Answer: ABC is not a right angled triangle
Step-by-step explanation:
total = 22cm
22-8-5= 9cm
Hypotuneus = 9 cm since its the longest angle
pythagoras theorum = a2+b2=c2
so we need to see if 8² +5² =9²
64+25 need to be 81 (9² )
but its 64+25=89
therefore it is not a right angles triangle.
g) a car rental agency has ten mid-sized and fifteen compact cars on its lot, from which six will be selected. assuming that each is equally likely to be selected, and that they will be selected at random, what is the probability that exactly two mid-sized cars and four compact cars will be selected?
The probability of selecting exactly two mid-sized cars and four compact cars out of a total of six cars is approximately 11.56%.
The answer to this question involves using the formula for combinations and multiplying the probabilities of each selected car.
Calculate the number of ways to select two mid-sized cars and four compact cars.
- Choose 2 mid-sized cars from 10: C(10, 2) = 10! / (2! * (10 - 2)!) = 45 ways
- Choose 4 compact cars from 15: C(15, 4) = 15! / (4! * (15 - 4)!) = 1365 ways
There are a total of 25 cars to choose from and we need to select 2 mid-sized cars from the 10 available and 4 compact cars from the 15 available. Using the formula for combinations, we get:
C(10,2) * C(15,4) = 45 * 1365 = 61,425
This represents the number of ways we can select exactly 2 mid-sized cars and 4 compact cars. To find the probability, we divide this number by the total number of possible selections:
C(25,6) = 53,130
So the probability of selecting exactly 2 mid-sized cars and 4 compact cars is:
61,425 / 53,130 ≈ 0.1156 or 11.56%
In conclusion, the probability of selecting exactly two mid-sized cars and four compact cars out of a total of six cars is approximately 11.56%.
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It is found that 15% of pupils at a school do not jog or swim or cycle, 8% do all three activities, 15% swim and cycle but do not jog, 15% do both jog and swim, 20% swim only, 18% cycle only and 42% do two or more activities
a) Define the cardinality of the complement of set
b) Workout the percentage of pupils who
i) Do both jog and cycle
ii) Swim or cycle
iii) Do not swim
iv) Do not jog, swim and cycle
Step-by-step explanation:
a) The complement of the set of pupils who do not jog or swim or cycle would be the set of pupils who do at least one of these activities.
b) We can use a Venn diagram to help us visualize the information given and answer the questions:
```
_____________
/ \
/ \
jog / A \ swim
/ \
/ \
________/_________ _______\_________
/ \ / \
/ \ / \
cycle B \ / C \ none
/ \ /
/ \____________/
/
/
/
/
/
```
- i) To find the percentage of pupils who do both jog and cycle, we look at the intersection of sets A and B, which is 8%. Therefore, 8% of pupils do both jog and cycle.
- ii) To find the percentage of pupils who swim or cycle, we add the percentages of sets B, C, and D (the parts of the circles that include swimming or cycling), which gives 8% + 15% + 18% = 41%. Therefore, 41% of pupils swim or cycle.
- iii) To find the percentage of pupils who do not swim, we add the percentages of sets A, B, and D (the parts of the circles that do not include swimming), which gives 15% + 8% + 18% = 41%. Therefore, 41% of pupils do not swim.
- iv) To find the percentage of pupils who do not jog, swim, or cycle, we look at the complement of the set of pupils who do at least one of these activities. This is given as 15%, so the percentage of pupils who do not jog, swim, or cycle is 15%.
15% of pupils do not jog, swim or cycle. Of the remaining pupils, 19% both jog and cycle, 61% either swim or cycle, and 39% do not swim. The numbers are based on a full 100% participation rate in regards to these three activities only.
Explanation:The cardinality of a complement of a set refers to the elements that are not in the original set. In context of this question, the complement of the set would be the 15% of pupils who do not partake in jogging, swimming or cycling.
To answer the other parts of the question:
The percentage of pupils who both jog and cycle can be found by adding the percentages of pupils who take part in two or more activities (42%) and then subtracting the percentage of pupils who swim and cycle but do not jog (15%) as well as those who do all three activities (8%). This gives 42% - 15% - 8% = 19%. The percentage of pupils who swim or cycle can be found by adding the percentage of those who swim only (20%), cycle only (18%), do all three activities (8%), as well as those who swim and cycle but do not jog (15%). This gives 20% + 18% + 8% + 15% = 61%. The percentage of pupils who do not swim can be found by subtracting the percentage of those who swim from 100%. This gives 100% - 61% = 39%.The percentage of pupils who do not jog, swim, or cycle is given directly as 15%.Please note that this solution is assuming that all pupils participate in at least one of these activities or none at all and that there are no other activities available.
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In the figure below, Z is the center of the circle. Suppose that QR = 14, SR = 14, UZ = 3x + 5, and VZ = 23. Find the following.
Answer:
x=6
Step-by-step explanation:
VZ=UZ
3x+5=23
3x=18
x=6
Use a double integral to find the area of the region.
The region inside the circle
(x +3)^2 + y^2 = 9
and outside the circle
x^2 + y^2 = 9
The area of the region is (27π/4) square units.
We have,
To find the area of the region inside the circle (x + 3)² + y² = 9 and outside the circle x² + y² = 9, we can use a double integral in polar coordinates.
The region is an annulus (a region between two concentric circles) with the smaller circle centered at (-3,0) and radius 3, and the larger circle centered at the origin and radius 3.
We can rewrite the equations of the circles in polar coordinates as:
(x + 3)² + y² = 9
And,
r² + 2r cos(theta) + 9 = 9
r² + 2r cos(theta) = 0
r = -2 cos(theta)
And,
x² + y² = 9
r² = 9
The region can be described as 0 ≤ r ≤ 3 and -π/2 ≤ θ ≤ π/2 since we are only interested in the part of the region above the x-axis.
The area of the region can be calculated using the following double integral:
A = ∫∫R r dr dθ
where R is the region in polar coordinates.
We can integrate with respect to r first:
A = ∫(-π/2)^(π/2) ∫0³ r dr dθ
= ∫(-π/2)^(π/2) [(1/2) r²]_0³ dθ
= ∫(-π/2)^(π/2) (9/2) dθ
= (9/2) [θ]_(-π/2)^(π/2)
= (9/2) [π - (-π/2)]
= (9/2) (3π/2)
= (27π/4)
Thus,
The area of the region is (27π/4) square units.
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Jackson was solving a two-step equation. Which property justifies the work done between steps one and two?
The work done between steps one and two is justified by applying the Addition Property of Equality.
In step one, we start with the equation 3x - 2 = 10.
To isolate the variable, we can use the Addition Property of Equality, which allows us to add 2 to both sides of the equation.
This yields 3x = 12 (step two).
The Addition Property of Equality states that if the same value is added to both sides of an equation, the equality remains true.
Hence, the property utilized between these steps is the Addition Property of Equality.
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when selecting your schedule in school, you can choose from three math courses, four english courses, two science courses, and two history courses. how many choices do you have for your schedule if you need to select one math, one english, one science, and one history course?
You have 48 different choices for your schedule if you need to select one math, one English, one science, and one history course. It's important to note that this calculation assumes that there are no restrictions or prerequisites for the courses, and that all options are available to all students.
When selecting your schedule in school, you have to choose one math course from the three options, one English course from the four options, one science course from the two options, and one history course from the two options. To find out how many different schedule options you have, you need to multiply the number of options for each subject. So, you have:
3 options for math x 4 options for English x 2 options for science x 2 options for history = 48 possible schedule combinations.
Therefore, you have 48 different choices for your schedule if you need to select one math, one English, one science, and one history course. It's important to note that this calculation assumes that there are no restrictions or prerequisites for the courses, and that all options are available to all students.
To determine the number of possible schedules, you need to multiply the number of choices for each subject together. You have three math courses, four English courses, two science courses, and two history courses. The formula for calculating the total number of choices is:
Total choices = (Math choices) x (English choices) x (Science choices) x (History choices)
Total choices = (3) x (4) x (2) x (2) = 48
So, you have 48 different possible schedules when selecting one math, one English, one science, and one history course.
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How are the pairs of figures alike? How are they different?
Answer: they all have the same amount of squares but are placed differently in each example.
Step-by-step explanation:
there are 6 yellow squares and 10 blue squares for each of the 4 examples. The only difference is how they’re arranged.
In AABC, mA = 58° and m2 B = 45°.
Select the triangle that is similar to AABC.
A. APQR, in which mZP = 58° and
mZR= 70°
B. AXYZ, in which mZX= 45° and
mZY= 103°
OC. AHIJ, in which mZH= 58° and
mZJ= 77°
OD. AMNP, in which m/M = 58° and
mZN = 103°
The triangle similar to ΔABC is ΔSTU, in which m∠S = 87° and m∠U = 70°. Option C
We have,
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,
In ΔABC, we know that m∠A = 87° and m∠B = 23°.
The angle m∠C must therefore be 70°,
since the sum of the angles in a triangle is always 180°.
now, we have,
In ΔSTU, we are given that m∠S = 87°, which corresponds to ∠A in ΔABC.
We are also given that m∠U = 70°, which corresponds to ∠C in ΔABC.
so, we get,
as, This is because two triangles are similar if their corresponding angles are congruent.
Therefore, ΔSTU is similar to ΔABC.
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The above answer is in response to the full question below
In Δ ABC, m∠A = 87° and m∠B = 23°.
Select the triangle that is similar to ΔABC.
A. ΔXYZ, in which m∠X= 87° and m∠z = 50°
B. ΔLMN, in which m∠M=20° and m∠N=87°
C. ΔSTU, in which m∠s = 87° and m∠U=70°
D. ΔPQR, in which m∠P= 110° and m∠R = 23°
Is it negative or positive to say that your gonna “destroy” someone in a race?
Saying you will destroy someone in a race could be positive or negative depending on the context of the situation.
What does it mean to destroy someone in a race?Using the word "destroy" to describe beating someone in a race can be viewed as negative or positive, depending on the context and the relationship between the individuals.
In some situations, it may be seen as a playful or friendly challenge, indicating a competitive but good-natured spirit. However, in other cases, it may come across as aggressive or intimidating, potentially damaging the relationship between the participants.
It is important to consider the tone and the relationship when using language that could be interpreted as confrontational or threatening.
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graph each image as well as the figure after each dilation with the origin as it's center and the given scale factor.
X(-3, 1), Y(-1, 2), Z(2, 1) K = 2
Answer:
Step-by-step explanation:
To perform a dilation with a center at the origin and a scale factor of 2, we multiply each coordinate by 2.
For point X(-3, 1):
x-coordinate: -3 * 2 = -6
y-coordinate: 1 * 2 = 2
So the image of point X after the dilation is X'(-6, 2).
For point Y(-1, 2):
x-coordinate: -1 * 2 = -2
y-coordinate: 2 * 2 = 4
So the image of point Y after the dilation is Y'(-2, 4).
For point Z(2, 1):
x-coordinate: 2 * 2 = 4
y-coordinate: 1 * 2 = 2
So the image of point Z after the dilation is Z'(4, 2).
Graph of the original triangle XYZ:
Y(0, 2)
/\
/ \
/____\
X(0, 0) Z(3, 0)
Graph of the triangle after dilation
Y'(-2, 4)
/\
/ \
/____\
X'(-6, 0) Z'(4, 0)
its hard
two balls are drawn simultaneously from a bag containing 2 yellow and 4 green balls. what is the probability of drawing 2 green balls
The probability of drawing 2 green balls simultaneously from a bag containing 2 yellow and 4 green balls can be determined using the following method:
First, calculate the total number of balls in the bag. There are 2 yellow balls and 4 green balls, so the total is 6 balls.
Now, let's find the probability of drawing 2 green balls. To do this, consider the number of green balls (4) and the total number of balls (6). When drawing the first green ball, there are 4 green balls out of 6 total balls. Therefore, the probability of drawing one green ball is 4/6.
Since the balls are drawn simultaneously, there's no change in the number of balls for the second draw. So, the probability of drawing a second green ball remains 4/6.
Now, we can calculate the probability of both events occurring simultaneously by multiplying the probabilities:
(4/6) * (4/6) = 16/36
To simplify the fraction, divide both numerator and denominator by their greatest common divisor (4):
16/36 = 4/9
So, the probability of drawing 2 green balls simultaneously is 4/9.
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find a value of c so that p(z ≥ c) = 0.55.
To find a value of c such that P(z ≥ c) = 0.55, we need to use a standard normal distribution table or calculator.From the standard normal distribution table, we find that the z-score corresponding to a right-tailed area of 0.55 is approximately 0.126.
Therefore, we have:
P(z ≥ c) = 0.55
P(z ≤ c) = 1 - P(z ≥ c) = 1 - 0.55 = 0.45
Using the standard normal distribution table, we find that the z-score corresponding to a left-tailed area of 0.45 is approximately -0.126.
So, c = -0.126.
Therefore, the value of c that satisfies P(z ≥ c) = 0.55 is approximately -0.126.
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Calculate the Curved Surface area of a Cone whose height IS 8Cm and radius is 5cm
The curved surface area of the cone is 148.19 square cm
Calculating the curved surface area of the coneFrom the question, we have the following parameters that can be used in our computation:
Radius, r = 5 cm
Height, h = 8 cm
The slant height l of the cone is calculated as
l² = 8² + 5²
So, we have
l² = 89
This gives
l = √89
The curved surface area of the cone is then calculaed as
Area = πrl
So, we have
Area = π * 5 * √89
Evaluate
Area = 148.19
Hence, the curved surface area of the cone is 148.19 square cm
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Whats the answer and how do i show work
The measure of <1 is 147 degree.
Given:
m∠2 = 12x - 15
m∠7 = 3x + 21
Since angles 2 and 7 are alternate Exterior angles, they are congruent.
So, 12x - 15 = 3x + 21
12x - 3x = 21 + 15
9x = 36
x = 4
So, <2 = 12x - 15= 48 - 15 = 33
Now, <1 + <2 = 180 (Linear Pair)
<1 + 33 = 180
<1 = 147 degree
Thus, the measure of <1 is 147 degree.
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Biologists introduced a population of bacteria to a test environment. The function � ff models the population size (in thousands) as a function of time (in days) after introduction.
The number of bacteria that were present when the antibiotic was first introduced is 14
How many bacteria were present when the antibiotic was first introduced?From the question, we have the following parameters that can be used in our computation:
The graph (see attachment)
The number of bacteria that were present when the antibiotic was first introduced is when the graph intersects with the y-axis
In this case, the graph intersects with the y-axis at
y = 14
Hence, the number of bacteria that were present when the antibiotic was first introduced is 14
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Complete question
Biologists introduced a population of bacteria to a test environment. The function f models the population size (in thousands) as a function of time (in days) after introduction.
The graph shows a bacteria population (see attacment)
How many bacteria were present when the antibiotic was first introduced?
HELP ASAP ! Write a function rule for the table.
A. ƒ(x) = 3x
B. ƒ(x) = x + 3
C. ƒ(x) = –3 – x
D. ƒ(x) = x – 3
Answer:
The correct answer is D. ƒ(x) = x – 3.
The function rule for a table is a mathematical expression that relates the input values to the output values. In this case, the input values are the numbers in the first column of the table, and the output values are the numbers in the second column of the table.
To find the function rule, we can look for a pattern in the table. We can see that each output value is 3 less than the corresponding input value. For example, when the input value is 1, the output value is -2. When the input value is 2, the output value is -1.
This pattern can be expressed mathematically as ƒ(x) = x – 3. This function rule tells us that the output value is equal to the input value minus 3.
Step-by-step explanation:
Determine the missing dimension of the area is 112 in.²
The missing dimension of the rectangle is 8 inches.
To determine the missing dimension of an area of 112 in.², we need to know at least one of the dimensions. Let's assume we know the length of the rectangle is 14 inches.
We can then use the formula for the area of a rectangle, which is length multiplied by width, to solve for the missing dimension.
We can rearrange the formula to solve for the width by dividing both sides by the length: width = area/length. Plugging in the values we know, we get: width = 112 in.² / 14 in. = 8 inches.
It's important to note that if we had started with the width instead of the length, we would have used the same formula but rearranged it to solve for the length instead. The formula for the area of a rectangle is very useful for solving these types of problems.
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HELP ASAP PLEASE :(((
The values of the third side that would make this a right triangle are C. √ 73 m.
Which values make this a right triangle ?The value that should make the shape a right triangle would be the value that obeys the Pythagorean Function which is:
Longest side ² = Side A ² + Side B ²
Picking √ 73, we have a value of :
= 8. 544 m
Plugging into the formula, we have:
8. 544 ² = 3 ² + 8 ²
72. 99 = 9 + 64
73 = 73
This shows that the value would be 8. 544 or any value that is around 8. 5 m as this can be rounded off.
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leanna needs no more than 2.5 hours to finish her homework. which inequality represents the number of hours, x, leanna needs to finish her homework?
This means that the value of x should not exceed 2.5, as Leanna needs no more than 2.5 hours to complete her homework.
The inequality that represents the number of hours, x, Leanna needs to finish her homework is: x ≤ 2.5.
The inequality x ≤ 2.5 means that the value of x should not exceed 2.5. Since Leanna needs no more than 2.5 hours to finish her homework, we can use this inequality to represent the possible values of x. If x is greater than 2.5, then Leanna would take more than 2.5 hours to finish her homework, which contradicts the given condition. Therefore, the inequality x ≤ 2.5 is the correct representation of the number of hours Leanna needs to finish her homework.
In conclusion, the inequality x ≤ 2.5 represents the number of hours, x, Leanna needs to finish her homework. This means that the value of x should not exceed 2.5, as Leanna needs no more than 2.5 hours to complete her homework.
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Help me with this please
Answer:
2/3
Step-by-step explanation:
3 times 2/3 will equal 2 (A - B)
4.5 times 2/3 will equal 3 (B - C)
6 times 2/3 will equal 2 (C - D)
to find the fraction just divide any of the numbers on the dialated figure (right side) by it's parallel side
do you think the question or problem you described could be investigated using a mathematical population model? why or why not?
It is possible that the question or problem described could be investigated using a mathematical population model. A population model is a mathematical representation of a population, which can be used to make predictions about the population’s behavior and characteristics.
The usefulness of such a model would depend on the specific question or problem at hand. If the question involves understanding how a population will grow or change over time, a mathematical model could be very helpful. However, if the question is more complex and involves multiple factors or variables, a mathematical model may not be sufficient on its own.
For example, if the question is about predicting the spread of a disease in a population, a mathematical model that takes into account the size of the population, the infectiousness of the disease, and the effectiveness of various interventions could be very useful. On the other hand, if the question is about understanding the motivations and behavior of individuals within a population, a mathematical model may not be the best approach. In this case, other methods such as surveys or interviews may be more appropriate.
In summary, whether or not a mathematical population model is appropriate for investigating a question or problem depends on the specific details of that question or problem. In some cases, a population model can provide valuable insights and predictions, while in other cases it may not be sufficient on its own.
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An army contingent of 1000 members is to march behind an army of 56 members in a parade. The 2 groups are to march in the same number of columns. What is the maximum number of columns in which they can march ?
The value of number of columns in which they can march is, 8
According to the problem ,
Members in army contingent = 1000
And, Members in army band = 56
Hence, To find maximum number of columns to march behind army band in the same number of columns,
we have to find HCF of 1000 and 56
1000 = 56 × 17 + 48
56 = 48 × 1 + 8
48 = 8 × 6 + 0
Here, Remainder has become zero.
Since, the divisor in this is, 8 .
HCF ( 1000 , 56 ) = 8
Thus, Required columns = HCF ( 1000 , 56 ) = 8
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Calculate the double integral ∫∫R 2x/1+xy dA, where R = [0,2] x [0,1].
The double integral ∫∫R 2x/(1+xy) dA over R = [0,2] x [0,1] is equal to -4ln(3) + 4.
We have:
∫∫R 2x/(1+xy) dA = ∫[0,2]∫[0,1] 2x/(1+xy) dy dx
Using u-substitution with u = 1 + xy, we have du/dy = x. Solving for x, we get x = du/dy / y. Substituting this into the integral, we get:
∫∫R 2x/(1+xy) dA = ∫[0,2]∫[0,1] 2u/(u) * (1/u) du dx
Simplifying and evaluating the inner integral, we get:
∫∫R 2x/(1+xy) dA = ∫[0,2] (-2ln|1+xy|)[y=0]^{y=1} dx
= ∫[0,2] -2ln(1+x) dx
= [-2(xln(1+x)-x)]_{x=0}^{x=2}
= -4ln(3) + 4
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explain step by step
Answer:
(a) $ 315000
(b) $ 3103448.28
Step-by-step explanation:
(a)
tax = 45% of buying price
Buying price = $700000
tax = 45% × 700000
= $ 315000
(b)
Final price = $4500000
145% = 4500000
buying price = 100%
= 4500000/145 × 100
= 3103448.28
2. When making a full batch of tuna, you will mix one pouch of tuna with 26oz (737g) of mayonnaise. How much tuna and mayonnaise would you need when making a double batch?
These measurements are based on the Original ratio of 1 pouch of tuna to 26 oz (737g) of mayonnaise. If you prefer a different ratio of tuna to mayonnaise, the amounts needed for a double batch may be different.
If one pouch of tuna is mixed with 26 oz (737g) of mayonnaise to make a full batch, then to make a double batch of tuna, we need to double the amounts of both the tuna and the mayonnaise.
we simply need to multiply the amount of tuna in a single batch by 2:
1 pouch of tuna x 2 = 2 pouches of tuna
So, we need 2 pouches of tuna for a double batch.
26 oz (737g) of mayonnaise x 2 = 52 oz (1474g) of mayonnaise
So, we need 52 oz (1474g) of mayonnaise for a double batch.
Therefore, to make a double batch of tuna, we would need 2 pouches of tuna and 52 oz (1474g) of mayonnaise. It's important to note that these measurements are based on the original ratio of 1 pouch of tuna to 26 oz (737g) of mayonnaise. If you prefer a different ratio of tuna to mayonnaise, the amounts needed for a double batch may be different.
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Which question was answered with variable data?
Math item stem image
CLEAR CHECK
Answer:
Question 1
only, because there are many cards in a standard deck of playing cards.
Question 2
only, because the snowfall was not the same for every month.
Neither question, because in each data set, there is only one outcome.
Both questions, because each one has more than one answer.
The term "Variable data" refers to data that can vary or change. It typically includes numerical data that can take on different values or measurements, such as temperature, height, weight, or time.the correct answer is "Neither question, because in each data set, there is only one outcome."
Neither question was answered with variable data, because in each data set, there is only one outcome.
The term "variable data" refers to data that can vary or change. It typically includes numerical data that can take on different values or measurements, such as temperature, height, weight, or time.
In this case, neither question involves variable data. Question 1 is about the number of cards in a standard deck of playing cards, which is a fixed quantity and does not vary. Question 2 is about the total snowfall for each month, but each month has a single, fixed value, so there is no variation in the data.
Therefore, the correct answer is "Neither question, because in each data set, there is only one outcome."
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Find the magnitude of vector AB where A=(-10,-9) and B(-7,4) . Round to the thousandths
Answer:
√((-10 - (-7))^2 + (-9 - 4)^2)
= √((-3)^2 + (-13)^2)
= √(169 + 9) = √178 = 13.342
Complete the proof.
Given: ZADB and ZBDC form a linear pair and ZADB = ZBDC.
Prove: ZADB and BDC are right angles.
Statements
1. ZADB and ZBDC form a linear pair and
ZADB ZBDC.
2. ZADB and ZBDC are Select Choice
3. m2ADB+ m2BDC = 180°
4. mzADB= mzBDC
5. mzADB+mzADB = 180°
6. 2mZADB= 180°
7. m2ADB= 90°
8. m2DBC= 90°
9. ZADB and ZDBC are right angles.
1. Given
Reasons
2. Linear Pair Theorem
3. Select Choice
4. Definition of congruence
5. Substitution
6. Substitution
7. Division Property of Equality
8. Congruent angles have the same measure
9. Select Choice
We can conclude that mZADB = mZBDC = 90° (statement 7) because a right angle is defined as an angle that measures 90° (statement 9). Thus, ZADB and ZBDC are both right angles (statement 9).
1. Given reasons
2. Linear Pair Theorem
3. Angle Addition Postulate
4. Definition of congruence
5. Substitution
6. Division Property of Equality
7. Simplification
8. Simplification
9. Definition of a right angle
Proof:
We are given that ZADB and ZBDC form a linear pair and that their measures are congruent. By the Linear Pair Theorem, we know that the measures of these two angles add up to 180° (statement 2). Let mZADB = x and mZBDC = x, then we can use the Angle Addition Postulate to write mZADB + mBDC = mZBDC (statement 3).
By substituting x for mZADB and mBDC, we get 2x = x + x, which simplifies to 2x = 2x. Using the Division Property of Equality (statement 6), we get x = x, which simplifies to 1 = 1. Therefore, we can conclude that mZADB = mZBDC = 90° (statement 7) because a right angle is defined as an angle that measures 90° (statement 9). Thus, ZADB and ZBDC are both right angles (statement 9).
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y=3x+10
what is the y-intercept
Answer: (0,10)
Step-by-step explanation:
To find the y-intercept, substitute in 0 for x and solve for y.
Answer:
The y-intercept is 10. Also can be thought of as the point (0, 10).
Step-by-step explanation:
This equation is in Slope-Intercept form. The y is all by itself on the left side of the equal sign. On the right, there is an x term. The number next to the x (the co-efficient of x) is the slope. The constant, the number all by itself is the y-intercept.
In the equation,
y = 3x + 10 the slope is 3 and the y-intercept is 10.
This is where the graph crosses the y-axis, the point (0,10)
For any equation you can find the y-intercept by letting x = 0.
y = 3(0) + 10
y = 0 + 10
y = 10
find dy/dx and d2y/dx2. x = 2 sin t, y = 3 cos t, 0 < t < 2π
Therefore, the value of derivatives dy/dx = -3 tan t/2 and d2y/dx2 = -3(1 - cos t)/(2(1+cos t)^2).
To find dy/dx and d2y/dx2, we need to first express y in terms of x:
x = 2 sin t --> sin t = x/2 --> cos t = ±sqrt(1 - sin^2 t) = ±sqrt(1 - x^2/4)
y = 3 cos t = ±3sqrt(1 - x^2/4)
Since 0 < t < 2π, we can determine the sign of cos t by looking at the quadrant that x lies in. Since x = 2 sin t, we have x > 0 when 0 < t < π and x < 0 when π < t < 2π. Therefore, when 0 < t < π, we have:
cos t = sqrt(1 - sin^2 t) = sqrt(1 - x^2/4)
y = 3 sqrt(1 - x^2/4)
dy/dx = -3x/2 sqrt(1 - x^2/4)^(-1)
Taking the derivative of dy/dx with respect to x, we get:
d2y/dx2 = -3/2 [sqrt(1 - x^2/4)^(-1) - 3x^2/8 (1 - x^2/4)^(-3/2)]
Plugging in x = 2 sin t and simplifying, we get:
dy/dx = -3 sin t / sqrt(4 - 4 sin^2 t) = -3 sin t / 2 cos t = -3 tan t/2
d2y/dx2 = -3/4 (sec^2 t/2 - 3 tan^2 t/2) = -3/4 [(2/(1+cos t) - 3 tan^2 t/2)]
Using the identity cos^2(t/2) = (1+cos t)/2 and simplifying, we get:
d2y/dx2 = -3/4 [(4/(1+cos t) - 3) / (1+cos t)] = -3(1 - cos t)/(2(1+cos t)^2)
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