A water slide is a straight ramp 20 m long that starts from the top of a tower 18 m high. Find the angle the slide forms with the tower. Approximate to the nearest degree.

Solution

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The circumference of circle is 2πr=176

2×

7

22

×r=176

r=176×

22

7

2

1

r=7×4=28cm

Area of circle is πr

2

=

7

22

×28×28=88×28=2464cm

2

The x-intercepts, y-intercept, vertex, and axis of symmetry for the given function g(x) = x² + 4x + 3 have been plotted on the graph below.

In Mathematics and Geometry, the graph of a quadratic function would always form a parabolic curve because it is a u-shaped. Based on the given quadratic function, we can logically deduce that the graph would be a upward parabola because the coefficient of x² is positive and the value of "a" is greater than zero (0).

Since the leading coefficient (value of a) in the given quadratic function g(x) = x² + 4x + 3 is positive 1, we can logically deduce that the parabola would open upward and the x-intercept (roots) is given by the ordered pair (-3, 0) and (-1, 0).

In conclusion, the vertex is given by the ordered pair (-2, -1) and the minimum value is -1.

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Answer:

x-intercepts = (-3, 0) and (-1, 0)

y-intercept = (0, 3)

Vertex = (-2, -1)

Axis of symmetry:  x = -2

Step-by-step explanation:

Given quadratic function:

[tex]g(x) = x^2 + 4x + 3[/tex]

[tex]\hrulefill[/tex]

To find the x-intercepts of the given function g(x), set g(x) equal to zero and solve for x.

Set g(x) = 0:

[tex]x^2 + 4x + 3 = 0[/tex]

Factor the quadratic equation:

[tex]x^2+x+3x+3=0[/tex]

[tex]x(x+1)+3(x+1)=0[/tex]

[tex](x + 3)(x + 1) = 0[/tex]

Set each factor equal to zero and solve for x:

[tex]x + 3 = 0 \implies x = -3[/tex]

[tex]x + 1 = 0 \implies x = -1[/tex]

Therefore, the x-intercepts are at (-3, 0) and (-1, 0).

[tex]\hrulefill[/tex]

To find the y-intercept of g(x), substitute x = 0 and solve for y.

[tex]\begin{aligned}x=0 \implies y&= (0)^2 + 4(0) + 3\\y& = 0 + 0 + 3 \\y&= 3\end{aligned}[/tex]

Therefore, the y-intercept is at (0, 3).

[tex]\hrulefill[/tex]

The x-value of the vertex of a parabola in the form y = ax² + bx + c is x = -b/2a.

For the function g(x), a = 1, and b = 4.

Therefore, the x-coordinate of the vertex is:

[tex]\textsf{$x$-coordinate of vertex} = \dfrac{-b}{2a} = \dfrac{-4}{2(1)} = -2[/tex]

To find the y-coordinate of the vertex, substitute x = -2 into function g(x):

[tex]\begin{aligned}x=-2 \implies y &= (-2)^2 + 4(-2) + 3\\y& = 4-8 + 3 \\y&= -1\end{aligned}[/tex]

Therefore, the vertex is at (-2, -1).

[tex]\hrulefill[/tex]

The axis of symmetry of a vertical parabola is the x-coordinate of its vertex.

As the x-coordinate of the vertex is -2, the axis of symmetry is x = -2.

[tex]\hrulefill[/tex]

Answer:

The person must score 136 to be in the top 5% of all scores in wechsler adult intelligence scale.

Step-by-step explanation:

What is defined as the normal distribution?

A normal distribution is a data set arrangement in which the majority of values cluster inside the center of the range and the remainder taper off symmetrically toward any extreme.

A histogram inside a normal distribution curve is sometimes used to design the curve.

The formula for the normal distribution is;

z = (x - μ)/σ

where,

z = z- score, taken fro table

Mean μ = 110

Standard deviation σ = 15

Sample mean x.

If we want to be in the top 5%, we must outperform 95% of the remaining scores. So we must investigate.

In with us standard normal probability table, look up 0.95 and get the Z score that corresponds to that.

z = 1.7

Put the value in formula ad find x.

1. 7 = (x - 110)/15

x = 25.5 + 110

x = 135.5

x = 136 (whole number)

Thus, the person must score 136 to be in the top 5% of all scores in wechsler adult intelligence scale.

The mapping shown does not represents a function

From the question, we have the following parameters that can be used in our computation:

The mapping

From the mapping, we have

(1, 7), (8, 3), (8, -1) and (3, 0)

The above ordered pair is not a function

This is so because the input value 8 have different output values 3 and -1

i.e. it would not pass the vertical line test when represented on a graph

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The best estimate for the amount of juice Barry made is 235 cups.

In this question, Jessica and Barry squeezed oranges for juice. Jessica squeezed 235 cups of juice. Barry made 14 cups less than Jessica. Barry estimated that Jessica squeezed about 212 cups of juice. We need to find the best estimate for the amount of juice Barry made.

Let's begin by finding the amount of juice Barry actually made. Barry made 14 cups less than Jessica, which means he made: 235 - 14 = 221 cups of juice.

Now, let's compare this to Barry's estimate. Barry estimated that Jessica squeezed about 212 cups of juice. Since Jessica actually squeezed 235 cups of juice, her estimate was too low by:235 - 212 = 23 cups.

So, we can apply this error to Barry's estimate to get a better estimate for the amount of juice he made. If Barry's estimate was 212 cups, and he underestimated by 23 cups, then he actually made:212 + 23 = 235 cups of juice. Therefore, the best estimate for the amount of juice Barry made is 235 cups.

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The missing dimensions from the given expression should be completed with the following:

(81.) A) 2

(82.) AD) x

(83.) E) 12

The expression as a product should be written as: DE) 2(x + 12).

In Mathematics and Geometry, a factored form simply refers to a type of quadratic expression that is typically written as the product of two (2) linear factors and a constant.

In this scenario and exercise, we would complete the table above by showing the factored form and expanded form of each of the given expressions as follows;

       x           12

2      2x         24

Note: 2x/2 = x.

        24/2 = 12.

Next, we would write the expression 2x + 24 as a product as follows;

(2x + 24) = 2(x + 12).

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The antiderivative of the function is f(x) = 2x + 5x³ + 2x⁶ - 9.

To find an antiderivative of f(x), we can integrate each term of f'(x) individually.

Given:

f'(x) = 2 + 15x² + 12x⁵

To integrate 2, we get:

∫2 dx = 2x + C₁, where C₁ is the constant of integration.

To integrate 15x², we get:

∫15x² dx = 5x³ + C₂, where C₂ is another constant of integration.

To integrate 12x⁵, we get:

∫12x⁵ dx = 2x⁶ + C₃, where C₃ is another constant of integration.

Putting it all together, the antiderivative of f(x) is:

f(x) = 2x + 5x³ + 2x⁶ + C,

where C = C₁ + C₂ + C₃ represents the constant of integration.

To find the specific value of C, we are given that f(1) = 0. Substituting x = 1 into the antiderivative equation:

0 = 2(1) + 5(1)³ + 2(1)⁶ + C,

0 = 2 + 5 + 2 + C,

0 = 9 + C.

Therefore, C = -9.

The final expression for f(x) is:

f(x) = 2x + 5x³ + 2x⁶ - 9.

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The statement is:

O True

Work/explanation:

The following statement is true, because 1x is indeed the same thing as x. So when combining like terms, 2x + x is the same thing as 2x + 1x, which evaluates to 3x.

Answer:

measure of arc JL = 55°

measure of angle PKJ = 27.5°

Answer:

C) -1/3

Step-by-step explanation:

Slope=rise/run

Slope=-1/3

Answer:El pintor debe pintar un muro de módulo de vigilancia, que es un pentágono regular, por tanto, procedemos a buscar cuántos metros debe pintar: P = 5·L 35 m = 5·L L = 35 m / 5 L = 7 m En consecuencia, al pintar un muro, el trabajador pintará 7 m.

Step-by-step explanation:

El trabajador pintará 7 metros de muro, ya que esa es la longitud de cada lado del pentágono regular cuyo perímetro es de 35 metros.

Un pentágono regular es una figura con cinco lados iguales. Si su perímetro total es de 35 metros, entonces cada lado del pentágono mide 35 metros dividido entre 5, que resulta igual a 7 metros. Entonces, si el trabajador debe pintar uno de los muros del pentágono regular, la cantidad de metros lineales a pintar será igual a la longitud de uno de sus lados. Por lo tanto, el trabajador pintará 7 metros de muro.

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The table that shows the same function as the given graph is: A 2-column table with 4 rows. Column 1 is labeled x with entries 0, 2, 4, 6. Column 2 is labeled y with entries 4, 5, 6, 7.

To determine which table shows the same function as the given graph, we need to find the values of y corresponding to the given values of x on the graph.

Point A: (0, 4)

Point B: (2, 5)

Let's check each table:

A 2-column table with 4 rows. Column 1 is labeled x with entries 0, 2, 4, 6. Column 2 is labeled y with entries negative 8, negative 4, 0, 4.

A 2-column table with 4 rows. Column 1 is labeled x with entries 0, 2, 4, 6. Column 2 is labeled y with entries 0, 4, 0, 4.

A 2-column table with 4 rows. Column 1 is labeled x with entries 0, 2, 4, 6. Column 2 is labeled y with entries 4, 5, 6, 7.

A 2-column table with 4 rows. Column 1 is labeled x with entries 0, 2, 4, 6. Column 2 is labeled y with entries 4, 8, 12, 16.

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Gabby can get €23.73 for £21 when using the exchange rate of £1 = €1.13.

To calculate how many euros Gabby can get for £21, we need to use the exchange rate of £1 = €1.13.

To find the number of euros, we multiply the amount in pounds (£21) by the exchange rate (€1.13):

£21 * €1.13 = €23.73

Therefore, Gabby can get €23.73 for £21 when using the exchange rate of £1 = €1.13.

This means that for every pound exchanged, Gabby will receive €1.13. So, by multiplying the amount in pounds (£21) by the exchange rate (£1 = €1.13), we can determine the equivalent amount in euros.

It's important to note that exchange rates can fluctuate, and the rate provided here is just an example. When exchanging currency, it's always advisable to check the current exchange rates as they may vary. Additionally, some currency exchange services may charge fees or have different rates, so it's essential to consider those factors as well.

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The reason why Figure A is congruent to Figure C is that they undergo the same sequence of transformations: a translation followed by a reflection.

The statement "Figure A is translated 3 units right and 2 units up. The translated figure is labeled Figure B. Figure B is reflected over the x-axis. The reflected figure is labeled Figure C" describes a sequence of transformations applied to Figure A to obtain Figure C.

When Figure A is translated 3 units right and 2 units up, it undergoes a rigid transformation known as a translation. This transformation preserves the shape and size of the figure. The translated figure, Figure B, will have the same dimensions and orientation as Figure A but will be shifted to the right and up.

When Figure B is reflected over the x-axis, it undergoes a reflection. This transformation flips the figure vertically, changing the sign of the y-coordinates of its vertices while keeping the x-coordinates the same. The reflected figure, Figure C, will have the same shape and size as Figure B, but it will be oriented in the opposite direction.

Since translations and reflections are both rigid transformations, they preserve congruence. Therefore, Figure A and Figure C are congruent because they undergo the same sequence of transformations (translation followed by reflection) from Figure A.

In conclusion, Figures A and C go through the same set of transformations, a translation and a reflection, which explains why they are congruent.

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Han will have 2 liters (or 2000 milliliters) of sparkling juice after combining 1.5 liters of juice and 500 milliliters of sparkling water.

To make sparkling juice, Han mixes 1.5 liters of juice and 500 milliliters of sparkling water.

To add the quantities together, we need to convert the units to the same measurement. We can convert the liters to milliliters since 1 liter is equal to 1000 milliliters.

1.5 liters is equal to 1.5 x 1000 = 1500 milliliters.

Now we have 1500 milliliters of juice and 500 milliliters of sparkling water.

To find the total quantity of the sparkling juice, we add the volumes of juice and sparkling water together:

1500 milliliters + 500 milliliters = 2000 milliliters

Therefore, Han will have a total of 2000 milliliters (or 2 liters) of sparkling juice by mixing 1.5 liters of juice and 500 milliliters of sparkling water.

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The statement "rank(AB) = n" is not always true for invertible n by n matrices A and B with rank(A) = rank(B) = n.

Counterexample:

Consider the following counterexample:

[tex]A = \begin{bmatrix} 1 & 0 \ 0 & 1 \end{bmatrix}\\B = \begin{bmatrix} 1 & 0 \ 0 & 0 \end{bmatrix}[/tex]

Both matrices A and B are invertible, as they are both identity matrices. However, when we multiply them together, we get:

[tex]AB = \begin{bmatrix} 1 & 0 \ 0 & 0 \end{bmatrix}[/tex]

The rank of AB is 1, not n. In this case, n = 2, but rank(AB) = 1. Therefore, the statement "rank(AB) = n" is not always true for all invertible n by n matrices A and B with rank(A) = rank(B) = n.

In general, the rank of the product AB is less than or equal to the minimum of the ranks of A and B. So, in order for rank(AB) to be equal to n, both A and B need to have rank n individually, but that does not guarantee the rank of their product to be n as well.

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Based on the pattern we identified, the next term in the sequence would be 55.

The sequence should be 7, 10, 19, 34, 55

To identify the pattern and determine what comes next in the given sequence (7, 10, 19, 34), we need to examine the relationship between the terms and look for a consistent pattern.

If we calculate the differences between consecutive terms, we get:

10 - 7 = 3

19 - 10 = 9

34 - 19 = 15

By examining the differences, we notice that they are increasing by 6 each time.

This suggests that the sequence might be formed by adding an increasing number to each term.

Let's calculate the next difference:

15 + 6 = 21

Now, let's add this difference to the last term of the sequence:

34 + 21 = 55

Therefore, based on the pattern we identified, the next term in the sequence would be 55.

To summarize:

7, 10, 19, 34, 55

It's important to note that without further context or information, this pattern is just one of the possibilities and may not be the only correct answer.

Additional terms or a different pattern may emerge if more information is provided.

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Answer:

(a) The graph is entirely above the x-axis and rises from left to right, more steeply than the graph of y = 5^x.

(b) The second coordinate of the point with first coordinate 0 is 2.

The second coordinate of the point with first coordinate 1 is 10.

In the context of a Cartesian coordinate system, the term "(-,-) quadrant" refers to the third quadrant, also known as Quadrant III.

The Cartesian coordinate system consists of four quadrants, numbered from I to IV in a counterclockwise direction. Each quadrant is defined by the signs of the x and y coordinates.

In Quadrant III, the x-coordinates are negative (represented by the "-") and the y-coordinates are also negative. This means that any point located in this quadrant will have both x and y values that are less than zero.

Visually, Quadrant III is situated below the x-axis and to the left of the y-axis. It is characterized by its lower left position in the coordinate plane.

Points in Quadrant III can be thought of as having a negative horizontal position (to the left of the origin) and a negative vertical position (below the origin).

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OThe presence of identical fossil plants in both Antarctica and Australia, within the same rock formations, supports the hypothesis of a supercontinent and the process of plate tectonics by providing evidence of past land connections and the subsequent separation of continents due to tectonic activity.

The presence of identical fossil plant species in rock formations of both Antarctica and Australia suggests that these two regions were once connected geographically. The similarity in the fossil record indicates that the plants existed in a shared ecosystem or environment at some point in the past.

The geological formations in which the fossil plants are found can provide further evidence. If the rock layers containing the fossils can be matched across Antarctica and Australia, it suggests that these regions were once part of the same landmass. This correlation supports the idea of a supercontinent.

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Answer:

x = 6

Step-by-step explanation:

the diagonal AC divides the rectangle into 2 right triangles.

Consider the right triangle ABC with legs AB , BC and hypotenuse AC

using Pythagoras' identity in right triangle ABC

the square on the hypotenuse is equal to the sum of the squares on the other 2 sides, that is

AB² + BC² = AC² ( substitute values )

x² + (x + 2)² = (x + 4)² ← expand factors using FOIL

x² + x² + 4x + 4 = x² + 8x + 16

2x² + 4x + 4 = x² + 8x + 16 ( subtract x² + 8x + 16 from both sides )

x² - 4x - 12 = 0 ← in standard form

(x - 6)(x + 2) = 0 ← in factored form

equate each factor to zero and solve for x

x - 6 = 0 ⇒ x = 6

x + 2 = 0 ⇒ x = - 2

however , x > 0 , then x = 6

Therefore, Paxton will need to invest her money for approximately 21.62 years to increase her investment from $4850 to $8000 at a simple interest rate of 7.6% per year.

To determine how long Paxton needs to invest her money in order for it to increase to $8000, we can use the formula for simple interest:

I = P * r * t

Where:

I = Interest earned

P = Principal (initial investment)

r = Interest rate per year (expressed as a decimal)

t = Time (in years)

Given that Paxton invests $4850 at an interest rate of 7.6% per year, we have:

4850 * 0.076 * t = 8000

Simplifying the equation:

369.8t = 8000

To find t, we divide both sides of the equation by 369.8:

t ≈ 8000 / 369.8 ≈ 21.62 years

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Answer:

Using the sine function, we have:

sin(angle) = opposite / hypotenuse

sin(22 degrees) = opposite / 18 feet

We can rearrange this equation to solve for the opposite side (height of the building):

opposite = sin(22 degrees) * 18 feet

Calculating this:

opposite ≈ 6.24 feet

Therefore, the base of the ladder from the base of the building is approximately 6.24 feet.

Cameron has 1 book left over after sorting it into group of 5

To determine the number of book left,

we need to first divide 56 by 5         [56 ÷ 5]

Quotient = 11

then find the remainder which is 1

therefore there os only 1 book left over

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Answer:

15 coins, d + q coins

Step-by-step explanation:

If asking for the amount (in $)

5(.10) + 10(.25) = 2.5+.5 = $3

He would have 0.1d + 0.25q for d dimes and q quarters.

Answer:

379.2 in^2

Step-by-step explanation:

Each cylinder's side area is  pi *d * h = 43.98 in^2

  you need six    :     =263.89 in^2

each ned of the cylinder area = pi r^2 = 9.621 in^2

    and you have 12 ends  for 115.45 in^2

For total : 379.3  in^2       (slight difference due to the value of pi used and rounding)

Answer:

let, perimeter of square = 4a

where a = side of square

let, perimeter of the equilateral triangle = 3b

where b= side of triangle

therfore, 4a=3b

a/b = 3/4

area of the square = [tex]a^{2}[/tex]

are of the triangle = [tex]\frac{\sqrt{3} }{4} b^{2}[/tex]

dividing both the areas we get,

[tex]\frac{a^{2} }{\frac{\sqrt{3} }{4}b^{2} }[/tex]

[tex]a^{2}*\frac{4}{\sqrt{3} b^{2}}[/tex]

[tex]\frac{a^{2} }{b^{2} } * \frac{4}{\sqrt{3} }[/tex]

[tex]\frac{3^{2} }{4^{2} } * \frac{4}{\sqrt{3} }[/tex]

[tex]\frac{3\sqrt{3} }{4}[/tex]

hope you understand

Step-by-step explanation:

Answer:

A critical number can have different meanings depending on the context. In mathematics, a critical number is a value of x where the derivative of a function is zero or undefined. It helps to find the maximum and minimum of a function. In business, a critical number is a metric that represents a weakness or vulnerability that needs to be addressed and corrected to improve the performance and security of the company

Step-by-step explanation:

Sure! Here’s the solution:

F(x)=k9−kx2​​

First, let’s square both sides to get rid of the square root:

F(x)2=k9−kx2​

Now, let’s multiply both sides by k to isolate the term with x^2:

kF(x)2=9−kx2

Next, let’s move all terms to one side of the equation:

kF(x)2+kx2=9

Finally, let’s factor out x^2:

x2(k+kF(x)2)=9

And solve for x^2:

x2=k+kF(x)29​

Answer:

Step-by-step explanation:

To show the work for evaluating the function f(x) = √(9 - kx^2) / k, we can follow these steps:

9 - kx^2

(9 - kx^2) / k

√((9 - kx^2) / k)