Simplify using the laws of exponents.
[2⁴/2³]⁵
To know this answer we need to know how to solve it. Many people skip this part which makes their answer wrong.
It is asking us to simplify it using exponents.
Exponents are these little numbers beside a big number Telling it how much you multiply it by.
EXAMPLES
2^3 is just 2x2x2
2^4 is just 2x2x2x2
Notice the pattern? I hope so!
Now 2 to the power of 4 is 16. Our new equation looks like this
{16/2^3}^5.
Now 2 to the power of 3 is 8.
So, our new equation is
{16/8}^5
In which you get 2^5 which is just 2x2x2x2x2
And you get 32 as the final answer
I hope this helped and if you have questions just tell me!!
y = 2x + 7
3x - 4y = -13
The ratio of three number is 5:6:7. If the sum of the numbers is 54. What
are the numbers?
[tex]5x + 6x + 7x = 54 \\ = > 18x = 54 \\ = > x = 3[/tex]
So, the numbers are (5 × 3) i.e., 15, (6 × 3), i.e., 18, (7 × 3), that is 21.Answer:
The numbers are 15, 18 and 21.
Hope you could get an idea from here.
Doubt clarification - use comment section.
Expand the following expressions and write in standard form. Show your work.
a) (3x + 2)(1 - 4x)
b) (x - 5)^2(2x + 7)
Please help!!!!
3x(1-4x)+2(1-4x)
3x-12x²+2-8x
-5x-12x²+2
What is the coefficient of the term x°ys in the
expansion of the binomial expression
(2x - y)8?
Answer:
if it is (2x-y)8
then it is 16x - 8y
[tex]x^0[/tex]y = 1.y = y
so the co efficient of y is -8
Step-by-step explanation:
four water bottles can hold 8 gallons of water how much water can ten big water bottles hold
Answer:
20 gallons of water.
Step-by-step explanation:
4 water bottles = 8 gallons
1 water bottle = 2 gallons
X = Number of Water bottles
N = Gallons Per Water Bottle
X * N
10 * 2
20
(03.02) If g(x) = x2 + 2, find g(3). (2 points) Group of answer choices 9 8 11 6
this answers is 8 am I right
Determine the intercepts of the line.
Answer:
y-intercept: (0,5)
x-intercept: (5/2,0)
Step-by-step explanation:
[tex]-4x+7=2y-3[/tex]
[tex]-4(0)+7=2y-3[/tex]
[tex]0+7=2y-3[/tex]
[tex]7=2y-3[/tex]
[tex]10=2y[/tex]
[tex]5=y[/tex] <-- y-intercept: (0,5)
[tex]-4x+7=2y-3[/tex]
[tex]-4x+7=2(0)-3[/tex]
[tex]-4x+7=-3[/tex]
[tex]-4x=-10[/tex]
[tex]x=\frac{5}{2}[/tex] <-- x-intercept: (5/2,0)
Shawna wanted to boat across the river, but did not know how wide it was. She walked along the shore for 90 feet and sighted across the water to the point she wanted to go. The angle that the sight line made with the shoreline was 65°. What was the distance across the river?
The distance across the river, given the angle of the line of sight and the
distance along the shoreline is found using trigonometric ratios.
The distance across the river is approximately 193 feet.Reasons:
The distance along the the shore Shawna walked before sighting across the river = 90 feet
The angle made by the line of sight and the shoreline, θ = 65°
Required:
The distance across the river.
Solution:
Taking the initial location of Shawna to be the closest place to point she wanted to go across the river, we have;
The shortest distance across the river = A perpendicular line
Therefore, the following sides, form a right triangle;
The line of sight.The distance along the shoreline Shawna walked, andThe closest distance across the river.Where:
The line of sight = The hypotenuse side
The distance she walked = The adjacent side to angle 65° angle
The closest distance across the river = The opposite side to the 65° angle
By trigonometric ratio, we have;
[tex]\displaystyle tan(\theta) = \frac{Opposite \, side \, to\ angle}{Adjacent\, side \, to\, angle} = \mathbf{\frac{Distance \ across \ the \ river}{Distance \ along \ the \ shoreline}}[/tex]Which gives;
Opposite side to angle = tan(θ) × Adjacent side to angle
Therefore;
Distance across the river = tan(65°) × 90 feet ≈ 193.0 feet
The distance across the river is approximately 193 feetLearn more about trigonometric ratios here:
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Write the name of a polynomial (using the degree) with the sequence of the
outputs: (5,2,-1,-4, ...}*
Type ONE word
Answer:
pentagon
Step-by-step explanation:
5 degree angle
numbers that equal to 39
Answer:
1 , 3 , 13 , and 39
Step-by-step explanation:
1 x 39 =39
3 x 13 = 39
13 x 3 = 39
39 x 1 =39
Answer:
Step-by-step explanation:
The product 3*13 equals 39. This is in addition to the identity 1*39 = 39.
A moneylender’s income decreased by $60 When the rate of interest dropped from 8% per annum to 7 3/4 % per annum . What was his principal?
Answer:
$24,000
Step-by-step explanation:
The difference for principal amount P is ...
(8% × P) - (7 3/4% × P) = $60
0.0025P = $60
P = $24,000 . . . . . multiply by 400
His principal was $24,000.
calculate the simple interest and compound interest on ₹5000 for 2 years at 10% per annum. how much more is the compound interest then the simple interest?
Answer:
Simple: 6000
Compound: 6050
Difference: 50
Step-by-step explanation:
Simple interest formula: A = P(1+rt), where A = final amount, P = initial amount, r = rate, and t = time. Plug our values in to get
A = 5000(1+10% * 2)
convert 10% to a decimal by dividing by 100 and plug that in
10% = 0.1
5000(1+0.1*2) = 5000(1.2) = A = 6000
Compound interest formula: A = P(1+r)^t
Plug our values in
5000(1+0.1)^2 = 6050
Difference = 6050 - 6000 = 50
pls help due soon i’ll mark brainliest
I can't see anything dude, you on something?
Brian has DVDs and CDs. The number of CDs he has can be modelled with the formula C = 2D + 11, where C represents the number of CDs and D represents the number DVDs. If he has 41 CDs, how many DVDs does he have?
Answer: 15 DVDs
Step-by-step explanation:
C = 2D + 11
41 = 2D + 11
2D = 30
D = 15 DVDs
Jim has 44 nickels and dimes totaling $2.95. How many nickels does he have?
29 Nickels
15 Dimes
Hope this is helpful!
A ball is thrown upward from a height of 15 feet with an initial upward velocity of 5 feet per second. Use the formula b(t)= -16t^2 + 5t + 15 to find the time it takes for the ball to reach the maximum height of the ball. Round to the nearest tenth
A. 0.2 seconds
B. 0.1 seconds
C. 0.3 seconds
D. 0.9 seconds
Answer:
0.2 seconds
Step-by-step explanation:
The graph of b(t) = -16t^2 + 5t + 15 is a parabola opening downward. The maximum value of b(t) occurs at the vertex. The t-coordinate of the vertex is t = -5 / (2(-16)) = 5/32 = 0.15625 sec ≈ 0.2 sec.
Answer:
A) 0.2 seconds
Step-by-step explanation:
[tex]b(t)=-16t^2+5t+15[/tex]
[tex]v(t)=-32t+5[/tex] <-- Take the derivative
[tex]0=-32t+5[/tex] <-- Set equal to 0
[tex]-5=-32t[/tex]
[tex]\frac{5}{32}=t[/tex]
[tex]t=\frac{5}{32}[/tex]
[tex]t\approx0.2[/tex]
Therefore, it will take the ball about 0.2 seconds to reach its maximum height (which happens to be about 15.4 feet BTW).
Alternatively, another non-calculus approach is the fact that the parabola opens downward, and as such, the maximum of [tex]b(t)[/tex] occurs at the vertex where [tex]t=-\frac{b}{2a}[/tex], therefore [tex]t=-\frac{5}{2(-16)}=\frac{-5}{-32}=\frac{5}{32}\approx0.2[/tex]
The cost of a jacket increased from $60.00 to $71.40. What is the percentage increase of the cost of the jacket?
Answer:
19%
Step-by-step explanation:
Percentage increase = ( (final value - original value) / original value ) x 100
= ( ($71.40 - $60.00) / $60.00 ) x 100
= 19%
[tex]71.40 - 60 = 11.40[/tex]
to find the increase of percentage, divide the amount of increasing price with intial price and multiply with 100%
[tex] \frac{11.40}{60} \times 100\% = 19\%[/tex]
so the cost of jacket has increased 19%
The standard configuration for a Colorado license plate is 3 letters followed by 3 digits. How many different license plates are possible if letters and digits can be repeated?
Answer:
17,576,000 different combinations possible.
Step-by-step explanation:
9 13 / 16 + 10 3 / 8 =
A T-shirt company charges $4 per T-shirt, plus a
flat shipping fee of $5. Terry bought some
T-shirts. How can you write an algebraic
expression to represent the total cost of Terry's
order including shipping?
Plz help plz
Answer:
y = 4x + 5
Step-by-step explanation:
4 times the number of shirts, which is unknown, +$5 no matter how many.
Answer:
4x + 5
Step-by-step explanation:
Four multiplied by the number of shirts purchased (x) plus five dollars for shipping.
I hope this helps!!
A dress originally priced at 8080 dollars was put on sale for 25\%% off. If 10\% tax was added to the sale price, then the total selling price (in dollars) of the dress was
Answer: If the dress orginially priced at 8080 dollars and put for 25 percent, that means that you have to move the decimal point to the left twice which will result as 0.25 and 10 percent tax ends up as 0.10. Multiply the two and the product, you have to add to the 8080!
Step-by-step explanation:
Can someone please help me with 54? It’s the last one and it’s due in 1 hour Tysm if you do!!
Answer:
The awnser should be 4. (3x4 = 12, 12 x 4 = 48, 48 x 12 = 192, 192 x 4 = 768. )
Step-by-step explanation:
(Hope this helps, Happy holidays!!)
Please answer both please please I’ll give brainly
Answer:
4. 9
5. 5x
Step-by-step explanation:
its an isocoles
HELP GIVING BRAINLIEST!
Answer:
C
Step-by-step explanation:
Answer:
y = 1/4x
Step-by-step explanation:
a
The eighth-grade class has a total of 162 students. The students need to be
divided evenly into homerooms. There needs to be at least 20 students in
each homeroom. List all the possible combinations. Which combination
makes the most sense? Explain.
Answer:
162/20 Would be your answer, however, it wouldn't make sense as you can not switch students into decimals. Therefore, you could make 7 classes of 20, and one of 22, and 6 classes of 20, and two of 21. Therefore, there are two combinations that are possible.
Step-by-step explanation:
Refer to the answer.
Answer:
56
Step-by-step explanation:
Need Help....
I can't understand the question so please help me.....
[tex]for \: x \: such \: that \: 0 < x < \frac{\pi}{2}[/tex]
It is the expression
[tex] \frac{ \sqrt{1 - {cos}^{2}x } }{sin \: x} \:- \frac{ \sqrt{1 - {sin}^{2}x } }{cos \: x} \\ \\ is \: equivalent \: to:[/tex]
[tex]f.0 \\ g.1 \\ h.2 \\j. - tan \: x \\ k. \: sin \: 2x[/tex]
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Don't answer if you don't know
Thank You!
If 0 < x < π/2, then both sin(x) and cos(x) are positive.
From the Pythagorean identity, we then have
cos²(x) + sin²(x) = 1
⇒ cos(x) = + √(1 - sin²(x)) and sin(x) = + √(1 - cos²(x))
Then
√(1 - cos²(x))/sin(x) = sin(x)/sin(x) = 1
and
√(1 - sin²(x))/cos(x) = cos(x)/cos(x) = 1
so that the overall expression reduces to
1 - 1 = 0
Q6 (i) please i don’t know what i’m doing wrong
Answer:
x = 4
Step-by-step explanation:
Square both sides
x+5 = 25-10sqrt(x)+x
20 = 10sqrt(x)
sqrt(x) = 2
Square both sides again
x=4
Verify sol
x = 4
John is 9 times as heavy as his dog.
Determine which of the statement's below is true.
O John weighs 900% more than his dog.
O John weighs 800% more than his dog.
O John's dog weighs 800% less than John.
sources
O John weight is 800% of his dog's weight.
Answer:
John weighs 900% more than his dog
Step-by-step explanation:
The weight of John is 8x more than his dog.
Given that, John is 9 times as heavy as his dog.
What is percentage?Percentage is defined as a given part or amount in every hundred. It is a fraction with 100 as the denominator and is represented by the symbol "%".
Let weight of John's dog be x, then weight of John will be 9x.
Difference of weight = 9x-x
= 8x
Therefore, the weight of John is 8x more than his dog.
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If 12g of a radioactive substance are present initially and 8yr later only 6g remain, how much if the substance will be present after 13 years?
The weight of substance remaining after 13 years is 2.25 g.
Given:
Present weight of substance = 12 g
After 8 years weight remains = 6 gm
Now, weight loss in 8 year will be,
12-6=6 gm
So, weight loss in 1 year will be,
[tex]\dfrac{6}{8} =\dfrac{3}{4}[/tex]
Total weight loss in 13 year will be,
[tex]\dfrac{3}{4}\times13=9.75[/tex]
The weight of substance remaining after 13 years will be,
[tex]12- 9.75 = 2.25 \;\rm g[/tex]
Therefore, the weight of substance remaining after 13 years is 2.25 g.
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