find the area of triangle qpm. round the answer to the nearest tenth. a. 5.2 square units b. 6.3 square units c. 6.5 square units d. 12.6 square units
Answers
We need to solve for the angles of the smaller triangle in order to solve for the angle of the larger triangle which would help us solve the missing measurement of a side.
Given:
51 degrees.
Cut the triangle into two equal sides and it forms a right triangle. All interior angles of a triangle sums up to 180 degrees.
180 – 51 – 90 = 39 degrees
39 degrees * 2 = 78 degrees.
Angle Q is 78 degrees.
In the bigger triangle, 4.3 is the hypotenuse. We need to solve for the measurement of the long leg which is the opposite of the 78 degree angle.
We will use the formula:
Sine theta = opposite / hypotenuse
Sin(78 deg) = opposite / 4.3
Sin(78 deg) * 4.3 = opposite
4.21 = opposite. This is also the height of the triangle.
Area of a triangle = ½ * base * height
A = ½ * 3units * 4.21units
A = 6.315 square units.
Related Questions
What is the measure of angle 4?
Answers
7x + 23x = 180
30x = 180
x = 6
m<4 = 7x = 7(6) = 42
answer
B. 42 (Second choice)
Number 8 please it will help a lot
Answers
what is 1 and 6/24 simplified as ?
Answers
Choose the system of equations which matches the following graph:
A. 5x - y = 7
2x - y = 0
B. 5x - y = 7
2x + y = 0
C. 5x + y = -7
2x + y = 0
D. 5x + y = -7
2x - y = 0
Answers
Answer:
Option B : [tex]5x - y = 7[/tex]
[tex]2x + y = 0[/tex]
Step-by-step explanation:
Intersecting point on the graph = (1,-2)
Substitute this point in the given options .
A. [tex]5x - y = 7[/tex]
[tex]2x - y = 0[/tex]
Substitute (1,-2)
[tex]5(1) - (-2) = 7[/tex] and [tex]2(1) -(-2) = 0[/tex]
[tex]7 = 7[/tex] and [tex]4 \neq 0[/tex]
So, this system of equations does not matches the graph.
B. [tex]5x - y = 7[/tex]
[tex]2x + y = 0[/tex]
Substitute (1,-2)
[tex]5(1) - (-2) = 7[/tex] and [tex]2(1)+(-2) = 0[/tex]
[tex]7 = 7[/tex] and [tex]0= 0[/tex]
So, this system of equations matches the graph.
C.[tex]5x + y = -7[/tex]
[tex]2x + y = 0[/tex]
Substitute (1,-2)
[tex]5(1) - (-2) = -7[/tex] and [tex]2(1)+(-2) = 0[/tex]
[tex]7\neq -7[/tex] and [tex]0= 0[/tex]
So, this system of equations does not matches the graph.
D. [tex]5x + y = -7[/tex]
[tex]2x - y = 0[/tex]
Substitute (1,-2)
[tex]5(1) - (-2) = -7[/tex] and [tex]2(1) -(-2) = 0[/tex]
[tex]7\neq -7[/tex] and [tex]4 \neq 0[/tex]
So, this system of equations does not matches the graph.
Answer:
B. 5x - y = 7
2x + y = 0
Step-by-step explanation:
took test
I WILL GIVE BRAINLIEST please answer both parts
If 365 work days are split among 12 employees evenly
PART: A How can you rewrite this as a fraction?
PART:B What does the fraction represent?
Answers
Part A: To understand this question, you need to read carefully and pick out key words that tells you what to do. All math word / puzzle problems have key words that tell you what you need to do.
For instance, the key word split tells us we need to divide. So, we know we have 365 work days that need to be split among 12 employees. So for Part A:
365 / 12
For Part B it wants to know what this represents. It represent the number of days each of the 12 employees will get if split evenly among each employee.
Find the area of the parallelogram shown below
Answers
5 * 7 =
35
Six less then two thirds of a number is negative ten what is the number
Answers
2/3X-6 = -10
2/3x = -4
x = -4 / 2/3 = -6
X = -6
check:
2/3(-6) - 6 = -4 -6 = -10 TRUE
Determine the sign of cos pi divided by seven without using a calculator.
Answers
Answer:
The [tex]\cos \frac{\pi}{7}[/tex] has positive sign.
Step-by-step explanation:
we need to determine the sign of [tex]\cos \frac{\pi}{7}[/tex] without using calculator
Cartesian system ( shown in figure -1)
The angle [tex]\cos \frac{\pi}{7}[/tex] lies in quadrant-1 , Where angles are zero (0) to [tex]\frac{\pi}{2}[/tex]
and in first quadrant all trigonometric ratios has positive sign
so, [tex]\cos \frac{\pi}{7}[/tex] has positive sign.
Jessie received the following scores on her math tests this year. (45, 65, 70, 80, 85, 100) Suppose the teacher removes the lowest and highest scores. (65, 70, 80, 85) What are the interquartile ranges of Jessie’s original scores and her new scores?
Answers
45,65,70,80,85,100
IQR = 85 - 65 = 20
new scores :
65,70,80,85
IQR = (80 + 85)/2 - (65 + 70)/2 = 82.5 - 67.5 = 15
Answer:
Interquartile ranges of Jessie’s original scores = 20
Interquartile ranges of Jessie’s new scores = 15
Step-by-step explanation:
Interquartile range IQR = Higher quartile (Q3) - lower quartile (Q1)
Where Q3 is the mid-value of the second half of a dataset and
Q1 is the mid-value of the first half of a dataset.
Original score = 45, 65, 70, 80, 85, 100
Q1 of original score:
First half of original score = 45, 65, 70
Therefore Q1 = 65
Q3 of original score:
Second half of original score = 80, 85, 100
Therefore Q3 = 85
:. Interquartile range IQR of original score = Q3 of original score - Q1 of original score
:. IQR = 85 - 65 = 20
New score = 65, 70, 80, 85
Q1 of new score:
First half of new score = 65, 70
Therefore Q1 = (65+70)/2 = 67.5
Q3 of new score:
Second half of new score = 80, 85
Therefore Q3 = (80 + 85)/2 = 82.5
:. Interquartile range IQR of new score = Q3 of new score - Q1 of new score
:. IQR = 82.5 - 67.5 = 15
Therefore:
Interquartile ranges of Jessie’s original scores = 20
Interquartile ranges of Jessie’s new scores = 15
Jeff takes 20 mins to jog around the race course one time. And 25 mins to jog arpund second time. What is his average speed in kms per hr fpr the whole jog if the course is 3 kms long?
Answers
Work=Rate*Time, or Distance=Speed*Time.
Thus, the time is: [tex]speed= \frac{distance}{time} [/tex].
In our problem, the total distance is 3 km + 3 km = 6 km.
the total time is 20 min + 25 min = 45 min.
60 minutes are 1 hour, then
45 minutes are [tex] \frac{45min*1h}{60min}= 0.75h[/tex]
Thus, the average speed is : distance/time = 6 km/ 0.75 h = 8 km/h
Answer: 8 km/h
Define a function f : R → R by the formula
f(x) = 2x − 8.
Prove that f is one-to-one.
Let a, b is in R, and suppose that
f(a) = f(b).
Then
2a − 8 =
Answers
Now, we have to think that the parent function is f(x) = 2x - 8 and f (a) = f (b). This means the value of the function f(a) is if a is substituted to x:
f (a) = 2a - 8, same goes for f (b):
f (b) = 2b - 8.
Since we have a condition that f(a) = f (b), then,
2a - 8 = 2b - 8.
If we simplify further,
2a = 2b - 8 + 8
( 2a = 2b ) / 2
the equation becomes:
a = b; this proves that f is a one-to-one function.
What is the sine value of pi over 6?
Answers
Answer:
The sine value of pi over 6 is:
[tex]\dfrac{1}{2}[/tex] or 0.5
Step-by-step explanation:
we have to find the value of [tex]sin\dfrac{\pi}{6}[/tex]
we know that value of [tex]sin\dfrac{\pi}{6}[/tex] is [tex]\dfrac{1}{2}[/tex]
Hence, the sine value of pi over 6 is:
[tex]\dfrac{1}{2}[/tex] or 0.5
In triangle ∆PQR, C is the centroid.
a. If CY = 10, find PC and PY
b. If QC = 10, find ZC and ZQ
c. If PX = 20, find PQ
Answers
Because C is the centroid,
PZ = ZR; QY = YR; and PX = XQ.
Part a.
If CY = 10, then PC = 2*CY = 20
PY = PC + CY = 20 + 10 = 30
Answer:
PC = 20
PY = 30
Part b.
If QC = 10, then ZC = QC/2 = 5
ZQ = ZC + QC = 5 + 10 = 15
Answer:
ZC = 5
ZQ = 15
Part c.
Given: PX = 20.
Because the median bisects side PQ, therefore PX = QX = 20
PQ = PX + QX = 40
Answer:
PQ = 40
Which expression is equal to 7(1+3)
A.) 7+21
B.) 7+3
C.) 1+21
D.) 7+4
Answers
I would say D. 7+4 because it is the only one that makes since to me
How to show numbers are related to each other
Answers
An architect plans to make a drawing of the room of a house. The segment LM represents the ceiling of the room. He wants to construct a line passing through Q and perpendicular to side LM to represent a wall of the room. He uses a straightedge and compass to complete some steps of the construction, as shown below:
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A regular pentagonal prism has a height of 14 in. and a base edge length of 10 in. Identify its lateral area and surface area.
Can anyone help me solve this?
Answers
So the lateral area = 5 * 10 * 14 = 700 (in squared)
Consider one of the bases of the prism.
As shown in the figure, the pentagon is made up of 5 isosceles triangles.
The vertex of each of these 5 triangles is 360°/5=72°.
Draw the altitude, which forms 2 right triangles with angle measures 36°-54°-90°.
Let he hypotenuse be s and the altitude be h in, as shown in the figure.
x*cos54°=5
x=5/(cos54°)=5/(0.588)=8.5
then,
h=x*sin54°=8.5*(0.8)=6.8 (in)
Thus, the area of one of the 5 congruent isosceles triangles is
[tex] \frac{1}{2}*10*6.8= 34[/tex] (in squared)
The area of the pentagonal base is 34*5 = 170 (in squared)
Thus the surface area = lateral area + 2 base area
= 700+2*170 = 700+340 = 1040 (in squared)
Answer:
lateral area: 700 in squared
surface area: 1040 in squared
Answer:
L = 700 in2 ; S = 1044.1 in2
Step-by-step explanation:
Lucky guess :)
Kayla has a tshirt store. she sold three times as many white tshirts as blue tshirts. she sold a total of 48 tshirts. How many white tshirts did kayla sell
Answers
1. x
2. 3x
x + 3x = 48
Now solve it:
x + 3x = 48
4x= 48
x=12
Now plug in x
1. x = 12
2. 3x = 36
So Kayla sold 12 blue t-shirts and 36 white t-shirts.
Three-fourths of the yard is covered in grass but 4/5 of the grass has died. How much of the yard has dead grass?
Answers
multiply the 2 together:
3/4 x 4/5 = 12/20 = 3/5 has dead grass
To find the area of the yard that has dead grass, multiply three-fourths (the grassy area) by 4/5 (the dead portion). Simplifying (3/4) × (4/5) gives us 3/5, which means 3/5 of the yard has dead grass.
To determine how much of the yard has dead grass, we need to calculate the portion of the yard covered in grass and then the fraction of it that has died. Given that three-fourths of the yard is covered in grass, we represent this as 3/4. It is known that 4/5 of this grass has died, hence we multiply the two fractions: (3/4) × (4/5).
Performing the multiplication of these two fractions:
Multiply the numerators: 3 × 4 = 12.Multiply the denominators: 4 × 5 = 20.Combine the products to form the new fraction: 12/20.Now, simplify the fraction 12/20 by dividing both the numerator and denominator by their greatest common divisor, which is 4:
Divide the numerator: 12 ÷ 4 = 3.Divide the denominator: 20 ÷ 4 = 5.The simplified fraction is 3/5.Therefore, the correct answer is that 3/5 of the yard has dead grass.
If T is the point at a distance 3pi/5 from P(1, 0) on the unit circle with its center at (0, 0), in what quadrant does T lie?
Answers
We know that 180 degrees on the unit circle is pi, or 5pi/5, which is the same as pi.
So 90 degrees is half of 180 and therefore half of 5pi/5 which is 2.5pi/5.
Since 2.5pi/5 is at the 90 degree mark we know that 3pi/5 has to be past this so it will be in Quadrant II.
I hope this helps.
Final answer:
The point T lies in the second quadrant of the unit circle when it is at an angular distance of 3π/5 from P(1, 0), because this angle falls between π/2 and π radians.
Explanation:
If T is the point at a distance 3π/5 from point P(1, 0) on the unit circle with its center at (0, 0), to determine in what quadrant T lies, we must consider where this angle places T on the unit circle.
Recall that a point on the unit circle has coordinates (x, y) = (cos θ, sin θ), where θ is the angle measured counterclockwise from the x-axis. An angle of 3π/5 radians is more than π/2 radians but fewer than π radians. Therefore, it falls in the second quadrant of the unit circle, where x-coordinates are negative and y-coordinates are positive.
a pair of jeans cost 75% as much as a pair of corduroy pants what is the cost of each if the total cost for the jeans and courds is $42
Answers
j= jeans
c= corduroy
jeans = 0.75C
0.75 +c = 42
1.75c = 42
c = 42/1.75 = 24
jeans cost 24*0.75 = 18
corduroys cost $24
Jeans cost $18
Answer with Step-by-step explanation:
Let j denote the cost of jeans
and c denotes the cost of corduroy
A pair of jeans cost 75% as much as a pair of corduroy pants.
i.e. j = 0.75c
The total cost for the jeans and corduroy is $42
i.e. j+c=42
⇒ 0.75c+c=42
⇒ 1.75c=42
Dividing both sides by 1.75,we get
c=24
Putting value of c in j= 0.75c gives
j=18
Hence, Cost of jeans=$18
and cost of corduroy=$24
The table shows the number of students in a school who like dodgeball and/or ping pong:
Like Dodgeball
Do Not Like Dodgeball
Total
Like Ping Pong
26
18
44
Do Not Like Ping Pong
24
32
56
Total
50
50
100
What is the relative frequency, by row, of students who like both dodgeball and ping pong?
0.22
0.40
0.48
0.59
PLEASE HELP !!!
Answers
I've included the table so it's easier to visualize.
Divide the amount of students who like ping pong and dodge ball (26, it's highlighted in the image) by the total amount of students that like ping pong (44).
26/44 = 0.59
The answer is 0.59
Hope this helps! :)
Answer:
0.59
Step-by-step explanation:
2n2-24n+72 factor completely
Answers
2(n^2-12+36)
2(n^2-6n-6n+36)
2(n(n-6)-6(n-6))
2(n-6)(n-6)
2(n-6)^2
There are two numbers, which sum up to 53. Three times the smaller number is equal to 19 more than the larger number. What are the numbers
Answers
the larger number = 3n-19
n + 3n - 19 = 53
4n = 53 + 19
4n = 72
n = 72/4
n = 18 ← smaller number
larger number = 53 - 18 = 35
Answer: 18 and 35.
Let x be the smaller number; then it'll be 3x = 19 + y
Set the first equation equal to x, then substitute the values and solve.
x + y = 53.
x = 53 - y.
3(53 - y) = 19 + y
x = 18; y = 35
140 - y = y
y = 70.
53 - 70 = -17
x = -17; y = 70.
-17 + 70 = 53;
Suppose you buy a movie for $12.98 the sales tax is 6% find the total cost
Answers
12.98*0.06=0.7788
Add the tax to 12.98, and you get 13.7588
The total cost is 13.76
hope this helps:)
The singing club keeps sheet music in files. Each file holds 12 sheets. Of all the club's music, 2/3 fit into 3 files. How many sheets of music does the club have?
Answers
Now for 3 files -> 3*12 = 36 sheets, it takes up 2/3 of the total
So the total number of sheets: 36 / (2/3) = 54
The singing club has a total of 36 sheets of music.
Explanation:To find the total number of sheets of music the club has, we can set up a proportion using the given information. Since 2/3 of the club's music fits into 3 files, this means that 1/3 of the music fits into 1 file. So, if 1/3 represents 12 sheets, then 1 represents 12 * 3 = 36 sheets. Therefore, the club has a total of 36 sheets of music.
Learn more about Total number of sheets of music here:
https://brainly.com/question/34207074
#SPJ2
5b-2=13 what does b equal
Answers
5b=15 divide both sides by 5
b=3
5b-2=13
add 2 to both sides
5b=15
divide both sides by 5
b = 15/5 = 3
b=3
Use the Distributive Property to simplify each expression:
6(a + 10)
(5 + w)5
14(4f - 8)
2.1(5w -15)
0(3.7x - 4.21)
-(-m + n + 1)
Answers
6a + 60
5w + 25
56 f - 122
10.5 w - 31.5
0
m - n -1
Which equation can be used to calculate the area of the shaded triangle in the figure below? A rectangle is shown with a width of 8 ft and a length of 14 ft. There is a diagonal line through the rectangle, and the bottom half is shaded in grey. 2(14 + 8) = 44 square feet 1 over 2.(14 + 8) = 11 square feet 2(14 × 8) = 224 square feet 1 over 2.(14 × 8) = 56 square feet
Answers
So:
A=xy/2, and x=8 and y=14 in this case so:
A=(8*14)/2 or as you are probably looking at it (which is the same thing)
(1/2)(8*14)=56 square feet.
Answer:
D) 1 over 2. (14 × 8) = 56 square feet
Step-by-step explanation:
You first need to look at the w x h formula (width x height).
W= 14
H= 8
14 x 8= 112
Then, you have to divide 112 by 2. The reason why is because 112 is the area of the whole rectangle, but you only need the area to the triangle, which is half of the rectangle.
112 ÷ 2= 56 sq. ft.
Therefore, the answer is D. Hope this helped!! <3
A pudding recipe makes 4 1/2 cups of pudding. How many 1/3 cup servings does this equal?
Answers
4 1/2 cups = 9/2 cups
9/2 / 1/3=
9/2 * 3/1 = 27/2 = 13 1/2 servings at 1/3 cup each
Answer:
13 1/2
Step-by-step explanation:Just trust