Answer:
[tex]\frac{s}{2t}[/tex]
Step-by-step explanation:
When you have exponents above a like term and they are being multiplied together, you add them.
For example:
[tex]a^{x} *a^{y} = a^{x + y}[/tex]
So let's group like terms in the numerator:
[tex]4r^{3} r^{-5} s^{-2} s^{-1}t[/tex] We can add terms like in the example.
[tex]4 r^{-2} s^{-3} t[/tex]
Let's rearrange the denominator.
[tex]8r^{-2} s^{-4} t^{2}[/tex]
Now we have:
[tex]\frac{4r^{-2} s^{-3}t}{8 r^{-2} s^{-4} t^{2} }[/tex] Cancel like terms
4/8 = 1/2
[tex]r^{-2} /r^{-2}[/tex] = 1 So it cancels
[tex]s^{-3} / s^{-4} = s^{-1}[/tex] = s Since s is raised to the -1 it goes on top and becomes s.
[tex]t / t^{2} = 1/t[/tex]
Now we combine everything back together:
[tex]\frac{s}{2t}[/tex]
Which ordered pair represents a point that is 3 points to the left and 2 points
above point T?
AY
10
9
8
7
6
5
4
3
2
1
.T
0 1 2 3 4 5 6 7 8 9 10
х
(1,7)
(6,0)
(0,6)
(5, 7)
Pio
Answer:
(0, 6)
Step-by-step explanation:
Point T has a coordinate pair of (3, 4). That is, at point T, x = 3, while y = 4.
3 points to the left of T would be a movement on the x-axis. This movement is a run across the x-axis. At T, x = 3. Therefore, 3 points to the left would be a decrease by 3 = 3 - 3 = 0.
3 points to the left of T would leave us with an x coordinate of 0.
2 points above T suggest a rise, which is on the y-axis.
Therefore, at T, y = 4. 2 points above 4 = 4 + 2 = 6. y coordinate would now be 6.
In conclusion, the ordered pair representing 3 points to the left, and 2 points above point T is (0, 6).
If the width of a rectangle is four feet less than the length
and the area is 165 square feet, find the length of the
rectangle.what is the length
Answer:
length (x) = 15 or -11
Step-by-step explanation:
step-by-step in attached picture
10 POINTS 3(2x+5) Plz help asap
Answer:
6x + 15.
Step-by-step explanation:
3(3x + 5)
= 3 * 2x + 3*5
= 6x + 15.
Hey There!! ~
The answer to this is: Apply the distributive property.
[tex]3 (2x) + 3 . 5[/tex]
Multiply. 2 by 3 [tex]6x + 3 . 5[/tex] Multiply
Multiply 3 by 5.
[tex]6 x + 15[/tex] Thus, for the answer is: 6x + 15.
Hope It Helped!~
[tex]ItsNobody[/tex]~
Simplify: 9y(-3y to the eighth power)
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!!
NEED IMMEDIATE HELP Water flows through a pipe at a rate of 6 fluid ounces per day. Express this rate of flow in cubic meters per year. Round your answer to the nearest hundredth.
Answer:
0.06 cubic meters per year...
Step-by-step explanation:
The rate of water flows through a pipe is 0.06 cubic meters per year.
What is rate of flow?It is the volume of fluid flows out from the container per unit time.
Given that,
Water flows through a pipe at a rate of 6 fluid ounces per day. It can be written as:
Water flows per day ⇔ 6 fluid ounces
∴ Water flows per year ⇔ 365 x (6 fluid ounces)
Volume of water in milliliter,
Water flows per year ⇔ 365 x (6 x 29.574 ml )
Volume of water in cubic meter,
Water flows per year ⇔ 365 x ([tex]\frac{6 x 29.574}{1000000}[/tex] [tex]m^{3}[/tex]) = 0.06477 [tex]m^{3}[/tex]
Hence Water flows per year round value to the nearest hundredth is 0.06 [tex]m^{3}[/tex].
To learn more about rate of flow, refer to the link:
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-8y=24
so i have to write more, so have a great day
Answer:
y=-3
Step-by-step explanation:
-8y=24
y= 24/-8
y=-3
Hope this helps! :)
pls mark brainliest
y = - 3
Step-by-step explanation:- 8y = 24 | (-)
8y = - 24
y = - 24 : 8
y = - 3
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
Qual é o resultado da multiplicação a seguir:
Answer:
que????? no entiendo??????
1) Paul is a software engineer and got paid $10,602
last month. If he estimated that he worked 186
hours in total for the month, how much did Paul earn
for each hour he worked?
Answer:
57
Step-by-step explanation:
all you have to do is take the 10,602 and divide it by 186
and you end up with 57. to check this just do 10,602 divided by 57 or 57 times 186.
I am very confused (I didn’t mean to press B)
Answer:
The anwer is A
Step-by-step explanation:
If it is a right angle triangle we use paythagoras theorem
a ×a + b× b= c × c
so we use the side which is straight to the 90° angle for the variable C. For variable A and B it doesn't matter we can use what we want.so the side which is straight to the 90° angle is 17.now let's substitute1. 15× 15( square of 15) + b× b(square of b) = 17 ×17 (square of 17)
;2. 225 + b×b(square of b ) = 289
3. b×b(square of b) = 289-225
4. b × b( square of b )= 64
[tex] \sqrt{b \times b} = \sqrt{64} [/tex]
b = 8
I hope it is helpful
What is written in standard form? 1.234 12.34 123.4 1234
Answer:
12.34
Step-by-step explanation:
how is -27 a rational number
Answer:
see explanation
Step-by-step explanation:
A rational number can be expressed in the form
[tex]\frac{a}{b}[/tex] where a and b are integers
Given
- 27 = [tex]\frac{-27}{1}[/tex] ← in rational form
Thus - 27 is a rational number
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.
HELP
Suppose A has a coordinate of 8 and AB = 3. What are the possible midpoints of AB?
Answer:
The possible midpoints of AB are [tex]\frac{19}{2}[/tex] and [tex]\frac{13}{2}[/tex].
Step-by-step explanation:
Let suppose that A and B have one-dimensional coordinates. GIven that [tex]A = 8[/tex] and [tex]AB = 3[/tex], there are two possible locations for B:
[tex]B_{1} = A+AB[/tex]
[tex]B_{1} =8+3[/tex]
[tex]B_{1} = 11[/tex]
[tex]B_{2} = A-AB[/tex]
[tex]B_{2} = 8-3[/tex]
[tex]B_{2} = 5[/tex]
The midpoint equations for each case are, respectively:
[tex]m_{1} = \frac{A+B_{1}}{2}[/tex]
[tex]m_{1}=\frac{8+11}{2}[/tex]
[tex]m_{1} = \frac{19}{2}[/tex]
[tex]m_{2} = \frac{A+B_{2}}{2}[/tex]
[tex]m_{2} = \frac{5+8}{2}[/tex]
[tex]m_{2} = \frac{13}{2}[/tex]
The possible midpoints of AB are [tex]\frac{19}{2}[/tex] and [tex]\frac{13}{2}[/tex].
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]
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)
Learn more about the coordinate visit:
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There are 82 people in a restaurant. Four groups of 3 leave and then five groups of 2 enter. Evaluate the expression 82 - 4(3) + 5(2) Find how many people are in the restaurant.
Answer:
80
Step-by-step explanation:
82-12+10
82+10-12
92-12
80
The number of people in the restaurant will be 80
What is an expression?Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.
Given that there are 82 people in a restaurant. Four groups of 3 leave and then five groups of 2 enter.
The expression will be solved as below:-
E = 82-12+10
E = 82+10-12
E = 92-12
E = 80
Therefore, the number of people in the restaurant will be 80
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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]
How many numbers are 3 units from 0 on the real numbers line
Answer:
2 right? 3 and -3?
Step-by-step explanation:
Answer:
2 numbers
Step-by-step explanation:
● -3 and 3 are both 3 units apart from 0
We can find it with calculations.
You are moving in a real numbers line.
You can move either right or left.
You starting point is 0.
When you go 3 units to the right then you are adding 3.
● 3+0 = 3
When you go back 3 units starting from 0 then you are substracting 3.
● 0-3 = -3
NYCab company charges an initial rate of $5.00 for a ride, plus $0.90 for each mile driven. What is the equation that models the total fee for using this cab company? Y+ x+
Answer:
y= 5 + 0.9x
Step-by-step explanation:
Giving the following information:
NYCab company charges an initial rate of $5.00 for a ride, plus $0.90 for each mile driven.
We need to structure the total cost formula:
y= total cost
x= miles driven
fixed cost= $5
Unitary variable cost= $0.9
y= 5 + 0.9x
I’m multiplying polynomials. And have no idea where to start. Please help, it’s almost 2 AM and it was due days ago!!
Answer:
length= 5 + x
breadth = 6 + 2x
area = 30 + 16x + 2x^2
Find the image of the point (5,3) after a 90 degree counterclockwise rotation
Answers
•(3,-5)
•(-3,-5,)
•(-3,5)
•(5,-3)
Answer:
(- 3, 5 )
Step-by-step explanation:
Under a counterclockwise rotation about the origin of 90°
a point (x, y ) → (- y, x ) , thus
(5, 3 ) → (- 3, 5 )
what is the reciprocal of 6 as a fraction
Answer:
The reciprocal of 6 is, 1/6..Step-by-step explanation:
Hope it helps you..
Thanks..
Answer:
1/6
Step-by-step explanation:
The reciprocal of a fraction can be found by flipping the numerator (top number) and denominator (bottom number).
The number 6 is equivalent to the fraction 6/1.
Find the reciprocal of 6/1. Invert the numerator and denominator.
6/1 ⇒ 1/6
The reciprocal of 6 is 1/6
Solve for c. 3(6 - 5c) - 2c > 4c -129 *
Answer:
c < 7
Step-by-step explanation:
3(6-5c)-2c>4c-129
You will first multiply 3 with 6-5c which will give you 18 and -15c.
18-15c-2c>4c-129
Then you will subtract 2c from -15c because they're like terms. That will give you -17c.
18-17c>4c-129
Next you will put all the variables to one side. To do this, you will add 17c to 4c. You add 17c because that way, you cancel out the -17c and all the variables will be on one side
18>21c-129
Then you will add 129 to both 18 and -129 so that all of the numbers without variables can go on on side.
147>13c
Finally you divide both 147 and 13c by 13. That should give you the final solution of 7>c, or c<7.
Find the surface area of a rectangular prism with a length of 15 cm height of 7 cm and a width of 5 cm
Answer:
430 cm² is right answer ✔️
Step-by-step explanation:
A=2(wl+hl+hw)
=2(5×15+7×15+7×5)
=430cm²
hope it helped you:)
solve the equation
show your work
9 + 12m = 6 + 15(m - 1)
Answer: m=6
Step-by-step explanation:
[tex]9+12m=6+15\left(m-1\right)[/tex]
[tex]6+15\left(m-1\right)=15m-9[/tex]
[tex]9+12m=15m-9[/tex]
subtract 9 on both sides
[tex]9+12m-9=15m-9-9[/tex]
[tex]12m=15m-18[/tex]
subtract 15m on both sides
[tex]12m-15m=15m-18-15m[/tex]
[tex]-3m=-18[/tex]
divide by -3 on both sides
[tex]\frac{-3m}{-3}=\frac{-18}{-3}[/tex]
since [tex]\frac{-a}{-b}=\frac{a}{b}[/tex]
[tex]\frac{-18}{-3}=6[/tex]
[tex]m=6[/tex]
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
how to do this question plz
Answer:
An adult ticket costs £7.
A child ticket costs £2.
Step-by-step explanation:
Let a represent the cost for adults and let c represent the cost for children.
Family 1 has a total of 2 adults and 3 children. Together, it cost them £20.
In an equation, this is:
[tex]2a+3c=20[/tex]
Family 2 has a total of 1 adult and 4 children. It cost them £15. In an equation, this is:
[tex]a+4c=15[/tex]
We know have a system of equations. Solve it. We can use the substitution method.
First, subtract both sides by 4c in the second equation:
[tex]a+4c=15\\a=15-4c[/tex]
Substitute this into the first equation:
[tex]2a+3c=20\\2(15-4c)+3c=20[/tex]
Distribute:
[tex]30-8c+3c=20[/tex]
Add:
[tex]30-5c=20[/tex]
Subtract 30 from both sides. The left cancels:
[tex]-5c=-10[/tex]
Divide both sides by -5:
[tex](-5c)/-5=(-10)/-5\\c=2[/tex]
Thus, the cost of a child ticket is £2.
Substitute 2 for c into the equation we manipulated at the start:
[tex]a=15-4c\\a=15-4(2)\\a=15-8=7[/tex]
Thus, the cost of an adult ticket is £7.
Answer:
Adult ticket= $7
Child Ticker=$2
Step-by-step explanation:
Family 1: 2x+3y=20
Family 2: x+4y=15
2x+3y=20
x+4y=15
Multiply by 2
2x+3y=20
-(2x+8y=30)
Change the signs
2x+3y=20
-2x-8y=-30
Eliminate x
-5y=-10
Divide both sides by -5
y=2<---- Price per children
Substitute the value of y
x+4(2)=15
x+8=15
x=15-8
x=7 <----Price per adult
Check:
Substitute the values of x and y to family 1
2(7)+3(2)=20
14+6=20
20=20
7+4(2)=15
7+8=15
15=15