Answer:
3×3×3⁄3×3×3×2
Step-by-step explanation:
27 = 3×3×3
54 = 3×3×3×2
The prime factored form of 27⁄54 is thus;
3×3×3⁄3×3×3×2
Answer:
D= 3×3×3/2×3×3×3
Step-by-step explanation:
A prime factored form breaks the number into prime numbers that give the same value when multiplied
27= 3×3×3
54=2×3×3×3
To get the simplest form of a fraction you proceed with division.
=3×3×3 / 2×3×3×3.............................cancel 3 in the numerator and denominator
= 1/2
If sin=3/5 then what does tan equal
Answer:
Not sure if this is correct but maybe it is 34?
Answer: [tex]tan(x)=\±\frac{3}{4}[/tex]
Step-by-step explanation:
You know that [tex]sin(x)=\frac{3}{5}[/tex] and you can identify that. Then:
[tex]sin^2(x)=(\frac{3}{5})^2[/tex]
[tex]sin^2(x)=\frac{9}{25}[/tex]
Remember that:
[tex]cos^2(x)=1-sin^2(x)[/tex]
Then [tex]cos^2(x)[/tex] is:
[tex]cos^2(x)=1-\frac{9}{25}\\\\cos^2(x)=\frac{16}{25}[/tex]
Apply square root to both sides to find cos(x):
[tex]\sqrt{cos^2(x)}=\±\sqrt{\frac{16}{25}}\\cos(x)=\±\frac{4}{5}[/tex]
Remember that:
[tex]tan(x)=\frac{sin(x)}{cos(x)}[/tex]
Then, this is:
[tex]tan(x)=\frac{\frac{3}{5}}{\±\frac{4}{5}}[/tex]
[tex]tan(x)=\±\frac{3}{4}[/tex]
What is the sum of the series?
For this case we must find the sum of the given series. For this we must expand the series for each value of k.
[tex](-2 (3) +5) + (- 2 (4) +5) + (- 2 (5) +5) + (- 2 (6) +5) =\\(-6 + 5) + (- 8 + 5) + (- 10 + 5) + (- 12 + 5) =[/tex]
Different signs are subtracted and the sign of the major is placed, while equal signs of sum and the same sign is placed.
[tex]-1-3-5-7 =\\-16[/tex]
The value of the series is -16
ANswer:
-16
Heya!
--------------------
Things to know before we solve:
The "6" at the top means that the the sequence only goes to the 6th term.
k = 3 represents that the sequence starts with the 1st term.
(-2k + 5) represents the rule of the sequence, we can substitute 3, 4, 5, and 6 to solve for the terms of the sequence.
--------------------
Solving for each term:
3rd term:
-2(3) + 5
-6 + 5
-1
4th term:
-2(4) + 5
-8 + 5
-3
5th term:
-2(5) + 5
-10 + 5
-5
6th term:
-2(6) + 5
-12 + 5
-7
--------------------
Simplifying:
Write these terms in expanded form:
(-1) + (-3) + (-5) + (-7)
Find the sum of the series:
(-1) + (-3) + (-5) + (-7) = -16
--------------------
Answer:
The sum of the series is -16
--------------------
Best of Luck!
Express the given logarithm in terms of common logarithms. Then approximate its value to four decimal places.
log2 11
Answer:
3.4594
Step-by-step explanation:
To change the base of a logarithm
• [tex]log_{b}[/tex] x = [tex]\frac{log_{c}x }{log_{c}b }[/tex]
where c represents the new base
Changing the base from 2 to 10
[tex]log_{2}[/tex] 11 = [tex]\frac{log_{10}11 }{log_{10}2 }[/tex] ≈ 3.4594
Over a period of 12 weeks, Carlos ran an average of 21 miles per week. How many kilometers is this? Round your answer to the nearest hundredth. (1 km = 0.621 mi.)
405.80
13.04
33.82
156.49
Answer:
405.80
Step-by-step explanation:
So, we know Carlos ran 21 miles per week, for 12 weeks....
That makes 21 mi/wk x 12 weeks = 252 miles.
Then we know each km is 0.621 mile.
So, we divide 252 miles by 0.621 mile/km to get= 405.80 km
Dividing miles by miles/km gives us the unit we want (km).
There was a trap in this question, because if instead of dividing the 252 miles by 0.621 you would have multiplied it, you would have gotten another answer listed... just not the right one. :-)
If x is 6, then 7x =
Answer:42
Step-by-step explanation:
7 multiplied by 6= 42
Insert 6 in the x place and solve
7x
7(6)
^^^The parentheses is the same as saying 7 × 6
so...
42
Hope this helped!
~Just a girl in love with Shawn Mendes
plz help god blees if you do it all i will give u BRAINLIEST
it's the first one !!! so it's A
if f(x) =-x^2+3x+5 and g(x)=x^2+2x, which graph shows the graph of (f+g)(x)?
For this case we have the following functions:
[tex]f (x) = - x ^ 2 + 3x + 5\\g (x) = x ^ 2 + 2x[/tex]
We must find (f + g) (x), by definition we have to:
[tex](f + g) (x) = f (x) + g (x)[/tex]
So:
[tex](f + g) (x) = - x ^ 2 + 3x + 5 + (x ^ 2 + 2x)\\(f + g) (x) = - x ^ 2 + 3x + 5 + x ^ 2 + 2x\\(f + g) (x) = 5x + 5[/tex]
ANswer:
See attached image
Answer:
Step-by-step explanation:
see graph below
What is the product of (-a+3)(a+4)
Answer:
-a^2 -4a +3a +12
-a^2 -1a +12
Step-by-step explanation:
i need help im stuck on this
Hello There!
Before getting started, we should remember that the top surface and the bottom surface of any cylinder are congruent to each other.
First, we use the formula pi*radius^2 to find the area of a circle since there is always a circle in a cylinder.
Next, we multiply pi*radius^2 * height because a cylinder has a height too.
HOW TO SOLVE
First, we multiply 3.14 which is equal to pi by 25 because the radius is 5 and in the formula we used, it states radius squared so 3.14 multiplied by 25 and then multiplied by the height of our cylinder which equals 6.
Once we multiply, we get a product of 471.
Our final answer is 471.units^3
Find the sum of the measures of the interior angles of each convex polygon decagon
Answer:
Nvm about those questions the answer is 1440 degrees
Step-by-step explanation:
What is the 6th term of this sequence? 8,-12,18-27
Answer:
-60.75
Step-by-step explanation:
-12 / 8 = -3/2
18 / -12 = -3/2
-27 / 18 = -3/2
This is a geometric sequence with a common ratio of -3/2.
an = 8 (-3/2)^(n-1)
The sixth term is:
a₆ = 8 (-3/2)^(6-1)
a₆ = 8 (-3/2)^5
a₆ = -60.75
Line t intersects the line given by y=4x-2 at the point (4,14) to form a right angle. Which is the equation of line t
Answer:
y = -1/4 x + 15.
Step-by-step explanation:
y = 4x - 2 has a slope of 4 ( = the coefficient of x).
The line at right angles to it will therefore of a slope of -1/4.
Using the point-slope form of a line the line t which passes through (4, 14) is found as follows:
y - 14 = -1/4(x - 4)
y = -1/4x + 1 + 14
y = -1/4x + 15
The function f(x) is graphed below.
Use the graph of the function to find, f(1).
-2
-1
1
2
Answer:
f(1) = 2
Step-by-step explanation:
Since y is a function of x, that is;
y = f(x)
f(1) implies the value of y when x = 1.
To obtain this value we draw the vertical line x = 1 and check where the line intersects the graph of f(x).
In this case, the line x = 1 will intersect with the graph of f(x) on the line y = 2. The function f(x) assumes the value 2 between x = 0 and x = 4. Therefore,
f(1) = 2
Answer:
f(1) = 2
Step-by-step explanation:
a school is running a fundraiser. for every $75 worth of wrapping paper sold, the school receives $20. how much wrapping paper must be sold to reach he fundraising goal of $2,500
Answer:
$9259.26
Step-by-step explanation:
The school receives $20 on $75.
We can calculate the percentage by using the values.
20/75 = 0.27%
The school recieved 0.27% of the payment.
Now we know the target amount and percentage, we can calculate the principal amount here.
Let x dennote the worth on which the school will recieve 2500 dollars. [tex]2500 = x * 0.27\\x = \frac{2500}{0.27}\\ x = 9259.26[/tex]
$9259.26 worth of ribbon has to be sold for the school to get $2500 ..
COSO ---
(3-
O Example: Find the a
a) u =<4,3% and v= <2,5)
calculator
may-
9/15V29)
35. Determine the values of x that cause the polynomial function to be zero, positive, and negative:
f(x) = (x-7)(3x + 4)(x + 4).
Answer:
• zero: -4, -4/3, 7
• positive: -4 < x < -4/3 . . . or 7 < x
• negative: x < -4 . . . or -4/3 < x < 7
Step-by-step explanation:
Zeros of the function are at x=-4, -4/3, +7. These are the values that make each of the individual factors be zero. For example, x-7=0 when x=7.
The function will be negative for x-values left of an odd number of zeros. It will be positive for x-values left of an even number of zeros (including left of no zeros, which is to say right of all zeros). This is because the sign of the factor giving rise to the zero changes for x-values on either side of that zero. (This is not true for zeros with even multiplicity, as the sign does not change at those.)
Write an equation for the line that passes through (-8.5,11) and (5,-2.5)
Answer:
The equation is y = -x + 2.5
Step-by-step explanation:
* Lets explain how to solve the problem
- The form of the equation of a line is y = mx + c , where m is the slope
of the line and c is the y-intercept
- The y-intercept means the line intersect the y-axis at point (0 , c)
- The slope of the line which passes through points (x1 , y1) , (x2 , y2)
is [tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
* Lets solve the problem
∵ The line passes through the points (-8.5 , 11) and (5 , -2.5)
- Let point(x1 , y1) = (-8.5 , 11) and point (x2 , y2) = (5 , -2.5)
∴ x1 = -8.5 , x2 = 5 and y1 = 11 , y2 = -2.5
∴ [tex]m=\frac{-2.5-11}{5-(-8.5)}=\frac{-13.5}{5+8.5}=\frac{-13.5}{13.5}=-1[/tex]
∴ The slope of the line is -1
∵ y = mx + c
∴ y = -x + c
- To find c substitute x and y in the equation by the coordinates of
one of the two points
∵ Point (5 , -2.5) lies on the line
∴ x = 5 at y = -2.5
∵ y = -x + c
∴ -2.5 = -(5) + c
∴ -2.5 = -5 + c
- Add 5 to both sides
∴ c = 2.5
∴ y = -x + 2.5
* The equation is y = -x + 2.5
The slope and y-intercept to get y = -x + 2.5.
The slope is calculated using the formula m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the given points. Substituting the given points into the formula, we get m = (-2.5 - 11) / (5 - (-8.5)) = -13.5 / 13.5 = -1.
Next, we use the slope-intercept form of a line, y = mx + b, to find the y-intercept (b). Substituting one of the points and the slope into this equation, for example, (-8.5, 11), gives us 11 = (-1)(-8.5) + b, which simplifies to b = 2.5.
Therefore, the equation of the line is y = -x + 2.5.
You ask a friend to think of a
number from four to twelve. What
is the probability that his number
will be 8?
The answer is 1/9 or about 11%.
Answer:8
Step-by-step explanation: it’s right
Ann needs 3/4 of a book in 2 days. At this rate how many books can she read in 4 1/3 days.
Answer: 1 5/8 or 13/8. They are the same.
Step-by-step explanation to find the amount of books she reads in 4 1/3 says, first you need to find how much she reads in 1 day.
3/4 divided by 2 = 3/4 x 1/2=3/8.
Now you need to multiply 3/8 by 4 1/3 to find how many books she can reed in a day. 4 1/3= 13/3. 13/3 x 3/8= 39/24 = 13/8 = 1 5/8
Answer: 2.888889
Step-by-step explanation:
3/4 book 4 1/3 book
------------- = ---------------
2 days x days
4 1/3= 13/3
3/4= 0.75
1.5x= 13/3
--------- -------
1.5 1.5
x= 2.888889 books
I need to know what is 7 percent of 98800
Answer:6,916
6,916
How to find the number:
The decimal of seven percent is 0.07. Take that times 9880
Which is a solution for this equation? Log base 2 x = 2 - log base 2 (x - 3)
X = 1
X = 2
X = 3
X = 4
X = 5
Answer: Fourth Option
[tex]x =4[/tex]
Step-by-step explanation:
First we write the equation
[tex]log_2(x) = 2- log_2(x-3)[/tex]
Now we use the properties of logarithms to simplify the expression
[tex]log_2(x)+log_2(x-3) = 2[/tex]
The property of the sum of logarithms says that:
[tex]log_a (B) + log_a (D) = log_a (B * D)[/tex]
Then
[tex]log_2[x(x-3)]= 2[/tex]
Now use the property of the inverse of the logarithms
[tex]a ^ {log_a (x)} = x[/tex]
[tex]2^{log_2[(x)(x-3)]}= 2^2[/tex]
[tex](x)(x-3))}= 4[/tex]
[tex]x^2-3x -4=0[/tex]
[tex]x^2-3x -4=(x-4)(x+1)=0[/tex]
Then the solution are
[tex]x= -1[/tex] and [tex]x= 4[/tex]
We take the positive solution because the logarithm of a negative number does not exist
Finally the solution is:
[tex]x =4[/tex]
17400 invested at a rate of 2.5% compounded annually; 8 years
Answer:
348
Step-by-step explanation:
PLEASE HELP!
The water tank in the diagram is in the shape of an inverted right circular cone. The radius of its base is 16 feet, and its height is 96 feet. What is the height, in feet, of the water in the tank if the amount of water is 25% of the tank’s capacity?
Answer:
The height of the water is [tex]60.5\ ft[/tex]
Step-by-step explanation:
step 1
Find the volume of the tank
The volume of the inverted right circular cone is equal to
[tex]V=\frac{1}{3}\pi r^{2} h[/tex]
we have
[tex]r=16\ ft[/tex]
[tex]h=96\ ft[/tex]
substitute
[tex]V=\frac{1}{3}\pi (16)^{2} (96)[/tex]
[tex]V=8,192\pi\ ft^{3}[/tex]
step 2
Find the 25% of the tank’s capacity
[tex]V=(0.25)*8,192\pi=2,048\pi\ ft^{3}[/tex]
step 3
Find the height, of the water in the tank
Let
h ----> the height of the water
we know that
If two figures are similar, then the ratio of its corresponding sides is proportional
[tex]\frac{R}{H}=\frac{r}{h}[/tex]
substitute
[tex]\frac{16}{96}=\frac{r}{h}\\ \\r= \frac{h}{6}[/tex]
where
r is the radius of the smaller cone of the figure
h is the height of the smaller cone of the figure
R is the radius of the circular base of tank
H is the height of the tank
we have
[tex]V=2,048\pi\ ft^{3}[/tex] -----> volume of the smaller cone
substitute
[tex]2,048\pi=\frac{1}{3}\pi (\frac{h}{6})^{2}h[/tex]
Simplify
[tex]221,184=h^{3}[/tex]
[tex]h=60.5\ ft[/tex]
Please help I'm very confused
30 ≥ g [keyword - "no more than"
4 ≤ i [keyword - "at least"]
Winona’s bowling scores for the past nine weeks are 195, 180, 195, 212, 208, 231, 179, 246, and 195. Find the mean, median, and mode. Round to the nearest tenth, if necessary.
Winona's bowling scores have a mean of 204.6, a median and mode both of 195.
To find the mean, median, and mode of Winona's bowling scores, we follow these steps:
Mean: Add all the scores together and divide by the number of scores.Median: Arrange the scores in ascending order and find the middle score.Mode: Identify the score that occurs most frequently.The bowling scores are 195, 180, 195, 212, 208, 231, 179, 246, and 195.
Mean: (195 + 180 + 195 + 212 + 208 + 231 + 179 + 246 + 195) / 9 = 1841 / 9 = 204.6
The mean score is 204.6.
To find the median, we first arrange the scores in ascending order: 179, 180, 195, 195, 195, 208, 212, 231, 246.
The median, or the middle score, is the fifth one since there are an equal number of scores on either side of it, which is 195.
The mode is the number that appears most often, which is also 195.
Therefore, Winona's mean score is 204.6, the median score is 195, and the mode is 195.
Find the distance between the points ( - 16, - 9) and ( - 16, - 18).
notice, the x-coordinate is the same for both points, thus is a vertical line.
Check the picture below.
To find the distance between the points (-16, -9) and (-16, -18), subtract the y-coordinates, which gives us a distance of 9 units.
To find the distance between the points (-16, -9) and (-16, -18), we can use the distance formula for two points in a Cartesian coordinate system. However, because the x-coordinates of the two points are the same, this means that the line connecting these two points is vertical, and we can simply subtract the y-coordinates to find the distance.
The distance formula in a two-dimensional Cartesian coordinate system is:
d = √((x₂ - x₁)² + (y₂ - y₁)²)
Since the x-coordinates are identical, the formula simplifies to:
d = |y₂ - y₁|
Applying this to the points given:
d = |-18 - (-9)|
d = |-18 + 9|
d = |-9|
Therefore, the distance is 9 units.
Help! Can someone please explain how to do this. I have my final in one hour.
Answer:
n= -3 and n= -6
Step-by-step explanation:
[tex]n^2 = -18 -9n[/tex]
We need to solve this equation to find the value of n.
Rearranging:
[tex]n^2 +9n +18 =0[/tex]
This is a quadratic equation and we can solve by using factorization method.
We need to make factors of 18n^2 such that their sum is equal to 9n.
So solving,
[tex]n^2 + 9n +18 =0\\n^2 + 6n + 3n +18 =0\\n(n+6) + 3(n+6)=0\\(n+3)(n+6) =0\\=> n+3 =0 \,\, and n+6 =0\\n= -3 \,\,and \,\,n=-6[/tex]
kate has 567 cars she put 77 on each table how many cars does she have left
Answer:
well how many tables are there?
Step-by-step explanation:
The volume of a sphere is 3052.08 units cubed what is its diameter?
The diameter of the sphere is approximately 19.82 units.
To calculate the diameter of a sphere given its volume, we'll use the formula for the volume of a sphere:
[tex]\[ V = \frac{4}{3}\pi r^3 \][/tex]
Where:
- [tex]\( V \)[/tex] is the volume of the sphere,
- [tex]\( \pi \)[/tex] is a mathematical constant (approximately equal to 3.14159),
- [tex]\( r \)[/tex] is the radius of the sphere.
Since we have the volume, we rearrange the formula to solve for the radius:
[tex]\[ r = \sqrt[3]{\frac{3V}{4\pi}} \][/tex]
Substituting the given volume [tex]\( V = 3052.08 \)[/tex], and the value of[tex]\( \pi \)[/tex], we can find the radius:
[tex]\[ r = \sqrt[3]{\frac{3 \times 3052.08}{4 \times 3.14159}} \][/tex]
[tex]\[ r \approx \sqrt[3]{\frac{9156.24}{12.56636}} \][/tex]
[tex]\[ r \approx \sqrt[3]{729.128} \][/tex]
[tex]\[ r \approx 9.85 \][/tex]
Now, to find the diameter, we double the radius:
[tex]\[ \text{Diameter} = 2 \times r \][/tex]
[tex]\[ \text{Diameter} = 2 \times 9.85 \][/tex]
[tex]\[ \text{Diameter} \approx 19.82 \][/tex]
So, the diameter of the sphere is approximately 19.82 units.
To recap, we first found the radius of the sphere using the formula for volume, then we doubled the radius to find the diameter.
Complete question:
The volume of a sphere is 3052.08 units cubed what is its diameter?
which equation can be used to solve for b?
Answer:
First option
b = (8) * Tan (30)
Step-by-step explanation:
Tan (B) = Oppo. / Adj.
Tan (B) = AC/BC
Tan (30) = b / 8
b = (8) * Tan (30)
Answer
First option
b = (8) * Tan (30)
The graph below is correct for the linear equation y=-3.
True
False
Answer:
False.
Step-by-step explanation:
The graph that is shown is correct for the equation x= -3. The graph for y= -3 would run vertically, not horizontally.
Answer:
True
Step-by-step explanation:flip it and reverse it its esrever dna ti pilf