between two intersecting lines or surfaces at or close to the point where they meet.
Given that:-
The arc angle is 68 degrees and we need to find the angle EFD.
As it is given in the question that the angle suspended by the arc is 68 degrees so the angle EFD will also be equal to 60 degrees.
Therefore the measure of the angle EFD will be 68 degrees. The correct answer is option B.
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What is the missing number below in the solution to 968 divided by 10
Answer: 484/5
Step-by-step explanation:
For this word problem, it seems confusing with the wording but the equation would just be:
968÷10=x
solving for x, we get 484/5.
Which equation has a graph that lies entirely above the x-axis?
y = -(x + 7)² + 7
y= (x-7)²-7
y= (x-7)² +7
y= (x-7)²
Heyo!
The equation when displayed on a graph that lies entirely above the x-axis would be Option 4) y = (x - 7)^2.
Hope this helps! If so, please lmk! Also, if you have any questions, feel free to comment below. Good luck!
Answer:
Step-by-step explanation:
PLEASE HELP ASAP
:) thank you
Answer:
(16, 0) should be right.
Step-by-step explanation:
Well, I used to do the math, but after using Acellus a while, I found Symbolab.
It's suuuper handy with Algebra. I highly recommend.
How I found this intercept was enter:
intercept -2x+8y=-32
and bam it lists you all intercepts!
24. Factorise completely the expression: 7x-21+ 2xy - 6y
Answer:
below
Step-by-step explanation:
7(x-3)+2(xy-3y)
I'm positive it's the correct answer
(a) By what least number must 27 be divided to make it perfect square
Answer:
3
Step-by-step explanation:
When you divide 27 by 3 it will give you 9 and the square root of 9 gives you a perfect answer indicating that 3 is the least number that must be divided into 27
Answer:
[tex]\fbox {3}[/tex]
Step-by-step explanation:
First, prime factorize 27 :
⇒ 27 = 3 × 3 × 3
If 27 was divided by 3, it would give 3 × 3, which would give 9, a perfect square.
Simplify
21x^6 y^5
14x^2y^9
Answer:
[tex]\frac{3x^{4} }{2y^{4} }[/tex]
Step-by-step explanation:
Factor out 7 from top and bottom :
[tex]\frac{7(3x^6y^5)}{7(2x^2y^9)}[/tex]
Divide top and bottom by 7 :
[tex]\frac{3x^6y^5}{2x^2y^9}[/tex]
Simplify :
[tex]\frac{x^6}{x^4}=x^{2}[/tex]
Simplify :
[tex]\frac{y^5}{y^9} = y^{-4} = \frac{1}{y^{4} }[/tex]
Collect everything together :
[tex]\frac{3x^{4} }{2y^{4} }[/tex]
Hope this helped and have a good day
Package Express, Inc. operates a small package delivery service in the Jacksonville suburbs. If the company uses a regression equation to forecast total operating costs, the coefficient of the equation's independent variable would correspond to the:
The coefficient of the equation's independent variable would correspond to the: variable operating cost per delivery.
What is variable operating cost?Variable operating cost can be defined as those cost that varies due to changes in a company or an organization day to day operating activity.
Delivery cost is an example of variables cost because cost of delivery a product or goods depends on the volume or units of the goods.
Therefore the coefficient of the equation's independent variable would correspond to the: variable operating cost per delivery.
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7. Which of the verbal descriptions best matches the function below?
f(x)=0.02x+150
Gene earns 2% interest after depositing $150 into his account , Option D.
What is a Function ?A function is a law that relates an independent variable and a dependent variable with each other.
The function given is
f(x) = 0.02 x +150
Option D , Gene earns 2% interest after depositing $150 into his account
So this verbal description matches the function given as it represents , the total account balance of Gene .
Therefore Option D is the correct answer.
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1.Simplify using suitable properties
(i) 13−51+2
Answer:
This is my answer:
Step-by-step explanation:
Javier is comparing costs of two cars. Car A costs $130 per month for insurance and $0.10 per mile to run. Car B costs $108 per month for insurance and $0.15 per mile to run. He defines x as the number of miles driven each month and y as the total cost to run the car. Which set of equations can be used to find the number of miles Javier would need to drive to make the costs equal?
0.10 x = 130. 0.15 y = 108
y = 0.10 x + 130. y = 0.15 x + 108
0.10 x = 108. 0.15 y = 130
y = 0.15 x + 130. y = 0.10 x + 108
Answer:
y = 0.10 x + 130. y = 0.15 x + 108
Step-by-step explanation:
0.10 and 0.15 are the slope in the equation y = mx + b since it requires an input (number of miles) to spit out an output (number of miles*0.10 = price) and the x intercept is 130 and 108 creating the equation y = 0.10 x + 130. y = 0.15 x + 108.
If k(x) = 5x – 6, which expression is equivalent to (k + k)(4)?
5(4 + 4) – 6
5(5(4) – 6) – 6
54 – 6 + 54 – 6
5(4) – 6 + 5(4) – 6
___________is a relation in which each element of the domain is paired with exactly one element of the range.
Answer:
A function
Step-by-step explanation:
A function is a relation in which each element of the domain is paired with exactly one element of the range.
Select all the correct answers.
The diagram shows the construction of two tangent lines to a circle from a point outside the circle.
A circle with a center O. Two tangents, JP and KP are drawn from the same external point P. A horizontal line is drawn from P to O. A vertical line is drawn through the tangent and intersects the horizontal line at M. A line connects JM.
From the diagram, which three statements are true?
- line segment MJ≅ Line segment MP
-∡OJP≅∡OML
-∡OJM≅∡JMO
- line segment OM≅line segment MP
- line segment OJ≅line segment MJ
- line segment LM≅line segment MP
1) line segment MJ≅ Line segment MP
2) ∡OJP≅∡OML
3) line segment OM≅line segment MP
The below mentioned statements are true according to the figure , Option A, B and D is the correct answer.
What are Tangents ?A line that intersects the curve at a single point at 90 degree is called a tangent.
In the given figure it can be seen that the
∡OJP≅∡OML (right angle)line segment OM≅line segment MP (as M is bisecting the line OP)line segment MJ≅ Line segment MPTherefore , Option A , B and D is the correct answer
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let a,b, and c be real numbers where a ≠ b≠c≠0. which of the following functions could represent the graph below?
The function will be f(x) = x²(x - a)²(x - b)(x - c). Then the correct option is A.
What is a function?A statement, principle, or policy that creates the link between two variables is known as a function. Functions are found all across mathematics and are required for the creation of complex relationships.
The graph is given below.
The factor of the function will be
(x - 0), (x - a), (x - b), and (x - c)
Then the function will be
Then the function can be written as
f(x) = x²(x - a)²(x - b)(x - c)
Then the correct option is A.
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Answer:
The answer on Edge is Choice A
Step-by-step explanation:
To determine whether a graph of a relation is also a function, Shayla declares that the y-axis is a vertical line and counts the number of times that the graph intersects the y-axis. If the graph has exactly one y-intercept, Shayla concludes that the graph shows a function. In all other cases, she declares that it is not a function.
Is Shayla applying the vertical line test correctly?
No, because the y-axis is a horizontal line.
No, because using the y-axis tests only whether x = 0 is mapped to multiple values.
Yes, because multiple y-intercepts represent multiple x-values being mapped to y = 0.
Yes, because the y-axis represents all vertical lines of the x-values.
Answer: Choice B
No, because using the y-axis tests only whether x = 0 is mapped to multiple values.
===================================================
Further Explanation:
Shayla stating that the y axis being used to conduct a vertical line test is part of the process. But she needs to move the vertical line around and not have it fixed in place.
If it is possible to have a vertical line (on the y axis or not) pass through more than one point on the curve, then we don't have a function. It is said the curve fails the vertical line test.
Otherwise, the graph passes the vertical line test and we have a function.
tch and his brother, Terry, went on a hiking expedition. Starting at sea level, the brothers climbed to a scenic cliff located 6.6 kilometers above them. From there, they descended 1.3 kilometers in one hour. Mitch discovered that he had left behind some essential supplies on the cliff. So, the brothers decide to head back up. They climbed 0.8 kilometer within the next hour. At this point, Mitch and Terry were
away from the scenic cliff.
Mitch and Terry were 0.5 km away from the scenic cliff
What is Sea Level ?Sea level is the base for calculating the depth and the elevation of Earth
It is given that
Total Height of the scenic Cliff = 6.6km
After 1 hour the brothers are at = 6.6 - 1.3 km = 5.3 km from the sea level.
They climb back 0.8 km in the next hour so they will be
5.3 +.8 = 6.1 km from the sea level
6.6 - 6.1 = 0.5 km
Therefore the brothers are 0.5 km away from the scenic cliff
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What is the measurable quantity given by its formula with the appropriate units
Answer:
Where is the formula
Step-by-step explanation:
which of the following sets of inequalities
Inequalities help us to compare two unequal expressions. The correct options are 2 and 3.
What are inequalities?Inequalities help us to compare two unequal expressions. Also, it helps us to compare the non-equal expressions so that an equation can be formed. It is mostly denoted by the symbol <, >, ≤, and ≥.
The inequality for the red portion is,
slope, m = (-2/-4) = 1/2
y-intercept is 2.
y ≤ (1/2)x + 2
The inequality for the blue portion is,
slope, m = (5-0)/(3-0.5) = 2
y-intercept is -1.
y > 2x - 1
Hence, the correct options are 2 and 3.
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Please Help!10.<ADC and <FDA are a linear pair. What is the reason?
Answer:
Linear pair of angles are formed when two lines intersect each other at a single point. Therefore, <ADC and <FDA are a linear pair.
Step-by-step explanation:
How much money do I need now if I am going to recieve $5000 every 6 months (starting in 6 months) for 10 years if the interest rates are 4%/a compounded semiannually?
He needs to have $205783 amount of money to receive $5000 every 6 months for 10 years.
What is Interest ?Interest is the amount of money received , when a certain lump sum amount is deposited.
It is given that the person is receiving ,
Interest = $5000 ,
after six months , every six month
Time Period = 10 years
Interest Rate = 4%
Compounded Semiannual
Let the principal amount be $x
Compound Interest is given by
Amount = P[ 1 + r/n]ⁿˣ
Here x is the time period
Therefore the Amount = x{ 1 +0.04/2}²⁰
x + 5000 *20 = x{ 1 +0.04/2}²⁰
x + 100000 = 1.486 x
x = $205783
Therefore he needs to have $205783 amount of money to receive $5000 every 6 months for 10 years.
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Gary and Georgia split £56 in the ratio
2:5.
How much money does Georgia get?
Give your answer in pounds (£).
Answer:
£40
Step-by-step explanation:
sum the parts of the ratio, 2 + 5 = 7 parts
divide the amount by 7 to find the value of one part of the ratio.
£56 ÷ 7 = £8 , then
5 parts = 5 × £8 = £40 ← amount Georgia gets
Out of £56, the money received by Georgia is equivalent to $40.
What is Ratio?
The ratio is defined as the comparison of two quantities of the same units that indicates how much of one quantity is present in the other quantity.
Given is Gary and Georgia who split £56 in the ratio 2:5.
There are total of 7 parts. This means that £56 is divided equally among the seven parts. Assume that the one part is equivalent to x. Then the cost of 7 parts = 7x. From the question, we can write -
7x = 56
x = 8
Georgia has 5 parts, therefore the money received by Georgia will be = 5 x 8 = 40
Therefore, out of £56, the money received by Georgia is equivalent to $40.
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Which statement describes the quadratic inequality in factored form that represents the relationship greater than or equal to the quadratic equation containing the point (6, -8) on the boundary and zeros -4 and 10?
In the equation given, the quadratic inequality that shows the relationship above is: option B. y ≥ 0.2(x + 4)(x - 10).
What is the quadratic inequality about?Note that a quadratic function exist in factored form is as:
y = a(x - a)(x - b)
The zeros of the equation is seen at x = (-4, 10)
Therefore, one need to write an expression for the quadratic inequality and so it will be:
y ≥ a(x - a)(x - b)
Also note that at At point (6, -8), we also have:
-8 = a(6 - (-4))(6 - 10)
-8 = a(6 + 4)(6 - 10)
-8 = a(10)(-4)
-8 = -a(40)
a = 0.2.
Therefore, In the equation given, the quadratic inequality that shows the relationship above is: option B. y ≥ 0.2(x + 4)(x - 10).
See full question below
Which statement describes the quadratic inequality in factored form that represents the relationship greater than or
equal to the quadratic equation containing the point (6, -8) on the boundary and zeros-4 and 10?
Oy2-0.2(x + 4)(x - 10)
Oy≥ 0.2(x + 4)(x - 10)
O y 20.2(x-4)(x + 10)
Oy2-0.2(x-4)(x + 10)
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PQ is a chord of length 8 cm of a circle of radius 5 cm. The tangents at P and Q intersect at a point T. the length TP in cm is:
Here, ΔTPQ is isosceles and TO is the angle bisector of ∠PTO.
[∵ TP=TQ = Tangents from T upon the circle]
⠀⠀⠀⠀⠀⠀⠀⠀∴ OT⊥PQ
So, PR = RQ = 4cm.⠀⠀⠀
___________________________________________
[tex]\longmapsto{}[/tex]By Applying Pythagoras Theorem in ∆OPR :
OR = √OP² - PR²
OR = √5² - 4²
OR = 3cm
__________________________________________
Now,
[tex]\leadsto[/tex]∠TPR + ∠RPO = 90° (∵TPO=90°)
[tex]\leadsto[/tex]∠TPR + ∠PTR (∵TRP=90°)
[tex]\leadsto[/tex]∴ ∠RPO = ∠PTR
⠀⠀
∴ Right triangle TRP is similar to the right triangle PRO. [By A-A Rule of similar triangles]
⟼[tex]\frac{TP}{PO} = \frac{RP}{RO} [/tex]
⟼[tex]\frac{TP}{5} = \frac{4}{3} [/tex]
⟼[tex]TP= \frac{20}{3} [/tex]
Hence you got your answer here.⠀⠀⠀⠀⠀
-MissAbhiAt which point in the business cycle would the unemployment rate begin to increase? 1 2 3 4
Answer:
2 & 3
Step-by-step explanation:
2. High Interest Rates
High-interest rates make it more difficult for businesses to invest. For instance, a small store that is just starting is going to find it hard to make repayments at an interest rate of 20 or 30 percent. It also sucks out money from the economy and re-directs it to the banks. As the interest rates are so high, businesses and consumers reduce their demand for credit. In turn, there is a contraction in the money supply which can lead to deflation.
The effects of high interest rates can be dire if not managed correctly and subtly by central banks. If the interest rates are increased too fast, too high, and too rapidly, we will see the aforementioned effects such as lower business investment and deflation. Therefore, it can contribute to a transition towards an economic contraction in the business cycle.
3. Declining Real Incomes
Inflation can create a drain on consumer incomes as it decreases its value year on year. Therefore, if firms do not increase wages in line with inflation, the average worker will be able to afford less than before.
If real incomes decline, it means consumers have less income to spend on goods and services in the economy. In turn, a prolonged period of decline in real incomes can contribute to an economic contraction in the business cycle.
Answer
is 3 just did it on edge
Step-by-step explanation:
