Molly starts riding her bike to school 20 minutes after her brother Jonas
does. Molly pedals 12 miles per hour, and Jonas pedals 9 miles per hour.
How much time will it take for Molly to catch up to Jonas?

Answer:

The sum of money deposited is approximately $22,021.74

Step-by-step explanation:

The given interest and amounts of the deposit are outlined as follows;

The simple interest per annum, R = 0.325%

The number of years the money is deposited, T = 4 years

The total amount received (Interest + Initial deposit), A = $50,650

We have;

I = P × R × T

Where;

P = The principal (initial amount deposited)

R = The (annual) interest rate = 0.325%

T = The time = 4 years

Therefore;

The total amount received, A = P + I

P + I = P + P × R × T = P × (1 + R × T)

∴ A = P + I = P × (1 + R × T)

P = A/(1 + R × T)

Plugging in the values, gives;

P = 50,650/(1 + 0.325 × 4) = 506,500/23 ≈ 22,021.74

The sum of money deposited, P = $22,021.74

Answer:

18,225

Step-by-step explanation:

L1=25

L2=75

L3=225

the pattern is (25)* 3^(n-1)

L1=3^0*25 = 25

L2=3^1*25 = 3* 25 = 75

L3=3^2*25 = 9* 25 = 225

.

.

L7=3^6*25 = 729* 25 = 18,225

Answer:

x=7

Step-by-step explanation:

x/3 +  x/6 = 7/2

Multiply each side by 6 to clear the fractions

6(x/3 +  x/6) = 7/2 *6

Distribute

2x +x = 21

Combine like terms

3x = 21

Divide by 3

3x/3 = 21/3

x = 7

Answer:

x = 7

Step-by-step explanation:

Given

[tex]\frac{x}{3}[/tex] + [tex]\frac{x}{6}[/tex] = [tex]\frac{7}{2}[/tex] ( multiply through by 6, the LCM of 3,6, 2 to clear the fractions )

2x + x = 21

3x = 21 ( divide both sides by 3 )

x = 7

The airplane has to fly approximately 7.47 miles farther before it is directly above the coastline (rounded to the nearest tenth).

Here,

Let's consider the situation described in the problem:

An airplane is flying 2 miles over the ocean, directly toward a coastline. The angle of depression from the airplane to the coastline is 15 degrees. We want to find out how much farther the airplane has to fly before it is directly above the coastline.

Let's represent the distance the airplane needs to fly before it is directly above the coastline as "x" miles.

Now, we have a right-angled triangle formed by the airplane, the coastline, and the point directly below the airplane on the coastline (the foot of the perpendicular).

The angle of depression is the angle between the horizontal line (the coastline) and the line of sight from the airplane to the foot of the perpendicular.

Since we know the angle of depression and the length of the opposite side (the height of the airplane above the coastline, which is 2 miles), we can use trigonometry (specifically, the tangent function) to find the length of the adjacent side, which is the distance the airplane needs to fly (x miles).

The tangent of an angle in a right-angled triangle is defined as the ratio of the length of the opposite side to the length of the adjacent side:

tan(angle) = opposite / adjacent

In our case, the angle is 15 degrees, the opposite side is 2 miles, and we want to find the adjacent side (x miles):

tan(15°) = 2 / x

Now, solve for x:

x = 2 / tan(15°)

Using a calculator:

x ≈ 2 / 0.26794919243 ≈ 7.47 miles

So, the airplane has to fly approximately 7.47 miles farther before it is directly above the coastline (rounded to the nearest tenth).

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Answer:

13 miles

Step-by-step explanation:

Distance from home to Field :

4² + 3² = d²

16 + 9 = d²

25 = d²

d = 5 miles

Field to Library :

8 lines so 8 miles

Total :

5 + 8 = 13 miles

He traveled 13 miles

If my answer is incorrect, pls correct me!

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-Chetan K

Answer:

If we multiply both the sides by 2, the inequality signs remains the same.

If we divide both sides by -2, the sign changes.

Step-by-step explanation:

The given inequality is

-8<2

If we multiply both the sides by 2, we get

-8 * 2 < 2*2

-16 < 4

The inequality signs remains the same.

On the other hand if we divide both sides by -2, we get -

-8/-2 < 2/-2

4 > -1

Here the sign changes.

Answer:

98

Step-by-step explanation:

because this is an isosceles triangle so base angle are equal and triangle add up to 180°. so H will be 41 as well to find out F

do 180-41-41=98 is the answer.

hope this helps :)

see your answer in Pic

Answer:

A

Step-by-step explanation:

Answer:

[tex]56.3[/tex]

Step-by-step explanation:

The Law of Sines works for any triangle and is given by [tex]\frac{\sin A}{a}=\frac{\sin B}{b}=\frac{\sin C}{c}[/tex] (the ratio of any angle and its opposite side is equal to the ratio of all other angles and their respective opposite sides).

Thus, we have:

[tex]\frac{\sin 28^{\circ}}{27}=\frac{\sin 102^{\circ}}{c},\\c=\frac{27\sin 102^{\circ}}{\sin 28^{\circ}}=56.2547070223\approx \boxed{56.3}[/tex]

Answer:

(x+1)² = 14

a = 1, b = 14

Step-by-step explanation:

Given the equation, x² + 2x = 13

We are to use the completing the square method to express in the form

(x + a)² = b

x² + 2x = 13

Add the square of half of the coefficient of x to both sides

Coefficient of x = 2

Half of the coefficient of x = 2/2

Square of the result = (2/2)²

Square of the result = 1²

Add (1/2)² to both sides

x² + 2x + (1)² = 13 + (1)²

(x+1)² = 13 + 1

(x+1)² = 14

Compare with  (x+a)² = b

a = 1 and b = 14

Answer:

12? 10 + d = 15 so d = 5.

Step-by-step explanation:

Answer:

d = 5

Step-by-step explanation:

The common difference d is the difference between consecutive terms, then

d = a₁₂ - a₁₁ = 15 - 10 = 5

The Equation of the line can be represented as :

[tex] \longrightarrow \: y = mx + b[/tex]

where, m is slope of the line.

now, let's solve for b , by plugging the values of "x" , "y" and "m"

[tex] \longrightarrow \: 5 = (4 \times 0) + b[/tex]

[tex] \longrightarrow \: b = 5[/tex]

Therefore, the equation of above line is

[tex] \large \boxed{ \mathrm{y = 4x + 5}}[/tex]

[tex] { \orange{ \mathfrak{ \underline{hope \: \: it \: \: helps \: \: you.....}}}}[/tex]

Answer:

Altitude of cylinder = 10 cm

Step-by-step explanation:

Given:

lateral surface area of cylinder = 90 cm²

Circumference of base = 9 cm

Find:

Altitude of cylinder

Computation:

Circumference of base = Circumference of cylinder

So,

2πr = 9

lateral surface area of cylinder = 2πrh

2πrh = 90

We know that; 2πr = 9

So,

9(h) = 90

h = 90 / 9

Altitude of cylinder = 10 cm

Answer:

Step-by-step explanation:

b(a + 1) + a = b*a + b + a = ab + b + a

1) b(2a +1 ) = b*2a + b*1 = 2ab + b  Not equivalent.

2)a + (a +1)*b = a + ab+ b     Equivalent

3) (a +1)(b+ a) = a*(b +a) + 1*(b+a) = ab+ a² +b + a  Not equivalent.

4) (a + 1)b + a = ab+ b + a   Equivalent

5) a + b(a+1) = a +ab + b Equivalent

6) a + (a +1) + b = a + a + 1 + b = 2a + 1 +b  Not equivalent.

7) a(b +1) + b = ab + a + b  Equivalent

Answer:

6

Step-by-step explanation:

Use Pythagorean Theorem to solve for the missing side:

[tex]a^2+b^2=c^2\\a^2+(7)^2=(\sqrt{85})^2\\a^2+49=85\\a^2=36\\\sqrt{a^2} =\sqrt{36}\\a=6[/tex]

Answer:

9

Step-by-step explanation:

Simply multiply 30 by .3.

Hope that this helps!

Answer:

A Hexagon has 6 sides so 6 Vertices

Answer:

44 euros

Step-by-step explanation:

if the ratio between an english pound and a euro is 3 to 4 respectivley, the ratios will hold true for any number. Since 33/3 = 11, we can stratigically multiply by 1,

3/4 = (3/4)(11/11)

so the ratios would be the same, multiplying, you would get 33/44, which means 33 pounds for 44 euros

Answer: 2,396,558 Ringgit

Step-by-step explanation:

J = P * ( 1 + k)^n

P = initial investment of 1,000,000 Ringgit

k = rate of return of 6% per annum

n = Number of years of investment

J = 1,000,000 * ( 1 + 6%)¹⁵

= 1,000,000 * 2.396558193

= 2,396,558 Ringgit

Answer:

There is no possible value for P

Step-by-step explanation:

In ΔPQR, p = 7.6 inches, r = 3.5 inches and ∠R=160°. Find all possible values of ∠P, to the nearest 10th of a degree

We solve using the law of sines

p/sin P = r/sin R

7.6/sin P = 3.5/sin 160

Cross Multiply

sin P × 3.5 = 7.6 × sin 160

sin P = 7.6 × sin 160/3.5

P = arc sin (7.6 × sin 160/3.5)

There is no possible value for P

3a) Answer: 84 degrees

Step-by-step explanation:

3x + 2(x+20)= 180 (total sum of angles in a triangle is 180 degrees)

5x+40 = 180

5x = 140

x= 28

3x= 28 x 3

   = 84

Answer:

-14-2= -16

I hope it helps :)

Answer:

x = -5

Step-by-step explanation:

50 = x+55

50 - 55 = x

-5 = x

Answer:

please transalate

porfavor transalate

Step-by-step explanation:

The total loan payment is $1,024,050.

Another name for mortgage loans is "loans against property." A mortgage loan can be used to refinance real estate or to buy, build, or remodel a home. Getting a new loan for a piece of property while the old one is still being paid off is referred to as refinancing. Typically, it is done to obtain a loan with better terms.

We have,

The 30-year mortgage loan of $205,000 at 5.5% interest rate

We know, the total cost of this loan can be calculated as

L=LM+PMI

So, LM=$205,000 x (1+0.055[tex])^{30[/tex]

LM=$205,000 x 4.984

LM = $1,021,710

Now, the PMI over 24 months

= $97.5 x 24

= $2,340

So, the total loan payment is:

= $1,021,710 + $2,340

= $1,024,050

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Answer:

x = 1, 2, 3, 4

Step-by-step explanation:

15x - 43 < 5x + 2

15x - 5x - 43 < 2

15x - 5x < 2 + 43

10x < 45

x < 4.5

x = 1, 2, 3, 4

The required value of the x in the given inequality is x < 4.5.

Inequality can be defined as the relation of the equation containing the symbol of ( ≤, ≥, <, >) instead of the equal sign in an equation.

here,
Given expression,
15x - 43 < 5x + 2

Adding 43 on both sides,
15x < 5x + 45

Subtract 5x from both sides,
10x < 45

Divide the inequality by 10
x < 4.5

Thus, the required value of the x in the given inequality is x < 4.5.

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Answer:

x = 12.2

Step-by-step explanation:

to solve for 'x', we can use the sine ratio of opposite/hypotenuse

we need to find the angle opposite side 'x', which can be found by:

180-(44+90) = 46

sin46° = x/17

x = 17·sin46°

x = 12.2

Answer:

Wavelength = 16 m

Step-by-step explanation:

Given that,

In 6 seconds, a total of 3 waves crash into a cliff.

The distance between 2 adjacent wave crests on the water is 8 meters.

We need to find the wavelength of the wave.

We know that, the distance between two consecutive wave is called wavelength of a wave.

We can understand that, total of 3 wave crests, the distance between first and second wave crest is 8 meters.

Hence, the wavelength is 8 m + 8 m = 16 m