What are the missing sides in the triangle written as integers or as decimals rounded to the
nearest tenth? The figure is not drawn to scale.
x= 18; y = 15.6
x= 12.7; y = 15.6
x= 12.7;y=9
x=9; y = 12.7
Answers
The value of x is 12.7 and the value of y is 9. The correct option is the third option x = 12.7; y = 9
TrigonometryFrom the question, we are to determine the values of the missing sides
From the diagram,
Opposite = 9
Adjacent = y
Hypotenuse = x
Included angle = 45°
Using SOH CAH TOA, we can write that
[tex]tan 45^\circ= \frac{9}{y}[/tex]
[tex]1 = \frac{9}{y}[/tex]
∴ y = 9
Since the triangle is a right triangle, we can write that
x² = y² + 9² (Pythagorean theorem)
x² = 9² + 9²
x² = 81 + 81
x² = 162
x = √162
x = 12.7
Hence, the value of x is 12.7 and the value of y is 9. The correct option is the third option x = 12.7; y = 9
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Related Questions
Find a formula for the sum of the first n even integers : 2 + 4 + 6 + ... + 2n.
Answers
Let S be the sum,
S = 2 + 4 + 6 + ... + 2 (n - 2) + 2 (n - 1) + 2n
Reverse the order of terms:
S = 2n + 2 (n - 1) + 2 (n - 2) + ... + 6 + 4 + 2
Add up terms in the same positions, so that twice the sum is
2S = (2n + 2) + (2n + 2) + (2n + 2) + ... + (2n + 2)
or
2S = n (2n + 2)
Divide both sides by 2 to solve for S :
S = n (n + 1)
What are the exact values of x and y?
x =
y =
Answers
Answer:
see the attachment photo!
According to the histogram shown, how many hostel rooms are there?
Answers
Answer:
10
Step-by-step explanation:
look at the y axis for the answer to a question like this
Answer:
There are 25 hostel rooms.
Step-by-step explanation:
We simply need to add up the height of each bar.
3+5+8+6+2+1=25 hostel rooms
What number is missing from this factor tree for the prime factorization of 425?
A. 2
B. 3
C. 5
D. 7
Answers
Because the prime factorization of 425 is 5x17
What is the surface area of the triangular prism shown?
In a test rn!! A right triangular prism. The height of the prism is 25 centimeters. The sides of the triangular ends have lengths 9 centimeters, 12 centimeters, and 15 centimeters.
86 cm2
1,008 cm2
1,350 cm2
1,080 cm2
Answers
The surface area will be equal to option B which is 1008 square centimeters.
What is surface area?The space occupied by any two-dimensional figure in a plane is called the area. The area of the outer surface of any body is called the surface area.
The surface area of the prism will be calculated as:-
SA = area of the three rectangular faces + area of the triangular faces
Area of the rectangular faces = ( 15 X 25 ) + ( 25 X 12 ) + ( 25 X 9 )
= 375 + 300 + 225
= 900 square cm
Area of the triangular [tex]=\sqrt{(s(s-a)(s-b)(s-c)[/tex]
= [tex]\sqrt{(18(18-15)(18-12)(18-9)}[/tex]
= √2916
= 64
Total area of the rectangular face = 2 x 54 = 108
So the total SA area of the prism will be = 900 + 108= 1008 square cm.
Therefore surface area will be equal to option B which is 1008 square centimeters.
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please help!! What is the most precise classification for the quadrilateral shown in the graph below?
Answers
Parallelogram is the most precise classification for the quadrilateral shown in the graph below.
What is a Parallelogram?This is a quadrilateral which has two pairs of parallel sides and the area is usually measured using base × height.
The opposite sides and angles are equal which is why parallelogram was chosen as the most appropriate choice.
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HELP PLEASE !!!!!!!!!!!
Answers
Answer:
I think A sorry if wrong
Step-by-step explanation:
have a good day
A plane is located at C on the diagram. There are two towers located at A and B. The distance between the towers is 7,600 feet, and the angles of elevation are given.
a. Find BC, the distance from Tower 2 to the plane, to the nearest foot.
b. Find CD, the height of the plane from the ground, to the nearest foot.
Please show work!
Answers
Answer:
part 1) BC is 17491 ft
part 2) CD is 6499 ft
Step-by-step explanation:
Answer:
part 1) BC is 17491 ft
part 2) CD is 6499 ft
One year, the population of a city was 358,000. Several years later it was 286,400. Find the percent decrease.
Answers
A percentage is a way to describe a part of a whole. The percentage decrease is 20%.
What are Percentages?A percentage is a way to describe a part of a whole. such as the fraction ¼ can be described as 0.25 which is equal to 25%.
To convert a fraction to a percentage, convert the fraction to decimal form and then multiply by 100 with the '%' symbol.
One year, the population of a city was 358,000. Several years later it was 286,400. Therefore, the percentage decrease is,
Percentage decrease = (358,000-286,400)/(358,000) × 100% = 20%
Hence, the percentage decrease is 20%.
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The median is a value in the data set
Answers
Answer:
Step-by-step explanation:
The median is defined as the middle value of a data set when all the data is arranged in numerical order.
If there is an even number of values, and therefore no middle value, then the median is calculated as the mean value of the two middle values.
St. augustine grass can grow at the rate of 4 over 7 centimeter per week.
how many weeks will it take the grass to grow 12 over 7 centimeters?
like im gonna need a written answer
explain your answer using words, and show your work using division of fractions.
Answers
The weeks will it take the grass to grow 12 over 7 centimeters is 3 weeks.
What is the unitary method?The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.
St. Augustine grass can grow at the rate of 4 over 7 centimeters per week.
The weeks will it take the grass to grow 12 over 7 centimeters
4/7 x = 12/ 7
28x = 84
x = 84/28
x = 3
The weeks will it take the grass to grow 12 over 7 centimeters is 3 weeks.
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Answer:
12/7 divided by 4/7 = 3
Step-by-step explanation:
If the measure of arc AB is 50 degrees, what is the measure of angle ADB?
90 degrees
100 degrees
25 degrees
50 degrees
Answers
Answer:
25 degrees
Step-by-step explanation:
arc divided by 2 = angle
50/2=25
Glen Cove has a population of 7,200, which is decreasing at a
rate of 80 people per year. Locust Valley has a population of
5,000 and is gaining 120 people per year. In how many years
will the populations of Glen Cove and Locust Valley be the same?
Please help!!
Answers
Answer:
11 years
Step-by-step explanation:
7200 - 80x = 5000 + 120x
-5000 + 80x -5000 + 80x
2200 = 200x
11 = x
Create a frequency distribution table for each of the following.
1.The heights in centimeters of twenty students are given below.
Construct a frequency table for the data.
Answers
The frequency of the data sets is defined as the number of times the data is repeated in the given dataset. The frequency of the given data is calculated in the table below.
What is the frequency of the data sets?The frequency of the data sets is defined as the number of times the data is repeated in the given dataset.
Height (cm) Frequency
146 -- 2
147 -- 1
148 -- 1
149 -- 1
150 -- 2
151 -- 1
152 -- 6
153 -- 2
154 -- 3
155 -- 1
As we can see that the height of 146 cm is repeated two times so its frequency is 2. From this concept, all the frequencies are calculated above.
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6 A cube has a surface area of 54 mm². The length of its sides is: A 3 mm B 4 mm C 5
mm D 6 mm E 7 mm
Answers
Answer:
A
Step-by-step explanation:
A cube has 6 square faces
given surface area = 54 mm² , then
area of one face = 54 mm² ÷ 6 = 9 mm²
the area (A) of a square is calculated as
A = s² ( s is the side length ) , so
s² = 9 ( take square root of both sides )
s = [tex]\sqrt{9}[/tex] = 3 mm
Write the following inequality in slope-intercept form. 5x-5y>70
Answers
The given inequality 5x - 5y > 70 when written in Slope intercept form is gotten as; y < x + (-14)
How to write slope intercept form?The formula for equation of a line in slope intercept form is given by;
y = mx + c
where;
m is slope
c is y-intercept
We are given the inequality as;
5x - 5y > 70
Thus;
Subtract 5x from both sides to get;
-5y > 70 - 5x
divide both sides by -5 to get
y < x + (-14)
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In a graph, x represents the number of months since a business opened, and y represents the total amount of money the business has earned. The following three points are from the graph:
Answers
The slope of the graph is 745 and the y-intercept of the graph is 500
Missing part of the questionThe following three points are from the graph: (2, 1990) (5, 4225) (9, 7205)
Find the slope and y-intercept
How to determine the slope?The points are given as:
(2, 1990) (5, 4225) (9, 7205)
The slope is calculated using:
m = (y2 - y1)/(x2 - x1)
So, we have:
m = (4225 - 1990)/(5 - 2)
Evaluate
m = 745
Hence, the slope of the graph is 745
How to determine the y-intercept?In (a), we have
m = 745
To calculate the y-intercept, we use the following points
(x1 , y1) = (0,y)
Recall that:
m = (y2 - y1)/(x2 - x1)
So, we have:
745 = (4225 - y)/(5 - 0)
Evaluate the difference
745 = (4225 - y)/(5)
Multiply both sides by 5
3725 = 4225 - y
Solve for y
y = 500
Hence, the y-intercept of the graph is 500
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martina must choose a number between 49 and 95 that is multiple of 2,8 and 10. write all the numbers that she could choose.
Answers
Answer:
80
Step-by-step explanation:
10 limits it to 50, 60, 70, 80, and 90
2 eliminates none since 50=25, 60=30, 70=35, 80=40 and 90=45
8 divided by each number only leaves one option of 80. (80/8= 10) (80/10=8) (80/2=40)
What is the amplitude of the graph below
Answers
The amplitude is 3
for a sine graph, the amplitude is the distance up or down from the midway point. The equation to find the amplitude is (max-min) / 2.
(3 - (-3)) / 2 = 3
A, B & C lie on a straight line.
BD = CD.
∠BDC = 40° and
∠ADB = 45°.
Work out x
Answers
Answer:
25
Step-by-step explanation:
Since triangle DBC is isosceles, angles DBC and DCB must be congruent. Angle BDC is 40 so the sum of the measures of the aforementioned angles must be 180 - 40 = 140; divide that by two and you get that the measure of angle DBC is 70. Angles DBC and ABD are supplementary, as they lie on a straight line, so we can deduce the measure of angle DBA is 180 - 70 = 110. The measure of angle DAB is 180 minus the measures of angle DBA and ADB, we figured out angle DBA is 110 degrees and the problem tells us angle ADB is 45 degrees, so we can subtract to get the measure of angle DAB to be 180 - (110 + 45) = 25.
Answer:
25
Step-by-step explanation:
i dont know how to explain i just know thats the answer hahaha
Cheryl has a horse and cow ranch that contains 100 animals. The value of each horse is $500 and the value of each cow is $200. If the total value of the 100 animals is $31,000, how many horses and cows does Cheryl have on her ranch?
Answers
The number of the cows is 63 and the number of the horses is 37.
What is an expression?Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication and division.
Given that:-
Cheryl has a horse and cow ranch that contains 100 animals. The value of each horse is $500 The value of each cow is $200. If the total value of the 100 animals is $31,000.The number of horses and cows will be calculated by forming the expression from the given data in the question. So the two expressions are as follows.
h + c = 100
500h + 200c = 31000
Solving the above two equations by substitution method:-
h = 100 - c
Put the value of h in the second equation:-
500 ( 100 - c ) + 200c = 31000
50000 - 500c + 200c = 31000
50000 - 300c = 31000
50000 - 31000 = 300c
c = 19000 / 300
c = 63
Put the value of c in the first equation we will get the number of the horses.
h + c = 100
h + 63 = 100
h = 100-67 = 37
Therefore the number of the cows is 63 and the number of the horses is 37.
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Let's calculate the surface of the ABC triangle from the image if the area of the triangle DBC is 40 square unit,| BC| = 8i| AB| = 14. Corners marked in the image are compliant.
ANSWER: 122.5 square
Answers
Answer:
122.5 squared
Step-by-step explanation:
bahh have have aheve shaved she sbdnabd sjsbd akdbd
Answer this for 10 pts pls
Answers
Answer:
c and a
Step-by-step explanation:
Answer:
it's both A and C
Step-by-step explanation:
2 x 3/8 is the same as 3/8 + 3/8
I need help to simplify this expression
Answers
Answer:
[tex]a^{7} +b^{6}[/tex]
Hope this helps :)
What is the length of segment BC?
Answers
Answer:
[tex]BC=x=(13;+\infty)[/tex]
Step-by-step explanation:
Existence of Triangle
[tex]x-(2x-24) < x-2 < x+(2x-24)\\[/tex]
[tex]13 < x > 11[/tex]
[tex]x=(13;+\infty)[/tex]
What is the relationship between the number of sides a regular polygon has and the number of lines of symmetry that can be found on it?
There are always more lines of symmetry than sides.
They are same value.
There are always more sides than lines of symmetry.
There is no relationship.
Answers
The number of sides equals the number of the line of symmetry. Then the correct option is B.
What is a polygon?The polygon is a 2D geometry that has a finite number of sides. And all the sides of the polygon are straight lines connected to each other side by side.
The relationship between the number of sides a regular polygon has and the number of lines of symmetry will be
In a regular polygon, the amount of symmetry lines is equal to the total of sides.
Then the correct option is B.
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Answer:
B They are the same value!
Step-by-step explanation:
Why? Well go look in your lesson although because i got this correct i forgot ago and yeah (TRUST++)
Dan invests £8200 into his bank account.
He receives 2% per year compound interest.
How much will Dan have after 7 years?
Give your answer to the nearest penny where appropriate.
Answers
Answer: £ 3675.79
Step-by-step explanation:
A = P(1 + r)^t
A = final amount = x
P = initial principal balance = 3200
r = interest rate = 0.02
t = number of years elapsed = 7
x = 3200(1.02)^7
x = 3200 * 1.14868567
x = 3675.79414
x = 3675.79
Solve for x:
e^(3x )+ e^x - 6 = 0
Right now I'm having trouble with the step u = e^x, u^3 + u - 6 = 0. Help!
Answers
The value of x of the cubic equation e³ˣ + eˣ - 6 = 0 will be 0.49
What is a cubic equation?The cubic equation is given as ax³ + bx² + cx + d = 0. Then degree of the equation will be 3. Then we have
The cubic equation will be
e³ˣ + eˣ - 6 = 0
Let eˣ = u, then the equation will be
u³ + u - 6 = 0
Then the root of the equation is calculated by the calculator, then we have
u = 1.634, -0.817, -0.817
eˣ = 1.634, -0.817, -0.817
Take log on both sides, then we have
x = ln 1.634, ln(-0.817), ln(-0.817)
x = 0.49, not defined, not defined
Then the value of x will be 0.49.
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Based on the information in the table what is the probability of being a girl and choosing lemonade?
Select one:
a.
21%
b.
.20
c.
20%
d.
38%
e.
.38
Answers
Using it's concept, it is found that the probability of being a girl and choosing lemonade is given by:
b. 0.2.
What is a probability?A probability is given by the number of desired outcomes divided by the number of total outcomes.
In this problem, out of 130 people, 26 are girls who choose lemonade, hence the probability is given by:
p = 26/130 = 0.2, which means that option b is correct.
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Hurry!!!!!!!!!!
the flood levels of some rivers and lakes in arkansas are listed in the table. which lake or river has a flood level that represents the outlier in this data set?
a. ozark
b. dardanelle
c. little rock
d. pine bluff
Answers
The lake whose flood level represents an outlier is Ozark.
What is an outlier?
An outlier is a number that is way smaller or way larger than that of other numbers in a data set. The flood level of Ozark is way greater than the other flood levels.
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