[tex]\bf ~~~~~~~~~~~~\textit{distance between 2 points} \\\\ (\stackrel{x_1}{0}~,~\stackrel{y_1}{-6})\qquad (\stackrel{x_2}{9}~,~\stackrel{y_2}{6})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ d=\sqrt{[9-0]^2+[6-(-6)]^2}\implies d=\sqrt{(9-0)^2+(6+6)^2} \\\\\\ d=\sqrt{9^2+12^2}\implies d=\sqrt{225}\implies d=15[/tex]
find the slope from the two points (9,-2) and (9,7).
find the slope from the two points (-4,-6) and (5,-6)
Answer:
Step-by-step explanation:
a) We have been given the points (9,-2) and (9,7)
Use the slope formula to solve this.
m= y2-y1/x2-x1
where (x1,y1)=(9,-2)
and (x2,y2)=(9,7)
m=7-(-2)/9-9
m=7+2/0
m=9/0
Having a zero in the denominator means the slope is undefined. Whenever you have a vertical line your slope is undefined....
b) We have been given (-4,-6) and (5,-6)
Use the slope formula to solve this.
m= y2-y1/x2-x1
where (x1,y1)=(-4,-6)
and (x2,y2)=(5,-6)
m=-6-(-6)/5-(-6)
m=-6+6/5+6
m=0/11
If the numerator of the fraction is 0, the slope is 0. This will happen if the y value of both points is the same. The graph would be a horizontal line and would indicate that the y value stays constant for every value of x....
What is the midpoint of the segment below? ( 3,5)(-6,-6)
Answer:
The mid-point is:
[tex]=(\frac{-3}{2},\frac{-1}{2})[/tex]
Step-by-step explanation:
We are given:
[tex](x_1,x_2) = (3,5)\\(y_1,y_2) = (-6,-6)[/tex]
We have to find the midpoint of the segment formed by these points.
The formula for mid-point is:
[tex]Mid-point=(\frac{x_1+x_2}{2},\frac{y_1+y_1}{2})\\ Putting\ the\ values\\Mid-point=(\frac{3-6}{2},\frac{5-6}{2})\\=(\frac{-3}{2},\frac{-1}{2})[/tex] ..
Answer:
The answer above is correct, but in decimal form it's
(-1.5,-0.5)
Step-by-step explanation:
Could use some help with this question please!
so we know the angle is 180° < x < 270°, which is another way of saying that the angle is in III Quadrant, where cosine as well as sine are both negative, which as well means a positive tangent, recall tangent = sine/cosine.
the cos(x) = -(4/5), now, let's recall that the hypotenuse is never negative, since it's just a radius unit, thus
[tex]\bf cos(x)=\cfrac{\stackrel{adjacent}{-4}}{\stackrel{hypotenuse}{5}}\qquad \impliedby \textit{let's find the \underline{opposite side}} \\\\\\ \textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies \pm \sqrt{c^2-a^2}=b \qquad \begin{cases} c=hypotenuse\\ a=adjacent\\ b=opposite\\ \end{cases} \\\\\\ \pm\sqrt{5^2-(-4)^2}=b\implies \pm\sqrt{9}=b\implies \pm 3 = b\implies \stackrel{III~Quadrant}{\boxed{-3=b}} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\bf tan(x)=\cfrac{\stackrel{opposite}{-3}}{\stackrel{adjacent}{-4}}\implies tan(x)=\cfrac{3}{4} \\\\\\ tan(2x)=\cfrac{2tan(x)}{1-tan^2(x)}\implies tan(2x)=\cfrac{2\left( \frac{3}{4} \right)}{1-\left( \frac{3}{4} \right)^2}\implies tan(2x)=\cfrac{~~\frac{3}{2}~~}{1-\frac{9}{16}}[/tex]
[tex]\bf tan(2x)=\cfrac{~~\frac{3}{2}~~}{\frac{16-9}{16}}\implies tan(2x)=\cfrac{~~\frac{3}{2}~~}{\frac{7}{16}}\implies tan(2x)=\cfrac{3}{~~\begin{matrix} 2 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}\cdot \cfrac{\stackrel{8}{~~\begin{matrix} 16 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}}{7} \\\\\\ tan(2x)=\cfrac{24}{7}\implies tan(2x)=3\frac{3}{7}[/tex]
Can someone help me?
(A) 1.5
(B) 3
(C) 4.5
(D) 6
Find the horizontal distance of 230 and find the Vertical distance , which is where the black dot is located.
The black dot is on 49 inches.
Now find the vertical distance f the black line at horizontal 230: This is on 47.5.
The difference between the two is : 49 - 47.5 = 1.5
The answer would be A. 1.5
Answer:
A) 1.5 inches
Step-by-step explanation:
If you draw a vertical line at 230", you will see that it will intersect the line of best fit at Vertical distance = 47.5"
However the actual vertical distance recorded was 49"
Hence the difference between the line of best fit and the actual distance,
= 49 - 47.5 = 1.5"
What is the area of this triangle?
Enter your answer in the box.
Answer:
8 units ^2
Step-by-step explanation:
The area of a triangle is given by
A = 1/2 bh where b is the length of the base and h is the height
b = LK = 4 units
h = J to where LK would be extended to, which would be 4 units
A = 1/2 (4) * 4
A = 8 units ^2
The per capita consumption of red meat by people in a country in a recent year was normally distributed, with a mean of 107107 pounds and a standard deviation of 39.339.3 pounds. Random samples of size 1818 are drawn from this population and the mean of each sample is determined.
Final answer:
The question involves the application of normal distribution and sample means in statistics to analyze per capita red meat consumption. The context provided includes dietary trend changes over time, reflecting shifts in consumer preferences and demand curves.
Explanation:
The student's question pertains to the normal distribution of red meat per capita consumption, a statistical concept used in mathematics to describe how values are spread around a mean. Based on a given mean of 107.107 pounds and a standard deviation of 39.339.3 pounds, we would analyze sample means for groups of 18 individuals. To do this, we use the Central Limit Theorem which states that the sampling distribution of the sample mean will be normally distributed if the sample size is large enough, typically n > 30, but even smaller samples from a normal population will be approximately normal.
As per the historical data from the USDA, we observe changes in per-capita consumption trends for chicken and beef, indicating shifts in consumer preferences affecting the demand curve over time. This information provides context to the type of data involved but does not directly affect the statistical analysis of sample means asked in the question.
Moreover, these statistical concepts could be used to estimate population parameters and analyze shifts in dietary patterns as suggested by the change in the consumption of chicken and beef over the years.
Which of the following sets of points are reflections of each other across the origin? (-5, 6) → (5, -6) (-5, 6) → (6, -5) (-5, 6) → (5, 6) (-5, 6) → (-5, -6)
Answer:
(-5, 6) → (5, -6)
Step-by-step explanation:
Reflection across the origin negates both coordinates.
(x, y) → (-x, -y)
(-5, 6) → (5, -6)
The focus of the parabola -40x = y 2 is: (-10, 0) (10, 0) (0, 10) (0, -10)
Answer:
(-10, 0)
Step-by-step explanation:
The parabola opens to the left, and its vertex is at (0, 0). The focus must have an x-coordinate that is negative. The only viable choice is ...
(-10, 0)
__
The equation is in the form ...
4px = y^2
where p is the distance from the vertex to the focus.
In the given equation, 4p = -40, so p=-10, and the focus is 10 units to the left of the vertex. In this equation, the vertex corresponds to the values of the variables where the squared term is zero: (x, y) = (0, 0).
Peter works part time for 3 hours every day and Cindy works part time for 2 hours every day.
a. If both of them get $4.50 an hour, write an inequality to compare Peter’s and Cindy’s earnings.
b. What should Cindy’s per-hour income be so that she earns at least $14 a day? Write an inequality and an explanation of
how to solve it.
Answer:
a. We can say that P > C, where 'P' represents Peter's earnings and 'C' represents Cindy's earnings.
Given that P = 3h and C = 2h, where h =$4.50. We can say also that 3h > 2h.
b. If Cindy wants to earn at least $14 a day working two hours. Then:
2h ≥ $14
To solve the problem, we just need to solve for 'h':
h ≥ $7
Therefore, se should earn more or equal to $14 per hour.
Answer:
Peter works part time for 3 hours every day and Cindy works part time for 2 hours every day.
Part A:
Peter's earning in 3 hours is = [tex]3\times4.50=13.5[/tex] dollars
Cindy's earnings in 2 hours is = [tex]2\times4.50=9[/tex] dollars
We can define the inequality as: [tex]9<13.50[/tex]
Part B:
Let Cindy's earnings be C and number of hours needed be H.
We have to find her per hour income so that C ≥ 14
As Cindy works 2 hours per day, the inequality becomes 2H ≥ 14
So, we have [tex]H\geq 7[/tex]
This means Cindy's per hour income should be at least $7 per hour so that she earns $14 a day.
Roberto purchased airline tickets for his family of 4. The tickets cost $1,250.The airline also charged a luggage fee,bringing the total cost to $1,400. What is the percent increase
Find the difference:
1400 - 1250 = 150
Divide the difference by the starting value:
150 / 1250 = 0.12
Multiply by 100:
0.12 x 100 = 12% increase.
Answer:
12% Increase.
Step-by-step explanation:
Help with these questions!! I need help! I will mark brainliest!!
Answer: I believe it's 85° i have no explanation and am sorry if it's wrong x
Step-by-step explanation:
Answer:
Question 1. Option (3) RT = 35°
Question 2. Option (3) y = 2
Step-by-step explanation:
By the definition of external angle, ∠PSY is the external angle formed by the secants PS and YS.
From the attached diagram.
Theorem says,
m(∠a) = [tex]\frac{1}{2}(\frac{y-x}{2})[/tex]°
Now we will apply this theorem in our question.
m(∠PSY) = 180° - [m(∠SMX) + m(∠MXS)]
= 180° - (95° + 45°)
= 180° - 140°
= 40°
Since m(∠PSY) = [tex]\frac{1}{2}[m(arcPY)-m(arcRT)][/tex] [By the theorem]
m(arc PY) = m(arc PW) + m(arc WY)
= (80 + 35)°
= 115°
Now m(∠PSY) = [tex]\frac{1}{2}[115-RT][/tex]
40° = [tex]\frac{1}{2}(115-RT)[/tex]°
80 = 115 - RT
RT = 115 - 80
RT = 35°
Therefore, Option (3). RT = 35° is the answer.
Question 2.
By the theorem, every angle at the circumference of a semicircle, that is subtended by the diameter of the semicircle is a right angle.
Therefore, (53y - 16)° = 90°
53y = 90 + 16
53y = 106
y = 2
Therefore, Option (3). y = 2 is the answer.
According to a recent study, 9.3% of high school dropouts are 16- to 17-year-olds. In addition, 6.4% of high school dropouts are white 16- to 17-year-olds. What is the probability that a randomly selected dropout is white, given that he or she is 16 to 17 years old?
Answer:
0.688 or 68.8%
Step-by-step explanation:
Percentage of high school dropouts = P(D) = 9.3% = 0.093
Percentage of high school dropouts who are white = [tex]P(D \cap W)[/tex] = 6.4% = 0.064
We need to find the probability that a randomly selected dropout is white, given that he or she is 16 to 17 years old. This is conditional probability which can be expressed as: P(W | D)
Using the formula of conditional probability, we ca write:
[tex]P(W | D)=\frac{P(W \cap D)}{P(D)}[/tex]
Using the values, we get:
P( W | D) = [tex]\frac{0.064}{0.093} = 0.688[/tex]
Therefore, the probability that a randomly selected dropout is white, given that he or she is 16 to 17 years old is 0.688 or 68.8%
HELP
Find the resulting vector matrix of this matrix multiplication.
Answer:
a = -21 and b = 15
Step-by-step explanation:
It is given a matrix multiplication,
To find the value of a and b
It is given that,
| 6 -5 | * | -1 | = | a |
|-3 4 | | 3 | | b |
We can write,
a = (6 * -1) + (-5 * 3)
= -6 + -15
= -2 1
b = (-3 * -1) + (4 * 3)
= 3 + 12
= 215
Therefore the value of a = -21 and b = 15
Answer:
-21 and 15
Step-by-step explanation:
You multiply the two matrices, -1*6+3*-5=-21 and -1*-3+3*4=15
Myas bed room is into shape of a rectangle Euler prism 15 feet long 12 feet wide and 10 feet high it has no windows Mier wants to pay all four walls including the door in the ceiling what is surface area will she paint
Answer:
15x12x10.
The roof is 12x15.
Two walls are each 12x10.
The other two walls are each 15x10.
12x15 + 12x10 + 15x10 = 180 + 120 + 150 = 450 ft^2
Step-by-step explanation:
Write (2x - 5)2 as a trinomial.
Answer:
[tex]4x^2-20x+25[/tex]
Step-by-step explanation:
[tex](2x-5)^{2} \\(2x)^2+2(2x)(-5)+(-5)^2\\4x^2-20x+25[/tex]
Answer:
[tex]4x^2-20x+25[/tex]
Step-by-step explanation:
You can use the formula:
[tex](u+v)^2=u^2+2uv+v^2[/tex].
[tex](2x-5)^2=(2x)^2+2(2x)(-5)+(-5)^2[/tex]
[tex](2x-5)^2=4x^2-20x+25[/tex].
You could also use foil:
[tex](2x-5)^2=(2x-5)(2x-5)[/tex]
First: 2x(2x)=4x^2
Outer: 2x(-5)=-10x
Inner: -5(2x)=-10x
Last: -5(-5)=25
--------------------------Add.
[tex]4x^2-20x+25[/tex]
Which relation is a function? A. {(–4, –6), (–3, –2), (1, –2), (1, 0)} B. {(–2, –12), (–2, 0), (–2, 4), (–2, 11)} C. {(0, 1), (0, 2), (1, 2), (1, 3)} D. {(8, 1), (4, 1), (0, 1), (–15, 1)}
Answer:
D. {(8, 1), (4, 1), (0, 1), (–15, 1)}
Step-by-step explanation:
A function can not contain two ordered pairs with the same first elements.
Let us look at the options one by one:
A. {(–4, –6), (–3, –2), (1, –2), (1, 0)}
Not a function because (1, –2), (1, 0) have same first element.
B. {(–2, –12), (–2, 0), (–2, 4), (–2, 11)}
Not a function because all the ordered pairs have the same first element.
C. {(0, 1), (0, 2), (1, 2), (1, 3)}
Not a function because (0, 1), (0, 2) have same first element.
D. {(8, 1), (4, 1), (0, 1), (–15, 1)}
This is a function because all the ordered pairs have different first elements i.e. no repetition in first elements of the ordered pairs
Therefore, option D is correct ..
A pyramid has a square base that is 160 m on each side. What is the perimeter of the base in kilometers? Question 19 options:
Answer:
1km=1000m 160m=0.160x4=0.64
Step-by-step explanation:
Ifl = 160m, then:
P = 4 * 160m\\P = 640m
Thus, the perimeter of the base of the pyramid is 640m.
On the other hand, by definition: 1Km = 1000m
By making a rule of three we have:
1Km ---------> 1000m
x --------------> 640m
Where "x" represents the perimeter of the base of the pyramid in Km.
x = \frac {640 * 1} {1000}\\x = 0.64km
For this case we must convert from meters to kilometers. By definition we have to:
[tex]1km = 1000m[/tex]
The perimeter of the base of the pyramid will be given by the sum of the sides:
[tex]P = 160m + 160m + 160m + 160m = 640m[/tex]
We make a rule of three:
1km ----------> 1000m
x ---------------> 640m
Where "x" represents the equivalent amount in km.
[tex]x = \frac {640} {1000}\\x = 0.64km[/tex]
Answer:
0.64km
Given the function f(x) = −3^2 + 4x + 6, find f(2) and f(3). Choose the statement that is true concerning these two values.
A.) The value of f(2) is the same as the value of f(3).
B.) The value of f(2) cannot be compared to the value of f(3).
C.) The value of f(2) is smaller than the value of f(3).
D.) The value of f(2) is larger than the value of f(3).
Answer:
D (assuming f(x)=-3x^2+4x+6)
Step-by-step explanation:
Let's find f(2) and f(3).
I'm going to make the assumption you meant f(x)=-3x^2+4x+6 (please correct if this is not the function you had).
f(2) means replace x with 2.
f(2)=-3(2)^2+4(2)+6
Use pemdas to simplify: -3(4)+4(2)+6=-12+8+6=-4+6=2.
So f(2)=2
f(3) means replace x with 3.
f(3)=-3(3)^2+4(3)+6
Use pemdas to simplify: -3(9)+4(3)+6=-27+12+6=-15+6=-9
So f(3)=-9
-9 is smaller than 2 is the same as saying f(3) is smaller than f(2) or that f(2) is bigger than f(3).
Answer:
The answer is statement D.
Step-by-step explanation:
In order to determine the true statement, we have to solve every statement.
In any function, we replace any allowed "x" value and the function gives us a value. This process is called "evaluating function". If we want to compare different values of the function for different "x" values, we just have to evaluate them first and then compare.
So, for x=2 and x=3
f(2)=-3*(2)^2+4*2+6=-12+8+6=2
f(3)=-3*(3)^2+4*3+6=-27+12+6=-9
f(2)>f(3)
According to the possible options, the true statement is D.
The number of wild flowers growing each year in a meadow is modeled by the function f(x)
f(x)=1000/1+9e^-0.4x
Which statements are true about the population of wild flowers?
Select each correct answer.
A: 42 more wildflowers will grow in the 11th year than in the 10th year.
B: After approximately 9 years, the rate for the number of wild flowers decreases.
C: Initially there were 100 wild flowers growing in the meadow.
D: In the 15th year, there will be 1050 wild flowers in the meadow.
Please no guessing, and remember to provide reasoning for your answer
Answer: A and C
Step-by-step explanation: Took the test |
\/
The true statement is (c) Initially there were 100 wild flowers growing in the meadow.
The function for the number of wild flowers is given as:
[tex]f(x)=\frac{1000}{1+9e^{-0.4x}}[/tex]
Set x to 0
[tex]f(0)=\frac{1000}{1+9e^{-0.4 * 0}}[/tex]
Evaluate the product
[tex]f(0)=\frac{1000}{1+9e^{0}}[/tex]
Evaluate the exponent
[tex]f(0)=\frac{1000}{1+9}[/tex]
Evaluate the sum
[tex]f(0)=\frac{1000}{10}[/tex]
Evaluate the quotient
[tex]f(0)=100[/tex]
The above represents the initial number of wild flowers
Hence, the true statement is (c) Initially there were 100 wild flowers growing in the meadow.
Read more about functions and equations at:
https://brainly.com/question/15602982
Consider one triangle whose sides measure units, units, and 2 units. Consider another triangle whose sides measure 2 units, units, and units.Are these triangles congruent, similar, or both? Explain your answer.
The triangles are both similar and congruent triangles
The side lengths of the triangles are given as:
Triangle A = x units, y units and 2 units.
Triangle B = 2 units, x units and y units.
In the above parameters, we can see that the triangles have equal side lengths.
This means that they are congruent by the SSS theorem.
Congruent triangles are always similar.
Hence, the triangles are both similar and congruent triangles
Read more about similar triangles at:
https://brainly.com/question/14285697
Answer:
Since there are three pairs of congruent sides, we know the triangles are congruent by the SSS congruence theorem. The corresponding sides of the triangle are also in proportion, so they are also similar by the SSS similarity theorem.
Step-by-step explanation:
Edge 23 sample response
The ages of students in a school are normally distributed with a mean of 16 years and a standard deviation of 1 year. Using the empirical rule, approximately what percent of the students are between 14 and 18 years old?
32%
68%
95%
99.7%
(i know its not B)
Answer:
The percent of the students between 14 and 18 years old is 95% ⇒ answer C
Step-by-step explanation:
* Lets revise the empirical rule
- The Empirical Rule states that almost all data lies within 3
standard deviations of the mean for a normal distribution.
- 68% of the data falls within one standard deviation.
- 95% of the data lies within two standard deviations.
- 99.7% of the data lies Within three standard deviations
- The empirical rule shows that
# 68% falls within the first standard deviation (µ ± σ)
# 95% within the first two standard deviations (µ ± 2σ)
# 99.7% within the first three standard deviations (µ ± 3σ).
* Lets solve the problem
- The ages of students in a school are normally distributed with
a mean of 16 years
∴ μ = 16
- The standard deviation is 1 year
∴ σ = 1
- One standard deviation (µ ± σ):
∵ (16 - 1) = 15
∵ (16 + 1) = 17
- Two standard deviations (µ ± 2σ):
∵ (16 - 2×1) = (16 - 2) = 14
∵ (16 + 2×1) = (16 + 2) = 18
- Three standard deviations (µ ± 3σ):
∵ (16 - 3×1) = (16 - 3) = 13
∵ (16 + 3×1) = (16 + 3) = 19
- We need to find the percent of the students between 14 and 18
years old
∴ The empirical rule shows that 95% of the distribution lies
within two standard deviation in this case, from 14 to 18
years old
* The percent of the students between 14 and 18 years old
is 95%
Answer:
Answer Choice C is correct- 95%
Tom and Becky can paint Jim's fence together in $12$ hours. If all people paint at the same rate, how many hours would it take to paint the fence if Huck joins Tom and Becky, and all three of them paint Jim's fence together?
Answer:
8 hours
Step-by-step explanation
The first thing one mus realize here is that this is an inverse proportion question. When one quantity increases, the other decreases. That is the time needed to paint the fence decreases as the number of people who work on it increase. This means therefore that we can set up a proportionality equation:
[tex]t \alpha \frac{k}{n}[/tex]
where t is time and n is the number of people. Given the information in the question we can find the proportionality constant k
[tex]t=\frac{k}{n}[/tex]
[tex]12=\frac{k}{2}[/tex]
so k=24
So how many hours does it take for 3 people
[tex]t=\frac{24}{3} =8[/tex]
Proportions in Triangles (9)
Answer:
3.6
Step-by-step explanation:
Divide 6 by 4
You get 1.5
Multiply 1.5 by 2.4
You get 3.6
A deli serves 6 kinds of lunch meat, 5 kinds of bread, and 4 types of sauce. How many sandwiches can be created with one type of lunch meat, one type of bread, and one type of sauce?
Question 7 options:
140
30
15
120
Answer:
Step-by-step explanation:
6 types of lunch multiplied by 5 kinds of bread then multiplied by 4 types of sauces equals 120
A motorboat takes 4 hours to travel 128 km going upstream. The return trip takes 2
hours going downstream. What is the rate of the boat in still water and what is the rate of the current?
Step-by-step explanation:
Rate × time = distance
If x is the rate of the boat and y is the rate of the water:
(x − y) × 4 = 128
(x + y) × 2 = 128
Simplifying:
x − y = 32
x + y = 64
Solve with elimination (add the equations together):
2x = 96
x = 48
y = 16
The speed of the boat is 48 km/hr and the speed of the water is 16 km/hr.
Soda Q is bottled at a rate of 500 liters/second, 24 hours a day. Soda V is bottled at a rate of 300 liters/second, 24 hours a day. If twice as many bottles of Soda V as of Soda Q are filled in a day, what is the ratio of the volume of a bottle of Soda Q to a bottle of Soda V?
Answer:
[tex]\frac{10}{3}[/tex]
Step-by-step explanation:
Let x be the filled bottles of soda Q,
As per statement,
The filled bottles of soda V = 2x,
Given,
Rate of filling of soda Q = 500 liters per sec,
So, the total volume filled by soda Q in a day = 500 × 86400 = 43200000 liters,
( ∵ 1 day = 86400 second ),
Thus, the volume of a bottle of Soda Q = [tex]\frac{\text{Total volume filled by soda Q}}{\text{filled bottles of soda Q}}[/tex]
[tex]=\frac{43200000}{x}[/tex]
Now, rate of filling of soda V = 300 liters per sec,
So, the total volume filled by soda V in a day = 300 × 86400 = 25920000 liters,
Thus, the volume of a bottle of Soda V
[tex]=\frac{25920000}{2x}[/tex]
Thus, the ratio of the volume of a bottle of Soda Q to a bottle of Soda V
[tex]=\frac{\frac{43200000}{x}}{\frac{25920000}{2x}}[/tex]
[tex]=\frac{10}{3}[/tex]
What is x? [A tangent and a decent]
Answer:
x= 45 degrees
Step-by-step explanation:
Take the larger angle - the smaller angle. 152-62= 90. Now we take this number and divide it by 2. 90/2 equals 45 degrees.
Answer:
45°
Step-by-step explanation:
The external angle measure is half the difference of the intercepted arcs:
x = (152° -62°)/2 = 45°
I need help please.
In triangle ABC, A = 35°, a = 20, and b = 32. Find B. impossible to tell 21° 33° 67°
Answer:
The measure of angle B is [tex]67\°[/tex]
Step-by-step explanation:
we know that
Applying the law of sines
[tex]\frac{a}{sin(A)}=\frac{b}{sin(B)}[/tex]
we have
[tex]a=20\ units[/tex]
[tex]b=32\ units[/tex]
[tex]A=35\°[/tex]
substitute the given values and solve for B
[tex]\frac{20}{sin(35\°)}=\frac{32}{sin(B)}[/tex]
[tex]sin(B)=(32)sin(35\°)/20[/tex]
[tex]B=arcsin((32)sin(35\°)/20)[/tex]
[tex]B=67\°[/tex]
Charmaine is riding her bike. The distance she travels varies directly with the number of revolutions (turns) her wheels make. See the graph below.
(a) How many revolutions does Charmaine make per foot of distance traveled?
(b) What is the slope of the graph?
Answer:
Part a) 0.20 revolutions per foot of distance traveled
Part b) The slope of the graph is [tex]m=5\frac{ft}{rev} [/tex]
Step-by-step explanation:
step 1
Find the slope
we know that
A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form [tex]y/x=k[/tex] or [tex]y=kx[/tex]
In a proportional relationship the constant of proportionality k is equal to the slope m of the line and the line passes through the origin
Let
x ----> the number of revolutions
y ----> the distance traveled in feet
we have the point (2,10) ----> see the graph
Find the value of the constant of proportionality k
[tex]k=y/x=10/2=5\frac{ft}{rev} [/tex]
Remember that in a direct variation the constant k is equal to the slope m
therefore
The slope m is equal to
[tex]m=5\frac{ft}{rev} [/tex]
The linear equation is
[tex]y=5x[/tex]
step 2
How many revolutions does Charmaine make per foot of distance traveled?
For y=1
substitute in the equation and solve for x
[tex]1=5x[/tex]
[tex]x=1/5=0.20\ rev[/tex]
Which description best explains the domain of (gof)(x)?
-the elements in the domain of f(x) for which g(f(x)) is defined
-the elements in the domain of f(x) for which g(f(x)) is not zero
-the elements in the domain of g(x) for which g(f(x)) is defined
-the elements in the domain of g(x) for whic
is not zero
Answer:
-the elements in the domain of f(x) for which g(f(x)) is defined
Step-by-step explanation:
In order for g(f(x)) to exist we first must have that f(x) exist, then g(f(x)).
So the domain of g(f(x)) will be the elements in the domain of f(x) for which g(f(x)) is defined.
The description which best explains the domain of (gof)(x) is the elements in the domain of f(x) for which g(f(x)) is defined.
What is Composition of Functions?Composition of two functions f and g can be defined as the operation of composition such that we get a third function h where h(x) = (f o g) (x).
h(x) is called the composite function.
For two functions f(x) and g(x), the composite function (g o f)(x) is defined as,
(g o f)(x) = g (f(x))
So the domain of g(x) where x contains f(x).
Here when we defined g (f(x)), the domain of the composite function will be the elements in the domain of f(X).
Also these elements must be defined for g(x).
Hence the correct option is A.
Learn more about Domain of Functions here :
https://brainly.com/question/30194233
#SPJ7