Step-by-step explanation:
Taking LHS of the identity:
(a + b +c)2
This can also be written as:
= (a + b + c) (a + b + c)
Multiply as we do multiplication of trinomials and we get:
= a(a + b + c) + b(a + b + c) + c(a + b + c)
= a2 + ab + ac + ab + b2 + bc + ac + bc + c2
Rearrange the terms and we get:
= a2 + b2 + c2 + ab + ab + bc + bc + ac + ac
Add like terms and we get:
= a2 + b2+ c2 + 2ab + 2bc + 2ca
Hence, in this way we obtain the identity i.e. (a + b + c)2 = a2 + b2 + c2 + 2ab + 2bc + 2ca
An advertiser goes to a printer and is charged $37 for 90 copies of one flyer $53 for 285 copies of another flyer. This printer charges a fixed setup cost plus a charge for every copy of single-page flyers. Find a function that describes the cost of a printing job, if x is the number of copies made.
Step-by-step explanation:
[tex]f(x) = 30 + 0.08205x[/tex]
that is the function you are looking for.
first, we know that it is a fixed set up cost and charge for individual paper
A right circular cone of radius 6 inches, side length of 16 inches and height of h inches. Which is closest to the height of a cone that has a slant height of 16 inches and a radius of 6 inches? f 10 in. g 14.8 in. h 20 in. j 17.1 in.
Answer:
Height of cone (h) = 14.8 in (Approx)
Step-by-step explanation:
Given:
Radius of cone (r) = 6 in
Slant height (l) = 16 in
Find:
Height of cone (h) = ?
Computation:
Height of cone (h) = √ l² - r²
Height of cone (h) = √ 16² - 6²
Height of cone (h) = √ 256 - 36
Height of cone (h) = √220
Height of cone (h) = 14.832
Height of cone (h) = 14.8 in (Approx)
?
12
Find the arc length of the semicircle.
Either enter an exact answer in terms of ar or use 3.14 for at and enter your answer as a decimal.
units
Answer:
6π
Step-by-step explanation:
Hope this helps!
A circle is a curve sketched out by a point moving in a plane. The arc length of the semicircle is 18.85 units or 6π units.
What is a circle?A circle is a curve sketched out by a point moving in a plane so that its distance from a given point is constant; alternatively, it is the shape formed by all points in a plane that are at a set distance from a given point, the centre.
The length of the arc on any semicircle is half the length of the circumference of the circle with the same radius.
Given the length of the diameter of the semicircle is 12 units. Therefore, the circumference of the circle with a diameter of 12 units is,
Circumference = π × Diameter
= π × 12 units
= 12π units
Now, the arc length of the semicircle is,
Length of the semicircle = Circumference /2
= 12π /2 units
= 6π units
= 18.85 units
Hence, the arc length of the semicircle is 18.85 units or 6π units.
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The 2nd and 3rd terms in the following algebraic sequence are x and y. Write down algebraic expressions for the first, fourth and fifth terms.
Answer:
see explanation
Step-by-step explanation:
To obtain a term in the sequence add the previous 2 terms, that is
[tex]a_{n}[/tex] = [tex]a_{n-1}[/tex] + [tex]a_{n-2}[/tex] ← in general terms
(a)
Given 1 4 5 9 14
Then the next 2 terms are 9 + 14 = 23 and 23 + 14 = 37
(b)
Given a₄ = 30 and a₅ = 49 , then
a₃ = 49 - 30 = 19
a₂ = 30 - 19 = 11
a₁ = 19 - 11 = 8
Sequence is 8 11 19 30 49 ....
(c)
Given a₂ = x and a₃ = y , then
a₁ = y - x
a₄ = a₃ + a₂ = y + x
a₅ = a₄ + a₃ = y + x + y = 2y + x
In an arithmetic progression the sum of the fifth and sixth terms is 44 and the sum of the first eighteen terms is thrice the sum of the first ten terms, find the value of the
Answer:
a = 5.5, d = 11/3
Step-by-step explanation:
An arithmetic progression is a sequence of number such that the difference between consecutive numbers is a constant. It is given by:
[tex]a_n=a+(n-1)d\\a_n \ is\ the \ nth\ term, d\ is\ the\ common\ difference\ and\ n \ is\ the \ number\ of\ terms[/tex]
The sum of fifth and sixth terms is 44
Therefore:
a + 4d + a + 5d = 44
2a + 9d = 44 (1)
The sum of the first n terms is:
[tex]S=\frac{n}{2} (2a+(n-1)d)\\Therefore\ the\ sum\ of\ the\ first\ 18\ term\ is:\\\\S=\frac{18}{2} (2a+(18-1)d) = 9(2a+17d)=18a+153d\\\\The\ sum\ of\ the\ first\ 10\ term\ is:\\\\S=\frac{10}{2} (2a+(10-1)d) = 5(2a+9d)=10a+45d[/tex]
Since the sum of the first eighteen terms is thrice the sum of the first ten terms:
18a + 153d = 3(10a + 45d)
18 a + 153d = 30a + 135d
18a - 30a + 153d - 135d = 0
-12a + 18d = 0 (2)
Multiply equation 1 by 6 and add to equation 2:
72d = 264
d = 11/3
Putting d = 11/3 in eqn 2
-12a + 18(11/3) = 0
-12a + 66 = 0
12a = 66
a = 5.5
T = WP [ M² - ( M-S)² ]
Answer:
W PM^2 − WP(M−S)^2=T
Step-by-step explanation:
this is what mathaway said
3. (01.05)
Which of the following best represents the average rate at which a person can quickly walk? (2 points)
3 steps per hour
3 steps per second
30 steps per minute
30 steps per second
Answer:
3 steps per second.
Step-by-step explanation:
3 steps per hour are way too slow.
30 steps per minute are too slow as well, that's half a step per second.
30 steps per second, is too fast, until your the Flash or something.
Zack wants his rectangular garden to be 8 feet longer than it is wide and for its area to be less than or equal to 660 ft2. What are the possible values for the length of his garden in feet (x)?
Answer:
L≤30ft
Step-by-step explanation:
The area of the garden A = Length(L)*Width(W)
If Zack wants his rectangular garden to be 8 feet longer than it is wide, then
L = 8+W
Also, if he wants the area to be less than or equal to 660 ft², the A ≤ 660
LW≤660 ........1
(8+W)W ≤ 660
W²+8W-660≤0
W²+30W-22W-660≤0
W(W+30)-22(W+30)≤0
(W-22)(W+30)≤0
W-22≤0
W≤22 (neglecting the positive value)
Substituting W = 22 into equation 1
22L≤660
L≤660/22
L≤30
Hence the possible values for the length of his garden in feet are values less than and equal to 30 feet.
Answer:
The correct answer is A 8 < x ≤ 30
Step-by-step explanation:
Good luck!!
simplify 5х + 6x — 3x
OA) 30°
O B) 60°
D) 50°
OC) 90°
Answer:
A
Step-by-step explanation:
We know that the sum of interior angles in a triangle is 180°. Looking at ΔWYZ, we can write:
? + 75 + 75 = 180
? + 150 = 180
? = 30°
The three inside angles of a triangle need to equal 180 degrees.
You are given the bottom two angles.
75 + 75 = 150
WYZ = 180 - 150 = 30
The answer is 30 degrees.
Aisle 2 of a furniture store stocks 4-legged chairs, 4-legged tables, and 3-legged stools. If there are t tables, c chairs, and s stools, which expressions show the total number of furniture legs in aisle 2?
Answer:
T = 4c + 4t + 3s
Step-by-step explanation:
Stocks contains:
4-legged chairs
4-legged tables
3-legged stools
So, 1 chair has legs = 4
So, c chairs has legs = 4c
1 table has legs = 4
So, t tables has legs = 4t
1 stool has legs = 3
So, s stools has legs = 3s
Let T denotes the total no. of legs
So, the total number of furniture legs in aisle 2 :
T = 4c + 4t + 3s
Hence, T = 4c + 4t + 3s expression show the total number of furniture legs in aisle 2.
Hope it helped u if yes mark me BRAINLIEST! :)
Tysm!
Also sorry for late reply... :(
1 + 8x + 5 -4x = 2(x-3) - 2(x-2)
Answer:
x = -2
Step-by-step explanation:
Eliminate parentheses and collect terms.
1 +8x +5 -4x = 2(x -3) -2(x -2) . . . . . given
6 +4x = 2x -6 -2x +4
6 + 4x = -2
4x = -8 . . . . . subtract 6
x = -2 . . . . . . divide by 4
Between which two consecutive whole numbers does \sqrt{78} 78 lie? Fill out the sentence below to justify your answer and use your mouse to drag \sqrt{78} 78 to an approximately correct location on the number line.
Answer:
A. 8 and 9
Step-by-step explanation:
Between which two consecutive whole numbers does √ 78 lie?
a.
8 and 9
b.
6 and 7
c.
9 and 10
d.
7 and 8
A. 8 and 9
8^2 = 8 × 8 = 64
9^2 = 9 × 9 = 81
B. 6 and 7
6^2 = 6 × 6 = 36
7^2 = 7 × 7 = 49
C. 9 and 12
9^2 = 9 × 9 = 81
12^2 = 12 × 12 = 144
D. 7 and 8
7^2 = 7 × 7 = 49
8^2 = 8 × 8 = 64
The correct answer is A. 8 and 9
The sum of three consecutive odd numbers is 93. What is the smallest of these numbers?
Answer:
30+31+32 =93. Smallest is 30
Answer:
31
Step-by-step explanation:
Let the three unknown numbers be x+x+x
[tex]x+x+x =93\\3x = 93[/tex]
Divide both sides by 3
[tex]\frac{3x}{3} = \frac{93}{3} \\\\x = 31\\\\[/tex]
The numbers are 31 , 33,35
Find the third side in simplest radical form:
25
Answer:
[tex] \boxed{ \bold{24}}[/tex]Step-by-step explanation:
[tex] \mathsf{given}[/tex]
[tex] \mathsf{hypotenuse(h) = 25}[/tex]
[tex] \sf{perpendicular (p) = 7}[/tex]
[tex] \sf{base(b) = }[/tex]?
Now, Using Pythagoras theorem
[tex] \sf{{h}^{2} = {p}^{2} + {b}^{2} }[/tex]
plug the values
⇒[tex] \sf{ {25}^{2} = {7}^{2} + {b}^{2} }[/tex]
Evaluate the power
⇒[tex] \sf{625 = 49 + {b}^{2} }[/tex]
Swap the sides of the equation
⇒[tex] \sf{49 + {b}^{2} = 625}[/tex]
Move constant to right hand side and change it's sign
⇒[tex] \sf{ {b}^{2} = 625 - 49}[/tex]
Calculate the difference
⇒[tex] \sf{ {b}^{2} = 576}[/tex]
Squaring on both sides
⇒[tex] \sf{b = 24}[/tex]
Hope I helped!
Best regards!
The diagonals of a rhombus are 16cm and 12cm long.Calculate the length of its side
Answer:
10 cm
Step-by-step explanation:
The diagonals of a rhombus are perpendicular bisectors of each other.
All sides are congruent.
The diagonals divide the rhombus into 4 congruent right triangles.
Applying Pythagoras' identity to 1 of the triangles with legs 6 and 8 and hypotenuse the side s of the rhombus, then
s² = 6² + 8² = 36 + 64 = 100 ( take the square root of both sides )
s = [tex]\sqrt{100}[/tex] = 10
evaluate the expression for x=3 and y=-6
3x+4y
Answer:
-15
Step-by-step explanation:
given 3x+4y
when x = 3 and y = -6
3x+4y
= 3(3)+4(-6)
= 9 - 24
= -15
Answer:
The answer is - 15Step-by-step explanation:
3x + 4y
When
x = 3
y = - 6
Substitute these values into the above expression and solve
We have
[tex]3(3) + 4( - 6) \\ = 9 - 24[/tex]
We have the final answer as
- 15Hope this helps you
A number y decreased by 11 is 4 HELP!!!!!!!!!!!!!!
Answer:
equation is y-11 =4
so the number is 15. thats all
Step-by-step explanation:
Answer:
7
Step-by-step explanation:
Solve for kkk. \dfrac{k}4+ 3= 14 4 k +3=14
Answer:
its -2
Step-by-step explanation:
The value of k in equation k/4 + 3 = 14 is 44 and in the other equation 4k + 3 = 14 it will be 11/4.
What is a linear equation?A linear equation is an equation in which the highest power of the variable is always 1. The standard form of a linear equation in one variable is of the form Ax + B = 0.
We have given equation as
k/4 + 3 = 14
subtract by 3 both sides
k/4 + 3 -3 = 14 -3
k/4 = 11
On cross-multiplication, the equation becomes
k = 11(4)
k = 44
similarly,
4k + 3 = 14
subtract by 3 both sides
4k +3 - 3 = 14 - 3
4k = 11
On cross-multiplication, the equation becomes
k = 11/4
Thus, the value of k in both the equation is 44 and 11/4.
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Jada is making lasagna and pizzas for a party recipe calls for 1 1/4 cups and she uses 1/2 she doubled her recipe and made 5 pizzas what's the evaluate and for how many 3/4 cans of tomato she need in all
This question is not correctly written
Complete Question
Jada is making lasagna and pizzas for a large party. Her lasagna recipe calls for 1 1/4 cups of tomato paste, and her pizza recipe uses 1/2 cup of tomato paste per pizza. She will double her lasagna recipe and make 5 pizzas. Write and evaluate an expression for how many 3/4- cup cans of tomato paste she will need in all.
Answer:
The evaluate and for how many 3/4-cup cans of tomato she need in all is 20/3
Step-by-step explanation:
Step 1
From the question, we are told that:
1 single lasgna recipe uses: 1 1/4 cups of tomato paste = 5/4 cups
If she doubles her recipe, the number of cups of tomato paste =
2 × 5/4 cups of tomato paste
= 10/ 4 = 5/2 cups of tomato pastes
Step 2
From the question, we are told that:
1 Pizza recipe = 1/2 cup of tomato pastes
5 Pizza =
5 × 1/2 cup of tomato paste
= 5/2 cups of tomato paste
Steps 3
The total number of cups of tomato paste Jada will use in making double lasagna and 5 pizzas is calculated as
= 5/2 + 5/2
= (5 + 5)/ 2
= 10/2
= 5 cups.
Step 4
We are asked to evaluate how many 3/4 -cup cans of tomato she need in all.
This means we should find how many 3/4 - cup cans can be found in the total number of cups of tomato paste that Jada used.
Total number of cups that Jada used = 5 cups of tomato paste
The number of 3/4-cup cans in 5 cups is calculated as:
5 ÷ (3/4)
= 5 × 4/3
= 20/3
Therefore, the evaluate and for how many 3/4-cup cans of tomato she need in all is 20/3
Collect population of states of India or of 10 large cities or of 10 countries and write them in words/Indian/ International both.
Step-by-step explanation:
Indian States
Rajasthan Madhya Pradesh Maharashtra Uttar Pradesh Gujarat Karnataka Andhra Pradesh Odisha Chhattisgarh Tamil NaduAt the city museum, child admission is 5.50 and adult admission is 8.8 . On Thursday, three times as many adult tickets as child tickets were sold, for a total sales of 663.60 . How many child tickets were sold that day?
Answer:
78
Step-by-step explanation:
Adult tickets = x
Child tickets = 3(Adult tickets) = 3x
The cost of child admission is $5.50, and the cost of adult admission is $8.80. Multiply the cost of admission by the variables and set equal to the total sales.
8.8(x) + 5.5(3x) = 663.6
8.8x + 16.5x = 663.6
25.3x = 663.6
x = 26
Child tickets = 3x
Child tickets = 3(26)
Child tickets = 78
78 child tickets were sold that day.
For the question 2.3 x 0.123, the answer will be to which place value?
tenths
hundredths
thousandths
ten-thousandths
0.2829
Step-by-step explanation:I think it would be thousandths I'm pretty sure :)
Each side of a quilt square measures approximately 4.25 inches. If there are about 2.54 centimeters in 1 inch, how long is each side of the square in centimeters? Express your answer using the appropriate level of accuracy and use complete sentences to explain your reasoning.
Answer:
Each side of the square in centimetres = 10.80 centimetres
Step-by-step explanation:
To convert from one unit to another or in between units we make use of conversion factors or conversion formulas
The conversion factor for the conversion of units in centimetres to units in inches is given as about 2.54 centimetres being equivalent to 1 inch
Therefore;
1 inch = 2.54 centimetres
4.25 inches = 2.54 × 4.25 = 10.795 ≈ 10.80 centimetres
Therefore, each side of the square in centimetres = 10.80 centimetres.
The sum of first an arithmatic sequence is 3n squared plus 4n what is first term
Answer:
The formula says that the sum of the first n terms of our arithmetic sequence is equal to n divided by 2 times the sum of twice the beginning term, a, and the product of d, the common difference, and n minus 1. The n stands for the number of terms we are adding together.
Step-by-step explanation:
Help please!!!! Tyyy
Answer:x= 45°
Step-by-step explanation:
The value of angle LKN is 75°becausw the theorem vertically oposite angles
Then the value of angle LPN is 45° because figure LKNP is a rectangle so the sum of the angles should be 360°so 120°+120°+75°+angle LPN is 360°so the value of angle LPN is 45°
The value of x is also 45° because of vertically oposite angles theorem
please help me on number 3
Answer:
D
Step-by-step explanation:
Well the total angle is of measure 8x+2 and
the bisected angle is of 5x-3 so that means
(8x+16)/2=5x-3
4x+8=5x-3
x=11°
so 5(11)-3=52° this is because the bisected angles are the same
BED=REB
P-18=3 solve for P??
Answer:
P=21
Step-by-step explanation:
The solution to the equation P - 18 = 3 for P is P = 21
How to determine the solution to the equation for PFrom the question, we have the following parameters that can be used in our computation:
P - 18 = 3
Add 18 to both sides of the equation
so, we have the following representation
18 + P - 18 = 3 + 18
Evaluate the like terms on the right hand side
This gives
18 + P - 18 = 21
Evaluate the like terms on the left hand side
This gives
P = 21
Hence. the solution is 21
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Question 10
If QR=16 and PR=95, find PQ.
Answer:
Okay, so the picture is a different question than the text.
The answer to the picture is:
67
The answer to the text is:
79
Step-by-step explanation:
I'll explain the picture one.
The line PQR can be represented as [tex]PQ + QR=PR[/tex]. Since we already know the measure of QR and PR, we can substitute inside the equation to try and find PQ.
[tex]PQ + 21 = 88[/tex]
Our goal is to isolate PQ on one side.
To do this we can subtract 21 from both sides.
[tex]PQ + 21 - 21 = 88-21\\\\PQ=67[/tex]
Hope this helped!
Answer:
PQ = 79
Step-by-step explanation:
PQ + QR = PR
PR - QR = PQ
95 - 16 = 79
h(x)=x•2+1 k(x)=x-2
(H+k)(2)
Answer:
What type of answer is it suppose to be? Essay, true or false, multiple answer?
Step-by-step explanation: