A triangle has sides with lengths of 40 inches, 75 inches, and 85 inches. Is it a right triangle?

The first ship sails on a bearing of 83° at 30 knots while the second on a bearing of 173° at 20 knots. After two hours, the distance between the ships is 72 NM

The two ships are travelling on different bearings and at different speeds. To calculate the distance between them after two hours, we need to use the formula:

Distance = Speed x Time

The distance the first ship has travelled after two hours:

Distance 1st ship = 30 knots x 2 hours = 60 nautical miles (NM)

The distance the second ship has travelled after two hours:

Distance 2nd ship = 20 knots x 2 hours = 40 nautical miles (NM)

The angle difference = 173° -  83°  = 90°

Since the port, the first ship, and the second ship form a right triangle, we can find the total distance between the two ships using the Pythagorean Theorem.

Distance² = (60 NM)² + (40 NM)²

Distance = √ (3600 + 1600) = √ 5200 = 72 NM


Therefore, after two hours, the two ships will be 72 NM apart.

Learn more about Pythagorean Theorem here:
https://brainly.com/question/24761611

#SPJ11

The value of  [tex]\sum _{n=1}^{400}\:\left(2n-1\right)[/tex] is 16000.

Sequence is an enumerated collection of objects in which repetitions are allowed and order matters.

Given equation is  [tex]\sum _{n=1}^{400}\:\left(2n-1\right)[/tex]

[tex]\sum \:a_n+b_n=\sum \:a_n+\sum \:b_n[/tex]

By Applying the sum rule

[tex]=\sum \:_{n=1}^{400}2n-\sum \:_{n=1}^{400}1[/tex]

=2×2(400+1)/2 -400

=2×200×401−400

=16000

Hence, the value of  [tex]\sum _{n=1}^{400}\:\left(2n-1\right)[/tex] is 16000.

To learn more on Sequence click:

https://brainly.com/question/21961097

#SPJ1

The simplified fraction is given as follows:

(2x - a)/(2x + a).

At the numerator, the fraction is simplified applying the least common factor as follows:

2 - (a/x) = (2x - a)/x.

At the denominator, the fraction is also simplified applying the common factor as follows:

2 + (a/x) = (2x + a)/x.

x is a common denominator to both of the fractions, hence it can be simplified, and then the simplified fraction is given as follows:

(2x - a)/(2x + a).

More can be learned about simplification of fractions at https://brainly.com/question/78672

#SPJ1

Option B, On a coordinate plane, the locations of the points (9, -5) and (9, 5) related reflection across the x-axis.

The two locations (9, -5) and (9, 5) have the same x-coordinate, but their y-coordinates are different. We need to see how the coordinates of two points change as they undergo various transformations to understand their relationship.

Learn more about the coordinate plane at

https://brainly.com/question/24134413

#SPJ4

(a) The average rate of change of f on [−3,1] is:
f(1)-f(-3)/(1-(-3)) = (1+3)/(1-(-3)) - ((-3)+3)/(-3-(-3)) = (4/4) - (0/6) = 1 - 0 = 1

(b) The average rate of change of f on [x,x+h] is:
f(x+h)-f(x)/(x+h-x) = (x+h+3)/(x+h-8) - (x+3)/(x-8) = (x+h+3)(x-8) - (x+3)(x+h-8)/(x+h-8)(x-8) = (x^2-5x-8h-11)/(x^2-8x-8h+64)

The average rate of change of a function is the slope of the line that passes through two points on the graph of the function. It is calculated by the difference in the y-values of the two points divided by the difference in the x-values of the two points.

The average rate of change of f on [−3,1] is:
f(1)-f(-3)/(1-(-3)) = (1+3)/(1-(-3)) - ((-3)+3)/(-3-(-3)) = (4/4) - (0/6) = 1 - 0 = 1

The average rate of change of f on [x,x+h] is:
f(x+h)-f(x)/(x+h-x) = (x+h+3)/(x+h-8) - (x+3)/(x-8) = (x+h+3)(x-8) - (x+3)(x+h-8)/(x+h-8)(x-8) = (x^2-5x-8h-11)/(x^2-8x-8h+64)

Therefore, the average rate of change of f on [x,x+h] is (x^2-5x-8h-11)/(x^2-8x-8h+64).

Learn more about Average rate

brainly.com/question/12395856

#SPJ11

The result obtained  when x^(4)-6x^(2)-x-19 is divided by x-3  using long division method is    x3 - 18x2 - 9x - 57 + 19/x-3.

The question is, "Use the long division method to find the result when x^(4)-6x^(2)-x-19 is divided by x-3".

To solve this problem using long division, we need to set up the division like this:

    x4 - 6x2 - x - 19

    ___________________      (x-3)

                      0

                           -3x3 - 18x2 - 9x - 57

Now, divide the first term of the numerator by the first term of the denominator, x4/x = x3, and write it above the division. Next, multiply the result x3 by the denominator (x-3) to get -3x3.

Now subtract -3x3 from the numerator (x4 - 6x2 - x - 19) to get -6x2 - x - 19. Divide this by the denominator (x-3) to get -18x2 - 9x - 57, and write it below the division. Now multiply the result -18x2 by the denominator (x-3) to get -54x2 - 27x - 171.

Finally, subtract -54x2 - 27x - 171 from -6x2 - x - 19 to get the remainder, -19.

To know more about long division click on below link:

https://brainly.com/question/28824872#

#SPJ11

3

x

+

7

(

3

x

+

4

)

3

x

+

7

×

3

x

+

7

×

4

3

x

+

21

x

+

28

24

x

+

28

Answer:

See image attached for complete answer

Step-by-step explanation:

The attached image shows the calculation of probabilities for each branch

I believe it is self-explanatory

Since P(bus to shops) = 0.4, P(walk to shops ) = 1- 0.4 = 0.6

Since P(bus from shops) = 0.7, P(walk from shops) = 1- 0.7 = 0.3

The probabilities at the leaves of the tree(rightmost entries) show the combined probabilities of to and from

For example if she takes a bus to the shops and takes a bus from the shops, the combined probability = 0.4 x 0.7 = 0.28

If she walks to the shops and takes a bus from the shops the combined probability = 0.6 x 0.7 = 0.42

The other two probabilities can be computed the same way

The probability that she walks at least one way
= P(walking to shop) or P(walking from shop)

= sum of the probabilities in the yellow shaded boxes

= 0.12 + 0.42 + 0.18

= 0.72

A rule to represent this translation include the following (x, y)  →  (x - 9, y + 4).

In Mathematics, the translation of a geometric figure to the right simply means adding a digit to the value on the x-coordinate (x-axis) of the pre-image of a function while a geometric figure that is translated upward simply means adding a digit to the value on the y-coordinate (y-axis) of the pre-image.

In Mathematics, a vertical translation to the positive y-direction (upward) is modeled by this mathematical expression g(x) = f(x) + N.

Where:

C(3, 2) → C'(-6, 6)

3 + x = -6

x = -6 - 3 = -9.

y + 2 = 6

y = 6 - 2 = 4.

Therefore, the transformation rule is (x, y)  →  (x - 9, y + 4)

Read more on translation here: brainly.com/question/16486008

#SPJ1

The exact values are:
cosα = -√7/3
sin2α = 8√7/9

cos2α = -7/9
tan2αcos2α/sin2α = 1

If sinα = −4/3, π⩽α⩽2π/3, we can find the exact value of cosα, sin2α, cos2α, and tan2αcos2α/sin2α by using the trigonometric identities.

cosα = √(1 - sin²α) = √(1 - (-4/3)²) = √(1 - 16/9) = √(-7/9) = -√7/3

sin2α = 2sinαcosα = 2(-4/3)(-√7/3) = 8√7/9

cos2α = 1 - sin²α = 1 - (-4/3)² = 1 - 16/9 = -7/9

tan2αcos2α/sin2α = (sin2α/cos2α)(cos2α/sin2α) = 1

Therefore, the exact values are:
cosα = -√7/3
sin2α = 8√7/9
cos2α = -7/9
tan2αcos2α/sin2α = 1

Learn more about Trigonometric identities

brainly.com/question/24377281

#SPJ11

The product of the number and its conjugate is 29.

The complex conjugate of a complex number is the number with the same real part and the opposite sign of the imaginary part. In other words, if a complex number is a + bi, then its complex conjugate is a - bi.

For the given number -5 - 2i:

(a) The complex conjugate is -5 + 2i. This is because the real part is the same (-5) and the imaginary part has the opposite sign (2i instead of -2i).

(b) To determine the product of the number and its conjugate, we simply multiply them together:

(-5 - 2i)(-5 + 2i) = 25 - 10i + 10i - 4i^2

Since i^2 = -1, we can simplify this to:

25 - 4(-1) = 25 + 4 = 29

So the product of the number and its conjugate is 29.

Learn more about conjugate

brainly.com/question/28175934

#SPJ11

Answer:

$3.30

Step-by-step explanation:

66 times 0.05

Answer:

To simplify the expression, we can combine the like terms.

(3x + 1/2) + (7x - 4 1/2)

= 3x + 7x + 1/2 - 4 1/2 (distributing the addition)

= 10x - 4 (combining the like terms)

Therefore, (3x + 1/2) + (7x - 4 1/2) simplifies to 10x - 4.

When we square the two sides, we obtain: Z = square (82) , YZ thus has a length of about 9.06 units.

The connection among all three opposites of a right triangle is a key idea in geometry known as Pythagoras' theorem. According to this rule, the square of the hypotenuse's length—the side that faces the right angle—in a right triangle is the product of the squares of the dimensions of the other two sides. You can write this as follows: [tex]a^2 + b^2 = c^2[/tex] where a and b are the sizes of the other two right triangle sides and c has been the angle of the hypotenuse. The theorem is named after Pythagoras, an ancient Greek mathematician who is credited with finding it and creating its mathematical proof.

given

We may apply the Pythagorean theorem to determine the length of YZ.

Triangle VYZ is a right-angled triangle with the legs VY and VZ and the hypotenuse YZ, as may be seen. From the information provided, we can determine the lengths of VY and VZ.

VY = 35 - 36 = -1 (we can see from the diagram that V is to the left of Y, hence VY is negative) (we can see from the diagram that V is to the left of Y, so VY is negative)

VZ = 44 - 35 = 9 (we can see from the graphic that Z is below V, hence VZ is positive) (we can see from the diagram that Z is below V, so VZ is positive)

Using the Pythagorean theorem, we have the following:

[tex]VY^2 + VZ^2 = YZ^2\\YZ^2 = (-1) (-1)^2 + 9^2 \\YZ^2 = 1 + 81 \\YZ^2 = 82[/tex]

When we square the two sides, we obtain: Z = square (82) , YZ thus has a length of about 9.06 units.

To know more about Pythagoras theorem visit :-

https://brainly.com/question/14461977

#SPJ1

The expression (z²+10z+25)/(z²-3z-40) in simplest form is (z+5)/(z-8), with the restriction that z cannot be equal to 8.

The expression (z²)+10z+25)/(z²-3z-40) can be simplified by factoring both the numerator and denominator.

First, factor the numerator:
(z²+10z+25) = (z+5)(z+5)

Next, factor the denominator:
(z²-3z-40) = (z-8)(z+5)

Now, the expression can be simplified by canceling out the common factor of (z+5):
(z+5)(z+5)/(z-8)(z+5) = (z+5)/(z-8)

Therefore, the expression in simplest form is (z+5)/(z-8).

There are restrictions on the variable in this expression. The denominator cannot be equal to zero, so we must exclude any values of z that would make the denominator zero.

The denominator is (z-8), so the restriction is:
z-8 ≠ 0

Solving for z, we find that the restriction is:
z ≠ 8

To know more about simplest form click on below link:

https://brainly.com/question/290068#

#SPJ11

The distance of the mall from the pet shop, based on the graphic given, is 2 miles.

The distance between the Pet Shop, the School, the Mall and the Park are all shown on the graphic. The intervals between the distance given is shown to be 1 / 2 miles.

The number of distance marks between the Pet Shop and the Mall is 4 marks which means that distance between the Pet Shop and the Mall would be :

= 4 x 1 / 2

= 4 / 2

= 2 miles

Find out more on distance at https://brainly.com/question/22444331

#SPJ1

Michael will need to pay a total of R276,000 over the 60 months for the Mex tractor.

First, let's calculate the total amount he will need to finance:

Total amount to finance = R160,000 + 0.15 x R160,000 (VAT at 15%) = R184,000

Next, let's calculate the total interest he will need to pay over the 60 months:

Total interest = (principal x rate x time) / 100

where

Total interest = (R184,000 x 10% x 5) / 100 = R92,000

Therefore, the total amount Michael will need to pay over the 60 months is the sum of the total amount financed and the total interest:

Total amount to pay = Total amount to finance + Total interest = R184,000 + R92,000 = R276,000

So, Michael will need to pay a total of R276,000 over the 60 months for the Mex tractor.

Learn more about interest here : brainly.com/question/20690803

#SPJ1

Answer:

Step-by-step explanation:

45 points for signing up.

2.5 points for each visit [tex]=2.5v[/tex]

Needs to total 75 points.

So [tex]45+2.5v=75[/tex] is the solution.

This is shown by option [tex](D)[/tex].

By answering the above question, we may state that A kite has graphs perpendicular diagonals, and the larger diagonal splits the shorter diagonal in half.

Mathematicians use graphs to visually express or chart facts or values in a logical way. Usually, a graph point will show the relationship between two or more objects. A graph is a non-linear data structure made up of nodes, also known as vertices, and edges. The nodes, sometimes referred to as vertices, should be joined with glue. Vertices in this graph are 1, 2, 3, and 5, whereas edges are 1, 2, 1, 3, 2, 4, and (2.5). (3.5). (4.5). Graphical depictions of exponential development in statistical charts, such as bar charts, pie charts, and line graphs. a triangle-shaped logarithmic graph

The measurements of the numbered angles in each kite cannot be given without a reference image or particular kite. We can, however, offer some general knowledge on kites and their angles.

With two sets of neighboring congruent sides and angles, a kite is a quadrilateral with congruent sides on all four sides. A kite has perpendicular diagonals, and the larger diagonal splits the shorter diagonal in half.

Let's give a generic kite's angles the labels displayed in the accompanying diagram:

  A-------B

 /         \

D-----------C

To know more about graphs visit:

https://brainly.com/question/11950136

#SPJ1

The surface area, in square centimeters, of the toy box is 370 cm²

The quantity of space enclosing a three-dimensional shape's exterior is its surface area. Surface area is measured in cm².

Given, the lengths are 9 cm, 5 cm, and 10 cm.

To calculate the surface area, the formula is2(h × W) + 2(h × L) + 2(W × L)

2 x 9 x 5 + 2 x 9 x 10 + 2 x 5 x 10

90 + 180 + 100

370

Therefore, the surface area of the box is 370 cm²

Learn more about surface area, here:

https://brainly.com/question/29298005

#SPJ1

The question is incomplete, the image of the box is attached below:

The equation of y=x^(2) can be translated 8 units to the left and then 6 units downward by modifying the equation as follows:

y=(x+8)^(2)-6

This equation represents the same parabola as y=x^(2), but it has been shifted 8 units to the left and 6 units downward.

The translation of a function can be represented by modifying the equation in the form y=f(x-h)+k, where h is the horizontal shift and k is the vertical shift. In this case, h=-8 and k=-6, so the equation becomes:

y=f(x-(-8))+(-6)
y=f(x+8)-6

Substituting the original function f(x)=x^(2) into this equation gives:

y=(x+8)^(2)-6

Therefore, the equation of y=x^(2) when it is translated 8 units to the left and then 6 units downward is y=(x+8)^(2)-6.

For more about equation:

https://brainly.com/question/29657992

#SPJ11

Answer:

This is an odd function

Step-by-step explanation:

Given a function f(x),

if f(-x) = f(x) then the f(x) is even
If f(-x) = -f(x0 then the function is odd

If neither of the above is true then the function is neither odd nor even

We are given
[tex]f(x) = 4x^3 - x^5 + 5x\\f(-x) = 4(-x)^3 -(x)^5 + 5(-x)\\\\(-x)^3 = - x^3\\(-x)^5 = -x^5\\\\\\\therefore\\f(-x) = 4(-x^3) - (-x^5) + 5 (-x)\\\\= -4x^3 + x^5 - 5x\\\\= -(4x^3 -x^5 + 5x)\\\\= -f(x)[/tex]

So the function is odd

The expression ((-8x⁵)(x⁻³))/(20x²) when simplified, making all exponents positive, will become -2/5.

To simplify the expression ((-8x⁵)(x⁻³))/(20x²), we need to apply the rules of exponents and simplify the coefficients.

First, let's simplify the coefficients:
-8/20 = -2/5

Next, let's apply the rules of exponents:

Product Rule: When multiplying two exponential expressions with the same base, you can add the exponents. That is, xᵃ · xᵇ = xᵃ⁺ᵇ

Quotient Rule: When dividing two exponential expressions with the same base, you can subtract the exponents. That is, xᵃ / xᵇ = xᵃ⁻ᵇ

(x⁵)(x⁻³) = x⁵⁺⁽⁻³⁾ = x²
x²/x² = x²⁻² = x⁰ = 1

So the expression simplifies to:
(-2/5)(1) = -2/5

Therefore, the simplified expression is -2/5.

Learn more about rules of exponents here: https://brainly.com/question/11975096.

#SPJ11

a) P (20 < or = X) =  0.8617: This is the probability that 20 or more of the 30 patients will be helped by the medicine.

b) P (18 < or = X < 25) = 0.8557: This is the probability that between 18 and 25 of the 30 patients will be helped by the medicine.

c) P ( X < 16) = 0.0266: This is the probability that less than 16 of the 30 patients will be helped by the medicine.

The given situation can be modeled using a binomial distribution, where the number of trials is 30, and the probability of success is 0.75. We can use the binomial probability formula to find the probabilities for each of the given conditions. The binomial probability formula is:

P(X = x) = (n choose x) * p^x * (1-p)^(n-x)
where n is the number of trials, x is the number of successes, p is the probability of success, and (n choose x) is the binomial coefficient.

a) P (20 < or = X) = 1 - P (X < or = 19) = 1 - sum_{x=0}^{19} (30 choose x) * (0.75)^x * (0.25)^(30-x) = 0.8617

b) P (18 < or = X < 25) = P (X < or = 24) - P (X < or = 17) = sum_{x=18}^{24} (30 choose x) * (0.75)^x * (0.25)^(30-x) = 0.8557

c) P ( X < 16) = sum_{x=0}^{15} (30 choose x) * (0.75)^x * (0.25)^(30-x) = 0.0266

Therefore, the probabilities are 0.8617, 0.8557, and 0.0266 for the conditions a), b), and c) respectively.

You can learn more about probability at

brainly.com/question/24756209

#SPJ11

0.142857.

To convert the rational number 1/7 to its decimal form and round to the nearest thousandth, let's start by converting the fraction into a long division problem.

Enter the numerator of the fraction, 1, into the division box, and then divide it by the denominator of the fraction, 7.

The result of this long division is 0.142857. Finally, round this decimal to the nearest thousandth, which gives us 0.143.

Learn more about decimal form

brainly.com/question/16361602

#SPJ11

The possible length of the third side of a triangle is l < 25

A triangle is a closed, 2-dimensional shape with 3 sides, 3 angles, and 3 vertices. A triangle is also a polygon.

Given that, we need to find the possible lengths to complete a triangle with side lengths of 11 in. and 14 in.

We know that, the triangle inequality states that for any triangle, the sum of the lengths of any two sides must be greater than or equal to the length of the remaining side.

Therefore,

11 + 14 = 25

Let the third side be l,

Therefore,

l < 25

Hence, the possible length of the third side of a triangle is l < 25

Learn more about triangles, click;

https://brainly.com/question/2773823

#SPJ9

The vector that is perpendicular to the tangent vector of the curve at (0, 1, 0) is <1, 0, -1>, or option c

The space curve given is r(t) = sin t i + e^t j + ln(t+1) k. To find the tangent vector of the curve at a given point, we need to take the derivative of the curve with respect to t. The derivative of the curve is r'(t) = cos t i + e^t j + (1/(t+1)) k.

At the point (0, 1, 0), t = 0. So, the tangent vector at this point is r'(0) = cos 0 i + e^0 j + (1/(0+1)) k = <1, 1, 1>.

Now, we need to find which of the given vectors is perpendicular to the tangent vector. Two vectors are perpendicular if their dot product is equal to 0. So, we need to find the dot product of the tangent vector with each of the given vectors and see which one is equal to 0.

a. <1, 1, 1> • <0, 1, 0> = 0 + 1 + 0 = 1 (not perpendicular)
b. <1, 1, 1> • <-1, 0, -1> = -1 + 0 - 1 = -2 (not perpendicular)
c. <1, 1, 1> • <1, 0, -1> = 1 + 0 - 1 = 0 (perpendicular)
d. <1, 1, 1> • <1, -1, 1> = 1 - 1 + 1 = 1 (not perpendicular)
e. <1, 1, 1> • <1, 0, 1> = 1 + 0 + 1 = 2 (not perpendicular)

Therefore, the vector that is perpendicular to the tangent vector of the curve at (0, 1, 0) is <1, 0, -1>, or option c.

Learn more about Vector

brainly.com/question/29740341

#SPJ11

Answer:

2 hours

Step-by-step explanation:

shhsjdnd

dididjd

djdjdjdj

Answer:

When dividing a whole number by a decimal, you can use long division to find the quotient (the answer to the division problem). Here's how to divide 9 by 0.85 using long division:

.        __________

0.85 | 9.00

        8.50    (0.85 goes into 9.00 one time)

      -----

        1.50    (subtract 8.50 from 9.00)

        1.27    (0.85 goes into 1.50 one time)

      -----

        0.23    (subtract 0.85 from 1.50)

When dividing a whole number by a decimal, you can use long division to find the quotient (the answer to the division problem). Here's how to divide 9 by 0.85 using long division:

sql

Copy code

.        __________

0.85 | 9.00

        8.50    (0.85 goes into 9.00 one time)

      -----

        1.50    (subtract 8.50 from 9.00)

        1.27    (0.85 goes into 1.50 one time)

      -----

        0.23    (subtract 0.85 from 1.50)

The quotient is the number above the division line, which is 10 with a remainder of 23/100. Therefore:

9 / 0.85 = 10 with a remainder of 23/100, or 10.5882 (rounded to four decimal places)

So, 9 divided by 0.85 is approximately 10.5882.