The solution set of 6 ㏑ e = e ^ ㏑ 2x is 3
What is relation between Exponents and logarithms ?
Exponents and logarithms are inverse functions, you can use exponents to "undo" logarithms and use logarithms to "undo" logarithms. Exponents specify the number of times you must multiply a value, while logarithms specify which exponent to apply to obtain a certain value.
The given expression is,
6 ㏑ e = e ^ ㏑ 2x
we know, ㏑ (e) = 1 and e ^ ㏑(x) = x
Put these values,
6 * 1 = 2x
Now, find x
6 = 2x
x = 3
Hence, the solution set of 6 ㏑ (e) = e ^ ㏑ (2x) is 3
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1
Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s).
7²
The expression above can also be written in the form
Va
For this expression, a =
b=
and c =
Undo
Next
In the given expression 7^(9/4) the values are found to be
a = 7b = 9c = 4How to determine the values of a, b, and cInformation given in the problem
the expression 7^(9/4)
This equation represents exponents in fraction form and the basics for the calculation is from
a^(b/c) = [tex]\sqrt[c]{a^{b} }[/tex]
Rewriting the expression is done as below
7^(9/4)
= [tex]\sqrt[4]{7^{9} }[/tex]
[tex]\sqrt[4]{7^{9} }[/tex] comparing with [tex]\sqrt[c]{a^{b} }[/tex] gives the following values
a will be equal to 7
b will be equal to 9
c will be equal to 4
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What is the probability that a standard normal random variable will be between. 3 and 3. 2?.
The probability that a standard normal random variable will be between. 3 and 3. 2 is 0.99932.
What is standard normal random?
We shall read probabilities out rather than directly working with Z's density function to compute probabilities for Z. The elements in the tables are probabilities of the kind P(Zz), and they are tables of cumulative probabilities. Following are a number of examples that will help to clarify how to use the tables.The standard normal random.
Z∼N(0,1)
P(Z<3)=.99865
P(Z>3.2)=.99931
P(3<Z<3.2)=2(0.99931-0.99865)−1=0.99932
Hence the standard normal random variable will be 0.99932.
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#Sam want to enlarge a triangle with side lengths 3, 6, and 9 inches. If the shortest side of the new triangle is 12 inches, what is the perimeter of the new triangle?
Answer: 72 in
Step-by-step explanation:
The shortest side length of the original triangle was 3in, and the newer one is now 12in. From 3in to 12in, you use a scale factor of 4. Hence, we multiply each side length of the original triangle by 4. And to find the perimeter of the new triangle, you add all the sides up.
3(4) + 6(4) + 9(4) = 72 in
Which equations model exponential decay?
Select each correct answer.
y = 0.25(2)
y = 2(0.20)*
y = 4.2(1.25)*
y = 0.55(0.91)*
Option2 and 4 are the exponential decay from the equation.
Given that,
We have to find which one is exponential decay function.
Exponential decay function is in the form of y=abˣ where a is the initial value and b≠0, 0<b<1. power is x.
Now, Take the 1st option
y=0.25(2)ˣ
Here a is 0.25 and 2 is b
b>1
So, Option 1 is not an exponential decay.
Now, Take the 2nd option
y=2(0.20)ˣ
Here a is 2 and 0.20 is b
b<1
So, Option 2 is an exponential decay.
Now, Take the 3rd option
y=4.2(1.25)ˣ
Here a is 4.2 and 1.25 is b
b>1
So, Option 3 is not an exponential decay.
Now, Take the 4th option
y=0.55(0.91)ˣ
Here a is 0.55 and 0.91 is b
b<1
So, Option 4 is an exponential decay.
Therefore, Option2 and 4 are the exponential decay from the equation.
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2x+54/x where x=9
what is the answer?
Find the surface area of the prism.
Answer:
312 m^2
Step-by-step explanation:
Start by separating the shapes.
you will get:
2 triangles with the dimensions 6m x 8m
1 rectangle with the dimensions: 9m x 8m
1 rectangle with the dimensions: 6m x 9m
1 rectangle with the dimensions: 10m x 9m
1) find the area of every shape
2 triangles with the dimensions 6m x 8m -----> 48m^2 and 48 m^2
1 rectangle with the dimensions: 9m x 8m ----> 72m^2
1 rectangle with the dimensions: 6m x 9m ----> 54 m^2
1 rectangle with the dimensions: 10m x 9m ---> 90m^2
2) add everything up
48m^2 + 48 m^2 + 72m^2 + 54 m^2 + 90m^2 =
312m^2
Find the measure of the marked angles.
The measure of the angles is ____ degrees.
Answer:
(3x + 36) is equal to (6x + 9) because they are vertically opposite angles.
3x + 36 = 6x + 9
3x = 27
x = 9
Substitute x = 9 into one of the angles to find the measure.
3(9) + 36 = 63
Angle measure is 63°.
The measure of the angles is 63 degrees.
Both (3x + 36) and (6x + 9) are equal to 63 degrees.
Given that are two vertically opposite angles (3x+36) and (6x+9) we need to find the measure of the angles,
Vertically opposite angles are formed when two lines intersect, and they are equal in measure.
In this case, we have two vertically opposite angles: (3x + 36) and (6x + 9).
Since the angles are equal, we can set them equal to each other and solve for x:
3x + 36 = 6x + 9
To isolate the x term, let's subtract 3x from both sides:
36 = 6x - 3x + 9
Combining like terms:
36 = 3x + 9
Next, let's subtract 9 from both sides:
36 - 9 = 3x
27 = 3x
To solve for x, we divide both sides by 3:
27/3 = 3x/3
9 = x
Now that we know the value of x, we can substitute it back into either of the original equations to find the measure of the angles.
Let's use the first angle (3x + 36):
Angle = 3x + 36
= 3(9) + 36
= 27 + 36
= 63
Hence, the measure of the angles is 63 degrees.
Both (3x + 36) and (6x + 9) are equal to 63 degrees.
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Simplify the complex expression to the standard form (a+bi). 2(8-8i)-9(8+4i)
The simplified expression for the complex expression is -56-52i
What is a complex expression?
A complex expression is an expression of the form a+ ib where a , b are constant and i is the imaginary number known as iota. In a + ib a is the real part and b is the imaginary part.
We are given two complex number as (8-8i) and (8+4i)
We have to simplify the given expression
As Complex number are added multiplied subtracted same as real number we can simplify the expression easily
2(8-8i)-9(8+4i)
We multiply the constants inside the bracket
16-16i-72-36i
Separating the terms and simplifying them we get
-56-52i
Hence the simplified expression is -56-52i
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mr. dyer pours 2 cups of blue paint into a jar for each art station. how many jars can he fill with 1 gallon of blue paint?
If Mr. Dyer pours 2 cups of blue paint into a jar for each art station, then the he can fill 8 jars with 1 gallon of blue paint.
Number of cups of blue paint for each art station = 2 cups
Given that,
One cup = 8 ounce
1 gallon = 128 ounce
2 cups of blue paint = 2 × 8
= 16 ounce of blue paint
1 gallon of blue paint = 128 ounce of blue paint
Number of jars that he can fill with 1 gallon of blue paint = 1 gallon of blue paint / 2 cups of blue paint
Here we have to use division
= 128/16
= 8 jars
Hence, if Mr. Dyer pours 2 cups of blue paint into a jar for each art station, then the he can fill 8 jars with 1 gallon of blue paint.
The complete question is:
Mr. dyer pours 2 cups of blue paint into a jar for each art station. how many jars can he fill with 1 gallon of blue paint? One cup = 8 ounce and 1 gallon = 128 ounce
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You are holding a balloon and have let out 24 feet of string. If the angle of elevation to the balloon is 32 degrees and you are 5 feet tall. How high is the balloon above the ground
The balloon is above 17.7180 the ground
What is the trigonometry ?
A branch of mathematics called trigonometry looks at how triangle side lengths and angles relate to one another. Applications of geometry to astronomical studies led to the development of the field in the Hellenistic world during the third century BC.
Given
The angle Ф is 32°
The hypotenuse becomes 24 feet
Let AB be the opposite side
Using trigonometric function of sinФ
ie sinФ = Opposite / hypotenuse
sin Ф = AB / 24
AB = sin Ф * 24
AB = sin 32° * 24
AB = 12.7180
As that person is 5 feet tall we have to add 5 to the value
ie
12.7180 + 5
= 17.7180
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In a farm composed of cows and chickens, there are total of 13 heads and 42 feet. How many cows are there?.
In a farm composed of cows and chickens, there are total of 13 heads and 42 feet.
Let 'h’ represent the number of hens the farmer has.
Let 'c’ represent the number of cows the farmer has.
Assume that all hens have two legs and all cows have four.
There are a total of 42 legs. So
2h + 4c = 42 (1)
There are 13 animals in total.
h + c = 13 (2)
Now that we have our system of equations, we can solve by either substitution or elimination.
Elimination
(2) x 2
2h + 2c = 26 (3)
(2)—(3)
2c = 6
c=3
From (2):
c + h = 13
3+h = 13
h= 10
Therefore, the farmer has 3 cows and 10 hens.
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(04.04 MC)
What is the 8th partial sum of 10,000 -2,000+400-80+...? Round your answer to the thousandths place.
12,499.970
O9,999.974
8,333.333
8,333.312
Answer:
C
Step-by-step explanation:
Answer:
8,333.312
Step-by-step explanation:
I did the test...
Estimate the quotient. 241 ÷ 5 A. 30 B. 250 C. 50 D. 60
I need help with this please
Select the correct answer. An archway is modeled by the equation y = -2x2 + 8x. A rod is to be placed across the archway at an angle defined by the equation x − 2.23y + 10.34 = 0. If the rod is attached to the archway at points A and B, such that point B is at a higher level than point A, at what distance from the ground level is point B? A. 8 units B. 6 units C. 5 units D. 3 units
Answer:
B. 6 units
Step-by-step explanation:
Given equations:
[tex]y = -2x^2 + 8x[/tex]
[tex]x-2.23y + 10.34 = 0[/tex]
The points at which the rod is attached to the archway are the points of intersection of the two equations.
Rearrange the second equation to make x the subject:
[tex]\implies x=2.23y-10.34[/tex]
Substitute this into the first equation to create a quadratic:
[tex]y = -2(2.23y-10.34)^2 + 8(2.23y-10.34)[/tex]
[tex]y = -2(4.9729y^2-46.1164y+106.9156) + 17.84y-82.72[/tex]
[tex]y=-9.9458y^2+92.2328y-213.8312+17.84y-82.72[/tex]
[tex]y=-9.9458y^2+110.0728y-296.5512[/tex]
[tex]-9.9458y^2+109.0728y-296.5512=0[/tex]
[tex]\boxed{\begin{minipage}{3.6 cm}\underline{Quadratic Formula}\\\\$x=\dfrac{-b \pm \sqrt{b^2-4ac}}{2a}$\\\\when $ax^2+bx+c=0$ \\\end{minipage}}[/tex]
Solve the quadratic using the quadratic formula:
[tex]\implies y=\dfrac{-(109.0728) \pm \sqrt{(109.0728)^2-4(-9.9458)(-296.5512)}}{2(-9.9458)}[/tex]
[tex]\implies y=\dfrac{-109.0728 \pm \sqrt{99.12}}{-19.8916}[/tex]
[tex]\implies y=\dfrac{109.0728 \pm \sqrt{99.12}}{19.8916}[/tex]
[tex]\implies y=5.983867702, \quad y=4.982851918[/tex]
As point B is at a higher level than point A, the y-value of point B is approximately 6 units.
Therefore, point B is 6 units from ground level.
a slice of cake is 20m due east and 10m due south. Another cake slice is 15m due west and 15m due north. Which slice is closer
The cake slice with 15m due west and 15m due north is closer
What is distance?Distance is a numerical or occasionally qualitative measurement of how far apart objects or points are. Distance is the total movement of an object without any regard to direction. We can define distance as to how much ground an object has covered despite its starting or ending point.Distance is how far apart objects are.Here , the slice of cake is 20m due east and then 10 m due south.
consider it as triangle ABC.
Required Displacement can be calculated by Pythagoras theorem -
AC = √ ( AB )² + ( BC )²
By substitution,
⇒ AC = √ ( 20 )² + ( 10 )²
⇒ AC = √ ( 400 + 100 )
Simplifying this equation, we get
⇒ AC = √500
⇒ AC = 10 √5
⇒ AC = 22.56
Thus , The cake slice is 22.56 m far away.
Here another slice of cake is 15m due west and 15m due north.
consider it as a triangle DEF.
Therefore,
⇒ DF = √ ( DE )² + ( EF )²
By substitution,
⇒ DF = √ ( 15 )² + ( 15 )²
Simplifying this equation, we get
⇒ DF = √ ( 225 + 225 )
⇒ DF = √ 450
⇒ DF = 15 √2
⇒ DF = 21.21
Thus the cake slice is 21.21 m far away.
Therefore this slice is closer.
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What is the slope-intercept form of the line represented in the table of values?
Answer:
y = -7x + 10
Step-by-step explanation:
As the y's are decreasing by 7, the x are increasing by 1. This gives us a slope of -7. When x is 0, y is 10 that is our y intercept.
If 21 le than 11 time a number reult in 7 time a number decreaed by 29, what i the number?
Based on expression for each side of the equation, the number is -2.
Let us assume the number to be x. So, there will be two sides of equation, that is Left Hand Side and Right Hand Side. Writing the equation for each side.
Left Hand Side = 11x - 21
Right Hand Side = 7x - 29
Equating both sides of the equation.
11x - 21 = 7x - 29
Rewriting the equation with identical values on each side
11x - 7x = 21 - 29
Performing subtraction on both sides of the equation
4x = -8
Shifting 4 to Right Hand Side of the equation
x = -8 ÷ 4
Performing division on Right Hand Side of the equation
x = -2
Thus, the number is -2.
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Enter the ratio of students who chose
alternative to the total number of students.
Answer:
1 : 4
Step-by-step explanation:
the ratio of
alternative : total
= 15 : 60 ( divide each part by 15 )
= 1 : 4
A line passes through the point (9, "-9)" and has a slope of -2
write an equation in point-slope form for this line.
Answer:
y + 9 = -2 (x - 9)
Step-by-step explanation:
M (slope) = -2
X=9 and Y=-9
Point-slope form
y - y1 = m(x - x1)
y - - 9 = -2( x - 9)
y + 9 = -2(x -9)
Substitution
3x + 5y = 5
Y = -x -2
Find ( x , y )
As per the substitution method, the value of (x , y) is (-15/2, 11/2)
Substitution method:
Substitution method is the process of solve one equation for one of the variables. And substitute (plug-in) this expression into the other equation and solve. Then resubstitute the value into the original equation to find the corresponding variable.
Given,
Here we have the following expression.
3x + 5y = 5
Y = -x -2
Now, we need to find the value of x and y.
According to the substitution method, let us consider
3x + 5y = 5 -------------------(1)
Y = -x -2 ---------------------(2)
Now, we have to apply the value of y as -x - 2 in equation (1), then we get,
=> 3x + 5(-x - 2) = 5
When we expand it then we get,
=> 3x - 5x - 10 = 5
Simplify the expression,
=> -2x - 10 = 5
=> -2x = 5 + 10
=> -2x = 15
Then the value of x is,
=> x = -15/2
If the value of x is -15/2. then the value of y is calculated by using the equation (2),
=> y = -(-15/2) - 2
=> y = 15/2 - 2
=> y = (15 - 4)/2
=> y = 11/2
Therefore, the value of (x, y) is (-15/2, 11/2).
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please answer this question
It's really important
10. Determine whether the following represents an identity.
cos x sin x tan x + cos²x = 1
Answer:
yes
Step-by-step explanation:
Given that [tex]\cos x\sin x\tan x+\cos^2x=1[/tex]
Substitute [tex]\tan x=\frac{\sin x}{\cos x}[/tex], we obtain:
[tex]\cos x\sin x\frac{\sin x}{\cos x}+\cos^2 x=1[/tex]
Simplifying this, we get:
[tex]\sin x\sin x+\cos^2x=1[/tex]
This is equivalent to:
[tex]\sin^2x+\cos^2x=1[/tex]
The points scored per game by a professional basketball player are represented by the box plot below. A number line plots points per game by the basketball player. The plots are 16 through 21 and 21 through 24. If the player scores 9 points and 35 points in the next two games, how is the median of the data set affected? A. The median points per game increases. B. The median points per game decreases. C. The median points per game is not affected. D. The effect on the median points per game cannot be determined.
Answer:
i think its C. The median points per game is not affected
Step-by-step explanation:
What is the domain of the function y = startroot x endroot 4?
The values of the domain is the which satisfies the function is x > - 4.
According to the statement
We have to find the domain of the given function
For this purpose, we know that the
In Mathematics,The domain of a function is the set of values that we are plug into our function.
The given function is a
[tex]y = \sqrt{x+4}[/tex]
And in this function
The domain is the values of the x which we able to put in the function according to the definition.
x+4=0
x=-4.
It means the value of the domain is the [tex]x > - 4[/tex].
The values according to the upper expression satisfies the domain of the function.
So, The values of the domain is the which satisfies the function is x > - 4.
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Alizay sold 15 shirts priced equally for Rs.2800. She spent Rs. 14,000 of her earned amount on shopping and Rs. 7500 on buying grocery. How much is she left with?
The amount of money left with Alizay after shopping is Rs 17700 .
Alizay sold shirts for Rs. 2800.
She sold 14 shirts.
Cost earned from selling 14 shirts = 14 × 2800 = Rs. 39200
Spent on shopping =Rs. 14000
Spent on Grocery = Rs. 7500
Total amount spent = Rs.(14000+7500) = Rs. 21500
Amount of money left = Rs 39200 - Rs 21500 = Rs 17700
Therefore she is left with Rs 17700 .
In the case of a single variable, there is only one viable response. This particular case, in which the variable is accurately referred to as the "unknown," is one to which the term linear equation sometimes relates implicitly.
The Cartesian coordinates of a point on the Euclidean plane can be used to understand each solution in the scenario with two variables. A linear equation's solutions define a line in the Euclidean plane, and each line is the collection of all solutions to a linear equation with two variables.
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pls help ill give all my points but please dont write anything down as the answer just for the points ):
Lara bought Philly soft pretzels. Each serving has 1.7 grams of fat. She ate 1.5 servings of the pretzels at lunch and 1.25 servings of the pretzels as a snack. How many grams of fat were in both servings? Explain how you got the answer
austin prepared 20 kilograms of dough after working 4 hours. how much dough did austin prepare if he worked for 5 hours? solve using unit rates.
Answer:
Answer: 9 hours. If austin prepared 20 kg of dough in 5 hours, this means he can prepare 4kg of dough an hour. This is because 20/5=4.
find m<1 if m<3=(4x+7) and m<6=(2x+53)
If the measurement of ∠3 & ∠6 is given,i.e.∠3 = 4x + 7 and ∠6 = 2x + 53 then ∠1 = 120 - 6x.
Given, ∠3 = (4x + 7) and ∠6 = (2x + 53)
Let ∠1 = a,
Now, as we know the angle sum property in triangles,
the sum of all the angles in a triangle is 180°.
So, ∠1 + ∠3 + ∠6 = 180°
a + (4x + 7) + (2x + 53) = 180°
a + 6x + 60 = 180
a = 180 - 60 - 6x
a = 120 - 6x
Hence, ∠1 = 120 - 6x, if the ∠3 = 4x + 7 and ∠6 = 2x + 53
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Which shows the following expression after the negative exponents have been eliminated? startfraction a cubed b superscript negative 2 baseline over a b superscript negative 4 baseline endfraction, a not-equals 0, b not-equals 0 startfraction a cubed b superscript negative 4 baseline over a b superscript negative 2 baseline endfraction startfraction a b superscript 4 baseline over a cubed b squared endfraction negative startfraction a cubed b superscript 4 baseline over a b squared endfraction startfraction a cubed b superscript 4 baseline a b squared endfraction.
Which shows the following expression after the negative exponents have been eliminated
[tex]a^{2} b^{2}[/tex]
Given the algebraic expression:
[tex]\frac{a^{3}b^{-2} }{ab^{-4} }, a\neq 0, b\neq 0[/tex]
We are required to eliminate the negative exponents and find the resulting expression.
Using the Negative Exponent Law of Indices: [tex]x^{-y} = \frac{1}{x^{y} }[/tex]
Using the Division Law of Indices: [tex]\frac{t^{x} }{t^{y} } = t^{x-y}[/tex]
Therefore:
[tex]\frac{a^{3}b^{-2} }{ab^{-4} } = a^{3-1}.b^{-2-(-4)}\\ \\ Simplifying\\ \\a^{3-1}.b^{-2-(-4)} = a^{2}b^{-2+4}\\ \\ =a^{2} b^{2}\\\\Therefore:\\\\\frac{a^{3}b^{-2} }{ab^{-4} } =a^{2} b^{2}\\[/tex]
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