Answers
The x and y values in the triangle are:
x = 58°
y = 26°
How to find x and y values in the triangle?Trigonometry deals with the relationship between the ratios of the sides of a triangle with its angles.
To find the x and y values in the triangle, check the attached image for labeling.
In the image:
Triangle ABC is isosceles. Thus,
t = 61° (base angles of isosceles triangles are equal)
x + t + 61 = 180 (sum of angles in a triangle is 180°)
x + 61 + 61 = 180
x = 180 - 61 - 61
x = 58°
x + v = 180 (sum of angles on a straight line is 180°)
58 + v = 180
v = 180 - 58
v = 122°
In triangle ACD:
32 + v + y = 180 (sum of angles in a triangle is 180°)
32 + 122 + y = 180
y = 180 - 32 - 122
y = 26°
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Related Questions
Find the 20th term of the following sequence.
-6, -4, -2, 0, ...
32
46
44
Answers
Step-by-step explanation:
Arithmetic sequence with d = 2 a1 = -6
a20 = -6 + 2(20-1) = 32
To find the 20th term, we can use the formula:
an = a1 + (n - 1)d
where
an is the nth term of the sequence
a1 is the first term of the sequence
d is the common difference between the terms
n is the term we want to find
We are given that a1 = -6, d = 2, and n = 20. Substituting these values into the formula, we get:
a20 = -6 + (20 - 1)2
a20 = -6 + 38
a20 = 32
Therefore, the 20th term of the sequence is 32.
7. find the values of c that satisfy Rolle's Theorem.
Show steps
Answers
The values of c that satisfy Rolle's Theorem is 2.15 or -0.15.
What is the value of c that satisfy Rolle's Theorem?The value of c that satisfies Roll's theorem is calculated as follows;
y = x³ - 3x² - x; [-1, 3]
Based on Roll's theorem conditions, since the function is a polynomial it is continuous.
The derivative is also a polynomial.
y' = 3x² - 6x - 1
The final condition;
y(-1) = (-1)³ - 3(-1)² - (-1)
y(-1) = -1 - 3 + 1
y(-1) = -3
y(3) = (3)³ - 3(3)² - 3
y(3) = 27 - 27 - 3
y(3) = -3
The three conditions of Rolle's theorem is statisfied, so there exists at least one value of c in the interval (-1, 3) such that y'(c) = 0.
y' = 3x² - 6x - 1
y'(c) = 3c² - 6c - 1
3c² - 6c - 1 = 0
Solve the quadratic equation using formula method;
a = 3, b = -6, c = -1
c = 2.15 or - 0.15
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A summer camp cookout is planned for the campers and their families. There is room for 450 people. Each adult costs $7, and each camper costs $4. There is a maximum budget of $1,150. Write the system of inequalities to represent this real-world scenario, where x is the number of adults and y is the number of campers
Answers
The system of inequalities that represents this real-world scenario is:
x + y ≤ 450 (The total people cannot be greater than 450)
7x + 4y ≤ 1150 (total price cap of $1,150)
What is system of inequalities ?
A group of two or more simultaneously true inequalities is referred to as a system of inequalities. A system of inequalities can be solved by finding the set of values that satisfies every one of the inequalities in the system.
Therefore, The system of inequalities that represents this real-world scenario is:
x + y ≤ 450 (The total people cannot be greater than 450)
7x + 4y ≤ 1150 (total price cap of $1,150)
Where x is the number of adults and y is the number of campers.
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A 1.75 litre bottle of water is poured into 250 ml paper cups. How many paper cups can be filled?
Answers
Answer:
The answer to your problem is, 7
Step-by-step explanation:
First you can either convert;
ml to liter
liter to ml
I will use liter to ml.
1.75 liters in ml is 1750 ml
So we can then divide, 1750 / 250 = 7
Which is the answer
Thus the answer to your problem is, 7
What is this equation? 24/x+8, for x=3
Answers
Answer:
16
Step-by-step explanation:
24 divided by X(3) is equal to 8, then 8+8 equals 16 (EASY)
Mrs.lealas living room has an area of 144 square feet.
Her dining room is ⅓ the area of the living room and ⅖ the area of the kitchen. What is the area, in square feet, of the kitchen?
Answers
The Area of Kitchen is 120 square feet.
We have,
Area of living room = 144 square feet
So, the dining room
= 1/3 (area of living room)
= 1/3 (144)
= 48 square feet
and, Area of Dining room = 2/5 x Area of kitchen
48 = 2/5 x Area of kitchen
Area of kitchen = 48 x 5/2
Area of Kitchen = 24 x 5
Area of Kitchen = 120 square feet
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Jasmine has a circular swimming pool with a radius of 4.2 meters. What is the circumference of the pool? Use 3.14 for π
. Round to the nearest hundredth if necessary.
__ m
Answers
If the radius of Jasmine's swimming pool is 4.2 meter, then it's circumference is 26.4 meters.
The "Circumference" of a circle is known as the distance around the boundary of a circle.
The circumference of a circle is given by the formula : 2 × π × radius,
where π (pi) is a mathematical constant approximately equal to 3.14,
We are given that Jasmine's swimming pool has a radius of 4.2 meters.
So, we can calculate the circumference of the pool as :
⇒ Circumference = 2 × 3.14 × 4.2 meters,
⇒ Circumference ≈ 26.4 meters,
Therefore, the circumference of Jasmine's swimming pool is 26.4 meters.
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Zayn and Attia are thinking of a number each. What is Attia's number? My number is greater than 2. 12 and 20 are multiples of my number. My number is the 11th multiple of Zayn's number.
Answers
Answer:
Me: 60
Zayn and Attia: 6
Step-by-step explanation:
12 = 2 × 2 × 3
20 = 2 × 2 × 5
LCM of 12 and 20 = 2 × 2 × 3 × 5 = 60
My number is 60.
Zayn's and Attia's numbers are 6.
Triangle 1 undergoes four different transformations.
The results of these transformations are shown.
1
4
2
5
3
Which statement best describes one of these
transformations?
Triangle 1 is rotated to result in triangle 2.
O Triangle 1 is dilated to result in triangle 3.
O Triangle 1 is reflected to result in triangle 4.
Triangle 1 is stretched to result in triangle 5.
Answers
time tables on the map mannnnn
Which of the points below correctly plots the point (5,−2π/3)?
Answers
Answer: the answer is E
Step-by-step explanation:
Remember that the coordinates (5,−2π3) tell us the radius r=5 and the angle θ=−2π3. So the point should be on the circle labeled 5 and form an angle of −2π3 with the positive x-axis. Point E is the correct point.
Answer:
Step-by-step explanation:
Remember that the coordinates (5,−2π/3) tell us the radius r=5 and the angle θ=−2π/3. So the point should be on the circle labeled 5 and form an angle of −2π/3 with the positive x-axis. Point E is the correct point.
Find the area of a parallelogram.
Answers
Answer:
60
Step-by-step explanation:
The area of a parallelogram is base x hight.
A = bh
10(b) x 6(h) = 60
HELP ITS DUE TODAY IM GIVING OUT 15 POINTS IM SORRY I ONLY HAVE 75
Answers
The values of the variables x and y are;
1, x = -y and y = 5. Option D
2. x= 1 and y = -1. Option A
How to determine the valueUsing the substitution method of solving simultaneous equations, we have;
4x + 7y = 19
y - x = 9
Now, make 'y' the subject from equation 2
y = 9 + x
Substitute the equation into equation 1
4x + 7(9 + x)= 19
expand the bracket, we have;
4x + 63 + 7x = 19
collect the like terms
11x = -44
x = -4
then,
y = 9 - 4 = 5
-3x + y = -4
4x + 3y = 1
make y' the subject from equation 1
y =-4 + 3x
Substitute the value
4x + 3(-4 + 3x) = 1
expand the bracket
4x - 12 + 9x = 1
13x = 13
x = 1
Substitute the value
y = -4 + 3
y = -1
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The displacement of a train starting from a stop is given by the equation s(t) = 8\sqrt{t}+1 meters. Estimate the instantaneous velocity of the train at t = 9 seconds by considering the average velocities over the intervals [8.5, 9], [8.7, 9], [8.9, 9], [8.99, 9], [9, 9.01], [9, 9.1], [9, 9.3], and [9, 9.5].
Answers
The instantaneous velocity of the train at t = 9 seconds is approximately 6.8 m/s
To estimate the instantaneous velocity of the train at t = 9 seconds, we can consider the average velocities over several small intervals of time that include the point t = 9. This is an approximation of the slope of the tangent line to the curve s(t) at t = 9, which is the instantaneous velocity.
We can calculate the average velocity over each interval by dividing the change in displacement by the change in time:
Average velocity from [8.5, 9] = (s(9) - s(8.5)) / (9 - 8.5) = (8√9 + 1 - 8√8.5 + 1) / 0.5 = 6.34 m/s (approx.)
Similarly, we can calculate the average velocities over the other intervals:
[8.7, 9]: 6.48 m/s (approx.)
[8.9, 9]: 6.60 m/s (approx.)
[8.99, 9]: 6.66 m/s (approx.)
[9, 9.01]: 6.67 m/s (approx.)
[9, 9.1]: 6.74 m/s (approx.)
[9, 9.3]: 6.87 m/s (approx.)
[9, 9.5]: 7.00 m/s (approx.)
As we consider smaller intervals closer to t = 9, the average velocities approach a limit, which is the instantaneous velocity at t = 9. In this case, we see that the average velocities are increasing as we approach t = 9, indicating that the instantaneous velocity at t = 9 is also increasing.
Based on these calculations, we can estimate that the instantaneous velocity of the train at t = 9 seconds is approximately 6.8 m/s (averaging the average velocities from [8.99, 9] to [9, 9.5]).
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10. The box plot shows donations in dollars to charity.
Describe the shape of the distribution.
Donations to Charity ($)
20 40 60 80 100 120 140 160 180 200 220
Answers
The given shape of the distribution is not symmetric.
Given that, a box plot shows donations in dollars to charity.
We need to describe the shape of the distribution.
Donations to Charity ($) =
20 40 60 80 100 120 140 160 180 200 220
so, as we can see,
The shape of the distribution is not symmetric since the lengths of each box and whisker are not the same. There is an outlier at 220.
Hence, the given shape of the distribution is not symmetric.
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Find the volume of the triangular prism described below
Answers
The volume of the triangular base prims is 21.6 inches cube.
How to find the volume of a triangular base prism?A triangular base prism is a prism with a triangular base. Therefore, let's find the volume of the triangular prism.
volume of a triangular prism = base area × height
Therefore,
base area = 1 / 2 bh
where
b = baseh = heightTherefore, the triangular base has angles 45, 45 and 90 degrees. Using trigonometric ratios let's find the other legs.
tan 45 = opposite / adjacent
tan 45 = x / 6
x = 6 inches
Therefore,
base area = 1 / 2 × 6 × 6
base area = 36 /2
base area = 18 inches²
Hence,
volume of the triangular base prism = 18 × 1.2
volume of the triangular base prism = 21.6 inches³
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help please i need the answer to thus question
Answers
The measure of angle 1 is 107° suing the concepts of corresponding angles and linear pair of angles..
Given a line t which is a transversal line that cuts the two parallel lines m and n.
Here the angle which is linear pair to angle 1 and the angle 73° are corresponding angles.
By the corresponding angle theorem, the corresponding angles formed by two parallel lines cut by a transversal are equal.
So,
Measure of angle which is linear pair to 1 = 73°
Now linear pair of angles are supplementary.
∠1 + 73° = 180°
∠1 = 180° - 73°
∠1 = 107°
Hence the measure of angle 1 is 107°.
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4. Chelsea determined that the value of x in the triangle at the right was 5.
a. Find the value of each angle by substituting 5 for x.
b. Was Chelsea's solution, x = 5, correct? How do you know?
15x
x
11x
(8x+5)
Z
Answers
Step-by-step explanation:
a) 11*5=55
15*5=75
8*5+5=45
b) No, because (55+75+45=175°) and the perimeter of a triangle is 180°
can someone help with this
Answers
The expected joint frequencies are
Male and Drama = 20Male and Comedy = 40Female and Drama = 75Female and Comedy = 25Calculating the expected joint frequenciesFrom the question, we have the following parameters that can be used in our computation:
The table of values
Also, we have
People = 160
This means that
Male and Drama = 12.5% * 160
Male and Drama = 20
Male and Comedy = 25% * 160
Male and Comedy = 40
Female and Drama = 46.9% * 160
Female and Drama = 75
Female and Comedy = 15.6% * 160
Female and Comedy = 25
In conclusion, we have
Because the expected and the joint frequencies are not the same, gender is not independent of movie type
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A Certain sum of money of simple
interest amount to $$1,300 ire 4 years
and to #11525 in 7 years - Find
the sum and the rate percent
Answers
The required rate of simple interest is 1.75%.
Here, we have,
(Principal + Interest) is a straightforward interest equation.
A = P(1 + rt)
Where: A is the sum of the accrued principal and interest.
Principal Amount is P.
I is the interest rate.
r is the annual percentage rate of interest, or R/100.
R is the annual percentage rate of interest; R = r * 100 t is the length of time involved in months or years.
Since I = Prt,
the initial formula A = P(1 + rt) evolved from A = P + I to A = P + Prt,
which may be represented as A = P(1 + rt).
Given: Principal is $1,300
Rate is 7% and the amount earned that is A-P is $159.25.
A = P(1 + rt)
Therefore substituting the values in the above mentioned equation, we get:
159.25= 1300(1+r×7)
On solving we get,
r= 1.75%
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complete question:
At the Blue Bank, Barry would earn $159.25 in simple interest in 7 years after depositing $1,300.
What rate of simple interest is offered at the
Blue Bank?
Solve the logarithmic equation by writing in exponential form or by graphing. Round to the nearest thousandth if necessary. log (x − 2) = 1
Answers
The solution in the equation is x = 12.
We have,
To solve the logarithmic equation log (x − 2) = 1,
We can use the definition of logarithm which states that log base b of x equals y if and only if b to the power of y equals x, where b is the base of the logarithm.
In this case, the base is not specified, so we assume it is 10, which is the common base used in most calculators and mathematical applications
Using the exponential form, we have:
log (x - 2) = 1
10^1 = x - 2
10 = x - 2
x = 12
Therefore,
The solution is x = 12.
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Question 10 (10 points)
You have this great idea for a business, but need to write at
least a 50 page business proposal to hand out to potential
investors. As of today, you have 15 pages done. How many
pages do you have left to write?
Inequality:
+p>
Solution: p>
Blank 1:
Blank 2:
Blank 3:
Answers
Answer:
p≥35
Step-by-step explanation:
because you have done 15 so you subtract 15 from 50 giving you 35 and then you would say p is greater than or equal to 35 cause 50 pages is your minimum
Simplify \sqrt{2} \cdot \sqrt{6} \cdot \sqrt{110} \cdot \sqrt{120} \cdot \sqrt{450} \cdot \sqrt{520}
Answers
The simplification of the given expression is equal to 192524.3.
The expression is equal to,
√2 × √6 × √110 × √120 × √450 × √520
Simplify this expression by first simplifying the square roots under the radical signs,
√2 = √(2 × 1)
= √2 × √1
√6 = √(2 × 3)
= √2 × √3
√110 = √(2 × 5 × 11)
= √2 × √5 × √11
√120 = √(2 × 2 × 2 × 3 × 5)
= 2√2 × √3 × √5
√450 = √(2 × 3² × 5²)
= √2 × (3 × 5)²
= 15√2
√520 = √(2³ × 5 × 13)
= 2√2 ×√5 × √13
Substituting these simplifications back into the original expression, we have,
√2 × √6 × √110 × √120 × √450 × √520
= √2 × √2 × √3 × √2 × √5 × √11 × 2√2 × √3 × √5 × 15√2 × 2√2 ×√5 × √13
= 2⁵ × 3² × 5²√(5 × 11 × 13)
= 7200√715
= 192524.3
Therefore, the simplification value of √2 × √6 × √110 × √120 × √450 × √520 is equal to 192524.3.
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The above question is incomplete, the complete question is:
Simplify
√2 × √6 × √110 × √120 × √450 × √520
Swathu buys a new scooter on loan. The loan is for Rs. 90,000 atrase of interest 8% per annum compounded half yearly for 2 years
Answers
After two years, Swathu will pay back the debt in full, which comes to Rs. 105287.27.
To find the total amount Swathu will pay back after 2 years on a loan of Rs. 90,000 with an interest rate of 8% per annum compounded half-yearly, we can use the formula for compound interest:
[tex]A = P(1 + r/n)^{nt[/tex]
where:
A = the total amount Swathu will pay back
P = the principal amount borrowed (Rs. 90,000)
r = the annual interest rate (8%)
n = the number of times the interest is compounded per year (2 times, since it is compounded half-yearly)
t = the time period (2 years)
Substituting these values into the formula, we get:
[tex]A = 90,000(1 + 0.08/2)^{2*2}\\\\A = 90,000(1 + 0.04)^4\\\\A = 90,000(1.04)^4\\\\A = 90,000(1.16985856)\\[/tex]
A = 105287.27 (rounded to the nearest tenth)
Therefore, Swathu will pay back a total of Rs. 105287.27 after 2 years on the loan.
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An ice-cream scoop has a shape of spherical cap. An engineer's goal is to maximize the volume of the scoop given that the surface area of the scoop is 36 cm2. Find the radius of the sphere and the height of the spherical cap of maximum volume. (Hint:
the volume of a spherical cap is [tex]Vcap=\frac{1}{3} \pi h^2(3R-h)[/tex], where R is the radius of the sphere and h is the height of the cap). Find the maximum volume of ice-cream scoop.
Write your answer in terms of π.
Answers
The radius is 5.316 cm, height is 10.362 cm and Maximum volume is
60.583 cm³.
We have,
Surface area of sphere = 36 cm²
4πr² = 36
πr² = 9
r = 3√π
r= 5.316
Now, Volume spherical cap
= 1/3 πh² (3R- h)
= 1/3π (10.362) (3 (5.316) - 10.362)
= 1/3 π (57.882132)
= 60.583 cm³
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I need help with this ?
Answers
The equation will have the solution in the form of an imaginary number "i" as: x = (3 ± 2i)/2
What is an imaginary number in a quadratic equationIn a quadratic equation, an imaginary number is a complex number that can arise when trying to take the square root of a negative number.
We shall solve for x in the equation as follows:
(2x + 3)² - 2 = -6
add 2 to both sides
(2x + 3)² = 2 - 6
(2x + 3)² = -4
2x + 3 = √(-4) {taking square root of both sides}
subtract 3 from both sides
2x = 3 ± √(-4)
divide through by 2
x = [3 ± √(-4)]/2
note that: √(-4) = √(1-) × √4 where √(-1) = I, so;
x = (3 ± 2i)/2.
Therefore, the equation will have the solution in the form of an imaginary number "i" as: x = (3 ± 2i)/2
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The velocity of an object is the distance it travels per unit time. Suppose the velocity of a gliding bird is measured to be 244. cm/s. Calculate the time it will take the bird to travel 1.4 m.
Answers
The time it will take the bird to travel 1.4 m is 0.5738 seconds.
What is velocity?In Science and Mathematics, velocity can be defined as the distance covered by an object per unit of time in a specific direction. This ultimately implies that, velocity is a vector quantity because it has both magnitude and direction.
How to calculate the velocity of a physical object?In Mathematics and Science, the velocity of any a physical object can be calculated by using this formula;
Velocity = distance/time
244 cm/s to m = 244/100 = 2.44 cm/s
By making time the subject of formula, we have:
Time = distance/velocity
Time = 1.4/2.44
Time = 0.5738 seconds.
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i need help with this lol
Answers
The trio of sides that will make a right triangle are the ones in the first option:
5, 12, and 13.
Which set would make a right triangle?Remember that for any right triangle, the sum of the squares of the two shorter sides must be equal to the square of the longest side.
So for example, for the first option we would have:
5^2 + 12^2 = 13^2
25 + 144 = 169
169 = 169
The equation is true, thus, these sides make a right triangle.
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Please help 50 points
Answers
Answer:
2(5(11) + 5(2.5) + 11(2.5))
= 2(55 + 12.5 + 27.5) = 2(55 + 40) = 2(95)
= 190 square centimeters
A 10-mile cab ride costs $40. A 15-mile cab ride costs $55. Find the rate of change (cost per mile) for the cab ride
Answers
The rate of change for the cab ride is A = $3 per mile
Given data ,
Change in cost = $55 - $40 = $15
Change in distance = 15 miles - 10 miles = 5 miles
Now, we can divide the change in cost by the change in distance to get the rate of change or cost per mile:
Rate of change or cost per mile = Change in cost / Change in distance
A = $15 / 5 miles
A = $3 per mile
Hence , the rate of change or cost per mile for the cab ride is $3 per mile
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help i will have more questions
Answers
Answer:
3/23 or 0.1304 or 13%
Step-by-step explanation:
Given 3 students have a brother and sister, and 20 students have only a brother, you want the probability that a student who has a brother also has a sister.
Conditional probabilityThe conditional probability formula is ...
P(A | B) = P(A&B)/P(B)
Here, this means ...
P(has a sister | has a brother) = P(has both)/P(has a brother)
= 3/(3 +20)
= 3/23 ≈ 0.1304 ≈ 13% . . . . . probability of a sister if has a brother
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