Riley wants to put a poster in a frame. The original poster is 11 inches wide and 14 inches tall. The frame will be x inches thick on each side. The

figure shows the poster and its frame.

xin.

xin.

14 in.

xin.

11 in.

xin.

Riley knows he wants the total area of the poster and frame together to be no more than 320 square inches.

Which inequality correctly models this situation?

A 2 + 11x + 14 = 320

B. 2 + 25x + 154 3 320

OC. 4x2 + 11x + 14 < 320

OD

4x2 + 50x + 154 3 320

The solutions to the equation x² + 10x + 22 = 13 are: x = -5 ± 4

To rewrite the equation by completing the square, we need to isolate the constant term on one side and group the x-terms together. Starting with:

x² + 10x + 22 = 13

Subtracting 13 from both sides:

x² + 10x + 9 = 0

Next, we add and subtract the square of half of the coefficient of x (which is 5 in this case) to complete the square:

x² + 10x + 25 - 25 + 9 = 0

x² + 10x + 25  - 16 = 0

Factor the perfect square trinomial:

(x + 5)² - 16 = 0

Now that we have rewritten the equation in the form (x + c)² = d, we can solve for x by taking the square root of both sides:

(x + 5)² - 16 = 0

Taking the square root of both sides and solving for x, we get:

x + 5 = ±4

So, we have

x = -5 ± 4

So the solutions to the equation are:

x = -5 + 4 = -1

x = -5 - 4 = -9

Therefore, the answer is x = -5 ± 4.

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By Tangent function, to the nearest foot, the plane has flown approximately 28,333 feet.

A closed, two-dimensional shape, a circle is also a curve. The radius of the circle or the line connecting the center O to the point of tangency is always vertical or perpendicular to the tangent line AB at P, i.e., OP is perpendicular to AB as illustrated in the accompanying figure.

We are aware of our side and degree. We must determine how far the aircraft has traveled.

To determine how far the plane has traveled, we can utilize the sine function. Keep in mind that the sine function's definition is

tan(θ) = opposite/adjacent = height/distance.

tan(3) = 850/d

Solving for d, we get:

d = 850/tan(3)

d ≈ 28,333 feet

Tangent figure given below:

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The statement "System analysts define an object's attributes during the systems design process" is true because  defining object attributes is an essential part of the systems design process to ensure that the system meets the desired functional requirements.

In systems design, objects are used to represent real-world entities that are relevant to the system being developed. These objects have attributes that describe their characteristics or properties, which are used to identify and manipulate them within the system. System analysts define these attributes during the systems design process to ensure that the system meets the desired functional requirements.

For example, in a library system, a book object may have attributes such as title, author, publisher, and ISBN. Defining these attributes helps ensure that the system can properly manage and retrieve books as needed. Object-oriented design is a popular approach to systems design that relies heavily on defining objects and their attributes.

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The diameter of the balloon is increasing at a rate of approximately 0.79 ft/min when the diameter is 1.5 feet.

We can use the formula for the volume of a sphere to relate the rate of change of volume with the rate of change of diameter

V = (4/3)πr^3 = (1/6)πd^3,

where V is the volume, r is the radius, and d is the diameter.

Taking the derivative with respect to time t, we get

dV/dt = (1/2)πd^2 (dd/dt),

where dd/dt is the rate of change of diameter.

We are given that dV/dt = 2.8 ft^3/min and d = 1.5 ft, so we can solve for dd/dt

dd/dt = (2dV/dt)/(πd^2) = (2(2.8))/(π(1.5)^2) ≈ 0.79 ft/min.

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Answer: x=0 and x=-9

Step-by-step explanation:

Answer:

40 beads

Step-by-step explanation:

First, let's find the length of string that the beads will be on.

The string is originally 20 cm, but 2 cm is taken off each side.

So, the string that the beads will be on is only 16 cm now.

Each bead is 4 mm wide, so we have to convert the bead width to centimeters.

4/10=0.4

So each bead is 0.4 cm.

Now to find how many beads will fit, we have to divide the length by the width of the bead.

16/0.4=40

So, Mona will need 40 beads.  Hope this helps ;)

Answer:

3/10

Step-by-step explanation:

Answer: The answer is state B because there is less variability in larger populations so estimates from samples are more accurate. The standard error of the mean is proportional to the standard deviation of the population and inversely proportional to the square root of the sample size. Since state B has a much larger population, it is more likely that our sample mean will be within $80 of $2,600 for state B than for state A.

Step-by-step explanation:

The measure of the angles formed by the lines are 30°, 30°,  150° and  150° by definition of vertically opposite angles.

When two straight lines intersect each other at some angle, say line AB intersect line CD, then the opposite angles formed by the two lines are called vertically opposite angles. A pair of vertically opposite angles are equal to each other.

There are two pairs of opposite angles formed by intersection of two straight lines.

The total sum of all the angles formed by intersection of two straight lines is 360°.

Let angle X = x° and angle Y= y° be a pair of opposite angles.

Let the other pair of opposite angles be of angle M = m° and angle N = n°.

Thus, by definition of opposite angles and sum of all angles on intersection of two lines we get,

angle X + angle Y + angle M + angle N = 360°

⇒ x° + y° + m° + n° = 360°

⇒ x° + x° + m° + m° = 360°

⇒ 2( x° + m°) = 360°

⇒ x° + m° = 180° ___ (1)

Also, the measure of one of the angles is five times the measure of another of the angles formed by the lines.

This relation can be written as,

angle X = 5 times of angle M

⇒ x° = 5m° ___(2)

Since angle X and angle M are not a pair of opposite angles but are supplementary angles as observed in equation (1).

Putting equation (2) in equation (1) we get,

5m° + m° = 180°

⇒ 6m° = 180°

⇒ m° = 30°

Thus, x° = 5(30°) = 150°

Hence the angles are 30°, 30°,  150° and  150°.

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In 2010, Haiti was hit by a devastating earthquake, which registered at 7.0 on the Richter scale. The largest recorded earthquake since 1900 occurred in 1960 in Valdivia, Chile, and registered at 9.5 on the Richter scale. About 316 times greater was the intensity of the Chilean earthquake.

Hence, the correct option is D.

The Richter scale is a logarithmic scale that measures the magnitude of an earthquake. Each increase of one on the Richter scale represents a tenfold increase in the amplitude of the seismic waves.

To find out how many times greater the intensity of the Chilean earthquake was compared to the Haitian earthquake, we will have to find the difference in magnitude between the two earthquakes.

9.5 - 7.0 = 2.5

Since each increase of one on the Richter scale represents a tenfold increase in the amplitude of the seismic waves, a 2.5 increase represents

10^(2.5) = 316.2

Hence, the intensity of the Chilean earthquake was about 316 times greater than the intensity of the Haitian earthquake.

Hence, the correct option is D.

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Answer:d

Step-by-step explanation:

its d

Answer:

The vertex is option C: (-6, -2)

Step-by-step explanation:

The equation for a parabola is y = a(x – h)² + k where h and k are the y and x coordinates of the vertex, respectively. Thus, the vertex is (-6,2)

Pls mark brainliest.

The length of the bridge is 980 feet.

Let's denote the length of the bridge as x. According to the problem, one bank of the river holds 3/7 of the bridge, which means that the other bank holds 4/7 of the bridge.

Therefore, we can write the following equation:

3/7 x + 1400 + 4/7 x = x

Simplifying this equation, we get:

6/7 x + 1400 = x

Subtracting 6/7 x from both sides, we get:

1/7 x + 1400 = 0

Subtracting 1400 from both sides, we get:

1/7 x = -1400

Multiplying both sides by 7, we get:

x = -9800

Since the length of the bridge cannot be negative, we need to discard this solution. Therefore, the only valid solution is:

x = 980

So the length of the bridge is 980 feet.

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A hexagonal pyramid has seven vertices.

A hexagonal pyramid contains 12 edges.

A hexagonal pyramid has seven faces.

A hexagonal pyramid is a type of pyramid that exists. A hexagonal pyramid has a hexagonal foundation and isosceles triangles as the faces that join the pyramid together at the top.

A hexagonal pyramid is a 3D pyramid with a hexagonal foundation and sides or faces in the shape of isosceles triangles that form the hexagonal pyramid at the apex or top of the pyramid. A hexagonal pyramid has six sides and six isosceles triangular lateral faces. Heptahedron is another name for a hexagonal pyramid. A hexagonal pyramid has seven faces, twelve edges, and seven vertices. For your convenience, an image of a hexagonal pyramid is provided below.

A hexagonal pyramid has seven vertices in toa

\x linking the triangle edges to the primary vertex and six base edges.

A hexagonal pyramid has seven faces, one for each side of the triangle, and one base.

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Answer: Bret spent $52.92 on the lunch, including tax and tip.

Step-by-step explanation:

Given:

The bill before tax = $42

Sales tax = 6%

Tip = 20% before tax

To find:The total amount of money Bret spent

Solution: Calculate the sales tax:

Sales tax = 0.06 * $42 = $2.52

Calculate the total bill, including tax:

Total bill = $42 + $2.52 = $44.52

Calculate the bill before tax, based on which the tip is calculated:

Bill before tax = $44.52 - $2.52 = $42

Calculate the tip amount:

Tip = 0.2 * $42 = $8.40

Calculate the total amount spent by Bret:

Total spent = $44.52 + $8.40 = $52.92

Therefore, Bret spent $52.92 on the lunch, including tax and tip.

Hence, it will take 2.6 hours for the two trains to be 520 miles apart.

Distance is a numerical or occasionally  qualitative measurement of how far apart objects or points are. In physics or everyday usage, distance may refer to a physical length or an estimation based on other criteria.

In everyday use and in kinematics, the speed of an object is the magnitude of the change of its position over time or the magnitude of the change of its position per unit of time; it is thus a scalar quantity..

The two trains are moving  away from each other,

so we can  add their speeds to get their relative speed:

relative speed = 95 mph + 105 mph = 200 mph

Now ,we determine  the time it takes for the trains to be 520 miles apart,

so we can use the formula:

distance = speed × time

let t be the time  it takes for the trains to be 520 miles apart.

Then we get,

520 = 200 × t

Solving for t, we get:

t = [tex]\frac{520}{200}[/tex]

t = 2.6 hours

Therefore, it will take 2.6 hours for the two trains to be 520 miles apart.

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The range of this data set include the following: D. 6.

In Mathematics and Geometry, a range is the set of all real numbers that connects with the elements of a domain.

Furthermore, the vertical extent of any graph of a function represents all range values and they are always read and written from smaller to larger numerical values, and from the bottom of the graph to the top.

By critically observing the graph (dot plot) shown in the image attached above, we can reasonably and logically deduce the following range:

Range = {18, 19, 20, 21, 22, 24} = 6.

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The value of the triple integral is 1920pi/3.

Here are five other iterated integrals that are equal to the given iterated integral:

[tex]\Integral^2_0 \Integral^y_0 \Integral^1_0 f(x, y, z) dx dy dz[/tex]

[tex]\Integral^2_0 \Integral^z_0 \Integral^1_z f(x, y, z) dx dz dy[/tex]

[tex]\Integral^1_0 \Integral^y_0 \Integral^1_z f(x, y, z) dx dz dy[/tex]

[tex]\Integral^1_0 \Integral^z_0 \Integral^1_y f(x, y, z) dx dy dz[/tex]

[tex]\Integral^z_0 \Integral^1_0 \Integral^y_z f(x, y, z) dx dy dz[/tex]

To evaluate the triple integral of[tex](4 + 5x^2yz^2) dV[/tex]over the cylindrical region [tex]x^2 + y^2[/tex] <= 4, -2 <= z <= 2, we can use geometric interpretation and symmetry.

Note that the integrand [tex](4 + 5x^2yz^2)[/tex] is an even function of x and y, and an odd function of z.

Therefore, the integral over the region where z is positive is equal in magnitude but opposite in sign to the integral over the region where z is negative.

Hence, we can evaluate the integral over the region 0 <= z <= 2, and then double the result.

The region of integration is a cylinder of radius 2 and height 4.

Since the integrand is not dependent on x and y, we can factor out[tex](4 + 5z^2)[/tex]  from the integrand, and evaluate the remaining integral over the unit disc in the x-y plane.

Thus, the triple integral can be written as:

[tex]8 * \Integral^2_0 \Integral^2pi_0 \Integral^2_0 (4 + 5z^2) r^3 sin(\theta) dr d(\theta) dz[/tex]

Integrating with respect to r from 0 to 2 and with respect to [tex]\theta[/tex] from 0 to [tex]2\pi[/tex], we get:

[tex]8 * \Integral^2_0 \Integral^2pi_0 (4 + 5z^2) sin(\theta) d(\theta) dz[/tex]

Integrating with respect to theta from 0 to 2pi, we get:

[tex]16pi * \Integral^2_0 (4 + 5z^2) dz[/tex]

Integrating with respect to z from 0 to 2, we get:

16pi * (32/3 + 80) = 1920pi/3.

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Answer: d

Step-by-step explanation:

Answer:

B: Range of round 1 were higher than the range of Round-2.

Step-by-step explanation:

Please give me Brainliest.

Answer:

x = -8 + sqrt(10) and x = -8 - sqrt(10)

Step-by-step explanation:

The quadratic equation to be solved is:

2(x + 8)² + 9 = 29

First, we need to simplify the left-hand side of the equation by expanding the squared term:

2(x + 8)(x + 8) + 9 = 29

Simplifying further, we get:

2(x² + 16x + 64) + 9 = 29

Distributing the 2, we get:

2x² + 32x + 128 + 9 = 29

Combining like terms, we get:

2x² + 32x + 137 = 29

Subtracting 29 from both sides, we get:

2x² + 32x + 108 = 0

Dividing both sides by 2, we get:

x² + 16x + 54 = 0

We can solve this quadratic equation by factoring or by using the quadratic formula :

The equation presented is a quadratic equation in standard form, ax² + bx + c = 0, where a = 1, b = 16, and c = 54. To solve this equation, we can use the quadratic formula, x = (-b ± sqrt(b² - 4ac)) / 2a. Plugging in the values, we get x = (-16 ± sqrt(16² - 4(1)(54))) / 2(1) = (-16 ± sqrt(16)) / 2 or (-16 ± 2sqrt(10)) / 2. Simplifying, we get x = -8 ± sqrt(10). Therefore, the two solutions to this equation are x = -8 + sqrt(10) and x = -8 - sqrt(10).

From the knowledge of vertical angle theorem, angle TXS is equal to angle RXU which is equal to

Vertical angles are a pair of non-adjacent angles formed by the intersection of two straight lines.

When two lines intersect at a point, they form four angles around that point, and the vertical angles are the pair of opposite angles, which are across from each other and not adjacent.

Vertical angel theorem have it that Vertical angles are congruent, which means that they have the same measure or size. This theorem helps us in providing a correct answer for the problem

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We can rewrite the following logarithms to common logarithms as follows:

1. 2.3768

2. 3.8173

To rewrite the logarithms in the common format we can use the following formula.

loga b = log10 b / log10 a

So, we have:

log5 46 = log10 46 / log10 5

Using a calculator, we find that log10 46 ≈ 1.66276 and log10 5 ≈ 0.69897, so:

log5 46 ≈ 1.66276 / 0.69897 ≈ 2.3768

For the second one, we can approach the problem this way:

loga b = log10 b / log10 a

So, we have:

log3 66 = log10 66 / log10 3

Using a calculator, we find that log10 66 ≈ 1.81954 and log10 3 ≈ 0.47712, so:

log3 66 ≈ 1.81954 / 0.47712 ≈ 3.8173

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we get the coordinates of Q' as (2,3) after rotation of the triangle.

What is rotation of axis?

Rotation of axes is a transformation in which the coordinate axes are rotated by a certain angle with respect to the original axes. This transformation can be used to simplify the equations of curves and to make it easier to solve problems involving them. The rotation is usually done by finding the angle of rotation, which is the angle between the original x-axis and the new x-axis. The formulae for converting coordinates from the old system to the new system can then be applied.

In the given problem, we are given that triangle PQR is located in the xy-plane with coordinates of Q being (2,-3). The task is to find the coordinates of Q' when triangle PQR is rotated 180 degrees clockwise about the origin and then reflected across the y-axis to produce triangle P'Q'R'.

To start, we apply the 180 degree clockwise rotation about the origin transformation rule to the coordinates of Q (2,-3) which gives us (-2,3).

Next, we reflect the point (-2,3) across the y-axis. Reflecting across the y-axis involves changing the sign of the x-coordinate while leaving the y-coordinate unchanged. Applying this rule,

Hence, we get the coordinates of Q' as (2,3) after rotation of the triangle.

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Answer:

(4, 0)

Explanation:

The difference between -5 and -1 is 4 and the difference between-3 and -3 is 0.

The roots (if any) are determined by the values of x that make f(x) = 0. To find them, we solve the quadratic equation associated with the function.

A quadratic equation is an equation of the form:

ax² + bx + c = 0

where a, b, and c are constants. For a quadratic function of the form:

f(x) = ax² + bx + c

the roots are the values of x that satisfy the equation f(x) = 0. To find the roots, we set f(x) equal to zero and solve for x using the quadratic formula:

x = (-b ± √(b² - 4ac))/2a

If the discriminant (b² - 4ac) is negative, then the quadratic equation has no real roots, and the function f(x) does not intersect the x-axis. If the discriminant is zero, then the quadratic equation has one real root, and the function f(x) touches the x-axis at that point. If the discriminant is positive, then the quadratic equation has two real roots, and the function f(x) intersects the x-axis at those points.

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To ensure that the replica will fit on an 8.5-by-11-inch paper, we need to choose a scale that will result in dimensions that are smaller than or equal to 8.5 inches by 11 inches.

Choosing an appropriate scale for a replica depends on the size of the original object and the desired size of the replica. To fit a replica on an 8.5-by-11-inch paper, we need to determine the maximum size that the replica can be while still fitting on the paper.

One common method for determining the appropriate scale is to measure the dimensions of the original object and then divide them by the desired size of the replica. For example, if the original object is 20 inches wide and we want to create a replica that is 8 inches wide, the scale would be 20/8, or 2.5.

In order to fit the replica on an 8.5-by-11-inch paper, we need to make sure that the dimensions of the replica are smaller than or equal to 8.5 inches by 11 inches.

We can use the scale factor to determine the maximum dimensions of the replica. For example, if the scale factor is 2.5 and we want the replica to be 8 inches wide, the maximum height of the replica would be 8/2.5, or 3.2 inches.

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The standard form of the polynomial 2m-3m²+4m⁵+21 is 4m⁵ - 3m² + 2m + 21.

The standard form of a polynomial is when the polynomial is written with the terms in descending order of degree, with each term having a coefficient and an exponent. To convert the given polynomial 2m-3m²+4m⁵+21 to standard form, we need to rearrange the terms in descending order of degree.

The degree of a term is the exponent of the variable in that term. For example, the degree of the term 4m⁵ is 5, and the degree of the term -3m² is 2.

So, we start by arranging the terms in descending order of degree:

4m⁵ - 3m² + 2m + 21

Next, we can simplify the coefficients of each term if possible. In this case, all of the coefficients are already simplified, so we leave them as they are.

In summary, to convert a polynomial to standard form, we arrange the terms in descending order of degree and simplify the coefficients of each term if possible. This makes it easier to compare and manipulate polynomials, and is often required when solving equations or finding roots of polynomials.

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