Answer:
[tex]m=6[/tex]
Step-by-step explanation:
Exponent properties:
We can use exponent property [tex]a^{b^c}=a^{(b\cdot c)}[/tex] to solve this problem.
Rewrite [tex]8[/tex] as [tex]2^3[/tex], then apply exponent property [tex]a^{b^c}=a^{(b\cdot c)}[/tex] to simplify:
[tex]2^{3^5}=2^{2m+3},\\2^{15}=2^{2m+3}[/tex]
If [tex]a^b=a^c[/tex], then [tex]b=c[/tex], because of log property [tex]\log a^b=b\log a[/tex]. Using this log property, you can take the log of both sides and divide by [tex]\log a[/tex] to get [tex]b=c[/tex]
Therefore, we have:
[tex]15=2m+3[/tex]
Subtract 3 from both sides:
[tex]12=2m[/tex]
Divide both sides by 6:
[tex]m=\frac{12}{2}=\boxed{6}[/tex]
Alternative:
Given [tex]8^5=2^{2m+3}[/tex], to move the exponent down, we'll use log properties.
Start by simplifying:
[tex]\log 32,768=2^{2m+3}[/tex]
Take the log of both sides, then use log property [tex]\log a^b=b\log a[/tex] to move the exponent down:
[tex]\log(32,768)=\log 2^{2m+3},\\\log (32,768)=(2m+3)\log 2[/tex]
Divide both sides by [tex]\log2[/tex]:
[tex]2m+3=\frac{\log (32,768)}{\log(2)}[/tex]
Subtract 3 from both sides:
[tex]2m=\frac{\log (32,768)}{\log(2)}-3[/tex]
Divide both sides by 2:
[tex]m=\frac{\log (32,768)}{2\log(2)}-\frac{3}{2}=\boxed{6}[/tex]
Find the equation of the circle in standard form for the given center (h, k) and radius
Someone help
Answer:
3rd choice
Step-by-step explanation:
You can find the attached files
I have another question I need help with. How do I solve for the missing angle?
Answer:
The angle measures approximately 18.19°.
Step-by-step explanation:
Since we want to find the angle and we are given the side adjacent to the angle and the hypotenuse, we can use the cosine ratio. Recall that:
[tex]\displaystyle \cos \theta = \frac{\text{adjacent}}{\text{hypotenuse}}[/tex]
The adjacent side is 19 and the hypotenuse is 20. Substitute:
[tex]\displaystyle \cos \theta = \frac{19}{20}[/tex]
We can take the inverse cosine of both sides:
[tex]\displaystyle \theta = \cos^{-1}\frac{19}{20}[/tex]
Use a calculator (make sure you're in Degrees Mode!). Hence:
[tex]\theta \approx 18.19^\circ[/tex]
The angle measures approximately 18.19°.
if <ABC measures 100 and is inscribed in a circle O. find <BAO and <BCO
Answer:
<BCO = <BAO = 20degrees
Step-by-step explanation:
If <ABC measures 100 and is inscribed in a circle O. find <BAO and <BCO
To get <BAO and <BCO, we need to get <AOC first.
From the figure, it can be seen that triangle ABC is an isosceles trinagle. Hence;
<BAC + <BCA + 100 = 180
Since <BAC = <BCA
<BAC + <BAC = 180 - 100
2<BAC = 80
<BAC = 80/2
<BAC = 40
Also;
<BAO = <BCO and <BAO = <BAC/2
<BAO = 40/2 = <BCO
Hence <BCO = <BAO = 20degrees
Using Euler's formula, how
many edges does a polyhedron
with 5 faces and 5 vertices have?
[?] edges
Euler's Formula: F + V = E + 2
Answer:
8 edges
Step-by-step explanation:
Form the formula F+V=E+2
U make E the subject by moving everything thing else to the left hand side
F+V-2=E
this implies 5+5-2=E
10-2=E
therefore Edges = 8
The polyhedron with 5 faces and 5 vertices has 8 edges.
To determine the number of edges in a polyhedron with 5 faces and 5 vertices using Euler's formula (F + V = E + 2).
we need to substitute the given values into the equation.
Given:
Number of faces (F) = 5
Number of vertices (V) = 5
Substituting these values into Euler's formula, we have:
5 + 5 = E + 2
Simplifying the equation:
10 = E + 2
Subtracting 2 from both sides:
E = 10 - 2
E = 8
Therefore, the polyhedron with 5 faces and 5 vertices has 8 edges.
To learn more on Euler's formula click:
https://brainly.com/question/12274716
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If f(x) = 3x^2 + 4x-5, then f(-2) =
f(x) = 3x² + 4x - 5
So, f(-2)
= 3(-2)² + 4(-2) - 5
= 3(4) + (-8) - 5
= 12 - 8 - 5
= 4 - 5
= -1
Answer:
-1
Step-by-step explanation:
[tex]f(x) = 3x {}^{2} + 4x - 5 \\ f( - 2) = 3( - 2) {}^{2} + 4( - 2) - 5 \\ = 12 - 8 - 5 \\ = - 1[/tex]
3√75
simplest rationalizing factor
PLEASE DO ANSWER ONLY IF YOU KNOW IT
Answer:
the square root of 75 is 8.6
and 8.6 times 3 is
the answer is 25.8
Hope This Helps!!!
For a right triangle ABC, you are told that cos A = x and sin A = y. Which option below gives an expression that is equivalent to tan A? a. x/y b. y/x c. x/√x^2+y^2 d. y/√x^2+y^2
Answer:
B
Step-by-step explanation:
We know that
cos A = adjacent / hypotenuse
sin A = opposite / hypotenuse
Therefore, sin A / cos A =
(opposite / hypotenuse) / (adjacent / hypotenuse)
= (opposite/hypotenuse) * (hypotenuse / adjacent)
= opposite / adjacent
= tan A
Therefore, tan A = sin A / cos A = y/x
T is directly proportional to
[tex] \sqrt{x} [/tex]
T=400 when x = 625
(a) Find a formula for T in terms of x.
pls help i need it urgently Pls pls pls
Answer:
(a) T = 16√x
Step-by-step explanation:
T is directly proportional to √x, so we can say,
T=k√x (where k is a constant)
now, according to the question,
400=k×√625
400=k×25
k=16
so, putting the value of k in the equation, T=16√x
Answered by GAUTHMATH
Step-by-step explanation:
Given that ,
T is directly proportional to √x .Mathematically we can write it as ,
[tex]\implies T \propto \sqrt{x}[/tex]
Let k be the constant , therefore ,
[tex]\implies T = kx [/tex]
Now when T = 400 and x = 625 , lets find the value of k , as ,
[tex]\implies 400 = k\times 625 \\\\\implies k =\dfrac{400}{625}\\\\\implies k= 0.64 [/tex]
Therefore the required formula will be ,
[tex]\implies \underline{\underline{ T = 0.64x}} [/tex]
The incubation time for Rhode Island Red chicks is normally distributed with mean of 22 days and standard deviation of approximately 3 days. Of 1000 eggs are being incubated, how many chicks do we expect will hatch in 19 to 28 days
Answer:
We should expect 818 chicks to hatch in 19 to 28 days
Step-by-step explanation:
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Normally distributed with mean of 22 days and standard deviation of approximately 3 days.
This means that [tex]\mu = 22, \sigma = 3[/tex]
Proportion between 19 and 28 days:
p-value of Z when X = 28 subtracted by the p-value of Z when X = 19.
X = 28
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{28 - 22}{3}[/tex]
[tex]Z = 2[/tex]
[tex]Z = 2[/tex] has a p-value of 0.977.
X = 19
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{19 - 22}{3}[/tex]
[tex]Z = -1[/tex]
[tex]Z = -1[/tex] has a p-value of 0.159.
0.977 - 0.159 = 0.818
Out of 1000:
0.818*1000 = 818
We should expect 818 chicks to hatch in 19 to 28 days
Si el largo de un rectángulo mide el doble del ancho que es "a", ¿cuál es su área?
Answer:
El área es 2 veces el cuadrado del ancho del rectángulo.
Step-by-step explanation:
El área de un rectángulo viene dado por:
[tex] A = a*l [/tex]
En donde:
a: es el ancho
l: es el largo
Si el largo es el doble del ancho:
[tex] l = 2a [/tex]
Entonces el área es:
[tex] A = a*l = a*(2a) = 2a^{2} [/tex]
Por lo tanto, el área es 2 veces el cuadrado del ancho del rectángulo.
Espero que te sea de utilidad!
According to class 8 please solve
Answer:
i) 4x
ii) Father's age = 3(x + 10)
Son's age = x + 10
iii) 4x + 10 = 3(x + 10)
iv) Present age of the son = x = 20
Present age of the father = 4x = 4(20)
= 80
Step-by-step explanation:
Present age of the son = x
Present age of the father = 4x
Age of the son in 10 years = x + 10
Age of the father in 10 years = 3(x + 10)
4x + 10 = 3(x + 10)
4x + 10 = 3x + 30
4x - 3x = 30 - 10
x = 20
Find the value of y...........
Answer:
y=0
Step-by-step explanation:
9514 1404 393
Answer:
y = 0
Step-by-step explanation:
Factor out 3^y:
3^(2y-1) +2(3^(y-1)) = 1 . . . . . . given
(3^y)^2(3^-1) +2(3^y)(3^-1) = 1 . . . . factor out 3^y
(3^y)^2 +2(3^y) -3 = 0 . . . . . . . . . . subtract 1, multiply by 3
Let x = 3^y. Substituting, we have ...
x^2 +2x -3 = 0
(x -1)(x +3) = 0
x = 1 or x = -3 . . . . . values of x that satisfy this equation
Then the corresponding values of y are ...
x = 3^y . . . . . . . . . . . . relation of x and y
log(x) = y·log(3) . . . . . take logs to solve for y
y = log(x)/log(3) . . . . . divide by the coefficient of y
For x = 1, this is y = log(1)/log(3) = 0
For x = -3, this is y = log(-3)/log(3) . . . . no real solutions
The only real solution is y = 0.
_____
The attachment shows the solution of f(x) = 0, where ...
[tex]f(x)=3^{2x-1}+2\times3^{x-1}-1[/tex]
That solution is x=0. This means the (real) solution to the given equation is y=0.
18 - (-f) = 91 (With work please)
18 - (-f) = 91
Subtracting a negative value changes to addition:
18 + f = 91
Subtract 18 from both sides:
F = 73
Answer:
f = 73
Step-by-step explanation:
Solve for f
18 - ( - f ) = 91
Remove the parantheses and change their sign.18 + f = 91
subtract each side by 1818 - 18 + f = 91 - 18
calculatef = 73
Set up a proportion to solve for x in the following similar triangles.
Answer:
C
Step-by-step explanation:
I took the quiz and it was C! Hope this helps :)
On a coordinate plane, line D F goes through points (negative 1, negative 3) and (2, 3). Point G is at (negative 4, negative 4).
The line passes through the y-axis at point (0,4).
Step-by-step explanation:
On a coordinate plane, line DF goes through points (-1,-3) and (2,3).
So, the slope of the line DF is \frac{- 3 - 3}{- 1 - 2} = 2
−1−2
−3−3
=2
Then the straight line which is parallel to DF will be given by
y = 2x + c.
Where, c is any constant and we have to evaluate it if this line passes through the point (-4,-4).
So, - 4 = 2(- 4) + c
⇒ c = 4
So, the straight line which is parallel to DF and passes through the point (-4,-4) is y = 2x + 4.
Now, putting x = 0, we get, y = 4.
Therefore, the line passes through the y-axis at point (0,4). (Answer)
Answer:
The answer would be D
Step-by-step explanation:
Somebody please help me! Very confused, the help is very much appreciated!
Answer:
18
Step-by-step explanation:
Because the diagonals in a parallelogram bisect each other, RS = SP = 18
BRAINLIEST PLEASEEEEE
Can someone help me with this math homework please!
Answer:
3. The number of students that rode on each bus
Step-by-step explanation:
The equation they give us is:
2b + 6 = 70
The question already tells us that in this equation:
2 is the 2 buses that the school hired
6 is the 6 leftover kids who couldn't fit on the 2 buses
The question also tells us that the 2 buses only have a total of 64 seats, so 32 seats on 1 bus (64/2 = 32).
So that means b would equal the 32 seats on 1 bus, or the number of students that rode on each bus.
Hope it helps (●'◡'●)
PLEASE HELP FAST WILL MARK BRAINLIEST!!!!!!
Which table of ordered pairs represents a proportional relationship? (Look at the picture and tap to see the full picture)
Answer: the second one
Step-by-step explanation:
Answer:
The asnwer is D
Step-by-step explanation:
D is a proportional relationship because
-3*-4 is 12
-6*-4 is 24
-9*-4 is 36
Hope this helps! :)
álgebra 1solve 4( -15x - 2) + 8
Answer:
-60x
Step-by-step explanation:
We simply open up the bracket and collect similar terms
So we have;
4(-15x-2) + 8 as:
4(-15x) -2(4) + 8
-60x -8 + 8
= -60x
Answer: 60x
Step-by-step explanation: -60x-8+8=-60x
the first day she walked 27 kilometers. each day since she walked 2/3 of what she walked the day before. what is the total distance cecelia has traveled be the end of the 5th day?
Answer: 70
Step-by-step explanation:
We are required to calculate the total distance Cecilia travelled in 5 days
The total distance Cecilia travelled for 5 days is 99 kilometers
Day 1 = 27 kilometers
Day 2 to day 5 = 2/3 of 27
= 2/3 × 27
= 2 × 9
= 18 kilometers each day
Total distance = day 1 + day 2 + day 3 + day 4 + day 5
= (27 + 18 + 18 + 18 + 18) kilometers
= 99 kilometers
Therefore, the total distance Cecilia travelled for 5 days = 99 kilometers
Read more:
https://brainly.com/question/17207658
Find the measure of the indicated angle to the nearest degree using trig functions. (if you can also give me step by step on how to get the answer that would be great)
A) 21°
C) 20°
B) 70°
D) 9°
Answer:
A ; 21
Step-by-step explanation:
Here, the side facing the right angle is the hypotenuse and it has a measure of length 42
The side facing the missing angle is the opposite and it has a length of 15
The trigonometric ratio that connects the hypotenuse and the opposite is the sine
The sine of an angle is the ratio of the opposite to the hypotenuse
Thus;
sine ? = 15/42
sine ? = 0.357
? = arc•sim 0.357
? = 21 degrees
Which equation in slope-intercept form represents a line that is parallel to y=1/2x-2 and passes through the point (-8,1)?
Answer:
[tex]\displaystyle y=\frac{1}{2}x+5[/tex]
Step-by-step explanation:
We want to find the slope in slope-intercept form of a line that is parallel to:
[tex]\displaystyle y=\frac{1}{2}x-2[/tex]
And passes through the point (-8, 1).
Recall that parallel lines have equivalent slopes.
Since the slope of our given line is 1/2, the slope of our new line must also be 1/2.
We are also given that it passes through the point (-8, 1). Since we are given a slope and a point, we can use the point-slope form:
[tex]y-y_1=m(x-x_1)[/tex]
Substitute 1/2 for m and (-8, 1) for (x₁, y₁). Hence:
[tex]\displaystyle y-(1)=\frac{1}{2}(x-(-8))[/tex]
Since we want the equation in slope-intercept form, we can isolate y. Distribute:
[tex]\displaystyle y-1=\frac{1}{2}x+4[/tex]
Therefore, our equation is:
[tex]\displaystyle y=\frac{1}{2}x+5[/tex]
use abc to find the value of sin b
Answer:
12/37
Step-by-step explanation:
We know ,
=> sin B = p/h
=> sin B = 12/ 37
Answer:
Step-by-step explanation:
[tex]Sin \ B = \frac{opposite \ side }{hypotenuse}\\\\Sin \ B = \frac{35}{37}\\\\[/tex]
What does 8 represent in the decimal 478.92?
Answer:
ones
Step-by-step explanation:
help me pllllllssssssssssssss
d, because the plastic has a difference of 2000 with respect to food
What term is used for a bell-shaped curve that is symmetrical regarding the average value of the population (the data being analyzed)?
Answer:
Normal distribution
Step-by-step explanation:
The answer is "normal distribution". This is because in a normal distribution, the mean, median and mode are equal. What this means is that the distribution will be symmetrical with a bell curve unlike in positive or negative skew where it is skewed to either the left or right.
This frequency table represents the number of cars owned by each family on a street.
What is the mean number of the cars owned by each family?
A. 2.5
B. 3
C. 4
D. 5.5
Step-by-step explanation:
1+2+3+4+5=14 divided by 5=2.8 so, A.would be your answer.
Can someone help me with this math homework please!
A ball is thrown straight out at 80 feet per second from an upstairs window that's 15 feet off the ground. Find the ball's horizontal distance from the window at the moment it strikes the ground.
a. 0.96825
b. Can't be found
c. 77.46
d. 6.33
e. 212.23
Answer:
Step-by-step explanation:
In order to find the horizontal distance the ball travels, we need to know first how long it took to hit the ground. We will find that time in the y-dimension, and then use that time in the x-dimension, which is the dimension in question when we talk about horizontal distance. Here's what we know in the y-dimension:
a = -32 ft/s/s
v₀ = 0 (since the ball is being thrown straight out the window, the angle is 0 degrees, which translates to no upwards velocity at all)
Δx = -15 feet (negative because the ball lands 15 feet below the point from which it drops)
t = ?? sec.
The equation we will use is the one for displacement:
Δx = [tex]v_0t+\frac{1}{2}at^2[/tex] and filling in:
[tex]-15=(0)t+\frac{1}{2}(-32)t^2[/tex] which simplifies down to
[tex]-15=-16t^2[/tex] so
[tex]t=\sqrt{\frac{-15}{-16} }[/tex] so
t = .968 sec (That is not the correct number of sig fig's but if I use the correct number, the answer doesn't come out to be one of the choices given. So I deviate from the rules a bit here out of necessity.)
Now we use that time in the x-dimension. Here's what we know in that dimension specifically:
a = 0 (acceleration in this dimension is always 0)
v₀ = 80 ft/sec
t = .968 sec
Δx = ?? feet
We use the equation for displacement again, and filling in what we know in this dimension:
Δx = [tex](80)(.968) +(0)(.968)^2[/tex] and of course the portion of that after the plus sign goes to 0, leaving us with simply:
Δx = (80)(.968)
Δx = 77.46 feet
what are the lengths of SV and QT? no links.
ok so we see that TR is 17 units, so RV is the same amount
3x+2 so 3x=15 so divide both sides by 3 we get x=5
now we know x=5 4x+1=21 and 9x-4=41
*drops microphone*
Answer:
TR = 12
=> 3x + 2 =17
=> x = 5
We have QT = QV (because QTV is an isosceles triangle)
=> QT = 4x+1=4x5+1=21 units
We have TS = SV (because TSV is an isosceles triangle)
=>SV = 9x-4= 9x5-4=41 units