Answer:
None of the expression are equivalent to [tex]49^{(2t - 0.5)}[/tex]
Step-by-step explanation:
Given
[tex]49^{(2t - 0.5)}[/tex]
Required
Find its equivalents
We start by expanding the given expression
[tex]49^{(2t - 0.5)}[/tex]
Expand 49
[tex](7^2)^{(2t - 0.5)}[/tex]
[tex]7^2^{(2t - 0.5)}[/tex]
Using laws of indices: [tex](a^m)^n = a^{mn}[/tex]
[tex]7^{(2*2t - 2*0.5)}[/tex]
[tex]7^{(4t - 1)}[/tex]
This implies that; each of the following options A,B and C must be equivalent to [tex]49^{(2t - 0.5)}[/tex] or alternatively, [tex]7^{(4t - 1)}[/tex]
A. [tex]\frac{7^{2t}}{49^{0.5}}[/tex]
Using law of indices which states;
[tex]a^{mn} = (a^m)^n[/tex]
Applying this law to the numerator; we have
[tex]\frac{(7^{2})^{t}}{49^{0.5}}[/tex]
Expand expression in bracket
[tex]\frac{(7 * 7)^{t}}{49^{0.5}}[/tex]
[tex]\frac{49^{t}}{49^{0.5}}[/tex]
Also; Using law of indices which states;
[tex]\frac{a^{m}}{a^n} = a^{m-n}[/tex]
[tex]\frac{49^{t}}{49^{0.5}}[/tex] becomes
[tex]49^{t-0.5}}[/tex]
This is not equivalent to [tex]49^{(2t - 0.5)}[/tex]
B. [tex]\frac{49^{2t}}{7^{0.5}}[/tex]
Expand numerator
[tex]\frac{(7*7)^{2t}}{7^{0.5}}[/tex]
[tex]\frac{(7^2)^{2t}}{7^{0.5}}[/tex]
Using law of indices which states;
[tex](a^m)^n = a^{mn}[/tex]
Applying this law to the numerator; we have
[tex]\frac{7^{2*2t}}{7^{0.5}}[/tex]
[tex]\frac{7^{4t}}{7^{0.5}}[/tex]
Also; Using law of indices which states;
[tex]\frac{a^{m}}{a^n} = a^{m-n}[/tex]
[tex]\frac{7^{4t}}{7^{0.5}}[/tex] = [tex]7^{4t - 0.5}[/tex]
This is also not equivalent to [tex]49^{(2t - 0.5)}[/tex]
C. [tex]7^{2t}\ *\ 49^{0.5}[/tex]
[tex]7^{2t}\ *\ (7^2)^{0.5}[/tex]
[tex]7^{2t}\ *\ 7^{2*0.5}[/tex]
[tex]7^{2t}\ *\ 7^{1}[/tex]
Using law of indices which states;
[tex]a^m*a^n = a^{m+n}[/tex]
[tex]7^{2t+ 1}[/tex]
This is also not equivalent to [tex]49^{(2t - 0.5)}[/tex]
What is the distance to the earth’s horizon from point P? Enter your answer as a decimal in the box. Round only your final answer to the nearest tenth. x = mi
Answer:
[Distance to the Horizon]^2 =Height of the skydiver x Diameter of the Earth
D^2 = 1.4 x 7918
D^2 = 11,085.2
D = Sqrt(11,085.2)
D = ~ 105.28628......miles - Distance to Horizon.
Step-by-step explanation:
Answer:
284.4 I took the test ;)
THINKING
4. Given is the Linear and Quadratic System g(x) = 3x2 + 8x + k and f(x) = 2x – 1.
Determine k such that g(x) = 3x2 + 8x + k intersects f(x) = 2x – 1 at one point.
Answer:
k = 2
Step-by-step explanation:
Given the equations:
g(x) = 3x² + 8x + k
f(x) = 2x - 1
At the intersection point:
g(x) = f(x)
3x² + 8x + k = 2x - 1
3x² + 6x + (k+1) = 0
If there is only one intersection point, the discriminant must be equal to zero:
b² - 4(a)(c) = 0
6² - 4(3)(k+1) = 0
36 - 12(k+1) = 0
36 - 12k - 12 = 0
24 = 12k
24/12 = k
2 = k
Find the total surface area of this Triangular Prism.
Answer:
1053 cm
Step-by-step explanation:
Answer:
1008cm^2
Step-by-step explanation:
The numbers 1 through 10 are put in one bag, and the numbers 5 through 14 are put in another bag. When you pick one number from each bag, what is the probability you get the same number? please answer as an unsimplified fraction.
Answer:
36/100
Step-by-step explanation:
this is because you find the overlapping ranges of each bag which is 5 - 10 on the first bag and 5 - 10 on the second bag. both bags have 10 total numbers, so 6/10 * 6/10 because there are six numbers on each bag and 10 overall choices, so we multiply these two because its an and statement which gives us 36/100.
The probability that we get the same number is 9/25.
What is probability?It is simply likeliness of happening an event. The probability of an event lies between 0 to 1.
How to find the probability?Numbers in first bag=10
Numbers in second bag=10
Common numbers=5,6,7,8,9,10
Total common numbers=6
So the probability that we get the same numbers will be
= 6/10* 6/10
=36/100
=18/50
=9/25
Hence the probability that we will get the same numbers is 9/25.
Learn more about probability at https://brainly.com/question/24756209
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If you are trying to conduct an experiment by taking a random sample of current college students, which of the groups below should NOT be included in your sample? Select all that apply. A) 5th graders B) Preschool students C) Presidents of different countries D) The local college math class
Answer:
A, b, and c
Step-by-step explanation:
They aren’t in college right now. It’s asking for current college students which is d
The quadratic $-6x^2+36x+216$ can be written in the form $a(x+b)^2+c$, where $a$, $b$, and $c$ are constants. What is $a+b+c$?
Answer:
-47
Step-by-step explanation:
Step 1: Factor GCF
-6(x² - 6x - 36) = 0
Step 2: Divide by -6 on both sides
x² - 6x - 36 = 0
Step 3: Isolate x's
x² - 6x = 36
Step 4: Complete the Square
x² - 6x + 9 = 36 + 9
(x - 3)² = 45
Step 5: Move everything to one side
(x - 3)² - 45 = 0
So, a = 1, b = -3, c = -45
1 - 3 - 45 = -47
The graphs below have the same shape. What is the equation of the blue
graph?
Answer:
The answer would be D.
Step-by-step explanation:
I know this, because all you have to do is plug in whatever number equals zero in the parenthesis.
It should look like this.
G(x) = (x-3)^2 - 5
So you would plug in 3 for x.
Then the answer to the equation would be -5.
Then I look to see if there is a point at (3, -5)
There was a point there, so then I knew that was the answer.
which point is a solution to y<_3x-4?
Answer:
D
Step-by-step explanation:
Replace by the coordinates
3*3 -1>1
Answer:
D. (3,1)
Step-by-step explanation:
Plug the X and Y values into the expression y<3x-4
Substitute 3 for X and 1 for Y and simplify
y < 3x - 4
1 < 3(3) - 4
1< 9 - 4
1< 5
In this case 1 is less than 5, that is a correct statement, so your answer is C.
MATHEMATICS POST I)
Find the interest on $1,200 at 5 1/2% annual interest for 9 months,
Answer:
$1200×5½×9
100
$1200×11×9
100×2
6×11×9=$594
50 points Please help Use the following random list of 100 numbers and the assignations 0-4 to represent girls and 5-9 to represent boys to answer the question below. 3199 9288 1023 1130 0809 1770 6231 7538 8927 4761 7258 7111 0209 0916 1450 9848 4654 7579 6150 3093 9608 0061 4014 9501 0382 3052 2385 9074 1664 6551 6577 1811 3454 5870 1277 5056 1063 5697 9141 4120 9181 1343 0168 3693 0463 4842 1704 3774 4908 4161 6404 9675 2518 3988 4268 6083 0636 9634 5295 5656 1918 3133 6831 8393 6363 2452 1531 1638 1317 2279 9395 0702 2091 5269 0422 0275 3373 1424 1958 0356 5163 0743 6658 6257 2772 0570 4522 2665 0890 3560 5549 2238 2172 9715 9741 4975 6617 9034 4441 8220 Based on the results of the simulation, what is the experimental probability that a group will include only boys? Based on the results of the simulation, what is the experimental probability that a group will not contain four boys? Based on the results of the simulation, if 224 groups are formed, about how many of them would you expect to contain all girls? Round your answer to the nearest number of groups.
Answer:
For the first question, there is a 39% chance for only boys and a 61% chance for only girls. For the second one it is, about 136 groups.
Step-by-step explanation:
100: 224 = 61:x → 61/100 = x/224
100x = 13664
x = 136.64 → 136 groups (You can't round up if you don't have enough people)
Hope this helped!
Answer: 39% chance for only boys and a 61% chance for only girls. For the second one it is, about 136 groups.
Step-by-step explanation:
:) The other answer is correct too! But just for clarification! :)
x^3+3x^2-2x-6. Show all work please.
━━━━━━━☆☆━━━━━━━
▹ Answer
(x + 3) * (x² - 2)
▹ Step-by-Step Explanation
x³ + 3x² - 2x - 6
x²(x + 3) - 2x - 6
x²(x + 3) - 2(x + 3)
(x + 3) * (x² - 2)
Hope this helps!
- CloutAnswers ❁
Brainliest is greatly appreciated!
━━━━━━━☆☆━━━━━━━
What's the total surface area of a covered box with a length of 4 ft, a width of 3 ft, and a height of 6 ft? Question 17 options: A) 108 sq ft B) 38 sq ft C) 84 sq ft D) 96 sq ft
Hey there! :)
Answer:
A. 108 ft².
Step-by-step explanation:
Find the area of each face using the dimensions 4, 3 and 6. Remember, there are 6 total faces with 3 sets of congruent faces. The faces are rectangular, so the formula A = l × w will be used to solve for the area of each:
2(4 ·3) = 2(12) = 24 ft²
2(4· 6) = 2(24) = 48 ft²
2(3 · 6) = 2(18) = 36ft².
Add up the areas of the faces:
24 + 48 + 36 = 108 ft².
Answer:
A) 108 sq ft
Step-by-step explanation:
SA = PH + 2LW
P = 2(L + W)
SA = 2(L + W)H + 2LW
SA = 2(4 ft + 3 ft)(6 ft) + 2(4 ft)(3 ft)
SA = 108 sq ft
what’s the answer of g
Answer:
[tex]\huge\boxed{g(a-1)=\dfrac{2-a}{a}=\dfrac{2}{a}-1}[/tex]
Step-by-step explanation:
[tex]g(t)=\dfrac{1-t}{1+t}\\\\g(a-1)-\text{substitute}\ t=a-1\ \text{to}\ g(t):\\\\g(a-1)=\dfrac{1-(a-1)}{1+(a-1)}=\dfrac{1-a-(-1)}{1+a+(-1)}=\dfrac{1-a+1}{1+a-1}=\dfrac{(1+1)-a}{(1-1)+a}=\dfrac{2-a}{a}[/tex]
WILL GIVE BRAINIEST TO THE FIRST ANSWER
Answer:x − 3 y = − 36
Step-by-step explanation:
Answer: The initial form is called slope intercept form// and the equation in standard form is 3y=37
Step-by-step explanation:
standard form = ax+by=c so you basically just have to take that and put it into the formula
Hope this helps
Use substitution to solve. PLEASE HELP!
Answ(2,4)
Step-by-step explanation:
Answer:
The answer is a because you substitute the numbers in and that is the correct equation brainliest please :)
Step-by-step explanation:
find the area of the iscoseles triangle first answer=brainliest
Answer:
[tex]60cm^{2}[/tex]
Step-by-step explanation:
so first we need to find the height so by splitting the isosceles triangle into two right-angled triangles and then applying Pythagoras' Theorem to one of them.
[tex]h^{2} =13^{2} -5^{2}[/tex]
[tex]h^{2} =169-25[/tex]
[tex]h^{2} =144[/tex]
[tex]h=\sqrt{144}[/tex]
[tex]h=12[/tex]
We now know the height of the triangle and can use this to go back and find the area of the isosceles triangle.
area of triangle = [tex]\frac{1}{2}[/tex] x base x height
area of triangle = [tex]\frac{1}{2}[/tex] x 10 x 12
area of triangle = 60
Answer:
[tex]\boxed{Area = 60 cm^2}[/tex]
Step-by-step explanation:
Perimeter of the isosceles triangle = 10+13+13
=> 36 cm
Semi Perimeter = 18 cm
Using Heron's formula to find the area:
=> [tex]Area = \sqrt{s(s-a)(s-b)(s-c)}[/tex]
Where s is the semi perimeter and a,b and c are the sides
=> Area = [tex]\sqrt{18(18-13)(18-13)(18-10) }[/tex]
=> Area = [tex]\sqrt{18(5)(5)(8)}[/tex]
=> Area = [tex]\sqrt{3600}[/tex]
=> Area = 60 cm²
You are making a welding fixture and must cut down a length of copper tubbing from 15 1/8 inches to 8 3/4 inches. If the leftover piece is long enough , you will use it in another fixture . How long will the leftover piece be ?
Answer: 51/8 inches
Step-by-step explanation:
Since you must cut down the length of copper tubbing from 15 1/8 inches to 8 3/4 inches, the leftover piece will be:
15 1/8 - 8 3/4
Change the mixed fraction to improper fraction.
121/8 - 35/4
The LCM will be 8
( 121 - 70 )/8
51/8 or 6.375 inches
Therefore, the leftover piece will be 51/8 inches long
Express as a product: 1+2cosα
Answer:
Step-by-step explanation:
1+2 cos α
[tex]=1+2(2 cos^{2} \frac{\alpha }{2} -1)\\=1+4 ~cos^2\frac{\alpha }{2} -2\\=4 ~cos^2\frac{\alpha }{2} -1\\=(2cos \frac{\alpha }{2} +1)(2 cos \frac{\alpha }{2} -1)[/tex]
What is the slope of the line that contains the points (9,-4) and (1, -5)
А 1/8
B. -1/8
C.-1
D. 1
Answer:
A. 1/8
Step-by-step explanation:
m = rise/run
m = (y2-y1)/(x2-x1)
m = (-5- - 4)/(1-9)
m = (-5+4)/(-8)
m = (-1)/(-8)
m = 1/8
Answer:
The answer is A.
Step-by-step explanation:
Given that the formula to find gradient, m, is :
[tex]m = \frac{y2 - y1}{x2 - x1} [/tex]
Then, you have to substitute the coordinates into the formula :
[tex]let \: (9, - 4) \: be \: (x1,y1) \\ let \: (1, - 5) \: be \: (x2,y2)[/tex]
[tex]m = \frac{ - 5 - ( - 4)}{1 - 9} [/tex]
[tex]m = \frac{ - 5 + 4}{ - 8} [/tex]
[tex]m = \frac{ - 1}{ - 8} [/tex]
[tex]m = \frac{1}{8} [/tex]
⚠ PLEASE HELP ⚠ Calculate the product. (1- 1/4) * (1- 1/9) * (1- 1/16) *...* (1- 1/225) will award BRAINLIEST.
Answer:
5/8
Step-by-step explanation:
The value of the expression is 8/15
What is expression?An expression in maths is a sentence with a minimum of two numbers or variables and at least one maths operation.
Given an expression, (1- 1/4) * (1- 1/9) * (1- 1/16) *...* (1- 1/225)
The expression is in the form of (1- 1/4) * (1- 1/9) * (1- 1/16) *...* (1- 1/n²)
We know, (1- 1/4) * (1- 1/9) * (1- 1/16) *...* (1- 1/n²) = (n+1)/2n
Here, n = 15.
So, (1- 1/4) * (1- 1/9) * (1- 1/16) *...* (1- 1/225) = (15+1)/(2.15) = 16/30
= 8/15
Hence, The value of the expression is 8/15
For more references on expressions, click;
https://brainly.com/question/14083225
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What is the sum of the first 20 terms of the series 3 + 14 + 25 + 36 + ...
226
0 1,252
1,860
2,010
2,150
Using the completing-the-square method, find the vertex of the function f(x) = 2x2 − 8x + 6 and indicate whether it is a minimum or a maximum and at what point.
Answer:
minimum at (2, - 2 )
Step-by-step explanation:
The equation of a parabola in vertex form is
f(x) = a(x - h)² + k
where (h, k) are the coordinates of the vertex and a is a multiplier
If a > 0 then the vertex is a minimum
If a < 0 then the vertex is a maximum
Given
f(x) = 2x² - 8x + 6 ← factor out 2 from the first 2 terms
= 2(x² - 4x) + 6
To complete the square
add/ subtract ( half the coefficient of the x- term)² to x² - 4x
f(x) = 2(x² + 2(- 2)x + 4 - 4) + 6
= 2(x - 2)² - 8 + 6
= 2(x - 2)² - 2 ← in vertex form
with vertex = (2, - 2) and a > 0
Thus minimum at (2, - 2 )
In which of the following cases would you most likely buy a point when closing on a home loan? a. The monthly payment is reduced by $8 and you plan to sell the home at the end of 3 years. b. The monthly payment is reduced by $10 and you plan to sell the home at the end of 4 years. c. The monthly payment is reduced by $12 and you plan to sell the home at the end of 5 years. d. The monthly payment is reduced by $14 and you plan to sell the home at the end of 7 years. Please select the best answer from the choices provided A B C D
Answer:
d. The monthly payment is reduced by $14 and you plan to sell the home at the end of 7 years.
Step-by-step explanation:
As we can see from the choices given that
In option A the monthly payment is declined by 8 and the sale of the home is done at the end of the 3 years
In option B monthly payment is declined by 10 and the sale of the home is done at the end of the 4 years
In option C monthly payment is declined by 12 and the sale of the home is done at the end of the 5 years
In option D monthly payment is declined by 14 and the sale of the home is done at the end of the 7 years
From the above choices, we can conclude that the declining percentage high in option D plus the time period is also high
Therefore the option D is chosen
Answer:
d. The monthly payment is reduced by $14 and you plan to sell the home at the end of 7 years.
Step-by-step explanation:
choose the correct simplification of (6x-5)(2x^2-3x-6)
Answer:
12x^3 -28x^2 -21x +30
Step-by-step explanation:
1) Distribute!
(6x-5)(2x^2-3x-6) = 12x^3 -18x^2 - 36x -10x^2 +15x+30
2) Combine like terms!
12x^3 -18x^2 - 36x -10x^2 +15x+30 = 12x^3 -28x^2 -21x +30
Answer is:
12x^3 -28x^2 -21x +30
Hope it helps!!
Parallelogram A B C D is shown. Sides A B and D C are parallel. The length of A B is 4 q minus 8 and the length of D C is q + 4. What is the length of side AB of parallelogram ABCD? units
Answer:
8
Step-by-step explanation:
Answer:
yes it is 8
Step-by-step explanation:
i did the assiment on edge 2021
Here is a circle touching a square.
The area of the square is 36 cm2
Work out the area of the circle.
Give your answer in terms of pie .
Answer: 9πcm²
Step-by-step explanation: area of the square= 36cm²
Therefore, the area of one side= √area = √36 = 6cms
Since the circle is touching the sides of the square, the side of the square = the diameter of the circle
Therefore the radius of the circle= side/2 = 3cm
The formula for the ares of the circle is πr²
π*3*3 = 9πcm²
What is the new cost if a $2.75 toy is marked up by 29%?
Answer:
$3.55
Step-by-step explanation:
You need to add 29% of $2.75 to $2.75.
That means the price will be 129% of $2.75.
129% of $2.75 =
= 1.29 * $2.75
= $3.55
You are taking 1500 US dollars on a trip. After checking the exchange rate, you figure out the exchange rate is 1 US dollar to 0.74 euros. Task: write an equation to convert US dollars to euros. Will mark most brainiest if you answer!
Answer:
y= 0.74x
0.74 (1500) = 1,110 euros
Step-by-step explanation:
Hi, to answer this question we have to write an equation with the information given:
Since: 1 US dollar = 0.74 Euros
To convert x US dollars to Euros we have to multiply it by 0.74:
y= 0.74x
Where:
y = value in EUROS
x = value in US dollars
For 1500:
y = 0.74 (1500) = 1,110 euros
Feel free to ask for more if needed or if you did not understand something.
3(-2a-4)+3a what would this be i have so many questions today to ask y'all
Answer:
[tex] - 3(a + 4)[/tex]Solution,
[tex]3( - 2a - 4) + 3a \\ = 3 \times ( - 2a) - 3 \times 4 + 3a \\ = - 6a - 12 + 3a \\ = - 6a + 3a - 12 \\ = - 3a - 12 \\ = - 3(a + 4)[/tex]
Hope this helps...
Good luck on your assignment...
Answer:
-3(a+4)
Step-by-step explanation:
need help figuring this one out
Answer:
4.426020408 × 10∧19
Step-by-step explanation:
First, I found what 540 multiplied by 0.0000000028 was. Next, I took 66921428571428.6 and divided it by the product I got on top.