Answer:
Ok, if we start with a number n, then we can write the consecutive numbers of n as:
n + 1
n + 2
n + 3..
etc.
Now, suppose that we have an integer x, and we want to write it as a sum of consecutive numbers.
There is a really trivial way.
We know that x + 0 = x.
now, we can write:
0 = (x - 1) + (x - 2) + ... + 1 + 0 + (-1) + (-2) + ..... + (-x + 2) + (x - 1)
Then we wrote zero as a sum of consecutive numbers.
Now we can write:
x = x + 0 = x + (x - 1) + (x - 2) + .... + 1 + 0 - 1 - 2 - ... - (x - 1) = x
Then we show that for any integer x, we can write it as a sum of consecutive integers.
Then it must work for all the integers x, then we prove that all the integers can be written as a sum of consecutive integers.
9x-4=3x-28 step by step
Answer:
Step-by-step explanation:
9x-4= 3x-28
We simplify the equation to the form, which is simple to understand
9x-4=3x-28
We move all terms containing x to the left and all other terms to the right.
+9x-3x=-28+4
We simplify left and right side of the equation.
+6x=-24
We divide both sides of the equation by 6 to get x.
x=-4
Which of the following is equivalent to 17g – 2g?
Answer:
Step-by-step explanation:
what following?
If x = 3y and y = 9, what is the value of 3x – 2?
Answer: 79
Step-by-step explanation: Lets first deal with the X. The equation would be 3 X 3 X 9. This answer is 81. Next we have 81 - 2. Therefore, our answer is 79. Do multiplacation first as M is before S in peMdaS.
Answer:
79
Step-by-step explanation:
x = 3y and y = 9
This means x = 3*9 = 27
3x -2
3 * 27 -2
81 -2
79
find the varible for 6-2x=6x-10x+18
Answer:
x=6
Step-by-step explanation:
How can I subtract 3x from both sides? Explanation and answer
Its not must that 3x have to be the one to be subtracted. You could take 8x as well.
But always subtract from the smaller one (in this case 3x) because its easier.
If you are subtracting 3x-3x and 8x-3x, the equation would be like
4 = 5x - 16
5x = 4+16
5x = 20
x = 4
what is the slope that passed through -3,6 and 5,1 ?
Answer: m=-5/8
Step-by-step explanation:
The formula for the volume of a sphere is V = Ar3, where Vis the volume
and ris the radius. Solve the formula for r, and then use it to answer the
question.
The volume of a basketball is about 435 cubic inches.
What is the radius of the basketball, to the nearest tenth of an inch? Use 3.14
for T.
it is 4 . 7 on a pex
I forgor
The radius of the basketball is 5 inches when the volume of a basketball is about 435 cubic inches.
What is Three dimensional shape?a three dimensional shape can be defined as a solid figure or an object or shape that has three dimensions—length, width, and height.
The formula for the volume of a sphere is V = 4/3πr³,
where V is the volume
and r is the radius.
Let us find the formula for r
3V/ 4π =r³
Take cube root on both sides
∛3V/ 4π = r
Now let us find the radius when the volume of a basketball is about 435 cubic inches.
∛3×435/ 4×3.14 = r
1305/12.56 = r
∛103.9 = r
4.7 = r
5=r
Hence, the radius of the basketball is 5 inches when the volume of a basketball is about 435 cubic inches.
To learn more on Three dimensional figure click:
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After Patrick spent 1/4 of his paycheck on a coat, he had $100 left. What was the cost of his coat?
Answer:
$100
Step-by-step explanation:
you divide 100 by .25 to equal 400 then take 400 - .25 = 100
What is the solution to the system of equations graphed below?
Answer:
A) (1,-2)
Step-by-step explanation:
the answer to a system of equations is where the 2 lines intersect and that would be at (1,-2)
- 8 = 6(x - 4) What is the slope of the line described by the equation?
Answer:
the slope is undefined
Step-by-step explanation:
How many lines of symmetry does the figure have?
If this is the triangle then it has 3 like the practice if you did it if not three lines of symmetry
A square of an unknown side length x inches has one side length increased by 4 inches and the other increased
by 7 inches
(a) If the original square is shown below with side lengths marked as x, label the second diagram to represent the new rectangle constructed by increasing the sides as described above.
Answer:
Length of new rectangle = (x + 7) inches
Width of new rectangle = (x + 4) inches
Step-by-step explanation:
A rectangle is a quadrilateral that has opposite sides to be parallel and equal. While a square has all its sides to be equal.
Given that: the square has unknown side length x inches.
Increasing one of its length by 4 inches = (x + 4) inches
Increasing the other by 7 inches = (x + 7) inches.
The new lengths results to a rectangle with length (x + 7) inches, and a width of (x + 4) inches.
the label diagram to represent the new rectangle is shown in the diagram attached to this answer.
Given RT below, if S lies on RT such that the
ratio of RS to ST is 3:1, find the coordinates
of S.
Answer:
(-2, -3)
Step-by-step explanation:
If a segment having extreme ends as [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] is divided by a point (x, y) in the ratio of m:n,
x = [tex]\frac{mx_2+nx_1}{m+n}[/tex]
y = [tex]\frac{my_2+ny_1}{m+n}[/tex]
Since, a line RT has extreme ends as R(-5, 3) and T(-1, -5) then a point S(x, y) which divides RT in the ratio of 3 : 1 will be,
x = [tex]\frac{3(-1)+1(-5)}{3+1}[/tex]
= [tex]\frac{-8}{4}[/tex]
= -2
y = [tex]\frac{3(-5)+1(3)}{3+1}[/tex]
= [tex]-\frac{12}{4}[/tex]
= -3
Therefore, coordinates of the point S will be (-2, -3).
Please help. I suck at math. Can someone simply the expression -3x-7(x+4)?
Answer:
[tex] - 3x - 7(x + 4) \\ = - 3x - 7x - 28 \\ = - 10x - 28[/tex]
hope it helped you:)
Answer:
[tex]-10x-28[/tex]
Step-by-step explanation:
[tex]-3x-7(x+4)[/tex]
Expand by using distributive law: [tex]a(b+c)=ab+ac[/tex]
Therefore,
[tex]-3x-7*x+\left(-7\right)\cdot \:4[/tex]
[tex]-3x-7x-7\cdot \:4[/tex]
[tex]-3x-7x-28[/tex]
Add the x:
[tex]-10x-28[/tex]
I just need to know the first 8 quick bc it’s almost due thanks!!
can someone help me me answer this question please and thankyou!??
Express 6^1/3 in simplest radical form.
Greetings from Brasil
From radiciation properties:
[tex]\large{A^{\frac{P}{Q}}=\sqrt[Q]{A^P}}[/tex]
bringing to our problem
[tex]\large{6^{\frac{1}{3}}=\sqrt[3]{6^1}}[/tex]
∛6The requried radical form of the given expression is ∛6.
What is radical form?Radical form is mathematical expression that represents the value under the nth roots.
What is simplification?The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Here,
Following the rule [tex]\sqrt[n]{x} = x^{1/n}[/tex]
Similarly,
[tex]6^{1/3} = \sqrt[3]{6}[/tex]
Thus, the requried radical form of the given expression is ∛6.
Learn more about simplification here:
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You are given the dollar value of a product in 2016 and the rate at which the value of the product is expected to change during the next 5 years. Use this information to write a linear equation that gives the dollar value V of the product in terms of the year t. (Let t = 16 represent 2016.)
2016 Value. $1850. Rate. $250 increase per year
Answer:
2071
Step-by-step explanation:
let t-16 then you multiple that by 4 and there is your answer 2071
Which of the following is a correct name for plane R below? * Which of the following is a correct name for plane R below? * plane m plane SPT plane SPQ plane SPV plane m plane SPT plane SPQ plane SPV
Answer:
Plane SPT and Plane SPV
Step-by-step explanation:
A plane is defined by the set of three points lying on the same (two dimensional) surface.
A plane 'R' has been given in the picture.
Points lying on this plane or surface are S, P, T and V.
Therefore, possible names may be,
SPT, STV, SPV, PTV
From the given options names of the plane R will be,
Plane SPT and Plane SPV,
A car is bought for $22,000. 5 years later it is worth $14,000
a)Write the linear model for this situation
b) How many years will it take for the car to be worth $7,000?
c)In 12 years how much will the car be worth?
Answer:
b) around 6 years
c) around 2,500
Step-by-step explanation:
What type of line is the x-axis
Answer:
Does this help
Step-by-step explanation:
A coordinate grid has two perpendicular lines, or axes, labeled like number lines. The horizontal axis is called the x-axis. The vertical axis is called the y-axis. The point where the x-axis and y-axis intersect is called the origin.
Answer:
horizontal
Step-by-step explanation:
Give 3 negative numbers and 2 positive numbers with the sum of 30.
what is the place value of 0 in 37.0691
Answer:
the tenths place
Step-by-step explanation:
Answer:
Step-by-step explanation:
The first place to the right of the decimal is the tenths place. That means it is 0.1 to 0.9 if the place is not zero as in this question.
Suppose that the question was 10.25
Then the 2 would be 2/10s
HELP ASAP PLEASE I DONT WANT TO FAIL
Michael had saved $257.40; he had deductions of $21.82 for dinner and $ 150.32 for clothes he purchased. After receiving his monthly allowance of $45, how much money does Michael have?
Answer:
$226.57
Step-by-step explanation:
if EF = 2x - 12, FG = 3x - 17, and EG = 26, find the values of X, EF, and FG.
Answer:
Step-by-step explanation:
2x - 12 + 3x - 17 = 26
5x - 29 = 26
5x = 55
x = 11
2(11) - 12 = 22 - 12 = 10 EF
3(11) - 17 = 33 - 17 = 16 FG
If 3x + 13 = 19, find the value of 2x + 1. 2x + 1 =
Answer: 7.4
Step-by-step explanation:
3x + 13 = 19
3x = 6
x = 2
Now substitute value of 'x' in the second equation:
2(2) + 1.2(2) + 1
= 4 + 2.4 + 1
= 5 + 2.4
= 7.4
Answer:
7.4
Step-by-step explanation:
The value of X is 2, so 3*2=6 6+13=19
So the second equation is 2*2=4 4+1.2*2=6.4 6.4+1=7.4
Hope this helps =3
Is -2 a solution for a in the inequality 2a +6 > a
Answer:
a > −6
Step-by-step explanation:
Step 1: Subtract a from both sides.
2a + 6 − a > a − a
a + 6 > 0
Step 2: Subtract 6 from both sides.
a + 6 − 6 > 0 − 6
a > −6
what would be the integer of 30/3?
Answer:
30
Step-by-step explanation:
if wrong plz tell me
Lin is delivering a package to a place located at 5,3 on the grid which house is getting the delivery
Answer:allen
Step-by-step explanation:
Lin is delivering a package to a place located at (5,3) on the grid.
Which house is getting the delivery?
Answer: Lin's
Lins is getting the delivery
Step-by-step explanation:
All you have to do is follow the directions that are being giving.
In the diagram, which pair of angles are vertical angles?
A transversal intersects 2 lines to form 8 angles. Clockwise from the top, the angles are 1, 2, 3, 4; 5, 6, 7, 8.
Angle 1 and Angle 2
Angle 4 and Angle 6
Angle 6 and Angle 8
Angle 5 and Angle 3
Step-by-step explanation:
Vertical angles are angles that are directly opposite to each other and are equal in magnitude.
Angles 6 and 8 are vertical angles.
Answer:
B
Step-by-step explanation:
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