Answers
The simplified exponential expression for this problem is given as follows:
xy^7/z^(14).
How to simplify the exponential expression?The first step in simplifying the exponential expression is applying the power of power rule at the numerator, as follows:
(y² x z^-5)² = y^4z^(-10).
(for the power of power rule, we keep the bases and add the exponents).
When two terms with the same base and different exponents are divided, we keep the base and subtract the exponents, hence the exponents are given as follows:
x: -1 - (-2) = -1 + 2 = 1.y = 4 - (-3) = 7.z = -10 - 4 = -14.The negative exponent means that the number appears in the denominator, hence the simplified expression is given as follows:
xy^7/z^(14).
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The simplified exponential expression for this problem is given as follows:
xy^7/z^(14).
How to simplify the exponential expression?The first step in simplifying the exponential expression is applying the power of power rule at the numerator, as follows:
(y² x z^-5)² = y^4z^(-10).
(for the power of power rule, we keep the bases and add the exponents).
When two terms with the same base and different exponents are divided, we keep the base and subtract the exponents, hence the exponents are given as follows:
x: -1 - (-2) = -1 + 2 = 1.y = 4 - (-3) = 7.z = -10 - 4 = -14.The negative exponent means that the number appears in the denominator, hence the simplified expression is given as follows:
xy^7/z^(14).
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Related Questions
the numerator is an x
Answers
Answer:
9
Step-by-step explanation:
Here is your answer
x=9
option B
What is the value of x?
Answers
Answer:
x = 5.4
Step-by-step explanation:
3/x = 4/7.2
cross-multiply:
4x = 21.6
x = 5.4
(2x+1)^2 - (x+3)^2 simplify
Answers
Answer:
Step-by-step explanation:
steps are below
step 1
(2x+1)^2 - (x+3)^2 equation
step 2
4x^2+4x+1+(-x^2)+(-6x)+(-9) distribute
step 3
4x^2+4x+1+(-x^2)+(-6x)+(-9)
(4x^2+-x^2)+(4x+(-6x)+(1+(-9) combine the like terms
3x^2-2x-8
You are purchasing Cotton swabs that come in 2 different sized containers. One box contains 300 swabs for 2.99 and the other box is specially marked at 30% more swabs for the same price. How much will you save per sawn by buying the larger box?
Answers
Answer:
Buying the larger box, I will be saving 23% compared to the original price.
Step-by-step explanation:
Given that a box contains 300 swabs for 2.99 and the other box is specially marked at 30% more swabs for the same price, to determine how much will I save per swab by buying the larger box the following calculation must be performed:
2.99 / 300 = X
0.0099 = X
2.99 / (300 x 1.3) = X
2.99 / 390 = X
0.0076 = X
0.0099 = 100
0.0076 = X
(0.0076 x 100) / 0.0099 = X
77 = X
100 - 77 = 23
Therefore, buying the larger box I will be saving 23% compared to the original price.
The equations y = 5x and y = -1/5x+ 4 represent what types of lines?
A) Lines that aren't perpendicular, parallel, or the same
B) Same lines
C) Parallel lines
D) Perpendicular lines
Answers
Answer:
I think its D:perpendicular lines
NO LINKS!! URGENT HELP PLEASE!!!
Solve ΔABC using the Law of Cosines
1. B= 36°, c = 19, a = 11
2. a = 21, b = 26, c = 17
Answers
Answer:
1) A = 32.6°, C = 111.4°, b = 12.0
2) A = 53.6°, B = 85.7°, C = 40.7°
Step-by-step explanation:
Question 1
Given values of triangle ABC:
B= 36°c = 19a = 11First, find the measure of side b using the Law of Cosines for finding sides.
\(\boxed{\begin{minipage}{6 cm}\underline{Law of Cosines (for finding sides)} \\\\$c^2=a^2+b^2-2ab \cos (C)$\\\\where:\\ \phantom{ww}$\bullet$ $a, b$ and $c$ are the sides.\\ \phantom{ww}$\bullet$ $C$ is the angle opposite side $c$. \\\end{minipage}}\)
As the given angle is B, change C for B in the formula and swap b and c:
\(b^2=a^2+c^2-2ac\cos(B)\)
Substitute the given values and solve for b:
\(\implies b^2=11^2+19^2-2(11)(19)\cos(36^{\circ})\)
\(\implies b^2=482-418\cos(36^{\circ})\)
\(\implies b=\sqrt{482-418\cos(36^{\circ})}\)
\(\implies b=11.9929519...\)
Now we have the measures of all three sides of the triangle, we can use the Law of Cosines for finding angles to find the measures of angles A and C.
\(\boxed{\begin{minipage}{7.6 cm}\underline{Law of Cosines (for finding angles)} \\\\$\cos(C)=\dfrac{a^2+b^2-c^2}{2ab}$\\\\\\where:\\ \phantom{ww}$\bullet$ $C$ is the angle. \\ \phantom{ww}$\bullet$ $a$ and $b$ are the sides adjacent the angle. \\ \phantom{ww}$\bullet$ $c$ is the side opposite the angle.\\\end{minipage}}\)
To find the measure of angle A, swap a and c in the formula, and change C for A:
\(\implies \cos(A)=\dfrac{c^2+b^2-a^2}{2cb}\)
\(\implies \cos(A)=\dfrac{19^2+(11.9929519...)^2-11^2}{2(19)(11.9929519...)}\)
\(\implies \cos(A)=0.842229094...\)
\(\implies A=\cos^{-1}(0.842229094...)\)
\(\implies A=32.6237394...^{\circ}\)
To find the measure of angle C, substitute the values of a, b and c into the formula:
\(\implies \cos(C)=\dfrac{a^2+b^2-c^2}{2ab}\)
\(\implies \cos(C)=\dfrac{11^2+(11.9929519...)^2-19^2}{2(11)(11.9929519...)}\)
\(\implies \cos(C)=-0.364490987...\)
\(\implies C=\cos^{-1}(-0.364490987...)\)
\(\implies C=111.376260...^{\circ}\)
Therefore, the remaining side and angles for triangle ABC are:
b = 12.0A = 32.6°C = 111.4°\(\hrulefill\)
Question 2To solve for the remaining angles of the triangle ABC given its side lengths, use the Law of Cosines for finding angles.
\(\boxed{\begin{minipage}{7.6 cm}\underline{Law of Cosines (for finding angles)} \\\\$\cos(C)=\dfrac{a^2+b^2-c^2}{2ab}$\\\\\\where:\\ \phantom{ww}$\bullet$ $C$ is the angle. \\ \phantom{ww}$\bullet$ $a$ and $b$ are the sides adjacent the angle. \\ \phantom{ww}$\bullet$ $c$ is the side opposite the angle.\\\end{minipage}}\)
Given sides of triangle ABC:
a = 21b = 26c = 17Substitute the values of a, b and c into the Law of Cosines formula and solve for angle C:
\(\implies \cos(C)=\dfrac{a^2+b^2-c^2}{2ab}\)
\(\implies \cos(C)=\dfrac{21^2+26^2-17^2}{2(21)(26)}\)
\(\implies \cos(C)=\dfrac{828}{1092}\)
\(\implies C=\cos^{-1}\left(\dfrac{828}{1092}\right)\)
\(\implies C=40.690560...^{\circ}\)
To find the measure of angle B, swap b and c in the formula, and change C for B:
\(\implies \cos(B)=\dfrac{a^2+c^2-b^2}{2ac}\)
\(\implies \cos(B)=\dfrac{21^2+17^2-26^2}{2(21)(17)}\)
\(\implies \cos(B)=\dfrac{54}{714}\)
\(\implies B=\cos^{-1}\left(\dfrac{54}{714}\right)\)
\(\implies B=85.6625640...^{\circ}\)
To find the measure of angle A, swap a and c in the formula, and change C for A:
\(\implies \cos(A)=\dfrac{c^2+b^2-a^2}{2cb}\)
\(\implies \cos(A)=\dfrac{17^2+26^2-21^2}{2(17)(26)}\)
\(\implies \cos(A)=\dfrac{524}{884}\)
\(\implies A=\cos^{-1}\left(\dfrac{524}{884}\right)\)
\(\implies A=53.6468753...^{\circ}\)
Therefore, the measures of the angles of triangle ABC with sides a = 21, b = 26 and c = 17 are:
A = 53.6°B = 85.7°C = 40.7°What the meaning of "a sequence of length n"?
Answers
In mathematics, a sequence is an ordered list of elements, often denoted by brackets or parentheses.
What the meaning of "a sequence of length n"?The term "a sequence of length n" refers to a sequence that contains a specific number of elements, where the number of elements is denoted by "n."
When the domain of a function is the set of natural numbers (N), it is called an infinite sequence. An infinite sequence can be thought of as an ordered list that continues indefinitely.
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Two boys earn money mowing lawns. Jacob mowed 12 lawns this week. He mowed
3 times as many lawns as Kevin mowed.
In which equation does the box represent the number of lawns Kevin mowed?
A. 3 + □ = 12
B. 3 × □ = 12
C. 12 + 3 = □
D. 12 × 3 = □
Answers
12/3=4
-> 3 x 4 = 12
Answer:
3 × □(4) = 12
Step-by-step explanation:
because Jacob mowed 12 lawns this week and He mowed
3 times as many lawns as Kevin mowed.
If ΔRST ≅ ΔWXY, then one pair of corresponding angles are:
∠S and ∠W.
∠T and ∠Y.
∠R and ∠X.
Answers
Answer:
∠ T and ∠ Y
Step-by-step explanation:
the corresponding angles are the letters that have the same position in the names of the 2 triangles , that is
∠ R and ∠ W ( first letters in each of the 2 triangles )
∠ S and ∠ X ( second letters in each of the 2 triangles )
∠ T and ∠ Y ( third letters in each of the 2 triangles )
then the only letters ( angles ) from the list ,corresponding are
∠ T and ∠ Y
Answer:
Angle T and angle Y are corresponding angles.
the dice was thrown 35 times and following numbers were obtained prepare frequency table51423266142545361526254132141626333
Answers
This table shows the frequency of each number obtained after throwing the die 35 times
How to prepare frequency tableTo prepare a frequency table based on the numbers obtained from throwing a die 35 times, we can list the numbers from 1 to 6 and count the frequency of each number.
Numbers: 1, 2, 3, 4, 5, 6
Frequency: 5, 14, 6, 4, 5, 1
Based on the given numbers, the frequency table would look like this:
Number | Frequency
1 5
2 14
3 6
4 4
5 5
6 1
This table shows the frequency of each number obtained after throwing the die 35 times.
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A graph has quantity on the x-axis and price on the y-axis. A supply line goes through (10, 25), (20, 30), (30, 35), (40, 40).A graph has quantity on the x-axis and price on the y-axis. A demand line goes through (10, 40), (20, 30), (30, 20), (40, 10). Based on the supply graph and the demand graph shown above, what is the price at the point of equilibrium? a. 20 b. 30 c. 40 d. There is not enough information given to determine the point of equilibrium. A graph has quantity on the x-axis and price on the y-axis. A supply line goes through (10, 25), (20, 30), (30, 35), (40, 40).A graph has quantity on the x-axis and price on the y-axis. A demand line goes through (10, 40), (20, 30), (30, 20), (40, 10). Based on the supply graph and the demand graph shown above, what is the price at the point of equilibrium? a. 20 b. 30 c. 40 d. There is not enough information given to determine the point of equilibrium. A graph has quantity on the x-axis and price on the y-axis. A supply line goes through (10, 25), (20, 30), (30, 35), (40, 40).A graph has quantity on the x-axis and price on the y-axis. A demand line goes through (10, 40), (20, 30), (30, 20), (40, 10). Based on the supply graph and the demand graph shown above, what is the price at the point of equilibrium? a. 20 b. 30 c. 40 d. There is not enough information given to determine the point of equilibrium.
Answers
A polygon with an area of 10 square inches is dilated by a scale factor of 4, what is the new area?
Answers
The new area would be 40 square inches. When a scale factor dilates a polygon, the area is multiplied by the square of the scale factor. If the original area is 10 square inches and the scale factor is 4, the new area would be 10 x 4^2 = 10 x 16 = 40 square inches.
Is a function represented by the table linear? 10 -6 11 -1 1 12 6 13 12
Answers
Answer:
If so then this table is linear
Step-by-step explanation:
when looking at a table, to check if it is linear, simply look at the x values and if there are any duplicates then ur answer would not be linear. but for this table their are no duplicate x values so it is linear
in an examination 30% of the candidates failed in English and 35% failed in general studies and 27% failed in both subjects.if310 candidates passed in both how many candidates appeared in the examination
Answers
Answer:
500
Step-by-step explanation:
The time until recharge for a battery in a laptop computer under common conditions is normally distributed with a mean of 253 minutes and a standard deviation of 45 minutes. What value of life in minutes is exceeded with 90% probability? Round your answer to the nearest minute.
Answers
The value of life in minutes is exceeded by 90% probability is 327.025.
What is a normal distribution?
A continuous probability distribution for a real-valued random variable is called a normal distribution or a Gaussian distribution. The normal distribution describes a symmetrical plot of data around its mean value, where the width of the curve is defined by the standard deviation.
Here, we have
Given: The time until recharge for a battery in a laptop computer under common conditions is normally distributed with a mean of 253 minutes and a standard deviation of 45 minutes.
We have to find the value of life in minutes is exceeded by 90% probability.
= Mean + Z (Standard Deviation)
= 253 + 1.645×45
= 327.025
Hence, the value of life in minutes is exceeded by 90% probability is 327.025.
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A senior citizens' group is making fruit baskets and plans to sell them as a fundraiser. They are able to make 10 fruit baskets and want to sell them for $35 each For domain and range
Answers
If a senior citizens' group is making fruit baskets and plans to sell them as a fundraiser. They are able to make 10 fruit baskets and want to sell them for $35 each . The domain is [0, 10] and range is [0, 350].
Domain and rangeGiven data :
Fruit basket produce = 10
Fruit basket sold = $35
Now let determine the domain and the range since we were told they make 10 baskets of fruits and as well intend to sell the basket of fruit for the amount of $35 :
Hence:
Domain :
[0, 10]
Range :
[ 0, 350 ]
Therefore If a senior citizens' group is making fruit baskets and plans to sell them as a fundraiser. They are able to make 10 fruit baskets and want to sell them for $35 each . The domain is [0, 10] and range is [0, 350].
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Divide £2.28 btw eve and amelie in the ratio 9:5 give your answer to the nearest penny Eve gets ? And amelie gets ?
Answers
Answer:
Eve gets 1.47 and Amelie gets 0.81
Step-by-step explanation:
the ratio is 9 to 5 so we can say 9x + 5x=2.28
14x=2.28
x=0.16
so eve gets 9x = 9(2.28/14) = 1.47
and amelie gets 5x = 5(2.28/14) = 0.81
Find the volume of the
triangular prism.
8 ft
6 ft
The volume of the triangular prism is ft³.
15 ft.
Answers
The volume of the triangular prism will be 400 cubic feet.
Given that:
Width, W = 15 feet
Height, h = 8 feet
Base length, b = 6²/₃ feet
Volume is a measurement of three-dimensional space that is utilized. The concept of length is linked to the notion of capacity.
The volume of the triangular prism is calculated as,
V = 1/2 · b · h · W
V = 0.5 · 6²/₃ · 8 · 15
V = 400 cubic feet
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Somebody please help meee
Answers
3√2/(√3 - √2) . (√3 - √2)/(√3 - √2)
3√2(√3 - √2)/(3 - 2)
3√2(√3 - √2)
3√6 - 6
3(√6 - 2)
Answer: 3(√6 - 2)
For each right triangle below, find the missing side (Pythagorean’s Theorem) and the missing angle (Angle Sum theorem.)
Answers
Answer:
n=4
a=36.82
Step-by-step explanation:
\(90+53.18+a=180\)
\(a+143.18=180\)
\(a=36.82\)
\(n^2+3^2=5^2\)
\(n^2+9=25\)
\(n^2=16\)
\(n=4\)
Find the constant proportionality for the ratio 4/7
Answers
but the answer is y
Step-by-step explanation:
yauyy
Hello, I need some help with this precalculus question for my homework, please HW Q16
Answers
we have the function
\(A(t)=A_0*e^{-0.0244t}\)Convert into an equivalent function of the form
\(y=a(b)^t\)so
\(A(t)=A_0e^{-0.0244t}=A_0(e^{-0.0244})^t=A_0(0.9759)^t\)therefore
the equivalent function is
\(A_0=A_0(0.9759)^t\)The rate of decay is equal to
b=1-r
b=0.9759
r=1-b
r=1-0.9759
r=0.0241
The answer Part a is -0.0241 (which is negative because is a decay rate)Part b
For t=10 years
A_0=500 grams
substitute
\(\begin{gathered} A(t)=500*e^{-0.0244*(10)} \\ A(t)=392\text{ grams} \end{gathered}\)The answer part b is 392 gramsPart c
For A(t)=200 grams
Find out the value of t
substitute given values
\(\begin{gathered} 200=500e^{-0.0244(t)} \\ \frac{200}{500}=e^{-0.0244(t)} \end{gathered}\)Apply ln on both sides
\(\begin{gathered} ln\frac{200}{500}=lne^{-0.0244(t)} \\ \\ ln\frac{2}{5}=-0.0244t \end{gathered}\)t=37.6 years
The answer part c is 37.6 yearsPart d
For A(t)=A_0/2
substitute
\(\begin{gathered} \frac{A_0}{2}=A_0e^{-0.0244(t)} \\ \frac{1}{2}=e^{-0.0244(t)} \end{gathered}\)Apply ln on both sides
\(ln\frac{1}{2}=lne^{-0.0244(t)}\)t=28.4 years
The answer part d is 28.4 yearsThe functions f(x) = −(x − 1^)2 + 5 and g(x) = (x + 2)^2 − 3 have been rewritten using the completing-the-square method. Apply your knowledge of functions in vertex form to determine if the vertex for each function is a minimum or a maximum and explain your reasoning.
Answers
If we write a quadratic in vertex form:
\(y=a(x-h)^2+k\)
Then:
\(\bold{a}\) \(\longrightarrow\) is the coefficient of \(x^2\)
\(\bold{h}\) \(\longrightarrow\) is the axis of symmetry.
\(\bold{k}\) \(\longrightarrow\) is the max/min value of the function.
Also:
If \(a > 0\) then the parabola will be of the form \(\cup\) and will have a minimum value.
\(a < 0\) then the parabola will be of the form \(\cap\) and will have a minimum value.
For the given functions:
\(a < 0\)
\(f(x)=-(x-1)^2+5\) this has a maximum value of \(\bold{5}\)
\(a > 0\)
\(f(x)=(x+2)^2-3\) this has a minimum value of \(\bold{-3}\)
What is the IQR for 10, 14, 15, 15, 16, 18, 19, 21
Answers
Answer:
15-18
Step-by-step explanation:
The IQR is the middle 50% of a set of numbers
There are 8 numbers, so its the middle 4
The middle 4 consists of 15,15,16,18
The range is 15-18
How would I graph 3x−y=1 ?
I got as far as -y = -3x + 1 but I think I have to make the y positive and I forgot how to do that
Answers
Step-by-step explanation:
3x-y= 1
bring 3x to the right so it become negative
-y= 1 - 3x
divide by -1 for each expression
y = -1 + 3x
arrange it by bring 3x to the front side
y = 3x-1
Please Help!! (brainliest fr best answer)
1. What is the measure of ∠E? Explain how you know.
2. Describe the relationship between ∠E and ∠K. What is the measure of ∠K?
(image below)
Answers
1. The measure of ∠E = 135°. 2. Angles ∠E and ∠K are alternate exterior angles, and the measure of ∠K = 135°
What is the Exterior Angle?An exterior Angle is defined as an angle produced on the outside of a polygon by extending the sides of the polygon.
The figure is given in the question, as shown.
Since we have a regular octagon that has :
∠I = 45° = ∠G = 45°
Here ∠G + ∠H = 90° (complementary angles)
45° + ∠H = 90°
∠H = 45°
So ∠H + ∠E = 180° (supplementary angles)
45° + ∠E = 180°
∠E = 135°
2. Here the relationship between angles ∠E and ∠K is that they are alternate exterior angles.
So the measure of ∠K = 135°
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The missing figure has been attached below.
Complete this sequence of numbers such that the difference between any two adjacent numbers is the same : 3/k, _, _, 9/2k.
Answers
The completed sequence is: 3/k, 3/k, 3/k, 9/2k.To complete the sequence of numbers with a constant difference between adjacent numbers, we can calculate the common difference by subtracting the first term from the second term.
Let's denote the missing terms as A and B.
The given sequence is: 3/k, A, B, 9/2k.
The common difference can be found by subtracting 3/k from A or B. Therefore:
A - 3/k = B - A = 9/2k - B.
To simplify, we can equate the two expressions for the common difference:
A - 3/k = 9/2k - B.
Next, we can solve for A and B using this equation.
Adding 3/k to both sides gives:
A = 3/k + 9/2k - B.
Now, we can substitute the value of A into the equation:
3/k + 9/2k - B - 3/k = 9/2k - B.
Simplifying further, we have:
9/2k - 3/k = 9/2k - B.
Cancelling out the common terms, we find:
-3/k = -B.
Multiplying both sides by -1, we get:
3/k = B.
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Solve the inequality for y.
y-5<-14
Answers
negative 9 remember that
Move the constant to the right-hand side and change its sign and calculate
if 270kg of corn would feed 42 horses for 21 days, for how many days would 36okg of it feed 21 horses?
Answers
Hi!
To find this, multiply 42, 21 and 360 first:
317520
Now, multiply 21 and 270:
5670
Now, divide 317520 by 5670:
56 days
(I've had problems like these before, this is how my teacher taught me to solve them. If you have any more trouble, try to use these steps!)
Hope this helps!
Which statement about rectangles is true?
1. Only some rectangles are parallelograms.
2. Parallelograms have exactly 1 pair of parallel sides.
3. So, only some rectangles have exactly 1 pair of parallel sides.
1. All rectangles are parallelograms.
2. Parallelograms have 2 pairs of parallel sides.
3. So, all rectangles have 2 pairs of parallel sides.
1. Only some rectangles are parallelograms.
2. Parallelograms have 2 pairs of parallel sides.
3. So, only some rectangles have 2 pairs of parallel sides.
1. All rectangles are parallelograms.
2. Parallelograms have exactly 1 pair of parallel sides.
3. So, all rectangles have exactly 1 pair of parallel sides.
Answers
The correct statement about rectangles is:
1. All rectangles are parallelograms.
2. Parallelograms have exactly 1 pair of parallel sides.
3. So, all rectangles have exactly 1 pair of parallel sides.
A rectangle is a type of parallelogram that has additional properties. By definition, a rectangle is a quadrilateral with four right angles. This means that opposite sides of a rectangle are parallel. Since all four sides of a rectangle are right angles, it follows that a rectangle has exactly 1 pair of parallel sides.
Option 1 states that only some rectangles are parallelograms, which is incorrect. All rectangles are parallelograms because they have opposite sides that are parallel.
Option 2 states that parallelograms have 2 pairs of parallel sides, which is also incorrect. Parallelograms have exactly 2 pairs of parallel sides, not 4. A rectangle is a special type of parallelogram that has additional properties such as all angles being right angles.
Option 3 states that only some rectangles have 2 pairs of parallel sides, which is incorrect. All rectangles have exactly 1 pair of parallel sides, not 2. Having 2 pairs of parallel sides would make a shape a parallelogram, not a rectangle.
Therefore, the correct statement is that all rectangles are parallelograms and have exactly 1 pair of parallel sides. 1,2,3 are correct.
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