using trig to solve for missing angle

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Answer:

10t + D = 40

Step-by-step explanation:

y = mx + b is the equation of a line in slope intercept form. We'll be using this equation since the slope, or distance traveled, is steady (linear). In this case, the slope is 10 since Sarah's pace is 10 km/hr. m is the slope, so m = 10.

y = 10x + b. However, she needs to run 40 km. So we're going to substitute 40 in for y.

40 = 10x + b. Now, we need to use t instead of x since that's what's been asked of us. (The slope represents the distance traveled over time, so t fits.)

10t + b = 40

b needs to become D, the distance in kilometers.

So now we have 10t + D = 40

Answer:

D(t)= 40-10t

Step-by-step explanation:

#KmNn

Answer:

given values are:

1200 = 20×30 + 1/2 × 30²a

1200= 600 + 1/2 × 900a

600 = 450a

a = 600 / 450

a = 1.33 m/s²

v² = 20² +2 × 1.33 × 1200

v²= 400 + 3192

v = √3592

v = 59.9 ≈ 60 m/s

The only 2-digit number that is lesser than 50 and the sum of its digits remain unaffected despite being multiplied by a number < 1 would be '18.'

To prove, we will look at some situations:

If we add up the two digits of 18. We get,

[tex]1 + 8 = 9[/tex]

And we multiply 18 by 2 which is greater than 1. We get,

[tex]18[/tex] × [tex]2 = 36[/tex]

The sum remains the same i.e. [tex]3 + 6 = 9[/tex]

Similarly,

If 18 is multiplied to 3(greater than 1), the sum of the two digits comprising the number still remains the same;

[tex]18[/tex] × [tex]3 = 54[/tex]

where (5 + 4 = 9)

Once more,

Even if 18 is multiplied to 4 or 5(greater than 1), the sum of its digits will still be 9.

 [tex]18[/tex] × [tex]4 = 72[/tex]

[tex](7 + 2 = 9)[/tex]

[tex]18[/tex] × [tex]5 = 90[/tex]

[tex](9 + 0 = 9)[/tex]

Thus, 18 is the answer.

Learn more about 'numbers' here: brainly.com/question/1624562

Answer:

Plant B

Step-by-step explanation:

When you compare the number of tomatoes she picks from plant B with plant A, you will notice that plant B has not produced less tomatoes than plant A in any day but it has either produced the same or more number of tomatoes.

Answer:

x=61.71428 or 61 5/7

Step-by-step explanation:

We can use a ratio to solve

7 pieces              12 pieces

-----------------   = ---------------

36 seconds          x seconds

Using cross products

7x = 36*12

7x = 432

Divide by 7

7x/7 = 432/7

61 5/7

x=61.71428

Answer:

66

Step-by-step explanation:

Answer:

14.4

Step-by-step explanation:

since the longest side is 24,find the shortest side

√20^2-12^2

√400-144

√256

=16

which means the other shortest side is 24-16

which is 8

then you have to use the 12 and 8 to find the unknown side

√12^2+8^2

144+64

√208

14.4

I hope this helps

Answer: [tex]\dfrac{8}{3}\ m[/tex]

Step-by-step explanation:

Given

Length of the plank is [tex]6\ m[/tex]

Foot of the flank is [tex]4\ m[/tex] away from the wall

Lizard climbs 2 m up the wall

from the figure, the two triangles are similar

[tex]\therefore \dfrac{2}{6}=\dfrac{x}{4}\\\\\Rightarrow x=4\times \dfrac{2}{6}\\\\\Rightarrow x=\dfrac{4}{3}\ m[/tex]

So, the distance from the wall is

[tex]\Rightarrow 4-x\\\\\Rightarrow 4-\dfrac{4}{3}\\\\\Rightarrow \dfrac{8}{3}\ m[/tex]

Answer:

A=2

B=4

C=6

D=5

E=7

F=8

G=3

H=1

Step-by-step explanation:

explanation is in the picture!

7^4/7^0

= 7^4/1 (n^0 = 1)

= 7^4

Must click thanks and mark brainliest

Answer:

the original population of the city is 7,505,833

Step-by-step explanation:

Given;

new of the population of the city, Y = 9,007,000

the percentage increase of the city, = 20% = 0.2

Let the original population of the city = X

New population, Y = X  + 0.2X

                           Y = X(1 + 0.2)

                           Y = X(1.2)

                           Y = 1.2X

                           X = Y/1.2

                           X = (9,007,000) / 1.2

                           X = 7,505,833

Therefore the original population of the city is 7,505,833

Answer:

Step-by-step explanation:

find the value of a and b if 5+√3/7+2√3=a-b√3

DC=CF

We know

[tex]\boxed{\sf L=\dfrac{\theta}{180}\times πr}[/tex]

[tex]\\ \large\sf\longmapsto L=\dfrac{90}{180}\times \dfrac{22}{7}\times 10[/tex]

[tex]\\ \large\sf\longmapsto L=\dfrac{1}{2}\times \dfrac{220}{7}[/tex]

[tex]\\ \large\sf\longmapsto L=\dfrac{110}{7}[/tex]

[tex]\\ \large\sf\longmapsto L=15.5[/tex]

Now

[tex]\\ \large\sf\longmapsto CF=L+r-DE[/tex]

[tex]\\ \large\sf\longmapsto CF=15.7+10-16[/tex]

[tex]\\ \large\sf\longmapsto CF=25.7-16[/tex]

[tex]\\ \large\sf\longmapsto CF=9.7cm[/tex]

[tex]\large\sf\red{⟼L=18090×722×10}[/tex]

[tex]\begin{gathered}\\ \large\sf\red{ ⟼ L=\dfrac{1}{2}\times \dfrac{220}{7}}\end{gathered}[/tex]

[tex]\begin{gathered}{ \large\sf\red{⟼ L=\dfrac{110}{7}}\end{gathered}[/tex]

⟼ L=15.5

Now

⟼ CF=L+r−DE

⟼ CF=15.7+10−16

⟼ CF=25.7−16

Seena’s mother is 4 times as old as Seena. After 5 years her mother will be 3 times as old as she will be then .Find their present ages.

✧ Let us assume :

Seena's age be x

Her mother's age be 4x

✧ After 5 years :

Seena's age = x + 5

Her mother's age = 4x + 5

✧ Ratio of age after 5 years :

Seena's mother = 3

Seena's ratio = 1

Hence, the equation is :

[tex] \looparrowright\frak{ \frac{4x + 5}{x + 5} = \frac{3}{1} }[/tex]

By cross multiplying we get

[tex] \looparrowright \frak{3(x + 5) = 4x + 5}[/tex]

[tex] \looparrowright \frak{3x + 15 = 4x + 5}[/tex]

[tex] \looparrowright \frak{x = 10}[/tex]

Hence, the ages are

Seena's age = x = 10 yrs

Her mother's age = 4x = 4 × 10 = 40 years

∴ Seena's age is 10 and her mother's is 40 respectively

Answer:

68 degrees 90+22=112 180 subtract 112 = 68

Answer:

C.

[tex]{ \tt{f(x) = \frac{12}{x} - 18}} \: and \: { \tt{g(x) = \frac{12}{x + 18} }}[/tex]

Step-by-step explanation:

[tex]{ \tt{f(x) = \frac{12}{x} - 18}}[/tex]

Let inverse be m:

[tex]{ \tt{m = \frac{12}{x} - 18 }} \\ { \tt{x(m + 18) = 12}} \\ { \tt{x = \frac{12}{m + 18} }} \\ \\ { \boxed{ \sf{f {}^{ - 1} (x) = g(x) = \frac{12}{x + 18} }}}[/tex]

▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓

[tex]\sf↦ Product ~of ~numbers = 10000\\\\↦ n × 16n = 10000\\\\↦ 16n² = 10000\\\\↦ n² = \sf \dfrac{10000}{16}\\\\↦ \sf n = \sqrt{\dfrac{10000}{16}}\\\\↦ \sf n = \sqrt{\dfrac{100\:\times\:100}{4\:\times\:4}}\\\\↦ \sf n = {\cancel{\dfrac{100}{4}}}\\\\➦\pmb{\underline{\boxed{\sf{\pink{n = 25}}}}}[/tex]

▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓

Answer:

Step-by-step explanation:

Let the numbers be x and y.

We have:

Substitute y and solve for x:

Then y is:

The numbers are:

I am not understanding the language

Answer:

its Vietnamese

Step-by-step explanation:

I just dont understand what that type of math is? sorry ):

Answer:

x = 4, -4, 7i, -7i

Step-by-step explanation:

(x^2 – 16)(x^2 + 49) = 0

x^2 – 16 = 0 or x^2 + 49 = 0

x^2 = 16 or x^2 = -49  

x = ± 4 or x^2 = ±7√-1  =±7i

Answer:

B or (-2/3)

Step-by-step explanation:

Perpendicuar lines have negative inverse slopes SO

3/2 ---> -2/3

Answer:

Arthur should select the Mount Joy Pool when there are less than 10 people at the party

Step-by-step explanation:

The initial fee to rent the Woodbridge Pool = $50

The additional fee per person after renting = $5

The initial fee to rent at Mount Joy Pool = 0 (no initial fee)

The fee per person at Mount Joy Pool = $10

The equation of a straight line is y = m·x + c

Ley y  represent the total cost of renting the pool, x, represent the number of persons in the pool, m represent the fee per person and c represent the initial charges, we get;

The total cost of renting Woodbridge Pool, y = 5·x + 50

The total cost of renting the Joy Pool, y = 10·x

Equating both values of y gives;

5·x + 50 = 10·x

∴ 5·x = 50

x = 50/5 = 10

x = 10

From the above equations, the cost of renting the pool is lower for the Joy Pool when there are less than 10 persons at the pool

It will cost the same amount to rent the pool when the number of persons in the pool are 10 persons and the cost of renting the Mount Joy Pool  will be more than the cost of renting the Woodbridge Pool, when there are more than 10 persons

Therefore, Arthur should select the Mount Joy Pool when there are less than 10 people at the party.

9514 1404 393

Answer:

Step-by-step explanation:

1. There will be no solution if the equation is a contradiction. Usually, it is something that can be reduced to 0 = 1.

If we choose to make our equation ...

  x = x +1

Subtracting x from both sides of the equation gives ...

  0 = 1

There is no value of the variable that will make this be true.

__

2. Something that reduces to x = c will have one solution. One such equation is ...

  0 = x+1

  x = -1 . . . . subtract 1 from both sides

__

3. Something that reduces to x = x will have an infinite number of solutions.

One such equation is ...

  x+1 = x+1

Subtracting 1 from both sides gives ...

  x = x . . . . true for all values of x

Answer:

Step-by-step explanation:

Answer:

Option c points at (-2,0) (-1, 0.5) and (1,1)

Step-by-step explanation:

Answer:

36

Step-by-step explanation:

(-6)² = (-6) × (-6)

= +36

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Work Shown:

(whole length)*(external part) = (whole length)*(external part)

(EG)*(FG) = (SG)*(HG)

(2x+4)*(4) = (x+5)*(5)

8x+16 = 5x+25

8x-5x = 25-16

3x = 9

x = 9/3

x = 3

Use this x value to find EF

EF = 2x

EF = 2*3

EF = 6

For more information, search out "secant secant formula". It's not a typo that I wrote "secant" twice.

Answer:

For number 5, it is D

For number 6, it is A

Step-by-step explanation:

For number 5, we have the dimensions options here.

We first need to check to see if all the choices give the perimeter of 34, as sometimes there are trick answers.

We know the 34 is the perimeter because we are looking for area, so we add the two given numbers and double it to find the perimeter since we have the length and width.

*(Formula for perimeter is 2(L + W)  )

(I already checked them all, and they all give to be 34 so they are all safe.)

Then we find the areas of each.

*(Formula for area is L * W   {the " * " symbol represents multiplication.)

We multiply 12 by 5 to get 60.

We multiply 13 by 4 to get 52.

We multiply 10 by 7 to get 70.

We multiply 9 by 8 to get 72.

Since we are looking for the greatest area, we look for the greatest number, which is the 72.

Therefore the 9 by 8 option, or D is correct.

For number 6, we are looking for the minimum perimeter and we have the area, so we set the same thing up except modified slightly.

We first check if all the areas are 64 to look for a trick answer.

We multiply 8 by 8 to get 64.

We multiply 1 by 64 to get 64.

We multiply 6 by 6 to get 36. (WHAT?!!?!! omg me big brain lolza. {nah jk})

We multiply 32 by 2 to get 64.

So we know the 6 by 6 option or C is wrong.

Then we look for the perimeters of the dimension solutions.

(This will skip C so it will go A, B, and then D, since we know C is incorrect and is unrelated now.)

2 ( 8 + 8 ) =  32

2 ( 1 + 64 ) =  130

2 ( 32 + 2 ) =  68.

Since we are looking for the smallest perimeter, it is the smallest answer this time.

So it must be A, since 32 is the smallest.

Hope this helps!

Answer:

101

10+6+16+6*5

I hope it's correct

Answer:

165 ver una pelicula de terror, 137.5 (138) ver una novela, y 247 ver una pelicula de ciencia ficcion.

Step-by-step explanation:

0.3 x 550 = 165

0.25 x 550 = 137.5 --> 138

165 + 138 = 303

550 - 303 = 247