An isosceles triangle has a vertex angle of 21.21°. two sides of the triangle are each 17.91 ft long. find the area of the triangle.
The Area of triangle is A= 58.02 (ft)^2
According to statement
Let
B is the measure of the vertex angle of the isosceles triangle ABC
A and C is the two congruent sides of the isosceles triangle ABC
we know that
The area of a triangle applying the law of sines is equal to the
A= 1/2 *AC *SinB
we have
A=C= 17.91 ft
And
B= 21.21
Substitute these values in the formula
A= 1/2* 17.91* 17.91 * Sin(21.21)
A= 58.02 (ft)^2
So, the Area of triangle is A= 58.02 (ft)^2
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Use complete sentences to describe the similarity between the three triangles shown in the diagram
below.
Answer: The three triangles shown are similar triangles. We can tell this by the Angle Angle theory. You can tell the angles are congruent by the matching marks in each corner of the triangles, the marks or “ticks” are the same in the same corners. The length of the sides can change but the angle measurements will still be the same.
Step-by-step explanation: explained in answer
Answer: Each of the corresponding angles of one triangle equal the corresponding angles of the other triangle.
he table shows a probability distribution for predicting how many people will come through the door of a fast food restaurant during the lunch hour. Each event represents the number of people for a ten-minute interval.
Use the six randomly generated numbers 18, 38, 87, 16, 56, and 5 to predict the number of people coming in during the lunch hour.
The number of people coming in during the lunch hour is 160
How to determine the number of people?The complete question is in the attached image
The random numbers are given as:
18, 38, 87, 16, 56, and 5
Regroup the numbers
Number Group Probability
5, 16, 18 1 - 20 3/6
38, 56 21 - 60 2/6
56 61 - 90 1/6
Based on the individual numbers and the probability table, we have:
X 20 30 40
P 3/6 2/6 1/6
The expected value is:
[tex]E(x) = \sum xp[/tex]
This gives
E(x) = 20 * 3/6 + 30 * 2/6 * 40 * 1/6
Evaluate
E(x) = 160/6
There are six ten-minute intervals.
So, we have:
People = 6 * 160/6
Evaluate
People = 160
Hence, the number of people coming in during the lunch hour is 160
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You are pouring canned sodas Into a cylindrical pitcher. Each can
of soda is 12 cm tall and has a diameter of 6.5 cm. The pitcher is
36 cm tall and has a diameter of 20 cm. How many cans of soda
will the pitcher hold?
Answer: 28.40 cans of soda
Step-by-step explanation:
Volume of cylinder: pi * r^2 * h
Volume of the can of soda = pi * 3.25^2 * 12 = 126.75 pi
Volume of the cylindrical pitcher = pi * 10^2 * 36 = 3600 pi
3600/126.75: 28.40 cans of soda
Answer:
28 whole soda cans or 28.4 soda cans (rounding to nearest tenth)
Step-by-step explanation:
The soda cans and the pitcher can be modeled as cylinders.
Volume of a cylinder
[tex]\sf Volume=\pi r^2h[/tex]
where:
r is the radiush is the heightDiameter of circle
[tex]\sf d= 2r[/tex]
[tex]\sf \implies r=\dfrac{1}{2}d[/tex]
Volume of Soda can
Given values:
d = 6.5 ⇒ r = 3.25 cmh = 12 cm[tex]\begin{aligned}\sf \implies Volume & = \sf \pi (3.25)^2 \cdot 12\\ & = \sf 126.75 \pi \:\:cm^3\end{aligned}[/tex]
Volume of Pitcher
Given values:
d = 20 ⇒ r = 10 cmh = 36 cm[tex]\begin{aligned}\sf \implies Volume & = \sf \pi (10)^2 \cdot 36\\ & = \sf 3600 \pi \:\:cm^3\end{aligned}[/tex]
To calculate how many cans of soda the pitcher will hold, divide the volume of the pitcher by the volume of one soda can:
[tex]\begin{aligned}\implies \textsf{Number of soda cans} & = \dfrac{\textsf{Volume of Pitcher}}{\textsf{Volume of one soda can}}\\\\&= \sf\dfrac{3600 \pi}{126.75 \pi}\\\\& = \sf 28.402366...\end{aligned}[/tex]
Therefore, the pitcher can hold 28 soda cans (nearest whole can), or 28.4 soda cans (nearest tenth).
Which of the following is the correct definition for dependent events? A. Two events are dependent if they have no outcomes in common and cannot occur at the same time. B. Two events are dependent if they have outcomes in common and can occur at the same time. C. Two events are dependent if the outcome of the first event does not affect the outcome of the second event. D. Two events are dependent if the outcome of the first event affects the outcome of the second event.
The correct definition of dependent events is two events are dependent if the outcome of the first event affects the outcome of the second event.
What are dependent events?Two events are dependent if the outcome of one of the event depends on the outcome of the first event. An example of a dependent event is if it rains, the floor would be wet.
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David is making a rectangular exercise yard for his turtle, Ralph. The perimeter of the yard is
16x² + 12x +18
3x
2x² + 6x +9
3x
inches in total. The length of the yard measures
inches. Find an expression to represent the measure of the width in inches
yd=
yd=
16x2+12x+18=3x=2x2+6x+9=3x=
sorry i try
Answer:
D
Step-by-step explanation:
What is the simplest form of the expression (–11.7y – 3.3x) + 1.2x + (5.2y + x)?
–16.9y – 5.5x
–16.9y – 4.5x
–6.5y – 2.1x
–6.5y – 1.1x
The simplest form of (–11.7y – 3.3x) + 1.2x + (5.2y + x) is -6.5y - 1.1x
How to simplify an equation?(–11.7y – 3.3x) + 1.2x + (5.2y + x)
We have to open the brackets.
Therefore,
(–11.7y – 3.3x) + 1.2x + (5.2y + x)
-11.7y - 3.3x + 1.2x + 5.2y + x
combine like terms
Hence,
-11.7y + 5.2y - 3.3x + 1.2x + x
Therefore,
-6.5y - 1.1x
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Answer: -6.5y - 1.1x
Step-by-step explanation:
Use the properties of 30-60-90 and 45-45-90 triangles to solve for x in each of the problems below. Then decode the secret message by matching the answer with the corresponding letter/symbol from the exercises.
The trigonometric function gives the ratio of different sides of a right-angle triangle. The given problems can be solved as given below.
What are Trigonometric functions?The trigonometric function gives the ratio of different sides of a right-angle triangle.
[tex]\rm Sin \theta=\dfrac{Perpendicular}{Hypotenuse}\\\\\\Cos \theta=\dfrac{Base}{Hypotenuse}\\\\\\Tan \theta=\dfrac{Perpendicular}{Base}\\\\\\Cosec \theta=\dfrac{Hypotenuse}{Perpendicular}\\\\\\Sec \theta=\dfrac{Hypotenuse}{Base}\\\\\\Cot \theta=\dfrac{Base}{Perpendicular}\\\\\\[/tex]
where perpendicular is the side of the triangle which is opposite to the angle, and the hypotenuse is the longest side of the triangle which is opposite to the 90° angle.
1st.) x = 5 /Sin(30°)
x = 10
!) sin(45°) = 4/x
x = 4/sin(45°)
x = 4√2
I) Cos(45°) = √3 / x
x = √3 / Cos(45°)
x = √6
E) Tan(60°) = 3√3 / x
x = 3√3 / 3
W) For isosceles right-triangle, the angle made by the legs and the hypotenuse is always 45°.
x = 45°
N) x² + x² = (7√2)²
x = 7
V) Tan(60°) = 7 / x
x = 7√3/3
K) x² + x² = (9)²
x = 9/√2
Y) Sin(60°) = 7√3/x
x = 14
M) Sin(30°) = x/11
x = 11/2
T) Sin(45°) = x/√10
x = √5
A) x + 2x + 90° = 180°
x = 30°
O) Sin(45°) = √2 / x
x = 2
R) Tan(30°) = x / 4
x = 4/√3 = 4√3 / 3
S) Sin(60°) = x / (10/3)
x = 5√3 / 3
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Suppose 58% of the registered voters in a country are Republican. If a sample of 536 voters is selected, what is the probability that the sample proportion of Republicans will differ from the population proportion by greater than 5%
The probability that the sample proportion of Republicans will differ from the population proportion by greater than 5% is 100%
Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and 1, where, roughly speaking, 0 indicates the impossibility of the event and 1 indicates certainty.
It is given that 58% of voters are Republican. The sample is 536 voters.
0.58×536 = 310.88 can be rounded off to 311.
536 - 311 = 225 are not republicans
311-225 = 86 is the difference
[tex]\frac{86}{536}[/tex]×100 = 16.044%
Hence, the probability is 100%.
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If f(x) = 4x - 8 and g(x) = 5x + 6, find (f+ g)(x).
Answer:
9x - 2
Step-by-step explanation:
f(x) = 4x - 8
g(x) = 5x + 6
because it's (f + g)(x), we can simply add the functions together
{note: don't get thrown off by the (x) being separate parentheses--distributing the x first can help it look familiar:
(x)(f + g)
fx + gx,
it's the same thing}
(4x - 8) + (5x + 6)
here, we want to combine like terms to simplify:
4x + 5x - 8 + 6
4x + 5x - 2
9x - 2
So, (f + g)(x) = 9x - 2
hope this helps!! have a lovely day :)
Find m given that the three angles of a triangle are (m plus18),(2m plus 28)and (3m plus 47)degree find all the angles
The value of m is 14.5 and the three angles of the triangle are 32.5°, 57°, and 90.5°.
How the angles of a triangle are related?There are three angles in a triangle. Consider as ∠A, ∠B, and ∠C.
The sum of all the three angles gives 180° in a triangle. I.e.,
∠A + ∠B + ∠C = 180°.
Calculation:The given triangle has three angles,
(m + 18)° , (2m + 28)°, and (3m + 47)°
On adding all these and equating to 180°,
(m + 18)° + (2m + 28)° + (3m + 47)° = 180°
⇒ 6m + 93 = 180
⇒ 6m = 180 - 93
⇒ 6m = 87
∴ m = 14.5
Then, the values of the three angles are:
(m + 18)° = (14.5 + 18)° = 32.5°
(2m + 28)° = (2 × 14.5 + 28)° = 57°
(3m + 47)° = (3 × 14.5 + 47)° = 90.5°
Therefore, the angles of the given triangle are 32.5°, 57°, and 90.5°.
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we can tell that side DE is parallel to side....
A) AB
B) We can't be sure it's parallel to any side
By the converse of the basic proportionality theorem, we can say DE║AB.
We need to check whether DE is parallel to AB.
What is the converse of the basic proportionality theorem?If a line divides any two sides of a triangle in the same ratio, then the line is parallel to the third side.
In triangle ABC, we can see on side AC, D is midpoint (∵AD=DC) and on side BC, E is midpoint (∵BE=CE).
Therefore, by the converse of the basic proportionality theorem, we can say DE║AB.
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The proof is shown below:
What is Mid point theorem?The line segment joining the mid points of any two sides of a triangle is parallel to the third side.
△ABC in which D and E are the mid points of AB and AC,.
If D and E are the mid points of AB and AC,
then AD=DB and AE=EC.
Thus,
AD/DB = AE/ EC
by the converse of Thales theorem, DE∥BC.
As, by theorem we can say that DE∥BC.
So, there is no other side parallel to DE.
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Using the Addition Method, solve for x in the following system of linear equations.
2y + x = 4
y - 3x = 2
a.) x = 1
b.) x = 2
c.) x = 8
d.) x = 0
Answer:
c. x=8
Step-by-step explanation:
make me a brain list.
Find the total surface area of this triangular prism.
Answer:
A ≈ 1194.5
The total surface area is 1194.53.
a = 24
b = 30
c = 7
h = 18
Rachel and Jennifer are taking the same biology class. They have a test in about a week during an 8-9AM class period. Both plan to study for about 5 hours, but because of different work schedules, Rachel will study one hour each day for 5 days and Jennifer will study 5 hours the day before the exam. What do you predict about their scores
Rachel should perform better because of the spacing effect.
Given,
Rachel will study one hour each day for 5 days and Jennifer will study 5 hours the day before the exam.
What do you predict about their scores?
Rachel should perform better because of the spacing effect.
The spacing effect demonstrates that learning is more effective when study sessions are spaced out. This effect shows that more information is encoded into long-term memory by spaced study sessions, also known as spaced repetition or spaced presentation, than by massed presentation.
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What is the value of this expression when c = -4 and d = 10?
A.
2
B.
9
C.
21
D.
41
How many different sets of initials can be formed if every person has one surname (i.e., last name) and either one or two given names (i.e., a first name, or a first and middle name).
The different sets of initials can be formed if every person has one surname (i.e., last name) and either one or two given names (i.e., a first name, or a first and middle name) is 15600.
There are 26 possible letters, each set of initials would have 3 letters in it, order doesn't matter, i.e. ABC does not equal ACB. using permutation 26P3 = 5600.
A permutation is a mathematical technique that determines the number of possible arrangements in a set when the order of the arrangements matters. Common mathematical problems involve choosing only several items from a set of items in a certain order.
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PLS HELP! I WILL GIVE BRAINLIEST!
PLEASE I NEED HELP QUICK
Deshaun wants to wallpaper the back wall of his bedroom. The wall is in the shape of a rectangle. Its length is 16 feet and its width is 8 feet. Suppose wallpaper costs $6 for each square foot. How much will wallpaper cost for the wall?
Answer: $768
Step-by-step explanation:
Here, you'll just multiply:
16x8x6 = 768
The function f(x) = three-fourths(10)–x is reflected across the x-axis to create the function g(x). which ordered pair is on g(x)?
The ordered pair that is on g(x) is (2, -3/400)
determine the ordered pair:
The function is given as:
f(x)=3/4(10)∧-x
The rule of reflection across the x-axis is:
g(x) = -f(x)
So, we have:
g(x) = -3/4(10)∧-x
Set x = 2.
So, we have:
g(2) = -3/4(10)∧-2
Evaluate the exponent
g(2) = -3/4 * 1/100
Evaluate the product
g(2) = -3/400
This means that:
(x, y) = (2, -3/400)
Hence, the ordered pair that is on g(x) is (2, -3/400)
Ordered pairs are pairs of two numbers (or variables) that are enclosed in parentheses and separated by commas. For example, (1, 2) is an ordered pair. Coordinate geometry represents points, and set theory represents elements of relations / Cartesian products.
Ordered pairs are pairs of numbers in a particular order. For example, (1, 2) and (-4, 12) are ordered pairs. The order of the two numbers is important. (1, 2) is not equivalent to (2, 1)-(1, 2) ≠ (2, 1).
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Rosie just moved to new york city and makes $2,700 per month at her new job. each month, she pays $2,000 for rent, $100 for the subway, and $200 for groceries. she saves $100 a month for a rainy day. how much can she spend on other things?
Answer:
2700 - 2000 = 700 - 100 = 600 - 200 = 400 - 100 = 300
300 dollars
Find the surface area. Round your answer to the nearest hundredths, if necessary. Leave your answer in terms of for answers that contain .
Answer:
C. 92.16π mi²
Step-by-step explanation:
Use the formula: 4 · π · r²
r=4.8
4 · π · 4.8²=
=4 · π · 23.04=
=92.16π mi²
Hope this helps!
If not, I am sorry.
In the following exercises, multiply the binomials. Use any method.
244. (x − 7)(x − 2)
Multiplying the binomials, we have (x - 7)(x - 2) = x² - 9x + 14.
How to Multiply Binomials?Applying the distribution property of multiplication, the given binomials, (x - 7)(x - 2) can be multiplied as shown below:
(x - 7)(x - 2)
x(x - 2) -7(x - 2)
x² - 2x - 7x + 14
x² - 9x + 14
Therefore, (x - 7)(x - 2) = x² - 9x + 14.
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Answer:
Hence the expression [tex]$$(x-7)(x-2)=x^2-9x-14$$[/tex]
Step-by-step explanation:
The given expression is (x-7)(x-2).
We have to multiply the given expression.
Multiply the (x-7) by-2, multiply the (x-7) by x then add like terms.
[tex]$$\frac{\begin{matrix}{} & {} & x & - & 7 \\ \times & {} & x & - & 2 \\ \end{matrix}}[/tex]
____________
[tex]{\frac{\begin{matrix}{} & - & 2x & - & 14 \\ {{x}^2} & - & 7x & {} & {} \\ \end{matrix}}{\begin{matrix}{{x}^2} & - & 9x & - & 14 \\ \end{matrix}}}$$[/tex]
Write an equation that represents the line.
Use exact numbers.
The equation of the line passing through the points is y = x + 2
How to determine the equation?The points are (-1, 1) and (4, 6).
The slope is calculated using:
m= (y2 - y1)/(x2 - x1)
So, we have:
m = (6 - 1)/(4 + 1)
Evaluate
m = 1
The equation of the line is then calculated as:
y = m(x -x1) + y1
This gives
y = 1 *(x + 1) + 1
Evaluate
y = x + 2
Hence, the equation of the line passing through the points is y = x + 2
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julia typed 410 words in five minutes in her keyboarding class at this rate how many words could she type in 13 minutes
Answer:
1066
Step-by-step explanation:
5 mins = 410 words
410/5 = 82 so she is typing 82 words a minute
Then do 82 times 13
find the inverse matrix or type "none". (use decimals) {11 -5 3 -1}
The inverse of the matrix [tex]\left[\begin{array}{cc}11&-5\\3&-1\end{array}\right][/tex] is the matrix [tex]\left[\begin{array}{cc}\frac{-1}{4} &\frac{5}{4} \\\\\frac{-3}{4} &\frac{11}{4} \end{array}\right][/tex] .
The inverse of a matrix A is calculated by the formula:
A' = (1/|A|)(Adj A),
where A' represents the inverse of matrix A,
|A| represents the determinant value of matrix A, and
Adj A represents the Adjoin matrix of matrix A.
So, to calculate the inverse of the matrix [tex]\left[\begin{array}{cc}11&-5\\3&-1\end{array}\right][/tex] , we will first calculate its Adj.
Adj = [tex]\left[\begin{array}{cc}-1&-3\\5&11\end{array}\right] ^{T}[/tex]= [tex]\left[\begin{array}{cc}-1&5\\-3&11\end{array}\right][/tex].
Now, we calculate |A| = 11*(-1) - (-5)*3 = -11 + 15 = 4.
Therefore A' = (1/|A|)(Adj A),
or, A' = [tex](1/4)*\left[\begin{array}{cc}-1&5\\-3&11\end{array}\right][/tex] ,
or, A' = [tex]\left[\begin{array}{cc}\frac{-1}{4} &\frac{5}{4} \\\\\frac{-3}{4} &\frac{11}{4} \end{array}\right][/tex] .
Therefore, the inverse of the matrix [tex]\left[\begin{array}{cc}11&-5\\3&-1\end{array}\right][/tex] is the matrix [tex]\left[\begin{array}{cc}\frac{-1}{4} &\frac{5}{4} \\\\\frac{-3}{4} &\frac{11}{4} \end{array}\right][/tex] .
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Using the two way table(in pic) what percentage of the students that do NOT like to travel out of state like camping? Round to the nearest whole percent. Thank you 3
A. 32>
B. 34>
C. 38%
D. 42%
Using it's concept, it is found that the percentage of the students that do NOT like to travel out of state that like camping is:
B. 34%.
What is a percentage?The percentage of an amount a over a total amount b is given by a multiplied by 100% and divided by b, that is:
[tex]P = \frac{a}{b} \times 100\%[/tex]
In this problem, there are 112 students that do not like traveling out of the state, and of those, 38 like camping, hence the percentage is:
[tex]P = \frac{38}{112} \times 100\% = 34\%[/tex]
Hence option B is correct.
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Event A has a probability of occurring of 4/5 . Event B has a probability of occurring of 1/3. If events A and B are independent of one another, what is the probability of both events occurring?
The probability of both events occurring is 4/15
How to determine the probability?The given parameters are:
P(A) = 4/5
P(B) = 1/3
Because the events are independent, we have:
p(A and B) = P(A) * P(B)
This gives
P(A and B) = 4/5 * 1/3
Evaluate
P(A and B) = 4/15
Hence, the probability of both events occurring is 4/15
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Please prove that
[tex]sec^{2} \beta - cosec^{2} = (tan \beta + cot \beta) * (tan \beta - cot \beta)[/tex]
Recall the Pythagorean identity.
[tex]\sin^2(x) + \cos^2(x) = 1 \implies \left\langle \begin{matrix} \tan^2(x) + 1 = \sec^2(x) \\ 1 + \cot^2(x) = \csc^2(x) \end{matrix} \right.[/tex]
[tex]\implies \sec^2(\beta) - \csc^2(\beta) = (\tan^2(\beta) + 1) - (1 + \cot^2(\beta)) \\\\ ~~~~~~~~= \tan^2(\beta) - \cot^2(\beta)[/tex]
Recall the difference of squares identity.
[tex]a^2 - b^2 = (a - b) (a + b)[/tex]
[tex]\implies \sec^2(\beta) - \csc^2(\beta) = (\tan(\beta) - \cot(\beta)) (\tan(\beta) + \cot(\beta))[/tex]
[tex]sec^2\beta -csc^2\beta \\(1+tan^2\beta )-(1+cot^2\beta )\\1+tan^2\beta -1-cot^2\beta \\tan^2\beta -cot^2\beta \\(tan\beta -cot\beta )(tan\beta +cot\beta )[/tex]
A circular swimming pool has a diameter of 8 m and a depth of 2 m. What is the volume of the swimming pool?