in a right triangle with one angle measuring 40 degrees, the leg opposite the 40 degree angle is 5cm. what is the length of the hypotenuse?

Answer:

 150 minutes, or 2 1/2 hours

Step-by-step explanation:

You want to know the time required to empty a pond with the given dimensions if the level drops 20 cm in the first 30 minutes of pumping.

The average depth of the pond is the average of the depth at the shallow end and the depth at the deep end:

  (0.6 m + 1.4 m)/2

  = 2.0 m/2 = 1.0 m = 100 cm

If the level drops at the rate of 20 cm in 30 minutes, the time required for dropping the level by 100 cm is ...

  t/(30 min) = (100 cm)/(20 cm)

  t = 5·30 min = 150 min

The time to empty the pond completely is 150 minutes, or 2 1/2 hours.

__

Additional comment

As you know from the formula for the area of a trapezoid —

  A = 1/2(b1 +b2)h

the area is equivalent to that of a rectangle with base equal to the average of the two base lengths.

Here, the volume of the pond is the product of the area of the trapezoidal face and the pond width (1 m). That trapezoidal face has an area equivalent to that of a rectangle 1 m high and 2 m wide. The 1 m height is the depth we used in the above calculation.

Answer:

6 weeks.

Step-by-step explanation:

Let x be the number of weeks to be found.

Then  4.5x + 18 / 4x = 15/8

Cross multiply:

36x + 144 = 60x

24x = 144

x =  6  (answer).

In approximately 1.67 weeks (or rounded to 2 weeks), Theo and James will have savings in the ratio 15:8.

We can set up an equation to represent the savings of Theo and James over time. Let x be the number of weeks they have saved. Theo will have saved £4.50x and James will have saved £4x. We can set up the equation:

£4.50x / £4x = 15 / 8

Cross-multiplying the equation gives us:

8 * £4.50x = 15 * £4x

Simplifying the equation gives us:

36x = 60x

Dividing both sides by 36x gives us:

1 = 5 / 3x

Cross-multiplying again gives us:

3x = 5

Dividing both sides by 3 gives us:

x = 5 / 3

Therefore, in approximately 1.67 weeks (or rounded to 2 weeks), Theo and James will have savings in the ratio 15:8.

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Answer:

1. 30

2. 150

3. obtuse

4. acute

5. Adjacent

Step-by-step explanation:

The correct expression for the angles are;

1) m SUT equals  30 Degrees.

2) m TUW equals  150 degrees

3) TUW is obtuse angle

4) SUT is acute angle

5) TUW and SUT are Adjacent angles

Similar to corners, right angles have a 90° measure. Acute angles are less than ninety degrees. More than 90° but less than 180° are obtuse angles. Additionally, a straight angle is 180°, which is the point at which two lines merge into one by going in the same direction.

Any angle is composed of two rays that converge at a point known as the vertex. When two angles share a ray, it indicates that they are adjacent to one another.

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Answer:

Median: 23

Mode: $20

Mean: The average of numbers added up and then divided, equalling in 23

Answer:

65 ft by 39 ft

Step-by-step explanation:

Let x ft be the length of each part and y ft be the width of each part. The total perimeter of all 5 parts is

[tex]6x+10y=780[/tex]

The length of the large rectangle is 5y ft and the width of the large rectangle is x, so the total area is

[tex]A=x\cdot 5y[/tex]

From the first equation,

[tex]y=78-0.6x[/tex]

Substitute it into the area expression:

[tex]A(x)=x\cdot 5(78-0.6x)=390x-3x^2[/tex]

Find the derivative:

[tex]A'(x)=390-3\cdot 2x=390-6x[/tex]

Equate it to 0:

[tex]390-6x=0\\ \\6x=390\\ \\x=65[/tex]

Then

[tex]y=78-0.6\cdot 65=78-39=39[/tex]

Answer:

a^3 + b^3

Step-by-step explanation:

(a + b )(a^2 - ab + b^2)

Distribute

a*a^2 -a*ab+a*b^2    + b*a^2 -b*ab +b*b^2

Simplify

a^3 -a^2b +ab^2 +a^2b -ab^2+b^3

Combining like terms

a^3 +b^3

Answer:

a^3 + b^3

Step-by-step explanation:

hope this helps you! have a good day/night :D

Answer:

C

Step-by-step explanation:

The slope m of the functions give the measure of the rate of change.

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

g(x) = [tex]\frac{5}{2}[/tex] x - 3 ← is in slope- intercept form

with slope m = [tex]\frac{5}{2}[/tex] = 2.5

Calculate the slope of f(x) using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (0, - 3.5) and (x₂, y₂ ) = (1, - 1) ← 2 points from the table

m = [tex]\frac{-1+3.5}{1-0}[/tex] = 2.5

Hence

The slopes of g(x) and f(x) are both m = 2.5, thus

The functions increase at the same rate → C

Answer: 52.5 units squared

Step-by-step explanation:

The formula to find the area of a trapezoid is, (base1 + base2)/2 * height

So you find out which variable is which

Base 1 = 4

Base 2 = 3

Height = 15

Then plug it into the formula,

(4+3)/2 * 15

Then solve the order of operations

7/2 * 15

3.5 * 15

52.5 is the answer

Answer:

52.5

Step-by-step explanation:

Formula

Area = (1/2) (a + b)*h

Givens

a = 4

b = 3

h = 15

Solution

Area = (4 + 3)*15/2

Area = 7 * 15/2

Area = 105/2

Area = 52.5

The transformed image will be located in Quadrant III.

To solve this problem, we can think about what happens to the hour hand when it is rotated 90 degrees counterclockwise around the origin, and then reflected across the x-axis.

Rotation: When the hour hand is rotated 90 degrees counterclockwise around the origin, it moves to the position of the 3 o'clock hour. This means that the x and y coordinates of the tip of the hour hand are swapped. For example, if the tip of the hour hand was originally at (3, 4), after the rotation it would be at (4, 3).

Reflection: When the hour hand is reflected across the x-axis, its y-coordinate is multiplied by -1. This means that if the tip of the hour hand was at (4, 3) after the rotation, after the reflection it would be at (4, -3).

Now, let's look at the quadrants:

Quadrant I: x > 0, y > 0

Quadrant II: x < 0, y > 0

Quadrant III: x < 0, y < 0

Quadrant IV: x > 0, y < 0

Before the rotation, the tip of the hour hand is in Quadrant I, because both its x and y coordinates are positive.

After the rotation and reflection, the tip of the hour hand is in Quadrant IV, because its x-coordinate is still positive and its y-coordinate is now negative.

Therefore, the image will be in Quadrant III.

Answer:

376

Step-by-step explanation:

2(8x10)=2(80)=160

2(10x6)==2(60)=120

2(6x8)=2(48)=96

160+120+96=376

When subtracting logs you actually divide.

logx^2 = log 160 - log 2

logx^2 = log (160/2)

logx^2 = log 80

Now remove the log from each side:

x^2 = 80

x = √80

x = 4√5 and -4√5

Because integrated math requires skills in trigonometry, I would highly recommend pre calc first

Answer:

I would say you first evaluate your strengths by checking on both the syllabuses. Find what really interests you, your passion. Is it pre-calculus or is it integrated math.

Ability and passion go hand in hand when it comes to the performance.

Answer:

x^8/y^20

Step-by-step explanation:

multiply the exponents by 4.

Answer:

Zero is neither positive nor negative integer and is known as origin.

Answer:

v = -3

Step-by-step explanation:

Step 1: Use the Distributive Property

6v + 3= -75v - 240

Step 2: Isolate v

81v = -243

Step 3: Simplify

v = -3

The value of v in the equation 3(2v + 1)=-15(5v + 16)​ is -3 after rearranging and solving.

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

We have a linear equation in one variable:

3(2v + 1)=-15(5v + 16)​

6v + 3 = -75v -240

6v + 75v = -240 - 3

81v = -243

v = -3

Thus, the value of v in the equation 3(2v + 1)=-15(5v + 16)​ is -3 after rearranging and solving.

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Answer:

r > - 12

Step-by-step explanation:

4r – 5 < 5r+7

4r - 5r < 7 + 5

-r <12

r > - 12 (when you multiply or divide a negative number, the sign will be flipped)

Answer:D

Step-by-step explanation:

Answer:

see explanation

Step-by-step explanation:

Given

ab - ac = d + e ← factor out a from both terms on the left side

a(b - c) = d + e ← divide both sides by (b - c)

a = [tex]\frac{d+e}{b-c}[/tex]

Answer:

Step-by-step explanation:

Answer:

D. 254.34 cubic inches

​Step-by-step explanation:

The volume of a cylinder is given by

V = pi r^2h

Where r = 3 in and h = 9 in

V = (3.14) * (3)^2 *9

V = 254.34 in ^3

Answer:

volume of a cylinder= \pi*r^2*h

81*pi

=254.34 in^3

Answer:

[tex]\frac{3}{10}[/tex]

Step-by-step explanation:

we know that

To find the fraction of the store's books that are fiction mysteries, multiply 1/2 by 3/5

so

[tex](\frac{1}{2})(\frac{3}{5})=\frac{3}{10}[/tex]

You have to begin by using the triangle sum therom. That means Angle DEC would be 64°, Angle D would be 76°, and angle C would be 40°

the missing exponent would be 2

[tex]\bf (5^?)^{3}=5^1\implies 5^{?\cdot 3}=5^1\implies \stackrel{\textit{same base, the exponents must also be the same}}{?3=1\implies ?=\cfrac{1}{3}}[/tex]

Answer:

Step-by-step explanation: the answer is 1 because line a and b are paralel so 1 , 5 are the same as well as (2,7)

Answer:

angle 1

Step-by-step explanation:

this is because they are alternating angles.

f(x)=20+300x

Also, Rex should find a different pool because that fee is ridiculous.

The function rule in the given situation is a linear function and can be represented as C=20+300x. In this rule, 'C' is the total cost in dollars, '20' is the initial membership fee, '300' is the cost of each pool visit and 'x' is the number of pool visits.

The function rule in this situation is called a linear function. A function rule describes how to convert an input (in this case, the number of times Rex visits the pool) into an output (the total cost).

The function rule for this specific situation could be represented as C=20+300x, where 'C' is the total cost, '20' is the initial membership fee, '300' is the cost each time Rex goes to the couple, and 'x' is the number of times Rex goes to the pool.

So, each time Rex goes to the pool, you would multiply that number by 300 (the cost per visit), and then add 20 (the initial fee) to get the total cost.

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Answer:

Ratio would be 9 : 10

Step-by-step explanation:

Liliana surveyed 20 students that how many hours they spend on their computers each week.

The results are as follows

8, 15, 0, 11, 12, 13, 16, 13, 0, 4, 17, 14, 30, 13, 5, 12, 1, 13, 12, 21

In the above results 2 students did not use computers out of 20 students.

Therefore, The total number of students who used their computers = 20 - 2 = 18

So the ratio would be 18 : 20 or 9 : 10

Answer:

C. 18/20 or 9/10

Answer: 5 • (2x2 - 17x - 2)

 ———————————————————

        x - 8      

Step-by-step explanation:

Step by step solution :

Step  1  :

Equation at the end of step  1  :

Step  2  :

           10x2 - 85x - 10

Simplify   ———————————————

                x - 8      

Step  3  :

Pulling out like terms :

3.1     Pull out like factors :

  10x2 - 85x - 10  =   5 • (2x2 - 17x - 2)  

Trying to factor by splitting the middle term

3.2     Factoring  2x2 - 17x - 2  

The first term is,  2x2  its coefficient is  2 .

The middle term is,  -17x  its coefficient is  -17 .

The last term, "the constant", is  -2  

Step-1 : Multiply the coefficient of the first term by the constant   2 • -2 = -4  

Step-2 : Find two factors of  -4  whose sum equals the coefficient of the middle term, which is   -17 .

     -4    +    1    =    -3  

     -2    +    2    =    0  

     -1    +    4    =    3  

Observation : No two such factors can be found !!  

Conclusion : Trinomial can not be factored

The loan's future amount is $9940

The formula to calculate Simple interest is :

I=PRT

where,

I(interest money created)

P(initial amount of money)

R(interest rate as a decimal)

T(time in years)

I=7000(.07)(6)

I=$2,940

So, the loan's future amount = $7000 + $2940 = $9940

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The minimum y-value is -7.

I'm only a few Brainliests away from ranking up, so one would be much appreciated.

Answer:  A) -7

Step-by-step explanation:

The Asymptote is 1 so the range of the graph is from +1 to -1.

However, there is also a shift down of 6 units, so the range of the transformed graph is from (+1-6 = -5) to (-1-6 = -7).

Therefore, the maximum is -5 and the minimum is -7.

Answer:

Rhode Island has 1,000,000 people within an area of 1000 sq miles.....

1,000,000/1000 = 1000 people per sq mile

Step-by-step explanation:

If Alaska had the same number of people per square mile as Rhode Island, its population would be calculated as 663,000 mi^2 times 1,000 people = 663,000,000 people.

Answer:

The entry terrace has an area of

48

square feet. The total area of the tree house including the entrance, porch, and side deck is

350

square feet.

Step-by-step explanation:

I just took a test with this question and this was the right answer

~Please mark me as brainliest : )

pretty sure it’s the crickets because the others one does not make sense, crickets are known for jumping up and down a lot so i’m pretty sure it’s the cricket