Given the side lengths, determine whether
the triangle is acute, right, obtuse, or not a triangle

1. ( 15,16,21 )
A. not a triangle
B. Acute
C. Right
D. Obtuse


2. ( 20,23,41 )
A. Not a triangle
B. Acute
C. Right
D. Obtuse

3. ( 10,24,26 )
A. Not a triangle
B. Acute
C. Right
D. Obtuse

4. ( 6,13,20 )
A. Not a triangle
B. Acute
C. Right
D. Obtuse

Point d is at (5, -5), which is five units to the right of the origin on the x-axis and five units below the origin on the y-axis. Similarly, point e is at (7, 3), point f is at (-1, 5), and point G is at (-3, -3).

The given points, d (5, -5), e (7, 3), f (-1, 5), and G (-3, -3) form quadrilateral DEFG. To plot these points, we can first draw the x and y axes on a graph paper.

Then, we can plot each point by locating its x-coordinate on the x-axis and its y-coordinate on the y-axis.

After plotting the points, we can click on the "Graph Quadrilateral" button to see the quadrilateral DEFG. It should be a closed shape with four sides, connecting the four points in the given order.

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Answer:

=x7+9

Step-by-step explanation:

Answer:

The piano has 88 keys, so there are 88 keys that can be pressed by the cat.

We can assume that each one of the 88 keys has the same probability of being pressed.

We want to find the probabiiity that the cat press the first four notes of the Fifth Symphony (i suppose we want to find the probability where the cat strikes the notes in the correct order), those notes are:

These notes, at least in the melody, are 3 LA´s, and one REb.

While in a piano the notes are repeated a lot of times, (in 88 keys we will have around 7 of each).

All of them have a different pitch (some are higher notes, and other are lower).

The ones in the beginning of the Fifth Symphony are already defined, this means that for each note, we have a probability of 1/88 of hitting the correct key.

Then the cat needs to do this four times.

The first LA will have a probability of 1/88 of being hit.

The second LA will have a probability of 1/88 of being hit.

The third LA will have a probability of 1/88 of being hit.

The REb will have a probability of 1/88 of being hit.

Then the joint probability will be the product of each individual probability, this means that the probability of the cat hitting those four notes in order is:

P = (1/88)*(1/88)*(1/88)*(1/88) = 1.7*10^(-8)

The probability that a cat, jumping on 4 keys in sequence and at random, will strike the first four notes of Beethoven's Fifth Symphony is \(\rm 1.7\times 10^{-8}\).

Given :

The Cat on the Piano A standard piano keyboard has 88 different keys.

The following steps can be used in order to determine the probability that a cat, jumping on 4 keys in sequence and at random, will strike the first four notes of Beethoven's Fifth Symphony:

Step 1 - The four notes of the piano are 3 LA's and 1 REb.

Step 2 - The probability that the first key is LA is 1/88.

Step 3 - The probability that the second key is LA is 1/88.

Step 4 - The probability that the third key is LA is 1/88.

Step 5 - The probability that the key is REb is 1/88.

Step 6 - So, the probability that a cat, jumping on 4 keys in sequence and at random, will strike the first four notes of Beethoven's Fifth Symphony is:

\(\rm P=\dfrac{1}{88}\times \dfrac{1}{88}\times \dfrac{1}{88}\times \dfrac{1}{88}\)

\(\rm P = 1.7\times 10^{-8}\)

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The length of line x in the figure of the cube given is 19.

Calculate the length of the base of the cube, which is the diagonal of the lower sides :

base length = √10² + 6²

base length = √136

The length of x is the diagonal of the cube

x = √(√136)² + 15²

x = √136 + 225

x = √361

x = 19

Therefore, the length of line x in the figure given is 19.

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Answer:

10 units

Step-by-step explanation:

600 units= 1 hour

1 hour= 60 minutes

600 units= 60 minutes

1 minute=600/60

1 minutes =10 units

Hope this helped! :)

[~S & (R V S)] ≡ (Q ⊃ S) is true when A = T, S = F, R = F, and Q = T by substituting the propositional variables.

A truth table is a table used to determine the truth values of a compound proposition, which is a logical statement made up of simpler propositions using logical operators such as "and" (represented by "&"), "or" (represented by "V"), "not" (represented by "~"), conditional (represented by "⊃"), and biconditional (represented by "≡").

Let's substitute the given truth values for the propositional variables in the given statement:

[~F & (F V F)] ≡ (T ⊃ F)

Using the truth table for conjunction (represented by "&") and disjunction (represented by "V"), we can simplify the left-hand side of the equivalence:

[T & F] ≡ (T ⊃ F)

Using the truth table for conditional (represented by "⊃"), we can simplify the right-hand side of the equivalence:

F ≡ F

Since both sides of the equivalence have the same truth value, the statement is true.

Therefore, [~S & (R V S)] ≡ (Q ⊃ S) is true when A = T, S = F, R = F, and Q = T.

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Answer:

40 slices

Step-by-step explanation:

I rounded 38 to 40 and divided by 8

The vertex of point A' in the dilated triangle A'B'C' is (6, 4.5).

1. Start by calculating the distance between the vertices of the original triangle ABC:

  - Distance between A(4, 3) and B(3, -2):

    Δx = 3 - 4 = -1

    Δy = -2 - 3 = -5

    Distance = √((-\(1)^2\) + (-\(5)^2\)) = √26

  - Distance between B(3, -2) and C(-3, 1):

    Δx = -3 - 3 = -6

    Δy = 1 - (-2) = 3

    Distance = √((-6)² + 3²) = √45 = 3√5

  - Distance between C(-3, 1) and A(4, 3):

    Δx = 4 - (-3) = 7

    Δy = 3 - 1 = 2

    Distance = √(7² + 2²) = √53

2. Apply the scale factor of 1.5 to the distances calculated above:

  - Distance between A' and B' = 1.5 * √26

  - Distance between B' and C' = 1.5 * 3√5

  - Distance between C' and A' = 1.5 * √53

3. Determine the coordinates of A' by using the distance formula and the given coordinates of A(4, 3):

  - A' is located Δx units horizontally and Δy units vertically from A.

  - Δx = 1.5 * (-1) = -1.5

  - Δy = 1.5 * (-5) = -7.5

  - Coordinates of A':

    x-coordinate: 4 + (-1.5) = 2.5

    y-coordinate: 3 + (-7.5) = -4.5

4. Thus, the vertex of point A' in the dilated triangle A'B'C' is (2.5, -4.5).

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The correct answer is A.

1) y = (5/2)√(3), x = 5/2, and 5, 2) y = 2i 3√(2), 4√3 and x = 2i√6 are radicals in simplest form.

In mathematics, an equation is a statement that shows that two expressions are equal to each other. An equation typically consists of two sides, the left-hand side (LHS) and the right-hand side (RHS), which are separated by an equals sign (=).

Equations are used to represent mathematical relationships and to solve problems in a variety of fields, including physics, engineering, economics, and finance. They can be linear or non-linear, and they may involve one or more variables.

Using the Pythagorean theorem in right triangle ABC, we have:

AC² = AB² + BC²

5² = y² + x²

x² = 25 - y²

Since angle BCA = 60 degrees, we know that:

tan(60) = y/x

√(3) = y/x

y = x√(3)

Substituting this into the equation x² = 25 - y², we get:

x² = 25 - 3x²

4x² = 25

x = √(25/4) = 5/2

And y = x√(3) = 5/2 ×√(3)

Therefore, AB = y = (5/2)√(3), BC = x = 5/2, and AC = 5.

Using the Pythagorean theorem in right triangle DEF, we have:

DF² = DE² + EF²

x² = y² + (4√3)²

x² = y² + 48

Since angle DEF = 60 degrees, we know that:

tan(60) = y/x

√(3) = y/x

y = x√(3)

Substituting this into the equation x² = y² + 48, we get:

x² = 3x² + 48

2x² = -48

x = √(-24) = 2i √(6)

And y = x √(3) = 2i√(18) = 2i 3√(2)

Therefore, DE = y = 2i 3√(2), EF = 4√3 and DF = x = 2i√6.

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Answer:

(a) The next tide will occur at 6:55pm

(b) \(y = 3.12 \cos(\frac{24\pi}{149}(x - 6.5)) + 2.74\)

(c) The height is: 2.904ft

Step-by-step explanation:

Given

\(T_1 = 12hr:25min\) --- difference between high tides'

Solving (a): The next time a high tide will occur

From the question, we have that:

\(High =6:30am\) --- The time a high tide occur

The next time it will occur is the sum of High and T1

i.e.

\(Next = High + T_1\)

\(Next = 6:30am + 12hr : 25min\)

Add the minutes

\(Next = 6:55am + 12hr\)

Add the hours

\(Next = 6:55pm\)

Solving (b): The sinusoidal function

Given

\(High\ Tide = 5.86\)

\(Low\ Tide = -0.38\)

\(T = 12hr:25min\) -- difference between consecutive tides

\(Shift = 6.5hr\)

The sinusoidal function is represented as:

\(y = A\cos(w(x - C)) + B\)

Where

\(A = Amplitude\)

\(A = \frac{1}{2}(High\ Tide - Low\ Tide)\)

\(A = \frac{1}{2}(5.86 - -0.38)\)

\(A = \frac{1}{2}(6.24)\)

\(A = 3.12\)

\(B = Mean\)

\(B = \frac{1}{2}(High\ Tide + Low\ Tide)\)

\(B = \frac{1}{2}(5.86 - 0.38)\)

\(B = \frac{1}{2}(5.48)\)

\(B = 2.74\)

\(w = Period\)

\(w = \frac{2\pi}{T}\)

\(w = \frac{2\pi}{12:25}\)

Convert to hours

\(w = \frac{2\pi}{12\frac{25}{60}}\)

Simplify

\(w = \frac{2\pi}{12\frac{5}{12}}\)

As improper fraction

\(w = \frac{2\pi}{\frac{149}{12}}\)

Rewrite as:

\(w = \frac{2\pi*12}{149}\)

\(w = \frac{24\pi}{149}\)

\(C = shift\)

\(C=6.5\)

So, we have:

\(y = A\cos(w(x - C)) + B\)

\(y = 3.12 \cos(\frac{24\pi}{149}(x - 6.5)) + 2.74\)

Solving (c): The height at 3pm

At 3pm, the value of x is:

\(x=3:00pm - 6:30am\)

\(x=9.5hrs\)

So, we have:

\(y = 3.12 \cos(\frac{24\pi}{149}(x - 6.5)) + 2.74\)

\(y = 3.12 \cos(\frac{24\pi}{149}(9.5 - 6.5)) + 2.74\)

\(y = 3.12 \cos(\frac{24\pi}{149}(3)) + 2.74\)

\(y = 3.12 \cos(\frac{72\pi}{149}) + 2.74\)

\(y = 3.12 *0.0527 + 2.74\)

\(y = 2.904ft\)

The steps of the proof are given as follows:

By the linear pair theorem, two consecutive angles that are linear pairs are supplementary.

By the congruent supplements theorem, if two angles are supplements of the same angle (or congruent angles), then the two angles are congruent.

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The quadratic equation so formed will be \(x^{2}\) - 2x - 15 = 0.

What is a quadratic equation?

Any algebraic equation that can be expressed in standard form as where x represents an unknown value and where a, b, and c represent known values, where a 0 is a quadratic equation.

We know that the standard form of a quadratic equation is represented as: a\(x^{2}\) + bx + c = 0.

Here, we are given a = 4, b = -8 and c = -60.

On substituting these values, we get

⇒ a\(x^{2}\) + bx + c = 0

⇒ 4\(x^{2}\) - 8x - 60 = 0

On dividing both sides by 4, we get

⇒ \(x^{2}\) - 2x - 15 = 0

Hence, the quadratic equation so formed will be \(x^{2}\) - 2x - 15 = 0.

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Answer:

The rates are not equivalent since Maria saves $0.50 more per month than Ralph.

Step-by-step explanation:

We can determine if two rates are equivalent by comparing the rates at which they save per month.

Maria's savings per month:

Both 50 and 4 can be divided by 2, which gives us 25/2.  As a regular number, this becomes 12.5/1 which means Maria saves $12.5 per month.

Ralph's savings per month:

Both 60 and 5 can be divided by 5, which gives us 12.  Thus, Ralph saves $12 per month.

Thus, the rates are not equivalent as Maria saves $0.50 more per month than Ralph.

We have a line segment like this:

We can write:

Then, we can find SU as:

Answer: SU = 5

The statement about probability that is correct would be that the probability of landing on yellow is less than the probability of landing on blue. That is option B.

Probability is defined as the total number of possible outcome of an event.

The repeated colour which are numbered from 1 to 8 are as follows:

Therefore, the probability of landing on yellow is less than the probability of landing on blue because 1/4 is less than 3/8.

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Answer: B: The probability of landing on yellow is less than the probability of landing on blue.

Step-by-step explanation:

Answer:

-32

Step-by-step explanation:

do you need me to explain?

Answer:

y = -32

Step-by-step explanation:

thanks for helping me

Answer:

  5x^3 -80x = 5x(x -4)(x +4)

Step-by-step explanation:

The denominator factors are ...

  (x -4)(x +4)

  x

  5(4 -x) = -5(x -4)

The unique factors are 5, x, (x -4), (x +4). The LCD is the product of these:

  5x(x^2 -16) = 5x^3 -80x

_____

Additional comment

When expressed over the LCD, the expressions are ...

  5x^2/(5x^3 -80x), 20(x^2 -16)/(5x^3 -80x), -8x(x +4)/(5x^3 -80x)

20

Step-by-step explanation:

The initial expression is:

So the denominator of the second fraction will multiply the numerator of the first one so

Answer:

what is your question

Step-by-step explanation: am not trying to steal ur points

The charges will be equal when each car travels 2000 miles. To find the charge for that distance, we substitute x = 2000 into either equation.

To determine the number of miles at which the charges for the two car services, A and B, are equal, we can set up an equation based on the given information.

Let's represent the charge for car service A as y_A and the charge for car service B as y_B. We can set up the following equations:

For car service A: y_A = 0.60x + 300 (in cents)

For car service B: y_B = 0.75x (in cents)

To find the number of miles at which the charges are equal, we set y_A equal to y_B and solve for x:

0.60x + 300 = 0.75x

Subtracting 0.60x from both sides:

300 = 0.15x

Dividing both sides by 0.15:

x = 300 / 0.15

x = 2000

Therefore, the charges will be equal when each car travels 2000 miles. To find the charge for that distance, we substitute x = 2000 into either equation. Let's use the equation for car service A:

y_A = 0.60(2000) + 300

y_A = 1200 + 300

y_A = 1500 cents or $15.00

So, when each car travels 2000 miles, the charges will be equal at $15.00.

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The slant height \(l = 29 \: mm\).

A cone is a three-dimensional geometric shape with a smooth transition from a flat, usually circular base to the apex or vertex, which forms an axis to the base's center.

As per the given data:

Height = 21 mm

Volume = 8792 mm

Radius = 20 mm

For slant height of the one (\(l\)):

\(l = \sqrt{r^2 + h^2}\) {using Pythagoras theorem}

\(l = \sqrt{(20)^2 + (21)^2}\)

\(l = \sqrt{(20)^2 + (21)^2}\)

\(l = \sqrt{400 + 441}\)

\(l = 29 \: mm\)

Hence, the slant height \(l = 29 \: mm\).

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Answer: -2

Step-by-step explanation:

First distribute the negative sign to the negative four then find the absolute value of 6

-(-4)-|-6| = 4-6

then subtract 4 from 6 and you get -2.

The correct value of 2f(a-1) is 2a^2 - 12a + 10.

To find the value of 2f(a-1), we need to substitute (a-1) into the function f(x) and then multiply the result by 2.

Given: f(x) = x^2 - 4x

Substituting (a-1) into the function:

f(a-1) = (a-1)^2 - 4(a-1)

Expanding and simplifying:

f(a-1) = (a^2 - 2a + 1) - (4a - 4)

f(a-1) = a^2 - 2a + 1 - 4a + 4

f(a-1) = a^2 - 6a + 5

Now, we multiply the result by 2:

2f(a-1) = 2(a^2 - 6a + 5)

Expanding:

2f(a-1) = 2a^2 - 12a + 10

Therefore, the value of 2f(a-1) is 2a^2 - 12a + 10.

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Answer:

Negative

Step-by-step explanation:

The following expression will be negative. This is because, the fraction in x is a negative fraction. The fraction in y is a positive fraction. The expression is    x * y, so if you were to multiply the two it would be negative. This is because a negative multiplied by a positive will be equal to a negative.

Hope this helps!!

-Ketifa

(Can I get brainliest?)

To find the area of a square, multiply the side length by itself, also known as sqaring the side length.We must solve 3/5 x 3/5.3/5 x 3/5 = 0.36The units we'll use is because units are the unt we're given, and it is squared because it is the area of a shape.

To find the area of a square, multiply the side length by itself, also known as sqaring the side length.We must solve 3/5 x 3/5.3/5 x 3/5 = 0.36The units we'll use is because units are the unt we're given, and it is squared because it is the area of a shape.Your final answer is 0.36 .

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