solve for θ:

sin(θ-70)=cos(θ)

pls help and explain step by step
thank you ​

Answer:

perimeter is 36 cm

Step-by-step explanation:

Answer:

[tex]\text{Exact: }AB=25\sqrt{6},\\\text{Rounded: }AB\approx 61.24[/tex]

Step-by-step explanation:

We can use the Law of Sines to find segment AD, which happens to be a leg of [tex]\triangle ACD[/tex] and the hypotenuse of [tex]\triangle ADB[/tex].

The Law of Sines states that the ratio of any angle of a triangle and its opposite side is maintained through the triangle:

[tex]\frac{a}{\sin \alpha}=\frac{b}{\sin \beta}=\frac{c}{\sin \gamma}[/tex]

Since we're given the length of CD, we want to find the measure of the angle opposite to CD, which is [tex]\angle CAD[/tex]. The sum of the interior angles in a triangle is equal to 180 degrees. Thus, we have:

[tex]\angle CAD+\angle ACD+\angle CDA=180^{\circ},\\\angle CAD+60^{\circ}+75^{\circ}=180^{\circ},\\\angle CAD=180^{\circ}-75^{\circ}-60^{\circ},\\\angle CAD=45^{\circ}[/tex]

Now use this value in the Law of Sines to find AD:

[tex]\frac{AD}{\sin 60^{\circ}}=\frac{100}{\sin 45^{\circ}},\\\\AD=\sin 60^{\circ}\cdot \frac{100}{\sin 45^{\circ}}[/tex]

Recall that [tex]\sin 45^{\circ}=\frac{\sqrt{2}}{2}[/tex] and [tex]\sin 60^{\circ}=\frac{\sqrt{3}}{2}[/tex]:

[tex]AD=\frac{\frac{\sqrt{3}}{2}\cdot 100}{\frac{\sqrt{2}}{2}},\\\\AD=\frac{50\sqrt{3}}{\frac{\sqrt{2}}{2}},\\\\AD=50\sqrt{3}\cdot \frac{2}{\sqrt{2}},\\\\AD=\frac{100\sqrt{3}}{\sqrt{2}}\cdot\frac{ \sqrt{2}}{\sqrt{2}}=\frac{100\sqrt{6}}{2}={50\sqrt{6}}[/tex]

Now that we have the length of AD, we can find the length of AB. The right triangle [tex]\triangle ADB[/tex] is a 30-60-90 triangle. In all 30-60-90 triangles, the side lengths are in the ratio [tex]x:x\sqrt{3}:2x[/tex], where [tex]x[/tex] is the side opposite to the 30 degree angle and [tex]2x[/tex] is the length of the hypotenuse.

Since AD is the hypotenuse, it must represent [tex]2x[/tex] in this ratio and since AB is the side opposite to the 30 degree angle, it must represent [tex]x[/tex] in this ratio (Derive from basic trig for a right triangle and [tex]\sin 30^{\circ}=\frac{1}{2}[/tex]).

Therefore, AB must be exactly half of AD:

[tex]AB=\frac{1}{2}AD,\\AB=\frac{1}{2}\cdot 50\sqrt{6},\\AB=\frac{50\sqrt{6}}{2}=\boxed{25\sqrt{6}}\approx 61.24[/tex]

Answer:

[tex] \displaystyle 25 \sqrt{6} [/tex]

Step-by-step explanation:

the triangle ∆ABD is a special right angle triangle of which we want to figure out length of its shorter leg (AB).

to do so we need to find the length of AD (the hypotenuse). With the help of ∆ADC it can be done. so recall law of sin

[tex] \boxed{ \displaystyle \frac{ \alpha }{ \sin( \alpha ) } = \frac{ \beta }{ \sin( \beta ) } = \frac{ c}{ \sin( \gamma ) } }[/tex]

we'll ignore B/sinB as our work will be done using the first two

step-1: assign variables:

step-2: substitute

[tex] \displaystyle \frac{100}{ \sin( {45}^{ \circ} )} = \frac{AD }{ \sin( {60}^{ \circ} )} [/tex]

recall unit circle therefore:

[tex] \displaystyle \frac{100}{ \dfrac{ \sqrt{2} }{2} } = \frac{AD }{ \dfrac{ \sqrt{3} }{2} } [/tex]

simplify:

[tex]AD = 50 \sqrt{6} [/tex]

since ∆ABD is a 30-60-90 right angle triangle of which the hypotenuse is twice as much as the shorter leg thus:

[tex] \displaystyle AB = \frac{50 \sqrt{6} }{2}[/tex]

simplify division:

[tex] \displaystyle AB = \boxed{25 \sqrt{6} }[/tex]

and we're done!

Answer:

4/3

Step-by-step explanation:

To find the slope, we can use the slope formula

m= (y2-y1)/(x2-x1)

   = ( -1 - -13)/( 3 - -6)

    = (-1+13)/( 3+6)

   = 12/9

   = 4/3

Answer:

G. [tex]\displaystyle \frac{4}{3}[/tex]

Step-by-step explanation:

Hi there!

[tex]slope=\displaystyle \frac{y_2-y_1}{x_2-x_1}[/tex]  where two given points are [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]

Plug in the given points (-6,-13) and (3,-1)

[tex]slope=\displaystyle \frac{-1-(-13)}{3-(-6)}\\\\slope=\displaystyle \frac{-1+13}{3+6}\\\\slope=\displaystyle \frac{12}{9}\\\\slope=\displaystyle \frac{4}{3}[/tex]

Therefore, the slope of the line is [tex]\displaystyle \frac{4}{3}[/tex].

I hope this helps!

Answer:

IN MY OPINION D NO IS THE CORRECT ANSWER OF YOUR QUESTION.

Answer:

in my opinion d is the correct answer of your questions.

Step-by-step explanation:

Because subtract subtract sign is always add.

hope this will help you

thanks

steAnswer:

Step-by-step explanation:

step1 5(9x-8)=4(x+2)

step2 45x -40=4x +8

step3 41x=48

step 4 x=48/41

Start with the answer format we want, and work your way toward forming a single fraction like so

[tex]a + \frac{b}{x+2}\\\\a*1+\frac{b}{x+2}\\\\a*\frac{x+2}{x+2}+\frac{b}{x+2}\\\\\frac{a(x+2)}{x+2}+\frac{b}{x+2}\\\\\frac{a(x+2)+b}{x+2}\\\\\frac{ax+2a+b}{x+2}\\\\\frac{ax+(2a+b)}{x+2}\\\\[/tex]

Compare that last expression to (2x+1)/(x+2). Notice how the ax and 2x match up, so a = 2 must be the case.

Then we have 2a+b as the remaining portion in the numerator. Plugging in a = 2 leads to 2a+b = 2*2+b = 4+b. Set this equal to the +1 found in (2x+1)/(x+2) to have the terms match.

So, 4+b = 1 leads to b = -3

Therefore, a = 2 and b = -3

------------------------------------------------

An alternative route:

[tex]\frac{2x+1}{x+2}\\\\\frac{2x+1+0}{x+2}\\\\\frac{2x+1+4-4}{x+2}\\\\\frac{(2x+4)+1-4}{x+2}\\\\\frac{2(x+2)-3}{x+2}\\\\\frac{2(x+2)}{x+2}+\frac{-3}{x+2}\\\\2-\frac{3}{x+2}\\\\[/tex]

I added and subtracted 4 in the third step so that I could form 2x+4, which then factors to 2(x+2). That way I could cancel out a pair of (x+2) terms toward the very end.

------------------------------------------------

Other alternative methods involve synthetic division or polynomial long division. They are slightly separate but related concepts.

Answer:

a = 2

b = -3

Step-by-step explanation:

the secret is seeing that the numerator (top part of the division) contains 2x. that means 2 times the factor of x in the denominator (bottom part of the division).

so, we want to change the numerator that we can simply say the result is 2 and some rest (remainder).

2×(x+2) would be 2x + 4

aha !

and we have 2x+1 up there. so, what had to happen to get from 2x+4 to 2x+1 ? we had to subtract 3. it to get to 2x+4 we have to add 3.

but if we add 3, we need also to subtract 3 to keep the value of the whole expression the same.

therefore we get

(2x+1)/(x+2) = (2x+4)/(x+2) - 3/(x+2) =

= 2×(x+2)/(x+2) - 3/(x+2) = 2 - 3/(x+2)

Answer:

30.

Step-by-step explanation:

x^2 = 24^2 + 18^2

x^2 = 576 + 324 = 900

x = sqrt900 = 30.

Answer: 27

Step-by-step explanation:

[tex]Mean=\frac{16 + 25 + 23 + 12 + 17 + x}{6}=20 \\16 + 25 + 23 + 12 + 17 + x=20(6)\\93+x=120\\x=120-93=27[/tex]

Answer:

27 years old

Step-by-step explanation:

There are originally 5 people in the room.

Their ages are: 16, 25, 23, 12, 17

The sum of their ages is: 93

One person enters the room. That person's age is unknown, so we call it x.

The sum of the ages of the 6 people is:

x + 93

There are 6 people in the room now, so the mean age is (total age divided by number of people):

(x + 93)/6

We are told the mean age is 20.

(x + 93)/6 = 20

x + 93 = 120

x = 27

Answer: 27 years old

Answer:

A and c

Step-by-step explanation:

1) Length arc = r*theta

5.11=1*theta. Theta is 5.11 rads

2) Law of cosines is the correct answer

Answer:

Letter B. Hyperbole is your answer

4x4=16 16x3=48 so I think the answer is 48

7/8 = x/56

x = 7 x 7

so, 49/56 = rod

so, 49 pieces will be made

hope it helps :)

Area of a circle: pi x r^2

---r is the radius of the circle

A = pi x 20^2

A = 3.14 x 400

A = 1256 square miles

Hope this helps!

Answer:

Height of the house = 3 meter (Approx.)

Step-by-step explanation:

Given:

Scale model;

1 centimeter = 0.6 meter

According to graph

Height of cube = 5 cube = 5 centimeter

Find:

Height of the house

Computation:

Height of the house = height of the house in scale model x Scale model

Height of the house = 5 x 0.6

Height of the house = 3

Height of the house = 3 meter (Approx.)

Answer:

[tex]{ \tt{ \tan {}^{4} \theta + { \sec }^{2} \theta }} \\ { \tt{ = ({ \tan }^{2} \theta ){}^{2} + { \sec }^{2} \theta }} \\ = { \tt{ {-(1 - { \sec }^{2} \theta) }^{2} + { \sec }^{2} \theta }} \\ { \tt{ = -(1 - 2 { \sec }^{2} \theta + { \sec }^{4} \theta) + { \sec}^{2} \theta}} \\ { \tt{ = -(1 - { \sec }^{2} \theta) + { \sec }^{4} \theta}} \\ { \tt{ = -{ \tan}^{2} \theta + { \sec }^{4} \theta }} \\ = { \tt{ { \sec}^{4} \theta - { \tan }^{2} \theta}} \\ { \bf{hence \: proved}}[/tex]

Answer:

[tex]-4p^3-3p^2-17p[/tex]

Step-by-step explanation:

Adding a negative number is the same as subtracting a number. Using this logic, we can change the equation to equal this:

[tex]-3p^3+5p^2-2p-p^3-8p^2-15p[/tex]

Combining like terms, we have negative 3p cubed minus another p cubed, which equals negative 4p cubed, we have 5p squared minus 8p squared, which equals negative 3p squared, and we have negative 2p minus 15p, which is negative 17p.

Answer:

No. The results speak to a possible difference between the proportions of people over 55 and under 25 who dream in black and white, but the results cannot be used to verify the cause of such a difference.  

Hence the correct option is option A.

Answer:

Stationary matrix S = [ 0.6   0.4 ]

limiting matrix  P = [tex]\left[\begin{array}{ccc}0.6&0.4\\0.6&0.4\\\end{array}\right][/tex]

Step-by-step explanation:

Transition matrix

[tex]p = \left[\begin{array}{ccc}0.8&0.2\\0.3&0.7\\\end{array}\right][/tex]

solving the equation SP = S ( using Markova chain with 2 states )

stationary matrix,  S = [ a , 1 - a ]

given that  SP  = S

[ a , 1 - a ] * [tex]\left[\begin{array}{ccc}0.8&0.2\\0.3&0.7\\\end{array}\right][/tex] =  [ a , 1 - a ]

= a*(0.8) + ( 1 - a ) ( 0.3 ) = a

∴ a = 0.6

hence;  stationary matrix S = [ 0.6   0.4 ]

             limiting matrix  P = [tex]\left[\begin{array}{ccc}0.6&0.4\\0.6&0.4\\\end{array}\right][/tex]

Answer:

SEE BELOW

Step-by-step explanation:

1. find value of m

a^2 + b^2 = c^2

7.5^2+10^2=c^2

15+100=c^2

115=c^2

square it

=10.7 (not answer)

a^2+b^2=c^2

10.7^2+30^2=c^2

114.49+900=c^2

1014.49=c^2

square it

m=31.9

2.20^2 + 21^2 = 841

29^2=841

yes the triangle is right angled !!!

hope this helps :)

Answer:

R = 35l-215

Step-by-step explanation:

total amount they earn = 35l

however, to account for the money used to rent the machines, we have to deduct 215 from the total cost.

hence,

R= 35l-215

total amount they raised = 35(26)-215 = $695

they would lose $215 if they were unable to aerate due to weather conditions

they could avoid this potential loss by checking the weather report before renting the machines

Answer:

-5/13

Step-by-step explanation:

sin theta = opp / hyp

sin theta = -12 /13

we can find the adj side by using the pythagorean theorem

adj^2 + opp ^2 = hyp^2

adj^2 +(-12)^2 = 13^2

adj^2 +144 =169

adj^2 = 169-144

adj^2 = 25

Taking the square root of each side

adj = ±5

We know that it has to be negative since it is in the third quad

adj = -5

cos theta = adj / hyp

cos theta = -5/13

Answer:

B) -5/13

Step-by-step explanation:

i hope it will help

plzz mark as brainliest if you want

For the given question,

Total number of outcomes

= 6 (i.e. 1, 2, 3, 4, 5 and 6)

Number of favourable outcomes

= 4 (i.e. 3, 4, 5, 6)

So,

[tex]P = \frac{Number \: of \: favourable \: outcomes}{Total \: number \: of \: outcomes} \\ = > P= \frac{4}{6} \\ = > P = \frac{2}{3} \\ = > P = 0.6666......[/tex]

Answer:

The answer is "Option b".

Step-by-step explanation:

The significant variance shows that the numbers in the set are far from the mean and far from each other as well. Alternatively, a little variation implies the reverse. The variance value of 0, on either hand, shows that all values inside a set of numbers are the same. If you need yet another test, use a greater sample variance as the numerator of the test statistic to avoid having to reference tables of the F distribution that primary device from of the lower tail.

Answer:

D and C

Step-by-step explanation:

1) You can cross check using desmos.

2) cos(120) is - 0.5

Answer:

5^1

Step-by-step explanation:

[tex]\sqrt{5} =5^{\frac{1}{2} }[/tex] (law of indices - fractional powers)

after converting all the numbers to this form:

[tex]\frac{5^{{\frac{2}{3} } } * 5^{\frac{1}{2} } }{5^{\frac{1}{6} } } \\[/tex]

combine using law of indices:

5^(2/3+1/2-1/6) = 5^1

Answer:

a is 1.58 and b is 0.42

Step-by-step explanation:

[tex]{ \sf{3 {x}^{2} - 6x + 2 = 0 }} \\ { \sf{x = \frac{ - b± \sqrt{ {b}^{2} - 4ac} }{2a} }} \\ \\ { \sf{x = \frac{ - ( - 6)± \sqrt{ {( - 6)}^{2} - (4 \times 3 \times 2) } }{(2 \times 3)} }} \\ \\ { \sf{x = \frac{6± \sqrt{12} }{6} }} \\ \\ { \sf{x = 1.58 \: and \: 0.42}}[/tex]

Answer:

c =4 4/9 minutes

Step-by-step explanation:

The formula is

1/a + 1/b = 1/c  where a and b is the time for each working alone and c is the time working together

1/8 + 1/10 = 1/c

Multiply by 40c to clear the fractions  ( 40c is the least common multiple)

40c(1/8 + 1/10 = 1/c)

5c + 4c = 40)

9c = 40

Divide by 9

9c/9 = 40/9

c =4 4/9 minutes