Answers
The solution is, the value of x is, x = 12.
What is triangle?A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. A triangle with vertices A, B, and C is denoted \triangle ABC. In Euclidean geometry, any three points, when non-collinear, determine a unique triangle and simultaneously, a unique plane.
here, we have,
from the given figure, we get,
the triangles are similar,
so, we know that, the sides are proportional to each other.
i.e. 8:4 = x: 6
or, x = 8 * 6 / 4
or, x = 2 * 6
or, x = 12
Hence, The solution is, the value of x is, x = 12.
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Related Questions
The shape above is composed of triangles and rectangles. Use the triangles and rectangles to find the total area of the figure.
A- 64.5 units squared
b- 39 units squared
c- 46.5 units squared
d- 54 units squared
Answers
Answer:
To find the total area of the figure, we need to find the area of each of the individual triangles and rectangles and then add them up.
The rectangle on the left has a length of 6 and a width of 3, so its area is 6 x 3 = 18 square units.
The triangle on the left has a base of 6 and a height of 5, so its area is 1/2 x 6 x 5 = 15 square units.
The triangle on the right has a base of 6 and a height of 3, so its area is 1/2 x 6 x 3 = 9 square units.
The rectangle on the right has a length of 3 and a width of 6, so its area is 3 x 6 = 18 square units.
Adding up the areas of each shape, we get:
18 + 15 + 9 + 18 = 60 square units
Therefore, the total area of the figure is 60 square units. Answer: (d) 60 units squared.
Evaluate h(x)=−2x+9
when x=−2,0,
and 5
.
h(−2)=
h(0)=
h(5)=
Answers
Answer:
h(-2) = 13, h(0) = 9, and h(5) = -1.
Step-by-step explanation:
To evaluate h(x) = -2x + 9 for the given values of x, we can substitute each value of x into the expression and simplify:
h(-2) = -2(-2) + 9 = 13
h(0) = -2(0) + 9 = 9
h(5) = -2(5) + 9 = -1
Therefore, h(-2) = 13, h(0) = 9, and h(5) = -1.
What happens to the value of the expression 100-x as x increases
Answers
The number 100-x has a decreasing worth as x rises.
What does a mathematical expression look like?A mathematical statement is referred to as an expression or an algebraic expression if it contains numbers, factors, and a numerical operation between them..For example, the arithmetic sign + separates the terms 4m and 5 from of the variable m in the expression 4m + 5..
The number 100-x has a decreasing worth as x rises. This is due to the fact that the phrase 100-x denotes a linear equation with a -1 slope. This indicates that the expression's value drops by one for each unit rise in x. As a result, the expression's value decreases as x increases. For instance, if x is 50, the expression's value is 50; however, if x is 70, the expression's value is 30. The meaning of the equation decreases in proportion to how much x increases.
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Question 13 A polynomial, P(x), has real coefficients and also has zeros at 1,1+i, and 2-i. Then this polynomial must have a degree of
Answers
The polynomial P(x) must have a degree of 4.
This is because a polynomial with real coefficients must have complex zeros in conjugate pairs. This means that if 1+i is a zero of the polynomial, then its conjugate, 1-i, must also be a zero. Similarly, if 2-i is a zero, then its conjugate, 2+i, must also be a zero. Therefore, the polynomial P(x) must have zeros at 1, 1+i, 1-i, 2-i, and 2+i. Since a polynomial's degree is equal to the number of its zeros, the polynomial must have a degree of 4.
In summary, a polynomial with real coefficients and zeros at 1, 1+i, and 2-i must have a degree of 4.
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The quotient of x and 3 plus 24 PLEASE HELP
Answers
Answer:
(24 divided by 3) + x
Step-by-step explanation:
i did it
The sum of two numbers is 72. The difference of the two numbers is 50. Let x be the larger number and ybe the smaller number. Set up and evaluate a system of equations to determine the values of x and y.
Write an equation that expresses the information in the sentence "The sum of two numbers is 72."
First equation:
Write an equation that expresses the information in the sentence "The difference of the two numbers is 50."
Second equation:
Solve the system you have written above to find x and y.
x= . y= .
Answers
the bigger number x= 61 and the smaller number y = 11. The system of equations are x + y= 72 and x - y = 50
The sum of two numbers is 72 can be expressed as a linear equation: x + y = 72. The difference of the two numbers is 50 can be expressed as a linear equation: x - y = 50. We can set up a system of equations to determine the values of x and y:
First equation: x + y = 72
Second equation: x - y = 50
To solve the system of equations, we can use the elimination method. We can add the two equations together to eliminate the y variable:
x + y = 72
x - y = 50
--------------
2x = 122
Next, we can solve for x by dividing both sides of the equation by 2:
2x/2 = 122/2
x = 61
Now that we know the value of x, we can plug it back into one of the equations to find the value of y:
61 + y = 72
y = 72 - 61
y = 11
So the solution to the system of equations is x = 61 and y = 11.
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Write an equation for the graph that passes through (4,-5) and (7,10).
Answers
The equation for the graph that passes through (4,-5) and (7,10) is: y = 5x - 25
What is equation ?
An equation is a mathematical statement that shows that two expressions are equal. It contains an equal sign (=) between two expressions, one on each side. An equation can contain variables, constants, numbers, and mathematical operations like addition, subtraction, multiplication, and division
To write an equation for the graph that passes through the points (4,-5) and (7,10), we can use the slope-intercept form of a linear equation:
y = mx + b
where m is the slope of the line and b is the y-intercept.
To find the slope of the line passing through the two points, we can use the slope formula:
m = (y2 - y1) / (x2 - x1)
where (x1, y1) = (4,-5) and (x2, y2) = (7,10).
m = (10 - (-5)) / (7 - 4)
m = 15 / 3
m = 5
Now that we know the slope of the line, we can use either point to solve for the y-intercept, b. Let's use the point (4,-5):
y = mx + b
-5 = 5(4) + b
-5 = 20 + b
b = -25
Therefore, the equation for the graph that passes through (4,-5) and (7,10) is: y = 5x - 25
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13. The volume of a rectangular box is given by the functionV(w)=(60−4w)w2. What is a reasonable domain for the function in this situation? Express the domain as an inequality, in interval notation, and in set notation. 14. Sketch a graph of the function in Item 13 over the domain that you found. Include the scale on each axis. 15. Use a graphing calculator to find the coordinates of the maximum point of the function given in Item 13. 16. What is the width of the box, in inches, that produces the maximum volume? 17. Reason abstractly. An architect uses a cylindrical tube to ship blueprints to a client. The height of the tube plus twice its radius must be less than60 cm. a. Write an expression forh, the height of the tube, in terms ofr, the radius of the tube. b. Write an expression forV, the volume of the tube, in terms ofr, the radius of the tube. c. Find the radius that produces the maximum volume. d. Find the maximum volume of the tube.
Answers
13. The reasonable domain for the function V(w) = (60-4w)w^2 is when the volume is greater than 0.
14. The graph will look like a parabola with a maximum point at w = 7.5.
15.The coordinates of the maximum point are (7.5, 506.25).
16. The width of the box that produces the maximum volume is 7.5 inches, as found in the previous question.
17. a. The expression for the height of the tube in terms of the radius is h = 60 - 2r.
This means that the values of w must be between 0 and 15, since the volume becomes negative when w is greater than 15. Therefore, the domain can be expressed as an inequality as 0 < w < 15, in interval notation as (0, 15), and in set notation as {w | 0 < w < 15}.
14. To sketch a graph of the function V(w) = (60-4w)w^2 over the domain (0, 15), we can plot points at different values of w and connect them with a smooth curve. The scale on each axis can be 1 unit per grid line.
15. Using a graphing calculator, we can find the coordinates of the maximum point of the function V(w) = (60-4w)w^2 by using the maximum function.
b. The expression for the volume of the tube in terms of the radius is V = πr^2h = πr^2(60 - 2r).
c. To find the radius that produces the maximum volume, we can take the derivative of the volume function and set it equal to 0. This gives us 2πr(60 - 4r) = 0. Solving for r, we get r = 7.5 cm.
d. The maximum volume of the tube is V = π(7.5)^2(60 - 2(7.5)) = 1265.49 cm^3.
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Using long division to find each quotient
(2x³ + x²-x-4) ÷ (x + 4)
Answers
Answer:
The quotient of (2x³ + x² - x - 4) ÷ (x + 4) is 2x^2 - 7x + 17, and the remainder is 27x - 4.
Step-by-step explanation:
2x^2 - 7x + 17
x + 4 | 2x^3 + x^2 - x - 4
- (2x^3 + 8x^2)
---------------
-7x^2 - x
+ (-7x^2 - 28x)
-------------
27x - 4
Therefore, the quotient of (2x³ + x² - x - 4) ÷ (x + 4) is 2x^2 - 7x + 17, and the remainder is 27x - 4.
A. Change y = 2x-3y- x' to polar form. Give exact values (no decimals) and show work. B. A certain tide repeats its cycle every 12 hours. High tide is 6 feet and low tide is 2 feet. High tide occurs a
Answers
A. The equation given can be expressed in polar form using the Pythagoras theorem.
Let the polar coordinate of a point be (r, θ).
Let r = √(x^2 + y^2)
=> r^2 = x^2 + y^2
=> r^2 = 2x^2 - 6xy - 2x
Let θ = tan^-1 (y/x)
Now, the equation in polar form is:
r^2 = 2x^2 - 6xy - 2x
tan^-1 (y/x) = θ
To find the exact values, solve the equation for the given values of x and y:
For x = 0 and y = 2:
r^2 = 0 - 6*2 - 0
=> r^2 = -12
=> r = √12
=> r = 2√3
tan^-1 (2/0) = θ
=> θ = 90°
Hence, the point (x, y) = (0, 2) has polar coordinates (2√3, 90°).
B. The given cycle has a period of 12 hours. This means that the time between each high and low tide is 12 hours. The height of high tide is 6 feet and the height of low tide is 2 feet. This means that the amplitude of the cycle is 4 feet (6 feet - 2 feet).
Hence, the equation for the tide cycle can be expressed as:
Height = 4sin (π/6 * t) + 4
Where t is time in hours.
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Aisha is going to invest in an account paying an interest rate of 2.7% compounded
quarterly. How much would Aisha need to invest, to the nearest ten dollars, for the
value of the account to reach $6,800 in 16 years?
Answers
[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\dotfill & \$ 6800\\ P=\textit{original amount deposited}\\ r=rate\to 2.7\%\to \frac{2.7}{100}\dotfill &0.027\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{quarterly, thus four} \end{array}\dotfill &4\\ t=years\dotfill &16 \end{cases}[/tex]
[tex]6800 = P\left(1+\frac{0.027}{4}\right)^{4\cdot 16} \implies 6800=P(1.00675)^{64} \\\\\\ \cfrac{6800}{(1.00675)^{64}}=P\implies 4420\approx P[/tex]
35 percent of 150 is about 50 is this reasonable or unreasonable
Answers
The statement that 35 percent of 150 is about 50 is completely false and hence unreasonable as 35 percent of 150 is exactly equal to 52.50.
In the given problem which is related to percentage of some specific number, the value is obtained by direct multiplication of percentage with the given number to get the answer. Percentage is defined as the ratio which is given with respect to number 100 or 100 units as a whole. Its symbol is %. It is a dimensionless quantity and hence has no units as ratios does not have units.
The given equation can be represented as follows to obtain the answer:
(35/100) × 150 = 52.50
Since 52.50 cannot be considered close to 50, hence the statement is u reasonable. Though 52.5 can be considered as about 52 or 53.
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2. Given the matrix
\( A=\left(\begin{array}{ccc}1 & -1 & 1 \\ 2 & -1 & 11-6 \\ 0 & 1 & 10-6\end{array}\right) \)
(a) Show that A is invertible and determine by caculate A^−1
Answers
Yes, matrix A is invertible.
Therefore, the inverse of matrix A is A-1 =
[tex]\begin{array}{ccc} -1 & -3 & 1 \\ 10-6 & 8 & 5 \\ -2 & -2 & -2\end{array}[/tex]
To calculate A-1, we can use the following formula:
A-1 = (1/detA) x adj(A)
Where detA is the determinant of A, and adj(A) is the adjugate of A.
To calculate the determinant of A, we can use the following formula:
detA = (1 x (-1) x 10-6) + (-1 x (11-6) x 1) + (1 x (-1) x (2))
= 1 x (-1) x 4 - (-1) x 5 x 1 + 1 x (-1) x 2
= 4 - 5 + 2
= 1
Now we can calculate the adjugate of A. To do this, we need to calculate the cofactors of each element in A, and then take the transpose of the matrix.
The cofactors of A can be calculated as follows:
[tex]\begin{array}{ccc} -1 & -3 & 1 \\ 10-6 & 8 & 5 \\ -2 & -2 & -2\end{array}[/tex]
Now, taking the transpose of this matrix, we get the following:
[tex]\begin{array}{ccc} -1 & -3 & 1 \\ 10-6 & 8 & 5 \\ -2 & -2 & -2\end{array}[/tex]
Now, multiplying the determinant of A and the adjugate of A, we can calculate A-1:
A-1 = (1/1) x
[tex]\begin{array}{ccc} -1 & -3 & 1 \\ 10-6 & 8 & 5 \\ -2 & -2 & -2\end{array}[/tex]
=
[tex]\begin{array}{ccc} -1 & -3 & 1 \\ 10-6 & 8 & 5 \\ -2 & -2 & -2\end{array}[/tex]
Therefore, the inverse of matrix A is:
A-1 =
[tex]\begin{array}{ccc} -1 & -3 & 1 \\ 10-6 & 8 & 5 \\ -2 & -2 & -2\end{array}[/tex]
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What are the following Sets for these two rational expressions:
22x + 11 x2 – 3x – 10 1 – 2c 20c2 + 10c
Answers
20c2 + 10c = {c | c ≠ 0}
The sets for these two rational expressions are as follows:
22x + 11 x2 – 3x – 10 = {x | x ≠ 1/2}
1 – 2c = {c | c ≠ 1/2}
20c2 + 10c = {c | c ≠ 0}
To simplify the expressions, use the following steps:
1. Factor out the greatest common factor (GCF) if one exists.
2. Simplify the numerator and denominator separately.
3. Combine the numerator and denominator.
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A pack of sweets that are 81 inside, must be divided in a ratio of 2:1, how many will each get
Answers
The each of two individuals will get 54 and 27 sweets according to provided ratio.
Let us assume the amount of sweets each get be 2x and x. Now we know the sum is 81, so representing the information in equation form.
2x + x = 81
Performing addition on Left Hand Side of the equation
3x = 81
Rewriting the equation
x = 81/3
Performing division on Right Hand Side of the equation
x = 27
So, first person will get amount of sweets = 2×27
First person = 54
Amount of sweets for second person = 27
Thus, each will get 54 and 27 sweets.
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how to solve 3 divided by 561 long division
Answers
Answer:
187
Step-by-step explanation:
how to do long division, you know how to start im assuming. then you then bring down and Divide, Multiply, Subtract, with the first number then bring the next number down and repeat that.
Answer:
187
Step-by-step explanation:
I personally just do multiplication whenever I can, but that's just me. Like for example I know 100 x 3 = 300 and 200 x 3 = 600. SO it has to be between 100 and 200.
150 x 3 = 450. So know it narrows it down to between 150 and 200.
175 x 3 = 525
180 x 3 = 540
185 x 3 = 555
190 x 3 =570
So now it's between 185 and 190.
Now I just need to do the following.
186 x 3 = 558
187 x 3 = 561
And there we have the answer.
solve for x: 1/2x+4=9
Answers
Answer:
x=10
Step-by-step explanation:
solve for x: 1/2x+4=9
First, you need to get the variable x to be on a side of the equation, by itself. That is your goal throughout the problem. The easiest way to start this is by removing 4 from the left side of the equation. We know that before the number 4 is a plus sign. In order to remove 4 from the left side of the equation, we must do the opposite of the plus sign. The plus sign represents addition, and the opposite of addition is subtraction. This means we need to subtract 4 from the left side. Remember, that whatever we do to one side, we must do to the other side! This means we must subtract 4 on BOTH sides of the equation.
On the left side of the equation, we have 4 and we subtract it by 4.
4-4=0
Since the answer is 0 we can forget about the number, because it does not hold any value.
Next, on the right side of the equation we have 9, and we subtract it by 4, as well because whatever we do to one side, we must do to the other side.
9-4=5
Our new equation should be: 1/2x=5
Our last step is to continue our goal from the beginning of the problem; to get x alone on one side of the equation. In order to complete that goal, we must remove 1/2 from the left side of the equation. Remember when we subtracted 4 one each side, we took the opposite of the sign. In this equation, we don't necessarily see a sign like before. However, whenever x is directly beside another number, that means that it is being multiplied by that number. Just like how the opposite of addition is subtraction, the opposite of multiplication is division. We need to divide 1/2 on both sides.
On the left side, we divide 1/2x by 1/2.
1/2 divided by 1/2 is 10
One isn't necessary to keep in the equation ONLY if it is next to x, like in this case.
Lastly, whatever we do to one side, we must do to the other. We finish the problem by dividing 5 by 1/2.
5 divided by .5 is 10
We are left with x=10.
The answer is 10.
Container a holds 750ml of liquid container b holds 1. 25 how much from container b must be poured into container a so they can be equal?
Answers
We need to pour 250 ml of liquid from container B to container A so they can be equal in volume.
To make container A and B equal in volume, we need to pour some liquid from container B into container A. Let's call the amount of liquid that we need to pour from container B to container A as "x" ml.
After pouring x ml of liquid from container B to container A, the total volume of liquid in container A will be (750 + x) ml, and the total volume of liquid in container B will be (1250 - x) ml.
Since we want the volumes of both containers to be equal, we can set up the equation:
750 + x = 1250 - x
Solving for x:
2x = 500
x = 250
Therefore, we need to pour 250 ml of liquid from container B to container A so they can be equal in volume.
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Please help!! Anything is fine
Answers
The missing angle is 90°. So, to obtain the values of the sides given the lengths we will have:
8. PT = 1
PV = 2
9. VT = 0.76
PV = 0.66
10. PT = 3
PV = 6
11. PV =0.58
PT =1.154
12. PT = 1.73
VT = 3
13. VT = 3
PV = 3.5
How to find the missing sidesThe given triangle is a scalene triangle because of the three different angles it has which sum up to 180 degrees. The sides will also be different.
For the first triangle whose known side is √3, the missing values can be obtained this way:
sin 60°/ √3 = sin 90/PV
PV = √3 Sin 90/ sin 60
PV = 1.732/0.866
= 2
PT = sin 60/ √3 = sin 30/ PT
PT = √3 sin 30/sin 60
PT = 1
Using this same pattern, the values for the other figures can be obtained.
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I need quick help with this, please.
Answers
Answer:
c
Step-by-step explanation:
it makes sense
a.) State the general exponential growth equation.
b.) State the general exponential decay equation.
Answers
a. The general exponential growth equation is given by: y = abˣ
b. The general exponential decay equation is given by: [tex]y = a (1 - r)^x[/tex]
Exponential growth:Exponential growth is a type of growth pattern in which a quantity grows at an increasing rate proportional to its current value. This means that the larger the quantity, the faster it grows.
a. The general exponential growth equation is given by:
y = abˣ
Where y is the final value, 'a' is the initial value, b is the growth factor or base, and x is the time or number of periods.
Exponential decay:Exponential decay is a type of decay pattern in which a quantity decreases at a decreasing rate proportional to its current value. This means that the larger the quantity, the slower it decays.
b. The general exponential decay equation is given by:
[tex]y = a (1 - r)^x[/tex]
Where y is the final value, a is the initial value, r is the decay rate, and x is the time or number of periods
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25. Find the scale factor of JKLM to EFGH.
26. List all pairs of congruent angles.
27. Write the ratios of the corresponding side lengths in a statement of proportionality
28. Find the values of x, y, and z.
29. Find the perimeter of each polygon
30. Find the ratio of the perimeters of JKLM to EFGH
31. Find the area of each polygon
32. Find the ratio of the areas of JKLM to EFGH
Answers
25. The scale factor is 2.5
26. The congruent angles include
∠ E = ∠ J = 65 degrees
∠ F = ∠ K = 90 degrees
∠ G = L = 90 degrees
∠ H = ∠ M = 115 degrees
How to find the scale factor25. The scale factor of JKLM and EFGH is calculated using corresponding sides
side EF * scale factor = side JK
8 * scale factor = 20
scale factor = 20 / 8
scale factor = 2.5
26. The congruent angles include
∠ E = ∠ J = 65 degrees
∠ F = ∠ K = 90 degrees
∠ G = L = 90 degrees
∠ H = ∠ M = 360 - 90 - 90 - 65 = 115 degrees
27. the ratios of the corresponding side lengths
JK / EF is proportional to KL / FG is proportional to LM / GH is proportional to MJ / EH
28. the values of x, y, and z
x = 2.5 * FG = 2.5 * 11 = 27.5
y = 30 / 2.5 = 12
z = 65 degrees
29. the perimeter of each polygon
the smaller polygon EFGH = 8 + 11 + 3 + 12 = 34
the bigger polygon JKLM = 20 + 27.5 + (3 * 2.5) + 30 = 85
30. the ratio of the perimeters of JKLM to EFGH
= 85 / 34 = 2.5
31. the area of each polygon
the smaller polygon EFGH = 0.5(3 + 8) * 11 = 60.5
the bigger polygon JKLM = 0.5(20 + 7.5) * 27.5 = 378.125
32. the ratio of the areas of JKLM to EFGH
= 378.125 / 60.5 = 6.25
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Imagine you deposited $500 in a savings account that had an annual interest rate of 5% for 5 years. Use the simple interest formula from the article to calculate how much you would earn each year (Column 1). Then, calculate how much money you would have at the end of each year (Column 2).
Answers
The interest earned each year is $25 and the total amount at the end of each year would be $525, $550, $575, $600, and $625 respectively.
What is simple interest?
Simple interest is a method of calculating interest on a loan or investment where the interest is calculated only on the principal amount. It is based on a fixed percentage of the principal amount and does not take into account any interest earned on previous interest payments.
The formula for calculating simple interest is I = PRT, where I is the interest, P is the principal amount, R is the annual interest rate, and T is the time period in years.
Using the simple interest formula:
I = P * r * t
where I is the interest earned, P is the principal or initial deposit, r is the annual interest rate, and t is the time in years.
For an initial deposit of $500 at an annual interest rate of 5%, the interest earned each year and the total amount at the end of each year would be:
Year 1:
I = 500 * 0.05 * 1 = $25
Total = 500 + 25 = $525
Year 2:
I = 500 * 0.05 * 1 = $25
Total = 525 + 25 = $550
Year 3:
I = 500 * 0.05 * 1 = $25
Total = 550 + 25 = $575
Year 4:
I = 500 * 0.05 * 1 = $25
Total = 575 + 25 = $600
Year 5:
I = 500 * 0.05 * 1 = $25
Total = 600 + 25 = $625
Therefore, the interest earned each year is $25 and the total amount at the end of each year would be $525, $550, $575, $600, and $625 respectively.
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Assume that A is a matrix with three rows. Find the matrix B such that BA gives the matrix resulting from A after the given row operations are performed.3R3+R1⇒R1−7R2⇒R2B=
Answers
The matrix B such that BA gives the matrix resulting from A after the given row operations are performed.3R3+R1⇒R1−7R2⇒R2B= is B = [[1, 0, 3], [0, -7, 0], [0, 0, 1]].
Assuming that A is a matrix with three rows, we can find the matrix B such that BA gives the matrix resulting from A after the given row operations are performed.3R3+R1⇒R1−7R2⇒R2B= by following these steps:
1. Start with the identity matrix, I, which is a matrix with ones along the main diagonal and zeros everywhere else:
I = [[1, 0, 0], [0, 1, 0], [0, 0, 1]]
2. Apply the first row operation, 3R3+R1⇒R1, to the identity matrix by adding three times the third row to the first row:
I = [[1+3(0), 0+3(0), 0+3(1)], [0, 1, 0], [0, 0, 1]]
I = [[1, 0, 3], [0, 1, 0], [0, 0, 1]]
3. Apply the second row operation, −7R2⇒R2, to the identity matrix by multiplying the second row by -7:
I = [[1, 0, 3], [0*(-7), 1*(-7), 0*(-7)], [0, 0, 1]]
I = [[1, 0, 3], [0, -7, 0], [0, 0, 1]]
4. The resulting matrix, I, is the matrix B that we are looking for:
B = [[1, 0, 3], [0, -7, 0], [0, 0, 1]]
Therefore, the matrix B such that BA gives the matrix resulting from A after the given row operations are performed.3R3+R1⇒R1−7R2⇒R2B= is B = [[1, 0, 3], [0, -7, 0], [0, 0, 1]].
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A picoliter is three metric units larger than a femtoliter. How many centiliters are in a picoliter?
Answers
The amount of centiliters in a picoliter is A = 1 x 10⁻¹⁰ cL
What is unit conversion?In order to translate measurements of a particular amount between different units, a mathematical conversion factor is usually used. This modifies the measurement of the quantity without altering its effects.
The particular circumstances or the intended result control the conversion process. This may be governed by law, a contract, a list of technical specifications, or other publicly available standards.
A precise conversion from one system to another is necessary for some measures in order to maintain the precision of both the original measurement and the conversion.
Based on the connection between a particular pair of original units and a particular pair of target units, each conversion factor is chosen.
Given data ,
Let the first unit of measurement be represented as A
where A = centiliters
Now , the amount of Liters in a centiliter is
From the unit conversion ,
1 L = 100 cL
And , 1 cL = 10⁻² L
Now , the amount of Liters in a picoliter is
1 L = 10¹² picoliters
And , amount of centiliters in a picoliter is A
where A = 10⁻¹⁰ cL
So , the 1 pL = 10⁻¹⁰ cL
Hence , the unit conversion of liters is solved
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what is the answer to 0.03 =
Answers
The answer to 0.03 as a fraction is 1/300. But as a percentage, it is 3%.
What is the difference between fraction and percentage?Fractions and percentages are both ways of expressing parts of a whole. A fraction represents a part of a whole, which is divided into equal parts, while a percentage is a fraction expressed as a number out of 100.
The main difference between fractions and percentages is their format. Fractions are typically written as a ratio of two numbers, with the numerator representing the part and the denominator representing the whole. Percentages, on the other hand, are typically written as a number followed by the symbol "%", which represents the part out of 100.
Full question "What is 0.03 as a fraction?"
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Given the function f(x)=x+3/x-8 aind the following. (a) the
average rate of change of f on [−3,1]: (b) the average rate of
change of f on [x,x+h]:
Answers
(a) The average rate of change of f on [−3,1] is:
f(1)-f(-3)/(1-(-3)) = (1+3)/(1-(-3)) - ((-3)+3)/(-3-(-3)) = (4/4) - (0/6) = 1 - 0 = 1
(b) The average rate of change of f on [x,x+h] is:
f(x+h)-f(x)/(x+h-x) = (x+h+3)/(x+h-8) - (x+3)/(x-8) = (x+h+3)(x-8) - (x+3)(x+h-8)/(x+h-8)(x-8) = (x^2-5x-8h-11)/(x^2-8x-8h+64)
The average rate of change of a function is the slope of the line that passes through two points on the graph of the function. It is calculated by the difference in the y-values of the two points divided by the difference in the x-values of the two points.
The average rate of change of f on [−3,1] is:
f(1)-f(-3)/(1-(-3)) = (1+3)/(1-(-3)) - ((-3)+3)/(-3-(-3)) = (4/4) - (0/6) = 1 - 0 = 1
The average rate of change of f on [x,x+h] is:
f(x+h)-f(x)/(x+h-x) = (x+h+3)/(x+h-8) - (x+3)/(x-8) = (x+h+3)(x-8) - (x+3)(x+h-8)/(x+h-8)(x-8) = (x^2-5x-8h-11)/(x^2-8x-8h+64)
Therefore, the average rate of change of f on [x,x+h] is (x^2-5x-8h-11)/(x^2-8x-8h+64).
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The shoe sizes of a group of middle school girls are shown. 5.5 6 7 8.5 6.5 6.5 8 7.5 8 5 If a shoe size of 9 is added to the data, how does the median change? The median stays 6.75. The median increases to 6.75. The median stays 7. The median increases to 7.
Answers
Answer:
The median is the middle value when a set of data is arranged in order from smallest to largest.
First, let's arrange the given shoe sizes in order:
5, 5.5, 6, 6.5, 6.5, 7, 7.5, 8, 8, 8.5
The median of this data set is 6.5 because it is the middle value.
Now, let's add a shoe size of 9 to the data set:
5, 5.5, 6, 6.5, 6.5, 7, 7.5, 8, 8, 8.5, 9
The new median of this data set is 7, which is greater than the previous median of 6.5.
Therefore, the answer is: The median increases to 7.
Answer: The median increases to 7.
Step-by-step explanation: I took the test and got a 100%
11. The distance round a circular hut is 17.6 m. What is the area of its floor?
12.A string measures 220 cm. Its two ends are joined to form a circle. What area
does the string enclose?
13. The area of a circular mat is 1.54 m². What is its circumference?
Answers
11. The area of the floor is 24. 62 m²
12. The area of the enclosed string is 3, 853. 09cm²
13. The circumference of the circular mat is 4.39m
How to determine the areaThe formula for the area of a circle is expressed with the equation;
A = πr²
Where;
A is the area.π takes the value 3.14r is the radius of the circle.Also, circumference of a circle is 2πr
For a circumference of 17. 6m, we have
17. 6 = 2×3.14r
r = 2. 80
Substitute the value
Area = 3.14 × (2. 80)²
Area = 24. 62 m²
For the string, circumference = 220cm
220 = 2× 31.4r
r = 35. 03 cm
Area of the enclosed string = 3.14 × (35. 03)²
Area = 3, 853. 09cm²
For the circular mat
1.54 = 3.14r²
r² = 0. 49
Take the square root
r = 0. 7m
Circumference = 2× 3.14 × 0. 7 = 4.39m
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Verify the identity. 2 sec? y - 2 cot? = cot(" - y) = 2 - 2 cot'( % - y) = 2 (sec?y- 2 sec? y - 2 2 ) X = 2 Need Help? Read it Watch It
Answers
2(cot2 y + tan2 y) = 2(1) Verified
Verify the identity:
2 sec2 y - 2 cot2 y = cot(2y) - 2 cot(2y) = 2 - 2 sec(2y)
To prove the identity, start by applying the identity:
cot2 y = 1 - tan2 y
Substitute this in the left side of the equation:
2 sec2 y - 2(1 - tan2 y) = 2 sec2 y - 2 + 2 tan2 y
Simplify the equation by factoring out a 2 from the right side:
2 sec2 y - 2 + 2 tan2 y = 2(sec2 y - 1 + tan2 y)
Next, apply the identity:
sec2 y - 1 = cot2 y
Substitute this in the equation and simplify:
2(sec2 y - 1 + tan2 y) = 2(cot2 y + tan2 y)
Finally, apply the identity:
cot2 y + tan2 y = 1
Substitute this in the equation and simplify:
2(cot2 y + tan2 y) = 2(1)
The identity is thus verified.
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