The result of the evaluation of the series described by 1/2, 3/2, 5/2, . . . . . . . , 15/2 is:
∑ = 28
What is a series?A series is the summation of a set of numbers or sequences.
What is sigma notation?The sigma notation is a mathematical operation used to determine the final value of the sum of "n" terms consecutively, when dealing only with numbers without variables this is known as an arithmetic series.
The equation for this type of problem is:
∑ = n(a1 + an)/2
n : number of termsa1 : first terman : last termOur values are:
1/2, 3/2, 5/2, . . . . . . , 15/2
a1 =1/2an = 15/2n = 7∑ = 7(1/2 + 15/2)/2
∑ = 7(8)/2
∑ = 28
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If z varies directly with the product of x and y(z=k x y) , then z is said to vary jointly with x and y .
c. Suppose z varies jointly with x and y , and x varies directly with w . Show that z varies jointly with w and y .
The value of z varies jointly with w and y.
What is the constant of proportion?
A constant of proportion is illustrated as the ratio which relates two given quantities with each other in the relationship of proportion. Constant of proportion is also called constant variation, rate of change, and constant ratio.
Solving for the value of constant of variation
let k be the constant of proportion
When a quantity varies directly with others, then we have a relation, y = kx
Given relation is z = kxy —-- 1
Also x varies directly with w i.e. x = k'w, where k' is constant of variation for x and w
Using in equation 1, we have,
z = k(k'w)y
z = kk'wy
z = Kwy, where K is constant of variation i.e. K = kk'
It shows that z varies directly with w and y.
Hence, z varies jointly with w and y.
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-4(x+7)+7x+2
combine like terms
Answer:
3x-26
Step-by-step explanation:
-4(x+7)+7x+2
Multiple -4 By 7
-4x -28 +7x +2
Group like terms
-4x +7x -28+2
-4+7= 3
3x -28 +2
-28+2=-26
3x-26
Hope this helps! ^^
Solve each system by substitution. Check your answers.
x + 12y = 68 , x=8y-12
By substitution, the solution of the system of equations, x + 12y = 68 and x = 8y - 12, is (20 , 4).
A system of linear equations is a set of two or more equations which includes common variables. To solve system of equations, we must find the value of the unknown variables used in the equations that must satisfy both equations.
There are three methods that can be used to solve system of linear equations.
1. Elimination
2. Substitution
3. Graphing
Using substitution method, given two linear equations in x and y,
x + 12y = 68 (equation 1)
x = 8y - 12 (equation 2)
Since the second equation is already expressed in x in terms of y, substitute the value of x to the first equation.
x + 12y = 68 (equation 1)
(8y - 12) + 12y = 68
8y - 12 + 12y = 68
Combining all terms containing the variable y on one side and the constants on the other side of the equality, and solving for y.
8y - 12 + 12y = 68
8y + 12y = 68 + 12
20y = 80
y = 4
Substitute the value of y in the second equation and solve for x.
x = 8y - 12 (equation 2)
x = 8(4) - 12
x = 32 - 12
x = 20
Hence, the solution of the given system of equations is (20 , 4).
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Ann, Claire and Josh collect stickers. One week, Ann collects 7 more stickers than Josh. Josh collects twice as many stickers as Claire. If they collect a total of 157 stickers, how much stickers did each collect?
Josh collected 60 stickers, Ann collected 67 stickers and Claire collected 30 stickers.
How to find the number of stickers each collect using variables?Ann, Claire and Josh collect stickers. One week, Ann collects 7 more stickers than Josh.
let use variables to represent the amount of stickers they collected.
Therefore, Ann collects 7 more stickers than Josh. Josh collects twice as many stickers as Claire
Josh stickers = x
Ann stickers = 7 + x
Claire stickers = 1 / 2 x
Total stickers collected = 157
Therefore,
x + 7 + x + 1 / 2 x = 157
x + x + 1 / 2 x = 157 - 7
2.5x = 150
divide both sides by 2.5
x = 150 / 2.5
x = 60
Therefore, Josh collected 60 stickers, Ann collected 67 stickers and Claire collected 30 stickers.
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what is 20x-14x=21-10
:))
20x-14x=21-10
6x=11
x=11/6
☞ user58580~ ♥
Answer:
The Answer is x=11/6
Step-by-step explanation:
Hope this helps!!
In this problem, you will investigate the relationship between the arcs of a circle that are cut by two parallel chords.
c. Verbal Draw another circle and repeat parts a and bfb . Make a conjecture about arcs of a circle that are cut by two parallel chords.
Chords within a circle can be related in a variety of ways. Parallel chords cut congruent arcs in the same circle. That is, the arcs whose endpoints include one of each chord's endpoints have equal measures.
When two chords of a circle are parallel are the arcs?
Chords within a circle can be related in a variety of ways. Parallel chords cut congruent arcs in the same circle. That is, the arcs whose endpoints include one of each chord's endpoints have equal measures.
The lengths of the arcs connecting two parallel chords of a circle are equal. Similarly, if the lengths of the two arcs connecting two distinct chords are the same, the chords are parallel. If two chords have the same length, the arcs between their endpoints will have the same measure.
The term "parallel" refers to how each note in the chord rises or falls by the same interval.
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solve for x in terms of y
4x+2y=7
Answer: [tex]x=\frac{7-2y}{4}\\[/tex]
Step-by-step explanation:
4x+2y-2y=7-2y
4x= 7-2y
[tex]\frac{4x}{4}=\frac{7}{4}-\frac{2y}{4}[/tex]
Simplify: [tex]\mathrm{Divide\:the\:numbers:}\:\frac{4}{4}=1[/tex] = x / [tex]\frac{7}{4}-\frac{2y}{4}[/tex] x = [tex]\frac{7-2y}{4}[/tex]
Two cyclists, 80 miles apart, start riding toward each other at the same time. One cycles 3 times as fast as the other. If they meet 4 hours later, what is the speed (in mi/h) of the faster cyclist?
The speed of the faster car is 15 miles per hour.
How to find the speed of the faster cyclist?Two cyclists, 80 miles apart, start riding toward each other at the same time.
One cycles 3 times as fast as the other. If they meet 4 hours later
speed = distance / time
distance = speed × time
let
speed of the slower cycle = x
speed of the faster cycle = 3x
Therefore,
4x + 3x(4) = distance
4x + 3x(4) = 80
4x + 12x = 80
16x = 80
divide both sides by 16
x = 80 / 16
x = 5
Therefore, the speed of the faster car is 15 miles per hour.
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Which of the following numbers is an imaginary number?
A. -3²
B. (-5)2
C. √5
D. √-49
E. -√36
Answer:
B
Step-by-step explanation:
-3^2 =+8999999999999999999999(9())))))))(-"""&+(()))))(&&%422222222222223
Exponential form is a shorter form of _______________ multiplication.
Answer:
repeated
Step-by-step explanation:
Please answer questions 10-16. It would help me a whole bunch! You would be a total lifesaver! DUE TONIGHT!
Answer:uh I think its a carrot
Step-by-step explanation:
what positive number raised to the second power is equal to 64
Given ABCD, solve for x. We
Omar deposits $300 in an account earning 3% interest compounded annually. How much will be in the account after 1 year if he makes no withdrawals?
Answer: 100 $
Step-by-step explanation:
300 divided by 3 is 100
Finding the initial amount and rate of change given a table for a linear function
Answer: X=Time(Minutes) Y=Gallons Y= 8x+70. I used slope intercept form: My example point would be (6, 118) (9, 142) 142-118/9-6=24/3=8. Therefore 8 is your slope. or you cold see that it increases by 24 everytime it skips 3 times.
Step-by-step explanation:
I need help with 19-22
Answer:
4
[tex]4x6 \div 17 \\ [/tex]
Answer:
Step-by-step explanation:
19-22= -3 becuase
22-19=3 but the other way around is -3
Write a flow proof.
Given: RQ ≅ ST and RQ || ST
Prove: Δ R U Q ≅ ΔT U S
We can say that ΔRUQ ≅ ΔTUS under RHS condition.
What exactly does this mean by the congruency of a triangle?If all three corresponding sides are equal and all three corresponding angles are equal in measure, two triangles are said to be congruent.These triangles can be moved, rotated, flipped, and turned to look exactly the same.They will coincide if they are repositioned.Two triangles are congruent if they satisfy the five congruence conditions.They are the side-side-side (SSS), the side-angle-side (SAS), the angle-side-angle (ASA), the angle-angle-side (AAS), and the right angle-hypotenuse-side (RHS).So,
Given: RQ ≅ ST and RQ || ST
To Prove: ΔRUQ ≅ ΔTUS
∠RUQ = ∠SUT = (Inversely proportional)(RHS)RQ = ST = (Given: parallel and as ∠U is same in front of the lines, so the lines will also be same)So, RU = TU = (RHS condition)So, we can say that ΔRUQ ≅ ΔTUS under RHS.
Therefore, ΔRUQ ≅ ΔTUS.
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Solve each system by elimination.
8y + 10 = 6x , 8y - 4x = -12
Using elimination method, the solution of the given system of equations is (-1, -2)
A system of equations can be solved using:
graphical methodsubstitution methodelimination methodThe given system of equations is:
8y + 10 = 6x ..... (1)
8y - 4x = -12 ...... (2)
Re-arrange equation (1) to
8y - 6x = -10 ........ (3)
To eliminate variable y, subtract equation (3) from equation (2):
8y - 4x = -12
8y - 6x = -10 –
2x = -2
x = -1
Substitute x = -1 into equation (2)
8y - 4x = -12
8y - 4. (-1) = -12
8y + 4 = -12
Add (-4) to both sides:
8y = -16
y = -2
Hence, the solution is (-1, -2)
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What is the product of all the common factors of 16 and 24?
Answer:
The GCF of 16 and 24 is 8. To calculate the GCF (Greatest Common Factor) of 16 and 24, we need to factor each number (factors of 16 = 1, 2, 4, 8, 16; factors of 24 = 1, 2, 3, 4, 6, 8, 12, 24) and choose the greatest factor that exactly divides both 16 and 24, i.e., 8.
Step-by-step explanation:
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Are the lines perpendicular?
no, because the slopes of the lines are equal
no, because the slopes of the lines are not opposite reciprocals
yes, because the slopes of the lines are equal
yes, because the slopes of the lines are opposite reciprocals
Myra is reading an article about the success of introduced species of animals into the United States.
Which person is most likely considered the authority on the subject?
a zoologist
a microbiologist
a physicist
a chemist
The person that is most likely considered the authority on the subject is A. a zoologist.
Who is a zoologist?It should be noted that a zoologist simply means the individual that study animals and how they interact with their ecosystem.
In this case, Myra is reading an article about the success of introduced species of animals into the United States.
Therefore, the person that is most likely considered the authority on the subject is a zoologist.
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Which line on the graph below has an undefined slope?
On a coordinate plane, line Q is horizontal, line P has a positive slope, line R is vertical, and line S has a negative slope.
P
Q
R
S
The line which has an undefined slope among the answer choices given in the task content as described is; the line R which is a vertical line.
Which line among the given answer choices is that which has an undefined slope?It follows from the task content that the line which has an undefined slope is to.be determined among the answer choices.
Since, the slope of a graph is the rate of change in the vertical axis to that in the horizontal axis; it follows that the slope of vertical lines is undefined.
The statement above is true because, no change is recorded in the X axis of vertical lines. Hence, the denominator in the slope formula is; 0 and ultimately, the slope is undefined.
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Answer:
Step-by-step explanation:
The answer is R
find two consecutive odd integers whose product is the same as fifteen more than three times their sum
The find two consecutive odd integers is 7 and 9
Linear functionsThese are functions that has a linear degree of 1. Let the two consecutive odd numbers be 2x + 1 and 2x + 3
If their product is the same as fifteen more than three times their sum, then;
(2x+1)(2x+3) = 3(2x+1+2x+3) +15
4x²+6x+2x+3 = 3(4x+4) +15
4x²+8x+3 = 12x+12 + 15
4x² - 4x + 3 = 27
4x² - 4x - 24 = 0
x² - x - 6 = 0
On factorizing, the value of x is 3 and -2
First number = 2(3) + 1 = 7
Second number = 2(3) + 2 = 9
Hence the find two consecutive odd integers is 7 and 9
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Find L in the cone
please hurry
The length of slant height l is √98 ft. when diameter of cone and height of cone is 7 ft.
What is Mathematical function ?
Function is defined as the expression or relation between any given two variables such as x and y and there must be an independent variable and dependent variable.
Here, the diameter of cone is given as : 14ft.
also, the height of cone is : 7 ft.
the radius r of base will be half of diameter :
r = b/2
r = 14/2 = b
Now to find the slant height of the cone we use Pythagoras theorem between the base of cone b, height of cone h and slant height l that is :
h² + r² = l²
7² + 7 ² = l²
l² = (2x7²)
l = 7 √2 ft. or √98 ft.
Therefore, the length of slant height l is √98 ft.
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We can use the pythagorean theorem to answer this question.
We know that [tex]l[/tex] is the hypotenuse, and the 2 sides are 7 and 7.
So, we can build the equation:
[tex]7^2+7^2 = l^2[/tex]
[tex]98 = l^2[/tex]
[tex]\sqrt{98} = l[/tex]
.
Simplify the equation please
Answer:
[tex]4(5) {m}^{3} \times {m}^{2} \times {n}^{2} \times {n}^{1} [/tex]
since you know the rules of exponents we are multiplying powers of the same bases meaning we will add the exponents.
[tex] = 20 {m}^{3 + 2} {n}^{2 + 1} \\ = 20 {m}^{5} {n}^{3} [/tex]
Solve each equation. 3(w-8)=36
The solution of the given linear equation 3(w -8) = 36 in one variable is at w = 20.
According to the given question.
We have a linear equation in one variable 3(w - 8) = 36.
Since, we have to solve the above equation for w.
As we know tha, the linear equations in one variable is an equation which is expressed in the form of ax+b = 0, where a and b are two integers, and x is a variable and has only one solution.
Therefore, the solution of the linear equation in one varibale 3(w - 8) = 36 is given by
3(w - 8) = 36
⇒3w - 24 = 36 ( by distributive property)
⇒ 3w = 36 + 24 (adding 24 both the sides)
⇒ 3w = 60
⇒ w = 60/3 (dividing both the sides by 3)
⇒ w = 20
Hence, the solution of the given linear equation 3(w -8) = 36 in one variable is at w = 20.
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A farmer raises chickens and pigs. If his animals have a total of 120 heads and a total of 300 feet, how many chickens does the farmer have?
F. 60 G. 70 H. 80 J. 90
The number of chickens are J. 90.
Let the chickens be represented by x and the pigs be represented by y.
Forming the equation according to first information -
Equation 1 : x + y = 120
x = 120 - y
Both chicken and pig has one head. Chicken has 2 feet while pig has 4 feet. Forming the equation according to second information -
Equation 2 : 2x + 4y = 300
Simplifying the equation 2 by dividing by number 2
x + 2y = 150
Keep the value of x from equation 1 in equation 2
120 - y + 2y = 150
Performing subtraction
120 + y = 150
Further shifting the value and performing subtraction
y = 150 - 120
Performing subtraction
y = 30
Now, 30 is the number of pigs.
Number of chickens = 120 - y
Number of chickens = 120 - 30
Number of chickens = 90
Hence, the number of chickens the farmer has is J. 90.
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A bicycle has tires that are 24 inches in diameter.
b. How many inches does the tire travel after 100 rotations?
The tire travels 7536 inches.
We are given the diameter of tire of bicycle. Now, to find the distance traveled, we will use the following formula -
Distance = number of rotations × circumference of tire.
Now, further calculating the circumference of tire using the formula -
Circumference = π×diameter.
Firstly keep the values in the formula of circumference to calculate it.
Circumference = 3.14×24
Performing multiplication
Circumference = 75.36 inch
Now, keep the values in formula to find the distance traveled by the tire of bicycle.
Distance = 100×75.36
Again performing multiplication
Distance = 7536 inches
Hence, the distance traveled by the tires 7536 inches.
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If w = 24, what is the value of 2w − 18?
30
8
206
66
Answer:
30
Step-by-step explanation:
Substitute 24 for w
2(24) - 18
multiply 24 by 2
48 - 18
Subtract 18 from 48
Answer: 30
mark wants to paint a mural. he has 1 1/3 gallons of yellow paint, 1 1/4 gallons of green paint, and 7/8 gallon of blue paint. Mark plans to use 3/4 gallons of each paint color. how many gallons of paint will he have left after painting the mural
Mark has: 1 1/3 = 4/3 gallons of Yellow
1 1/4 = 5/4 gallons of Green
7/8 gallons of Blue.
Total = (4/3 + 5/4 + 7/8) LCM = 24
= (32 + 30 + 21)/24 = 83/24 Gallons of Paint in total.
If he used 3/4 of each, he would have = 1/4 of each left.
Therefore gallons left = 1/4 * (83/24) = 83/96 gallons left.
= 0. 8646 gallons left in total.
