Answer:
d. AB
e. A/B
Step-by-step explanation:
From the concept of homogeneity of dimension. The principle is that if two quantities occurs in the same direction, addition and subtraction of those two variable tends to occur but if two quantities occur in different direction, then we can only have either the division and multiplication of those quantities.
From the given information;
Suppose two quantities, A and B, have different dimensions.
The arithmetic operations that could be physically meaningful are :
d. AB
e. A/B
there are 15 black marbles and 10 white marbles in a bag. If you pick a marble from the bag without looking, what are your chances of picking a white marble?
Answer: 40%
Step-by-step explanation:
Answer: 2/5 or 40%
Step-by-step explanation: 15 + 10 = 25 and 10/25 simplifies to 2/5.
the lunch lady has 6 pounds of lasagna. if she makes 1/2-pounds servings using this lasagna, how many servings can she make?
Answer:
[tex]\boxed{12}[/tex]
Step-by-step explanation:
[tex]6/\frac{1}{2} =6*2=12[/tex]
A price decreases from $986 to $828.24. What is the percent change?
Answer:
-16% change
Step-by-step explanation:
The formula for a percent decrease is [tex]\frac{original-new}{original}\cdot100[/tex]. The original value was 986, and the new value is 828.24, so we can substitute inside the equation.
[tex]\frac{986-828.24}{986} \cdot100\\\\\frac{157.76}{986} \cdot100\\\\0.16\cdot100\\\\16[/tex]
So the percent change is -16%.
Hope this helped!
Expand and combine like terms.
(8 – n^7)(8 +n^7)
Answer:
Step-by-step explanation:
(a - b)(a + b) = a² - b²
(8 - n⁷)(8 + n⁷) = 8² - (n⁷)² = 64 - n¹⁴ {(aˣ)ⁿ = aˣ*ⁿ }
Or
Use FOIL method
(8 - n⁷)(8 + n⁷) = 8*8 + 8*n⁷ + (-n⁷)*8 + (-n⁷)*n⁷
= 64 + 8n⁷ - 8n⁷ - n⁷⁺⁷
= 64 - n¹⁴
Does anyone know how to solve this? It’s really starting to stress me out.
PS: You just can solve the lim(x->2) instead of lim(u->0) if u want
Answer:
π − 12
Step-by-step explanation:
lim(x→2) (sin(πx) + 8 − x³) / (x − 2)
If we substitute x = u + 2:
lim(u→0) (sin(π(u + 2)) + 8 − (u + 2)³) / ((u + 2) − 2)
lim(u→0) (sin(πu + 2π) + 8 − (u + 2)³) / u
Distribute the cube:
lim(u→0) (sin(πu + 2π) + 8 − (u³ + 6u² + 12u + 8)) / u
lim(u→0) (sin(πu + 2π) + 8 − u³ − 6u² − 12u − 8) / u
lim(u→0) (sin(πu + 2π) − u³ − 6u² − 12u) / u
Using angle sum formula:
lim(u→0) (sin(πu) cos(2π) + sin(2π) cos(πu) − u³ − 6u² − 12u) / u
lim(u→0) (sin(πu) − u³ − 6u² − 12u) / u
Divide:
lim(u→0) [ (sin(πu) / u) − u² − 6u − 12 ]
lim(u→0) (sin(πu) / u) + lim(u→0) (-u² − 6u − 12)
lim(u→0) (sin(πu) / u) − 12
Multiply and divide by π.
lim(u→0) (π sin(πu) / (πu)) − 12
π lim(u→0) (sin(πu) / (πu)) − 12
Use special identity, lim(x→0) ((sin x) / x ) = 1.
π (1) − 12
π − 12
find the sum of the following series
(a) 3+7+11+14+.......(20 terms)
(b)2+6+10+14+.......(15 terms)(c)30+27+24+21+......(40 terms)
(d)5+1+-3+-7+.....(14 terms)
(e)5+7+8+.........+75
(f)4+7+10+.........+91
need explanation
will give the brainliest!
Answer:
a) 820
b)450
c) -540
d) -294
e) 1440
f) 1425
Step-by-step explanation:
a) it is an arithmetic progression with ratio=4
a1=3,
a2=3+r=3+4=7.....
a20=a1+19r
so a20=3+19*4=3+76=79
S=(a1+an)*n/2 where n=20
so S=(3+79)*20/2=820
b) a15=a1+14*r=2+14*4=2+56=58
S=(a1+a15)*15/2=(2+58)*15/2=60*15/2=30*15=450
It is the same formula for all the exercises
S=(a1+an)*n/2 , where n is the number of terms
c) a40=30+39*(-3)=30-87=-57
So S=(30-57)*40/2=-540
d) a14=5+13*(-4)=5-52=-47
S=(5-47)*14/2=-42*14/2=-42*7=-294
e) it is 5+7+9+......+75
nr of terms = (an-a1) :r+1=(75-5):2+1=36
S=(5+75)*36/2=36*40=1440
f) ratio=7-4=3
the same formula for n= (91-4):3+1=87:3+1=29+1=30
S=(4+91)*30/2=95*30/2=2850/2=1425
the sum of two squares of two consecutive natural numbers is 41.Find the numbers
The 2 unknown numbers are 4 and 5 .
Explanation :Let the numbers be x and x + 1.
From the given information,
[tex]\dashrightarrow\sf \ \ \ x^2 + (x + 1)^2 = 41 \\ \\ \\ [/tex]
[tex]\dashrightarrow\sf \ \ \ 2 {x}^{2} + 2x + 1 = 41 \\ \\ \\ [/tex]
[tex]\dashrightarrow\sf \ \ \ 2 {x}^{2} + 2x + 1 - 41=0 \\ \\ \\ [/tex]
[tex]\dashrightarrow\sf \ \ \ {x}^{2} + x - 20 = 0 \\ \\ \\ [/tex]
[tex]\dashrightarrow\sf \ \ \ (x + 5)(x - 4)=0 \\ \\ \\ [/tex]
[tex]\dashrightarrow\sf \ \ \ { \underline{ \boxed{ \bf{ \red{x = - 5,4}}}}} \ \bigstar \\ \\ [/tex]
But, as we know -5 is not a natural number,
Hence, x = 4 .
So the 2 unknown numbers are :
x = 4 [1st number]x + 1 = 4 + 1 = 5 [2nd number]━━━━━━━━━━━━━━━★ Solution :
Let the number be x and x + 1.
[tex]\rule{130}1[/tex]
[tex]\underline{ \large \purple{ \mathscr{\dag\:A \bf{ccording} \: to \: \mathscr {Q} \bf{uestion} ....}}}[/tex]
[tex]:\implies\sf x^2 + (x + 1)^2 = 41 \\\\\\:\implies\sf 2x^2 + 2x + 1 - 41 = 0\\\\\\:\implies\sf 2x^2 + 2x + 40 = 0\\\\\\:\implies\sf x^2 + x - 20 = 0\\\\\\:\implies\sf x^2 + x - 20 = 0\\\\\\:\implies\sf x^2 + x - 20 = 0\\\\\\:\implies\sf x^2 + 5x - 4x - 20 = 0\\\\\\:\implies\sf x(x + 5) - 4(x + 5) = 0\\\\\\:\implies\sf (x + 5)(x - 4) = 0\\\\\\:\implies\underline{\boxed{\sf x = -5, 4}}[/tex]
⠀
We know that -5 is not a natural number. Hence, x = 4.
[tex]\therefore\:\underline{\textsf{The two consecutive natural number is \textbf{4 and 5}}}.[/tex]
what is the image of (8,-1) after a reflection over the line y=x
Answer:
(- 1, 8 )
Step-by-step explanation:
Under a reflection in the line y = x
a point (x, y ) → (y, x ) , thus
(8, - 1 ) → (- 1, 8 )
The image of (8, -1) after a reflection over the line y = x is, (- 1, 8).
What is Coordinates?A pair of numbers which describe the exact position of a point on a cartesian plane by using the horizontal and vertical lines is called the coordinates.
We have to given that;
A point (8, - 1) is reflected over the line y = x.
Now, We know that;
The image of point (x, y) after reflection over the line y = x is,
⇒ (x, y) → (y, x)
Thus, The image of (8, -1) after a reflection over the line y = x is,
⇒ (8, - 1) → (- 1, 8)
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Owen plots the numbers 4, –6, –8, and –3 on a horizontal number line. Which list shows the numbers in the order in which they would appear from left to right on the number line? –8, –6, –3, 4
Answer:-8, -6,-3, 4 is the correct answer
Step-by-step explanation:
Answer:
Answer A
Step-by-step explanation:
The list price of the item is 80 percent of the original price. The price of the item has been reduced by 80 percent. Write a pair of linear equations using variables of your choice to prove that these two statements are not equivalent. Explain how a calculation for change in percentage (increase or decrease) is different from a calculation that involves multiplying by percentages. Why is the wording of percentage problems so important? Give examples to illustrate your point.
Answer:
Step-by-step explanation:
Given the expressions :
The list price of the item is 80 percent of the original price. The price of the item has been reduced by 80 percent.
Write a pair of linear equations using variables of your choice to prove that these two statements are not equivalent.
Let the original price = x
Expression 1 : The list price of the item is 80 percent of the original price
List price = 80% of x
List price = 0.8x
Expression 2: The price of the item has been reduced by 80 percent
Price = x - 80% of x
Price = x - 0.8x
Price = 0.2x
Multiply by percentages is different from an Incremental or decrement in percentage. The first expression above signifies a direct multiplication by the stated percentage while the second signifies a decrease in price based on a certain percentage of the original price.
Wording of percentages are so important for clarity in other to understand if the statement signifies a direct application of the percentage prescribed or a change in quantity, amount or size relative to the base unit.
What is the area of a square with the vertices (3, 3), (6, 6), (9,3), and (6,0)?
Answer:
A = 18 square unitsStep-by-step explanation:
taking A(3, 3), B(6, 6), C(9,3) and D(6,0)
we have: [tex]y_A=y_C\quad and\quad x_B=x_D[/tex] so the AC and BD are diagonals, that means:
AB = BC = CD = DA = s
[tex]s=\sqrt{(6-3)^2+(6-3)^2}=\sqrt{3^2+3^2}=\sqrt{18}\\\\\\A=s^2=(\sqrt{18})^2=18[/tex]
x+2/x–2 –x–2/x+2 = 5/6
Answer:
(x-10)(5x+2)
Step-by-step explanation:
this is the answer of the question.you can clearly see in the pic of the solution
x2 + 2x -1 = 0 in English words
Answer:
a number squared plus twice a number minus one equals zero
Step-by-step explanation:
Please help me to prove this..
Step-by-step explanation:
1 / (sin 10°) − √3 / (cos 10°)
Multiply top and bottom of the first fraction by ½ cos 10°.
½ cos 10° / (½ cos 10° sin 10°) − √3 / (cos 10°)
Multiply top and bottom of the second fraction by ½ sin 10°.
½ cos 10° / (½ cos 10° sin 10°) − ½√3 sin 10° / (½ sin 10° cos 10°)
Combine fractions.
(½ cos 10° − ½√3 sin 10°) / (½ sin 10° cos 10°)
Change ½ to sin 30°, and change ½√3 to cos 30°.
(sin 30° cos 10° − cos 30° sin 10°) / (½ sin 10° cos 10°)
Use angle sum formula.
sin(30° − 10°) / (½ sin 10° cos 10°)
sin 20° / (½ sin 10° cos 10°)
Multiply top and bottom by 4.
4 sin 20° / (2 sin 10° cos 10°)
Use double angle formula.
4 sin 20° / sin 20°
4
We are given the equation 1 / sin(10°) - √3 / cos(10°) = 4, and want to prove that 1 / sin(10°) - √3 / cos(10°) equals 4.
Let's start by combining the expressions '1 / sin(10°)' and '√3 / cos(10°)' in the expression '1 / sin(10°) - √3 / cos(10°).'
1 / sin(10°) - √3 / cos(10°)
= cos(10°) - √3sin(10°) / sin(10°) [tex]*[/tex] cos(10°)
Now let's multiply the numerator and denominator by a common value. In this case it's most suitable to multiply both by 2. We will receive the expression 2(cos(10°) - √3sin(10°)) / 2(sin(10°) [tex]*[/tex] cos(10°)). We can further simplify this expression knowing that 2(sin(10°) [tex]*[/tex] cos(10°)) = 2sin(20°).
2(cos(10°) - √3sin(10°)) / 2sin(20°)
We can now bring the two on the bottom to the numerator, becoming 1 / 2. Remember that the ' 1 / 2 ' will be distributed now. After the distribution we receive the expression 4( 1 / 2(cos(10°) - √3 / 2sin(10°)) / 2sin(20°). We can now use the trivial functions 1 / 2 = sin(30°), and √3 / 2 = cos(30°).
4(sin(30°)(cos(10°) - cos(30°)(sin(10°) ) / sin(20°))
= 4((sin(30 - 10°)) / sin(20°) = 4
A gaming console cost $299.99. Each game that comes with the console is an additional cost of $20.00. Mr. Yao decide to by x number of games Write a variable expression for the number of games Mr. Yao bought
This question is not correctly written
Complete Question
A gaming console cost $299.99. Each game that comes with the console is an additional cost of $20.00. Mr. Yao decide to by x number of games Write a variable expression for cost of the number of games Mr. Yao bought
Answer:
Variable expression for the cost of the number of games that Mr Yao bought =
$20x
Where x = number of games that he bought.
Step-by-step explanation:
A variable expression can be defined as a mathematical expression where there is at least one (or more) unknown variable(s)that we have to look or solve for.
The unknown variable is always represented by letters of the alphabet, a, b, x, y e.t.c.
A variable expression can also be called an algebraic expression.
From the above question, we are told that:
Cost of a gaming console = $299.99
If you buy a game with the console = Additional $20.00
My Yao bought = x number of games
Variable expression for the cost of the x number of games that Mr Yao bought
$20 × x
= $20x
Where x = number of games that Mr Yao bought.
The discount on a new refrigerator was $250. This was a discount of 18 %
Step 2 of 3: What was the sale price? Follow the problem-solving process and round your answer to the nearest cent, if necessary.
Answer:
x = 1388.89
Step-by-step explanation:
x - the sale price of new refrigerator
18%x = 0.18x - the discount
0.18x = 250
x = 250÷0.18 = 1388.8888...
x = 1388.89
Foreshadowing is a storytelling device that...
A)Gives hints to reader about a future event.
B)Provides details about a past event.
C)Tells readers that something bad always happens.
D)Creates confusion for the reader.
Answer:A)Gives hints to reader about a future event.
Step-by-step explanation:
Answer:
A) Gives hints to reader about a future event.
Step-by-step explanation:
Foreshadowing is one of the storytelling device that gives hints to readers about the future events.
Hope this helps ;) ❤❤❤
Name the line and plane shown in the diagram. PLZ ANSWER ASAP, DUE IN 1 HOUR
Answer:
Line PQ. Not enough Info for the Plano tho.
Step-by-step explanation:
Look at the 2 points, and thats the name of the line.
8) За (x-y) - (х-у)
Answer:
[tex]3a \times x - y - x - y \\ 3a \times x - x - y - y \\ 3a \times - 2y - \\ - 6ay[/tex]
Answer:
8,3
Step-by-step explanation:
Susan charges $8 per hour walking her neighbor’s dog. She charges $12 per hour babysitting. Part A: Define the variables. Part B: Write an expression to represent the amount Susan earns dog walking and babysitting
Answer:
the total she earns with "d" hours of dog walking and "b" hours of babysitting is given by: 8 d + 12 b
Step-by-step explanation:
If we use "d" to represent the number of hours that Susan walks the dog, and we define "b" as the number of hours she babysits, then the expression that represents the amount she earns by walking the dog is: $8 times d = 8 d
Similarly, the amount she earns by babysitting is $12 times b = 12 b
Then the total she earns with "d" hours of dog walking and "b" hours of babysitting is: 8 d + 12 b
what is this −n+(−4)−(−4n)+6
Answer:
3n + 2
Step-by-step explanation:
[tex]−n+(−4)−(−4n)+6[/tex]
Open the parentheses
[tex] - n - 4 + 4n + 6 \\ [/tex]
Add similar elements
[tex] - n + 4n - 4 + 6 \\ 3n + 2 \\ [/tex]
Answer:
[tex] - n + 6[/tex]
Step-by-step explanation:
[tex] - n + ( - 4) - ( - 4n) + 6 = - n - 4n + 4n + 6 = - 5n + 4n + 6 = - n + 6[/tex]
Taho Earns His Regular Pay Of $11 Per Hour For Up To 40 Hours Of Work Per Week. For Each Hour Over 40 Hours Of Work Per week.For each hour over 40 hours of work per week. Taho earns 1½ times his regular pay. How much does Taho earn in a week in which he works 50 hours?
a. $550
b. $605
c. $625
d. $750
e. $825
Answer:
$605
Step-by-step explanation:
The correct question is
Taho Earns His Regular Pay Of $11 Per Hour For Up To 40 Hours Of Work Per Week. For each hour over 40 hours of work per week. Taho earns 1½ times his regular pay. How much does Taho earn in a week in which he works 50 hours?
a. $550
b. $605
c. $625
d. $750
e. $825
For the first $40 that Taho works, he earns $11 x 40 = $440
For the extra $10 (since he worked 50 hrs that week)
1½ of $11 per hr = 1.5 x $11 = $16.5
for the 10 days extra = $16.5 x 10 = $165
total pay = $440 + $165 = $605
14b + 6 = 6 14b = Subtract 6 from both sides b = Divide both sides by 14
Answer:
Step-by-step explanation:
((b+2)(b+12)/(b+2)(b+3))*(b+3)
= (b+12)
write and equation that represents a vertical stretch by a factor of 3 and a reflection in the x-axis of the graph of g(x)=|x|
Answer:
g(x) = -3|x|.
Step-by-step explanation:
Multiplying by 3 stretches the graph vertically by a factor 3 and the negative reflects in the x-axis.
The equation that represents a vertical stretch by a factor of 3 and reflection in x-axis of the graph of function g ( x ) = | x | is given by
f ( x ) = -3 | x |
How does the transformation of a function happen?
The transformation of a function may involve any change.
Usually, these can be shifted horizontally (by transforming inputs) or vertically (by transforming output), stretched (multiplying outputs or inputs),
If the original function is y = f(x), assuming the horizontal axis is the input axis and the vertical is for outputs, then:
Horizontal shift (also called phase shift):
Left shift by c units: y=f(x+c) (same output, but c units earlier)
Right shift by c units: y=f(x-c)(same output, but c units late)
Vertical shift:
Up by d units: y = f(x) + d
Down by d units: y = f(x) - d
Stretching:
Vertical stretch by a factor k: y = k × f(x)
Horizontal stretch by a factor k: y = f(x/k)
Given data ,
Let the function be g ( x ) = | x |
Now , let the transformed function be f ( x )
The value of the function f ( x ) is calculated by
Step 1 :
Vertical stretch by a factor of 3
The Vertical stretch by a factor is done by
k: y = k × f(x)
So , multiplying the parent function by 3 , we get
f ( x ) = 3 | x |
Step 2 :
Reflection in the x-axis ,
The value of f ( x ) is multiplied by -1
So ,
f ( x ) = -3 | x |
Therefore , the transformed function f ( x ) = -3 | x |
Hence , The equation that represents a vertical stretch by a factor of 3 and reflection in x-axis of the graph of function g ( x ) = | x | is given by
f ( x ) = -3 | x |
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Which table shows a proportional relationship between x and y? A. x y 2 4 3 6 4 9 B. x y 3 4 9 16 15 20 C. x y 4 12 5 15 6 18 D. x y 1 4 2 8 3 15
Answer:
C.
Step-by-step explanation:
The relationship is proportion if y/x is constant.
So it is C because 12/4 = 15/5 = 18/6 = 3.
Which number, when substituted for x, makes the equation 4x+8=16 true?
Answer:
[tex] \boxed{ \bold{ \boxed{ \sf{2}}}}[/tex]
Step-by-step explanation:
[tex] \sf{4x + 8 = 16}[/tex]
Move 8 to right hand side and change its sign
⇒[tex] \sf{4x = 16 - 8}[/tex]
Subtract 8 from 16
⇒[tex] \sf{4x = 8}[/tex]
Divide both sides of the equation by 4
⇒[tex] \sf{ \frac{4x}{4} = \frac{8}{4} }[/tex]
Calculate
⇒[tex] \sf{x = 2}[/tex]
Hope I helped!
Best regards!!
simplify (7776/343)^2
Answer:
513.95
Step-by-step explanation:
First you have to divide 7776 by 343. Then you raise the answer to the second power
Simplify: 9y(-3y to the eighth power)
It says to simplify this, by combinding like terms
8 + 9x + 4 ( 11 – 2x )
Answer:
52+xStep-by-step explanation:
[tex]8 + 9x + 4(11 - 2x) \\ = 8 + 9x + 44 - 8x \\ = 8 + 44 + 9x - 8x \\ = 52 + x[/tex]
GUYS I NEED HELP I have no idea what to do and I can’t ask the teacher for help because it’s night already-
Answer:
x=6
Step-by-step explanation:
127-83=9x-10
44=9x-10
+10.0 +10.0
54=9x
divide by 9 on both sides
x = 6