A boat took 4 hours to make a downstream
trip with a current of 6 km/h. The return trip
against the same current took 6 hours. Find
the speed of the boat in still water.

By definition of perimeter, direct observation and Pythagorean theorem, the perimeter of kite OBDE is 38 units. (Correct choice: C)

In geometry, the perimeter is the sum of the lengths of the sides of a figure.  Herein we must determine the perimeter of a quadrilateral, the kite OBDE, that is, the sum of the lengths of its four sides:, which can be found both by direct observation or by the use of the Pythagorean theorem.

Please notice that the quadrilateral has an axis of symmetry passing through the points O and D, which implies that OB = OE and BD = DE. The length of sides BD and DE is 6 units and the length of the sides OB and DE are:

OB = DE = 0.5 · √(24² + 10²)

OB = DE = 13

Lastly, the perimeter of kite OBDE is p = 2 · 6 + 2 · 13 = 38 units.  

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Answer:  C. 38 units

Step-by-step explanation:  TRUST ME!!! Answer is correct on Edge!!!  :)

Just did it and got it correct!

Step-by-step explanation:

x:y=0.75:0.90

Here,

Dividing by the value of y=0.90,

x:y=0.75/0.90:0.90/0.90

=5/6:1

Similarly,

y:z=1/3:1/4

Dividing by 1/3,we get,

y:z=1:3/4

Now,

X:y:z=5/6:1:3/4

Multiplying by both value of y,0.90×1/3=3/10

x:y:z=5/6×3/10:1×3/10:3/4×3/10

By solving this,

Given that angle ABD and angle DBC are adjacent angle, the value of angle ABC is 120 degrees.

Given the data in the question;

Since angle ABD and angle DBC are adjacent angle, there addition will give us the value of angle ABC.

∠ABD + ∠DBC = ∠ABC

We substitute in the given values

61° + 59° = ∠ABC

∠ABC = 120°

Given that angle ABD and angle DBC are adjacent angle, the value of angle ABC is 120 degrees.

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Answer:

168 square inches

Step-by-step explanation:

A = BH

or

Area = Base x Height

In other words multiply 12 and 14.

Answer:

1. No

2. No

3. Yes

4. No

5. Yes

6. No

Step-by-step explanation:

If you want to check if a graph is a function, do a vertical line test. For every vertical line, there should be only 1 point on the line if the graph is a function.

Answer:

The scale factor is 1/5.

Step-by-step explanation:

You can find the side length of triangles by looking at the points or it might be easier to see if you look at the graphs that I have attached.  I can see that the legs of the small triangle are 3 and the legs of the large triangle are 15.  What do I need to multiple 3 by to get 15?  5.  That is the scale factor from the little triangle to the big triangle.  If I go the other way, the scale factor is the reciprocal of 5 or 1.5

Let's solve your inequality step-by-step.

x+25>50

Step 1: Subtract 25 from both sides.

x+25−25>50−25

x>25

Answer:

x>25

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The angle the pole makes with the tent is 39.7°.

Trigonometric ratio: the trigonometric ratio is used to demonstrate the relationship between the sides and angles of a right-angled triangle.

Let θ represent the angle the pole makes with the tent.

Using trigonometric ratios:

Therefore, the angle the pole makes with the tent is 39.7°.

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Answer:

cashier needed to divide by 1000, not 3.

Step-by-step explanation:

there are 1000ml in one liter. in order to find the amount of liters, youd have to divide the milliliters by 1000. its only after then that you can multiply by $2. answer would be $36

Answer:

shown below

Step-by-step explanation:

1) tanY = 0.2334

Y = arctan(0.2334)

Y = 13.14 degrees

2) X = 12 / tan(40)

X = 14.3km

3) x = arctan(5/8)

x = 32°

Step-by-step explanation:

Reduce 13/100 to lowest terms

13

100

is already in the simplest form. It can be written as 0.13 in decimal form (rounded to 6 decimal places).

Steps to simplifying fractions

Find the GCD (or HCF) of numerator and denominator

GCD of 13 and 100 is 1

Divide both the numerator and denominator by the GCD

13 ÷ 1

100 ÷ 1

Reduced fraction:

13

100

Therefore, 13/100 simplified to lowest terms is 13/100.

The mixed number [tex]7\dfrac{13}{100}[/tex] is [tex]\dfrac{713}{100}[/tex] on simplification.

A mixed number is a mathematical representation of a number that consists of a whole number and a fraction. It's called a "mixed number" because it combines both a whole number and a proper fraction. The whole number part represents a whole quantity, while the fractional proportion represents a proportion of a whole.

Mixed numbers are generally employed to represent measures that aren't whole numbers but are still greater than 1. They're particularly useful when dealing with magnitudes, such as lengths or quantities of things, that concern both whole units and fractional parts.

Given that

[tex]7\dfrac{13}{100}[/tex] [tex]= 7 + \dfrac{13}{100}[/tex]

       [tex]= \dfrac{700}{100}+ \dfrac{13}{100}\\= \dfrac{700+13}{100} \\= \dfrac{713}{100}[/tex]

Hence, The mixed number [tex]7\dfrac{13}{100}[/tex] can be simplified as [tex]\dfrac{713}{100}[/tex].

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Answer:

600

Step-by-step explanation:

since it is a right triangle based pyramid, 2 of them will make a cube. so, it is bwh / 2.

base = 24

width = 10

height = 5

volume = 1200

volume of pyramid = 600

The 15th term in the given A.P. sequence is a₁₅ = 33.

According to the statement

we have given that the A.P. Series with the a = 5 and the d is 2.

And we have to find the 15th term of the sequence.

So, for this purpose we know that the

An arithmetic progression or arithmetic sequence is a sequence of numbers such that the difference between the consecutive terms is constant.

And the formula is a

an = a + (n-1)d

After substitute the values in it the equation become

an = 5 + (15-1)2

a₁₅ = 5 + 28

Now the 15th term is a₁₅ = 33.

So, The 15th term in the given A.P. sequence is a₁₅ = 33.

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Answer:

3, 1, - 1, - 3, - 5

Step-by-step explanation:

using the recursive formula and f(1) = 3 , then

f(2) = f(1) - 2 = 3 - 2 = 1

f(3) = f(2) - 2 = 1 - 2 = - 1

f(4) = f(3) - 2 = - 1 - 2 = - 3

f(5) = f(4) - 2 = - 3 - 2 = - 5

first 5 terms are 3, 1, - 1, - 3, - 5

La altura del triangulo está dada por el polinomio:

p(x) = a + 4

Recordar que para un triangulo de base B y altura H, el area es

A = B*H/2

En este caso, sabemos que la base es B = (4*a^2 + 6)

Y el area es A = 2a^3 + 8a^2 +3a +12

Entoces la altura será un polinomio tal que:

P(a)*(4*a^2 + 6)/2 = 2a^3 + 8a^2 +3a +12

P(a)*(4*a^2 + 6) = 2*(2a^3 + 8a^2 +3a +12) = 4a^3 + 16a^2 + 6a + 24

Podemos ver que p(a) va a ser un polinomio de grado 1, entonces:

p(a) = (c*a + b)

Reemplazando eso:

(c*a + b)*(4*a^2 + 6) = 4a^3 + 16a^2 + 6a + 24

Expandiendo:

(4c)*a^3 + (6c)*a + (4b)*a^2 + 6*b = 4a^3 + 16a^2 + 6a + 24

Comparando terminos del mismo exponente, podemos ver que:

(4c) = 4

6c = 6

4b = 16

6b = 24

Resolviendo esas ecuaciones para c y b, podemos ver que:

b = 16/4 = 4

c = 4/4 = 1

Entonces la altura del triangulo está dada por el polinomio:

p(x) = a + 4

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Since the product of the slope is -1, hence the lines are perpendicular

Two lines are known to be parallel if they have the same slope while if two lines are perpendicular if the product of the slope is -1

Given the coordinates of line 1 passing through (0, 6) and (6, 4), the slope is given as;

Slope = 4-6/6-0
Slope = -2/6
Slope = -1/3

Similarly for the coordinate points (-1, -7) and (1, -1).

Slope = -1+7/1+1
Slope of line 2 = 6/2

Slope = 3

Take the product of the slopes

Slope = -1/3 * 3
slope = -1

Since the product of the slope is -1, hence the lines are perpendicular

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The value of length ER rounded to the nearest tenth is 17.9 units (Option C)

The trigonometric ratios which has been proven as regarding right angle triangles are given below:

Sine θ = Opposite / Hypothenus

Cos θ = Adjacent / Hypothenus

Tan θ = Opposite / Adjacent

With above information in mind, we can easily determine the length of ER in the question. This is illustrated below:

From the question given above, which is summarized in the diagram (see attached photo) the following data were obtained:

Since we looking for the Adjacent (ER), the best trig ratio to use is the Cos θ ratio. This can be obtained as illustrated below:

Cos θ = Adjacent / Hypothenus

Cos 61 = ER / 37

Cross multiply

ER = 37 × Cos 61

ER = 37 × 0.4848

ER = 17.9 units

Thus, the length of ER to the nearest tenth is 17.9 units

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Answer:

irrational,  it can't be written as a fraction

Step-by-step explanation:

By using what we know about right triangles, we conclude that the height is 11ft.

We can think of this as a right triangle.

Where the length of the escalator is the hypotenuse

We know that the angle of depression is 42.51°, then the top angle of our right triangle is:

90° - 42.51° = 47.49°

Now, the height of the top of the escalator would be the adjacent cathetus to said angle, then we can use the relation:

cos(a) = (adjacent cathetus)/(hypotenuse)

Replacing what we know:

cos(47.49°)  = height/16ft

cos(47.49°) *16ft = height = 10.8ft

Rounding to the nearest foot, we get:

height = 11ft

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Answer:

2.1 litres

Step-by-step explanation:

the 5 part of the ratio refers to 3.5 litres of red paint

divide this amount by 5 to find the value of one part of the ratio

3.5 litres ÷ 5 = 0.7 litres ← value of 1 part of the ratio , then

3 parts = 3 × 0.7 litres = 2.1 litres ← amount of blue paint used

Answer:

1) 9.69

2) 87.36

3) 171.42

4) 18.75

5) 16.29

Step-by-step explanation:

Treat each value's full price as x. then, all of the values are (2/3)x. To get (2/3)x back to x, we must multiply (2/3)x*(3/2)=x. Multiply each of the questions given by 3/2 or 1.5

Answer:

-3

Step-by-step explanation:

If you reflect over the y-axis and then move 2 units to the left(x-2), then ABCD will be 3 units above EHGF. Since you need to move it down 3 units to map ABCD onto EHGF, you will need to do y-3, which is the same as y+-3

To form a system of equation from a word problem, we must recognize different variables to form different equations.

Let a represent the number of child tickets.

Let b represent the number of adult tickets.

We're given:

Because we're given that a and b in total is 163, we can form the following equation:

[tex]a+b=163[/tex]

We're also given that the total sales made is $1221.80. Because we know that 1a = $6.20 and 1b = $9.40, we can also form the following equation:

[tex]6.2a+9.4b=1221.8[/tex]

Here are our two equations:

[tex]a+b=163[/tex]

[tex]6.2a+9.4b=1221.8[/tex]

We can solve using the method of elimination. Multiply both sides by 6.2 in the first equation:

[tex]6.2(a+b)=6.2(163)\\6.2a+6.2b=1010.6[/tex]

Subtract this new equation from the second equation to cancel out a:

[tex]\hspace{10}6.2a+9.4b=1221.8\\- 6.2a+6.2b=1010.6\\\rule{100}{0.5}\\3.2b=211.2[/tex]

Solve for b:

[tex]b=66[/tex]

Therefore, the number of adult tickets sold is 66.

66

Using it's concept, the approximate perimeter of pentagon ABCDE is given as follows:

34.4 units.

The perimeter of a figure is given by the sum of the lengths of it's outside dimensions.

In this problem, the vertices are in a coordinate-plane, hence the distances are found using the formula for the distance between two points.

Suppose that we have two points, [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]. The distance between them is given by:

[tex]D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

The length of segment AB is:

[tex]AB = \sqrt{(6 - 0)^2+(0 - 7)^2} = 9.2[/tex]

The length of segment BC is:

[tex]BC = \sqrt{(6 - 3)^2+(0 + 4)^2} = 5[/tex]

The length of segment CD is:

[tex]CD = \sqrt{(-3 -3)^2+(-4 + 4)^2} = 6[/tex]

The length of segment DE is:

[tex]DE = \sqrt{(-6 + 3)^2+(0 + 4)^2} = 5[/tex]

The length of segment EA is:

[tex]EA = \sqrt{(-6 +0)^2+(0 - 7)^2} = 9.2[/tex]

Hence the perimeter is:

P = AB + BC + CD + DE + EA = 9.2 + 5 + 6 + 5 + 9.2 = 34.4 units.

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The given statement is false because the triangles may not be identical if their corresponding angles are genuinely different.

Based only on the information given in the diagram, it is guaranteed that PQR~ STU:

Two right triangles, ΔPQR and  ΔSTU—are shown in the illustration with their right angles at ∠P and ∠S, respectively.

It is also demonstrated that TU = 12 units and QR = 6 units.

Because we only provided one set of congruent angles, we are unable to apply the A postulate of similarity to it.

Additionally, since there is only one pair of comparable sides, we are unable to determine whether they are proportionate.

The statement "based purely on the information presented in the diagram, it is assumed that triangle PQR triangle STU" is False because the triangles may not be identical if their corresponding angles are genuinely different.

Hence, The given statement is false.

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Considering the definition of perpendicular line, the slope of a line perpendicular to the line whose equation is 3x+y= -9 is  [tex]\frac{1}{3}[/tex].

A linear equation o line can be expressed in the form y = mx + b.

where

Perpendicular lines are lines that intersect at right angles or 90° angles.

Two nonvertical lines are perpendicular if the slope of one is the negative reciprocal of the slope of the other. In other words, if you multiply the slopes of two perpendicular lines, you get –1.

In this case, the line is 3x+y=-9. Expressed in the form y = mx + b, you get: y= -9 - 3x or, what is the same, y= -3x -9

If you multiply the slopes of two perpendicular lines, you get –1. In this case, the line has a slope of  -3. So:

(-3)× slope perpendicular line= -1

slope perpendicular line= (-1)÷ (-3)

slope perpendicular line=  [tex]\frac{1}{3}[/tex]

Finally, the slope of a line perpendicular to the line whose equation is 3x+y= -9 is  [tex]\frac{1}{3}[/tex].

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The solution to the system of equations y = 1/2x - 6, x = -4 is x = -4 and y = -8. (x, y) = (-4, -8)

There are different types of equation. Namely;

y = 1/2x - 6

x = -4

y = 1/2x - 6

y = 1/2(-4) - 6

= -4/2 - 6

= -2 - 6

y = -8

Therefore,

The solution to the system of equations y = 1/2x - 6, x = -4 is x = -4 and y = -8. (x, y) = (-4, -8)

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If the p-value is smaller than the level of significance, then it indicates strong evidence against the null hypothesis, as there is less than a 5% probability the null hypothesis is correct.

In this question,

A p-value is a probability, calculated after running a statistical test on data and it lies between 0 and 1. The p-value only tells you how likely the data you have observed is occurred under the null hypothesis.

One of the most commonly used p-value is 0.05. If the value is greater than 0.05, the null hypothesis is considered to be true. If the calculated p-value turns out to be less than 0.05, the null hypothesis is considered to be false, or nullified (hence the name null hypothesis).

A small p-value (< 0.05 in general) means that the observed results are unusual, assuming that they were due to chance only. Now, the smaller the p-value, the stronger the evidence that should reject the null hypothesis.

Hence we can conclude that if the p-value is smaller than the level of significance, then it indicates strong evidence against the null hypothesis, as there is less than a 5% probability the null hypothesis is correct.

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