Answers
[tex]\text{In}~ \triangle ABC,\\\\~~~~~~~~\sin 45^{\circ} =\dfrac{BC}{AC} \\\\\implies \dfrac 1{\sqrt 2} = \dfrac{BC}{6\sqrt 2}\\\\\\ \implies BC= 6\\\\\text{Now, In}~ \triangle BCD\\\\~~~~~~\cos 60^{\circ} = \dfrac{BD}{BC}\\\\\ \implies \dfrac 12 = \dfrac{x}{6}\\\\\\\implies x = \dfrac 62\\\\\\\implies x = 3[/tex]
Answer:
x = 3
Step-by-step explanation:
using the sine ratio in right triangle ABC and the exact value
sin45° = [tex]\frac{1}{\sqrt{2} }[/tex] , then
sin45° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{BC}{AC}[/tex] = [tex]\frac{BC}{6\sqrt{2} }[/tex] = [tex]\frac{1}{\sqrt{2} }[/tex] ( cross- multiply )
BC × [tex]\sqrt{2}[/tex] = 6[tex]\sqrt{2}[/tex] ( divide both sides by [tex]\sqrt{2}[/tex] )
BC = 6
using the cosine ratio in right triangle BCD and the exact value
cos60° = [tex]\frac{1}{2}[/tex] , then
cos60° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{BD}{BC}[/tex] = [tex]\frac{x}{6}[/tex] = [tex]\frac{1}{2}[/tex] ( cross- multiply )
2x = 6 ( divide both sides by 2 )
x = 3
Related Questions
Find the area of the regular polygon 10, 4
Answers
A triangle has sides with lengths of 10 millimeters, 25 millimeters, and 28 millimeters, is it a right triangle
Answers
Answer:
No, it is not a right triangle.
Step-by-step explanation:
Let's take it as,
→ Hypotenuse = 28 mm
→ Perpendicular = 25 mm
→ Base = 10 mm
Now use Pythagoras theorem,
→ Hypotenuse² = Perpendicular² + Base²
→ 28² = 25² + 10²
→ 784 = 625 + 100
→ 784 ≠ 725
→ [ LHS ≠ RHS ]
Hence, it does not forms a right triangle.
What is the probability of a red on this spinner?
Be sure to reduce.
? 1
Answers
Answer:
1/4 is the correct answer
Suppose A and B are dependent events. If P(AIB) = 0.55 and P(B) = 0.3, what is P(AB)?
A. 0.22
B. 0.11
C. 0.165
D. 0.275
Answers
Answer: C. 0.165
Step-by-step explanation:
The value of P(A∪B) = 0.835
What is probability?Probability is a measure of the likelihood of an event to occur. Many events cannot be predicted with total certainty. We can predict only the chance of an event to occur i.e., how likely they are going to happen, using it.
Given that, A and B are dependent events. If P(AIB) = 0.55 and P(B) = 0.3,
0.55 = P(A∩B) / 0.3
P(A∩B) = 0.165
P(A) = 1-P(B)
P(A) = 1-0.3
P(A) - 0.7
P(A∪B) = P(A) + P(B) - P(A∩B)
P(A∪B) = 0.3+0.7-0.165
P(A∪B) = 0.835
Hence, the value of P(A∪B) = 0.835
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240inches equals how many feet
Answers
Since 12 inches = 1 foot
If you were to track coffee preferences among your co-workers for the next two weeks, which type of statistical study would you be performing? (statistics)
Answers
Answer:
Well I would say inferntial because its more testing your hyptohsis between two friends to see which coffe they like more
Sam wants to rent a boat and spend less than $37. The boat costs $6 per hour, and Sam has a discount coupon for $5 off. What are the possible numbers of hours Sam could rent the boat? Use t for the number of hours. Write your answer as an inequality solved for t.
Answers
What is the simplest form of StartRoot 3,025 EndRoot?
16
55
52(112)
52+(112)
Answers
Find the perimeter of ABC
Answers
Answer:
36 ft
Step-by-step explanation:
[tex]\triangle ABC\sim\triangle DEF[/tex] (Given)Perimeters and corresponding sides of similar triangles are in proportion[tex]\implies\frac{P( \triangle ABC)}{P(\triangle DEF)}=\frac{BC}{EF}[/tex] [tex]\implies\frac{P( \triangle ABC)}{12}=\frac{15}{5}[/tex] [tex]\implies\frac{P( \triangle ABC)}{12}=3[/tex] [tex]\implies P( \triangle ABC) =12(3)[/tex] [tex]\implies P( \triangle ABC) =36 \: ft[/tex]Can you guys help me please :(
Answers
Answer:
Step-by-step explanation:
18:44yd x 27 yd = 1188 yd,
then subtract the two unshaded squares, 2 x (22 x 6) = 264
1188 - 264 = 924[tex]yd^{2}[/tex]
What equation would you use to solve for x?
Answers
Answer:
x² + 6.8² - 10.6²
Step-by-step explanation:
This is probably wrong there
Answer:
First option [tex]x^{2} +6.8^{2} -10.6^{2}[/tex]
Step-by-step explanation:
[tex]x^{2} +6.8^{2} -10.6^{2}=0[/tex]
[tex]x^{2} =10.6^{2} -6.8^{2}[/tex]
10.6 = hypotenuse, 6.8 and "x" are cathets
Hope this helps
Solve the following equation. 14 = w2
Answers
Take 2 divided by 2 and 14 divided by 2
7=w
Kathleen says that all quadrilaterals have right angles. Grace says that quadrilaterals do not have to have right angles. Explain who is correct.
Answers
Answer: Grace is correct because a rhombus does not have right angles
Step-by-step explanation:
Grace's assertion is on point. Right angles are not present in all quadrilaterals.
What is quadrilateral?A quadrilateral in geometry is a four-sided polygon with four edges and four corners.
As per the definition of Quadrilateral and rectangle, the rectangle is the type of quadrilateral that has 4 right angles.
Other varieties of quadrilaterals consist of:
Trapezium: Doesn't must have four right angles, but has one pair of opposite sides that are parallel.
A parallelogram has four right angles, but not necessarily two sets of opposite sides that are parallel.
All four sides of a rhombus are equal in length, although there aren't always four right angles.
Kite: Does not must have four right angles, but two adjacent pairs of sides that are equal in length.
Therefore, Grace's assertion is right.
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The following table gives data relating the intensity of exercise on a scale of 0-1 and the pulse rate of the person. If the intensity were to increase to 0.90(assuming. the rate stays the same), approximately what would be the associated pulse rate?
SHOW STEPS
Answers
Answer: [tex]The[/tex] [tex]answer[/tex] [tex]is[/tex] [tex]C.[/tex] [tex]200[/tex]
Step-by-step explanation:
[tex]I ~can ~see ~that ~it ~does~ not ~appear ~to ~be[/tex] [tex]LINEAR[/tex]
[tex]y = 73e^kx[/tex] [tex]< ---~pulse~rate[/tex]
[tex].7[/tex] [tex]when[/tex] [tex]y = 155[/tex] [tex]< ---~sub ~in ~x[/tex]
[tex]155 = 73 e^(.7 * k)[/tex]
[tex]ln ( 155/73) = .7k[/tex]
[tex].75296567 = .7k[/tex]
[tex]k = 1.07567[/tex]
[tex]for[/tex] [tex]x = 0.9 :[/tex] [tex]pulse rate = y = 73 e^(1.07567[/tex] [tex]^. .9) = ~ 192[/tex]
[tex]Therefore~your~answer~is:~C.~200[/tex]
Write a simplified expression that represents the...
a. area of the large rectangle.
b. area of the small rectangle.
c. area of shaded region.
Answers
Answer:
See below
Step-by-step explanation:
a.
Area of the large rectangle = (6 + x) (6 - x)->Area of the large rectangle [tex]=(6)^2-x^2[/tex]-> Area of the large rectangle [tex]= 36-x^2[/tex]b.
Area of the small rectangle = (2 + x) (2 - x)->Area of the small rectangle [tex]=(2)^2-x^2[/tex]->Area of the large rectangle [tex]= 4-x^2[/tex]c.
Area of shaded region = Area of the large rectangle - Area of the small rectangle-> Area of shaded region [tex]=( 36-x^2)-(4-x^2)[/tex]-> Area of shaded region = [tex]=36-x^2-4+x^2[/tex]-> Area of shaded region [tex]=32 \:units^2[/tex]The radius of a circle is 19 meters. What is the circle's circumference?
r=19 m
Use 3.14 for .
Answers
Answer:
59.66
Step-by-step explanation:
Use the graph to complete the table.
Answers
(12, 7)
(14, 9)
Solve: h9 = 2781
this is a fun fact belh bla
Answers
Answer:
309
Step-by-step explanation:
2781/9
pls help
find f(p-5)
Answers
[tex]\text{Given that,}~f(j) = -5j-4\\\\f(p-5) = -5(p-5) -4\\\\~~~~~~~~~~~~=-5p+25-4\\\\~~~~~~~~~~~~=-5p+21[/tex]
Pema is 85 months old and Rinzin is 7⅔ years old. who is older? How do you know?
help me slove this please
Answers
Answer:
Rinzin is older
Step-by-step explanation:
The reason is that since you probably already know that there are 12 months in a year it would be 85/12=7.0833 years and 23/12=7.666 so that makes rinzin older
Hope that helps :)
Pema is older than Rinzin if Pema is 85 months old and Rinzin is 7⅔ years old.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Pema is 85 months old and
Rinzin is 7⅔ years old.
We have to check who is older.
We know that 1 year = 12 months
So if 85 months are conveted to years by dividing 85 by 12
Pema, 85/12 years= 7.08 years
Rinzin, 7⅔ years = 7.06 years
We know that 7.08>7.06
Hence, Pema is older than Rinzin if Pema is 85 months old and Rinzin is 7⅔ years old.
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Solve the system of two linear inequalities graphically.
2x +4y <-16
x ≥ 2
graph the solution set of the first linear inequality
Answers
Answer:
See attachment
Step-by-step explanation:
Isolate y in the first inequality:
[tex]2x + 4y < -16\\4y < - 16 -2 x\\y < -4 -\frac{1}{2} x\\y < -\frac{x+8}{2} \\[/tex]
Now, with both x and y inequalities found, graph it.
What is the slope of the line?
m=
Answers
Answer:
The slope is [tex]-\frac{4}{3}[/tex]
Step-by-step explanation:
Standard form for a linear equation/graph:
[tex]y = mx + b[/tex]
[tex]m[/tex] is the slope, and [tex]b\\[/tex] is the Y- intercept (basically where the graph crosses the y axis).
[tex]m[/tex] can be shown by a fraction: [tex]\frac{Rise}{Run}[/tex]
In this graph, measuring from the two points of contact, the rise is 4 and the run is -3. If the graph moves towards the left while rising, then the run part of the slope should be negative, and vice versa.
Thus, the slope of this graph is [tex]-\frac{4}{3}[/tex]
Here's the function for the line if you need it:
[tex]y = - \frac{4}{3} x + 3[/tex]
hat is the area of one base of the triangular prism? 24 square units 48 square units 160 square units 200 square units
Answers
Answer:
24 a.)
Step-by-step explanation:
the base is a triangle
A freight elevator can hold a maximum weight of 3,500 pounds.
A deliveryman weighs 200 pounds. He is delivering cartons that each
weigh 48 pounds. He wants to know how many cartons he can safely
put on the elevator at one time. Let c represent the number of cartons.
Answers
Answer:
C
Step-by-step explanation:
[tex]200 + 48c \leqslant 3500[/tex]
[tex]48c \leqslant 3300[/tex]
[tex]c \leqslant 68.75[/tex]
Determine whether the sequence is arithmetic, geometric or neither.
0.25, 2, 16, 128, 1024
Answers
if you have a 12 side die and a 6 side die what is the probrability it lands on 5
Answers
Answer:
For the 12 sided one it would be 1/12
For the 6 sided one it would be 1/6
Combine those together and it would be 3/12 which is equal to 1/4
Step-by-step explanation:
The equation of a circle is x 2 + y 2 + 6 y = 7 x 2 + y 2 + 6 y = 7 . What are the coordinates of the center and the length of the radius of the circle?
Answers
Answer:
Vertex: (0,-3)
Radius: 4
Step-by-step explanation:
Complete the square
[tex]x^2+y^2+6y=7\\\\x^2+y^2+6y+9=7+9\\\\x^2+(y+3)^2=16[/tex]
The equation of a circle takes the form of [tex](x-h)^2+(y-k)^2=r^2[/tex] where its center is [tex](h,k)[/tex] and its radius is [tex]r[/tex].
Hence, the vertex is [tex](0,-3)[/tex] and the radius is [tex]4[/tex].
What is the last number in the 9th line
Answers
44 is the last number
most likely
19. If the base is 4, what is the value if the exponent is 2? What if the exponent is -2?
O 16, -16
O 16, 1/16
O 8,-8
O 8,1/8
Answers
Answer:
16, 1/16
Step-by-step explanation:
[tex](4)^2 =16[/tex]
[tex](4)^{-2} =\frac{1}{16}[/tex]
Hope it helps you in your learning process.
[tex]\large{\textsf{\textbf{Answer\::}}[/tex]
Option B
[tex]\large{\textsf{\textbf{Calculations\::}}[/tex]
If the base is 4 , and the exponent is 2 , then the expression looks as follows :
[tex]\textbf{\textsf{$4^2$}}[/tex]
So we multiply 4 times itself .
The answer is :
[tex]\textsf{\textbf{16}}[/tex]
Detail : 4² is not equal to 4×2 , and here's why .
4² = 4 × 4 = 16
4 × 2 = 8
Now , if the exponent is negative , then we turn the number over as follows :
4⁻² = [tex]\mathsf{\dfrac{1}{16} }[/tex]
So the right option is :
[tex]\bigcirc[/tex] 16 , -16
[tex]\bigcirc\!\!\!\!\!\!\bigstar[/tex] 16 , 1/16
[tex]\bigcirc[/tex] 8 , -8
[tex]\bigcirc[/tex] 8 , 1/8
(Option B is right)
[tex]\footnotesize\text{hope\:helpful~}[/tex]
Which equation can be used to determine the value of x?
(6x + 2) + 40 = 90
(6x +2) + 40 = 180
None of these
(6x + 2) = 40
All of these
Answers
Complementary angles have sum 90°
Hence
6x+2+40=90Option A
6x+42=1806(x+7)=6(30)x+7=30x=23Answer:
A)(6x + 2) + 40 = 90
Step-by-step explanation:
(for convenience, I have labelled it with alphabets)
Line ED has crossed line AB perpendicularly resulting [tex]\angle BFC[/tex] and [tex]\angle CFD[/tex] complimentary to each other. That means
[tex]\angle BFC+\angle CFD=90^{\circ}[/tex]
Here:
[tex]\angle BFC=(6x+2)^{\circ}[/tex] [tex]\angle CFD=40^{\circ}[/tex]Hence,
The equation can be used to determine the value of x is
(6x + 2) + 40 = 90In conclusion
Our answer is A)