Solve the triangle. Round your answers to the nearest tenth.
Answer Options:
A. m∠B=47, m∠C=28, b=24
B. m∠B=47, m∠C=28, b=28
C. m∠B=43, m∠C=32, b=28
D. m∠B=46, m∠C=29, b=24
Answers
Answer:
Option B
You use sine rule to find the missing angles
Answered by GAUTHMATH
For any triangle ABC, The correct option the given triangle is B. m∠B=47, m∠C=28, b=28.
What is law of sines?For any triangle ABC, with side measures |BC| = a. |AC| = b. |AB| = c,
we have, by law of sines,
[tex]\dfrac{sin\angle A}{a} = \dfrac{sin\angle B}{b} = \dfrac{sin\angle C}{c}[/tex]
Remember that we took,
[tex]\dfrac{\sin(angle)}{\text{length of the side opposite to that angle}}[/tex]
We have been given angle A = 105 degrees and side a = 37, side c = 18.
[tex]\dfrac{sin\angle A}{a} = \dfrac{sin\angle C}{c}\\\\\dfrac{sin\angle 105}{37} = \dfrac{sin\angle C}{18}\\\\sin\angle C = \dfrac{sin\angle 105}{37} \times 18 \\\\sin\angle C = 28[/tex]
By angle sum property;
A + B + C = 180
105 + 28 + B = 180
B = 180 - 133
B = 47
Therefore,
[tex]\dfrac{sin\angle A}{a} = \dfrac{sin\angle B}{b}\\\\\dfrac{sin\angle 105}{37} = \dfrac{sin\angle 47}{b} \\\\b = 28[/tex]
Hence, the correct option the given triangle is B. m∠B=47, m∠C=28, b=28.
Learn more about law of sines here:
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Hai giá sách có 450 cuốn sách .Nếu chuyển 50 quyển từ giá thứ nhất sang giá thứ hai thì số sách ở giá số hai sẽ bằng 4/5 số sách ở giá thứ nhất ?Tính số sách ở mỗi giá.
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Step-by-step explanation:
hơi khó hiểu thông cảm UwU
Line segment QR is dilated to create line segment Q'R' using the dilation rule DT,1.5. Point T is the center of dilation. Line segment Q R is dilated to create line segment Q prime R prime. The length of R T is 6 and the length of R prime R is y. What is y, the distance between points R and R'?
Answers
Answer:
[tex]y= 3[/tex]
Step-by-step explanation:
Given
[tex]RT = 6[/tex]
[tex]k = 1.5[/tex] --- dilation ratio
See attachment
Required
Determine length, y
First, we calculate length R'T.
Since point T is the center of dilation, then:
[tex]R'T = k * RT[/tex]
Substitute known values
[tex]R'T = 1.5 * 6[/tex]
[tex]R'T = 9[/tex]
y is between R'T and RT;
So:
[tex]y = R'T - RT\\[/tex]
[tex]y = 9 -6[/tex]
[tex]y= 3[/tex]
Answer:
either 4 or 9
Step-by-step explanation:
Grandfather Giovanni's hens lay 180 eggs per day, which are placed in containers of 6 each. How many containers will you need per day?
Answers
Answer:
6
Step-by-step explanation:
A square has a perimeter of 4 cm. What is the length of each side?
Answers
Answer:
1 cm
Step-by-step explanation:
Since the perimeter is 4 cm and all the sides of the square have the same length, each side must be 1 cm long.
The area of that square is 1 cm x 1 cm, which is 1 cm2.
Step-by-step explanation:
since the all side is same,the side length is just 1 cm. And the area is just the side length square =1cmsquare× 1 cm
= ans is 1cm^2
Solve the system of equations using the substitution method. -x − 2y = 0 y = -8x (x, y) = ( , )
Answers
Answer:
[tex] = { \tt{(0, \: 0)}}[/tex]
Step-by-step explanation:
Let:
[tex]{ \bf{ - x - 2y = 0 - - - (a)}} \\ { \bf{y = - 8x - - - (b)}}[/tex]
Substitute for y in equation (b) to equation (a):
[tex]{ \tt{ - x - 2( - 8x) = 0}} \\ { \tt{ - x + 16x = 0 }} \\ { \tt{x = 0}}[/tex]
Also, y = 0
Rotate the vector 3,-2 90 degrees clockwise about the origin.
Answers
Answer:
-2,-3
Step-by-step explanation:
Answer:
-2 -3
It worked for me on acellus
Step-by-step explanation:
When simplified and written in standard form, which quadratic function is equivalent to the polynomial shown?
Answers
Answer:
The Polynominal is not shown. So how can i answer???
Step-by-step explanation:
Thank You! Hope it helps! Please Mark me brainliest!
With one method of a procedure called acceptance sampling, a sample of items is randomly selected without replacement and the entire batch is rejected if there is at least one defective unit. The ABCD Electronics Company has just manufactured 7000 write-rewrite CDs, and 180 are defective. If 6 of these CDs are randomly selected and tested, what is the probability that the entire batch will be rejected
Answers
Answer:
[tex]P = 0.1447[/tex]
Step-by-step explanation:
Given
[tex]n = 7000[/tex] -- total
[tex]d = 180[/tex] --- defective
[tex]r = 6[/tex] --- selected
Required
The probability of rejecting the batch
This means that at least one of the selected piece is defected.
So, we first calculate the probability that all the selected piece are accepted.
So, we have:
[tex]Pr = \frac{7000 - 180}{7000} * \frac{6999 - 180}{6999}* \frac{6998 - 180}{6998}* \frac{6997 - 180}{6997}* \frac{6996 - 180}{6996}* \frac{6995 - 180}{6995}[/tex]
The denominator decreases by 1 because it is a probability without replacement; 180 is subtracted from the numerator to represent the number of non-defective CDs
So, we have:
[tex]Pr = \frac{6820}{7000} * \frac{6819}{6999}* \frac{6818}{6998}* \frac{6817}{6997}* \frac{6816}{6996}* \frac{6815}{6995}[/tex]
[tex]Pr = 0.8553[/tex]
Using the complement rule, the probability that the batch will be rejected is:
[tex]P = 1 - 0.8553[/tex]
[tex]P = 0.1447[/tex]
SEE QUESTION IN IMAGE
Answers
Answer:
B. 48°Step-by-step explanation:
∠OST = 90° as ST ⊥ OS (tangent is perpendicular to radius at same point)
m∠OSP = 1/2(180° - m∠SOP) = 90° - 96°/2 = 42° (sum of interior angles of the triangle SOP)
m∠PST = 90° - m∠OSP = 90° - 42° = 48° (angle addition postulate)
Correct choice is B
Find the perimeter of the polygon
Answers
Answer:
Answer 60
Step-by-step explanation:
The distance from an exterior point to the incircle is equal to the tangent length in both cases.
So the 19 is made up of 9 and 10.
The length of the other portion of the tangent from the end of 19 to the tangent point on the right is also 10.
By a similar argument the lower length of the line to the tangent point is 11.
So you have
9 + 9 + 10 + 10 + 11 + 11
18 + 20 + 22 = 60.
Identify the correct explanation and the similarity statement for the similar triangles.
A: By the Isosc. Δ Thm., ∠B ≅ ∠C, so by the Def. of ≅, m∠B = m∠A.
This gives m∠A = 75° by Substitution.
Then, by the Δ Subt. Thm., m∠C = 30°.
Now apply the Isosc. Δ Thm. and the Δ Subt. Thm. to ΔPQR to find that m∠P = m∠Q = 75°.
Therefore ΔABC ~ ΔPQR by SSS ~.
B: By the Isosc. Δ Thm., ∠B ≅ ∠C, so by the Def. of ≅ , m∠B = m∠C.
This gives m∠C = 75° by substitution.
Then, by the Δ Sum Thm., m∠A = 30°.
Now apply the Isosc. Δ Thm. and the Δ Sum Thm. to ΔPQR to find that m∠P = m∠Q = 75°.
Therefore ΔABC ~ ΔPQR by AA ~.
C: By the Isosc. Δ Thm., ∠B ≅ ∠C, so by the Def. of ≅, m∠B = m∠C.
This gives m∠C = 30° by Substitution.
Then, by the Δ Subt. Thm., m∠A = 75°.
Now apply the Isosc. Δ Thm. and the Δ Subt. Thm. to ΔPQR to find that m∠P = m∠Q = 75°.
Therefore ΔABC ~ ΔPQR by SSS ~.
D: By the Isosc. Δ Thm., ∠B ≅ ∠C, so by the Def. of ≅, m∠B = m∠A.
This gives m∠A = 75° by Substitution.
Then, by the Δ Sum Thm., m∠C = 30°. Now apply the Isosc. Δ Thm. and the Δ Sum Thm. to ΔPQR to find that m∠P = m∠Q = 75°.
Therefore ΔABC ~ ΔPQR by AA ~.
Answers
Answer:
Option B
Step-by-step explanation:
From the picture attached,
In ΔABC,
m∠B = m∠C = 75° [Isosceles triangles]
By applying triangle sum theorem,
m∠A + m∠B + mC = 180°
m∠A + 75° + 75° = 180°
m∠A = 180° - 150°
m∠A = 30°
In triangle PQR,
m∠P = m∠Q [Isosceles triangle]
By applying triangle sum theorem,
m∠P + m∠Q + m∠R = 180°
2(m∠P) + 30° = 180°
m∠P = 75°
m∠P = m∠Q = 75°
In ΔABC and ΔRPQ,
m∠B ≅ m∠Q [Given]
m∠C ≅ m∠R [Given]
Therefore, by AA property of similarity of two triangles, both the triangles will be similar.
ΔABC ~ ΔRPQ
Option B will be the answer.
write in simplest form :
36 minutes to 3/2hrs
Answers
Answer:
⅗hrs
Step-by-step explanation:
1hr =60 min
? = 36 min
cross-multiply .........
36 min × 1hr/60 min= 36min/60min × 1hr
=36/60 × 1 hr
= ⅗hrs
Will give brainliest need a quick answer
Answers
6c+5c+37=180
11c+37=180
11c=143
c=13
Then if you need the values of the angles, just substitute 13 for c.
Here are the ages (in years) of 12 professors at a college.
51, 34, 56, 48, 37, 39, 59, 53, 52, 45, 3367
What is the percentage of these professors who are younger than 50?
=__%
Answers
Answer:
50%
Step-by-step explanation:
6 professors younger than 50 years = 6/12 = 50
Answer:
%50
Step-by-step explanation:
If you count the number of proffessors that are under 50, there are six. If there are 12 proffessors then it would be 1/2. One half in percentage is %50.
Pls give Brainliest!
What is the circumference, in inches, of the front tire of Susan’s bike?
Answers
Answer:
The bike will travel approximately 1,272 inches or 106 feet.
Step-by-step explanation:
The diameter of a circle (wheel) can be used to find the circumference, which is the total perimeter around the wheel. The formula used to find circumference is: C = dπ, where 'd' is the diameter and π = 3.14. In this case C = 27 x 3.14 ≈ 84.78 inches. Since this measurement represents the perimeter of wheel, we would need to multiply this number by 15 in order to find the total distance after 15 complete rotations of the wheel: 84.78 x 15 ≈ 1,272 inches. 1,272 inches is a large measurement, so we can easily convert this to feet by dividing by the number of inches per foot, or 12: 1272/12 = 106 feet.
Hope this answer helps you :)
Have a great day
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A pizza delivery man makes $50.00 a shift. If he makes $3.00 on each delivery he makes, how much
money will he make, if he makes 22 deliveries in one shift. Create an equation to represent this
situation. Write the equation in function notation. State the ordered pair for 22 deliveries and explain
your solution.
Answers
Answer:50+(3x22)=116
Step-by-step explanation:
Given: The equation of a parabola is x2 = 8y.
Step 3: Where does the directrix for the given parabola lie? Enter the equation for the directrix line. Use your keyboard and the keypad to enter your answer. Then click Done.
Answers
Answer:
x=-2
Step-by-step explanation:
Answer:
Since a = 2, the equation for the directrix line will be y = −2.
Step-by-step explanation:
PLSSS HELP MEE
Equation: c = n
Is there any way for this equation to be true? How?
Answers
Step-by-step explanation:
if
c = 3 + 6 = 9
and
n = 4 + 5 = 9
then it could be true
40 POINTS- please help me
Answers
Answer:
a, c, d,
Step-by-step explanation:
I'm not sure if this is right but i think.
First you cant have exponents in a linear equation, so its not e or f. Then i just graphed the rest.
One side length of a rectangle is 1/3 of a foot. The second length is 1 2/3 times the length of the first. Find the area of the rectangle.
Answers
Answer:
5/27 ft²
Step-by-step explanation:
a = 1/3
b = 1/3 × 5/3 = 5/9, as 1 2/3 = 5/3
the area of the rectangle is a×b
Ar = 1/3 × 5/9 = 5/27 ft²
Answer the question written in the image.
Answers
Answer: 28
Step-by-step explanation:
The pattern is multiply the right and bottom, add the left
For example, 9*8+7=79
So, 24*3+x=100
72+x=100
x=28
Please solve this:
[tex] {2}^{y - 3} \times {3}^{2y - 8} = 36[/tex]
Solve for y.
Explain please!!
Answer only if you can.
Answers
Answer:
y is 5.
Step-by-step explanation:
[tex]{ \sf{{2}^{y - 3} \times {3}^{2y - 8 } = 36}} \\ \frac{ {2}^{y} }{ {2}^{3}} \times \frac{ {3}^{2y} }{ {3}^{8} } = 36 \\ \\ {2}^{y} . {3}^{2y} = 36 \times {2}^{3} \times {3}^{8} [/tex]
Introduce log base 10:
[tex] log_{10}( {2}^{y} \times {3}^{2y} ) = log_{10}(36 \times {2}^{3} \times {3}^{8} ) \\ log_{10}( {2}^{y} ) + log_{10}( {3}^{2y} ) = 6.28 \\ y log_{10}(2) + 2y log_{10}(3) = 6.28 \\ 0.3y + 0.95y = 6.28 \\ 1.25y = 6.28 \\ y = 5[/tex]
Determine the y-intercept of the quadratic equation Y = x^2 - 4x + 8
Answers
9514 1404 393
Answer:
(0, 8)
Step-by-step explanation:
The y-value of the y-intercept is the function value when x=0. That is the constant in the equation, since x=0 will make all of the x-terms be zero.
y-intercept = 8
log 55 is the power to which ---- must be raised in order to produce a value of 55
Answers
Answer:
10
Step-by-step explanation:
just took the quiz
pls for the LOVE OF GOD. i can't do graphs
Answers
Answer:
Second Option
Step-by-step explanation:
We need to graph the equation
[tex]y = \frac{2}{3} x - 1[/tex]
The -1 represent the y intercept. So our y intercept will be at (0,-1).
We then would move up 2 and right 3 units because that represent our slope. So the second option.
When (8x − 4) = 2x is solved, the result is:
Answers
Answer:
x = 1
General Formulas and Concepts:
Pre-Algebra
Distributive Property
Equality Properties
Multiplication Property of EqualityDivision Property of EqualityAddition Property of EqualitySubtraction Property of EqualityAlgebra I
Terms/CoefficientsStep-by-step explanation:
Step 1: Define
Identify
1/2(8x - 4) = 2x
Step 2: Solve for x
[Distributive Property] Distribute 1/2: 4x - 2 = 2x[Subtraction Property of Equality] Subtract 2x on both sides: 2x - 2 = 0[Addition Property of Equality] Add 2 on both sides: 2x = 2[Division Property of Equality] Divide 2 on both sides: x = 1Answer:
x = 2/3
Step-by-step explanation:
(8x − 4) = 2x
8x - 4 = 2x
6x = 4
x = 2/3
Simplify this expression: 4(1 – 26) + 76 – 10.
Answers
Answer:
-b - 6
Step-by-step explanation:
4(1 - 2b) + 7b - 10
Apply the distributive property:
4(1 - 2b) + 7b - 10
(4)(1) + (4)(−2b) + 7b + (−10)
4 + (−8b) + 7b + (−10)
Combine like terms:
4 + −8b + 7b + −10
(−8b + 7b) + (4 - 10)
-b - 6
Answer:
-b - 6
Step-by-step explanation:
4 (1 - 2b) + 7b - 10
4 - 8b + 7b - 10
-b - 6
determine the equation of a line that is vertical and goes through (-5,6)
Answers
Answer:
x = -5
Step-by-step explanation:
A vertical line is a line that goes up and down. It is of the form x = constant
To go through (-5,6) is has to have the value of the x coordinate
x = -5
Select the correct answer.
Which is the correct simplified form of the expression ?
A.
B.
C.
D.
Answers
Answer:
it should be letter b sorry if its wrong
the answer should be choice B
Does this graph represent a function? Why or why not?
A. Yes, because it passes the vertical line test.
B. No, because it is not a straight line.
C. No, because it fails the vertical line test.
D. Yes, because it has two straight lines.
Answers
Answer:
with my own opinion the answer is b
