the distance between (33,18) and (33,-72) is what unit

Answer:

A triangle with side lengths of 38, 38, and 104 is an isosceles triangle. This is because it has two sides of equal length (the two sides that are both 38 units long).

Step-by-step explanation:

Answer:

This Ratio Division Calculator allows you to divide an amount by a specific ratio (with multiple ratio values, for example 2:5:9:11:18, click on the "Example" buttons for ratio division examples), if you are new to ratio division or want to understand the formulas used in ratio division you should use our Divide Ratio Calculator as this ratio division calculator assumes you already understand the basics of ratio division, you may also find our Equivalent Ratio Calculator useful. A ratio is a numerical comparison of 2 or more quantities and indicate the relative size of each quantity. Ratios are used in a number of daily activities and business markets, the Ratio Division Calculator can be used to divide a specific ratio, you can also access additional Ratio Calculators for application in math, engineering and other every day scenarios.

Step-by-step explanation:

d =   c × b a  ,

d =   3 × 8 4  = 6

If we divide £42 in the ratio of 1:5 so it comes 7 and 35.

Given that,

Based on the above information, the calculation is as follows:

\(= 42 \times 1 \div (1 + 5)\)

= 7

And

\(= 42 \times 5 \div (1 + 5)\)

= 35

Therefore we can conclude that If we divide £42 in the ratio of 1:5 so it comes 7 and 35.

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Expressing or writing 7+21 as a product of two factors requires the application of Distributive Property

The expression that shows 7+21 written as a product of two factors is

7(1 + 3).

       a (b + c) = ab + ac

Where

a is the common factor

We are given the expression:

7 + 21

Splitting this into two factors using the distributive property

7 + 21

The common factor for 7 and 21 is 7

Hence, by factorising we have:

7 + 21 = 7(1 + 3)

Therefore, the expression that shows 7+21 written as a product of two factors is :

7(1 + 3)

The correct option is D

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The customers of Rhythm Time, an online music service, downloaded 397,970 songs last year.

Rhythm Time, an online music service, had 278,579 songs downloaded this year by its customers. That figure is 30% less than last year. Last year

We can begin by assuming that the total number of songs downloaded last year was x. According to the problem statement, 278,579 songs were downloaded this year, which is 30% less than last year. We can write it as an equation:x - 0.30x = 278,579 Simplifying, we get:0.70x = 278,579 Dividing both sides by 0.70, we get:x = 397,970Therefore, last year, Rhythm Time's customers downloaded 397,970 songs.

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The exact value of cos^-1( √3/2) = 30°

The trigonometric functions are real functions which relate an angle of a right-angled triangle to ratios of two side lengths.

There are special angles in trigonometry, this angles have exact value and can be obtained without using calculator. Examples of this calculator are; 30°, 60°, 45°

sin30 = 1/2

cos 30 = √3/2

tan 30 = 1/√3

cos 60 = 1/2

sin 60 = √3/2

tan 60 = √3

Therefore, if cos^-1( √3/2) = x

cos x = √3/2

cos 30 = √3/2

cos x = cos 30

therefore x = 30

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Answer:

She will pay $1,047.12 interest for one year

Step-by-step explanation:

Simple Interest

Occurs when interest is calculated on the original principal only.

Unlike compound interest where the interest earned in the compounding periods is added to the new principal, simple interest only considers the principal to calculate the interest.

The interest earned is calculated as follows:

I=P.r.t

Where:

I = Interest

P = initial principal balance or loan

r = interest rate

t = time

Samantha takes out a loan for $17,452 at r=6%=0.06 simple interest for t=1 year. Calculating the interest:

\(I=\$17,452*0.06 *1\)

I = $1,047.12

She will pay $1,047.12 interest for one year

The exponential growth or decay of a certain phenomenon, such as population growth or decay, over time. The graph typically looks like an “S” or exponential curve, with an initial slow start then an increasing or decreasing rate of change.

20An example of an exponential graph is one that shows the exponential growth or decay of a certain phenomenon, such as population growth or decay, over time. The graph typically looks like an “S” or exponential curve, with an initial slow start followed by an increasing or decreasing rate of change. This rate of change is often characterized by a mathematical function, such as an exponential function, which can be used to calculate the expected change in the phenomenon over a given period of time. For example, an exponential graph can be used to show how a population will grow or decline over time, based on its current population size, growth rate, and other factors. Exponential graphs can also be used to show the growth or decay of a chemical reaction, the rate of change of a financial asset, or any other phenomenon that can be characterized by an exponential function.

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The common end point I believe :)

Answer: A, C, D

Step-by-step explanation:

Answer:

phle follow karo yrr tab hee bat u ga,

Each of the pairs of angles should be identified as follows;

Complementary angles = ∠HJ and ∠FJ

Adjacent angles = ∠LON and ∠NOM

Supplementary angles = ∠EFA and ∠EFB

Vertical angles = ∠LOP and ∠MO

In Mathematics and Geometry, a complementary angle can be defined as two (2) angles or arc whose sum is equal to 90 degrees (90°).

Mathematically, a complementary angle can be represented by using this mathematical equation:

Q + R = 90°

Where:

Q and R are measure of the angles subtended.

In Mathematics and Geometry, adjacent angles can be defined as two (2) angles that share a common vertex and a common side. This ultimately implies that, both angle LON and angle NOM are adjacent angles.

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Answer:

4 + 12 = 16

thats so easy you just put the 4 in for the x and add it, you will then get 16

Step-by-step explanation:

thanks for basically free points:))

Answer: 50, 60, 70, 80, 90

Answer:

k < -1 or k > 11

Step-by-step explanation:

Given quadratic equation:

\(3x^2-x+ k = kx-1\)

First, rearrange the given quadratic equation in standard form ax² + bx + c = 0:

\(\begin{aligned}3x^2-x+ k &= kx-1\\3x^2-x+ k-kx+1&=0-kx+1\\3x^2-x-kx+ k+1&=0\\3x^2-(1+k)x+ (k+1)&=0\end{aligned}\)

\(3x^2-(1+k)x+ (k+1)=0\)

Comparing this with the standard form, the coefficients a, b and c are:

\(\boxed{\begin{minipage}{7 cm}\underline{Discriminant}\\\\$\boxed{b^2-4ac}$ \quad when $ax^2+bx+c=0$\\\\when $b^2-4ac > 0 \implies$ two real roots.\\when $b^2-4ac=0 \implies$ one real root.\\when $b^2-4ac < 0 \implies$ no real roots.\\\end{minipage}}\)

If the quadratic equation has two distinct roots, its discriminant is positive.

\(b^2-4ac > 0\)

Substitute the values of a, b and c into the discriminant:

\((-1 - k)^2-4(3)(k+1) > 0\)

Simplify:

\((-1 - k)(-1-k)-12(k+1) > 0\)

\(1+2k+k^2-12k-12 > 0\)

\(k^2+2k-12k+1-12 > 0\)

\(k^2-10k-11 > 0\)

Factor the left side of the inequality:

\(k^2+k-11k-11 > 0\)

\(k(k+1)-11(k+1) > 0\)

\((k-11)(k-1) > 0\)

If we graph the quadratic k² - 10k - 11, it is a parabola that opens upwards (since its leading coefficient is positive), and crosses the x-axis at k = -1 and k = 11. Therefore, the curve will be positive (above the x-axis) either side of the x-intercepts, so when k < -1 or k > 11.

Therefore, the range of values of k for which the given quadratic equation has two distinct roots is:

\(\boxed{k < -1 \; \textsf{or} \;k > 11}\)

The Perimeter of the hexagon that Pete made by putting the trapezoids together is 22 inches.

To find the perimeter of the hexagon formed by putting the trapezoids together, we need to add up the lengths of all the sides.

Let's analyze the given trapezoids:

Trapezoid 1: It has two parallel sides measuring 3 inches and 5 inches, and two non-parallel sides measuring 3 inches each.

Trapezoid 2: It also has two parallel sides measuring 3 inches and 5 inches, and two non-parallel sides measuring 3 inches each.

When we put these trapezoids together to form a hexagon, we can observe that the parallel sides of the trapezoids become consecutive sides of the hexagon.

Since the hexagon has six sides, we need to consider the lengths of all six sides. By examining the trapezoids, we can determine that the lengths of the sides are as follows:

Side 1: 5 inches (one of the sides of the trapezoid)

Side 2: 3 inches (one of the sides of the trapezoid)

Side 3: 3 inches (one of the sides of the trapezoid)

Side 4: 3 inches (one of the sides of the trapezoid)

Side 5: 3 inches (one of the sides of the trapezoid)

Side 6: 5 inches (the other side of the trapezoid)

To find the perimeter, we add up the lengths of all six sides:

Perimeter = Side 1 + Side 2 + Side 3 + Side 4 + Side 5 + Side 6

        = 5 + 3 + 3 + 3 + 3 + 5

        = 22 inches

Therefore, the perimeter of the hexagon that Pete made by putting the trapezoids together is 22 inches.

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Answer:

7/54

Step-by-step explanation:

A hockey bag contains 5 red jerseys, 6 blue jerseys and 7 white jerseys.

Let the total number of jerseys =

5 red jerseys + 6 blue jerseys 7 white jerseys.

= 18

P(White) = 7/18

P(Blue) = 6/18

Hence, the probability that Jack picks a white then a blue jersey if he puts the first one back.

This is probability with replacement, hence:

7/18 × 6/18

= 7/18 × 1/3

= 7/54

Answer:

39

Step-by-step explanation:

Answer: Alright, lets get started.

Roberto has already run miles = 16

Total miles for marathon = 26.2

As per percentage formula :

So, percentage completed =

Rounding the answer to whole number 62 %

62 percent of the marathon  he has completed.   :  Answer

Hope it will help :)

Step-by-step explanation:

The statement, "Colbert "Real-Estate" Agency's number of home showings by its agents is same "each-day" of week, then variable for number of showings, is a continuous distribution" is False, because it represents a discrete distribution.

If the Colbert "Real-Estate" Agency has determined the number of "home-showings" by their agents is "same" each day of week, then variable "number of showings" is not a continuous distribution. Rather, it is a discrete distribution,

where the values can take on only  finite number of values. In this case, the number of home showings can only be a whole number, such as 0, 1, 2, 3, etc.

A continuous distribution is the one where the possible values of the variable are not restricted to any particular set of numbers, and can include any value in a given range.

An example of a continuous distribution would be the height of adult humans, where any real number between 0 and infinity is a possible value.

Therefore, the statement is False.

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The exchange rate of the euro/pound expressed to four decimal places is 1.0100 euro/pound.

To find the exchange rate of the euro/pound, we can use the given exchange rates of dollar/pound and dollar/euro.

Let's denote the exchange rate of euro/pound as E.

Given:

Exchange rate of dollar/pound = 1.21 dollar/pound

Exchange rate of dollar/euro = 1.22 dollar/euro

To find the exchange rate of euro/pound, we can divide the exchange rate of dollar/euro by the exchange rate of dollar/pound:

E = (Exchange rate of dollar/euro) / (Exchange rate of dollar/pound)

E = 1.22 dollar/euro / 1.21 dollar/pound

Simplifying this expression, we get:

E = 1.01 euro/pound

Therefore, the exchange rate of the euro/pound, is 1.0100 euro/pound.

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Answer:

2x-3y<7

Step-by-step explanation:

Hope it helps (:

The directional derivative of the function f(x,y) = 2xy - 3y^2 at the point P0 = (5,5) in the direction of the vector u = 4i + 3j is 6√2.

Explanation:

The directional derivative measures the rate of change of a function in a specific direction. It is denoted by ∇_u f(x,y), where u is the unit vector in the direction of interest. To compute the directional derivative, we need to take the dot product of the gradient of f with the unit vector u.

First, we need to find the gradient of f(x,y).

∇f(x,y) = [2y, 2x - 6y]

Next, we need to normalize the vector u to get the unit vector in the direction of interest.

|u| = √(4^2 + 3^2) = 5

u^ = (4/5)i + (3/5)j

Taking the dot product of the gradient of f with the unit vector u, we get:

∇_u f(x,y) = ∇f(x,y) · u^ = [2y, 2x - 6y] · (4/5)i + (3/5)j

At the point P0 = (5,5), we have:

∇_u f(5,5) = [2(5), 2(5) - 6(5)] · (4/5)i + (3/5)j = 10(4/5) + (-6)(3/5) = 8 - 3.6 = 4.4

Therefore, the directional derivative of f(x,y) at the point P0 = (5,5) in the direction of the vector u = 4i + 3j is:

∇_u f(5,5) = 4.4

Finally, we need to scale the result by the magnitude of the vector u to get the directional derivative in the direction of u.

Directional derivative = ∇_u f(5,5) / |u| = 4.4 / 5 = 0.88 * √(2)

Directional derivative = 6√2.

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You would prove \(\angle EFD \cong \angle HFG\) because they are vertical angles, and then the triangles would be congruent by ASA.

the volume of the region contained in the cylinder x² + y² = 9, bounded above by the plane z = x and below by the xy-plane is 0.

Given: The cylinder is x² + y² = 9, bounded above by the plane z = x and below by the xy-planeWe know that, the cylinder is x² + y² = 9Which is (x/a)² + (y/b)² = 1Where a = 3 and b = 3The plane is z = xThe region is bounded below by the xy-plane Thus, the volume of the region can be found by integrating z = x with limits of x² + y² ≤ 9.So, V = ∭ dx dy dz where the limits are given by the cylinder and the plane.V = ∫∫∫ (x) dV ... (1)Now, converting the integral into cylindrical coordinates we have,∫∫∫ (x) dV = ∫θ = 0 to 2π ∫r = 0 to 3 ∫z = 0 to r cos θ (r cos θ) rdzdrdθ ... (2)x = r cos θ, y = r sin θ, and z = z.We know that the limits of x² + y² ≤ 9 in cylindrical coordinates are 0 ≤ θ ≤ 2π, 0 ≤ r ≤ 3, 0 ≤ z ≤ r cos θ.Using (2) in (1), we haveV = ∫θ = 0 to 2π ∫r = 0 to 3 ∫z = 0 to r cos θ (r cos θ) rdzdrdθ= ∫θ = 0 to 2π ∫r = 0 to 3 [r² cos θ / 2] dr dθ= ∫θ = 0 to 2π [ 9 cos θ / 2 ] dθ= 9 [ sin θ ]θ = 0 to 2π= 0Thus, the volume of the region contained in the cylinder x² + y² = 9, bounded above by the plane z = x and below by the xy-plane is 0.

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Answer:

Okay bestie ‼️

Step-by-step explanation:

The 50th term of this arithmetic sequence is equal to: D. -213.

Mathematically, the nth term of an arithmetic sequence can be calculated by using this expression:

aₙ =  a₁ + (n - 1)d

Where:

Next, we would determine the common difference as follows.

Common difference, d = a₂ - a₁

Common difference, d = 27 - 32

Common difference, d = -5

Substituting the given parameters into the formula, the 50th term of this arithmetic sequence is given by;

a₅₀ =  a₁ + (50 - 1)d

a₅₀ =  32 + (49)(-5)

a₅₀ =  32 - 245

a₅₀ =  -213.

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The area of the rectangle is 150 square feet, and the area of the semicircle is approximately 39.27 square feet. Thus, the total area of the key on the basketball court is approximately 189.27 square feet.

To calculate the area of the key on a basketball court, we need to find the area of the rectangle and the area of the semicircle separately and then sum them up.

Area of the Rectangle:

The length of the rectangle is 15 feet and the width is 10 feet.

Area of the rectangle = Length * Width = 15 feet * 10 feet = 150 square feet.

Area of the Semicircle:

The radius of the semicircle is half the width of the rectangle, which is 10 feet / 2 = 5 feet.

The formula for the area of a circle is A = π * \(r^2\), where π is approximately 3.14159 and r is the radius.

Area of the semicircle = (π *\((5 feet)^2\)) / 2 = (3.14159 * 25 square feet) / 2 ≈ 39.27 square feet.

Total Area of the Key:

To find the total area of the key, we add the area of the rectangle and the area of the semicircle:

Total area of the key = Area of the rectangle + Area of the semicircle

Total area of the key = 150 square feet + 39.27 square feet ≈ 189.27 square feet.

Therefore, the area of the key on the basketball court is approximately 189.27 square feet.

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The area of the key on the basketball court is approximately 189.25 square feet.

To find the area of the key on a basketball court, we need to calculate the combined area of the rectangle and semicircle.

The rectangle's area is calculated by multiplying its length by its width:

Rectangle Area = Length × Width = 15 feet × 10 feet = 150 square feet

The semicircle's area is half the area of a full circle with a radius equal to the width of the key. Since the width of the key is 10 feet, the radius is 5 feet.

Semicircle Area = (1/2) × π × \(Radius^2\) = (1/2) × 3.14 ×\((5 feet)^2\) ≈ 39.25 square feet

Therefore, the area of the key is the sum of the rectangle's area and the semicircle's area:

Key Area = Rectangle Area + Semicircle Area = 150 square feet + 39.25 square feet ≈ 189.25 square feet

So, the area of the key on the basketball court is approximately 189.25 square feet.

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The key of a basketball court is made up of a rectangle and on semicircle. the length of the rectangle is 15 feet and the width is 10 feet. find the area of the key on the basketball court.

(1, x, x, x) is linearly independent in \(P_{3}\).

(1+x, 1+x, 1+x) and (1-x, 1+x, 1-x-2x) are linearly dependent in \(P_{3}\).  

(x-x, x, -x+x) is linearly dependent in\(P_{3}\).

To determine whether the given sets of polynomials are linearly independent in \(P_{3}\),

We need to check if the only solution to the following linear combination is the trivial solution:

(a) \(a_0 + a_1 x + a_2 x^2 + a_3 x^3 = 0\)

(b) \(b_0 (1+x) + b_1 (1+x^2) + b_2 (1+x^3) = 0\)

(c) \(c_0 (1-x^2) + c_1 (1+x) + c_2 (1-x-2x^2) = 0\)

(d) \(d_0 (x^2-x^3) + d_1 x - d_2 x = 0\)

If the only solution is the trivial solution \((a_0 = a_1 = a_2 = a_3 = 0)\),

Then the given set of polynomials is linearly independent.

Otherwise, they are linearly dependent.

Solving for (a), we see that the coefficients must all be zero.

Therefore, the set \((1, x, x^2, x^3)\) is linearly independent in \(P_{3}\).

Solving for (b), we get the system of equations:

\(b_0 + b_1 + b_2 = 0\\ b_0 + b_1 = 0\\ b_0 + b_1 = 0\\ b_0 + b_1 = 0\\b_2 = 0\)

The third and fourth equations give us the same information, so we can ignore one of them.

From the first equation, we get \(b2 = -b_0 - b_1.\)

Substituting this into the second equation, we see that \(b_1 = -b_0\). Therefore, \(b_1 = b_2 = -b_0\), and \(b_0\) can be any non-zero value.

This means that the set \((1+x, 1+x^2, 1+x^3)\) is linearly dependent in P{3}.

Solving for (c), we get the system of equations:

\(-c_0 + c_2 = 0\\ c_1 - c_2 = 0\\ c_0 + c_1 - 2c_2 = 0\\ c_0 + c_1 + c_2 = 0\)

Simplifying the third equation, we get \(c_0 + c_1 = 2c_2\).

Substituting this into the fourth equation, we get,

\(c_2 = -1/3 c_1 - 1/3 c_0\).

Substituting this into the first equation, we get \(c_0 = c_2\),

Which implies that \(c_1 = -2c_2\).

Therefore, the set \((1-x^2, 1+x, 1-x-2x^2)\) is linearly dependent in P{3}.

Solving for (d), we get the system of equations:

\(-d_0 + d_2 = 0\\ d_1 - d_2 = 0\\ d_0 = 0\)

From the first equation, we get \(d2 = d_0\).

From the second equation, we get \(d_1 = d_2 = d_0\).

Therefore, the set \((x^2-x^3, x, -x+x)\) is linearly dependent in P{3}.

So, the only linearly independent set of polynomials in \(P_{3}\) is \((1, x, x^2, x^3)\).

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Answer:

a

Step-by-step explanation:

a