Shen invested in a savings bond for 4 years and was paid simple interest at an annual rate of 6%. The total interest that he earned was $2160. How much did he invest?

Given:

[tex]\sin x=-\dfrac{15}{17}[/tex]

x lies in the III quadrant.

To find:

The values of [tex]\sin 2x, \cos 2x, \tan 2x [/tex].

Solution:

It is given that x lies in the III quadrant. It means only tan and cot are positive and others  are negative.

We know that,

[tex]\sin^2 x+\cos^2 x=1[/tex]

[tex](-\dfrac{15}{17})^2+\cos^2 x=1[/tex]

[tex]\cos^2 x=1-\dfrac{225}{289}[/tex]

[tex]\cos x=\pm\sqrt{\dfrac{289-225}{289}}[/tex]

x lies in the III quadrant. So,

[tex]\cos x=-\sqrt{\dfrac{64}{289}}[/tex]

[tex]\cos x=-\dfrac{8}{17}[/tex]

Now,

[tex]\sin 2x=2\sin x\cos x[/tex]

[tex]\sin 2x=2\times (-\dfrac{15}{17})\times (-\dfrac{8}{17})[/tex]

[tex]\sin 2x=-\dfrac{240}{289}[/tex]

We know that,

[tex]\cos 2x=1-2\sin^2x[/tex]

[tex]\cos 2x=1-2(-\dfrac{15}{17})^2[/tex]

[tex]\cos 2x=1-2(\dfrac{225}{289})[/tex]

[tex]\cos 2x=\dfrac{289-450}{289}[/tex]

[tex]\cos 2x=-\dfrac{161}{289}[/tex]

Using the trigonometric ratios, we get

[tex]\tan 2x=\dfrac{\sin 2x}{\cos 2x}[/tex]

[tex]\tan 2x=\dfrac{-\dfrac{240}{289}}{-\dfrac{161}{289}}[/tex]

[tex]\tan 2x=\dfrac{240}{161}[/tex]

Hence, the required values are [tex]\sin 2x=-\dfrac{240}{289},\cos 2x=-\dfrac{161}{289},\tan 2x=\dfrac{240}{161}[/tex].

Answer:

use proportions??

Step-by-step explanation:

i

d

k

h

o

w

t

o

do

this i am only in 5th grade yikes

Answer:

55 or 53.

Step-by-step explanation:

Answer:

z^1/7

Step-by-step explanation:

trust me

Answer:  C≈ 31.42m

C=2πr=2·π·5≈31.41593m

Step-by-step explanation: hope this helps

Answer:

I think the answer is 7x+ 6a

Step-by-step explanation:

3 (x - 6) + 5 (a + 1) - 2 (4x + 2)

3 (-6x) + 5 (1a) -2 (6x)

3x + 6a + 4x

= 7x+ 6a answer!

Answer:

Step-by-step explanation:

The simple interest on a certain sum for 5years at 8% per annum is Rs200 less than the simple interest on the same sum for 3years and 4months at 18% per annum.Find the sum​

The formula for Simple Interest = PRT

From above question, we have to find the Principal

The simple interest on a certain sum for 5years at 8% per annum is Rs200

Hence,

R = 8%

T = 5 years

Rs 200 = P × 8% × 5

P = 200/8% × 5

P = Rs500

The principal = Rs 500

The simple interest on the same sum for 3years and 4months at 18% per annum.

Simple Interest = PRT

R = 18%

T = 3 years and 4 months

Converted to years

T = 3 + (4 months/12 months)

T = 3.33 years

Hence,

Simple Interest = Rs 500 × 18% × 3.33 years

= Rs 299.7

Answer:

See solution below

Step-by-step explanation:

According to the diagram shown

m<1 = m<5 = 5=65 degrees (corresponding angle)

m<5 = m<4 - 65 degrees (alternate interior angle)

m<9 = m<8 = 65degrees (corresponding angle)

m<5 = m<8 = 65dgrees (vertically opposite angles)

m<6+m<8 = 180

m<6 + 65 = 180

m<6 = 180 - 65

m<6 = 115degrees

m<2 = m<6 = 115degrees (corresponding angles)

m<6 = m<7 = 115degrees (vertically opposite angles)

m<3 = m<7 = 115degrees(corresponding angle)

)

The measures of the other seven angles are evaluated as:

[tex]m\angle 1 = 65^\circ = m\angle 5\\m\angle 2 =115^\circ = m\angle 6\\m\angle 3 =65^\circ = m\angle 7\\m\angle 4 = 115^\circ =m\angle 8[/tex]

Two angels whose sum is 180° are called supplementary angles.

When they are added together graphically, they form a straight line.

Each of the pairs of the opposite angles made by two intersecting lines are called vertical angles. They are of same measurement.

In literal sense, corresponding means pair wise angles. Like the right corner angles of two triangles etc. But usually we take them as:

For two similar figures, the pair by pair similar angles of those two similar figures are called corresponding angles. They are of same measurement.

For this case, we have:

Angle 1,2,3 and 4 corresponding to 5,6,7 and 8 angle respectively.  It is because the two lines A and B are parallel and the traversing line intersects both of them. When single line intersect two parallel lines, it makes same corresponding angles on both of the sides. That means

[tex]m\angle 1 = m\angle 5\\m\angle 2 = m\angle 6\\m\angle 3 = m\angle 7\\m\angle 4 = m\angle 8[/tex]

where that small 'm' denotes that we're taking about their measurements.

Thus, we will only find 1,2,3,and angle 4's measurements and rest four would be found.

Since angle 1 and angle 4 are vertical angles, they are same measurement. Since angle 1 is of 65 degrees, thus:

[tex]m\angle 1 = 65^\circ = m\angle 4[/tex]

Now, since angle angle 3 is supplementary to angle 1 and so as angle 2 to angle 4, thus:

[tex]m\angle 2 + m\angle 4 = 180^\circ\\m\angle 2 = 180-m\angle 4= 115^\circ\\\\m\angle 3 + m\angle 1 = 180^\circ\\m\angle 3 = 180-m\angle 1= 115^\circ[/tex]

Thus, we get the measurement of all angles as:

[tex]m\angle 1 = 65^\circ = m\angle 5\\m\angle 2 =115^\circ = m\angle 6\\m\angle 3 =65^\circ = m\angle 7\\m\angle 4 = 115^\circ =m\angle 8[/tex]

Learn more about corresponding angles here:

https://brainly.com/question/23134162

Answer:

x = 13

Step-by-step explanation:

When we say side AB is congruent to Side AC it means both side are the same.

This is written Mathematically as:

AB = AC

We are asked to find x

angle B = 5x +9 , angle C = 8x-30

5x + 9 = 8x - 30

Collect like terms

9 + 30 = 8x - 5x

8x - 5x = 30 + 9

3x = 39

Divide both sides by 3

x = 39/3

x = 13

Answer:

48 questions

Step-by-step explanation:

There are 60 questions on the test

to see how many questions he needs to solve to get 80% we multiply 60 with 80 and divide it by 100

60 x 80 ÷ 100 = 48

Answer:

Step-by-step explanation:  lets say the fod is chicken 3/4 is 75 out of 100 1/10 out of 100 is 10 lets see how many times we can take 10 out of 75 .

you can do it 7 time because 7 rimes 10 is 70 meaning that you have 7 weeks

and half a week hope this helps B)

Answer:

The radian measure of 30° is [tex]\frac{\pi}{6}[/tex] radians.

Step-by-step explanation:

A complete revolution equals 360°, that is, 2π radians. If the given angle is 30°, then the value of the radian measure is calculated by the following simple rule of three:

[tex]x = \frac{30^{\circ}}{360^{\circ}}\times 2\pi[/tex]

[tex]x = \frac{\pi}{6}\,rad[/tex]

The radian measure of 30° is [tex]\frac{\pi}{6}[/tex] radians.

Answer:

Step-by-step explanation:

b.

[tex]\frac{a^2+6a+9}{a^2-9} *\frac{3a-9}{a+3} \\=\frac{a^2+2*a*3+3^2}{a^2-3^2} *\frac{3(a-3)}{a+3} \\=\frac{(a+3)^2}{(a+3)(a-3)} *\frac{3(a-3)}{a+3} \\=\frac{3(a+3)^2}{(a+3)^2} \\=3[/tex]

d.

[tex]\frac{3x^2-6x}{3x+1} *\frac{x+3x^2}{x^2-4x+4} \\=\frac{3x(x-2)}{3x+1} *\frac{x(1+3x)}{x^2-2x-2x+4} \\=\frac{3x(x-2)}{3x+1} *\frac{x(1+3x)}{x(x-2)-2(x-2)} \\=\frac{3x(x-2)}{3x+1} *\frac{x(1+3x)}{(x-2)(x-2) } \\=\frac{3x^2}{x-2)}[/tex]

e.

[tex]\frac{2x^2-10x+12}{x^2-4} *\frac{2+x}{3-x} \\=\frac{2[x^2-5x+6]}{x^2-2^2} *\frac{2+x}{-(-3+x)} \\=\frac{2[x^2-2x-3x+6]}{(x+2)(x-2)} *\frac{x+2}{-(x-3)} \\=\frac{2[x(x-2)-3(x-2)]}{(x+2)(x-2)} *\frac{x+2}{-(x-3)} \\=\frac{2(x-2)(x-3)}{(x+2)(x-2)} *\frac{x+2}{-(x-3)} \\=\frac{2}{-1} \\=-2[/tex]

k.

[tex]\frac{6x^2-11x-10}{6x^2-5x-6} *\frac{6-4x}{25-20x+4x^2} \\=\frac{6x^2-15x+4x-10}{6x^2-9x+4x-6} *\frac{-4x+6}{4x^2-10x-10x+25} \\=\frac{3x(2x-5)+2(2x-5)}{3x(2x-3)+2(2x-3) } *\frac{-2(2x-3)}{2x(2x-5)-5(2x-5)} \\=\frac{(2x-5)(3x+2)}{(2x-3)(3x+2)} *\frac{-2(2x-3)}{(2x-5)(2x-5)} \\=\frac{-2}{2x-5}[/tex]

Answer:

ec and  obtuse triangle

Answer:

Explanation:

Radius: 1.9

Height: 2.6

π: 3.14

Round: 9.8

Answer:

Horizontal (Braniest pls)

Step-by-step explanation:

Since (3,3) and (1,3) is on the same line, it is moving horizaontally (Braniest pls)

Answer:

9y

Step-by-step explanation:

Add 7y and 5y which equals 12y. Then subtract 3y from 12y and u get 9y. It might be wrong

Answer:

7.6

Step-by-step explanation:

1is less than 5 so let it rest

Answer:

Step-by-step explanation:

Answer:

sometimes

Step-by-step explanation:

The following examples to illustrate

[tex]\sqrt{2}[/tex] is irrational

[tex]\sqrt{2}[/tex] × [tex]\sqrt{2}[/tex] = 2 ← which is rational

[tex]\sqrt{3}[/tex] is irrational and

[tex]\sqrt{2}[/tex] × [tex]\sqrt{3}[/tex] = [tex]\sqrt{6}[/tex] ← which is irrational

Result is therefore sometimes

Step-by-step explanation:

f(x) = 2x²+ 8x -1

f(6) = 2(6) + 8(6)-1

= 13 + 48 - 1

= 61-1

= 60.

Answer:

(-8, -5)

Step-by-step explanation:

If (-8, 5) is reflected across the x-axis, the x-coordinate stays the same (-8), but the y coordinate becomes -5.  Hence the coordinates of the reflection are (-8, -5).

If point (-8, 5) is reflected across the x axis, the new point is (-8, -5)

Transformation is the movement of a point from its initial location to a new location. Types of transformation are reflection, translation, rotation and dilation.

If point (-8, 5) is reflected across the x axis, the new point is (-8, -5)

Find out more on transformation at: https://brainly.com/question/4289712

Answer:

v=-16

Step-by-step explanation:

-2=2+v/4

(we know that 2+-4=-2 so we can see if that works)

(4*-4=-16)

2+-16/4=-2

(-16/4=-4)

2+-4=-2

Answer:

Part A: 25% of 50 = 12.5

Part B: 25% of 60 = 15

Part C: 50% of 60 = 30

Part D: 75% of 60 = 45

Part E: 75% of 30 = 22.5

Part F: 100% of 22.5 = 22.5

Part G: 10% of 22.5 = 2.25

Part H: 50% of 45.7 = 22.85

Step-by-step explanation:

To find - Do you know the answer to

              Part A: 25% of 50 =

              Part B: 25% of 60 =

              Part C: 50% of 60 =

              Part D: 75% of 60 =

              Part E: 75% of 30 =

              Part F: 100% of 22.5 =

              Part G: 10% of 22.5 =

              Part H: 50% of 45.7 =

Proof -

Part A :

25% of 50 =  [tex]\frac{25}{100} *50[/tex] = [tex]\frac{1}{4}*50[/tex] = 12.5

⇒25% of 50 = 12.5

Part B :

25% of 60 =  [tex]\frac{25}{100} *60[/tex] = [tex]\frac{1}{4}*60[/tex] = 15

⇒25% of 60 = 15

Part C :

50% of 60 =  [tex]\frac{50}{100} *60[/tex] = [tex]\frac{1}{2}*60[/tex] = 30

⇒50% of 60 = 30

Part D :

75% of 60 = [tex]\frac{75}{100} *60[/tex] = [tex]\frac{75}{10}*6[/tex] = 45

⇒75% of 60 = 45

Part E :

75% of 30 = [tex]\frac{75}{100} *30[/tex] = [tex]\frac{75}{10}*3[/tex] = 22.5

⇒75% of 30 = 22.5

Part F :

100% of 22.5 = [tex]\frac{100}{100} *22.5[/tex] = 22.5

⇒ 100% of 22.5 = 22.5

Part G :

10% of 22.5 = [tex]\frac{10}{100} *22.5[/tex] = 2.25

⇒ 10% of 22.5 = 2.25

Part H :

50% of 45.7 =  [tex]\frac{50}{100} *45.7[/tex] = [tex]\frac{1}{2}*45.7[/tex] = 22.85

⇒50% of 45.7 = 22.85

Answer:

Step-by-step explanation:

Solve 2x−9y=14;−5x+9y=−8

Steps:

I will solve your system by substitution.

(You can also solve this system by elimination.)

2x−9y=14;−5x+9y=−8

Step: Solve2x−9y=14for x:

2x−9y+9y=14+9y(Add 9y to both sides)

2x=9y+14

2x

2

=

9y+14

2

(Divide both sides by 2)

x= 9

2

y+7

Step: Substitute

9

2

y+7forxin−5x+9y=−8:

−5x+9y=−8

−5(

9

2

y+7)+9y=−8

−27

2

y−35=−8(Simplify both sides of the equation)

−27

2

y−35+35=−8+35(Add 35 to both sides)

−27

2

y=27

−27

2

y

−27

2

=

27

−27

2

(Divide both sides by (-27)/2)

y=−2

Step: Substitute−2foryinx=

9/ 2

y+7:

x= 9/ 2 y+7

x= 9/ 2 (−2)+7

x=−2(Simplify both sides of the equation)

Answer:

x=−2 and y=−2

Infanite many solutions

Answer: 5.3571

Step-by-step explanation:

The formula used to calculate direct proportion is: y = kx

We will find the constant of proportionality when y=10 and x=5.6. This will be:

y = kx

10 = 5.6k

k = 10/5.6

k = 1.7857143

The value of y when X=3 will be:

y = kx

y = 1.7857143 × 3

y = 5.3571

Answer:8/15

Step-by-step explanation:

Tanθ in a right angle triangle is the ratio of its perpendicular to its base. The ratio that represents the Tan(∠H) is [tex]\dfrac{8}{15}[/tex].

The tangent or tanθ in a right angle triangle is the ratio of its perpendicular to its base. it is given as,

[tex]\rm{Tangent(\theta) = \dfrac{Perpendicular}{Base}[/tex]

where,

θ is the angle,

Perpendicular is the side of the triangle opposite to the angle θ,

Base is the adjacent smaller side of the angle θ.

As it is given that the two of the given triangles are similar triangles, therefore, their corresponding sides will be in the same ratio.

[tex]\dfrac{QR}{HJ} = \dfrac{RP}{JG} = \dfrac{PQ}{GH}[/tex]

Further, the sides can be written as,

[tex]\dfrac{QR}{HJ} = \dfrac{RP}{JG}\\\\\dfrac{QR}{RP} = \dfrac{HJ}{JG}=\dfrac{15}{8}[/tex]

Now, the Tan(∠H) can be written as,

[tex]\rm{Tangent(\theta) = \dfrac{Perpendicular}{Base}[/tex]

Substituting the value for the ∠H in ΔHJG,

[tex]\rm Tangent(\angle H) = \dfrac{JG}{HJ}[/tex]

As the ratio is already known, therefore,

[tex]\rm Tangent(\angle H) = \dfrac{8}{15} = 0.5\bar3[/tex]

Hence, the ratio that represents the Tan(∠H) is [tex]\dfrac{8}{15}[/tex].

Learn more about Tangent (Tanθ):

https://brainly.com/question/10623976

Answer:

D

Step-by-step explanation:

The point on the Number line is a closed( shaded circle) So it will include a greater than or equal sign.  Since the arrow is pointing right it will be B is greater than/ equal to 135. if the arrow was pointing the opposite way it would be less than or equal to  symbol.