tell wheter the lines through the given points are parallel, perpendicular or neither.
a. Line 1: (2,-3), (-4, -6)
Line 2: (-3, 2), (2, -8)
b. Line 1: (-4, -5), (4, 1)
Line 2: ( 6, 10), (-3, -2)
c. Line 1: (0, -4), (-2, -8)
Line 2: (-1, 5), (1, 9)
Help I need this by tomorrow :c
Answers
Answer:
a. Perpendicular
Make sure to read the step-by-step explanation to figure out how to do the other 2.
Step-by-step explanation:
I will not be providing answers to all three, but I will answer the first one (this is, so you don't depend on people to solve this for you).
Parallel lines have one thing in common, their slope. Two lines that have the same slope never intersect because they are both facing the same direction and moving the same distance. So, you can find the slope of two lines by using the slope formula.
[tex]m=\frac{y_2-y_1}{x_2-x_1}\\\\m_1=\frac{-6-(-3)}{-4-2}=\frac{-3}{-6}=\frac{1}{2}\\m_2=\frac{-8-2}{2-(-3)}=\frac{-10}{5}=-2[/tex]
This is evidence that the two lines are not parallel. But, by finding the slope, we can conclude that it is perpendicular.
This brings me to how to identify perpendicular lines. The slope of perpendicular lines is negative reciprocals. A reciprocal is just a fraction that is flipped, and it's negative. For example, [tex]\frac{-2}{3}[/tex]'s negative reciprocal would be [tex]\frac{3}{2}[/tex]. The negative of -2/3 is a positive, and the reciprocal of 2/3 is 3/2. So, the negative reciprocal is 3/2.
How does this apply to what I said earlier?Well, [tex]-2[/tex] is the negative reciprocal of [tex]\frac{1}{2}[/tex]. The reciprocal of [tex]\frac{1}{2}[/tex] is 2, and the negative of 2 is -2. So, simply, lines 1 and 2 are perpendicular.
Use this method to solve the other questions. If they don't have the same slope and aren't negative reciprocals, then they are neither.
Answer:
Step-by-step explanation:
To solve this problem, we use the following formula:
[tex]\displaystyle\\\boxed {\frac{x-x_1}{x_2-x_1}=\frac{y-y_1}{y_2-y_1} }[/tex]
a) (2,-3) (-4,-6)
[tex]x_1=2\ \ \ \ x_2=-4\ \ \ \ y_1=-3\ \ \ \ y_2=-6[/tex]
[tex]\displaystyle\\\frac{x-2}{-4-2} =\frac{y-(-3)}{-6-(-3)} \\\\\frac{x-2}{-6}=\frac{y+3}{-6+3} \\\\\frac{x-2}{-6} =\frac{y+3}{-3}[/tex]
Multiply both parts of the equation by -3:
[tex]\displaystyle\\\frac{x-2}{2}=y+3\\\\0.5x-1=y+3\\\\0.5x-1-3=y+3-3\\\\0.5x-4=y\\[/tex]
⇔ Line 1: y=0.5x-4 m₁=0.5
(-3,2) (2,-8)
[tex]\displaystyle\\\frac{x-(-3)}{2-(-3)}=\frac{y-2}{-8-2} \\\\\frac{x+3}{2+3} =\frac{y-2}{-10} \\\\\frac{x+3}{5} =\frac{y-2}{-10} \\\\[/tex]
Multiply both parts of the equation by -10:
[tex]-2(x+3)=y-2\\-2x-6=y-2\\-2x-6+2=y-2+2\\-2x-4=y[/tex]
⇔ Line:y=-2x-4 m₂=-2
[tex]\displaystyle\\m_1=-\frac{1}{m_2}[/tex]
⇒ The given lines are perpendicular
b)
(-4,-5) (4,1)
[tex]\displaystyle\\\frac{x-(-4)}{4-(-4)}=\frac{y-(-5)}{1-(-5)} \\\\\frac{x+4}{4+4}=\frac{y+5}{1+5} \\\\\frac{x+4}{8} =\frac{y+5}{6} \\[/tex]
Multiply both parts of the equation by 6:
[tex]\displaystyle\\\frac{6(x+4)}{8} =y+5\\\\\frac{3}{4} x+3=y+5\\\\\frac{3}{4} x+3-5=y+5-5\\\\\frac{3}{4} x-2=y\\[/tex]
⇔ Line 1: y=(3/4)x-2 m=3/4
(6,10) (-3,-2)
[tex]\displaystyle\\\frac{x-6}{-3-6} =\frac{y-10}{-2-10} \\\\\frac{x-6}{-9} =\frac{y-10}{-12} \\\\[/tex]
Multiply both parts of the equation by -12:
[tex]\displaystyle\\\frac{-12(x-6)}{-9} =y-10\\\\\frac{4}{3}x-8=y-10 \\\\\frac{4}{3}x-8+10=y-10+10\\\\\frac{4}{3}x+2=y[/tex]
⇔ Line 2: y=(4/3)x+2 m=4/3
⇒ The given lines are neither perpendicular and neither parallel
c)
(0,-4) (-2,-8)
[tex]\displaystyle\\\frac{x-0}{-2-0} =\frac{y-(-4)}{-8-(-4)} \\\frac{x}{-2}=\frac{y+4}{-8+4} \\\\\frac{x}{-2}=\frac{y+4}{-4}[/tex]
Multiply both parts of the equation by -4:
[tex]2x=y+4\\2x-4=y+4-4\\2x-4=y[/tex]
⇔ Line 1: y=2x-4 m₁=2
(-1,5) (1,9)
[tex]\displaystyle\\\frac{x-(-1)}{1-(-1)} =\frac{y-5}{9-5} \\\\\frac{x+1}{1+1} =\frac{y-5}{4}\\\\\frac{x+1}{2} } =\frac{y-5}{4} \\[/tex]
Multiply both parts of the equation by 4:
[tex]2(x+1)=y-5\\2x+2=y-5\\2x+2+5=y-5+5\\2x+7=y[/tex]
⇔ Line 2: y=2x+7 m₂=2
m₁=m₂
⇒ The given lines are parallel
Related Questions
HELP HELP ME ASAP!!!
At LEAST ONE value of x MUST be 7 (x = 7 or x = ?)
My teacher said that a, b, and c ALL have to be greater than 0 and b has to be greater than 1
At LEAST ONE extraneous solution
Answers
Part a
Let [tex]a=2[/tex]. Then, we have that
[tex]7+2=\sqrt{7b+c}\\\\81=7b+c[/tex]
We can let [tex]b=11[/tex] and [tex]c=4[/tex], meaning the equation is [tex]x+2=\sqrt{11x+4}[/tex].
Part b
[tex]x+2=\sqrt{11x+4}\\\\x^2 +4x+4=11x+4\\\\x^2 -7x=0\\\\x(x-7)=0\\ \\ x=0, 7[/tex]
Substituting both of these values into the equation, we see they are both solutions.
Part c
[tex]x+10=\sqrt{10x+219}[/tex]
Click an item in the list or group of pictures at the bottom of the problem and, holding the button down, drag it into the correct position in the answer box. Release your mouse button when the item is place. If you change your mind, drag the item to the trashcan. Click the trashcan to clear all your answers.
Find the missing part.
l = 8, w = 4, h = 2
Find the diagonal (d) of the rectangular solid.
Answers
The diagonal of the rectangular solid that has l = 8, w = 4, h = 2, is calculated as: d = 2√21 units.
How to Find the Diagonal of a Rectangular Solid Shape?A rectangular solid has a length (l), height (h), and width (w). The diagonal of the rectangular solid, d, can be calculated using the given formula below:
Diagonal of rectangular solid (d) = √(l² + w² + h²).
Given the following dimensions of the rectangular box:
Length of the rectangular box = 8 unitsWidth of the rectangular box = 4 unitsHeight of the rectangular box = 2Substitute l = 8, w = 4,a nd h = 2 into the equation d = √(l² + w² + h²):
Diagonal of rectangular solid (d) = √(8² + 4² + 2²)
Diagonal of rectangular solid (d) = √(64 + 16 + 4)
Diagonal of rectangular solid (d) = √84
Simplify √84 further
Diagonal of rectangular solid (d) = √(4 × 21)
Diagonal of rectangular solid (d) = 2√21 units
Therefore, the rectangular solid has a diagonal that is: 2√21
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The area of a rectangular pool is 7084 m^2.
If the length of the pool is 92 m, what is its width?
Answers
I need help on it too. Can any one help me find the answer
the balance of bob's account is overdrawn $21. jim account is $7 overdrawn. what is the difference between their account balances
Answers
Answer: -14
Step-by-step explanation:
-21 - (-7)
-21 + 7
-14
Quadrilateral STUV is a rectangle, SU=z+53, and TV=2z. What is the value of z?TSVURz=Submit
Answers
Recall that the diagonals of a rectangle are congruent. Therefore, we can set the following equation:
[tex]z+53=2z.[/tex]Solving the above equation for z, we get:
[tex]\begin{gathered} 2z-z=53, \\ z=53. \end{gathered}[/tex]Answer:[tex]z=53.[/tex]
Golfer Lexi Thompson is one of the top golfers on the LPGA tour. The distribution of scores for each of
the more than 700 rounds over her LPGA career is approximately normal with a mean of about u= 70.6
strokes and a standard deviation of about o= 3.2 strokes.
Use the empirical rule to answer the following questions.
What percent of Thompson's Scores are greater than 73.8?
What percent of Thompson's scores are between 64.2 and 67.4
Answers
The percent of Thompson's Scores that are greater than 73.8 is 95%
The percent of Thompson's Scores that are between 64.2 and 67.4 is 69% to 94%
How to find what percent of Thompson's Scores are greater than 73.8given data
a mean of about 70.6 strokes
a standard deviation of about 3.2 strokes
Applying the 68%, 95%, and 99.7% Rule. This rule says that standard deviations is changed to percentages when:
68% of scores fall within 1 Standard Deviation of the mean.95% of all scores fall within 2 Standard Deviation of the mean.99.7% of all scores fall within 3 Standard Deviation of the mean.Hence we calculate how many standard Deviations that gives 73.8 as follows
mean ± standard deviationsince the73.8 is greater than the mean we add the SD to the mean
70.6 + 3.2 = 73.8
73.8 is 1 SD but we are looking for value greater than 73.8. This should be just above 73.8, hence from 2 SD which is 95%
What percent of Thompson's scores are between 64.2 and 67.4
Applying the 68%, 95%, and 99.7% Rule
mean ± standard deviationThe numbers asked is less than the mean hence we subtract
70.6 - 3.2 = 67.4 ( 1 SD = 68% )
70.6 - 3.2 - 3.2 = 64.2 ( 2 SD = 95% )
The question asks the percent of Thompson's scores between 68% and 95%. This is 69% to 94%.
The question said between hence the end values are not inclusive
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Giải phương trình lượng giác sau
sin2x+cos2x+sin4x=1
Answers
Answer:
2
Step-by-step explanation:
Given, cosx+cos
2
x=1
⇒cosx=1−cos
2
x
⇒cosx=sin
2
x
Squaring both sides we get
⇒cos
2
x=sin
4
x .....(1)
⇒sin
4
x−cos
2
x=0
Adding both side 1, we get
⇒sin
4
x+1−cos
2
x=1
∴sin
2
x+sin
4
x=1 Proved.
Find the remainder when 4x3 +6x2 −8x − 2 is divided by each of the
following:
x−1 x−2
x−3 x+1
x+2 x+3
Answers
Using the remainder theorem, the remainder of the divisions of p(x) = 4x³ + 6x² - 8x - 2 by the polynomials are given as follows:
x - 1: 0.x - 2: 38.x - 3: 136.x + 1: 8x + 2: 6x + 3: -32.What is the remainder theorem?Suppose that we have a polynomial p(x), that is divided by a linear term x - a, the remainder is given by the numeric value of p(x) at x = a, that is, p(a).
For this problem, the polynomial is given as follows:
p(x) = 4x³ + 6x² - 8x - 2.
Then the remainder for each division is given as follows:
x - 1: a = 1, p(a) = 4(1)³ + 6(1)² - 8(1) - 2 = 0.x - 2: a = 2, p(a) = 4(2)³ + 6(2)² - 8(2) - 2 = 38.x - 3: a = 3, p(a) = 4(3)³ + 6(3)² - 8(3) - 2 = 136.x + 1: a = -1, p(a) = 4(-1)³ + 6(-1)² - 8(-1) - 2 = 8.x + 2: a = -2, p(a) = 4(-2)³ + 6(-2)² - 8(-2) - 2 = 6.x + 3: a = -3, p(a) = 4(-3)³ + 6(-3)² - 8(-3) - 2 = -32.More can be learned about the remainder theorem at https://brainly.com/question/27749132
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HELPP ME ASAP
Which point is located on the y axis iready
Answers
Answer:
-3
Step-by-step explanation:
your x-axis has to be 0 then the point on the y-axis is the y-intercept
i need help with this, thanks
Answers
Answer:
m < 1 = 146
m < 3 = 146
m < 4 = 34
Step-by-step explanation:
Angles 2 and 3 are suplementary angles that equal 180
angle 2 + angle 3 = 180
34 + angle 3 = 180
angle 3 = 180 - 34
angle 3 = 146
angles 2 (34 degrees) and 4 and angles 1 (146 degrees) and 3 are congruent so...
m < 1 = 146
m < 2 = 34
m < 3 = 146
m < 4 = 34
Hope this helps! :)
Answer:
[tex]m \angle 1= \boxed{146}\;^{\circ}\\\\m \angle 3= \boxed{146}\;^{\circ}\\\\m \angle 4= \boxed{34}\;^{\circ}[/tex]
Step-by-step explanation:
Angles on a straight line sum to 180°.
⇒ m∠1 + m∠2 = 180°
⇒ m∠1 + 34° = 180°
⇒ m∠1 = 146°
Vertical Angle Theorem
When two straight lines intersect, the opposite vertical angles are congruent.
Applying the Vertical Angle Theorem:
m∠4 = m∠2 = 34°m∠3 = m∠1 = 146°Find P on NM that is the given fractional distance from N to M. Such that, 1/5 is the fractional distance from N to M, and N(-3,-2),M(1,1)
please help
Answers
The point P is ( -2.2 , -1.4) on the line segment NM, which represents the fractional distance from N to M.
Given:
Fractional Distance from n to m is 1/5 and
points are N (-3, -2), M (1, 1).
From the graph we can see that the distance from M to R is 4,
And the distance between N to R is 3.
So, 1/5 MR = 1/5 (4)
=4/5
And, 1/5 NR=1/5 (3)
=3/5
By substituting these values in N (-3, -2),
We get a point p on MN.
-3 + 4/5 = -2.2
and -2 + 3/5 = -1.4
Hence p(-2.2, -1.4) is the point on line segment NM.
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Please help first person will get all the brainliest
Which equation does not represent a direct variation? *
O y = -x
O y = 3x + 2
O y=-3x
O y = 0.5x
Answers
y = -x equation does not represent a direct variation.
y = 3x + 2
y=-3x
y = 0.5x
equations are represent a direct variation
How can you tell if there is a direct variation?
Simply build ratios from a table of values if you have one and wish to determine whether the data indicate a direct variation. You have a straight variation if all the ratios are the same.
The constant of variation is k = = 3, for instance, if y varies straight as x and y = 6 when x = 2. So, y = 3x serves as the equation to describe this direct variation.
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The formula t= represents the time t in seconds that it takes an object
4
to fall from a height of h feet. If a rock falls from 125 feet, estimate how long
it will take the rock to hit the ground. Estimate the square root to the nearest
integer.
Answers
Answer: 3 seconds
Step-by-step explanation:
t = √h / 4
t = (√125) / 4
t = (5√5) / 4
t = 2.795 seconds
Because integer numbers can't be decimals so we round it to 3.
I beg for help please!
What is the equation of the line in slope-intercept form?
Answers
Answer:
The equation of the line is written in the slope-intercept form, which is: y = mx + b, where m represents the slope and b represents the y-intercept.
Answer:
y = x + 6
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (0, 6) and (x₂, y₂ ) = (4, 10) ← 2 points on the line
m = [tex]\frac{10-6}{4-0}[/tex] = [tex]\frac{4}{4}[/tex] = 1
the line crosses the y- axis at (0, 6 ) ⇒ c = 6
y = x + 6 ← equation of line
7.
4
-2698
13
=m/4 =26/13
Answers
The value of m is 104/13
What is Fraction?
A fraction, which also symbolizes a piece of a whole, is a mathematical symbol for any number of equal parts. When expressed in common English, a fraction, such as 1/2, 8/5, or 3/4, represents the number of components of a specific size.
The value of m must be determined.
As can be seen in light of the query
The formula is m/4 = 26 / 13
The equation will now be solved for m m/4 = 26 / 13
The result of multiplying 4 on both sides is
(m/4) x 4 = (26/13) x 4
m = (26 x 4)/13
m = 104/13.
Consequently, m has a value of 104/13.
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A person driving her car at 12.5 m/s approaches an intersection just as the traffic light turns yellow. She knows that the yellow light lasts only 2.0 s before turning red, and she is 28 m away from the beginning of the intersection, which is 15 m wide, as shown below. Using the gas pedal she can accelerate at 3.5 m/s2 and using the brake pedal she can accelerate at –5.8 m/s2. Ignoring reaction time and car length, determine whether she should try to stop or speed up to be a legal driver.
Answers
She should try to stop the car.
We will discuss the possibilities of trying to stop and trying to speed up in 2s and find the distance she travels to get into a conclusion.
If she try to stop, then the acceleration, a = -5.8 m/s²
Initial velocity, v₀ = 12.5 m/s
Final velocity, v₁ = 0 m/s [Since the car is stopped]
Let d be the distance the car travels before stopping.
Then, we have, v₁² = v₀² + 2ad
Therefore, d = v₁²-v₀²/2a
= 0-(12.5)²/2 x (-5.8)
= 156.25/11.6
= 13.47 m
So she can stop in time as she is 28m far from the beginning of the intersection.
If she try to speed up, then the acceleration of the car, a = 3.5 m/s²
Initial velocity of the car, v₀ = 12.5 m/s
Time she have, t = 2 s
Let d be the distance the car travels in 2 s.
Then, d = v₀t +(1/2)at²
= 12.5 x 2 + (1/2) x 3.5 x 2²
= 25 + 7
= 32 m
She is 28 m before the beginning of the intersection which is 15 m wide. So if she speed up she will be in the middle of the intersection when the light turns red and may have to stop.
Hence as a legal driver, she should try to stop the car.
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The result of (2)x(-7)=
Answers
Answer:
-14 is the correct answer
Marisol claims that each pair of remote interior angles in a triangle has two exterior angles. Do you agree? Use a diagram to support your answer.
Choose the correct answer below.
О А.
A.
No. 23 is the only exterior angle for
remote interior angles 21 and 22.
OB.
No. 23 is the only exterior angle for
remote interior angles 21 and 22.
O C.
Yes. 21 and 22 are both remote
interior angles for 23 and 24.
OD.
Yes. 21 and 22 are both remote
interior angles for 23 and 24.
Answers
Choose the correct answer below.
О А.
A.
No. 23 is the only exterior angle for
remote interior angles 21 and 22.
OB.
No. 23 is the only exterior angle for
remote interior angles 21 and 22.
O C.
Yes. 21 and 22 are both remote
interior angles for 23 and 24.
OD.
Yes. 21 and 22 are both remote
interior angles for 23 and 24.
following is the probability distribution of a random variable that represents the number of extracurricular activities a college freshman participates in.
Answers
The probabilities from this problem are given as follows:
a) The probability that a student participates in exactly three activities is 0.23.
b) The probability that a student participates in less than three activities is 0.68.
c) The probability that a student participates in at least two activities is 0.82.
Item aThe event associated with exactly three activities is given by:
X = 3.
Hence, from the table on the image at the end of the answer, the probability is:
P(X = 3) = 0.23.
Item bThe events associated with less than three activities are given by:
X = 0, X = 1 and X = 2.
Hence, from the table on the image at the end of the answer, the probability is:
P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2) = 0.05 + 0.13 + 0.45 = 0.68.
Item cThe events associated with at least two activities are given by:
X = 2, X = 3, X = 4.
P(X ≥ 2) = P(X = 2) + P(X = 3) + P(X = 4) = 0.45 + 0.23 + 0.14 = 0.82.
What is the missing information?The problem is missing, and is given by the image at the end of the answer.
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Un árbol que mide 22 metros de altura está creciendo a un ángulo de 83° con respecto al suelo (ver la figura siguiente). Miranda se para a cierta distancia de la base del árbol, se da cuenta que el ángulo de elevación desde el suelo hasta la parte alta del árbol es 32°. ¿A qué distancia está ella de la base del árbol? Redondear la respuesta a la décima más cercana de un metro.
Answers
Answer: ≈37.8 m
Step-by-step explanation:
The sum of the angles of a triangle is equal to 180°.
⇒ х+32°+83°=180°
х+115°=180°
x+115°-115°=180°-115°
x=65°
The sine theorem goes like this: the sides of a triangle are proportional to the sines of the opposing angles.
[tex]\displaystyle\\\frac{22}{sin32^0} =\frac{S}{sin65^0} \\\\Multiply\ both \ parts\ of \ the \ equation\ by\ sin65^0:\\\\S=\frac{22(sin65^0)}{sin32^0} \\\\S\approx\frac{22(0.91)}{0.53}\\\\ S\approx37.8 \ m[/tex]
99 is what percent of 150 please help?
Answers
Answer:
66%
Step-by-step explanation:
99 of 150 is 66%
and 150 of 99 is 151%
Complete the point-slope equation of the line through (-1,-10)(−1,−10)left parenthesis, minus, 1, comma, minus, 10, right parenthesis and (5,2)(5,2)left parenthesis, 5, comma, 2, right parenthesis.
Answers
Answer:
y + 10 =2( x +1)
or
y -2 + 2( x -5)
These both name the same line.
Step-by-step explanation:
First we need to find the slope. The slope is the change in y over the change in x. In the point (-1,-10)
-1 is the x and -10 is the y.
In the point (5,2)
5 is the x and 2 is the y.
[tex]\frac{2- -10)}{5 - -1)}[/tex] Subtracting a negative is the same as adding a positive.
[tex]\frac{2+ 10}{5+1}[/tex] = [tex]\frac{12}{6}[/tex] = 2
We know know the slope. We will use the form
y - [tex]y_{1}[/tex] = m (x-[tex]x_{1}[/tex]) we will plug in the numbers that we know.
If we use point (-1, -10)
y -- -10 = 2(x - -1)
y + 10 = 2( x+1)
If we use the point (5,2)
y -2 = 2(x -5)
Both equations mean the same thing.
To enroll in lessons to learn about pottery wheel throwing, you must pay an enrollment of $20 for each lesson. The pottery studio also charges you $2. 99 per pound for the amount of clay used.
Write an expression for the total cost of a person using c pounds of clay during a lesson. Use the expression to calculate the cost of a lesson where Sam uses 3. 5 pounds of clay
Answers
The expression will be (2.99c + 20 = Total cost) and the total cost of Sam's consumption will be $30.465.
What are expressions?Using the operations +, -, ×, or ÷, a group of numbers or variables can be combined to form an expression. Expressions in algebra that include variables, numbers, and mathematical operators differ from expressions in arithmetic that only contain numbers and mathematical operators.So, the expression for the total cost of the person using c pounds of clay:
2.99c + 20 = Total costTotal cost when Sam uses 3.5 pounds of clay:
2.99c + 20 = Total cost2.99(3.5) + 20 = Total cost10.465 + 20 = Total cost$30.465 = Total costTherefore, the expression will be (2.99c + 20 = Total cost) and the total cost of Sam's consumption will be $30.465.
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suppose a snowball remains spherical while it melts, with the radius r shrinking at 2 inch(es) per hour. what is the rate of change of the surface area s when the radius is 4?
Answers
When the radius of the snowball is 4 and shrinks at a rate of 2 inches per hour then the rate of change of the surface area s is equal to 64π in²/hr
As the radius r is shrinking at the rate of two inches per hour, it can be represented as;
dr/dt = -2 in / hr
Here, the negative sign represents the shrinking of the snowball with time t.
The surface area of a sphere can be represented by the formula;
S = 4πr²
Now we differentiate S with respect to t by keeping radius (r) as a variable as follows;
dS/dt = d/dt (4πr²)
dS/dt = 4π (d/dt) (r²)
dS/dt = 4π × 2r (dr/dt)
Putting the value of r = 4 and calculated value of dr/dt = -2 in the equation as follows;
dS/dt = 4π × 2(4)(-2)
dS/dt = -64π
Therefore, the rate of change of surface area s is calculated to be 64π in²/hr.
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suppose that you have 15 quarters, 10 dimes, 10 nickels, and 10 pennies in your pocket. you reach in and choose a coin at random so that you can give it to your child. what is the expectation? (round your answer to two decimal places.)
Answers
If you have 15 quarters, 10 dimes, 10 nickels and 10 pennies, then the probabilities of getting quarter, dimes, nickels and pennies are 0.33, 0.22, 0.22 and 0.22 respectively.
Total number of quarters = 15 quarters
Total number of dimes = 10 dimes
Total number of nickels = 10 nickels
Total number of pennies = 10 pennies
Total number of coins = 15+10+10+10 = 45
The probability of getting a quarters = 15/45
= 0.33
The probability of getting a dimes = 10/45
= 0.22
The probability of getting a nickel = 10/45
= 0.22
The probability of getting penny = 10/45
= 0.22
Hence, if you have 15 quarters, 10 dimes, 10 nickels and 10 pennies, then the probabilities of getting quarter, dimes, nickels and pennies are 0.33, 0.22, 0.22 and 0.22 respectively.
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A
D
C
If m4BAC = 45°, what is mZDBC?
22.5°
45°
50°
B
35°
Answers
The measure of m∠DBC in the semicircle is 90°
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Equations are classified based on degree (value of highest exponents) as linear, quadratic, cubic and so on. Variables can be dependent or independent. Dependent variables depend on other variable while an independent variable do not depend.
From the image:
∠BAC = ∠BDC = 45° (angle in same segment are equal)
∠BCD = 90° (angle subtended at circumference by semicircle)
In triangle BDC:
∠BDC + ∠BCD + ∠DBC = 180° (angle in a triangle)
45 + 90 + ∠DBC = 180°
∠DBC = 90°
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If Vivian is eating pizza, then she is at Big Slice Pizza.
If Vivian is at Big Slice Pizza, then she is eating pizza.
Is the second conditional the contrapositive, converse, or inverse of the first conditional?
contrapositive
converse
inverse
Answers
The second conditional statement is the converse of the first.
A conditional statement has two phrases and each phrase starts with an 'if' and the other with a 'then'.
Symbolically, it is also expressed as 'p ⇒ q'.
The converse of such a statement is expressed as 'q ⇒ p'.
The first conditional statement given is 'If Vivian is eating pizza, then she is at Big Slice Pizza.'
The second conditional statement given is 'If Vivian is at Big Slice Pizza, then she is eating pizza.'
From the definition of the converse of a conditional statement, the second statement is clearly the converse of the first statement.
Contrapositive of the conditional statement 'p ⇒ q ' is 'not q ⇒ not p'.
Inverse of the conditional statement 'p ⇒ q ' is 'not p ⇒ not q'
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If x and y vary directly and y is 24 when x is 6, find y when x is 9.
Answers
Y is 2.25 when x is 9.
What is direct proportional?The relationship between two values where their ratio equals a constant number is known as a direct proportion or direct variation. It is symbolized by the proportional sign (). According to the direct proportion formula, if y is directly proportional to x, we can state that y = kx, where k is a constant. The generic form of the direct proportion equation is also y = kx. where k is the proportionality constant.
Given Data
If x and y vary directly and y is 24 when x is 6, find y when x is 9.
It is direct proportional
So,
y = kx
To find constant,
k = [tex]\frac{y}{x}[/tex]
x = 6 and y = 24
k = [tex]\frac{6}{24}[/tex]
k = [tex]\frac{1}{4}[/tex]
When x = 9,
k = [tex]\frac{1}{4}[/tex]
y = kx
y = [tex]\frac{1}{4}[/tex](9)
y = [tex]\frac{9}{4}[/tex]
y = 2.25
Y is 2.25 when x is 9.
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The Tour de France is a bicycle road race. The whole race is made up of 21 small races called stages. The table shows how several stages compare to the whole Tour de France. Order the stages from shortest to longest.
Answers
The stages of the race ordered from shortest to longest are:
Stage 21 : 4%
Stage 4: 0.044 x 100 = 4.4%
Stage 8: (6 / 125) x 100 = 4.8%
Stage 1 : (11 / 200) x 100 = 5.5%
Stage 17 : 0.06 x 100 = 6%
What are the stages?The first step is to convert the given decimals, percentages and fractions to the same measure to aid comparison. All would be converted to percentages.
Percentage is the fraction of an amount expressed as number out of 100. In order to convert a number to a percentage, multiply by 100. The sign that represents percentage is %.
Stage 1 : (11 / 200) x 100 = 5.5%
Stage 4: 0.044 x 100 = 4.4%
Stage 8: (6 / 125) x 100 = 4.8%
Stage 17 : 0.06 x 100 = 6%
Stage 21 : 4%
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Find the unknown measures. Round lengths to the nearest hundredth and angle measures to the nearest degree.
Answers
The unknown measures of the right angle triangle are m∠V = 69° , RV = 12.85 and m∠R = 21°
How to find the angles and side of a right triangle?A right triangle is a triangle that has one of its angles as 90 degrees.
Therefore, the side and angles of a right triangle can be found using trigonometric ratios.
Hence,
tan v = opposite / adjacent
opposite side = 12
adjacent side = 4.6
Therefore,
tan V = 12 / 4.6
v = tan⁻¹ 2.60869565217
v = 69.0265065627
m∠V = 69°
Let's find m∠R
m∠R = 180 - 69 - 90
m∠R = 21°
Let's find RV
sin 69° = opposite / hypotenuse
sin 69 = 12 / h
cross multiply
h = 12 / sin 69
h = 12 / 0.93358042649
h = 12.8537402885
RV = 12.85 units
Therefore, the unknown side and angles of the triangle are as follows:
RV = 12.85m∠R = 21°m∠V = 69°learn more on right triangle here: https://brainly.com/question/12917275
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