Answers
Answer: <MQR to be 15 degrees
The value of RQ = 9, from the given details, using the sine rule and other properties of triangles.
What is the sine rule?According to the sine rule, in a triangle ABC,
a/sin A = b/sin B = c/sin C
where a = BC, b = AC, and c = AB.
How to solve the question?In the question, we are given a diagram and the following details:
∆PQR, m ∠R = 90° m ∠PQR = 75°, m ∠MQR = 60° M ∈ PR , MP = 18. We are asked to find the value of RQ.
Now, since m ∠PQR = 75° and m ∠MQR = 60°,
we can say that m ∠PQM = m ∠PQR - m ∠ MQR = 75° - 60° = 15°.
In Δ MQR,
m ∠R = 90°, m ∠Q = 60°.
∴ m ∠M = 180° - (m ∠R + m ∠Q) = 180° - (90° + 60°) = 30°. {using angle sum property of triangle}
At point M, m ∠RMQ + m ∠ QMP = 180° {Adjacent angles}
or, 30° + m ∠ QMP = 180° {∵ m ∠RMQ = 30°, calculated above}
or, m ∠ QMP = 180° - 30° = 150°.
Now, in ΔPQM,
m ∠P + m ∠Q + m ∠M = 180°.
or, m ∠P + 15° + 150° = 180°
or, m ∠P + 165° = 180°,
or, m ∠P = 15°.
Since, m ∠P = m ∠Q, Δ QPM is an isosceles triangle, with MP = MQ = 18 {Since, MP = 18 is given}.
Now in ΔRQM, by applying the sine rule, we can say that:
MQ/sin R = RQ/sin M,
or, 18/sin 90° = RQ/sin 30°,
or, RQ = (18*sin 30°)/sin 90° = (18*0.5)/1 {Since, sin 30° = 0.5 and sin 90° = 1},
or, RQ = 9.
Therefore, RQ = 9, using the sine rule.
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Related Questions
Categorize the graph as linear increasing, linear decreasing, exponential growth, or exponential decay. A. linear decreasing B. exponential growth C. exponential decay D. linear increasing
Answers
Answer:
B
Step-by-step explanation:
it is exponential growth because the graph isn't linear and it the rate of change increases, so the only possible answer is b.
Given graph is representing the graph of exponential growth.
What is graph?" Graph is defined as the representation of relation between variables on the coordinates plane along x-axis and y-axis."
According to the question,
As per the given graph,
A. Linear decreasing : It is not a graph of linear decreasing function as it is not representing a straight line which intersect y-axis at (0, k) and x-axis at (h,0).
B. Exponential growth: For exponential growth [tex]y = ab^{x}[/tex] a>0 , b>1.
This graph representing the condition for exponential growth.
C. Exponential decay : For exponential decay [tex]y = ab^{x}[/tex] a >0 , 0 < b < 1.
Therefore , it is not a graph of exponential decay.
D. Linear increasing : It is not a graph of linear increasing function as it is representing a straight line which starts from (0,0) and increasing towards the first quadrant.
Hence, given graph is representing the graph of exponential growth.
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Are quadrilaterals ABCD and EFGH similar?
Answers
Answer:
Option 1
Step-by-step explanation:
To check that quadrilaterals ABCD and EFGH are similar, we'll take the proportion of any of their two sides and check whether they are equal or not.
=> [tex]\frac{3}{2} = \frac{5}{4}[/tex]
Cross Multiplying
=> 3 * 4 = 2 * 5
=> 12 ≠ 10
Since, the proportion is not equal, the quadrilaterals are not similar
a particular dam contains approximately 1,900,000,000,000 cubic feet of water. for a week long spike flood, the dam released at a rate of 24,600 cubic feet per second. how much water was released during the flood?
what percentage of the dam was released during the flood?
Answers
Answer:
a) How much water was released during the flood?
14878080000 cubic feet or 14,878,080,000ft³
b) What percentage of the dam was released during the flood?
0.78%
Step-by-step explanation:
a) How much water was released during the flood?
The first step would be to find out how many seconds are in a week
60 seconds = 1 minute
60 minutes = 1 hour
24 hours = 1 day
7 days = 1 week
Hence, the number of seconds in a week =
1 week × (7 days/1 week)× (24 hours/1 day )×( 60 minutes/1 hour) ×( 60 seconds/1 minute)
= 604800 seconds
Therefore, the quantity of water released per week =
604800 seconds × 24,600 cubic feet per second
= 14,878,080,000 cubic feet or 14,878,080,000ft³
b) What percentage of the dam was released during the flood?
This is calculated as quantity released during the week ÷ Quantity of water in the dam × 100%
Quantity of water released during the flood in a week = 14,878,080,000 cubic feet
Quantity of water in the dam= 1,900,000,000,000 cubic feet of water
Percentage of the dam released during the flood =
14,878,080,000 cubic feet ÷ 1,900,000,000,000 × 100
= 0.7830568421%
Approximately = 0.78%
Graph the data in the table. Which kind of function best models the data? Write an equation to model the data.
x y
0 -6
1 -9
2 -12
3 -15
4 -18
A. quadratic; y = -x^2 - 2x
B. exponential; y = -6 • 1.5x
C. linear; y = -3x - 6
D. quadratic; y = -x^2 + 2x - 6
Answers
Answer: The correct answer is c
Step-by-step explanation: you would have to plot your graph and the put the answer in slop intercept for y=mx+b or y=-3x-6
Answer:
exponential; y = –6 • 1.5x
Step-by-step explanation:
1.5 x 1 = 1.5
1.5x-6= -9
does this graph represents a function? why or why not?
Answers
Answer:
Yes, it passes the vertical line test
Step-by-step explanation:
This graph has a one to one correspondence and will pass the vertical line test, there fore it is a function
Find the coordinates of a point that divides the directed line segment PQ in the ratio 5:3. A) (2, 2) B) (4, 1) C) (–6, 6) D) (4, 5)
Answers
Answer:
The answer is explained below
Step-by-step explanation:
The question is not complete we need point P and point Q.
let us assume P is at (3,1) and Q is at (-2,4)
To find the coordinate of the point that divides a line segment PQ with point P at [tex](x_1,y_1)[/tex] and point Q at [tex](x_2,y_2)[/tex] in the proportion a:b, we use the formula:
[tex]x-coordinate:\\\frac{a}{a+b}(x_2-x_1)+x_1 \\\\While \ for\ y-coordinate:\\\frac{a}{a+b}(y_2-y_1)+y_1[/tex]
line segment PQ is divided in the ratio 5:3 let us assume P is at (3,1) and Q is at (-2,4). Therefore:
[tex]x-coordinate:\\\frac{5}{5+3}(-2-3)+3 \\\\While \ for\ y-coordinate:\\\frac{5}{5+3}(4-1)+1[/tex]
The volume of a cuboidal box is 21952 cubic cm. Find the length of each side of the box.
Answers
Answer:
28 cm
Step-by-step explanation:
V=a³
a= ∛V= ∛21952 cm³ = 28 cm
Answer:
28 is the answer because you have to find the cube root of the volume.Step-by-step explanation:
28 is the answer because you have to find the cube root of the volume. This is because a cube has equal sides so it means that the sides have to be equal. When you find volume, you have to multiply the length, width, and height. So you have to find the cube root of 21952. The cube root is 28.
Hope this helped,
Kavitha
What is the slope of the line with equation y−3=(x−2)?
Answers
Answer:
1
Step-by-step explanation:
The slope of the line (when in point-slope form) will be the coefficient of the term on the right side of the equation. In this case that is 1.
Answer:
1
Step-by-step explanation:
y - 3 = (x - 2)
Solve for y. Then when the equation is in the slope-intercept form, y = mx + b, m is the slope.
y - 3 = x - 2
Add 3 to both sides.
y = x + 1
Compare to y = mx + b: y = 1x + 1
m = 1
Answer: The slope is 1.
Find the x-intercepts for the parabola defined
by this equation:
y=2x^2+ 4x - 6
Write your answer as two ordered pairs:
(x1.yı), (x2, y2)
Answers
Answer:
(-3,0) (1,0)
Step-by-step explanation:
y=2x^2+ 4x - 6
Factor out the greatest common factor
y = 2( x^2 +2x -3)
Factor inside the parentheses
y = 2( x+3)(x-1)
Setting the equation equal to zero to find the x intercepts
0 = 2( x+3)(x-1)
Using the zero product property
x+3 = 0 x-1 =0
x = -3 x = 1
The x intercepts are
(-3,0) (1,0)
Gabe can wrap 1 2/3 presents in 1/3 hour. how many presents can Gabe wrap per hour?
Answers
Answer:
5.06
Step-by-step explanation:
1 2/3 = 1/3
x = 1 (cross multiply)
1/3 x = 1 2/3 (divide both sides by 1/3)
x = 5.06
Sorry the final answer is in decimal. I think better in decimal.
Answer:
Gabe can wrap 5 presents in an hour.
Step-by-step explanation:
So, to find the answer all you have to do is just multiply how many presents he can wrap in 1/3 hours and multiply that by 3. That is then your answer.
Brainliest would be appreciated.
I hope that I was able to help you.
If m∠1 = 3x, m∠3 = 2x + 20 and m∠5 = 30, what is the value of x?
10
20
26
50
Answers
Answer:
50 degrees
Step-by-step explanation:
The diagram is attached below.
Theorem: The Exterior angle of a triangle is equal to the sum of two opposite interior angles.
By the theorem stated above:
m∠3+m∠5=m∠1
2x+20+30=3x
3x-2x=50
x=50
The value of x is 50 degrees.
Answer:
50
Step-by-step explanation:
Find the equation of the line.
Use exact numbers.
Answers
Answer:
y=-3x+7
Step-by-step explanation:
Take a look at the graph and notice the trend that it goes down by three and over one notice that it starts at a y-intercept of 7 so boom there's your equation.
In order to solve for the variable in the equation 1-(x+2)+ 2X= 5(2x-5)- Mikel first applies the distributive property.
Which equation is a result of this step?
O 1 - X+2+2x– 10x-5-X
O 1-x-2+2x– 10x-25-
O 1- x-1+2x = 10x-25- X
O 1-X-1+ 2x - 10x-5-X
Nex
Submit
Save and Exit
Mark this and retum
Answers
The triangular prisms are similar. Find the volume of the larger prism. Round your answer to the nearest hundredth.
A. 85.33 in³
B. 86.38 in³
C. 87.07 in³
D. 88.16 in³
Answers
4)
If the first three Fibonacci numbers are x, = 1, .x = 1, x3 = 2,
what is the value of n for which .x. +x... + x = 68?
Answers
Answer:
The value of n for which xₙ₋₂ + xₙ₋₁ + xₙ = 68 is n = 9
Step-by-step explanation:
The nth term of Fibonacci number is given by the following relation;
[tex]F_n = \dfrac{(1 + \sqrt{5} )^n - (1 - \sqrt{5} )^n }{2^n\sqrt{5} }[/tex]
Given that we have ;
[tex]\Sigma x_n = \dfrac{(1 + \sqrt{5} )^{n-2} - (1 - \sqrt{5} )^{n-2} }{2^{n-2}\sqrt{5} } + \dfrac{(1 + \sqrt{5} )^{n-1} - (1 - \sqrt{5} )^{n-1} }{2^{n-1}\sqrt{5} }+\dfrac{(1 + \sqrt{5} )^{n} - (1 - \sqrt{5} )^{n} }{2^{n}\sqrt{5} }[/tex]When n = 3, we have;
∑xₙ = 4
When n = 4 we have
∑xₙ = 4
When n = 6 we have
∑xₙ = 16
When n = 9 we have
∑xₙ = 68
Therefore, we have the value of n for which xₙ₋₂ + xₙ₋₁ + xₙ = 68 is n = 9.
is this right? someone please help! i’ll give brainliest :)
Answers
Answer:
you're right
Step-by-step explanation:
2 + 5x ≥ 52
5x ≥ 50
x ≥ 10
7 - x > -2
-x > -9
x < 9
Answer: Yes
The only difference between simplifying equations and inequalities is that if you ever divide both sides by a negative, flip the sign.
Hope it helps <3
Hi People, I have another question - Please help. Again, I will mark a Brainliest answer.
Answers
Answer:
Step-by-step explanation:
hello
a)
0+5=5, 1+5=6, 2+5=7, 3+5=8, 4+5=9, ...., 10+5=15
b)
2*0-1=-1, 2*1-1=1, 2*2-1=3, 2*3-1=5, 2*4-1=7, .... 2*10-1=19
hope this helps
Sam always has eggs for breakfast. He either has boiled,
poached or fried eggs.
The probability that he has fried eggs is 0.65 and the
probability that he has poached eggs is 0.25.
a) What is the probability that he has boiled eggs?
b) Work out the probability that
i)He has boiled eggs on the first day and fried
eggs on the second
ii) He has fried eggs both days
iii) He has boiled eggs on at least one day
Answers
Answer:
a) 0.1 [ 0.10 ] probability
Step-by-step explanation:
Workout for a) question
Propability of hving boiled eggs + Propability of hving poached eggs + Propability of hving fried eggs = 100
x + 25 + 65 = 100
x=10
Writing as decimal
x=0.10=0.1
b)
i) 10 percent of hving boiled eggs on first day 65 percent of hving fried eggs in second day
ii) 65 percent of hving fried eggs on both days
iii) 10 percent propability of hving atleat one boiled egg in 1 day
Hope this helps....
Pls mark my answer as brainliest :)
For the decimal 0.09, (a) write a fraction and (b) write a percent.
Answers
Answer:
9/100, 9%
Step-by-step explanation:
0.09 is equal to 9/100
0.09 is equal to 9 percent
Answer:
0.09=9/100
9%
Step-by-step explanation:
0.09=9/100
9%
Which division problem does the diagram below best illustrate? A diagram with 8 ovals containing 4 squares each. 16 divided by 4 = 4 32 divided by 4 = 8 36 divided by 4 = 9 8 divided by 2 = 4
Answers
Answer: 32 divided by 4 = 8
Step-by-step explanation:
If the diagram is 8 ovals with 4 squares each, and we know that this is a division, then we have that an unknown number X is such that:
X/4 = 8
this is because we know that the division is by 4 (the number of squares in each oval) and the solution of the division is the number of ovals.
Then we can solve the equation for X.
X/4 = 8
We multiply each side of the equality by 4
X = 4*8 = 32
Then the diagram represents the division:
32/4 = 8 or " 32 divided by 4 = 8"
Answer:
32 divided by 4 = 8
Step-by-step explanation:
6. Round the following numbers to the place given. 579 032 to the nearest ten thousand _______________________________ B) 9053 to the nearest ten __________________________________ C) 8.045 to the nearest thousandth _______________________________
Answers
Answer:
A: 580 000
B:9050
C:8.045
Step-by-step explanation:
Answer:
A= 580,000
B=9050
C=8.045
Solve the following system of equations by elimination. What is the value of x?
Answers
Answer:
Answer is x = 3
Step-by-step explanation:
x = 2+ 1/2 * 2
x = 3
Answer:
x= 3 and y = 2 is the answer..
WILL AWARD BRAINLIEST
What is the value of x?
Answers
Answer:
Option (3)
Step-by-step explanation:
By applying mean proportional theorem in the given triangle ABC,
[tex]\frac{\text{AD}}{\text{BD}}=\frac{\text{BD}}{\text{CD}}[/tex]
AD × CD = BD²
(x)(4x) = (10)²
4x² = 10²
4x² = 100
x² = [tex]\frac{100}{4}[/tex]
x = [tex]\sqrt{25}[/tex]
x = 5
Therefore, measure of segment AD Or x = 5 units
Option (3) will be the answer.
Type SSS, SAS, ASA, SAA, or HL to justify why the two larger triangles are congruent.
Answers
Answer:
Step-by-step explanation:
a.
x = 40
c.
x = 20
b.
x = 10
d.
x = 15
Answers
Answer:
B
Step-by-step explanation:
Multiply x/20 each side
Answer:
b
Step-by-step explanation:
20/x=2
*x *x
20=2x
:2 :2
10=x
Please Help!
Consider the graph of f(x) on the interval [−6,2] shown.
The local minimum of f(x) is at the point _[blank ]_.
Enter your answer the ordered pair that correctly fills in the blank in the previous sentence, like this: (42, -53)
Answers
This set of 3 numbers are measurements of a right triangle. 26, 24, 10
True
False
Answers
Answer:
True
Step-by-step explanation:
24^2 = 576
10^2 =100
576+100=676
26^2=676
Answer:
True
Step-by-step explanation:
Use the pathagorean theorum:
a squared +b squared=c squared
(the numbers squared)
676, 576, 100
a=576 b=100 c=676
because 676=576+100
is this right? someone help i’ll give brainliest!
Answers
Answer:
yes this is right
Step-by-step explanation: i dont even no the answer i just said its right
Answer:
-10< x< 3
Step-by-step explanation:
Please see attached picture for full solution.
*Sign changes when you divide inequality with a negative number.
Further explanation:
When you add, subtract, divide or multiply an inequality, it applies throughout. This means that from step 1 to 2, if you subtract 1 from the constant 58 to obtain 57, your inequality should be:
19< -6x -3< 57
Note that you do not subtract 1 from the coefficient of x (which means -6x does not become -7x since -7 is not a constant here).
Thus, the easiest way to solve an inequality with 2 inequality signs is to split them up into 2 different inequalities first and solving them separately before combining them into 1 to solve the question.
Heeeeeeeeeeeeeeeeeeeeeeeeeeeeeeelp
Answers
Answer:
1. not possible, 2. a. 65 b. 115 c.115
Step-by-step explanation:
def. sup. <
vertical angles post.
corresponding angles thm.
Answer:
Step-by-step explanation:
(a) 27 degrees: complementary angle is (90 - 27) degrees, or 63 degrees; recall that complementary angles add up to 90 degrees.
(b) Since supplementary angles add up to 180 degrees, we subtract 105 degrees from 180 degrees, obtaining the supplementary angle 75 degrees. There's no complementary angle here, because 105 degrees is greater than 90 degrees.
(c) complementary angle is (90 - 18) degrees, or 72 degrees; supplementary angle is (180 - 18) degrees, or 162 degrees.
These cylinders are similar. Find the surface area of the smaller cylinder. Round to the nearest tenth.
Thank you in advance for your help!
Answers
Answer:
Surface area = 80.4 cm²
Step-by-step explanation:
The diagram of both cylinders is attached below for a better understanding.
First find the radius of larger cylinder:Surface area = 2πrh + 2πr²
236 = 2(3.14)(5)r + 2(3.14)r²
236 = 31.4r + 6.28r²
236 = 6.28(r² + 5r)
35.58 = r² + 5r
r = 3.97 cm
Find the radius of Smaller cylinder:
Two cylinders are in proportion if their heights and radius are in proportion:
Ratio of height of small cylinder to big cylinder = 3/5 = 0.6
So ratio of radius of both is also 0.6
Let R be the radius of small cylinder
ratio of radius of small cylinder to big cylinder = R / 3.97
R = (0.6)(3.97)
R = 2.38
Surface Area for small cylinder:R = 2.38cm and h = 3 cm
Surface area = 2πrh + 2πr²
Surface area = 2(3.14)(2.38)(3) + 2(3.14)(2.38)²
Surface area = 80.4115cm²
Round of to nearest tenth
Surface area = 80.4 cm²