Answers
Answer:
[tex]m\angle CED= 64\°[/tex]
[tex]m\angle ACD=124\°[/tex]
Step-by-step explanation:
In the figure given:
∠ABC = 93°
∠BAC = 31°
∠CDE = 60°
To find ∠CED and ∠ACD.
Solution:
In triangle ABC, we are given two vertex angles. We can find the third angle as angle sum of triangle = 180°.
∠ABC = 93° , ∠BAC = 31°
∠BCA= [tex]180\°-(93\°+31\°)[/tex]
∠BCA = 56°
[tex]m\angle BCA+m\angle ACD=180\°[/tex] [Supplementary angles forming a linear pair]
[tex]m\angle ACD=180\°-56\°[/tex]
[tex]m\angle ACD=124\°[/tex] (Answer)
In triangle CDE:
[tex]m\angle CDE+m\angle CED = m\angle ACD[/tex] [Exterior angle theorem :Exterior angle of a triangle is equal to sum of opposite interior angles ]
[tex]60\°+m\angle CED = 124\°[/tex]
[tex]m\angle CED= 124\°-60\°[/tex]
[tex]m\angle CED= 64\°[/tex] (Answer)
Answer:
m\angle CED= 64\°
m\angle ACD=124\°
Step-by-step explanation:
get an A!
Related Questions
Two taxi companies charge different rates. Metro taxi charges $3.00 for the first mile and $2.50 for each additional mile. City taxi charges $5.00 for the first mile and $2.25 for each additional miles. After how many miles will both companies charge the same amount?
Answers
Answer: it will take 9 miles for both costs to be the same.
Step-by-step explanation:
Let x represent the number of miles it will take for both companies to charge the same amount.
Metro taxi charges $3.00 for the first mile and $2.50 for each additional mile. This means that the total charge for x miles would be
3 + 2.5(x - 1) = 3 + 2.5x - 2.5
= 2.5x + 0.5
City taxi charges $5.00 for the first mile and $2.25 for each additional miles. This means that the total charge for x miles would be
5 + 2.25(x - 1) = 5 + 2.25x - 2.25
= 2.25x + 2.75
For the costs to be the same, then
2.5x + 0.5 = 2.25x + 2.75
2.5x - 2.25x = 2.75 - 0.5
0.25x = 2.25
x = 2.25/0.25
x = 9
The optimal height h of the letters of a message printed on pavement is given by the formula [tex]h = \frac{0.00252 d^{2.27}}{e}[/tex]. Here d is the distance of the driver from the letters and e is the height of the driver's eye above the pavement. All of the distances are in meters. Find h for the given values of d and e.
d = 92.4 m, e = 1.7 m.
Answers
Answer:
The value of h is 42.956 approximately.
Step-by-step explanation:
Consider the provided formula [tex]h=\dfrac{0.00252 d^{2.27}}{e}.[/tex]
Here d is the distance of the driver from the letters and e is the height of the driver's eye above the pavement. All of the distances are in meters.
We need to find the value of h where the value of d = 92.4 m, e = 1.7 m.
Substitute d = 92.4 m, e = 1.7 m in above formula and solve for h.
[tex]h=\dfrac{0.00252\left(92.4\right)^{2.27}}{1.7}[/tex]
[tex]h\approx\dfrac{0.00252\left(28978.4648\right)}{1.7}[/tex]
[tex]h\approx\dfrac{73.0257}{1.7}[/tex]
[tex]h\approx42.956[/tex]
Hence, the value of h is 42.956 approximately.
Final answer:
Using the formula provided, the optimal height of the letters for a message to be seen by a driver is approximately 30.447 meters, when the driver is 92.4 meters away and their eye height is 1.7 meters above the pavement.
Explanation:
To find the optimal height h of the letters for a message printed on pavement, where d is the distance to the driver and e is the height of the driver's eye above the pavement, we use the given formula: h = [tex]\(\frac{0.00252 d^{2.27}}{e}\)[/tex]
Substituting the provided values d = 92.4 m and e = 1.7 m into the formula, we calculate:
h = [tex]\(\frac{0.00252 \times 92.4^{2.27}}{1.7}\)[/tex]
First, raise 92.4 to the power of 2.27:
92.42.27 ≈ 20546.45
Then, multiply this result by 0.00252:
0.00252 × 20546.45 ≈ 51.76
Finally, divide by e, the driver's eye height (1.7 m):
h ≈ [tex]\(\frac{51.76}{1.7}\)[/tex] ≈ 30.447 m
Therefore, the optimal letter height h is approximately 30.447 meters.
A chicken broth container is in the shape of a rectangular prism, with a length of 9.5 centimeters, a width of 6 centimeters, and a height of 16.5 centimeters. The container is 90% full. How many liters of chicken broth are in the container? ( ) 3 1 L 1000 cm = Round your answer to the nearest hundredth.
Answers
Answer:
846,45cm³
Step-by-step explanation:
V = 9.5 * 6 * 16.5
V = 940.5cm³
90% = 940.5 * 0.9 = 846,45cm³
Answer:
0.85 liters
Step-by-step explanation:
Step 1. Find the volume of the full prism
V=9.5 x 6 × 16.5 = 940.5 [tex]cm^{3}[/tex]
Step 2. Find 90% of the full volume of the prism
90% x 940.5 = 0.9 × 940.5 = 846.45 [tex]cm^{3}[/tex]
Step 3. Convert [tex]cm^{3}[/tex] to liters (1 liter = 1000 [tex]cm^{3}[/tex] )
846.45 [tex]cm^{3\\[/tex] = 0.84645 ≈ 0.85
Answer - 0.85 liters
A kind of lava , block lava , is moving away from the base of a volcano at a rate of 1.5 meters per day . If the lava continues to flow at this rate, how far away has the lava flowed from the base if the volcano in 30 days
Answers
Final answer:
The block lava has flowed 45 meters from the base of the volcano after 30 days, based on a rate of 1.5 meters per day.
Explanation:
To calculate how far the block lava has flowed from the base of a volcano after 30 days at a rate of 1.5 meters per day, we simply multiply the rate of flow by the number of days.
Distance traveled = Rate × Time
Distance traveled = 1.5 meters/day × 30 days = 45 meters.
So, if the lava continues to flow at this constant rate, after 30 days, it will have moved 45 meters away from the base of the volcano. This calculation offers valuable insights into the potential extent of volcanic activity, aiding in risk assessment and mitigation strategies for areas surrounding the volcano.
please help me with this giving lots of points
Answers
x° = 43° and y° = 120°
Solution:
Given ABCD is a parallelogram.
∠A = (y + 9)°, ∠C = (3x)°, ∠D = (x + 8)°
In a parallelogram, sum of the adjacent angles = 180°
⇒ ∠C + ∠D = 180°
⇒ (x + 8)° + (3x)° = 180°
⇒ x° + 8° + 3x° = 180°
⇒ 4x° + 8° = 180°
⇒ 4x° = 180° – 8°
⇒ 4x° = 172°
⇒ x° = 43°
Substitute x° = 43° in ∠C.
∠C = (3x)°
= 3 × 43°
∠C = 129°
In parallelogram, opposite angles are equal.
⇒ ∠A = ∠C
⇒ ∠A = 129°
⇒ (y + 9)° = 129°
⇒ y° = 129° – 9°
⇒ y° = 120°
Hence the value of x° = 43° and y° = 120°.
Answer:
120 degrees
Step-by-step explanation:
What is the average rate of change of the function f(x)= x^2 -3 from x=1 to x=2?
Answers
Answer:
3
Step-by-step explanation:
The average rate of change of f(x) in the closed interval [ a, b ] is
[tex]\frac{f(b)-f(a)}{b-a}[/tex]
Here [ a, b ] = [ 1, 2 ]
f(b) = f(2) = 2² - 3 = 4 - 3 = 1
f(a) = f(1) = 1² - 3 = 1 - 3 = - 2, thus
average rate of change = [tex]\frac{1-(-2)}{2-1}[/tex] = 3
Answer:
3
Step-by-step explanation:
Average rate of change
= [f(2)-f(1)] ÷ (2-1)
= [(2²-3) - (1²-3)] ÷ 1
= (4-3) - (1-3)
= 1 - (-2)
= 1 + 2
= 3
Let M be the midpoint of side \overline{AB} of \triangle ABC. Angle bisector \overline{AD} of \angle CAB and the perpendicular bisector of side \overline{AB} meet at X. If AB = 40 and MX = 9, then how far is X from line {AC}?
Answers
Final answer:
To find the distance from X to line AC, we can use the angle bisector theorem and the fact that M is the midpoint of AB. By substituting the known values, we can solve for the distance d and find that X is 12 units away from line AC.
Explanation:
We are given that M is the midpoint of side AB of triangle ABC. Angle bisector AD of angle CAB and the perpendicular bisector of side AB meet at X. We are also given that AB = 40 and MX = 9.
To find the distance from X to line AC, we can use similar triangles. Let's denote the distance from X to line AC as d. According to the angle bisector theorem, we have:
AD/CD = AB/CB
Since M is the midpoint of AB, we have:
MD = MB = AB/2 = 40/2 = 20
Therefore, we can rewrite the angle bisector theorem as:
AD/(AD + CD) = AB/CB
Substituting the known values, we get:
9/(9 + d) = 40/20
Cross multiplying, we have:
20 * 9 = 40 * (9 + d)
Simplifying, we find:
d = 12
Therefore, X is 12 units away from line AC.
At the North campus of a performing arts school 30% of students are music majors at the South campus 80% of the students are music majors the campuses are merged into one East campus if 45% of the 1000 students at the East campus our music majors, how many students did the north and south campuses have before the merger?At the North campus of a performing arts school 30% of students are music majors at the South campus 80% of the students are music majors the campuses are merged into one East campus if 45% of the 1000 students at the East campus are music majors, how many students did the north and south campuses have before the merger
Answers
Answer:
It should be option B
Step-by-step explanation:
To find the number of students the North and South campuses had before the merger, set up an equation and solve for the unknowns. Use the given percentages and total number of students to determine the number of music majors at each campus.
Explanation:To find the number of students the North and South campuses had before the merger, we can set up two equations based on the given information. Let's assume the number of students at the North campus is N and the number of students at the South campus is S.
From the information provided, we know that 30% of the students at the North campus are music majors, so the number of music majors at the North campus is 0.3N. Similarly, 80% of the students at the South campus are music majors, so the number of music majors at the South campus is 0.8S.
Since the campuses are merged into the East campus, which has 1000 students and 45% of them are music majors, we can set up the equation 0.45(1000) = 0.3N + 0.8S to represent the total number of music majors at the East campus. From this equation, we can solve for N and S to find the number of students at the North and South campuses before the merger.
Learn more about Solving Equations here:https://brainly.com/question/17595716
#SPJ12
if the slope of a line is -3/7 then its perpendicular line will have the following slope
Answers
Answer:
The slope of the line is: [tex]$ \frac{\textbf{7}}{\textbf{3}} $[/tex]
Step-by-step explanation:
The product of the slope of two perpendicular slopes = - 1.
Given the slope of one of the perpendicular lines, say, [tex]$ m_{1} $[/tex] = [tex]$ -\frac{3}{7} $[/tex].
We have to determine the slope of the line perpendicular to the first line, We call this slope - [tex]$ m_{2} $[/tex].
We know that the product of the slopes [tex]$ m_{1}. m_{2} = - 1 $[/tex]
[tex]$ \implies -\frac{3}{7} . m_2 = - 1 $[/tex]
[tex]$ \implis m_{2} = - 1 \times - \frac{7}{3} $[/tex]
[tex]$ \therefore m_{2} = \frac{\textbf{7}}{\textbf{3}} $[/tex]
Hence, the answer.
which savings goal would most commonly be pursued by a retiree?
a.) a car down payment
b.) an IRA
c.) a 529 fund
d.) a house down payment
Answers
Answer:
The answer is an (IRA)
Step-by-step explanation:
The IRA means "Individual retirement account"
Help meh!
Which is the BEST estimate of the average rate of change for the function graphed, over the interval 1 ≤ x ≤ 3?
A) 2
B) 3
C) 4
D) 6
Answers
Answer:
The answer is B) 3
Step-by-step explanation:
The reason why is because 1 is less than OR equal to x and 3 is less than or equal to x and is x = 3 then it fits both descriptions the best.
Answer:
-3
Step-by-step explanation:
3 is the average rate of change for the exponential graph shown over the interval 1 ≤ x ≤ 3.
Start by determining the two distinct points: (1, 2) and (3, −4).
Therefore,
Δf(x)
Δx
=
−4 − 2
3 − 1
=
−6
2
= −3
Lyric is fencing her garden, which is in the shape of a right triangle. She measures the base to be 10 feet, the height to be 7 feet. How many feet of fencing will Lyric need to enclose the triangular garden? (round to the nearest tenth)
Answers
Answer:
Step-by-step explanation:
The perimeter of a plane figure is the distance around the figure.
Lyric's garden is triangular. The formula for determining the perimeter of a triangle is expressed as
Perimeter = a + b + c
Where a, b and c are the side lengths of the triangle.
Since the triangle is a right angle triangle, to determine the length, c of the third side, we would apply Pythagoras theorem. It is expressed as
Hypotenuse² = opposite side² + adjacent side²
c² = 10² + 7² = 100 + 49
c = √149 = 12.2 feet
The number of feet of fencing that Lyric needs to enclose the triangular garden is
10 + 7 + 12.2 = 29.2 feet
Final answer:
Lyric will need approximately 29.2 feet of fencing to enclose her garden, which is calculated using the Pythagorean theorem to find the hypotenuse of the right triangle and then adding all sides for the perimeter.
Explanation:
To determine how much fencing Lyric will need for her garden, we have to find the perimeter of the right triangle. We are given the base and the height, which are 10 feet and 7 feet respectively.
To find the length of the hypotenuse, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
Calculating,
Hypotenuse = √(base2 + height2)
= √(102 + 72)
= √(100 + 49)
= √149
= 12.2 feet (rounded to the nearest tenth)
Now, to find the total amount of fencing required, we add the lengths of all three sides of the triangle:
Total fencing needed = base + height + hypotenuse
= 10 feet + 7 feet + 12.2 feet
= 29.2 feet (rounded to the nearest tenth)
Therefore, Lyric will need approximately 29.2 feet of fencing to enclose her garden.
Sam deposited $4400 in a savings account earning 6% compounded monthly. If she makes no other deposits or withdrawals, how much will she have in her account in two years?
Group of answer choices
$4959.50
$4928.00
$9342.76
$9328.00
Answers
Answer: $4959.50
Step-by-step explanation:
We would apply the formula for determining compound interest which is expressed as
A = P(1+r/n)^nt
Where
A = total amount in the account at the end of t years
r represents the interest rate.
n represents the periodic interval at which it was compounded.
P represents the principal or initial amount deposited
From the information given,
P = 4400
r = 6% = 6/100 = 0.06
n = 12 because it was compounded 12 times in a year.
t = 2 years
Therefore,
A = 4400(1 + 0.06/12)^12 × 2
A = 4400(1+0.005)^24
A = 4400(1.005)^24
A = 4959.5
please help me with this question, image attached
Answers
Answer:
[tex]W=(x-6)\ m[/tex]
Step-by-step explanation:
we know that
The area of rectangle is equal to
[tex]A=LW[/tex]
we have
[tex]A=(x^{2} -11x+30)\ m^2[/tex]
[tex]L=(x-5)\ m[/tex]
substitute the given values in the formula of area
[tex](x^{2} -11x+30)=(x-5)W[/tex]
Remember that
[tex]x^{2} -11x+30=(x-5)(x-6)[/tex] ----> by completing the square
substitute
[tex](x-5)(x-6)=(x-5)W[/tex]
Simplify
[tex]W=(x-6)\ m[/tex]
Diseases I and II are prevalent among people in a certain population. It is assumed
that 10% of the population will contract disease I sometimes during their lifetime, 15% will contract disease II eventually, and 3% will contract both diseases. Find the probability that a randomly chosen person from this population will contract at least one disease in his/her lifetime. Also, Find the conditional probability that a randomly selected person from this population will contract both diseases, given that he or she has contracted at least one disease in his/her lifetime.
Answers
Answer: a) 0.22 b) 0.1363
Step-by-step explanation:
People who contract disease I are= 10%
People who contract disease II are= 15%
People who contract both diseases are= 3%
a)
People who contract has at least one disease needs to be found out so it is given as
P(D1 or D2)= P(D1) + P(D2) - P(D1 and D2)
P(D1 or D2)= 10% + 15% - 3%
P(D1 or D2)= 22%
P(D1 or D2)= 0.22
b)
Conditional probability that randomly selected person will get get diseases given she has contracted at least one disease is gven as
Probability= P(D1 and D2) / P(D1 or D2)
Probability= [tex]\frac{0.03}{0.22}[/tex]
Probability= 13.63%
Probability= 0.1363
On a coordinate plane, an exponential function approaches y = 0 in quadrant 1 and increases into quadrant 2. It goes through points (3, StartFraction 108 Over 5 EndFraction), (2, 36), (1, 60), (0, 100). Which function represents the given graph? f(x) = 100 · (Three-fifths)x f(x) = (100 · Three-fifths)x f(x) = 100 + Three-fifthsx f(x) = 100 · (Two-fifths)x
Answers
Answer:
[tex]f(x)=100(\frac{3}{5} )^x[/tex]
Step-by-step explanation:
Since the exponential function approaches y=0, its equation is of the form,
[tex]f(x)=a(b^x)[/tex]
The point (0,100) is this graph so it must satisfy its equation
[tex]100=a*b^0[/tex]
[tex]100=a(1)[/tex]
a=100
The equation now becomes:
[tex]f(x)=100*b^x[/tex]
We now substitute the point (1,60)
[tex]60=100*b^1[/tex]
[tex]b=\frac{60}{100} =\frac{3}{5}[/tex]
Therefore the required equation is [tex]f(x)=100(\frac{3}{5} )^x[/tex]
Answer:
the correct answer is A
Step-by-step explanation:
Students at Hampton Middle School sold T-shirts as a school fundraiser. Sylvie asked 12 random seventh-grade students how many T-shirts they sold for the fundraiser. The number of T-shirts each student sold is listed below. 3, 4, 8, 5, 2, 5, 0, 5, 3, 4, 3, 7 What is the mean of the data set rounded to the nearest tenth? a. 4.0 shirts b. 4.1 shirts c. 4.5 shirts d. 4.9 shirts
Answers
Answer:
b. 4.1 shirts
Step-by-step explanation:
Given data:
number of terms = 12
Terms given are 3, 4, 8, 5, 2, 5, 0, 5, 3, 4, 3, 7
Mean = (sum of terms)/ (number of terms)
Mean = (3 +4+ 8+ 5+2+5+0+ 5+ 3+ 4+3+ 7)/12
Mean = 49/12
Mean = 4.083
Mean = 4.1 (to the nearest tenth)
Answer:
Answer is 4.1 shirts.
Step-by-step explanation:
What does twice 3 means
Answers
Answer:
Could be 6
Step-by-step explanation:
The reason I'm saying could is that I don't know of any mathematical system that uses the word twice. I could very easily be wrong. As far as I know twice means double, though.
Twice 3 most likely means like two times of 3,or 3 of something two times.or 3 times two..I hope thi helps in any way.
In the context of data patterns in a time series, a(n) _____ is a one-time variation that is explainable.
Answers
Final answer:
In a time series, an explainable one-time variation is known as an outlier. Outliers can be important for understanding data, but they differ from inexplicable random components which include variations not explained by trend, cyclical, or seasonal patterns.
Explanation:
In the context of data patterns in a time series, a one-time variation that is explainable is usually referred to as an outlier. An outlier can be a potential key to understanding the data or it may be due to some abnormality or error. In a time series, data is analyzed over time to determine components such as the trend, cyclical, seasonal, and random components.
Trend component displays the long-term progression of the series, the cyclical component deals with fluctuations occurring at non-fixed intervals, the seasonal component reflects regular variations within a specific period, like quarters within a year, and the random component comprises those elements that cannot be attributed to the trend, cyclical, or seasonal patterns.
It's essential to distinguish outliers from the random components, which are, by definition, inexplicable variations. However, if an outlier can be explained by a particular event or change, it's not part of the random component but a distinct deviation from the expected pattern.
City Park: You are desinigng a marble planter for a city park. You want the length of the planter to be sic times the height, and the width to be three times the height.The sides should be one foot thick. BEcause the planter will be on the sidewalk, it doesnot need a bottom. What should the outer dimensions of the planter be if it is to hold 4 cubic feet of dirt.
Answers
Answer: 6 feet x 3 feet
Step-by-step explanation:
Let the height be given by= x
The length is= 6x -2 (1) from both sides= 6x-2
The width is= 3x-2(1) from both sides= 3x-2
The total volume= length * width * height
4=(6x-2)*(3x-2)*x
Solving we get,
x=1 and other factor is not the valid option.
So the outer dimensions should be 6 feet x 3 feet
Compare the light gathering power of an 8" primary mirror with a 6" primary mirror. The 8" mirror has how much light gathering power?
Answers
Answer:
1.778 times more or 16/9 times more
Step-by-step explanation:
Given:
- Mirror 1: D_1 = 8''
- Mirror 2: D_2 = 6"
Find:
Compare the light gathering power of an 8" primary mirror with a 6" primary mirror. The 8" mirror has how much light gathering power?
Solution:
- The light gathering power of a mirror (LGP) is proportional to the Area of the objects:
LGP ∝ A
- Whereas, Area is proportional to the squared of the diameter i.e an area of a circle:
A ∝ D^2
- Hence, LGP ∝ D^2
- Now compare the two diameters given:
LGP_1 ∝ (D_1)^2
LGP ∝ (D_2)^2
- Take a ratio of both:
LGP_1/LGP_2 ∝ (D_1)^2 / (D_2)^2
- Plug in the values:
LGP_1/LGP_2 ∝ (8)^2 / (6)^2
- Compute: LGP_1/LGP_2 ∝ 16/9 ≅ 1.778 times more
To celebrate its grand opening a store is giving customers gift certificates which customer is the first to get two gift certificates every 8th gets a $50 gift certificate and every 6th person gets a $10 gift certificate
Answers
Answer:
The 24th Customer is the first to get two gift certificates.
Since, 2 x 2 x 2 x 2 x 3 = 24
The first customer to receive two gift certificates is the customer at the 24th position in the sequence of customers.
The LCM of 8 and 6 is 24. This means that the first customer to receive two gift certificates will be the one who appears at the 24th position in the sequence.
To calculate the position of this customer, we can consider the multiples of 24:
24, 48, 72, and so on.
The 24th customer is the first to receive two gift certificates, as they satisfy both the every-8th and every-6th customer criteria.
The Greatest Common Factor (GCF) and the Least Common Multiple (LCM) are fundamental concepts in number theory. The GCF of two or more numbers is the largest positive integer that divides all the given numbers without leaving a remainder. On the other hand, the LCM of two or more numbers is the smallest positive multiple that is divisible by all the given numbers.
In this scenario, the GCF and LCM were used to determine the customer who would receive two gift certificates. The GCF was not explicitly required to solve this particular problem, but it is a useful concept in various mathematical contexts.
To know more about GCF here
https://brainly.com/question/26526506
#SPJ3
Complete Question:
To celebrate its grand opening, a store is giving -customers gift certificates. Which customer is the first to get two gift certificates? Every 8 th customer gets Every 6th customer gets a $10 gift certificate. 200 4-2 Find Greatest Common Factor and Least Common Multiple
A company that sells seeds wants to check that at least 90% of its corn seeds are viable. An independent testing lab plants 1000 randomly chosen seeds and observes that 903 of them germinate. What does this data imply about the claim that 90% of the seeds are viable?
Answers
Answer:
The data claims that 90% of the seeds are viable meaning that 90% of the seeds are likely to germinate and grow into healthy plants under good conditions.90% 0f 1000seeds gives 900seeds,and 903seeds germinated so the claim is true
Step-by-step explanation:
Total number of seeds=1000
Seeds that germinate =903
90% of 1000=>90/100×1000 =900seeds.
On Saturday a minor league baseball team gave away baseball cards to each person entering the stadium. One group received 28 baseball cards. A second group r
Answers
Question: on saturday, a minor league baseball team gave away baseball cards to each person entering the stadium. One group received 28 baseball cards . a second group received 68 baseball cards. If each person entering the stadium received the same number of cards, what was the greatest possible number of cards that each person could have received?
Answer:
4 baseball cards
Step-by-step explanation:
Since each person entering the stadium receive the same number of cards, we look for the Highest Common Factors HCF of the number of members of the groups.
The factors of 28 = 1 x 2² x 7
The factors of 68 = 1 x 2² x 17
Looking at the factors, the higest common factor HCF is 2² or 4.
This implies that the higest possible number of baseball cards that each person would have received is 4 baseball cards
Solve sin theta + 1 = cos2 theta on the interval
Answers
Step-by-step explanation:
Hope it helps you in your learning process.
Answer:
Θ = 0, [tex]\frac{7\pi }{6}[/tex], [tex]\frac{11\pi }6}[/tex]
Step-by-step explanation:
sin(theta) + 1 = cos^2(theta) - sin^2(theta)
sin(theta) + 1 = (1 - sin^2(theta)) -sin^2(theta)
sin(theta) = -2sin^2(theta)
2sin^2(theta) + sin(theta) = 0
sin(theta)[2sin(theta) + 1] = 0
sin(theta) = 0 and 2sin(theta) + 1 = 0
sin(theta) = 0 and sin(theta) = -1/2
Θ = 0, [tex]\frac{7\pi }{6}[/tex], [tex]\frac{11\pi }6}[/tex]
Question 6 options: What is the approximate area of a circle with a diameter of 56 cm? Use your calculator button for π. Round your answer FOUR decimal places. _________cm2
Answers
The area of circle is 2463.0086 cm².
Step-by-step explanation:
Given,
Diameter of circle = 56 cm
Radius of circle = [tex]\frac{Diameter}{2}[/tex]
Radius of circle = [tex]\frac{56}{2}=28\ cm[/tex]
We know that;
Area of circle = [tex]\pi r^2[/tex]
Area of circle = [tex]\pi *(28)^2[/tex]
Area of circle = π * 784
Area of circle = 2463.00864041 cm²
Rounding off to four decimal places
Area of circle = 2463.0086 cm²
The area of circle is 2463.0086 cm².
Keywords: area, circle
Learn more about area at:
brainly.com/question/11416224brainly.com/question/11638377#LearnwithBrainly
There are 100 bags each with 100 coins, but only one of these bags has gold coins in it. The gold coin has weight of 1.01 grams and the other coins has weight of 1 gram. We are given a digital scale, but we can only use it once. How can we identify the bag of gold coins?
Answers
Answer:
So, with one measurement, we can determine the bag of gold coins.
Step-by-step explanation:
We will number the bags with numbers from 1 to 100. Then we will take one coin from the first bag, from the second we will take 2 coins, from the third we will take 3 coins. We will continue the process to the last bag, from which we will take all 100 coins. Then we'll put it all on a digital scale.
Depending on how many numbers in the decimal notation we mean what the bag of gold coins is. For example, if the decimal number is .02, we will conclude that 2 is a bag of gold coins. For example, if the decimal number is .33, we would conclude that 33 is a bag of gold coins. If there are no decimal numbers, we conclude that the gold bag is the last bag on the digital scale, because 100 · 1.01 = 101.
So, with one measurement, we can determine the bag of gold coins.
Tina wrote mathematical expressions for five statements. Her work is shown. Statement Tina's Expressions A The product of a number and seven. 7n B The sum of three consecutive numbers. n+(n+1)+(n+2) C The square of a number times three. 3n2 D Twice the sum of a number and 8. 2n+8 E The cube of a number divided by two. n3÷2 Did Tina write the correct expressions? Select Correct or Incorrect for each expression. Select Linear or Nonlinear to correctly identify each of Tina's expressions.
Answers
Answer:
See explanation
Step-by-step explanation:
Linear expression is usually an expression of 1st degree.
A. The product of a number and seven [tex]=7\cdot n=7n[/tex]
Correct, linear
B. The sum of three consecutive numbers.
Let the smallest number be n, the next number is n + 1 and the last number is n + 2. Then their sum is
[tex]n+(n+1)+(n+2)[/tex]
Correct, linear
C. The square of a number times three.
Let the number be n, then its square is [tex]n^2[/tex] and the square of a number times three is
[tex]n^2\cdot 3=3n^2[/tex]
Correct, nonlinear
D. Twice the sum of a number and 8.
If the number is n, then the sum of the number anf 8 is n + 8. Twice the sum is
[tex]2\cdot (n+8)=2(n+8)[/tex]
Incorrect, linear
E. The cube of a number divided by two.
If the number is n, then its cube is [tex]n^3.[/tex] The cube of the number divided by 3 is
[tex]n^3\div 3[/tex]
Correct, nonlinear
Divide the following polynomials. Then place the answer in the proper location on the grid. Write your answer in order of descending powers of x. Do not include parentheses in your answer.6x3 + 11x2 - 4x -4 / 3x - 2
Answers
Answer:
The Final answer will be [tex]2x^2+5x+2[/tex] with remainder 0.
Step-by-step explanation:
We have attached the division for your reference.
Given:
Dividend = [tex]6x^3 + 11x^2 - 4x -4[/tex]
Divisor= [tex]3x - 2[/tex]
Explaining the division we get;
Step 1: First when we divide the Dividend [tex]6x^3 + 11x^2 - 4x -4[/tex] with divisor [tex]3x - 2[/tex] we will first multiply [tex]2x^2[/tex] with the divisor then we get the Quotient as [tex]2x^2[/tex] and Remainder as [tex]15x^2-4x-4[/tex]
Step 2: Now the Dividend is [tex]15x^2-4x-4[/tex] and Divisor is [tex]3x - 2[/tex] we will now multiply [tex]5x[/tex] with the divisor then we get the Quotient as [tex]2x^2+5x[/tex] and Remainder as [tex]6x-4[/tex]
Step 3: Now the Dividend is [tex]6x-4[/tex] and Divisor is [tex]3x - 2[/tex] we will now multiply 2 with the divisor then we get the Quotient as [tex]2x^2+5x+2[/tex] and Remainder as 0.
Hence The Final answer will be [tex]2x^2+5x+2[/tex] with remainder 0.
A student and a pet run straight towards each other at constant speed, starting with a separation of 30 m. They meet somewhere in between. Draw a picture at the beginning and another at the end, and establish a coordinate system. Give names to important quantities.
Answers
Answer:
View graph
Step-by-step explanation:
we have that at constant speed the student and the pet must travel equal distances in equal times, so they must be in the middle of the distance with the same travel time
As can be seen in graph 2 the distance of P = -15 m, and that of S = 15, the sign is due to the orientation, P goes to the left and S to the right