Applying the angle bisector and triangle proportionality theorem, the solutions are:
16. x = 1/2 or x = 4
17. x = 5
18. x = −1 or x = 6.
What is the Angle Bisector Theorem?The angle bisector theorem states that when a line segment divides one of the angles of a triangle into two halves, it also divides the triangle to form segments that are proportional to each other.
16. 3x/(x - 1) = (x + 4)/(x - 2) [triangle proportionality theorem]
Cross multiply
(x - 1)(x + 4) = 3x(x - 2)
x² + 3x - 4 = 3x² - 6x
x² - 3x² + 3x - 4 + 6x = 0
-2x² + 9x - 4 = 0
Factorize -2x² + 9x - 4
(−2x + 1)(x − 4)
-2x = -1
x = 1/2
or
x = 4
17. (2x + 2)/(x + 3) = (4x - 2)/(2x + 2)
(2x + 2)(2x + 2) = (4x - 2)(x + 3)
4x² + 8x + 4 = 4x² + 10x - 6
Combine like terms
4x² - 4x² + 8x - 10x = -4 - 6
-2x = -10
x = -10/-2
x = 5
18. (2x + 3)/(x + 4) = x/(x - 2) [angle bisector theorem]
Cross multiply
(2x + 3)(x - 2) = x(x + 4)
Expand
2x² - x - 6 = x² + 4x
2x² - x - 6 - x² - 4x = 0
x² - 5x - 6 = 0
Factorize x² - 5x - 6 = 0
(x+1)(x−6) = 0
x = −1 or x = 6
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(06.02) which of these is the algebraic expression for "seven more than the product of three and some number?" 7 3 x 3 10 ÷ x 3x 7 3 7x
Answer:
Step-by-step Explanation:
The correct option is C.
The algebraic expression for "seven more than the product of three and some number = 3x + 7 = 0
What is Algebraic Expression?An algebraic expression is one that is composed of variables, integer constants, and algebraic operations. An algebraic expression is, for instance, 3x² 2xy + c.
According to the given Information:we can search for the product of 3 and "some number",
Let the number be x.
So, the product of x is 3 times = 3x
And now
7 more then the Product .
we add the 7 to the product .
3x + 7 = 0
So the equation will be 3x + 7 = 0
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I understand that question you are looking for is:
Which of these is the algebraic expression for "seven more than the product of three and some number?"
A. 7 + 3 + x
B. 3 + 10 ÷ x
C. 3x + 7
D. 3 + 7x
one endpoint of a line segment is (1,2) and the midpoint of the midpoint of the segment is (-1,4) what is the other end point ?
If a true-false test with 10 questions is given what is the probability of scoring?
Answer:50%
Step-by-step explanation: It doesn't matter how many questions there are because for each question, you have a 50% chance of getting it right. So, the probability is 50%.
If the infinite curve y = e^−2x, x ≥ 0, is rotated about the x-axis. Find the area of the resulting surface.
The area of the resulting surface of this infinite curve is π units.
In this question,
The infinite curve is y = e^−2x, x ≥ 0.
The curve is rotated about x-axis.
Since x ≥ 0, the limits will be 0 to ∞.
Then the area of the resulting surface is,
[tex]A= 2\pi \lim_{b\to \infty} (\int\limits^\infty_0{e^{-2x} } \, dx )[/tex]
Now substitute,
u = -2x
⇒ du = -2dx
⇒ dx = [tex]-\frac{1}{2} du[/tex]
Then,
[tex]\int\limits{-\frac{1}{2}e^{u} } \, du =-\frac{1}{2}\int\limits{e^{u} } \, du[/tex]
Now substitute u and du, we get
⇒ [tex]-\frac{1}{2} \int\limits {e^{-2x} }(-2) \, dx[/tex]
⇒ [tex]-\frac{-2}{2} \int\limits {e^{-2x} } \, dx[/tex]
⇒ [tex](1) \int\limits {e^{-2x} } \, dx[/tex]
⇒ [tex]\int\limits {e^{-2x} } \, dx[/tex]
Thus the area of the resulting surface is
[tex]A= 2\pi \int\limits^\infty_0{e^{-2x} } \, dx[/tex]
⇒ [tex]A= 2\pi [{e^{-2x}(\frac{1}{-2} ) } \,]\limits^\infty_0[/tex]
⇒ [tex]A= \frac{2\pi}{-2} [{e^{-2(\infty)}-e^{-2(0)} } \,]\\[/tex]
⇒ [tex]A= -\pi [0-1} \,]\\[/tex]
⇒ [tex]A= \pi[/tex]
Hence we can conclude that the area of the resulting surface is π units.
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pls help questions 5-7
Answer: 0.032, 18, 4224, 7.58
Step-by-step explanation:
5. 5 L = 5000 mL = 5000 [tex]cm^{3}[/tex]
5000/(6*6*6) = 23 r 32 so 5 L of water can fill up 23 cubic tanks length 6 cm and is left with 0.032 L
6. There is (13 - 11) x 20 x 10 = 400 [tex]cm^{3}[/tex] left unoccupied in the box
400/23 = 17.4 so it takes 18 balls to overflow the water
7. 1 mL = 1 [tex]cm^{3}[/tex]
(a) 22 x 12 x 16 = 4224 [tex]cm^{3}[/tex] = 4224 mL
(b) 2 L = 2000 mL = 2000 [tex]cm^{3}[/tex]
22 x 12 = 264
2000/264 = 7.58 cm
If a function has a positive average rate of change over
an interval, does that mean that the function must be increasing over that
interval? Explain.
Step-by-step explanation:
Yes, an positive average rate of change means that our endpoint of the interval is greater than the initial point of our interval. By definition, a function, f is increasing over an interval [a,b], if f(b)> f(a)
Yes, a positive average rate of change means that our endpoint of the interval is greater than the initial point of our interval.
What is the average rate of change?It is the average amount by which the function changed per unit throughout that time period. It is calculated using the slope of the line linking the interval's ends on the graph of the function.
Yes, a positive average rate of change indicates that the endpoint of our period is higher than the interval's starting point. A function f is rising over the range [a,b] by definition if f(b)> f. (a)
Therefore, the positive average rate of change over an interval must be increasing over that interval.
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Geometry: Write the theorem or postulate for each of the following, ASAP!!!
The theorems or postulates for the given pair of angles are as follows:
2. ∠2 ≅ ∠8 → Alternate exterior angles are congruent;
3. ∠2 ≅ ∠4 → Vertically opposite angles are congruent;
4. ∠3 ≅ ∠5 → Alternate interior angles are congruent;
5. ∠3 is supplementary to ∠6 → Consecutive interior angles are supplementary;
6. ∠4 ≅ ∠8 → Corresponding angles are congruent;
What are the types of pairs of angles?Consider two lines m and n are parallel. A transversal t is intersecting the lines m and n.
So, it forms 8 angles with the lines m and n. They are ∠1, ∠2, ∠3, ∠4, ∠5, ∠6, ∠7, and ∠8.
Based on their position, they are paired into different categories. Such as:
Interior angles: ∠3, ∠4, ∠5, ∠6
Exterior angles: ∠1, ∠2, ∠7, ∠8
'Alternate interior angles' are the pair of interior angles on the opposite side of the transversal 't'. I.e., (∠3, ∠5), (∠4, ∠6) are congruent.'Alternate exterior angles' are the pair of exterior angles which are on the opposite side of the transversal 't'. I.e., (∠2, ∠8), (∠1, ∠7) are congruent.'Consecutive interior angles' are the pair of interior angles which are on the same side of the transversal 't'. I.e., (∠3, ∠6), (∠4, ∠5). These are also called "Supplementary angles" which mean they add up to 180°.'Consecutive exterior angles' are the pair of exterior angles on the same side of the transversal 't'. I.e., (∠2, ∠7), (∠1, ∠8). These are also called "Supplementary angles" which mean they add up to 180°.'Vertically opposite angles' are the pair of angles that are opposite to each other at the point of intersection. I.e., (∠1, ∠3), (∠2, ∠4), (∠5, ∠7), (∠6, ∠8)'Corresponding angles' are the pair of consecutive angles in which one of the angles is exterior and the other is interior. I.e., (∠1, ∠5), (∠2, ∠6), (∠4, ∠8), (∠3, ∠7)Theorems or postulates for the given pair of angles:Classifying the given pair of angles and their corresponding theorems:
2. ∠2 ≅ ∠8 → These angles belong to pair of Alternate exterior angles.
Theorem - "The alternate exterior angles are congruent"
3. ∠2 ≅ ∠4 → These belong to pair of vertically opposite angles.
Theorem - "The verticle angles are congruent"
4. ∠3 ≅ ∠5 → These belong to pair of alternate interior angles.
Theorem - "The alternate interior angles are congruent"
5. ∠3 is supplementary to ∠6 → These angles belong to pair of consecutive interior angles. Thus, they are supplementary.
Theorem - " The supplementary angles add up to 180°"
6. ∠4 ≅ ∠8 → These angles belong to pair of corresponding angles.
Theorem - " The corresponding angles are congruent".
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How does changing the function from f(x) = -5 cos 2x to g(x) = -5 cos 2x-3 affect the range of the function?
Each element in the range of g(x) is 3 less than the corresponding element in the range of f(x).
Answer:
See below.
In short, by having vertical shift will affect range from -1 ≤ y ≤ 1 to -1 + a ≤ y ≤ 1 + a
Step-by-step explanation:
Generally, a cosine function without vertical shift will always have range equal to -1 ≤ y ≤ 1
If there is given vertical shift, our range will change to -1 + a ≤ y ≤ 1 + a
An example is if we are given the function of cos(x), this always has range of -1 ≤ y ≤ 1 because there is no vertical shift.
But if we have cos(x) + 1, we have vertical shift which is 1. Then the range will be -1+1 ≤ y ≤ 1+1 which equals to 0 ≤ y ≤ 2.
Hence, the function of -5cos(2x) has only range of -1 ≤ y ≤ 1 but the function of -5cos(2x) - 3 will have range of -1-3 ≤ y ≤ 1-3 which equals to -4 ≤ y ≤ -2
What is 0.08 written as a fraction in simplest form?
Answer:
[tex]\frac{2}{25}[/tex]
Step-by-step explanation:
Each "place" in the decimal, can be represented with a base 10 in the numerator.
For example the "tenths" place can be represented as: [tex]\frac{a}{10^1}[/tex] where a=decimal.
The hundredths place can be represented as: [tex]\frac{a}{10^2}[/tex]
The thousandths place can be represented as: [tex]\frac{a}{10^3}[/tex]
and so on...
In this case, we have a decimal in the hundredths place which can be represented as: [tex]\frac{8}{10^2} = \frac{8}{100}[/tex]. Now to simplify this fraction, you simply divide both sides by 4 (greatest common factor of 8 and 100), or in other words multiply it by 0.25/0.25 which is just 1, so the value is the same. [tex]\frac{8}{100} * \frac{0.25}{0.25} = \frac{2}{25}[/tex]
o trees are growing in a clearing. The first tree is 5.6 feet tall and casts a 4.2-foot shadow. The second tree casts a 42.3-foot shadow. How tall is the second tree to the nearest tenth of a foot?
The second tree is 56.4 ft tall.
Triangles with the same shape but different sizes are said to be similar triangles. Squares with any side length and all equilateral triangles are examples of related objects. In other words, if two triangles are identical, their respective sides are equal in number and their corresponding angles are congruent.
Let the length of the tall tree be x. Thus by similarity of triangles we get,
Length of small tree/ Shadow Length of small tree =
Length of Tall tree/ Shadow Length of tall tree
Substituting the values we get,
5.6/4.2 = x/42.3
x = 56.4
Thus the second tree is 56.4 ft tall.
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A function has a slope of 3, and one solution is given in the table. identify the missing outputs. x: 5 6 7 8 9 y: -50
The remaining value will increase by the value of the slope. Hence the remaining missing values are -47, -44, -41, -38 and -35
Slope and tablesThe slope of a line is the ratio of the rise to run of a line. It is also defined as the rate of change of coordinate y with respect to x. Mathematically;
slope = change in y/change in x
If the slope of the table given is 3, then using the coordinate points (5, -50)and (6, y)
Substitute
3 = y-(-50)/6-5
3 = y+50/1
y+50 = 3
y = -47
The remaining value will increase by the value of the slope. Hence the remaining missing values are -44, -41, -38 and -35
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Factors to zero inverse operations
The zeros of the given equation are -5 and -7
Zeros of a quadratic equationQuadratic equations are equations that has a leading degree of 2. Given the factors of a quadratic equation as expressed below;
(-3x - 15)(x+7) = 0
The expressions -3x -15 and x + 7 are the factors of the equation. Equating both factors to zero
-3x - 15 = 0
Add 15 to both sides of the equation
-3x -15 + 15 = 0 + 15
-3x = 15
Divide both sides of the equation by -3
-3x/-3 = 15/-3
x = -5
Similarly;
x + 7 = 0
x = -7
Hence the zeros of the given equation are -5 and -7
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An astronaut visited mars. his weight on earth was 180 pounds, and his weight on mars was only 72 pounds. he removed a rock with a weight of 16 pounds on mars. what is the weight of the rock on earth? a. 1.4 pounds c. 6.4 pounds b. 4 pounds d. 40 pounds
Answer: d. 40 pounds
Step-by-step explanation: let e equal the number of pounds weigh on Earth and m equal the number of pounds weighs on Mars.
so
72m=180e
1m= 72m/72
e= 180/72 = 2.5
1m=2.5e
16m=1 x16
e= 16 x 2.5
e= 40
so therefore, 16m=40e
I hope this helps
My car uses 8.5L of petrol per 100km travelled. If petrol costs $2.05 per litre, how much will the petrol cost for my trip?
the petrol cost for the trip is:
C = 2.125*$2.05 = $4.36
How to get the cost of the trip?After a search online, I've found that the trip is of 25km.
Here we know that the car uses 8.5L per 100km, then in 25 km, the car will use one-fourth of 8.5L, that is:
8.5L/4 = 2.125L
So the volume of petrol that the car uses for the trio is 2.125 liters of petrol.
And each liter costs $2.05, then the petrol cost for the trip is given by the product between the total volume of petrol consumed and the cost per liter.
C = 2.125*$2.05 = $4.36
Thus, we conclude that the petrol cost for the trip is 4.36 dollars.
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Solve the given differential equation by undetermined coefficients. y'' 4y = 7 sin(2x)
The solution to the given differential equation is yp=−14xcos(2x)
The characteristic equation for this differential equation is:
P(s)=s2+4
The roots of the characteristic equation are:
s=±2i
Therefore, the homogeneous solution is:
yh=c1sin(2x)+c2cos(2x)
Notice that the forcing function has the same angular frequency as the homogeneous solution. In this case, we have resonance. The particular solution will have the form:
yp=Axsin(2x)+Bxcos(2x)
If you take the second derivative of the equation above for yp , and then substitute that result, y′′p , along with equation for yp above, into the left-hand side of the original differential equation, and then simultaneously solve for the values of A and B that make the left-hand side of the differential equation equal to the forcing function on the right-hand side, sin(2x) , you will find:
A=0
B=−14
Therefore,
yp=−14xcos(2x)
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Please help what is the answer?
Answer:
C
Step-by-step explanation:
[tex]-15x+60\leq 105 \\ \\ -15x \leq 45 \\ \\ x \geq -3[/tex]
[tex]14x+11 \leq -31 \\ \\ 14x \leq -42 \\ \\ x \leq -3[/tex]
The intersection is x = 3.
The following data are the temperatures of effluent at discharge from a sewage treatment facility on consecutive days: Sample No.1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 Temperature 40 45 49 47 52 45 51 46 44 48 51 50 56 44 48 50 49 50 46 46 49 49 51 50 Use the data above to calculate the descriptive statistics.
The descriptive statistics for the above data is given as follows:
X = 12.5
What is Descriptive Statistics?
A set of concise descriptive coefficients that describe a particular data set indicative of a whole or sample population is known as descriptive statistics.
For X (mean) = [tex]{\displaystyle X={\frac {1}{n}}\sum _{i=1}^{n}X_{i}[/tex]
= 300/24
= 12.5
For sample variance = [tex]s^2 = \frac{1}{n-1}\biggl[\, \sum_{i=1}^n X_i^2 - \frac{\Bigl(\,\sum\limits_{i=1}^n X_i\Bigr)^{\!2}}{n} \biggr][/tex]
= (1/(24-1) (4,900 - (300²/24)
= 50
Standard deviation s = √s²
= √50
= 7.0711
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how to do questions 28-29?
thanks!
28. 1.45l ÷ 0.32l = 4.53125
so approximately 5 glasses to leave the bottle empty
29. 5.6kg + 2.5kg = 8.1kg
8.1kg ÷ 0.48 = 16.875
he can make 16 complete doughs
there will be 0.875kg of flour left
Solve the system of equations by graphing.
2x^2 + 8y^2 = 50
x^2 + y^2 = 13
The solutions for the given system are (3,2), (3,-2), (-3,2) and (-3,-2).
What is a Quadratic Function?
The quadratic function can represent a quadratic equation in the Standard form: ax²+bx+c=0 where: a, b and c are your respective coefficients. In the quadratic function the coefficient "a" must be different than zero (a≠0) and the degree of the function must be equal to 2.
The solution of these equations represents the points at which the parabolas intersect.
2x²+8y²=50 (1)
x² + y²= 13 (2)
Multiplying the equation 2 by -2, you have:
2x²+8y²=50 (1)
-2x² -2 y²= -26(2)
Sum both equations, you have: 6y²= 24. Now, you can find y.
6y²= 24
y²=4
y=±2
If y=2, from equation 2, you have
x² + y²= 13
x² + 2²= 13
x² + 4= 13
x² =13-4
x² =9
x=±3
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Figure A is a scalr image of figur B. Figure A maps to Figure B with scale factor of 2/3. what is tge value of x?
Answer:
7
Step-by-step explanation:
You take the corresponding side that you know which is 10.5 and you multiply that by your scale factor of 2/3.
Another name for 10.5 is 10 [tex]\frac{1}{2}[/tex] and that can be changed to [tex]\frac{21}{2}[/tex]
([tex]\frac{21}{2}[/tex])([tex]\frac{2}{3}[/tex]) The two's cancel out and we are left with [tex]\frac{21}{3}[/tex] Which is the same as 7.
Evaluate the double integral. 7x cos(y) da, d is bounded by y = 0, y = x2, x = 7 d
The double integral. 7x cos(y) da, d is bounded by y = 0, y = x2, x = 7 d is given as
[tex]\int _D 7xcosydA =7/2(-cos49+1)[/tex]
What is the double integral 7x cos(y) da, d is bounded by y = 0, y = x2, x = 7 d?Generally, the equation for is mathematically given as
The area denoted by the letter D that is bordered by y=0, y=x2, and x=7
The equation for the X-axis is y=0.
y=x² ---> (y-0) = (x-0)²
Therefore, the equation of a parabola is y = x2, and the vertex of the parabola is located at the point (0,0), and the axis of the parabola is parallel to the Y axis.
The equation for a straight line that is parallel to the Y-axis and passes through the point (7,0) is x=7.
[tex]\int _D 7xcosydA\\\\\int^7_0 \int^x^2 _0 7xcosydA[/tex]
Integrating we have
[tex]7/2 \int^7_0 (2xsinx^2)dx[/tex]
If x equals zero, then we know that u equals zero as well.
When x equals seven, we know that u=72=49.
Therefore, by changing x2=u into our integral, it becomes from
[tex]7/2 \int^7_0 (2xsinx^2)dx[/tex]
[tex]7/2 \int^49_0 sin u dx[/tex]
Hence
=7/2(-cos49+1)
In conclusion,
[tex]\int _D 7xcosydA =7/2(-cos49+1)[/tex]
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Find the inverse of function f
f(x)9x+7
The inverse of function f(x) = 9x+7 is f-1(x) = x/9 - 7/9
How to determine the inverse of the function?The function is given as:
f(x) = 9x + 7
Express f(x) as y
y = 9x + 7
Swap the positions of x and y in the above equation
x = 9y + 7
Subtract 7 from both sides
9y = x - 7
Divide through by 9
y = x/9 - 7/9
Express as an inverse function
f-1(x) = x/9 - 7/9
Hence, the inverse of function f(x) = 9x+7 is f-1(x) = x/9 - 7/9
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What is the probability distribution of X when X~B(1,1/25)?
P(X= 0) = 0.96
P(X= 1) = 0.04
P(X= 0) = 0.75
P(X= 1) = 0.25
P(X= 0) = 0.04
P(X= 1) = 0.96
P(X= 0) = 0.25
P(X= 1) = 0.75
The probability distribution of X when X~B(1,1/25) is (Option A)
P(X= 0) = 0.96P(X= 1) = 0.04See the explanation below.
What is the explanation to the above solution?Given X~B(n,p)
P(x=1) = C¹ₙ * P¹ * (1-P)ⁿ⁻¹ (n≥1)
Thus, X~B [1, 1/25]
1/25 = 0.04
hence, p(x=0)
= C⁰₁ * 0.04⁰ (1 - 0.04)¹
= 0.96
P (x=1)
= C¹₁ 0.04¹ (1-0.04)⁰
= 0.04
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Laura completed the following steps to find a product.
Multiply: Three-sevenths times 8
Step 1: 8 times three-sevenths
Step 2: StartFraction (8 plus 3) over 7 EndFraction
Step 3: Eleven-sevenths
Step 4: 1 and four-sevenths
In which step did Laura make her first mistake?
Step 1
Step 2
Step 3
Step 4
The solution to the product of 8 and three-seventh is 2 2/7. According to Laura, she made mistake in step 2 by adding 8 and 3 instead of multiplying
Multiplication of fractions and integers
Fractions are written as a ratio of two integers. For instance a/b is a fraction where a and b are integers.
Given the following equation
Multiply 3/7 and 8
This is expressed mathematically as;
3/7 * 8
Step 1: Swap to have;
8 * 3/7
Step 2: Group the numerator
(8*2)/7
Step 3; Simplify
16/7
Step 4; Convert to mixed fraction
16/7= 2 2/7
The solution to the product of 8 and three-seventh is 2 2/7. According to Laura, she made mistake in step 2 by adding 8 and 3 instead of multiplying
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Kent has two similar cylindrical pipes, pipe a and pipe b. the radius of pipe a is 6 cm, and the radius of pipe b is 2 cm. what is the ratio of the volume of pipe a to the volume of pipe b?
The ratio of the volume of pipe a to the volume of pipe b is 27:1 .
What is cylinder?A cylinder is a three-dimensional shape consisting of two parallel circular bases, joined by a curved surface. The center of the circular bases overlaps each other to form a right cylinder.
Given that,
Radius of pipe a is 6 cm, and the radius of pipe b is 2 cm.
We know that the volume of cylinder is :- [tex]\pi r^{2}h[/tex]
where r is radius and h is height of the cylinder.
If two figures are similar then ratio of volume is equal to the cube of any dimension.
The ratio of the volume of Pipe a to the volume of Pipe b :-
[tex]\frac{V(a)}{V(b)}=\frac{6^{3} }{2^{3} }[/tex]
= [tex]\frac{27}{1}[/tex]
Hence, The ratio of the volume of pipe a to the volume of pipe b is 27:1 .
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A circle is circumscribed around a rectangle with sides lengths 6 and 8 what is the area of the circle?
A. 16[tex]\pi[/tex]
B. 20[tex]\pi[/tex]
C. 24[tex]\pi[/tex]
D. 25[tex]\pi[/tex]
E. 30[tex]\pi[/tex]
Answer:
D. 25pi
Step-by-step explanation:
"circumscribed" means the rectangle is inside the circle and just the corners (vertices) of the rectangle are touching the circle. This means the diagonal of the rectangle is the diameter of the circle. See image. If the sides of the rectangle are 6 and 8 then the third side that makes the triangle(half the rectangle) is 10. You can find this using Pythagorean Theorem or Pythagorean triples (shortcut)
6^2 + 8^2 = d^2
36 + 64 = d^2
100 = d^2
d = 10
This is the diameter of the circle. The radius would then be 5.
Area of a circle is:
A = pi•r^2
= pi•5^2
= 25pi
Solve the compound inequality and graph the solution on a number line
5x + 9 ≤ 2 and x + 6 > 12
Answer:
First:
5x + 9 < 2
x= 9/5= 1,8 < 2
Second:
x + 6 < 12
x= 12/6= 2 < 12
I thought I just had to half the diameter and then put it into the volume formula for cylinders but ig I was wrong? Help please?
Answer:
10830.87 mm³
Step-by-step explanation:
Hello!
Volume of a cylinder: [tex]V = \pi r^2(h)[/tex]
[tex]\pi[/tex] = pir = radius (half diameter)h = heightThe radius for this cylinder is 9.525, after dividing 19.05 by 2.
Plug it into the volume formula to solve for the volume.
Find the Volume[tex]V = \pi r^2(h)[/tex][tex]V = \pi (9.525)^2(38)[/tex][tex]V = \pi (90.725625)(38)[/tex][tex]V = 3447.57375\pi[/tex][tex]V = 1083087236570...\approx10830.87[/tex]The volume is approximately 10830.87 cubic millimeters.
divide $800 between kofi and kweku so that kofi gets three times what kweku gets
Answer:
600 and 200
Step-by-step explanation:
kofi : kweku is 3 :1
so Kofi gets 3 out of ( 3 +1) = 3/4 of 800 = 3/4 * 800 = 600
kweku get s the rest 800- 600 = 200
If (fg)(x) = h(x) such that h of x is equal to the square root of the quantity 8 times x plus 6 end quantity which of the following could accurately represent f and g?
The value of the functions f(x) and g(x) will be √(4x + 3) and √2. Then the correct option is B.
What is a function?A statement, principle, or policy that creates the link between two variables is known as a function. Functions are found all across mathematics and are required for the creation of complex relationships.
If (f g)(x) = h(x) such that h(x) = √(8x + 6). Then we have
(f g)(x) = h(x)
f(x) · g(x) = h(x)
Then put the value of h(x), then we have
f(x) · g(x) = √(8x + 6)
f(x) · g(x) = √2(4x + 3)
f(x) · g(x) = √(4x + 3) × √2
Thus, the value of the functions f(x) and g(x) will be √(4x + 3) and √2.
Then the correct option is B.
More about the function link is given below.
https://brainly.com/question/5245372
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