Which description matches the graph of the inequality y > |x + 4| – 1? a shaded region above a solid boundary line a shaded region above a dashed boundary line a shaded region below a dashed boundary line a shaded region below a solid boundary line

The value of x in the triangles are 9.

For variable x : ax² + bx + c = 0, where a≠0 is a standard quadratic equation, which is a second-order polynomial equation in a single variable. It has at least one solution since it is a second-order polynomial equation, which is guaranteed by the algebraic basic theorem.

Given:

The triangles are congruent.

That means, their corresponding angles are also congruent.

In ΔJKL,

the sum of all the angles of the triangle is 180°.

So,

x²-2x + x + 29 + 3x + 52 = 180

x² + 2x - 99 = 0

Solving the quadratic equation,

x² +11x - 9x - 99 = 0.

x (x + 11) -9 (x + 11) = 0

x = 9 and x = -11

Here, we take x = 9.

Therefore, the value of x is 9.

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Answer 58 1/2:

Step-by-step explanation:

The image of the original figure after the translation and reflection is congruent to the original figure.

A particular type of transformation on the coordinate plane called translation keeps the size of the point or geometrical shape constant while only changing the position. Along the x-axis and y-axis in the coordinate system, the point or the figure can be moved in any direction, including up, down, right, left, and multiple directions.

1. By taking away 4 from the x-coordinate and adding 8 to the y-coordinate, we can translate a point 4 units left and 8 units up.

2. Point A after translation is situated at (-2, 9).

3. We negate the x-coordinate and leave the y-coordinate unaltered to indicate a point over the y-axis.

4. Point B is obtained by reflecting point A over the y-axis (2, 9).

5. Indeed, the resulting representation is consistent with the original figure since the rigid transformations of translation and reflection maintain angles and distances. As a result, the original figure's picture after translation and reflection corresponds to the original figure.

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The surface area of the wooden structure is approximately 1012 cm².

To calculate the surface area of the wooden structure, we need to find the surface area of the cone and the surface area of the hemispherical base, and then add them together.

Surface Area of the Cone:

The surface area of a cone is given by the formula:

A_{cone = \(\pi \times r_{cone} \times (r_{cone} + s_{cone})\), \(r_{cone\) is the radius of the base of the cone and \(s_{cone\) is the slant height of the cone.

The vertical height of the cone is 24 cm, and the base radius is 7 cm, we can calculate the slant height using the Pythagorean theorem:

\(s_{cone\) = \(\sqrt{(r_{cone}^2 + h_{cone}^2).\)

Using the given measurements:

\(s_{cone\) = √(7² + 24²) cm

\(s_{cone\) ≈ √(49 + 576) cm

\(s_{cone\) ≈ √625 cm

\(s_{cone\) ≈ 25 cm

Now, we can calculate the surface area of the cone:

\(A_{cone\) = π × 7 cm × (7 cm + 25 cm)

\(A_{cone\) = (22/7) × 7 cm × 32 cm

\(A_{cone\) = 704 cm²

Surface Area of the Hemispherical Base:

The surface area of a hemisphere is given by the formula:

\(A_{hemisphere\) = \(2 \times \pi \times r_{base}^2\), \(r_{base\) is the radius of the base of the hemisphere.

Given that the base radius is 7 cm, we can calculate the surface area of the hemispherical base:

\(A_{hemisphere\) = 2 × (22/7) × (7 cm)²

\(A_{hemisphere\) = (22/7) × 2 × 49 cm²

\(A_{hemisphere\) = 308 cm²

Total Surface Area:

To calculate the total surface area, we add the surface area of the cone and the surface area of the hemispherical base:

Total Surface Area = \(A_{cone} + A_{hemisphere}\)

Total Surface Area = 704 cm² + 308 cm²

Total Surface Area = 1012 cm²

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The probability of digits 0 to 9 represent the medicine being not effective.

It is a branch of mathematics that deals with the occurrence of a random event.

As the digit 9 is not effective

So the number of not effective is 2+1+2+2+1+3

=11

The probability=effective numbers/all numbers

=30-11/30

=19/30

Hence, the probability of digits 0 to 9 represent the medicine being not effective.

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the x-coordinate of the point that is 2/5 of the way from V to W on this line segment is approximately 8.08.

A coordinate is a number or set of numbers that specifies the position of a point in a space. Coordinates are used to describe the position of objects in various mathematical systems, including two-dimensional and three-dimensional Euclidean spaces, as well as non-Euclidean spaces like spherical or hyperbolic geometries.

by the question.

The x-coordinate of the point that is 2/5 of the way from V to W can be found by first determining the x-coordinate of the point that is 2/5 of the way from V to W and then using the formula for finding the x-coordinate of a point on a line given its y-coordinate.

To find the point that is 2/5 of the way from V to W, we need to first find the distance between V and W. Using the distance formula:

d =\(\sqrt{11-(-4)^{2} }\) + (2 - \((-4)^{2}\)) = \(\sqrt{225+36}\)= \(\sqrt{261}\)

Then, the distance between V and the point we're looking for is (2/5) * \(\sqrt{261}\), and the distance between the point we're looking for and W is (3/5) * \(\sqrt{261}\).

To find the x-coordinate of the point we're looking for, we can use the formula:

x = (distance from V to point we're looking for)/ (total distance) * x

coordinate of W + (distance from point we're looking for to W)/(total distance) * x-coordinate of V.

Substituting the values, we found:

x = (2/5 *\(\sqrt{261}\))/\(\sqrt{261}\)) * 11 + (3/5 * \(\sqrt{261}\))/\(\sqrt{261}\)) * (-4) = 8.08

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The height of the hexagonal-based pyramid is approximately 101.61 inches.

To find the height of the hexagonal-based pyramid, we can use the formula for the volume of a pyramid:

Volume = (1/3) × Base Area × Height

In this case, the base of the pyramid is a regular hexagon, and we have the side length (s) and apothem (a) given.

The base area of a regular hexagon can be calculated using the formula:

Base Area = (3√3/2) × s²

Let's calculate the base area first:

Base Area = (3√3/2) × (6 in)²

Base Area = (3√3/2) × 36 in²

Base Area ≈ 93.53 in²

Now, we can rearrange the volume formula to solve for the height:

Height = Volume / ((1/3) × Base Area)

Height = 3168 in³ / ((1/3) × 93.53 in²)

Height = 3168 in³ / (31.177 in²)

Height ≈ 101.61 in

Therefore, the height of the hexagonal-based pyramid is approximately 101.61 inches.

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Answer:

x = 0.39 or

x = -1.72

Step-by-step explanation:

The quadrateic formula is:

\(x = \frac{-b\pm\sqrt{b^2 - 4ac} }{2a}\)

eq: 3x² + 4x - 2

which is of the form ax² + bx + c = 0

where a = 3, b = 4 and c = -2

sub in quadratic formuls,

\(x = \frac{-4\pm\sqrt{4^2 - 4(3)(-2)} }{2(3)}\\\\=\frac{-4\pm\sqrt{16 + 24} }{6}\\\\=\frac{-4\pm\sqrt{40} }{6}\\\\=\frac{-4\pm2\sqrt{10} }{6}\\\\=\frac{-2\pm\sqrt{10} }{3}\\\\=\frac{-2+\sqrt{10} }{3} \;or\;=\frac{-2-\sqrt{10} }{3}\\\\=0.39 \;or\; -1.72\)

Answer:

644 dollars a week and 2567 each month

Answer:

Jason

Step-by-step explanation:

Answer:

It's Seth

Step-by-step explanation:

The two equations which can be used to represent the situation are;

r + s = 1787

4r + 3s = 5,792

The correct answer choice is option B and E

Reserved seat for basketball game = r

Students seat for basketball game = s

Cost of reserved seat tickets = $4

Cost of students tickets = $3

Total number of people who attended the basketball game= 1,787 people

Total amount earned for tickets sales= $5,792

r + s = 1787

4r + 3s = 5,792

Therefore, the basketball game situation can be represented by the equation r + s = 1787; 4r + 3s = 5,792

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Answer:

x = 5/4

y = 15/16

Step-by-step explanation:

System of 2 equations

Applying substitution method

3/4x = y

5/2x + 2(3/4 x) = 5

5/2 x + 6/4 x = 5

16/4 x = 5

4x = 5

x= 5/4

3/4 * 5/4 = 15/16

Answer:

Width - 12ft  Length - 30ft

Step-by-step explanation:

Width is 12ft

Length is 30ft

Depth is 6ft

The length, 30ft, is 2.5 times longer than the width which is 12 ft which confirms the two dimensions to be correct.

When you multiply all three of the dimensions of the swimming pool you will get 2940 cubic feet

Answer: 40 km

Step-by-step explanation:

As corresponding sides of similar triangles are proportional, if we let the distance across Clarence lake be x,

\(\frac{x}{8}=\frac{15}{3}\\\\\frac{x}{8}=5\\\\x=\boxed{40 \text{ km}}\)

Answer:

4b = 50; 1a = 80

Step-by-step explanation:

So let's say that bananas = b and apple = a

Then we could set up the equations that are:

4b = 50 (cents)

1a = 80 (cents)

That means we have 2 equations of 4b = 50 and 1a = 80

Answer:

Step-by-step explanation:

banana = b = 50¢ = $.50

apple = a = 80¢ = $.80

Total cost of fruit = f

She bought 4 bananas for .50 each so we multiply 4*.50 to find the total cost of the bananas and she bought 1 apple for .80, so we add them together to get the total cost of the fruit, f.

4b + a = f     Now substitute the values.

(4*.50) + .80 = f       This is you expression, let's solve for fun.

(4*.50) + .80 = f

2 + .80 = f

$2.80 = f   Sylvia spend $2.80 on the fruit.

The function f(x) = \(-2(x+4)^2\) + 1 has a greater maximum.

1. The given function is f(x) = \(-2(x+4)^2\) + 1.

2. To find the maximum of the function, we need to determine the vertex of the parabola.

3. The vertex form of a quadratic function is given by f(x) = \(a(x-h)^2\) + k, where (h, k) represents the vertex.

4. Comparing the given function to the vertex form, we see that a = -2, h = -4, and k = 1.

5. The x-coordinate of the vertex is given by h = -4.

6. To find the y-coordinate of the vertex, substitute the x-coordinate into the function: f(-4) = \(-2(-4+4)^2\) + 1 = \(-2(0)^2\) + 1 = 1.

7. Therefore, the vertex of the function is (-4, 1), which represents the maximum point.

8. Comparing this maximum point to the information provided about the other function g(x) on the coordinate plane, we can conclude that the maximum of f(x) = \(-2(x+4)^2\) + 1 is greater than the maximum of g(x).

9. The given information about g(x) is not sufficient to determine its maximum value or specific equation, so a direct comparison is not possible.

10. Hence, the function f(x) =\(-2(x+4)^2\) + 1 has a greater maximum.

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Answer:

30, 35 and 40

Step-by-step explanation:

The given sequence 10, 15, 20, 25... is an arithmetic sequence

nth term of an arithmetic sequence Tn = a +(n-1)d

a is the first term = 10

d is the common difference = 15-10 = 20-15 = 5

n is the number of terms

For the 5th term

T5 = 10 + (5-1)*5

T5 = 10+4(5)

T5 = 10+20

T5 = 30

For the 6th term

T5 = 10 + (6-1)*5

T6 = 10+5(5)

T6 = 10+25

T6 = 35

For the 7th term

T7 = 10 + (7-1)*5

T7 = 10+6(5)

T7 = 10+30

T7 = 40

Hence the next 3 terms are 30, 35 and 40

Answer:

-1/2

Step-by-step explanation:

Use the two points shown.

slope = rise/run

Start at teh left point.

Go down 2 units. That is a rise of -2.

Now go right 4 units. That is a run of 4.

slope = rise/run = -2/4 = -1/2

The probability, if Greg gets dressed in the dark, that he winds up wearing the white shirt and tan pants is 0.125 or 12.5%.

To find the probability that Greg winds up wearing the white shirt and tan pants while getting dressed in the dark, we need to find out all the possible outfit options. According to the question given, first we nned to find out number of outfit combinations possible.

Total number of Outfit Combinations:

There are 4 shirts: a white one, a black one, a red one, and a blue one and also two pairs of pants, one blue and one tan. So, total number of possible outfit combinations would be 4 * 2 = 8.

No of favourable options:

As given in the question, Greg wears white shirt and tan pants. There is only one white shirt and one tan pant. So, number of favourable options would be only 1 .

Probability = Number of favourable outcomes/Total no. of combinations

Probability = 1/8

Probability = 0.125 or 12.5%

Therefore, the probability, if Greg gets dressed in the dark, that he winds up wearing the white shirt and tan pants is 0.125 or 12.5%.

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Answer:

10

Step-by-step explanation:

Since G = B (and 284 + 76 = 360), then FE = CD

Answer:

(a) \(y'= 2cos(2x - \pi)\)

(b) \(y=2x - \pi + 1\)

(c) \(y=-\frac{x}{2} +\frac{\pi + 4}{4}\)

Step-by-step explanation:

\(y=sin(2x-\pi)+1\)

Find the derivative of this function by using the chain rule and the power rule.

We know that the derivative of sinx = cosx. Find the derivative of this entire function first, \(sin(2x-\pi)+1\), then multiply this by the derivative of the inside function, \(2x-\pi\).

Use the chain rule to find the derivative of sin(2x - π) + 1, which is cos(2x - π), then multiply this by the derivative of (2x - π). The derivative of π is 0, because it is a constant. The derivative of 2x is 2 based on the Power Rule.

Simplify this expression.

This is the derivative of \(y=sin(2x-\pi)+1\); therefore, we can write:

In order to find the equation of the tangent line at \(x=\frac{\pi}{2}\), we will need to find the slope of the tangent line and the x- and y- coordinates (we already know the x- cord).

The steps to finding the equation of the tangent line at a certain are:

We know that y' = 2cos(2x - π). Let's plug x = π/2 into this equation for x to find the slope of the tangent line.

Simplify inside the parentheses.

Now we know that the slope of the tangent line is 2.

Let's plug x = π/2 into the original function, y.

Simplify inside the parentheses.

This tells us that the y-value, when x = π/2, equals 1. Our coordinates that we can use are (π/2, 1).

Now we can use point-slope form to write an equation for the tangent line to y at x = π/2.

Point-slope equation:

We have \((x_1, \ y_1)\), which are the x- and y- coordinates, and \(m\), which is the slope of the tangent line.

Substitute these values into the equation:

Distribute 2 inside the parentheses.

Add 1 to both sides of the equation.

This is the equation of the tangent line of \(y=sin(2x-\pi)+1\) at \(x=\frac{\pi}{2}\).

In order to find the equation of the normal line at x = π/2, we can use the information that the tangent line is perpendicular to the normal line.

This information is helpful because this means that their slopes are opposite reciprocals.

Let's use the point-slope equation again, but instead of m = 2, m will be the opposite reciprocal of 2 ⇒ -1/2. We will still use the same coordinate points.

Distribute -1/2 inside the parentheses.

Add 1 to both sides of the equation.

You can leave it written as this, or write it as:

This is the equation of the normal line of \(y=sin(2x-\pi)+1\) at \(x=\frac{\pi}{2}\).

Answer:

His unit rate per month is 25 dollars

Step-by-step explanation:

Cole has saved 25 dollars per month. by subtracting 190 from 265 you are left with 75. when left with 75 you can divide by 3 for the the 3 months hes been saving his money. 75 divided by 3 is 25.

The correct value of particle's acceleration at t = 2 seconds is -1/12 m/s^2.

To find the particle's velocity, we need to take the derivative of the position function with respect to time (t).

Given the position function:

s = √24 + 6t

To find the velocity, we differentiate the position function with respect to time:

v = ds/dt

Applying the power rule and chain rule for differentiation, we get:

v = (1/2) * (24 + 6t)^(-1/2) * 6

Simplifying further:

v = 3 / √(24 + 6t)

To find the velocity at t = 2 seconds, we substitute t = 2 into the velocity equation:

v = 3 / √(24 + 6(2))

v = 3 / √(24 + 12)

v = 3 / √36

v = 3 / 6

v = 1/2 m/s

So, the particle's velocity at t = 2 seconds is 1/2 m/s.

Now, let's find the particle's acceleration. Acceleration is the derivative of velocity with respect to time.

a = dv/dt

To find the acceleration, we differentiate the velocity function with respect to time:

a = d(3 / √(24 + 6t)) / dt

Applying the quotient rule and chain rule, we get:

a = -3 * (24 + 6t)^(-3/2) * 6

Simplifying further:

a = -18 / (24 + 6t)^(3/2)

To find the acceleration at t = 2 seconds, we substitute t = 2 into the acceleration equation:

a = -18 / (24 + 6(2))^(3/2)

a = -18 / (24 + 12)^(3/2)

a = -18 / 36^(3/2)

a = -18 / 36^(3/2)

a = -18 / 216

a = -1/12 m/s^2

So, the particle's acceleration at t = 2 seconds is -1/12 m/s^2.

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If the water snake is initially 30 meters below the ground level and then climbs 20 meters upward, it will be 30 - 20 = 10 meters below the ground level. However, if it then slips down 10 meters, it will be 10 + 10 = 20 meters below the ground level.

Answer:

(x)^2+ (y+2)^2 = 49

Step-by-step explanation:

The standard form of a circle is

(x-h)^2+ (y-k)^2 = r^2 where (h,k) is the center and r is the radius

(x-0)^2+ (y--2)^2 = 7^2

(x)^2+ (y+2)^2 = 49