Answer:
The exponential form is 49 to the power of one-half equals 7 ⇒ 4th answer
Step-by-step explanation:
The exponential equation of [tex]log_{b}(m)=n[/tex] is [tex]b^{n}=m[/tex] , where b is the base, n is the exponent of b and m is the value of [tex]b^{n}[/tex]
Ex: If [tex]log_{3}(81)=4[/tex] , that means b = 3 , n = 4 and m = 81, then its exponential form is [tex]3^{4}=81[/tex]
Now let us solve the question
∵ The equation is [tex]log_{49}(7)=\frac{1}{2}[/tex]
∴ The base is 49
∴ The exponent is [tex]\frac{1}{2}[/tex]
∴ The answer is 7
- Substitute them in the form of the exponential form
∴ The exponential form is [tex](49)^{\frac{1}{2}}=7[/tex]
The exponential form is 49 to the power of one-half equals 7
The given equation is log49(7) = 1/2. To convert it to exponential form, we can write it as 49^(1/2) = 7.
Explanation:The given equation is:
log49(7) = 1/2
To convert this equation to exponential form, we need to remember that logarithms and exponentials are inverse functions. Therefore, we can write the equation as:
491/2 = 7
Hence, the exponential form of the given equation is 49 raised to the power of 1/2 equals 7.
What is the median of 4,3,5,9,3,4
Answer:
THE ANSWER IS 4
Step-by-step explanation:
Answer:
4
Step-by-step explanation:
3, 3, 4, 4, 5, 9
The median is 4
Determine o período, a imagem e construa o gráfico de cada uma das funções abaixo: a) f(x) = 3sen(x) b) f(x) = 1 - sen(3x) c) f(x) = -1+2sen(0,5x)
Answer:
Please read the answer below
Step-by-step explanation:
The general form of a sinusoidal function is given by:
[tex]f(x)=Asin(\omega x)[/tex] (1)
where A is the amplitude, and the period is given by:
[tex]T=\frac{2\pi}{\omega}[/tex]
The image of a function is the available values of the function f(x) in the domain of f(x). For sinusoidal function the image of f(x) is determined with the aid of the amplitude. For example, in the case of (1), f(x) varies from -A to A.
Due to the information given above you have (the plots are attached below):
a)
[tex]f(x)=3sin(x)\\\\T=\frac{2\pi}{1}=2\pi\\\\Im\ f(x)=[-3,3][/tex]
b)
[tex]f(x)=1-sin(3x)\\\\T=\frac{2\pi}{3}\\\\Im\ f(x)=[0 \ ,2][/tex]
in the last case the first term of f(x) modifies the image of f(x) because the sinusoidal function is displaced to y=1.
c)
[tex]f(x)=-1+2sin(0.5x)\\\\T=\frac{2\pi}{0.5}=4\pi\\\\Im\ f(x)=[-3,1][/tex]
Australian glitter ants reproduce so that their population doubles every 15 days. If there are 3 ants initially, the equation is represented by y=3(2)^t/15, where t represents the number of days. Rewrite the equation in the form y=a(1+r)^t and find the daily increase rate represented by r.
Answer:
4.73%
Step-by-step explanation:
y = 3×2^(t/15) = 3×(2^(1/15))^t = 3×1.0472941^t
In this form, ...
1 +r = 1.0472941
r = .0472941 ≈ 4.73%
The daily increase is about 4.73%.
A sign at the store says that all music equipment has been marked down 30% off the original price. You buy an electric guitar for the sale price of $315. What was the original price?
write an expression for " the quotient of q and 9
Answer:
q/9
Step-by-step explanation:
The quotient is an number or variable that is the product of division. My answer may be reversed or wrong, but it should be close to the correct one.
A gym charges a $615 yearly fee for membership plus $50 for each hour of personal training. What is the average total cost per hour of training if a member works with a personal trainer for 30 hours in a year? Do not include the dollar sign ($) in your answer.
Answer:
The average total cost per hour of training is $70.5
Step-by-step explanation:
The form of the linear function is f(x) = m x + b, where
m is the average rateb is the initial value∵ The gym charges a $615 yearly fee for membership plus
$50 for each hour of personal training
- That means the initial amount is 615 and the average rate is 50
∴ m = 50 dollars per hour
∴ b = 615 ⇒ fixed fee
- Substitute m and b in the form of the linear function
∴ c(x) = 50 x + 615, where c(x) is the cost per year for x
training hours
∵ A member works with a personal trainer for 30 hours in a year
- That means x = 30
∴ x = 30
- Find the total cost of this year by substituting x by 30
∴ c(30) = 50(30) + 615
∴ c(30) = 1500 + 615
∴ c(30) = 2115
∴ The total cost of this year is $2115
To find the average cost per hour divide the total cost by the number of the training hours
∵ Average cost per hour = 2115 ÷ 30
∴ The average cost per hour = 70.5 dollars
∴ The average total cost per hour of training is $70.5
Based on the number of hours and the cost per hour of using the trainer, the average cost per hour is $70.50 per hour.
First find the total cost of using a trainer for 30 hours.
= Fixed membership cost + (Cost per hour x Number of hours)
= 615 + (50 x 30)
= $2,115
The total cost for the year is $2,115.
The average cost per hour will be:
= Total cost / Number of hours
= 2,115 / 30
= $70.50
In conclusion, the total average cost per hour is $70.50.
Find out more at https://brainly.com/question/24157928.
"Lashonda swam 4 kilometers against the current in the same amount of time it took her to swim 16 kilometers with the current. The rate of the current was 3 kilometers per hour. How fast would Lashonda swim if there were no current?"
Answer:
5 km/h
Step-by-step explanation:
In this problem, Lashonda swam 4 km against the current. So the distance covered in this case is
[tex]d_1=4 km[/tex]
Calling [tex]v[/tex] the velocity of Lahonda without the current, and [tex]c[/tex] the velocity of the current, in this situation Lahonda's velocity is
[tex]v-c[/tex]
So we can write:
[tex]t_1=\frac{d_1}{v-c}[/tex]
where [tex]t_1[/tex] is the time taken to cover the distance.
When Lashonda swims with the current, her velocity is
[tex]v+c[/tex]
So we can write
[tex]t_2=\frac{d_2}{v+c}[/tex]
where
[tex]d_2=16 km[/tex] is the distance covered in this case, and [tex]t_2[/tex] the time taken.
The velocity of the current is
[tex]c=3 km/h[/tex]
Since Lashonad takes the same time to cover the two distances,
[tex]t_1=t_2[/tex]
So we can write
[tex]\frac{d_1}{v-c}=\frac{d_2}{v+c}[/tex]
And solving for v, we find Lashonda's velocity without the current:
[tex]d_1(v+c)=d_2(v-c)\\d_1 v+d_1c = d_2v-d_2c\\v(d_2-d_1)=c(d_1+d_2)\\v=\frac{d_2+d_2}{d_2-d_1}c=\frac{16+4}{16-4}(3)=5 km/h[/tex]
Final answer:
To find Lashonda's swimming speed without the current given the rate of the current and the distances swam with and against it.
Explanation:
The rate of the current is 3 kilometers per hour. To find the speed of Lashonda without the current, we can set up equations using the formula: speed = distance/time.
Let's denote Lashonda's speed in still water as x kilometers per hour. When swimming against the current, her effective speed is x - 3 km/h, and when swimming with the current, her effective speed is x + 3 km/h.
By setting up and solving the equations, we find Lashonda's speed without the current is 9 kilometers per hour.
Does anyone get this??
Answer:
The distance from the feet to the wall is 9 ft
Step-by-step explanation:
Using trig,
We must use cosine to find the missing side.
The equation is cos 60 = [tex]\frac{adjacent}{18}[/tex]
The cosine of 60 is 1/2
So, we multiply 1/2 by 18
to get 9
Hope this helps!
Branliest would really be nice!
What are the lengths of the sides of the right triangle
that is formed? Check all that apply.
h
K
h-k
x-h
y-k
The answer is third one and last one
Answer: the answer is x-h and y-K
Step-by-step explanation:
This represents the side lengths of the right triangle that is formed
In this circle, AB is tangent to the circle at point B, AC is tangent to the circle at point C, and point D lies on
the circle. What is m BAC ?
a. 264
b. 84
c. 96
d. 90
Answer:
c. 96
Step-by-step explanation:
Answer:
96
Step-by-step explanation:
Pedro has 9 coins. His friend John gives him 9 more coins. Pedro decides to share his coins evenly with his two brothers. Which expression shows how many coins each brother will get
Answer:
6 if pedro and his two brother will have coins. If he doesnt get any for himself and gives it all to his brothers then they each get 9.
Step-by-step explanation:
I used my calculator.
A race is 9/10 kilometers long. Lamar ran 2 of these races . How far did he run together?
Answer:
1.8
Step-by-step explanation:
9/10 times 2 equals 1.8
/Answer:
The answer would be 18/10.
Step-by-step explanation:
This is because when you add fractions with common denominators, like 9/10+9/10, you don't add the denominators. But if you multiply 9/10*2 it would be like 9/10*2/1 which would equal 18/10 still.
The rectangle below has an area of 81-x^2 square meters and a width of 9-x meters. What expression represents the length of the rectangle?
For this case we have that by definition, the area of a rectangle is given by:
[tex]A = w * l[/tex]
Where:
w: Is the width of the rectangle
l: is the length of the rectangle
According to the data of the statement we have:
[tex]A = 81-x ^ 2\\w = 9-x[/tex]
So, the length is given by:
[tex]l = \frac {A} {w}\\l = \frac {81-x ^ 2} {9-x}[/tex]
We factor the numerator:
[tex]l = \frac {(9 + x) (9-x)} {9-x}[/tex]
We simplify:
[tex]l = 9 + x[/tex]
So, the length is [tex]9 + x[/tex]
Answer:
[tex]9 + x[/tex]
Simplify.
V18
What is this simplify
Answer:
v To the power of 18
Step-by-step explanation:
N A
Answer:
v to the power of 18
Step-by-step explanation:
The area of a trapezoid is 322m2 one base is 12m and the height 14m what is the measure of the other base
Answer:
b = 34m
Step-by-step explanation:
Answer:
Depends on which base you mean, the longer base would be b=41.67
The shorter base would be a=39.67
Hope this helps :)
If f(x) = 2(3x) + 1, what is the value of f(2)?
Answer:
when x is 2. f(2)=3(2)+1. f(2)=6+1. f(2)=7.
Step-by-step explanation:
A sphere has a diameter of 10 ft. What is the surface area
Answer:
314.15926 square feet
Step-by-step explanation:
Formula for sphere surface area = 4*π r^2
radius = (1/2)*diameter = (1/2)* 10 feet = 5 feet
Area = 4* π*(5)^2 = 100π = 314.15926 square feet
Final answer:
The surface area of a sphere with a diameter of 10 ft is 100π square feet, or approximately 314.16 square feet.
Explanation:
The surface area of a sphere can be calculated using the formula 4πr², where r is the radius of the sphere. Given that the diameter of the sphere is 10 ft, the radius is half of that, which is 5 ft. Plugging the radius into the formula, we get the surface area as 4π(5 ft)² = 4π x 25 ft² = 100π ft². Therefore, the surface area of the sphere with a diameter of 10 ft is 100π square feet, which is approximately 314.16 square feet when π is approximated to 3.1416.
A 92.0 kg football player at 6.50 m/s North collides with an 85.0 kg football player running at 6.00 m/s south. The 92.0 kg football player continues moving at a velocity of 2.00 m/s after the collision. What is the velocity of the 85.0 kg football player after the collision?
Answer:
-1.13 m/s
Step-by-step explanation:
Parameters given:
Mass of first footballer, M = 92 kg
Initial velocity of first footballer, U = 6.5 m/s (taking North to be the +ve y axis)
Mass of second footballer, m = 85 kg
Initial velocity of second footballer, u = -6.0 m/s (taking South to be the -ve y axis)
Final velocity of first footballer, V = 2.0 m/s
We need to find the final velocity of the second football (v)
Applying the principle of conservation of momentum, we have that, in a system:
Total Initial Momentum = Total Final Momentum
(M * U) + (m * u) = (M * V) + (m * v)
(92 * 6.5) + (85 * -6) = (92 * 2) + (85 * v)
598 - 510 = 184 + 85v
88 = 184 + 85v
88 - 184 = 85v
-96 = 85v
=> v = -96 / 85
v = -1.13 m/s
The final velocity of the 85 kg player is -1.13 m/s i.e 1.13 m/s South
Final answer:
To find the unknown velocity of the 85.0 kg football player after the collision, we use the conservation of momentum, setting up an equation based on the initial and final momenta of both players and solving for the unknown velocity.
Explanation:
The question concerns the topic of conservation of momentum during a collision between two football players, which falls under the category of Physics. To solve for the velocity of the 85.0 kg football player after the collision, we can use the principle that the total momentum before the collision is equal to the total momentum after the collision in an isolated system.
The total momentum before the collision can be calculated as follows:
Momentum of the 92.0 kg player = mass × velocity = 92.0 kg × 6.50 m/s (North).
Momentum of the 85.0 kg player = mass × velocity = 85.0 kg × 6.00 m/s (South).
Since they are moving in opposite directions, we assign a positive direction (e.g., north) as positive momentum and the opposite direction (south) as negative momentum.
The total momentum after the collision consists of:
Momentum of the 92.0 kg player = 92.0 kg × 2.00 m/s (North).
Momentum of the 85.0 kg player = 85.0 kg × v (where v is the unknown velocity).
By applying the conservation of momentum, we can write the equation:
(92.0 kg × 6.50 m/s) + (85.0 kg × -6.00 m/s) = (92.0 kg × 2.00 m/s) + (85.0 kg × v).
Solving for v gives:
v = [(92.0 kg × 6.50 m/s) - (92.0 kg × 2.00 m/s) - (85.0 kg × -6.00 m/s)] / 85.0 kg.
Calculate the value to find the final velocity of the 85.0 kg player.
v = 10.87 m/s
I NEED HELP WITH MY MATHS HOMEWORK PLEASE!!
USE THE ATTACHED IMAGE BELOW TO HELP ME WORK OUT
B)
Answer:
What is your exact question?
Step-by-step explanation:
Explanation:
The notation [tex]A \cap B[/tex] means "the overlapped region between circles A and B". There is only one value in this region, and it is the "8". This is in the lower half of this region as the upper half is empty.
There are 12 values in the set {2,4,6,8,10,12,14,16,18,20,24} which we can see by counting them out, or we can note how 24 = 2*12 and how we started with 2 = 2*1. So basically we have...
2 = 2*14 = 2*26 = 2*38 = 2*410 = 2*512 = 2*614 = 2*716 = 2*818 = 2*920 = 2*1022 = 2*1124 = 2*12So again we have 1 value in the overlapped region between A and B, out of 12 values total. So that's why the answer is 1/12.
In an arcade, 12 tickets are awarded for every game won. Which table represents this relationship?
Answer:
B
Step-by-step explanation:
i hate edgunity too
Answer: b
Step-by-step explanation:
I need help please?!!!!
Answer: The answer would be .03 or A.
Step-by-step explanation: You add all of the marbles up to get a total of 10 then you divide 10 by 3 and you get 3.333333333 but then you just take off the 3 before the decimal. DONT USE THIS ON ANY OTHER EQUATIONS!!! This only happens to work with this equation!!!
Find the value of the expression
Answer:
The answer to your question is the letter C.
Step-by-step explanation:
Data
sin Ф = 1/5
cos Ф = ?
To solve this problem use trigonometric functions.
1.- The first condition is that the angle must be in the first quadrangle
(0° < Ф < 90°).
2.- Write the trigonometric function sine.
sin Ф = Opposite side / hypotenuse and sin Ф = 1/5
then, Opposite side = 1 hypotenuse = 5
3.- Use the Pythagorean theorem to find the adjacent side.
Hypotenuse² = Opposite side² + Adjacent side²
-Solve for Adjacent side
Adjacent side² = Hypotenuse² - Opposite sie²
-Substitution
Adjacent side² = 5² - 1²
-Simplification
Adjacent side² = 25 - 1
Adjacent side ² = 24
Adjacent side = √24
4.- Find the cosФ
cos Ф = Adjacent side/hypotenuse
-Substitution
cosФ = √24 / 5
The net below can be folded to form a square pyramid.
A square pyramid. The square base has side lengths of 9 inches. The triangular sides have a height of 6.1 inches and side length of 7.6 inches.
What is the surface area of the pyramid?
190.8 square inches
217.8 square inches
300.6 square inches
354.6 square inches
Answer:
190.8 square inches
Step-by-step explanation:
The area of one of its triangular sides is given by A = bh/2 were b = base = 9 inches and h = perpendicular height = 6.1 inches.
A = bh/2. Since we have 4 triangular sides, the total area of its sides A₁ = 4A = 4bh/2 = 2bh = 2 × 9 × 6.1 = 109.8 square inches.
The area of is base is the area of a square = 9² = 81 square inches.
So te total surface area is 109.8 square inches + 81 square inches = 190.8 square inches
Answer:
190.8
Step-by-step explanation:
Which of these is equal to 50 + 21?
The question is asking for the sum of 50 and 21. This is a mathematical operation known as addition. Following the steps of addition, the sum of 50 and 21 equals 71.
Explanation:The question is essentially asking for the sum of 50 and 21. In Mathematics, when we talk about 'equal to', we are referring to the result of an equation or mathematical operation.
So, to find out what is equal to 50 + 21, you simply add these two numbers together. The process is as follows:
Start by lining up the numbers by their place value.Add the ones place (0 + 1).Then, add the tens place (50 + 20).
After following these steps, you will find that 50 + 21 equals 71.
Learn more about Addition here:https://brainly.com/question/35006189
#SPJ2
out of 40 students In a class7 20% were absent how many students were present
Answer:
8 were absent
Step-by-step explanation:
20% of 40 is 8
Answer:
32 students were present
Step-by-step explanation:
total students =40
absent percent=20%
present percent= 100-20
=80%
total present student =80%of 40=32
Ann increased the quantities of all the ingredients in a recipe by 60%, percent. She used 80 grams (\text{g})(g)left parenthesis, start text, g, end text, right parenthesis of cheese. How much cheese did the recipe require?
Answer:
The recipe required 50 grams of cheese
Step-by-step explanation:
Here in the question, we are made to know that she increased all ingredients by 60%.
Now we want to know the original mass of the cheese if she used 80grams after the 60% increment.
Mathematically, the formula for percentage increase is;
% increase = increment/old value * 100%
Where increment is new value - old value
since we do not know the old value, we can say that it is x. This means that the increment is 80-x
Hence;
60= (80-x)/x * 100
60x = 100(80-x)
60x = 8000-100x
100x + 60x = 8000
160x = 8000
x = 8000/160
x = 50g
Which point is the center of the circle defined by the equation 2+(−9)2=81 x 2 + ( y − 9 ) 2 = 81 2+(−9)2=81 x 2 + ( y − 9 ) 2 = 81 Group of answer choices (0, -9) (-9, 0) (0, 9) (9, 0)
Answer:
(0, 9)
Step-by-step explanation:
The circle defined by the equation ...
(x -h)^2 +(y -k)^2 = r^2
has its center at (h, k).
We think your circle's equation is ...
x^2 + ( y − 9 )^2 = 81
so it would have its center where h = 0 and k = 9.
The center is (0, 9).
_____
Comment on the question
Sometimes, copying and pasting seems to cause things to be repeated 3 times, usually in different formats. It would be nice to have one clean copy of the equation, so we can easily tell what it is supposed to be. Editing may be required, to make sure all necessary math symbols are included.
Answer:
the whitebord is cool
Step-by-step explanation:
fun cool! 1234567890
9. Betsy's softball team won 47 games, lost
15 games, and tied none. What fractional
part of the games played did the team
win?
Answer:
47/62
Step-by-step explanation:
62 total games won 47 therefore 47/62
Final answer:
The fractional part of the games won by Betsy's softball team is 47/62, representing the number of games won out of the total games played.
Explanation:
To calculate the fractional part of the games won by Betsy's softball team, you need to divide the number of games won by the total number of games played. The team won 47 games and lost 15 games, giving a total of 47 + 15 = 62 games played.
The fraction representing the part of the games won is therefore 47/62. When simplified, this fraction may be reduced to a simpler form by finding the greatest common divisor and dividing both the numerator and the denominator by it. However, as 47 is a prime number and does not divide evenly into 62, the fraction can't be simplified further. Therefore, the fractional part of the games won by the team is 47/62.
Line k is parallel to line l. Lines k and l are parallel. Lines m and n intersect to form 2 triangles. The top triangle has angles 1, 2, 3 and the bottom triangle has angles 4, 5, 6. Which angle is congruent to Angle 4? Angle 1 Angle 2 Angle 5 Angle 6
Answer:
The line that is congruent to angle 4 is angle 1
hope this helped :)
Angle 4 is congruent to Angle 2 because they are alternate interior angles formed by the transversal intersecting two parallel lines.
Given that lines k and l are parallel, and lines m and n intersect to form two triangles, we need to determine which angle is congruent to Angle 4.From geometry, we know that alternate interior angles are congruent when two parallel lines are cut by a transversal. Here, lines m and n intersecting parallel lines k and l can be visualized as forming such alternate interior angles.Since Angle 4 is within the lower triangle, the angle in the upper triangle that is on the 'opposite' side of the transversal, corresponding to the same spot, is Angle 2.Congruence of Angles
Angle 4 ≈ Angle 2 (alternate interior angles)
Find two natural numbers whose product
is 50 and whose sum is 27.
Answer:
25 & 2
Step-by-step explanation: