The final simplified expression is 2 over the square root of 5, represented as [tex]\( \frac{2}{\sqrt{5}} \).[/tex]
Let's break it down step by step:
1. Simplify the square roots:
[tex]- \(\sqrt{4}\) equals 2 because \(2 \times 2 = 4\). So, \(\sqrt{4} = 2\).[/tex]
- We have [tex]\(\sqrt{5}\)[/tex] in the denominator, which cannot be simplified further because 5 is a prime number and doesn't have any perfect square factors.
2. Substitute the simplified square roots:
- After simplifying [tex]\(\sqrt{4}\)[/tex] to 2, the expression becomes [tex]\(\frac{3 \times 2}{3\sqrt{5}}\).[/tex]
3. Cancel out the common factor:
- Both the numerator and the denominator have a factor of 3. So, we can cancel out 3 from both sides:
[tex]\[\frac{3 \times 2}{3\sqrt{5}} = \frac{2}{\sqrt{5}}\][/tex]
4. Final simplification:
- The expression [tex]\(\frac{2}{\sqrt{5}}\)[/tex] is simplified as far as it can go because the square root of 5 cannot be simplified further.
So, the simplified expression is [tex]\(\frac{2}{\sqrt{5}}\).[/tex]
Help answering the question and explain
Answer:
it linear
Step-by-step explanation:
Answer:
linear
Step-by-step explanation:
For each increase of 1 in x, we decrease 2 in y
The slope is -2
It has a constant slope for all the points
There fore it is linear
We know the slope and the y intercept( when x=0, y =-3)
y = mx+b
y = -2x -3
We can check by picking a random point and verifying
(2,-7)
-7 = -2(2) -3
-7 = -4-3
-7=-7
The temperature falls 3 degrees Celsius each hour for 8 hours. What is the total change in temperature over this eight-hour period?
Help plz
Answer:
–24°C
Step-by-step explanation:
(–3°C) × 8 = –24°C
HELP PLS and quick find the volume
Answer:
V =96 pi
Step-by-step explanation:
The volume of a cone is given by
V = 1/3 pi r^2 h
Where r is the radius and h is the height
V = 1/3 pi (6)^2 *8
V = 1/3 pi (36)8
V =96 pi
write an expression for the product of 11 and w
Answer:
11 * w
Step-by-step explanation:
"product" in math means "multiply". "The product of 11 and w" is "the multiplication of 11 and w".
Write the expression:
The Multiplication: *
11 and w: 11 * w
11 * w is your answer.
~
which is the graph of y=3/4x-3
Factor 4x^2+ 8x + 3 by applying the distributive property to the last step shown on the left
Answer:
(2x + 3)(2x + 1)
Step-by-step explanation:
4x² + 8x + 3
4x² + 6x + 2x + 3
2x(2x + 3) + 1(2x + 3)
(2x + 3)(2x + 1)
A zookeeper predicted the weight of a new baby elephant to be 252 pounds when it was born. The elephant actually weighed
284 pounds at birth. What was the percent error of the Zookeeper's prediction?
Answer:
11.7%
Step-by-step explanation:
284-252=32
32 is about 11.7% of 284
Which Expression is equivalent to -0.3(1.5x-0.6)-2(-0.4+0.9x)
A. 0.45x+0.20
B. 0.45x-1.98
C. -2.25x-0.62
D. -2.25x+0.98
The right answer is of option D.
Hope it will help u....
PLEASE ANSWER! WILL GIVE BRAINLIEST!!!
$750 at a 4% annual compound interest rate over a period 4 years
Which of the following statements are true of the data? Check all that apply.
The starting balance of the 3rd year is $811.20.
The interest earned in the 3rd year is $31.20.
The ending balance for the 3rd year is $843.65.
The interest earned in the 4th year is $33.75.
The ending balance for the 4th year is $874.85.
Answer:
The starting balance of the 3rd year is $811.20.
The ending balance for the 3rd year is $843.65.
The interest earned in the 4th year is $33.75.
Step-by-step explanation:
750 × (1 + 4%)^n
750 × (1.04)^n
750 × 1.04² = 811.2
(End of second year, starting of third year)
750 × 1.04³ = 843.648
In third year: 843.648 - 811.2
= 32.448
750 × 1.04⁴ = 877.39392
During the fourth year:
877.39392 - 843.648
33.74592
Answer:
The starting balance of the 3rd year is $811.20.
The ending balance for the 3rd year is $843.65.
The interest earned in the 4th year is $33.75.
Step-by-step explanation:
I did it on edg.
Which shows the fraction rewritten with their LCD?
3/8 and 1/4
A. 6/16 and 12/16
B. 3/8 and 4/8
C. 3/8 and 2/8
D. 6/16 and 4/16
The Answer will be A, I just took the Quiz!! :)
Answer:
C. 3/8 and 2/8
Step-by-step explanation:
LCM of 8 and 4: 8
3/8
1/4 = (1×2)/(4×2) = 2/8
Find The measure of angle BEC
Answer:
148
Step-by-step explanation:
Answer:116
Step-by-step explanation:
Point D is the midpoint of HJ. Point D is located at (-3,4) and point His located at (9,-6). Where is point J located?
Answer:
(-15,14)
Step-by-step explanation:
as the question states, d is a mid point. so, if there is a -12 difference in x, then you must apply that to d to create the opposite point. the same goes for y but its a +10 difference. when you apply it, d is (-15,14)
Answer: (-15,14)
Step-by-step explanation:
1. You weigh six packages and find the weights to be 32, 22, 72, 27, 67, and 10 points
62 ounces. If you include a package that weighs 152 ounces, which will
increase more, the median or the mean?
Answer:
MEAN INCREASES MORE
Step-by-step explanation:
Which set of numbers may represent the lengths of the sides of a triangle?
A.
5, 7, 9
C.
8, 5, 3
B.
1, 3, 4
D.
4, 4, 9
Answer:
A
Step-by-step explanation:
because for the sides to make a triangle the sum of the two shorter sides must be greater than the longest
Answer:
A, 5, 7, and 9
Step-by-step explanation:
There is a rule that states that the two shorter sides of a triangle have to be greater than the largest side.
A is correct because 5 + 7 > 9
B is incorrect because 5 + 3 = 8
C is incorrect because 1 + 3 = 4
D is incorrect because 4 + 4 < 9
I hope this helps.
An object is launched straight into the air. The projectile motion of the object can be modeled using h(t) = 96t – 16t2, where t is the time since launch and h(t) is the height in feet of the projectile after time t in seconds.
Answer with Step-by-step explanation:
We are given that height of projectile after t seconds is given by
[tex]h(t)=96t-16t^2[/tex]
a.h(t)=144 ft
[tex]144=96t-16t^2[/tex]
[tex]16t^2-96t+144=0[/tex]
[tex]t^2-6t+9=0[/tex]
[tex]t^2-3t-3t+9=0[/tex]
[tex]t(t-3)-3(t-3)=0[/tex]
[tex](t-3)(t-3)=0[/tex]
t-3=0
t=3
After 3 s, the height of the project will be 144 feet in the air.
b.h(t)=0
[tex]96t-16t^2=0[/tex]
[tex]16t(6-t)=0[/tex]
[tex]16t=0\implies t=0[/tex]
[tex]6-t=0\implies t=6[/tex]
At t=0, the initial position of projectile
At t=6 s , the projectile will hit the ground.
Answer:
The first one is 3 seconds. The second one is 6 seconds
Step-by-step explanation:
5. Which choice below could match the following ratio: 4 to 5 Look at
answer choiced first and simplify to see which one leaves you 4 to 5. *
O
A A teacher has 12 girls and 15 boys in her class.
O
B A restaurant sells 3 salads for every 2 steaks.
O
CA garden has 3 pepper plants for every 5 tomato plants.
O
DA car dealership sells 30 cars for every 5 trucks.
Answer:
A- A teacher has 12 girls and 15 boys in her class.
Step-by-step explanation:
12/3= 4
15/3= 5
This means that it will have a ratio of 4 to 5 because it is the only problem where you are able to divide both with a common number, which is 3.
A first number plus twice a second number is 14. Twice the first number plus the second totals 19. Find the numbers.
Answer:
first number is 8 second number is 3
on the unit circle, where 0<0<2pi, when is tan 0 undefined?
Answer: C
Step-by-step explanation:
How to solve the 30° 60° and 90° of a right triangle
Answer:
Step-by-step explanation:
Divide the hypotenuse by 2 to find the short side. Multiply this answer by the square root of 3 to find the long leg. Type 3: You know the long leg (the side across from the 60-degree angle). Divide this side by the square root of 3 to find the short side.
hope this helps you for a math problem~
: )
Suppose a single bacterium is placed in a bottle at 11:00am. It grows and at 11:01 divides into two bacteria. These two bacteria each grow and at 11:02 divide into four bacteria. Which grow and at 11:03 divide into eight bacteria, and so on. Now, suppose the bacteria continue to double every minute until the bottle is full at 12:00.
a. How many bacteria are in the bottle at 11:53?
b. What fraction of the bottle is full at that time?
Answer:
Number of bacteria at 11:53 for 53 min = [tex]2^{53}[/tex] = 9.007199 × [tex]10^{15}[/tex]
fraction that is full = [tex]2^{-7}[/tex]
Step-by-step explanation:
solution
Number of bacteria is express as here
Number of bacteria = [tex]2^t[/tex] ............1
so
bacteria at 1 min , 2 min and 3 min are
Number of bacteria at 1 min = [tex]2^1[/tex] = 2
Number of bacteria at 3 min = [tex]2^2[/tex] = 4
Number of bacteria at 3 min = [tex]2^3[/tex] = 8
and
as that Number of bacteria at 11:53 is for 53 min is
Number of bacteria at 11:53 for 53 min = [tex]2^{53}[/tex] = 9.007199 × [tex]10^{15}[/tex]
and
bottle is full at 12:00
so Number of bacteria at 12:00 for 60 min = [tex]2^{60}[/tex]
so fraction that is full = [tex]\frac{2^{53}}{2^{60}}[/tex]
fraction that is full = [tex]2^{-7}[/tex]
A geometric sequence is a sequence of numbers in which the ratio between consecutive terms is constant.
Number of bacteria present in bottle at 11:53 are [tex]2^{53}[/tex].
At that time, fraction [tex]2^{-7}[/tex] or 0.00781 of bottle is full.
Since, single bacterium is placed in a bottle at 11:00am. It grows and at 11:01 divides into two bacteria. These two bacteria each grow and at 11:02 divide into four bacteria. Which grow and at 11:03 divide into eight bacteria.
So, a sequence is obtained 1, 2, 4, 8, 16, 32, 64, .........
We can also write as,
At 11:00 am, [tex]2^0[/tex] bacteria
At 11:01 am, [tex]2^1[/tex] bacteria
At 11:02 am, [tex]2^2[/tex] bacteria
Similarly, At 11:53 am, Number of bacteria present in bottle are [tex]2^{53}[/tex].
When the bottle will be full, that time number pf bacteria will be [tex]2^{60}[/tex].
S0, fraction of bottle is full at 11:53 is [tex]2^{53} /2^{60} = 2^{-7} = 0.00781[/tex]
Learn more:
https://brainly.com/question/13394473
Solve the following system via elimination
3x - y = 28
3x+y=14
Answer:
Point Form:
( 7 , − 7 )
Equation Form:
x = 7 , y = − 7
Step-by-step explanation:
Answer:
x=7,y=-7
Step-by-step explanation:
1: add the equations
3x+3x+y-y=28+14
6x=42
x equals 7
2:plug that in to get y
3(7)-y=28
21-y=28
-y=7
y=-7
Which diagram shows ∠1 and ∠2 as supplementary angles?
A) A
B) B
C) C
D) D
Answer:
Step-by-step explanation:please upload diagram.
Answer:
A
Step-by-step explanation:
Supplementary angles are two angles that when added together equal 180 degrees, forming a straight line when placed beside each other.
Question in image. Thanks!
Answer:
B (i do also slightly lean towards C, but i'm pretty sure it would be B because it gives a specific measurement)
Step-by-step explanation:
If all angles that are either adjacent or opposite are supplementary, all angles must be 90°
If at all times adjacent sides are 5 inches, all sides are equal.
Knowing this, it has to be a square because all angles would be 90° and all sides would be equal.
What is the answer to this
Answer:
250decay0.05Step-by-step explanation:
The value with the exponent is the "multiplier". It is 0.05.
This value is less than 1, so the function represents decay.
The initial value is the number that multiplies the exponential term. It is the value of A when t=0: 250.
original amount: 250growth or decay: decaymultiplier: 0.05
Mya's lunchbox is shown. What is the volume of the lunchbox? Round to the nearest tenth if necessary.
The volume of Mya's lunchbox can be calculated by multiplying its length, width, and height. However, the dimensions were not provided in the question.
Explanation:The volume of a three-dimensional object like Mya's lunchbox can be found by multiplying the object's length, width, and height together. If Mya's lunchbox is a rectangular prism, for instance, and we know its measurements, we can calculate its volume using the formula Volume = Length x Width x Height. However, the question didn't provide the necessary dimensions of the lunchbox. Therefore, you need to provide the dimensions of the lunchbox for me to be able to help you calculate its volume.
Learn more about Volume calculation here:https://brainly.com/question/33318354
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Bruce is going to call one person from his contacts at random. He has 25 total contacts. 20 of those are from his neighborhood.
What is p(call a person not from his neighborhood)?
Answer:
Depends on if you count his parent(s) if not then the answer is 5
Step-by-step explanation:
Answer:
[tex]0.2[/tex]
Step-by-step explanation:
Probability = Number of favorable outcomes / Number of posssible
outcomes
There are [tex]5[/tex] favorable outcomes ( the [tex]25-20 = 5[/tex] people not from his neighborhood).
There are 25 possible outcomes ( the [tex]25[/tex] total contacts).
P (call a person not from his neighborhood) [tex]= \frac{5}{25} = 0.2[/tex]
Simplify the expression square root 18 + square root 50 .
Final answer:
To simplify the expression sqrt(18) + sqrt(50), find the square roots of 18 and 50 individually and then add them together.
Explanation:
To simplify the expression sqrt(18) + sqrt(50), we need to find the square roots of 18 and 50 individually and then add them together. The square root of 18 is approximately 4.2426 and the square root of 50 is approximately 7.0711. Adding these two values gives us approximately 11.3137. Therefore, the simplified expression is sqrt(18) + sqrt(50) = 11.3137.
please please please help meeeeee
Answer:
x = -4
Step-by-step explanation:
Square both sides:
[tex](\sqrt{-5-2x})^2 =(\sqrt{-1-x} )^2[/tex]
The square root and the square will cancel to leave simply the argument within the square root:
-5 - 2x = -1 - x
Now simply isolate the variable x:
x = -5 + 1 = -4
Check to see if x = -4 will work:
[tex]\sqrt{-5-2*(-4)} =\sqrt{-1-(-4)}[/tex]
[tex]\sqrt{3} =\sqrt{3}[/tex]
This works, so we know that x = -4 is a solution.
Hope this helps!
Find the center and the radius of the circle then graph the circle (x+4)2 +(y-1)2=4
Answer:
Step-by-step explanation:
hello :
us the standard form : (x+4)² +(y-1)²=4
the center is : (-4 , 1) and the radius 2
Which of these numbers is in the solution set of x – 15 = 5? A. 10 B. 3 C. 20 D. –10
Answer:
3
Step-by-step explanation:
15 x 3 is 15
Answer:
C. 20
Step-by-step explanation:
Your main goal is to isolate X to find your answer. To do that, bring the -15 to the other side. Then it would be x =20