The measure of two angles are 39 degree and 69 degree. By the Triangle Sum Theorem, the sum of all angles in a triangle is 180 degree, so the final angle is 72 degree. Therefore, the largest angle in the triangle is 72 degree.
Describe the Triangle Angle Sum property?According to the triangle's "angle sum property," a triangle's interior angles add up to 180°.
Given:
[tex]The\;sum\;of\;two\;angles\;in\;a\;triangle\;is\;\frac{6}{5}\;of\;a\;right\;angle\;is,\;\frac{6}{5} \times 90^{\circ} = 108^{\circ}[/tex]
[tex]let\;x\;is\;the\;measure\;of\;the\;first\;angle[/tex]
[tex]one\;of\;these\;two\;angles\;is\;30\;larger\;than\;the\;other,\;is\;x+30=108[/tex]
We know that sum of two angles is 108
[tex]x+x+30=108^{\circ}[/tex]
[tex]2x+30=108[/tex]
[tex]2x=108-30[/tex]
[tex]2x=78[/tex]
[tex]x=39^{\circ}[/tex]
Second angle y is,
[tex]y=x+30[/tex]
[tex]y=39+30[/tex]
[tex]y=69^{\circ}[/tex]
By the Triangle Sum Theorem, the sum of all angles in a triangle is 180 degree,
Third angle z is,
[tex]x+y+z=180[/tex]
[tex]39+69+z=180[/tex]
[tex]108+z=180[/tex]
[tex]z=180-108[/tex]
[tex]z=72^{\circ}[/tex]
[tex]By\;comparing\;the\;angles\;39^{\circ},\;69^{\circ}\;and\;72^{\circ}, 72^{\circ}\; is\;greater[/tex]
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The clock face in a famous clock tower has a radius of about 5 meters. What is the area of the clock face to the nearest square meter? Use 3.14 as an approximation for pie.
Answer:
78.5m
Step-by-step explanation:
Area of circle = [tex]\pi[/tex]r^2
Area of clock = 3.14 x 5^2 = 78.5m
How many simple random samples of size 4 can be selected from a population of size 8?
a. 70
b. 32
c. 1680
d. 4
70 simple random samples of size 4 can be selected from a population of size 8
According to the question, samples of size 4 have to be selected from a population of size 8. The selection can be made in
8C4 ways.
Selection=8C4=8!(8−4)!4!
Selection=8!(8−4)!4!
Selection=8×7×6×5×4!4!×4×3×2
Selection=2×7×5
Selection=70
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Brainliest for correct answer
The correct symbols that complete the statements are
h(0) = g(0)
h(1) > g(1)
Graph of functionsFrom the question, we are to determine the correct symbols that complete the given statements
The given statements are
h(0) ___ g(0)
and
h(1) ___ g(1)
To complete the statements, we will find the values of the given functions from the graph
From the graph of h(x), we can observe that
h(0) = 4
and
From the graph of g(x), we can observe that
g(0) = 4
Thus,
The two functions are equal
h(0) = g(0)
Also,
From the graph of h(x),
h(1) = 3
and
From the graph of g(x),
g(1) = 2
That is, h(1) is greater than g(1)
Thus,
h(1) > g(1)
Hence, the correct symbols that complete the statements are
h(0) = g(0)
h(1) > g(1)
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What fraction must 7/6x be multiplied by to result in it having the least common denominator
Answer:
Step-by-step explanation:
1/6
assuming 69.6 heartbeats/minutes, estimate the total number of times the heart of a human beats in an average lifetime of 89.3 y. assume 365.25 days per year. answer in units of heartbeats. your answer must be within ± 5.0%
The total number of times a human heart beats in an average lifetime of 89.3 years is estimated to be 3,268,988,688.8 heartbeats.
To calculate time:
We are to estimate the total number of times a human heart beats in an average lifetime based on the question.Based on the information provided,We will assume 69.6 heartbeats per minute.To calculate the total number of times the heart of human beats in an average lifetime of 89.3 years,
In 89.3 years, we will calculate the number of minutes.
89.3 years = 89.3 × 365.25 × 24 × 60 minutes89.3 years = 46968228 minutesBecause there are 69.6 heartbeats per minute
Then,
There are 46968228 heartbeats in 46968228 minutes.
46968228 × 69.6 = 3,268,988,688.8 heartbeatsTherefore, the total number of times a human heart beats in an average lifetime of 89.3 years is estimated to be 3,268,988,688.8 heartbeats.
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Members of a softball team raised $2045.50 to go to a tournament. They rented a bus
for $1041.50 and budgeted $62.75 per player for meals. Which equation or tape
diagram could be used to represent the context if p represents the number of players
the team can bring to the tournament?
Answer: B
Step-by-step explanation:
what is 343250394065834698350968549846÷57547547
Answer: 5.9646399e+21
Directions: Translate equation DO NOT SOLVE!
"four times the difference of a number and 7
is 32"
Number 11:
“ten increased by the quotient of a number and 2 is -15”
Sorry for taking so long :/
Step-by-step explanation:
*Four times the difference of a number and 7 is 32*
Answer-
4(x-7)=32
ten increased by the quotient of a number and 2 is 15-
Answer-
10+(x/2= -15
or
10+x/2=-15
anyone of them
M∠1=19 , m∠2 what is the answer?
Answer:
161 degrees since 180 - 19 would be 161 since they are supplementary if they are
Step-by-step explanation:
equivalent expression to 2x7 + 2x3
Answer: 20
Step-by-step explanation:
2x7 + 2x3=
2*7 + 2*3=
14+6=20
find the equations that describe the circle of radius 3 centered at (8, 5, 6) that is parallel to the xy-plane.
The equation of the circle can be given by: (x - 8)² + (y - 5)² = 9.
What is a circle's equation?The equation for a circle in standard form is (x - x1)² + (y - y1)² = r², where (x, y) denotes arbitrary coordinates on the circle's perimeter, r denotes the circle's radius, and (x1, y1) denotes the coordinates of the circle's center.
Now,
Every point on a circle fulfills the equation describing it. A circle with radius r and a point (h, k, l) parallel to the xy plane have the following equation: (x - h)² + (y - k)² = r²We are given the values of h as 8, k as 5 and r as 3. On substituting them in the given equation, we get:=> (x - 8)² + (y - 5)² = 9
Hence, the equation that describe the circle of radius 3 centered at (8, 5, 6) that is parallel to the xy-plane is given by: (x - 8)² + (y - 5)² = 9
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1) alice decides to take a trip from the east coast of the united states to the west coast. while planning, she chooses to drive, fly, and ride a train. her first leg of the trip is traveling by car, from sacramento, california to denver, colorado. along the way, she fills up her tank using regular unleaded gas, costing $4.65 per gallon, and premium gas, $4.95 per gallon. after driving for many hours, alice finally makes it to denver, colorado spending $874.80 in gas. a) let r represent gallons of regular unleaded gas and let p represent gallons of premium gas. create an equation that models the situation.
The equation will be: 4.65r + 4.95p = 874.80
The total cost of gas will be sum of the individual costs of both the types of gas. Firstly, calculating cost of regular and premium gas followed by forming the equation.
The total cost of regular gas = Amount of regular gas × Cost of regular gas per gallon
The total cost of regular gas = 4.65 × r
The total cost of premium gas = Amount of premium gas × Cost of premium gas per gallon
The total cost of regular gas = 4.95 × p
We are given overall spending = 874.80
Forming the equation -
Total cost of regular gas + total cost of premium gas = overall spending on gas
4.65r + 4.95p = 874.80
Hence, the equation that models the situation is 4.65r + 4.95p = 874.80.
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2 tickets cost 11.00 they bought 2 drinks and used a 5.00 off coupon. the total cost was 29.18 how much was 1 drink
After buying tickets and drinks the total cost is 29.18 and using 5.00 off coupon, the cost of one drink is 11.59
As per the question statement, 2 tickets cost 11.00 and they bought 2 drinks and used a 5.00 off coupon. The total cost was 29.18. We are supposed to find out the cost of one drink.
Let the cost of one drink be "x"
Cost of 2 tickets = 11
Off coupon is of 5.00
Cost of two drinks = [tex]2x[/tex]
Total money paid = 29.18
Hence, [tex]11+2x-5=29.18\\2x=29.18+5-11=23.18\\x=\frac{23.18}{2} \\x=11.59[/tex]
Therefore the cost of one drink is [tex]x=11.59[/tex]
This question was a classic example of how to form equations when all the given conditions are in statements.
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A foreign exchange student from Denmark would like to buy gifts for her family. She finds a special deal, 7 t-shirts for $90.93, that she would like to purchase for her family. However, her family only consists of 5 people. If she wants to purchase 5 t-shirts for her family members at that special rate, what would be the cost of these t-shirts in her currency of Krona? (Currency conversion rate is 1 U.S. Dollar = 8.6964 Krona)
Using proportions, it is found that the cost of the 5 t-shirts would be of 564.83 Kronas.
What is a proportion?A proportion is a fraction of a total amount, and equations can be built to find the desired measures in the problem using a rule of three, that can be either direct(cross multiplication) or inverse(line multiplication), deriving from proportional relationships. One example of application of proportions is for currency conversion problems, as multiplication or division operations are applied according to the rates of each coin.
For this problem, we have that 7 t-shirts cost $90.93, hence the cost of a t-shirt in U.S. dollars is given applying the proportion to find the unit rate as follows:
$90.93/7 = $12.99.
The cost of 5 t-shirts will be given by:
5 x 12.99 = $64.95.
Applying the proportion 1 U.S. Dollar = 8.6964 Krona, the cost in Kronas is:
64.95 x 8.6964 = 564.83 Kronas.
The cost of the 5 t-shirts would be of 564.83 Kronas.
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(2-y)(3y+8)=0 solve
Answer:
Step-by-step explanation:
(2 - y)(3y + 8) = 0
2 - y = 0
y = -2
3y + 8 = 0
y = -8/3
how the unit circle in the coordinate plane enables the extension of trigonometric functions to all real numbers, interpreted as radian measures of angles traversed counterclockwise around the unit circle.
"Extend the domain of the trigo functions using the unit circle" Cluster A.
What is unit circle?The following steps can be used to calculate the sine and cosine of any angle thetatheta and allow us to extend the domain of sine and cosine to any real numbers:
Move counterclockwise around the unit circle starting at (1, 0), (1, 0), (1, comma, 0, right parenthesis, until the angle created by your position, the origin, and the positive xxx-axis equals thetatheta.
The yyy-coordinate of your point is equal to sin(theta)sin(theta)sine, and the xxx-coordinate is equal to cos(theta)cos(theta)cos(theta)cosine, left parenthesis, theta, right parenthesis.
There are several references to and issues with in the worlds of calculus, pre-calculus, and trigonometry.
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Select the correct product of the exponential expression.
3^5
OA. 3.5
OB. 3.3.3.3.3
OC. 5.5.5
OD. 15
The correct product of the exponential expression 3⁵ is equal to 3.3.3.3.3.
As given in the question,
Given exponential expression is equal to 3⁵
General form of exponential expression is given by aˣ
a is the base and x is the exponent
This means 'x' times ' a ' is multiplied to ' a '
Compare 3⁵ with general form
3 is base
5 is exponent
This means '5' times ' 3 ' is multiplied to '3'
3⁵ = 3.3.3.3.3
Therefore, the correct product of the exponential expression 3⁵ is equal to 3.3.3.3.3.
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pls help! marking brainliest
Answer:
296
Step-by-step explanation:
Use long division.
296
21 |6216
-42
201
-189
126
-126
0
Hope this helps!
An angel measures 109 what is the measure of it it’s supplement
Answer:
71°
Step-by-step explanation:
A supplementary angle is the sum of two angles whom are less than 180 degrees, yet the sum will only be 180 degrees. Because we are finding the supplement angle, we must subtract.
[tex]\sf Long\:Subtraction\\9\:doesnt\:go\:into\:10,borrow\:1\\= 10\\= 10 - 9\\= 1\\8\:cant\:go\:into\:0,take\:1\:since\:you\:just\:borrowed\\= 7\\= 7 - 0\\= 7\\1 - 1\\= 0\\\\= \boxed{71}[/tex]
➲ Hope this helps.
Bashir is the youngest of four siblings whose ages are consecutive integers. If the sum of their ages is 66, find Bashir's age.
Answer:
15
Step-by-step explanation:
x+x+1+x+2+x+3=66
simplify into 4x+6=66
subtract 6 from both sides to get 4x=60
divide both sides by 4 to get x=15
The age of Bashir is 15 years.
What is Algebra?A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.
Variables are the name given to these symbols because they lack set values.
In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.
Given:
let the consecutive age be x, x+1, x+2 and x+3.
Now, sum of their ages is 66
So, x+ x+1 + x+2 + x+3 = 66
Simplifying for x, we get
4x+6=66
subtract 6 from both sides
4x=60
divide both sides by 4
4x /4 = 60/4
x= 15
Hence, Bashir age is 15 years.
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evaluate 3(x-4)+2x-x2 for x=5
Answer:-12
Step-by-step explanation:
Im going to assume that x2 means x squared. You can just substitute "x" for 5. 3(5-4)+2(5)-5^2. First parenthesis equals 3(1)+10-5^2. Then it equals 3+10-5^2. So then it would be 13-5^2. 5^2 equals 25. so it would be 13-25. Which equals -12.
So you see...
The question in my math workbook is,
45 ÷ 3 = (30 + ___) ÷ 3
= 30 ÷ 3 + ___ ÷ 3
= 10 + 5
= 15
sorry my brain is broken right now- I have a feeling this problem is really easy to solve, but as I said my brain is broken lol
The blank will be filled with 15.
The Bodmas rule is arranged according to the letters in the acronym BODMAS, which stand for brackets, position of power or roots, division, and multiplication. A stands for addition and S for subtraction. According to the BODMAS rule, multi-operator mathematical equations must be resolved in the BODMAS order from left to right.
The explanation goes like:
45 ÷ 3 = ( 30 + 15 ) ÷ 3
= 30 ÷ 3 + 15 ÷ 3
= 10 + 5
= 15
Hence the answer is 15.
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Eve is mixing paint to match a specific shade of orange. She mixes red paint and yellow paint
in different ratios. The color matches best when Eve uses 4 ounces of red paint and ounces of
yellow paint.
Eve has 1 ounce of red paint left. How many ounces of yellow paint should she add to match the
same shade of orange?
In order to get a precise orange color, Eve is mixing paint. She combines various ratios of red and yellow paint.
Eve finds that using 4 ounces of red paint and 1 ounce of yellow paint results in the best color matching. Eve still has one ounce of red paint. To get orange shade she has to add 4 ounces of yellow paint to get same shade.
Given that,
In order to get a precise orange color, Eve is mixing paint. She combines various ratios of red and yellow paint. Eve finds that using 4 ounces of red paint and 1 ounce of yellow paint results in the best color matching. Eve still has one ounce of red paint.
We have to see the ratio
4:1
extra 1 red paint that is
4+1:1
5:1
Therefore, To get orange shade she has to add 4 ounces of yellow paint to get same shade.
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Please help me please help me
Answer: T (4,4)
Step-by-step explanation:
Melina receives a chain e-mail that she forwards to 7 of her friends. Each of her friends
forwards it to 7 of their friends.
Chain E-Mail
Melina
How many people will receive the e-mail after 6 forwards?
Answer:
823543 Or 7^7
Step-by-step explanation:
Some students were surveyed about their favorite type music and school-subject preferences. The results are displayed below. Which of the following is true, according to the graph? There is a much larger preference for science among those who prefer R&B. There is a much larger preference for English among those who prefer rock. There is a much smaller preference for math among those who prefer country. The percentages for class preference are relatively the same among the different music groups.
The 4th statement is the most correct, imo
"There is a much larger preference for science among those who prefer R&B", but there is only less than 20% of the students who prefer science.
"There is a much larger preference for English among those who prefer rock", but there is only a little more than 20% of the students who prefer english.
"There is a much smaller preference for math among those who prefer country", but nearly 40% of the students prefer math.
And looking at it, all the subject preferences for all kind of music groups are pretty much evenly distributed.
The solution to the box plot is the percentages for class preference are relatively the same among the different music groups
What is box plot?A box and whisker plot, often known as a box plot, shows a data set's five-number summary. The minimum, first quartile, median, third quartile, and maximum make up the five-number summary.
A box is drawn from the first quartile to the third quartile in a box plot. At the median, a vertical line passes through the box.
It is used when showing the distribution of data points across a selected measure and if the box in a box plot is stretched in one direction or the other, then the data is skewed in that direction.
Given data ,
Let the plot be represented as A
Now , the x axis represents the favorite music type
And , the y axis represents the relative frequency
From the R and B column , the science people is less than mathematics people
From the Rock column , the English people is less than mathematics people
From the country column , mathematics people is greater than English people
And , from the plot we can say that percentages for class preference are relatively the same among the different music groups
Hence , the box plot represents similar percentages
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Katie invested a total of $8000 part at 5% simple interest in part at 6% simple interest. at the end of one year the investments had earned $454 interest. how much was invested at each rate?
If Katie invested a total of $8000, part at 5% simple interest and part at 6% simple interest and at the end of one year the investments had earned $454 interest, then she invested $2600 at 5% and $5400 at 6% simple interest
Given,
The total invested amount = $8000
Consider the amount invested at 5% simple interest as x and the amount invested at 6% simple interest as y
Then, the equations will become
x + y= 8000
x = 8000-y
At the end of one year the investment = $454
0.05x + 0.06y =454
Substitute the value of x in the equation
0.05(8000-y) + 0.06y =454
400-0.05y+0.06y =454
0.01y+400=454
0.01y =54
y = 5400
Substitute the value of x in
x + y = 8000
x+5400=8000
x=8000-5400
x=2600
Hence, if Katie invested a total of $8000, part at 5% simple interest and part at 6% simple interest and at the end of one year the investments had earned $454 interest, then she invested $2600 at 5% and $5400 at 6% simple interest
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if a1 = 10 and an = an - 1 + 1 then find the value of a4
The value of the fourth element of the series is 13.
How to determine the value of an element of the series by using recurrence formulas
In this problem we must use a recurrence formula and a initial value to derive the fourth element of the series. Recurrence formulas are expressions that calculate succesive elements of a series in terms of its previous elements.
Now we proceed to find the value of the fourth element of the series:
n = 2
a₂ = a₁ + 1
a₂ = 10 + 1
a₂ = 11
n = 3
a₃ = a₂ + 1
a₃ = 11 + 1
a₃ = 12
n = 4
a₄ = a₃ + 1
a₄ = 12 + 1
a₄ = 13
The value of the fourth element of the series is 13.
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Answer:
Step-by-step explanation:
The value of the fourth element of the series is 13.
How to determine the value of an element of the series by using recurrence formulas
In this problem we must use a recurrence formula and a initial value to derive the fourth element of the series. Recurrence formulas are expressions that calculate succesive elements of a series in terms of its previous elements.
Now we proceed to find the value of the fourth element of the series:
n = 2
a₂ = a₁ + 1
a₂ = 10 + 1
a₂ = 11
n = 3
a₃ = a₂ + 1
a₃ = 11 + 1
a₃ = 12
n = 4
a₄ = a₃ + 1
a₄ = 12 + 1
a₄ = 13
The value of the fourth element of the series is 13.
select the correct answer. which measurement is equivalent to 350 milliliters? a. 3.5 × 102 liters b. 3.5 × 101 liters c. 3.5 × 10–2 liters d. 3.5 × 10–1 liters
According to the given information the measurement is equivalent to 350 milliliters = 3.5 x 10⁻¹.
The correct option is D.
What is conversion factor?A conversion factor is a quantity that is used to multiply as well as divides one set of units by another. When converting to an equivalent value, the appropriate conversion factor must be utilized. To convert inches to feet, for example, the suitable conversion value is 12 inches equal 1 foot.
What is the significance of conversions?Conversion KPIs are critical for determining the efficacy of marketing campaigns. Only by measuring how many users convert as a result of that spend can you calculate your ROAS.
According to the given data:We are given an amount of 350 milliliters and asked to convert it to liters.
We know that :
1 liter = 1000 milliliters
We are given an amount of 350 milliliters and asked to convert it to liters.
1 liter/x liter = 1000/350
x = 350/1000
x = 3.5 x 10⁻¹
The given information the measurement is equivalent to 350 milliliters = 3.5 x 10⁻¹.
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I understand that the question you are looking for is:
Which measurement is equivalent to 350 milliliters?
A. 3.5 × 102 liters
B. 3.5 × 101 liters
C. 3.5 × 10–2 liters
D. 3.5 × 10–1 liters
help with explanation!
In a heptagon, the sum of all seven angles is 900 degrees. If you add up the four given angles you will get 600 degrees. In the question it says, "the remaining interior angles are EQUAL" so therefore, the only way to get from 600 to 900 from the remaining three angles is 100. Each remaining angle is 100 degrees
Answer:
Heptagons are known to have seven interior angles that add up to 900°, so we must find the last 3. First, add the first four they gave us.
[tex]160\circ + 130\circ = 290\circ\\= 290\circ + 170\circ + 140\circ\\170\circ + 140\circ = 310\circ\\= 290\circ + 310\circ\\= 600\circ[/tex]
We now know that the remaining angles are all 100°, because the question mentions the rest of the interior angles being equal. The only reasonable 3 equal numbers to add up to 900° would be three 100s in this case.