The graph of this system of equations is used to solve 4 x squared minus 3 x + 6 = 2 x Superscript 4 Baseline minus 9 x cubed + 2 x. StartLayout Enlarged left-brace 1st row 4 x squared minus 3 x + 6 2nd row y = 2 x Superscript 4 Baseline minus 9 x cubed + 2 x EndLayout What represents the solution set? y-intercepts of the graph x-intercepts of the graph y-coordinates of the intersection points x-coordinates of the intersection points

Answer:

64 square ft^3

Step-by-step explanation:

If the side lengh is 3 then you would have 4^3 which is 64.

Answer:

64

Step-by-step explanation:

Step-by-step explanation:

Find the radius: 6 ÷ 2 = 3m

Circumference = 2r with pi = 3cm x 3.14cm x 2 = 18.84m

Area = pi x 3cm x 3cm = 28.27m2

Calculate the circumference and area of given triangle.

Circumference of circle = 2πr

Area of circle = πr²

Radius,r = diameter/2 => 6/2 = 3 m

( i ) As we know that formula of circumference,

Circumference of circle = 2πr

\( \bf \: \star \: putting \: the \: values\)

\( \implies \: 2 \times 3.14 \times 3\)

\( \implies \: 6.28 \times 3\)

\( \implies \: 18.84 \: m\)

(ii) As we know,

Area of circle = πr²

\( \bf \star \: putting \: the \: values\)

\( \implies \: 3.14 \times {(3)}^{2} \)

\( \implies \: 3.14 \times 9\)

\( \implies \: 28.26 \: m {}^{2} \)

4 chocolate and 6 butter cookies are included in a box of cookies. Miguel chooses a cookie at random and consumes it. He then chooses another cookie at random and eats it. He take 10 cookies.

Science, art, statistics, encryption, gaming, gambling, and other industries all make extensive use of randomness. To test hypotheses, for instance, random assignment in randomized controlled trials and pseudorandom or random numbers in computer games like video poker. In order to produce non-deterministic data (such as a series of integers) to seed security algorithms, a TRNG is a function or apparatus based on an unpredictably occurring physical event termed an entropy source. Although chance and randomness are sometimes used interchangeably, they can have different meanings in various scientific contexts as well as in everyday life. Chance specifically has a wider range than randomness, which is frequently interpreted in accordance with more specialized mathematical connotations.

Based on the given condition,

4+6

Calculate the sum.

10

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The limit of {2n³-1/3n³+1} is 2/3. So option a) is the right answer. The sequence does not diverge.

To determine the limit of the given sequence {2n³-1/3n³+1}, we can use the concept of limit rules. We can simplify the given sequence by dividing both numerator and denominator by n³, which gives:

{2n³-1/3n³+1} = {2-1/n³}/{3+1/n³}

As n approaches infinity, 1/n³ approaches zero, which means that the denominator of the fraction approaches 3. The numerator of the fraction approaches 2. Therefore, we can conclude that the given sequence approaches the limit of 2/3 as n approaches infinity.

Hence, the correct choice is:

A. The limit of the sequence is 2/3.

It is essential to find the limit of the sequence as it helps in determining the behavior of the sequence as it approaches infinity. In mathematics, the concept of the limit of a sequence is widely used in analyzing and solving many problems.

By finding the limit of a sequence, we can understand the behavior of the sequence, and we can use it to make predictions or analyze the given situation. Repetition of a sequence of measurements helps us to obtain an average or expected value, which can be used for further analysis.

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Answer:

Step-by-step explanation:

To find the surface area of a square pyramid, we need to add the area of the base to the sum of the areas of the four triangular faces.

The area of the base of the pyramid is:

Area of square base = (base length)^2

Area of square base = 3^2

Area of square base = 9 square inches

To find the area of each triangular face, we need to first find the length of each side. Since the base is a square, all sides are equal to 3 inches. The slant height is given as 7 inches, which is the height of each triangular face.

Using the Pythagorean theorem, we can find the length of each side of the triangular face:

(side length)^2 + (height)^2 = (slant height)^2

(side length)^2 + 7^2 = 7^2

(side length)^2 = 7^2 - 7^2

(side length)^2 = 24.5

side length ≈ 4.95

The area of each triangular face is:

Area of triangular face = (1/2) × (base length) × (height)

Area of triangular face = (1/2) × 3 × 7

Area of triangular face = 10.5 square inches

Therefore, the total surface area of the square pyramid is:

Total surface area = Area of base + Sum of areas of four triangular faces

Total surface area = 9 + 4(10.5)

Total surface area = 42 square inches

Hence, the surface area of this square pyramid is 42 square inches.

Answer:

1) False

2) True

3) True

4) False

Step-by-step explanation:

For the first statement, we can look at a graph with the line of y = 3.69x plotted. If we check the points (7.38, 2) and (11.07,3), they do not intersect with the line. So, the first statement is false.

For the second statement, we can check the equation for the line to find the slope. The equation, y = 3.69x, is in slope-intercept form, or \(y = mx + b\). In this form, \(m\) is the slope of the line. \(b\) is the y-intercept. In this line, there is no y-intercept specified, so we can take this to mean the y-intercept is 0. The slope, we can see, is 3.69. The slope, multiplied by x, shows us any point of the line. The second statement, then, is true.

The next statement can be verified by finding just how much 16 gallons will cost. Like we've seen before, the slope can be multiplied by x, the number of gallons, to see where that point will be plotted. So, we can multiply the slope by 16.

3.69 · 16 = 59.04

The (x) value, we already know, is 16. The (y) value, we've found, is 59.04. So 16 gallons will be plotted at  (16, 59.04). The third statement is true.

The last statement says that if the price increases by $0.05, the slope will be 3.64. We can tell this is false by adding 0.05 to the original slope, 3.69.

3.69 + 0.05 = 3.74

3.74 ≠ 3.64, so the last statement is false.

I hope this was helpful to you ^^

Good luck

The equation of the tangent line to the Witch of Agnesi at a given point (x0, y0) is:  \(\(y - y_0 = \frac{-64a^3x_0}{(x_0^2 + 4a^2)^2}(x - x_0)\)\)

The tangent lines to the curve called the Witch of Agnesi at a given point can be determined by finding the derivative of the curve and evaluating it at that point.

To find the equation of a tangent line, we need the derivative of the curve. The equation of the Witch of Agnesi is given by:

\(y = \frac{8a^3}{x^2 + 4a^2}\)

where 'a' is a constant that determines the shape of the curve.

Taking the derivative of y with respect to x, we can find the slope of the tangent line:

\(\frac{dy}{dx} = \frac{-64a^3x}{(x^2 + 4a^2)^2}\)

Let's assume we want to find the tangent lines at the point (x0, y0). We can substitute these coordinates into the derivative expression:

\(\frac{dy}{dx}\Bigr|_{x=x_0} = \frac{-64a^3x_0}{(x_0^2 + 4a^2)^2}\)

This gives us the slope of the tangent line at the point (x0, y0).

Now, using the point-slope form of a line, we can write the equation of the tangent line:

\(y - y_0 = \frac{dy}{dx}\Bigr|_{x=x_0}(x - x_0)\)

Substituting the values we obtained earlier, the equation of the tangent line becomes:

\(y - y_0 = \frac{-64a^3x_0}{(x_0^2 + 4a^2)^2}(x - x_0)\)

This equation represents the tangent line to the Witch of Agnesi at the point (x0, y0).

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a² + b² = c²

50² + 51² = c²

2500 + 2601 = c²

5101 = c²

√5101 ≈ 71.42 cm.

Answer: Area of the rectangle = 102.5 cm²  Round to 103 cm²

Step-by-step explanation:

The diagonal is the hypotenuse, c So subtract the square on the base (length) to find the altitude (height).

a² + b² = c²

a² + 50² = 51²

a² = 51² - 50²

a² = 2601 -2500

a² = 101  take the square root of both sides

a = √101

a = 10.04987562  Round to 10.05

Area = LW

Area = 50 × 10.05

Area = 102.5 cm²  Round to 103 cm²

Find the equation of the dotted line:

1. Find the slope:

2. Find the y-intercept (b): the value of y when the line cross y-axis:

b=4

Then, the eqution of the line is: y=-2x+4

To write the inequality:

When the line is a dotted line you use > or <, whne it is a full line you use ≥ or ≤

When the sahdow area is under the line use < or ≤, when the shadow area is over the line you use > or ≥

Then, as you have a dotted line and the shadow area in under that line, you get the next inequality:

Step-by-step explanation:

as, the traingle is equilateral triangle Which means it's all sides are equal

therefore, VT and BT are x

→ BV = VT = BT = x

hope this answer helps you dear take care!

The length and width of the new scale drawing is 36 inches and 24 inches respectively.

The given parameters:

The original length and width of the soccer field is calculated as follows;

1 inch : 12 yards

For the new scale of 1 inch : 3 yards, the new length and width are represented as;

the new width:

\(\frac{1 \ inch}{x} = \frac{3 \ yards}{72 \ yards} \\\\x = 24 \ inches\)

the new length:

\(\frac{1 \ inch}{x} = \frac{3 \ yards}{108 \ yards} \\\\x = 36\ inches\)

Thus, the length and width of the new scale drawing is 36 inches and 24 inches respectively.

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The quadratic model for the ball's height as a function of time are given below

Equation 1: t₁²a + t₁b + c = y₁

Equation 2: t₂²a + t₂b + c = y₂

Equation 3: t₃²a + t₃b + c = y₃

To find a quadratic model for the ball's height as a function of time, we can use the given data table to fit a quadratic equation to the points. The general form of a quadratic equation is:

y = ax² + bx + c

Let's use the given data to determine the values of a, b, and c.

Assuming the table contains the time (t) in the first column and the corresponding height (y) in the second column, we can use three data points to form three equations.

Let's say the data points are:

t₁, y₁

t₂, y₂

t₃, y₃

The three equations we can form are:

y₁ = a(t₁)² + b(t₁) + c

y₂ = a(t₂)² + b(t₂) + c

y₃ = a(t₃)² + b(t₃) + c

To solve for a, b, and c, we can rewrite these equations as a system of linear equations:

Equation 1: t₁²a + t₁b + c = y₁

Equation 2: t₂²a + t₂b + c = y₂

Equation 3: t₃²a + t₃b + c = y₃

We have three equations with three unknowns (a, b, and c). Solving this system of equations will give us the quadratic model for the ball's height as a function of time.

Note: Without the specific data points, I cannot provide the exact quadratic model. Please provide the values in the table, and I'll be able to help you find the quadratic equation that models the ball's height.

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(a) The set {(3, -2), (-4, -6)} is orthogonal, (b) The set {(3, -2), (-4, -6)} is orthogonal but not orthonormal, (c) The set {(3, -2), (-4, -6)} is not a basis for R^2.

To determine whether the set of vectors {(3, -2), (-4, -6)} in R^2 is orthogonal, we can compute the dot product of the vectors and check if it equals zero.

The dot product:

(3, -2) · (-4, -6) = (3 * -4) + (-2 * -6) = -12 + 12 = 0

Since the dot product is zero, the set of vectors {(3, -2), (-4, -6)} is orthogonal.

To determine if the set is orthonormal, we need to check if each vector in the set has a magnitude of 1.

The magnitude of (3, -2) is given by:

∥(3, -2)∥ = sqrt(3^2 + (-2)^2) = sqrt(9 + 4) = sqrt(13)

The magnitude of (-4, -6) is given by:

∥(-4, -6)∥ = sqrt((-4)^2 + (-6)^2) = sqrt(16 + 36) = sqrt(52) = 2 * sqrt(13)

Since the magnitudes are not equal to 1, the set {(3, -2), (-4, -6)} is orthogonal but not orthonormal.

To determine if the set is a basis for R^2, we need to check if the set is linearly independent. If the vectors are linearly independent, then they span the entire space and form a basis.

Let's create a matrix with the vectors as columns and perform row reduction to check for linear independence:

| 3  -4 |

| -2 -6 |

Performing row reduction:

R2 = R2 + (2/3)R1

| 3  -4 |

| 0   0 |

The row-reduced form has a row of zeros, indicating that the vectors are linearly dependent.

Therefore, the set {(3, -2), (-4, -6)} is not a basis for R^2.

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Answer:

\( \frac{1}{2} \)

Step-by-step explanation:

Red: 2, Blue: 15, Black: 8, Green: 5

Total number of pencil = 2 + 15 + 8 + 5 = 30 pencils

probability of picking a blue pencil at random= Number of blue pencil divided by Total number of pencil

=

\( \frac{15}{30} \)

=

\( \frac{1}{2} \)

Answer: e

Step-by-step explanation:

It’s the largest fraction

Answer:

event 5

Step-by-step explanation:

event 5 has a 40% chance of happening, all the others are around 20-30% chances

Let's try to understand how we can solve this equation

Given equation,4f+2=6f-12

Now we will take the terms on one side and constants on the other.

=> 2+12=6f-4f

=> 14=2f

=>7=f

So, the value of f would be 7. Remember that while bringing value to another side, the sign of that value changes. If it is a positive sign then it is going to be transformed into a negative one and vice versa.

The distance between the end of the water supply pipe and the sink should be 2 times the diameter of the supply pipe. Option B is the correct answer.

The distance between the end of the water supply pipe and the sink is determined by plumbing codes and standards to ensure safe and efficient water delivery.

The National Standard Plumbing Code requires a minimum distance of 2 times the diameter of the supply pipe between the end of the pipe and the nearest point of use, such as a faucet or sink.

This helps prevent any potential contamination from the supply pipe and ensures adequate flow and pressure for efficient operation.

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Answer:

15) 30°

16) 49.5°

Step-by-step explanation:

15) We solve using the Trigonometric function of Sine

sin θ = Opposite/Hypotenuse

Opposite = 12

Hypotenuse = 24

sinθ = 12/24

θ = arc sin(12/24)

= 30°

Approximately = 30°

16)We solve using the Trigonometric function of Cosine

cos θ = Adjacent/Hypotenuse

Adjacent = 13

Hypotenuse = 20

cos θ = 13/20

θ = arc cos (13/20)

= 49.458398126°

Approximately = 49.5°

Answer:

A the first one

Step-by-step explanation:

hope this helps

Answer:

The answer is -37x - 48

When the distance is 100ft, the height of the rocket is 98.914 ft.

We know that the relation between height and distance is:

\(d = \sqrt{216 + h^2}\)

In this case, we know that the distance is 100ft, so we can replace d by 100 in the above equation and solve that for h.

\(100 = \sqrt{216 + h^2} \\\\100^2 = 216 + h^2\\\\10,000 - 216 = h^2\\\\\sqrt{10,000 - 216} = h = 98.914\)

So when the distance is 100ft, the height of the rocket is 98.914 ft.

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Answer:

Step-by-step explanation:

Answer:

your answer will be option D) all real numbers

Step-by-step explanation:

have a nice day/night !! ^_^

C=46

using simultaneous equation method to find the minimum values of x and y. As Y is equal in both equations you can cancel them out and minus x from 4x and 24 -15 leaving 3x=9 , x=3, placing this value into one of the equation such as 3+3y = 15 then solving finds y=4 . use these values to find C

Answer

83400000

Step-by-step explanation:

Answer:

892.38

Step-by-step explanation:

Answer:

What are the options

Step-by-step explanation:

The cartons hold 1305 blocks.

What are Comparing quantities?

- Finding an unknown quantity that has a relationship with a certain condition associated to it is the process of comparing quantities.

- One or more quantities with their units will be provided to us, and we will   be required to determine the value of the same quantity in other units (i.e.  in higher values or in lower values).

We given that,

A carton holds 87 blocks.

It means, 1 carton holds = 87 blocks

So find 15 cartons holds how much of blocks.

15 cartons holds = 15 * 87

                            = 1305 blocks

Hence, we can say that the cartons hold 1305 blocks.

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Carol can do the same work in 3 hours as it is did by bob

What is Arithmetic equation?

The area of mathematics known as arithmetic deals with the study of numbers and the numerous operations that can be performed on them.

Addition, subtraction, multiplication, and division are the fundamental mathematical operations.

bob + carol = 2 hours

bob = 6 hours

L.C.M of both equation is 6

∴efficiency of  bob + carol is 3

∴efficiency  bob is 1

Then, 3 - 1 = 2

total work ÷ 2

6 ÷ 2 = 3

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Answer:

27,44,95

Step-by-step explanation:

These numbers are in order from least to greatest, hope this helped!

Answer:

27, 44, 95

Step-by-step explanation:

Since 27 is smaller than 44 and 95 it goes first and since 95 is bigger than 27 and 44 it goes at the end and 44 is in the middle