Answers
Answer:
x = 24
Step-by-step explanation:
using the rule of exponents
[tex]a^{m}[/tex] × [tex]a^{n}[/tex] = [tex]a^{(m +n)}[/tex]
consider left side
[tex]5^{\frac{x}{6} }[/tex] × [tex]5^{\frac{x}{2} }[/tex]
= [tex]5^{\frac{x}{6} }[/tex] × [tex]5^{\frac{3x}{6} }[/tex]
= [tex]5^{\frac{4x}{6} }[/tex]
then
[tex]5^{\frac{4x}{6} }[/tex] = [tex]5^{16}[/tex]
since the bases on both sides are equal, both 5 then equate exponents
[tex]\frac{4x}{6}[/tex] = 16 ( multiply both sides by 6 )
4x = 96 ( divide both sides by 4 )
x = 24
Related Questions
If we want to know if diagonals or sides are congruent we would use the
formula.
distance
midpoint
slope
Answers
When we want to know if the diagonals or sides are congruent we would use the D. Slope.
What is congruent?It should be noted that congruent in geometry simply means when two objects have same shapes and size.
In this case, when we want to know if the diagonals or sides are congruent we would use the slope. This can show the equality in the shape.
Learn more about congruent on:
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helppp plsss. i have to turn this in asap
Answers
Answer:
y= 2x-5
Step-by-step explanation:
The slope formula is m=(y2-y1)/(x2-x1)
-3-1 / 1-3 = -4/-2= 2=m
The Y interception- y=mx+b using coordinates (3,1)
1=2(3)+b
1=6+b (subtracting 6 on both sides to isolate b)
-5=b
plug it in
y=2x-5
Write the log equation as an exponential equation. You do not need to solve for x.
log 5 (5) = 3x
Answers
Answer:
[tex]5=5^{3x}[/tex]
Step-by-step explanation:
[tex]log_5(5)=3x\\\\5=5^{3x}[/tex]
A polynomial p(x) has 3, 2-i, and √3 as its roots and goes through (0,-90), find p(x)
Answers
Answer:
p(x) = -2x⁵ +14x⁴ -28x³ -12x² +102x -90
Step-by-step explanation:
Assuming the desired polynomial has real and rational coefficients, each of the complex and irrational roots has a corresponding conjugate. That is, the roots of p(x) must include ...
{3, 2 -i, 2 +i, √3, -√3}
Each of these roots corresponds to a linear factor. Root p corresponds to factor (x -p), for example.
__
Factored formThen the factored p(x) will be ...
p(x) = k(x -3)(x -(2 -i))(x -(2 +i))(x -√3)(x +√3) . . . . for some scale factor k
Simplifying a bit, we have ...
p(x) = k(x -3)((x -2)² +1)(x² -3) = k(x -3)(x² -4x +5)(x² -3)
__
Scale factorAt x=0, this evaluates to ...
p(0) = k(0 -3)(0² -4·0 +5)(0² -3) = 45k
We want p(0) = -90, so we require ...
45k = -90
k = -2
__
Then the function p(x) factored to integers is ...
p(x) = -2(x -3)(x² -4x +5)(x² -3)
When we multiply this out, we find the standard form equation is ...
p(x) = -2x⁵ +14x⁴ -28x³ -12x² +102x -90
For a lab experiment, Jeremy needs to know the volume of a sample of tin with a mass of 189.8 grams.
Use the chart to find the volume of this sample of tin.
Answers
Answer:
26 cm^3
Step-by-step explanation:
189.8 gm / ( 7.3 gm / cm^3) = 26 cm^3
Answer:
C) 26cm
Step-by-step explanation:
hope it helps!
Which statements are true regarding the regular dodecagon? Check all that apply
Answers
Answer:
A dodecagon is a shape with 12 sides
Step-by-step explanation:
Decagon is 10 and do is 2 so 12
The table below shows Ashley's earnings on the job. Time (hours) Earnings (dollars) 18 $514.80 23 $657.80 31 $886.60 How much does she make in 11.25 hours
Answers
Answer:
$321.75
Step-by-step explanation:
k = y/x
514.80/18= 28.6
28.6 * 11.25 =321.75
Thus, Ashley will earn 321.75 in 11.25 Hours
~Lenvy~
Answer:
$321.75
Step-by-step explanation:
Formula ⇒ k = y/x
Dollar = y
x = Hour
Hence,
514.80/18= 28.6
28.6 × 11.25 =321.75
Therefore, Ashley will make $321.75 in 11.25 Hour
[RevyBreeze]
Which transformations are needed to change the parent cosine function to y = 0. 35 cosine (8 (x minus StartFraction pi Over 4 EndFraction))? vertical stretch of 0. 35, horizontal stretch to a period of 16 pi, phase shift of StartFraction pi Over 4 EndFraction units to the right vertical compression of 0. 35, horizontal compression to a period of 4 pi, phase shift of StartFraction pi Over 4 EndFraction units to the left vertical compression of 0. 35, horizontal compression to a period of StartFraction pi Over 4 EndFraction, phase shift of StartFraction pi Over 4 EndFraction units to the right vertical stretch of 0. 35, horizontal stretch to a period of StartFraction pi Over 4 EndFraction, phase shift of StartFraction pi Over 4 EndFraction units to the right.
Answers
The transformations that are needed to change the parent cosine function to y = 0.35×cos(8(x-π/4)) are:
vertical stretch of 0.35horizontal compression of period of [tex]\pi/4[/tex]phase shift of [tex]\pi/4[/tex] to rightHow does transformation of a function happens?The transformation of a function may involve any change.
Usually, these can be shift horizontally (by transforming inputs) or vertically (by transforming output), stretching (multiplying outputs or inputs) etc.
If the original function is [tex]y = f(x)[/tex], assuming horizontal axis is input axis and vertical is for outputs, then:
Horizontal shift (also called phase shift): Left shift by c units: [tex]y = f(x+c)[/tex]earlier)Right shift by c units: [tex]y = f(x-c)[/tex]output, but c units late)Vertical shift:Up by d units: [tex]y = f(x) + d[/tex]Down by d units: [tex]y = f(x) - d[/tex]Stretching:Vertical stretch by a factor k: [tex]y = k \times f(x)[/tex]Horizontal stretch by a factor k: [tex]y = f(\dfrac{x}{k})[/tex]For this case, we're specified that:
y = cos(x) (the parent cosine function) was transformed to [tex]y = 0.35\cos(8(x-\pi/4))[/tex]
We can see its vertical stretch by 0.35, right shift by [tex]\pi/4[/tex]horizontal stretch by 1/8
Period of cos(x) is of [tex]2\pi[/tex] length. But 1.8 stretching makes its period shrink to [tex]2\pi/8 = \pi/4[/tex]
Thus, the transformations that are needed to change the parent cosine function to y = 0.35×cos(8(x-π/4)) are:
vertical stretch of 0.35horizontal compression to period of [tex]\pi/4[/tex] (which means period of cosine is shrunk to [tex]\pi/4[/tex] which originally was [tex]2\pi[/tex] )phase shift of [tex]\pi/4[/tex] to rightLearn more about transformation of functions here:
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Element X decays radioactively with a half life of 7 minutes. If there are 980 grams of Element X, how long, to the nearest tenth of a minute, would it take the element to decay to 40 grams?
Answers
Answer:
32.3m
Step-by-step explanation:
Use equation A = Ao(0.5)^(t/t½)
Now input values: 40 = 980(0.5)^(t/7)
rearrange for t: t = [7ln(2/49)]/ / ln(0.5). Then from here, you can extract 32.3 as your answer
Answer:
t = 32.3 min
Step-by-step explanation:
This is an example of half-life exponential decay.
For situations like this we have a formula.
[tex]N = N_{0} * (\frac{1}{2})^n[/tex]
N represents the end amount of parent element, N (naught) represents the starting amount of the parent element, and n being the amount half-lifes that have occurred.
Now n, can be broken down further into t/p, which means the time elapsed (t) divided by time it takes for one decay period (p), which essentially gives you the amount of half-lifes that have occurred. So you can represent the formula as:
[tex]N = N_{0} * (\frac{1}{2})^{t/p}[/tex]
The question tells you you start off with 980 grams of Element x, so put that for N naught. [tex]N = 980g * (\frac{1}{2})^{t/p}[/tex]. Then it tells you half-life is 7 minutes, which means the period it takes for one half-life to occur is 7, which is p. [tex]N = 980g * (\frac{1}{2})^{t/7min}[/tex]. You are also told that you end up with 40 grams, so put that in for N. [tex]40g = 980g * (\frac{1}{2})^{t/7min}[/tex]. Now we solve for t, the time elapsed.
(This is the part where you use logs to solve, but if you are still rough on this, I'll walk you through it)
Start off by dividing on both sides.
[tex]\frac{40g}{980g} = (\frac{1}{2})^{t/7min} \\, \frac{2}{49} = (\frac{1}{2})^{t/7min}[/tex]
Take the log of both sides.
[tex]log(\frac{2}{49}) = log( (\frac{1}{2})^{t/7min})[/tex]
Now we gotta get t out of the exponent, we'll do this by using log laws. More specifically the exponent law for log laws which states. [tex]log(b^x) = x*log(b)[/tex]. If we apply that to our situation like so.. [tex]log((\frac{1}{2})^{t/7min}) = \frac{t}{7min} * log(\frac{1}{2})[/tex]
Now our whole equation now looks like this:
[tex]log(\frac{2}{49}) = \frac{t}{7min} * log( \frac{1}{2})[/tex]
keep simplifying,
[tex]\frac{log(\frac{2}{49}) }{log(\frac{1}{2}) } = \frac{t}{7min}[/tex]
[tex]7min *\frac{log(\frac{2}{49}) }{log(\frac{1}{2}) } = t\\\\t = 32.3min \\[/tex]
Now you have your answer!
Consider a dust mite that measures 10−3 millimeters in length and a gecko that measures 10 centimeters long. How many orders of magnitude as long as the mite is the gecko?
Answers
The gecko is about 10⁵ times bigger than the mite in length.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
1 cm = 10 ml
The dust mite measures 10⁻³ ml. The gecko measures 10 cm
Length of gecko = 10 cm = 10 cm * 10 ml per cm = 100 ml
Magnitude of gecko to mite = 100 ml / 10⁻³ ml = 10⁵
The gecko is about 10⁵ times bigger than the mite in length.
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Answer:
it is 5
Step-by-step explanation:
WILL GIVE BRAINLIEST FOR THE CORRECT ANSWER
Answers
Answer:
(3,5)
Step-by-step explanation:
We first need to substitute x for 3 in the equation :)
y = 2(3) - 1
y = 6 - 1
y = 5
The cordinate will be (3,5)
Have an amazing day!!
Please rate and mark brainliest!!
Which geometric figure would be the best to model a suitcase?
Answers
Answer:
A rectangular prism would be best to model a suitcase
Step-by-step explanation:
Hope that helps!
Answer:
Rectangular Prism
Step-by-step explanation:
If you look at a suitcase, it resembles a rectangular prism quite well.
Round to the ten millions place.
3,025,285,000
o a. 3,025,290,000
o b. 3,020,000,000
c. 3,025,000,000
d. 3,030,000,000
o e. 3,030,285,000
Answers
Draw a picture to answer.
what is 1/4 of 12?
Answers
Answer:
3
Step-by-step explanation:
1/4 x12= 12/4
12/4=3
Ms. Lee takes out a loan to start a business. She borrows $5,000 of a simple annual interest rate of 6. 5% for 5 years. What is the total amount of interest Ms Lee must pay
Answers
Answer:
A = $6,625.00
Step-by-step explanation:
A = P(1 + rt)
A = 5000(1 + (0.065 × 5)) = 6625
An isosceles triangle has an angle that measures 38degrees. What measures are possible for the other two angles? Choose all that apply.
Answers
Answer:
71° and 71°.⠀
Step-by-step explanation:
The triangle having two sides equal along with one different side is called an isosceles triangle.
⠀
So, Let us assume the other sides (two equal sides) of the isosceles triangle as x. As the different side is already given in the question.⠀
We know that,
The sum of all angles of a triangle is 180°⠀
So, According to the question :
⠀
[tex]{\longrightarrow \it\qquad { \ { { 38 \: }^{ \circ} + x + x = 180{}^{ \circ} }}}[/tex]
⠀
[tex]{\longrightarrow \it\qquad { \ { { 38 \: }^{ \circ} + 2x = 180{}^{ \circ} }}}[/tex]
⠀
[tex]{\longrightarrow \it\qquad { \ { 2x = 180{}^{ \circ} - { 38 \: }^{ \circ}}}}[/tex]
⠀
[tex]{\longrightarrow \it\qquad { \ { 2x = 142{}^{ \circ} }}}[/tex]
⠀
[tex]{\longrightarrow \it\qquad { \ { x = \dfrac{142{}^{ \circ}}{2} }}}[/tex]
⠀
[tex]{\longrightarrow \it\qquad { \pmb { x = 71^{ \circ} }}}[/tex]
⠀
Therefore,
The measure of the two other angles of the isosceles triangle are 71° and 71°.if there are 15 plane 2 crash 1 breakdown how many planes are left
Answers
Answer:
15 planes
Step-by-step explanation:
none disappear, just change shape/ability. its a riddle.
Answer:
15-2-1 = 15-3 = 12.
there are 12 planes left.
Step-by-step explanation:
hope this helped have a nice day
jeff is 1.67 meters tall how many centimeters tall is jeff
Answers
Answer:
167
Step-by-step explanation:
determine if the relationships are linear and if so are they proportional
Answers
Vertex ( 0, 2 )
Focus : ( 0, 7/4 )
Axis of symmetry : x = 0
Directrix : y = 9/4
Solve the equation for x:
3x+5=20
Answers
Answer:
x = 5
Step-by-step explanation:
3x+5=20
Subtract 5 from both sides.
3x=20−5
Subtract 5 from 20 to get 15.
3x=15
Divide both sides by 3.
x= 15/3
Divide 15 by 3 to get 5.
x=5
Please help! Will mark brainliest <3. (Click on the photo too see the question!) you need to select all angle pairs that are vertical angles.
Answers
Answer:
B and D
Step-by-step explanation:
vertical angles are ones that are formed by intersecting lines, and they are also equal to each other and opposite of each other.
its not A because they are not equal to each other.
B is correct because they are formed by intersecting line and equal to each other
C is incorrect since theres some random line that doesnt completely pass through on either side
D is correct
What is the reciprocal of look at the attachment
Answers
Answer:
5/2
Step-by-step explanation:
to find the reciprocal you just flip the fraction.
Answer:
the answer is 5/2 because reciprocal means to flip the equation
Step-by-step explanation:
please help I'm trying to write this in scientific notation
will give brainliest
Answers
Answer:
8.0 * 10^4
Step-by-step explanation:
Move the decimal so there is one non-zero digit to the left of the decimal point. The number of decimal places you move will be the exponent on the 10. If the decimal is being moved to the right, the exponent will be negative. If the decimal is being moved to the left, the exponent will be positive.
Answer:
8.0 x 10 4
Step-by-step explanation:
This is right
please no guessing (WILL GIVE BRAINILIST)
STATISTICS
Answers
Answer:
#2 mean is 90.3846154 and range is 40
#3 mean 91.9230769 and range is 20
(you might have mixed the second and third graph up)
Step-by-step explanation:
PLEASE HURRY! (once more)
A cooler contains three colas, seven root beers, and three ginger ales. Three people grab a drink at random, one at a time.
a) What is the probability that the first person grabs a cola, the second person grabs a ginger ale, and the third person grabs a cola?
b) What is the probability that the third person grabs a root beer given that the first two grabbed colas?
Answers
Answer:
a) 3/286
b) 7/286
Step-by-step explanation:
We start with 13 drinks. After the first person takes one drink, there are 12 drinks left, After the second person takes one drink, there are 11 drinks available for the third person.
a) From the 13 drinks, there are 3 colas, From the 12 remaining drinks, there are 3 ginger ales. From the 11 remaining drinks, there are 2 colas. We have:
[tex] \frac{3}{13} \times \frac{3}{12} \times \frac{2}{11} = \frac{3}{286} [/tex]
b) From the 13 drinks, there are 3 colas. From the 12 remaining drinks, there are 2 colas. From the 11 remaining drinks, there are 7 root beers. We have:
[tex] \frac{3}{13} \times \frac{2}{12} \times \frac{7}{11} = \frac{7}{286} [/tex]
A plane flies 100km north and then flies 400km south, what is its new position?
Answers
Answer:
300km south
Step-by-step explanation:
Go up once from original position then down four times
Help pleaseee i am awful at math
Answers
Step-by-step explanation:
use the above process and answer is $3.60
What is 3/7 as a decimal rounded to 3 decimal places?
Answers
What is the approximate volume of the tube? round to the nearest whole cubic centimeter. 1,005 cm3 1,340 cm3 3,351 cm3 4,021 cm3
Answers
The approximate volume of the cylinderical tube is 1005 cm³ round to the nearest whole cubic centimeter.
What is of volume of cylinder?Volume of cylinder is the amount of quantity, which is obtained by the bylinder in the 3 dimensional space.
Volume of cylinder is the can be given as,
[tex]V=\pi r^2h[/tex]
Here, (r) is the radius of the base of the cylinder and (h) is the height of the cylinder.
A cylindrical cardboard tube with a diameter of 8 centimeters and a height of 20 centimeters is used to package a gift.
The diameter is 8 cm and the radius of a cylinder is half of its radius. Thus the radius of the cylinder is,
[tex]r=\dfrac{8}{2}\\r=4\rm\; cm[/tex]
Put the values in the above formula a,s
[tex]V=\pi (4)^2(20)\\V=320\pi\\V=1005.31\\V=\approx 1005\rm\;cm^3[/tex]
The approximate volume of the cylinderical tube is 1005 cm³ round to the nearest whole cubic centimeter.
Learn more about the volume of cylinder here;
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The bearing of a point K from a point L is 084 degrees. What is the bearing of L from K
Answers
Answer:
if point bearing of k-l is 084 degree so the bearing of point l-k is 84 degree
The bearing of a point L from a point K is 264 degrees.
What is Addition?
A process of combining two or more numbers is called addition.
Given that;
The bearing of a point K from a point L is 084 degrees.
Now,
Since, The bearing of a point K from a point L is 084 degrees.
Hence, The bearing of a point L from a point K = 180° + 84°
= 264°
Thus, The bearing of a point L from a point K is 264 degrees.
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