Answer:
Step-by-step explanation:
2/a = 1/b - 1/d
2d/a = d/b - 1
2d/a - d/b = -1
d(2/a - 1/b) = -1
d(2b-a)/(ab) = -1
d(a-2b)/(ab) = 1
d = ab/(a-2b)
In ΔABC, m∠A=a, m∠B=β, m∠C=y. AB = c, AC = b, BC = a. Find the remaining parts of each triangle if the following parts are given.
a=6.00, b=7.56, y = 54°
Answer:
c=6.31, a=50.28 degrees, B=75.72 degrees
Step-by-step explanation:
The sine rule of trigonometry helps us to equate the side of the triangles to the angles of the triangles. The remaining parts of the triangle can be found as shown.
What is Sine rule?The sine rule of trigonometry helps us to equate the side of the triangles to the angles of the triangles. It is given by the formula,
[tex]\dfrac{Sin\ A}{\alpha} =\dfrac{Sin\ B}{\beta} =\dfrac{Sin\ C}{\gamma}[/tex]
where Sin A is the angle and α is the length of the side of the triangle opposite to angle A,
Sin B is the angle and β is the length of the side of the triangle opposite to angle B,
Sin C is the angle and γ is the length of the side of the triangle opposite to angle C.
Given that the length of side a and b is 6 and 7.56, also, the measure of the angle γ is 54°.
Now, Using the law of cosine, we can write,
[tex]c =\sqrt{a^2 + b^2 -2ab\cdot \cos\gamma}[/tex]
[tex]c =\sqrt{(6)^2 + (7.56)^2 -2(6)(7.56)\cdot \cos(54^o)}[/tex]
c = √39.8297
c = 6.311
Now, using the sine law the ratio of the sides and angles can be written as,
[tex]\dfrac{\sin\alpha}{a} =\dfrac{\sin\beta}{b} =\dfrac{\sin\gamma}{c}[/tex]
[tex]\dfrac{\sin\alpha}{6} =\dfrac{\sin\beta}{7.56} =\dfrac{\sin (54^o)}{6.311}[/tex]
[tex]\dfrac{\sin\alpha}{6}=\dfrac{\sin (54^o)}{6.311}[/tex]
α = 50.2775°
[tex]\dfrac{\sin\beta}{7.56} =\dfrac{\sin (54^o)}{6.311}[/tex]
β = 75.726°
Hence, the remaining parts of the triangle can be found as shown.
Learn more about Sine Rule here:
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Solve for x: -5 < 8x + 11 < 19
Answer:
-2<x<1
Step-by-step explanation:
-5 < 8x + 11 < 19
Subtract 11 from all sides
-5-11 < 8x + 11-11 < 19-11
-16 < 8x<8
Divide by 8
-16/8 < 8x/8 <8/8
-2<x<1
what is the probability of choosing a green marble from a jar containing five red, 6 green, and four blue marbles
Answer:
6/15
Step-by-step explanation:
add all the marbles up and you get 15
6 green ones out of 15 marbles
Answer:
2/5
Step-by-step explanation:
6 green+5 red+4 blue = 15 marbles
P(green) = number of green/ total
= 6/15 = 2/5
Match all the part of the circle to their correct name.
1. YW
2. Q
3. WX
4. W
5. ST
6. VQ
7. TW
a. Center
b. Secant Line
c. Chord
d. Radius
e. Point of Tangency
f. Diameter
g. Tangent Line
Answer:
halo
1. YW - chord
2. Q - center
3. WX - tangent line
4. W - point of tangency
5. ST - secant line
6. VQ - radius
7. TW - diameter
please mark brainliest???
The correct matches are,
1. YW - chord
2. Q - center
3. WX - tangent line
4. W - point of tangency
5. ST - secant line
6. VQ - radius
7. TW - diameter
What is diameter?In geometry, a diameter of a circle exists as any straight line segment that passes via the center of the circle and whose endpoints lie on the circle. It can also be described as the longest chord of the circle. Both descriptions exist also valid for the diameter of a sphere.
The correct matches are,
1. YW - chord
2. Q - center
3. WX - tangent line
4. W - point of tangency
5. ST - secant line
6. VQ - radius
7. TW - diameter
To learn more about diameter refer to:
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Find the area of this circle. Use 3 for .
A = r2
12 cm
[?] cm2
Answer:
452.16 cm²
Step-by-step explanation:
Given :-
Radius = 12cm .To find :-
Area of circle .Solution :-
As we know that ,
A = πr² A = 3.14 * (12 cm)² A = 3.14 * 144cm² A = 452.16 cm²Step-by-step explanation:
[tex]area = \pi {r}^{2} \\ = \pi \times {12}^{2} \\ = \pi \times 144 \\ = 3.14 \times 144 \\ = 452.16 {cm}^{2} \\ thank \: you[/tex]
There are 3200 students at Lake High School and 2/5 of these students are sophomores. If 3/8 of the sophomores are opposed to the school forming a crew team and 1/8 of the remaining students (not sophomores) are also opposed to forming a crew team, how many students are in favor of this idea?
Answer:
4
Step-by-step explanation:
2/5*3000 = 1200 seniors
then
3000 - 1200 = 1800 students not seniors
therefore
4/5* 1200 = 960 do not like rock climbing
and
9/10** 1800 = 1620 also do not like it:
"how many students are in favor of this idea?"
subtract the "don't likes" from 3000
3000 - (960+1620) = 420 like rock climbing:
3x-x+2=4
Step-by-step explanation:
here's the answer to your question
15) A new BMW decreases in value exponentially after it is purchased. If a new BMW is valued at $55,000 and
depreciate at a rate of 22% a year, what is the value after 4 years? After 8 years)
The values of BMW after 2, 4 and 8 years according to the EXPONENTIAL FUNCTION are $33,462, $20,358.28 and $7,535.63 respectively.
Using the parameters given, we define an decreasing exponential function :
[tex]A = A_{0} (1 - r)^{t}[/tex]
Where,
[tex]A_{0}[/tex] = initial amount ; r = Rate ; t = time ; A = final amount
Value after 2 years :
t = 2
A = 55000(1 - 0.22)²
A = 55000(0.78)²
A = $33,462
Value after 4 years :
t = 4
A = 55000(1 - 0.22)^4
A = 55000(0.78)^4
A = $20,358.28
Value after 8 years :
t = 4
A = 55000(1 - 0.22)^8
A = 55000(0.78)^8
A = $7,535.63
Therefore, the value of BMW after 2, 4 and 8 years are $33,462, $20,358.28 and $7,535.63 respectively.
Learn more about Exponential functions :
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HELP FAST! D: TWENTY POINTS
A group of friends goes Sky diving, using a parachute to fall in a straight line from (1,45) to (3,36). If they keep going in a straight line, at what coordinates will they land on the x-axis?
Answer:
0 =-4.5X +49.5
x = 11
Step-by-step explanation:
x1 y1 x2 y2
1 45 3 36
(Y2-Y1) (36)-(45)= -9 ΔY -9
(X2-X1) (3)-(1)= 2 ΔX 2
slope= -4 1/2
B= 49 1/2
Y =-4.5X +49.5
Which function is represented by this graph?
Answer:
it is an absolute function
or more precisely
y = - I x - 1 I + 8 (shown in the screenshot)
PLS HELP ME ON THIS QUESTION!!!
Answer:
210 in³
Step-by-step explanation:
length = 10 in
Width = 7 in
Height = 3 in
Volume of rectangular prism = length * width * height
= 10 * 7 * 3
= 210 in³
Answer: Option D
210 in³
Volume of Rectangular prism = lwh
Height = 3in
Width = 7in
Length = 10in
Volume = 10(7)(3)
Volume = 210 in³
Must click thanks and mark brainliest
Use the identity property to answer the question.
Answer:
3k + 0 = 3k
Step-by-step explanation:
Identity property of addition states that the sum of 0 and the term would result in the term.
∴ in this case, 3k + 0 will result in 3k.
~
Identify a transformation of the function f(x) = x by observing the equation of
the function g(x) = VX+3.
Answer:
1st option
Step-by-step explanation:
Given f(x) then f(x + a) is a horizontal translation of f(x)
• If a > 0 then a shift left of a units
• If a < 0 then a shift right of a units
Here g(x) = [tex]\sqrt{x+3}[/tex]
The base graph f(x) has been shifted left 3 units
This equation shows how the total number of necklaces Denise owns is related to the amount of money she spends on additional necklaces.
n = d + 74
The variable d represents the amount of money she spends on additional necklaces, and the variable n represents the total number of necklaces she owns. With $16 to spend on new necklaces, how many total necklaces can Denise own?
help me to solve tan^3 2x-3tan2x+2=0
Answer:
Step-by-step explanation:
let tan 2x=y
y³-3y+2=0
y³-y-2y+2=0
y(y²-1)-2(y-1)=0
y(y+1)(y-1)-2(y-1)=0
(y-1)[y(y+1)-2]=0
(y-1)(y²+y-2)=0
(y-1)(y²+2y-y-2)=0
(y-1)[y(y+2)-1(y+2)]=0
(y-1)(y+2)(y-1)=0
y=1,1,-2
tan 2x=1=tanπ/4=tan (nπ+π/4)=tan π/4(n+1)
2x=π/4(n+1)
x=π/8(n+1)
where n is an integer.
tan 2x=-2
[tex]2x=tan^{-1}(-2)\\x=\frac{1}{2} tan^{-1}(-2)[/tex]
This two-way frequency table shows the results of a survey of users of the mass-transit system in a city. People were asked their age and whether they used the system regularly (three or more times per week).
Answer:
if Q={1,3,5,7,9}Express it in description methods
Answer: With the condition that age is 30 or under, the sample space is restricted to the first column. This simplifies the problem to:
P(uses mass transit |age is 30 or under) = 125/575=0.217
Step-by-step explanation:
edmentum
Write the polynomial in standard form 8-5x+x^3-2x^4
Answer:
-2x^4+x^3-5x+8
Step-by-step explanation:
8-5x+x^3-2x^4
Write the polynomial from highest powers of x to lowest
-2x^4+x^3-5x+8
A diameter of a circle is 12 inches. What's the distance when rotate 3 circle ?
Answer:
36π inches which is 113.10 inches to the nearest hundredth
Step-by-step explanation:
The circumference = 12 * π
Rotating 3 times the distance moved is 3 * 12π.
HELP ILL GIVE BRAINLIEST
Answer:
linear increasing
Step-by-step explanation:
For the section labeled B, the line goes up as x increases. This means the line is increasing
Answer:
Linear increasing
Step-by-step explanation:
The slope of interval B is constant since it's a straight line, which makes it linear. The line in interval B is pointing upward so it's increasing.
1. 9+x-7
2. 8-2x+5x
3. -x-9+3x
4. 4x-6-4x
Answer:
1)9-7+x
2+x
2)8-2x+5x
8+3x
3)-x+3x-9
2x-9
4)4x-4x-6
-6
you have to group the like terms
I hope this helps and sorry if they are wrong
solve 7y 4/y 2 = -4/3
Answer:
Step-by-step explanation:
(7y+4)/(y+2)=-4/3
[tex]\dfrac{7y+4}{y+2}=\dfrac{-4}{3}\\\\[/tex]
Cross multiply,
(7y + 4) * 3 = -4*(y+ 2)
Use distributive property,
7y*3 + 4*3 = -4*y + 2*(-4)
21y + 12 = -4y - 8
Subtract 12 from both side
21y = -4y - 8 - 12
21y = -4y - 20
21y + 4y = -20
25y = -20
y = -20/25
[tex]y=\dfrac{-4}{5}[/tex]
[tex]\\ \sf\longmapsto \dfrac{7y+4}{y+2}=\dfrac{-4}{3}[/tex]
[tex]\\ \sf\longmapsto 3(7y+4)=-4(y+2)[/tex]
[tex]\\ \sf\longmapsto 21y+12=-4y-8[/tex]
[tex]\\ \sf\longmapsto 21y+4y=-8-12[/tex]
[tex]\\ \sf\longmapsto 25y=-20[/tex]
[tex]\\ \sf\longmapsto y=\dfrac{-20}{25}[/tex]
[tex]\\ \sf\longmapsto y=\dfrac{-4}{5}[/tex]
Question 2 Evaluate the expression 2(x - 3) + 3y when x = 5 and y = 3. Mark the correct answer.
A. 13
B. 15
C. 16
D. 25
Answer:
A. 13
Step-by-step explanation:
2(x - 3) + 3y
2(5 - 3) + 3×3
2× 2 + 3×3
4 + 9
13
Answer:
The correct answer is A
Step-by-step explanation:
2(x-3) + 3y so you replace them and get 2( 5 - 3) +3(3)
next,
you would solve it
2 x 5 and 2 x 3 you get 10-6 + 9, the 9 is from multiplying 3 by 3
finally you solve it
10-6 = 4 +9
= 13!
11. solve for x!
please help:(
[tex]\\ \sf\longmapsto 2(4x-1)+3(3-2x)=0[/tex]
[tex]\\ \sf\longmapsto 8x-2+9-6x=0[/tex]
[tex]\\ \sf\longmapsto 8x-6x-2+9=0[/tex]
[tex]\\ \sf\longmapsto 2x+7=0[/tex]
[tex]\\ \sf\longmapsto 2x=-7[/tex]
[tex]\\ \sf\longmapsto x=\dfrac{-7}{2}[/tex]
Ai đó giúp mình với. Bài này mình không nghĩ ra cách giải
Answer:
-3 -2. 1 0 2 3 -2 3Step-by-step explanation:
please make it a brainliest answer.
A company prices its tornado insurance using the following assumptions:
• In any calendar year, there can be at most one tornado.
• In any calendar year, the
probability of a tornado is 0.15.
. The number of tornadoes in any calendar year is independent of the number of tornados in any other
calendar year.
Using the company's assumptions, calculate the probability that there are fewer than 3 tornadoes in a 19 year period.
Answer:
.441320612
or
44.132%
Step-by-step explanation:
This is binomial
fewer than 3 is equal to p(0)+p(1)+p(2)
[tex]p(0)={19\choose0}*.15^0*(1-.15)^{19}=.045599448\\p(1)={19\choose1}*.15^1*(1-.15)^{18}=.152892268\\p(2)={19\choose2}*.15^2*(1-.15)^{17}=.242828896\\p(0)+p(1)+p(2)=.441320612[/tex]
A father is now twice as old as his son. If the sum of their ages ten years ago was fifty two, how old are they today?
Answer:
24 and 48
Today, the son is 24 years old, and the father is 48 years old.
Step-by-step explanation:
(x - 10) + (2x - 10) = 52
3x + 20 = 52
3x = 72
x = 24
The father is 2 times his son's age.
2x
= 2(24)
= 48
So, the son is 24 and the father is 48.
10 years ago, son was 14 and father was 38, if added, this adds up to 52, so we know our calculations are correct.
Answer:
So the son’s age is 24 and the father’s is 48. Ten years ago, they were 14 and 38, which adds up to 52.
Step-by-step explanation:
If the son’s age is x, the father’s age is 2x.
Ten years ago:
(x - 10) + (2x - 10) = 52
3x + 20 = 52
3x = 72
x = 24
2x = 48
What is the value of the expression below when w=2 and x=2
9w - x
Here, all we need to do is subtitute w = 2 and x = 2 into the expression, by multiplying and adding. First, we will muliply 9w:
9w
9 · w =
9 · 2 =
18
Now, all we have to do is use our answer for 9w, and subtract x from it:
9w - x
18 - (2) =
18 - 2 =
16
So, our answer is 16.
Let me know if you have any other questions! :)
A fruits seller bought some lemon for Re 1 for 15 lemon. if he sold all lemons at 25% profit, how many lemons were sold for Rs 1.
Answer:
12 lemons
Step-by-step explanation:
CP of 15 lemon = ₹ 1
Profit = 25 %
SP of 15 lemons = [tex]\frac{100+profit}{100}*CP[/tex]
[tex]= \frac{125}{100}*1\\\\= \frac{5}{4}[/tex]
SP of 15 lemons = ₹ [tex]\frac{5}{4}[/tex]
Number of lemon for ₹ [tex]\frac{5}{4}[/tex] = 15
Number of lemons for ₹ 1 = 15 ÷ [tex]\frac{5}{4}[/tex]
[tex]= 15 *\frac{4}{5}\\\\= 3*4\\\\= 12[/tex]
Anyone here who can help me with this?
Answer:
D. 16 years old
Step-by-step explanation:
Step 1: Let T be Tien's age and J as Jordan's age (today),
[tex]T=\frac{1}{4}J[/tex]
Step 2: Let T be Tien's age and J as Jordan's age (in 2 years),
[tex]T+2=\frac{1}{3} (J+2)[/tex]
[tex]T=\frac{1}{3}(J+2)-2[/tex]
Step 3: As their age differences will always be similar we can have the two equations above equal to find Jordan's age,
[tex]\frac{1}{4} J=\frac{1}{3}(J+2)-2\\\frac{1}{4}J-\frac{1}{3}J=\frac{2}{3} -2 \\-\frac{1}{12}J= -\frac{4}{3} \\\\J=16[/tex]
Find the approximate side length of a square game board with an area of 128 in2. HELP PLZ
Answer:
The side length is approximately 11.3 inches
Step-by-step explanation:
The area of a square is given by
A = s^2 where s is the side length
128 = s^2
Take the square root of each side
sqrt(128) = sqrt(s^2)
11.3137085= s
The side length is approximately 11.3 inches
Answer:
11.3
Step-by-step explanation:
Formula for square: x^2 = A
Plug in:
x^2 = 128
√x^2 = √128
x = 11.3
Hope this helped.
Which is the correct answer?
Answer:
a reflection in the y axis followed by a translation 1 unit down
Step-by-step explanation:
Reflection over the y-axis then a unit down
