Step-by-step explanation:
When you multiply exponents of the same base (variable), add the exponents.
1. The exponents are 12 - 4 + 6 = 14 or c^14
When you divide exponents of the same base, subtract them.
2. 8 - 2 = 6 or c^6
When you raise a power to a power, you multiply the exponents.
3. 4 * 5 = 20 or c^20
When a number is raised to a negative exponent it can be re written like this x^-n = 1/x^n.
4. x^-2 * y / x^4 * y^-1; using the above information, rewrite everything to have positive exponents. If the negative exponent is in the denominator, then it becomes x^n/1
y * y / x^2 * x^4 ; then just add your exponents to simplify
y^2 / x^6
As we said before, a power raised to a power is exponent x exponent.
5. (a^2 * b) ^-1 / (a^-3 * b^2)^-1 ; as before a power raised to a power, multiply the powers.
a^-2 * b-1 / a^3 * b^-2 rewrite this as before, inverting negative exponents. a^3 / a^2 * b^1 * b^2 = a^3 / a^2 * b^3
Simolifynthe new expression to reduce the a variable by subtracting the bottom a^2 from the top a^3 and are left with
a / b^3
Work number 6 like 5, no negative exponents, so there won't be any inversions. Just multiply the outside power times every exponent, then do the division by subtracting exponents of like bases.
When figuring out the problems with constants, treat them like the variables. In number 7 the 5a^2 when raised to the 2nd power would be 5^2*(a^2)^2 = 25 a^4
Im sorry, out of time.
Here is a number machine
Given: in a right triangle, cot0 = 28/45
1. what is csc0
2. what is sec0
Answer:
i) [tex]cosec0 = \frac{hypotenuse}{opposite side} = \frac{53}{45}[/tex]
ii) [tex]sec0 = \frac{hypotenuse}{adjacent side} = \frac{53}{28}[/tex]
Step-by-step explanation:
Step(i):-
Given that
[tex]cot 0 = \frac{28}{45} = \frac{adjacentside}{opposite side}[/tex]
Hypotenuse AC² = AB²+BC²
⇒ AC² = 45²+28² = 2809
⇒ AC = √2809
⇒ AC = 53
Hypotenuse AC =53
Step(ii):-
i) [tex]cosec0 = \frac{hypotenuse}{opposite side} = \frac{53}{45}[/tex]
ii) [tex]sec0 = \frac{hypotenuse}{adjacent side} = \frac{53}{28}[/tex]
Lin says that 23 is a prime number. Is Lin correct?
Answer:
Yes, Lin is correct.
Step-by-step explanation:
23 is a prime number because it has only two distinct divisors: 1 and itself (23).
The dimensions of a rectangle are given in terms of S as shown below or above.
Q. Which expression represents the perimeter of the rectangle? Mark all that apply.
Answer:
A and D
Step-by-step explanation:
It should be Sx2 + 2(S+ 1/2)
Which is equal to 4s+1
and 2(2s + 1/2) is equal to 4s+1 as well
The camp cook made 5 5/8 pints of baked beans. Each serving of beans is 5/8 of a pint. How many servings of beans did the cook make?
Will give Brain!! To this
Answer: 13.2
Step-by-step explanation:
the ratio between the given measurements (11 and 5) is 2.2 [5 x 2.2 = 11]
so, i just multiplied 6 by 2.2 , which equals 13.2 .
hope this helps! xoxo
Answer:
13.2
Step-by-step explanation:
6x2.2=13.2 The triangles are equal and its size is increased by 2.2
Two friends share 4 oranges equally. how much does each friend get?
Answer:
2
Step-by-step explanation:
4 divided by 2
Answer:
2 oranges
Step-by-step explanation:
because half of 4 oranges is 2
plz follow me
Please help would mean a lot
Answer: What grade work is this? I think I can help...
Step-by-step explanation:
Find the volume of a cylinder that has a diameter of 12 cm and a height of 5
cm. Use 3.14 for pi and round to the nearest tenth. *
Answer:
V≈565.5cm³ is the answer
Use the discriminant to determine the nature of the roots of the following equation.
x2 + 2x + 5 = 0
imaginary root
Double root
real and rational root
real and irrational root
Answer:
Step-by-step explanation:
disc.=b²-4ac=2²-4×1×5=4-20=-16<0
it has imaginary roots.
20% of what number is 36?
Provide an exact fraction answer. (Mixed fraction) please show how you got your answer ;) Thank you in advance
Answer:
180
Step-by-step explanation:
180 * .2 = 36
20% is the same thing as 1/5 of something, so read the question again,
"36 is 1/5 of what number?"
Multiply 36 by 5 to get 180
Double check yourself by finding 20% of 180
180 * .2 = 36
Hope this helped, queen!
A boarding school distributes 5% of its actual profit Rs.97440 among 20 teachers as a bonus. Find the bonus amount that the each teacher get.
The value of y varies directly with x. If x = 5 when y = 12, what is the value of x when y = 30?
Answer:
12
Step-by-step explanation:
12/5 = 2.4
2.4(x)
if x = 5 then,
2.4(5) = 12
Answer:
12.5 or 25/2
Step-by-step explanation:
you do 30/12 get 2.5 then do 2.5 times 5 to get 12.5 or 25/2
please help like right now
Answer:
y-interceptSloperise over runnegativepositiveUndefinedZeroSlopey-interceptStep-by-step explanation:
I'm not sure about what the answer is for the last two questions. If somebody else does know please right it in the comment section. :)
This is a pond in the shape of a prism. It is completely full of water
Colin uses a pump to empty the pond.
The level goes down by 30 cm in the first 30 minutes.
Work out how many minutes Colin has to wait for
the pond to completely empty.
Kindly check picture to the question below.
Answer:
150 minutes
Step-by-step explanation:
Volume of prism = height * base area
Height of prism = 1m
Base area = area of a trapezium
Area of trapezium = 0.5(a + b) h
a, b = parallel sides, h= height of trapezium
Area of trapezium = 0.5(1.4+0.6)*2
Area = 0.5(2)*2 = 2m²
Hence,
V of prism = area of trapezium * height of prism
Volume = 2m² * 1m = 2m³
Decrease in water level due to pumping
20cm decrease in 30minutes
(20/100)m in 30 minutes
0.2 m decrease in height of water
Hence, height of water in prism after 30 minutes pumping :
height - 0.2 = 1 - 0.2 = 0.8m
Volume after 30 minutes of pumping :
Base area * new height
2m² * 0.8m = 1.6m³
Decrease in volume over 30 minutes :
(Initial volume - volume after pumping)
2m³ - 1.6m³ = 0.4m³
If ;
0.4m³ = 30 minutes
1.6m³ = x
0.4x = 48
x = 48 / 0.4
x = 120
Hence, it takes 120 minutes for the remaining 1.6m³ to be emptied.
Hence, total wait time :
120 minutes + 30 minutes
= 150 minutes
5=1/3(2x+12)
Solve for X in simplest form
9514 1404 393
Answer:
x = 3/2
Step-by-step explanation:
Multiply by 3 and solve the resulting 2-step equation.
5 = (1/3)(2x +12)
15 = 2x +12 . . . . . . multiply by 3
3 = 2x . . . . . . . . . . subtract 12
3/2 = x . . . . . . . . . . divide by 2
HELP!!!!!!!!!!!!!!!!!!!!
Answer:
3
Step-by-step explanation: set the two equations equal to each other. 5-2x=-4x+9 and you'd get x=2. insert 2 into the expression, and you'd get 1. to find the perimeter, a triangle has 3 sides. 1+1+1 =3
PLS help quickest and accurate answer gets brainliest Mrs. Meadows wants to tile a wall to serve as a splashguard above a basin in the basement. She plans ot use equal-sized tiles to cover an area that measures 48 inches by 36 inches. What is the area of the maximum-size square tile Mrs. Meadows can use and not have to cut any of the tiles? Write your answer as inches squared.
Answer
1729 in^2
Step-by-step explanation:
48 in x 36 in= 1728 in^2. A=LxW
Caterer A charges $15 per person and $100 to set up tables. Caterer B charges $20 per person and $50 to set up tables.
For what number of guests will the cost of Caterer A be the same as the cost of Caterer B? number or guest
Answer:
Number of guests = 10
Step-by-step explanation:
Given that:
Caterer A charges $15 per person and $100 to set up tables. Caterer B charges $20 per person and $50 to set up tables.
Let,
x be the number of guests.
A(x) = 15x + 100
B(x) = 20x + 50
For the cost to be equal;
A(x) = B(x)
15x + 100 = 20x + 50
100 - 50 = 20x - 15x
50 = 5x
Dividing both sides by 5
[tex]\frac{5x}{5}=\frac{50}{5}\\x=10[/tex]
Hence,
Number of guests = 10
Can someone help me with this? Please n thank u
Answer:
1. 15°
2.64°
3. 50°
4.38°
Step-by-step explanation:
A farmer bought 36 ducks and 52 pigeons. Approximately how many birds did the farmer buy?
Convert decimals to fractions
.37
2.4
.33
Please help
Answer:
1. 37/100
2. 2 2/5 or 12/5
3. 33/100
Step-by-step explanation:
Answer: 37/100.
2 2/5.
33/100
Step-by-step explanation:
I recommend using symbolab.com for further steps and calculator
Write an equation of the line with the given slope and y-intercept.
slope: −3
y-intercept: 5
y=
Answer:
Y=-3X+5
Step-by-step explanation:
Consider the 4th roots of 16[cos(π) + i sin(π)].
The roots are located on a circle with center at the origin and radius of ....
The arguments of two successive roots differ by.... π units along the circumference of a circle.
Answer:
2 1/2
Step-by-step explanation:
The roots are located on a circle with a center at the origin and a radius of 4. The arguments of two successive roots differ by (1/2)π units along the circumference of a circle.
What is the Circumference of a circle?The circumference of a circle is defined as the product of the diameter of the circle and pi.
The 4th roots of 16[cos(π) + i sin(π)] are the 4th roots of -16i. These roots are located on a circle with a center at the origin and a radius of 4 because the 4th roots of a complex number are equally spaced on a circle with a radius equal to the absolute value of the complex number.
The arguments of two successive roots differ by π/2 units along the circumference of a circle. This is because there are 4 roots and the circle has a circumference of 2π, so each root is spaced 2π/4 = π/2 units apart along the circumference of the circle.
For example, the first root is located at (4, 0) on the complex plane, which corresponds to an argument of 0.
The second root is located at (0, 4) on the complex plane, which corresponds to an argument of π/2.
The third root is located at (-4, 0) on the complex plane, which corresponds to an argument of π.
The fourth root is located at (0, -4) on the complex plane, which corresponds to an argument of 3π/2.
Thus, you can see that the arguments of the roots differ by π/2 units.
To learn more about the roots of complex numbers click here:
https://brainly.com/question/28182680
#SPJ2
The graph of the piecewise function f(x) is shown.
What is the range of f(x)? On edg
Sam writes on a white board the positive integers from 1 to 6 inclusive, once each, She then writes p
additional fives and q sevens on the board. The mean of all the numbers on the board is then 5.3.
What is the smallest possible value of q?
Answer: The smallest possible value of q is 9.
Step-by-step explanation:
If we have the set of N numbers:
{x₁, x₂, x₃, ..., xₙ}
The mean of this set is:
M = (x₁ + x₂ + x₃ + ... + xₙ)/N
Now, in this case our set is:
{1, 2, 3, 4, 5, 6, p times 5, q times 7}
Then we have a total of:
6 + q + p numbers.
The mean of this set will be:
Mean = 5.3 = (1 + 2 + 3 + 4 + 5 + 6 + p*5 + q*7)/(6 + p + q)
This is the equation that we will use now.
First, we can simplify this as:
5.3 = (21 + p*5 + q*7)/(6 + p + q)
Now we can pass the denominator in the right to the other side as:
5.3*(6 + p + q) = (21 + p*5 + q*7)
31.8 + p*5.3 + q*5.3 = 21 + p*5 + q*7
Now we want to isolate the variable p in one side of the equation.
p*5.3 - p*5 = 21 - 31.8 + q*7 - q*5.3
p*0.3 = q*1.7 - 10.8
p = (q*1.7 - 10.8)/0.3 = q*(1.7/0.3) - 36
p = q*(1.7/0.3) - 36
p = q*(17/10)*(10/3) - 36
p = q*(17/3) - 36
Now we can see that the denominator is 3, so q should be a multiple of 3.
We want to start with the smallest multiples of 3, but if we use q = 3, then we will have a negative value of p (the same happens if we use 1 = 6)
We do not want that, then we need to use q = 9
p = 9*(17/3) - 36
p = 3*17 - 36
p = 15
Then we have;
9 times the number 7
15 times the number 5 (plus one, because it was already on the first 6 numbers that Sam wrote)
The smallest possible value of q is 9.
Now we want to get the smallest possible value of q.
Remember, p and q need to be positive numbers.
Can someone please help me
9514 1404 393
Answer:
41.7 nautical miles
Step-by-step explanation:
It can help to draw yourself a diagram. It will show you the desired distance is the hypotenuse of a right triangle with side lengths 36 and 21. The Pythagorean theorem can be used to find the distance of interest.
d² = 36² +21²
d² = 1296 +441 = 1737
d = √1737 ≈ 41.6773
The ship is about 41.7 nautical miles from the starting point.
Find the measure of angle B
Answer:
15 - 86
16 - 115
17 - 60
18 - 74
Step-by-step explanation:
Dax is buying coffee for 5 people in his office. He also leaves a $2.00 tip for the barista.
If his total, with tip, is $18.25, how much is each cup of coffee, not including the tip?
Answer:
3.25
Step-by-step explanation:
20 inchs of gold chain we used 3/8 how much is left?
Answer:
12.5 inches
Step-by-step explanation:
3/8 of 20 = 3/8 * 20 = 60/8 = 15/2 = 7.5
20 - 7.5 = 12.5
Answer:
12.5 inches
Step-by-step explanation:
20/8=2.5
2.5*3=7.5
20-7.5=12.5