27 exponent x/3 = 1/81
we can say exponent as power also
(27 power x) × (3 power -1) = 81 power -1
(3 power 3x) × ( 3 power -1) = 3 power -4
IN MULTIPLICATION WHEN BASES ARE SAME THEN POWERS ARE ADDED
3 power 3x + (-1) = 3 power -4
IN AN EQUATION WHEN BASES ARE EQUAL POWERS ALSO EQUAL
3x +(-1) = -4
3x - 1 = -4
3x = -4 + 1
3x = -3
x = -3/3
x = -1
Answer:
x = -1
Step-by-step explanation:
27 exponent x = [tex]27^x[/tex]
Divided by 3 = [tex]\frac{27^x}{3}[/tex]
Is equal to : [tex]\frac{1}{81}[/tex]
Therefore,
[tex]\frac{27^x}{3} = \frac{1}{81}[/tex]
Cross multiplying :
[tex]27^x \times 81 = 1 \times 3[/tex]
[tex]27^x = \frac{3}{81}[/tex]
[tex]27^x = \frac{1}{27}[/tex]
[tex]27^x = 27^{-1}[/tex]
[tex]x = -1[/tex] [tex][a^x = a^y => x = y][/tex]
Find the value of x
A. 20
B. 28
C. 10
D. 50/7
Answer:
x=28
Step-by-step explanation:
Step 1, comparing triangles:
Let us look at [tex]\triangle ABC[/tex] and [tex]\triangle ADE[/tex].
They both share [tex]\angle A[/tex] ([tex]\angle A=\angle A[/tex])[tex]\angle ABC = \angle BDE[/tex] (Corresponding Angle Theorem)[tex]\angle ACB = \angle CED[/tex] (Corresponding Angle Theorem)Therefore, because of AAA (Angle Angle Angle), [tex]\triangle ABC[/tex] and [tex]\triangle ADE[/tex] are similar.
Step 2:
Because the two triangles are similar, their sides should be proportional. Notice that [tex]\overline{AB}[/tex] and [tex]\overline {AD}[/tex] should be proportional.
Therefore, [tex]\overline{AB}[/tex]: [tex]\overline {AD}[/tex] =
[tex]12:30+12=\\12:42=\\2:7[/tex]
(Note, [tex]\overline {AD}[/tex] = [tex]\overline{AB}[/tex]+ [tex]\overline{BD}[/tex]=12+30)
Step 3:
We figured out that [tex]\triangle ABC[/tex] and [tex]\triangle ADE[/tex] have proportional sides of 2:7. Therefore, [tex]\overline{BC}[/tex] and [tex]\overline{DE}[/tex] should also have a ratio of 2:7.
[tex]8: \overline{DE}=2:7\\8:\overline{DE}=8:28\\\overline{DE}=\fbox{28}[/tex]
x=28
I hope this helps! Let me know if you have any questions :)
Answer:
x = 20
Step-by-step explanation:
If we look at the given diagram, we will see that ΔABC and ΔADE are similar. Because they a similar we know that corresponding sides are in proportion. In order to solve this question, we need to know what the coefficient of similarity is.
AB and AD are corresponding sides, in order to get from 12 to 30 we need to multiple 12 by 2.5. That means that the coefficient of similarity between the two triangles is 2.5. To get x (length of DE) we need to multiply the length of BC by the coefficient of similarity. And so we get...
x = 2.5(BC)
x = 2.5(8)
x = 20
Triangle ABC is similar to triangle EFD what scale factor is required to dilate triangle abc so that it's image, ABC is congruent to triangle EFD
Step-by-step explanation:
the scale factor k = 5/12
The scale factor k = 5/12 is required to dilate triangle ABC thus, its image, ABC is congruent to triangle EFD.
What is the scale factor?The ratio between comparable measurements of an item and a representation of that thing is known as a scale factor in arithmetic.
From the figure attached, we are given that Triangle ABC is similar to triangle EFD.
Therefore,
BC/ FD = AC/ ED
These corresponding sides are proportional.
Scale factor;
EF / AB = 5/12
Then Angle between this sides is also equal.
The SAS rule of similarity of triangles states that two triangles will be similar if their corresponding two sides are proportional and the angle between these two sides is equal.
The scale factor k = 5/12 is required to dilate triangle ABC thus, its image, ABC is congruent to triangle EFD.
Learn more about scale factors here:
https://brainly.com/question/11178083
#SPJ2
determine the value of a in the figure shown
Answer:
d
Step-by-step explanation:
180-149= 31.
31+ 122= 153
180-153= 27
a= 27
A recent study suggested that 70% of all eligible voters will vote in the next presidential election. Suppose 20 eligible voters were randomly selected from the population of all eligible voters. What is the probability that fewer than 11 of them will vote
Answer:
0.0479 = 4.79% probability that fewer than 11 of them will vote
Step-by-step explanation:
For each voter, there are only two possible outcomes. Either they will vote, or they will not. The probability of a voter voting is independent of any other voter, which means that the binomial probability distribution is used to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
70% of all eligible voters will vote in the next presidential election.
This means that [tex]p = 0.7[/tex]
20 eligible voters were randomly selected from the population of all eligible voters.
This means that [tex]n = 20[/tex]
What is the probability that fewer than 11 of them will vote?
This is:
[tex]P(X < 11) = P(X = 10) + P(X = 9) + P(X = 8) + P(X = 7) + P(X = 6) + P(X = 5) + P(X = 4) + P(X = 3) + P(X = 2) + P(X = 1) + P(X = 0)[/tex]
In which
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 10) = C_{20,10}.(0.7)^{10}.(0.3)^{10} = 0.0308[/tex]
[tex]P(X = 9) = C_{20,9}.(0.7)^{9}.(0.3)^{11} = 0.0120[/tex]
[tex]P(X = 8) = C_{20,8}.(0.7)^{8}.(0.3)^{12} = 0.0039[/tex]
[tex]P(X = 7) = C_{20,7}.(0.7)^{7}.(0.3)^{13} = 0.0010[/tex]
[tex]P(X = 6) = C_{20,10}.(0.7)^{6}.(0.3)^{12} = 0.0002[/tex]
[tex]P(X = 5) = C_{20,5}.(0.7)^{5}.(0.3)^{15} \approx 0[/tex]
The probability of 5 or less voting is very close to 0, so they will not affect the outcome. Then
[tex]P(X < 11) = P(X = 10) + P(X = 9) + P(X = 8) + P(X = 7) + P(X = 6) + P(X = 5) + P(X = 4) + P(X = 3) + P(X = 2) + P(X = 1) + P(X = 0) = 0.0308 + 0.0120 + 0.0039 + 0.0010 + 0.0002 = 0.0479[/tex]
0.0479 = 4.79% probability that fewer than 11 of them will vote
Use logarithmic differentiation to differentiate the question below
[tex]y = x \sqrt[3]{1 + {x}^{2} } [/tex]
Answer:
[tex] \orange{ \bold{\frac{dy}{dx} =\frac{ 5{x}^{2} + 3 }{3\sqrt[3]{(1 + {x}^{2})^{2} } }}}[/tex]
Step-by-step explanation:
[tex]y = x \sqrt[3]{1 + {x}^{2} } \\ assuming \: log \: both \: sides \\log y = log(x \sqrt[3]{1 + {x}^{2} } ) \\ \therefore log y = logx + log(\sqrt[3]{1 + {x}^{2} } ) \\ \therefore log y = logx + \frac{1}{3} log({1 + {x}^{2} } ) \\ differentiating \: both \: sides \: w.r.t.x \\ \frac{1}{y} \frac{dy}{dx} = \frac{1}{x} + \frac{1}{3} . \frac{1}{(1 + {x}^{2}) } (0 + 2x) \\ \frac{1}{y} \frac{dy}{dx} = \frac{1}{x} + \frac{2x}{3(1 + {x}^{2}) }\\ \frac{1}{y} \frac{dy}{dx} =\frac{3(1 + {x}^{2}) + 2 {x}^{2} }{3x(1 + {x}^{2}) }\\ \frac{1}{y} \frac{dy}{dx} =\frac{3 + 3{x}^{2} + 2 {x}^{2} }{3x(1 + {x}^{2}) }\\ \frac{1}{y} \frac{dy}{dx} =\frac{3 + 5{x}^{2} }{3x(1 + {x}^{2}) }\\ \frac{dy}{dx} =\frac{y(3 + 5{x}^{2} )}{3x(1 + {x}^{2}) } \\ \\ \frac{dy}{dx} =\frac{x \sqrt[3]{1 + {x}^{2} } (3 + 5{x}^{2} )}{3x(1 + {x}^{2}) }\\ \\ \frac{dy}{dx} =\frac{(3 + 5{x}^{2} )\sqrt[3]{1 + {x}^{2} } }{3(1 + {x}^{2}) }\\ \\ \purple{ \bold{\frac{dy}{dx} =\frac{ 5{x}^{2} + 3 }{3\sqrt[3]{(1 + {x}^{2})^{2} } }}}[/tex]
I’ll need brainliest
Answer:
I think no B
if wrong correct me pls
I HOPE IT HELPS
HAVE A GREAT DAY
[tex]#Liliflim[/tex]
Answer:
B
Step-by-step explanation:
C=7s
The subjects of an experiment should be selected at random so that they
represent the population from which they come.
O
A. True
O
B. False
Answer: True
Step-by-step explanation:
The subjects of an experiment should be selected at random so that they
represent the population is true.
Once the sample size has been decided, a sample should be taken from the sample size which will represent the population. This gives everyone an equal chance of being selected as there's no bias.
for the function g defined above, a is a constant and g(4) = 8 what is the value of g(-4)
Answer:
-8
Step-by-step explanation:
g(4)=8
8÷4=2
g=2
g(-4)=2(-4)
=(-8)
holp it can help you.
How do you do an explicit formula for a geometric problem
Answer:
State the initial term.
Find the common ratio by dividing any term by the preceding term.
Substitute the common ratio into the recursive formula for a geometric sequence.
PLEASE HELP I WILL GIVE BRAINLIEST TO THE FIRST PERSON THAT ANSWER PLEASE
Answer:
[tex]a) x = k \times \frac{1}{y^2} \ , \ where \ k \ is \ a \ constant\\\\b) x = 3, \ when\ y\ =\ 10\\\\c) y = 10, \ when \ x = 3[/tex]
Step-by-step explanation:
a)
[tex]x \ \alpha \ \frac{1}{y^2}\\\\x = k \times \frac{1}{y^2}\\\\[/tex] [tex][ \ where \ k \ is \ a \ constant \ ][/tex]
Find k.
Given x = 12, y = 5,
[tex]12 = k \times \frac{1}{5^2}\\\\k = 12 \times 25 = 300[/tex]
b)
Find x.
Given y = 10
We have k = 300
[tex]x = k \times \frac{1}{y^2}\\x = 300 \times \frac{1}{10^2} \\\\x= \frac{300}{100} = 3[/tex]
c)
Find y
Given x = 3
We have k = 300
[tex]x = k \times \frac{1}{y^2}\\\\3 = 300 \times \frac{1}{y^2}\\\\\frac{1}{y^2} = \frac{3}{300}\\\\\frac{1}{y^2} = \frac{1}{100}\\\\y^2 = 100\\\\y = \sqrt{100} = 10[/tex]
Pythagorean theorem.
I hope this is help full to you
Answer:
3
Step-by-step explanation:
because this is the formula of Pythagorean theorem a^2 + b^2 = c^2 so all I did was 5^2 = 25 - 4^2 = 25-16 = 9 and square root of 9 = 3 i hope this helps. :D please give brainliest
A factory manufactures motorcycles. One of its employees, working in the quality control department, checks the first 10 and the last 10 motorcycles manufactured in a day. This is what type of sampling?
Answer:
Convenience sampling
Step-by-step explanation:
When sampling is done based in degree of ease or samples picked from observations that are easily accessible rather than prioritizing randomness or selection which will most be representative of the population, then such sampling is called convenience sampling. In some texts, it is also referred to as grab sampling as researchers choose from close, easy to reach samples. In the scenario above, the quality control takes the easy procedure of checking the first and last 10 motorcycles as this is easier than having to take samples at random tune intervals which will be a better representation of the entire motorcycles.
Keiko brought $51.75 to the art supply store. She bought a brush, a sketchbook, and a paint set. The brush was 1/6 as much as the sketchbook, and the sketchbook cost 3/4 the cost of the paint set. Keiko had $3.00 left over after buying these items.
What was the cost of each item?
Step-by-step explanation:
[(1/6 × 3/4) + (3/4) + 1] n = 51.75 -3
(⅛ + ¾ +1)n = 48.75
15/8 n = 48.75
1.875 n = 48.75
n = 48.75/1.875
n = 26
so, the cost of :
the brush = ⅛×26 = $ 3.25
the sketchbook = ¾×26 = $ 19.5
the pain set = $ 26
Given the function defined in the table below, find the average rate of change, in simplest form, of the function over the interval
Answer:
Average rate of change = 5
Step-by-step explanation:
Average rate of change of a function is defined by the expression over the interval a ≤ x ≤ b,
Average rate of change = [tex]\frac{f(b)-f(a)}{b-a}[/tex]
Using this rule for the average rate of change of the function (defined by the table) over the interval 4 ≤ x ≤ 5,
Average rate of change = [tex]\frac{f(5)-f(4)}{5-4}[/tex]
From the table,
f(5) = 10
f(4) = 5
Therefore, average rate of change of the function = [tex]\frac{10-5}{5-4}[/tex]
= 5
Answer:
=5
Step-by-step explanation:
Given a circle with a radius of 22 inches, what is the circumference in terms of π?
Answer:
[tex]circumference = 2\pi \: r \\ = 2 \times \pi \times 22 \\ = 44\pi \: inches[/tex]
Answer:
The circumference is 44 pi.
Step-by-step explanation:
You have to use the formula, C=2 Pi R but since it's in terms of pi, we can not include pi in the equation. 2 times r (radius) is 44, therefor the answer is 44 pi.
405, 397,389, ...
Find the 31st term.
2. Determine the sum of the measures of the interior angles of a dodecagon.
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Answer:
1800°
Step-by-step explanation:
The interior angles of a convex polygon with n sides have the sum ...
angle sum = (n -2)×180°
For the 12-sided dodecagon, the angle sum is ...
angle sum = (12 -2)×180° = 1800°
please help! (listing BRAINLIST and giving points) :D
Answer:
40°
Step-by-step explanation:
because angle In an isosceles triangle base angles are same and angle in a triangle add up to 180° and angle on a straight line add up to 180°
hope this helps:)
Solve the triangle.
B = 36°, a = 41, c = 17 (5 points)
Answer:
b = 29.0, A = 123.9°, C = 20.1°
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Answer:
b = 29.0; A = 123.9°, C = 20.1°
Step-by-step explanation:
The given angle lies between the given sides, so the Law of Cosines is the appropriate relation.
b² = a² +c² -2ac·cos(B)
b² = 1681 +289 -1394cos(36°) ≈ 842.2303
b ≈ √842.2303 ≈ 29.021
__
The Law of Sines can be used to find angle C:
sin(C)/c = sin(B)/b
C = arcsin(c/b·sin(B)) = arcsin(17/29.021×sin(36°))
C ≈ 20.1°
A = 180° -36° -20.1° = 123.9°
The remaining side and angles are ...
b ≈ 29.0; A ≈ 129.9°; C ≈ 20.1°
_____
Additional comment
By choosing to find the smaller angle C first, we avoid having to deal with the ambiguity associated with the arcsine when the angle is greater than 90°.
A couple purchased a home and signed a mortgage contract for $900,000 to be paid with half-yearly payments over a 25-year period. The interest rate applicable is j2=5.5% p.a applicable for the first five years, with the condition that the interest rate will be increased by 12% every 5 years for the remaining term of the loan.
a) Calculate the half-yearly payment required for each five-year interval
Did you manage to solve it?
Find the limit of the function by using direct substitution Lim x-0(x^2+10)
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Answer:
10
Step-by-step explanation:
Maybe you want ...
[tex]\displaystyle\lim_{x\to 0}(x^2+10)=0^2+10=\boxed{10}[/tex]
There are 2 people in the Hill family. Each person
reads the same number of books. They read 12 books
in all. How many books does each person read?
A
18 books
B
6 books
C
8 books
D
10 books
Answer:
6
Step-by-step explanation:
i need help with this one plz! (marking BRAINLIST) :)
Answer:
x=22
Step-by-step explanation:
the triangle in which x is in is an equilateral triangle.
44 is an exterior angle to that triangle.
an exterior angle is always equal to tbe sum of the opposite 2 interior angles.
because that triangle is equilateral
x =44 ÷ 2
x=22
A 25 foot ladder is leaning against a tree. If the base of the ladder is 6 feet
away from the base of the tree, how high, to the nearest tenth, does the
ladder reach up the tree?
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Answer:
24.3 ft
Step-by-step explanation:
If h is the height of the ladder up the tree, the geometry can be modeled as a right triangle with legs h and 6, and hypotenuse 25. The Pythagorean theorem gives you the relation ...
h² +6² = 25²
h² = 625 -36 = 589
h = √589 ≈ 24.3
The ladder reaches about 24.3 feet up the tree.
3. It refers to the number of values an interval may contain
a. class interval
c. frequency
b. class width
d. range
Answer:
An interval scale is one where there is order and the difference between two values is meaningful. Examples of interval variables include: temperature (Farenheit), temperature (Celcius), pH, SAT score (200-800), credit score (300-850).
Step-by-step explanation:
thank me later
Please help!! This is timed!!
Use a double integral to find the area of the following regions. The region bounded by all leaves of the rose r=2cos3θ
Answer:
Hence the area of the region bounded by all leaves of the rose is [tex]\pi[/tex].
Step-by-step explanation:
Here,
[tex]2 cos (3\Theta )=0\\\Rightarrow cos(3\Theta)=0\\\Rightarrow cos(3\Theta )=cos\left (\frac{\pi }{2} \right )\\\Rightarrow \Theta =\left (\frac{\pi }{6},-\frac{\pi }{6} \right )[/tex]
Now consider for one leaf of rose:-
[tex]Area = 3\int_{-\frac{\pi }{6}}^{\frac{\pi }{6}}\frac{r^{2}}{2}d\Theta \\\\ = \frac{3}{2}\int_{-\frac{\pi }{6}}^{\frac{\pi }{6}}4 cos^{2}\left ( 3\Theta \right ) d\Theta \\\\ = \frac{12}{2}\int_{-\frac{\pi }{6}}^{\frac{\pi }{6}} \frac{cos(6\Theta +1)}{2}d\Theta\\\\ =\frac{6}{2}\left [ \frac{sin(6\Theta +\Theta )}{6} \right ]_{-\frac{\pi }{6}}^{\frac{\pi }{6}}\\\\ =3\times \left [ \frac{\pi }{6}+\frac{\pi }{6} \right ]\\\\ =3\times \frac{2\pi }{6}\\\\ = \pi[/tex]
Negative six multiplied by negative ten is subtracted from eight multiplied by five. Find the number
Answer:
The answer is -20.
Step-by-step explanation:
(8 × 5) - (-6 × -10)
= 40 - 60
= -20
PLSSSS HELP ASAP PLS !! will mark brainliest to whoever gets it right
Answer:
last option is correct
Step-by-step explanation:
angle 4 is 128 degree because it is corresponding with angle 3.
Corresponding angles are angles that are in the same position relative to lines intersected by a transversal. When a transversal intersects two lines, the two lines are parallel if and only if corresponding angles are congruent (equal in measure).
Answer:
128 because it is corresponding with 3
5+x^2-7x in standard form
