Mike needs to position a 16-foot ladder so it reaches a window that is 12 feet above the ground. How far from the building should he place the base of the ladder?

Answer: 160

Step-by-step explanation:

12+37+78

Answer: 3.5

Step-by-step explanation:  33.20-29.7

Answer:

Step-by-step explanation:

Answer:

8 boys left and10 girls left

Step-by-step explanation:

Answer:

two boys out of 10 boys = 2/10

two boys out of the whole classroom of girls and boys = 2/20

hope this helps!

god bless your heart!

Have a wonderful day! <3333

Step-by-step explanation:

The translation from preimage P(9. 1.5) to image P'(12, 1)) in ordered pair is (3, -0.5)

Translation refers to a type of transformation that involve a straight line movement.

The type of movements related to translation includes

The up and down movements are on the vertical direction controlled by the y coordinate. In the question, the preimage moved form 1.5 to 1

hence we say

The left right movement is controlled by the x coordinate. The preimage moved from 9 to 12 ⇒ 9 + 3. Hence we say that

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Answer:

C

Step-by-step explanation:

The associated homogeneous equation is v (t) + ½' (t) -6y(t) = 0. To find a solution to this equation, we can assume that the solution is in the form of y(t) = e^(rt), where r is a constant. Plugging this into the equation, we get the characteristic equation r^2 - 6 = 0. Solving for r, we get r = ±√6.

Thus, the general solution to the associated homogeneous equation is y(t) = c1e^(√6t) + c2e^(-√6t), where c1 and c2 are constants.

To find a solution to the original differential equation, we can use the method of undetermined coefficients. Assuming that the particular solution is in the form of y(t) = At + B, we can plug this into the equation and solve for A and B.

Taking the derivative of y(t), we get y'(t) = A. Plugging this and y(t) into the differential equation, we get:

A + ½ - 6(At + B) = g(t)

Simplifying, we get:

A(1-6t) + ½ - 6B = g(t)

To solve for A and B, we need to have information about the function g(t). Once we have that, we can solve for A and B and find the particular solution to the differential equation.

In summary, the solution to the associated homogeneous equation is y(t) = c1e^(√6t) + c2e^(-√6t), and the particular solution to the differential equation can be found using the method of undetermined coefficients with information about the function g(t).

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Answer:

(-8,-71)

Step-by-step explanation:

I assume by turning point it means the vertex:

\(y=x^2+16x-7\\y+71=x^2+16x-7+71\\y+71=x^2+16x+64\\y+71=(x+8)^2\\y=(x+8)^2-71\)

Now that we converted our equation to vertex form \(y=(x+h)^2+k\), we can see our vertex, or turning point, is (h,k)=(-8,-71)

A scaled function is a dilated function

The function g(x) is: \(\mathbf{g(x) = \frac 12x^2}\)

Function f is given as:

\(\mathbf{f(x) = x^2}\)

Function g is a scaled version of f(x).

So, we have:

\(\mathbf{g(x) = kx^2}\) --- where k is the scale

The graph of g(x) passes through (4,8).

So, we have:

\(\mathbf{8 = k \times 4^2}\)

\(\mathbf{8 = k \times 16}\)

Divide both sides by 16

\(\mathbf{\frac 12 = k }\)

So, we have:

\(\mathbf{k = \frac 12 }\)

Substitute \(\mathbf{k = \frac 12 }\) in \(\mathbf{g(x) = kx^2}\)

\(\mathbf{g(x) = \frac 12x^2}\)

Hence, the function g(x) is: \(\mathbf{g(x) = \frac 12x^2}\)

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Answer:

Boxes of pizza: 16

Sodas: 6

Step-by-step explanation:

Use system to solve:

x : boxes of pizza

y: soda

x + y = 20

8x + 1.5y = 137

She bought 16 boxes of pizza and 6 cans of sodas.

Given is that Diana bought a total of 22 items including boxes of pizza and sodas for an upcoming event. Each box of pizza cost $8.00 and each soda cost $1.50. Diana spent a total of $137.

Assume that she bought [x] boxes of pizza and [y] cans of sodas. So, we can write -

x + y = 22

8x + 1.5y = 137

Let -

x = 22 - y

So, we can write -

8(22 - y) + 1.5y = 137

176 - 8y + 1.5y = 137

176 - 137 = 8y - 1.5y

39 = 6.5y

y = (39/6.5)

y = 6

and

x = 22 - 6

x = 16

Therefore, she bought 16 boxes of pizza and 6 cans of sodas.

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The general solution to the given differential equation is

y = ± √(1 / (2ln|t| + 4/t - C2))

To solve the given differential equation, we can use the method of separable variables. Let's go through the steps:

Rearrange the equation to separate the variables:

t^2y' + 2ty - y^3 = 0

Divide both sides of the equation by t^2:

y' + (2y/t) - (y^3/t^2) = 0

Now, we can rewrite the equation as:

y' + (2y/t) = (y^3/t^2)

Separate the variables by moving the y-related terms to one side and the t-related terms to the other side:

(1/y^3)dy = (1/t - 2/t^2)dt

Integrate both sides of the equation:

∫(1/y^3)dy = ∫(1/t - 2/t^2)dt

To integrate the left side, let's use a substitution. Let u = y^(-2), then du = -2y^(-3)dy.

-1/2 ∫du = ∫(1/t - 2/t^2)dt

-1/2 u = ln|t| + 2/t + C1

-1/2 (y^(-2)) = ln|t| + 2/t + C1

Multiply through by -2:

y^(-2) = -2ln|t| - 4/t + C2

Now, take the reciprocal of both sides to solve for y:

y^2 = (-1) / (-2ln|t| - 4/t + C2)

y^2 = 1 / (2ln|t| + 4/t - C2)

Finally, taking the square root:

y = ± √(1 / (2ln|t| + 4/t - C2))

Therefore, the general solution to the given differential equation is:

y = ± √(1 / (2ln|t| + 4/t - C2))

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The z-limits of integration to find the volume of the region D, bounded below by the cone z = √(x² + y²) and above by the sphere x² + y² + z² = 25, using rectangular coordinates and taking the order of integration as dz dy dx, are, z = 0 to z = √(25 - x² - y²)

To determine the z-limits of integration, we consider the intersection points of the cone and the sphere. Setting the equations of the cone and sphere equal to each other, we have:

√(x² + y²) = √(25 - x² - y²)

Simplifying, we get:

x² + y² = 25 - x² - y²
2x² + 2y² = 25
x² + y² = 25/2

This represents a circle in the xy-plane centered at the origin with a radius of √(25/2). The z-limits of integration correspond to the height of the cone above this circle, which is given by z = √(25 - x² - y²).

Thus, the z-limits of integration to find the volume of region D, using the order of integration as dz dy dx, are from z = 0 to z = √(25 - x² - y²).

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Semantics is the branch of linguistics that explores how meaning is conveyed through language. In the context of big data, it refers to the changes in the interpretation of data and how it can be used to yield meaningful insights.

Semantics is a branch of linguistics that deals with the study of meaning in language. In the context of big data, semantics relates to how data is interpreted and how it can be used to gain meaningful insights. Semantic analysis looks at the context of data and how it changes in meaning over time. This analysis helps to understand how the data can be used to make decisions, solve problems, and improve processes. Semantic analysis also helps to identify trends, relationships, and patterns in data that can be used to formulate decisions, plans, and strategies. By understanding the changes in meaning, organizations can use the data to make more informed and accurate decisions.

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Answer:

  4 cm

Step-by-step explanation:

You want the length of the smaller of two similar pieces of cardboard when the larger has an area of 150 cm² and a length of 10 cm, while the smaller has an area of 24 cm².

The scale factor for lengths is the square root of the scale factor for areas. It will be ...

  √(24/150) = 0.4 . . . . . . = smaller / larger

The smaller cardboard has a length of ...

  0.4 × 10 cm = 4 cm

__

Additional comment

Sometimes folks like to write this as a proportion:

  \(\dfrac{\text{smaller length}}{\text{larger length}}=\sqrt{\dfrac{\text{smaller area}}{\text{larger area}}}\)

Solving this for "smaller length" gives the expressions we used above:

  smaller length = (larger length) × √(smaller area/larger area)

Answer:

.15¢

Step-by-step explanation:

1.20$ total divided by 8 and its .15¢

The probability of drawing a red chip and then drawing a blue chip from the bin without replacement is 7/100.

To find the probability of drawing a red chip from the bin without replacement, and then drawing a blue chip, we need to calculate the probabilities of each event separately and then multiply them together.

Let's start by calculating the probability of drawing a red chip.

There are a total of 7 + 9 + 3 + 6 = 25 chips in the bin.

The probability of drawing a red chip on the first draw is 7/25 since there are seven red chips and 25 total chips.

After the first draw, there are now 24 chips left in the bin (since one red chip has been removed). Out of these, there are still 6 blue chips remaining.

The probability of drawing a blue chip on the second draw, without replacing the red chip, is 6/24.

To find the overall probability, we multiply the probability of the first event (drawing a red chip) by the probability of the second event (drawing a blue chip):

P(red, then blue) = (7/25) * (6/24)

= 42/600

= 7/100

Therefore, the probability of drawing a red chip and then drawing a blue chip from the bin without replacement is 7/100.

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By factor theorem (v+5) is not a factor of the given polynomial f(v).

What does factor theorem mean?

When thoroughly factoring the polynomials, mathematicians apply the factor theorem. The polynomial's zeros and factors are connected by this theorem.

                   The factor theorem states that if a is any real number and f(x) is a polynomial of degree n 1 then (x-a) is a factor of f(x) if f(a)=0.

The factor theorem states that

f(x) has a factor (x-k) if and only if f(k) = 0

We are given the following information.

F(v) = v 4 + 16v 3 + 8v 2 - 725

        We have to check whether (v+5) is a factor of given polynomial.

( v + 5 ) = ( v - ( - 5 )

 f( -5 ) = \(( -5 )^{4} + 16( -5)^{3} + 8( -5)^{2} - 725\)

          = - 1900

 f(-5) ≠ 0

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Answer:

Step-by-step explanation:

4x − 3= −12x + 13​

4x + 12x = 13 + 3

16x = 16

x = 1

1)

The slope of the line passing through these points is 2.

2)

The slope of the line passing through these points is -1/4.

3)

The slope of the line passing through these points is -1/7.

4)

The slope of the line passing through these points is 1/2.

5)

The slope of the line passing through these points is -7.

6)

The slope of the line passing through these points is 6.

7)

The slope of y = -4x + 6 is -4 and the y-intercept is 6.

8)

The slope is 0 and the y-intercept is -1.

9)

The slope is -4 and the y-intercept is -1.

10)

The slope of y = 6x - 4 is 6 and the y-intercept is -4.

11)

The slope is -1/4 and the y-intercept is 2.

12)

The slope is 1/6 and the y-intercept is 5/6.

The equation of a line is given by:

y = mx + c

where m is the slope of the line and c is the y-intercept.

Example:

The slope of the line y = 2x + 3 is 2.

The slope of a line that passes through (1, 2) and (2, 3) is 1.

We have,

Slope = (d - b) / (c - a)

Where (a, b) and (c, d) are the two points.

Now,

The slope between (-10, -12) and (-8, -8) is 2.

The slope between (-8, -8) and (-6, -4) is 2.

The slope between (-6, -4) and (-4, 0) is 2.

Therefore,

The slope of the line passing through these points is 2.

The slope between (-4, 2) and (0, 1) is -1/4.

The slope between (0, 1) and (4, 0) is -1/4.

The slope between (4, 0) and (8, -1) is -1/4.

Therefore,

The slope of the line passing through these points is -1/4.

The slope between (-7, -7) and (0, -8) is -1/7.

The slope between (0, -8) and (7, -9) is -1/7.

The slope between (7, -9) and (14, -10) is -1/7.

Therefore,

The slope of the line passing through these points is -1/7.

The slope between (-2, 2) and (0, 3) is 1/2.

The slope between (0, 3) and (2, 4) is 1/2.

The slope between (2, 4) and (4, 5) is 1/2.

Therefore,

The slope of the line passing through these points is 1/2.

The slope between (2, -11) and (4, -25) is -7.

The slope between (4, -25) and (6, -39) is -7.

The slope between (6, -39) and (8, -53) is -7.

Therefore,

The slope of the line passing through these points is -7.

The slope between (-11, -38) and (-5, -14) is 6.

The slope between (-5, -14) and (1, 10) is 8.

The slope between (1, 10) and (7, 34) is 6.

Therefore,

The slope of the line passing through these points is 6.

Now,

The equation in slope intercept form is y = mx + c

where m is the slope of the line and c is the y-intercept.

So,

The slope of y = -4x + 6 is -4 and the y-intercept is 6.

The equation y = -1 represents a horizontal line, so the slope is 0 and the y-intercept is -1.

To find the slope-intercept form, we can rewrite 4r + y = -1 as y = -4r - 1.

Therefore,

The slope is -4 and the y-intercept is -1.

The slope of y = 6x - 4 is 6 and the y-intercept is -4.

To find the slope-intercept form, we can rewrite -x - 4y + 8 = 0 as -4y = x - 8, then divide both sides by -4 to get y = (-1/4)x + 2.

Therefore,

The slope is -1/4 and the y-intercept is 2.

To find the slope-intercept form, we can rewrite 2r - 12y + 10 = 0 as 12y = 2r + 10, then divide both sides by 12 to get y = (1/6)r + 5/6.

Therefore,

The slope is 1/6 and the y-intercept is 5/6.

Thus,

The slope and the y-intercept are given above.

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The rank of matrix A can be determined based on the given information in the question is as follows.

The rank of a matrix refers to the maximum number of linearly independent columns (or rows) in the matrix. From the given information:

a. Since A has linearly independent columns, the rank is equal to n, where n is the number of columns.

b. If Null(A)={0}, it means that the only solution to the homogeneous equation Ax=0 is the trivial solution (where x=0). This implies that the columns of A are linearly independent. Since A is a 6-by-4 matrix, the rank is equal to the number of columns, which is 4.

c. The dimension of the null space (denoted as dim(Null(A))) is equal to the number of linearly independent solutions to the homogeneous equation Ax=0. In this case, dim(Null(A))=3, which means that there are 3 linearly independent solutions. Since A is a 5-by-6 matrix, the rank can be found by subtracting the dimension of the null space from the number of columns: rank(A) = 6 - dim(Null(A)) = 6 - 3 = 3.

d. The determinant of a square matrix measures its invertibility. If det(A) is non-zero, it means that A is invertible, and an invertible matrix has full rank. Therefore, the rank of A is equal to the number of columns, which is 3.

e. The dimension of the row space (denoted as dim(Row(A))) represents the number of linearly independent rows in A. Since dim(Row(A))=3, it means that there are 3 linearly independent rows. Thus, the rank of A is 3.

f. An invertible matrix is non-singular and has full rank. Therefore, if A is a 4-by-4 invertible matrix, its rank is equal to the number of columns, which is 4.

g. If the system Ax=b has either a unique solution or no solution, it means that the column space of A has dimension 3. Hence, the rank of A is 3.

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Answer:

x=2

Step-by-step explanation:

3x+4=10

subtract four on both sides, you will get 3x=6, divide by three on both sides, x=2

To show that the total charge contained in the charge distribution is Q, we integrate the charge density over the entire volume. The charge density is given by:

ρ(r) = ρ₀(1 - r/R) for r ≤ R,

ρ(r) = 0 for r > R,

where ρ₀ = 3Q/πR³.

To find the total charge, we integrate ρ(r) over the volume:

Q = ∫ρ(r) dV,

where dV represents the volume element.

Since the charge density is spherically symmetric, we can express dV as dV = 4πr² dr, where r is the radial distance.

The integral becomes:

Q = ∫₀ᴿ ρ₀(1 - r/R) * 4πr² dr.

Evaluating this integral gives:

Q = ρ₀ * 4π * [r³/3 - r⁴/(4R)] from 0 to R.

Simplifying further, we get:

Q = ρ₀ * 4π * [(R³/3) - (R⁴/4R)].

Simplifying the expression inside the parentheses:

Q = ρ₀ * 4π * [(4R³/12) - (R³/4)].

Simplifying once more:

Q = ρ₀ * π * (R³ - R³/3),

Q = ρ₀ * π * (2R³/3),

Q = (3Q/πR³) * π * (2R³/3),

Q = 2Q.

Therefore, the total charge contained in the charge distribution is Q.

To show that the electric field in the region r > R is identical to that created by a point charge Q at r = 0, we can use Gauss's law. Since the charge distribution is spherically symmetric, the electric field outside the distribution can be obtained by considering a Gaussian surface of radius r > R.

By Gauss's law, the electric field through a closed surface is given by:

∮E · dA = (1/ε₀) * Qenc,

where ε₀ is the permittivity of free space, Qenc is the enclosed charge, and the integral is taken over the closed surface.

Since the charge distribution is spherically symmetric, the enclosed charge within the Gaussian surface of radius r is Qenc = Q.

For the Gaussian surface outside the distribution, the electric field is radially directed, and its magnitude is constant on the surface. Hence, E · dA = E * 4πr².

Plugging these values into Gauss's law:

E * 4πr² = (1/ε₀) * Q,

Simplifying:

E = Q / (4πε₀r²).

This is the same expression as the electric field created by a point charge Q at the origin (r = 0).

To derive an expression for the electric field in the region r ≤ R, we can again use Gauss's law. This time we consider a Gaussian surface inside the charge distribution, such that the entire charge Q is enclosed.

The enclosed charge within the Gaussian surface of radius r ≤ R is Qenc = Q.

By Gauss's law, we have:

∮E · dA = (1/ε₀) * Qenc.

Since the charge distribution is spherically symmetric, the electric field is radially directed, and its magnitude is constant on the Gaussian surface. Hence, E · dA = E * 4πr².

Plugging these values into Gauss's law:

E * 4πr² = (1/ε₀) * Q.

Simplifying:

E = Q / (4πε₀r²).

This expression represents the electric field inside the charge distribution for r ≤ R.

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Measurement is closest to the number of kilometers between these

two lighthouses is 219.2 kilometers.

Assume the distance between two lighthouses is x kilometers in 137 miles.

It knows there are approximately 8 kilometer in 5 miles.

Since the number of kilometers per mile is same

So    x:137=8:5

x/137=8/5

5x=1096

5x/5=1096/5

x=219.2

1 kilometer is equal to 0.621371 miles (often shortened to . 62). 1 mile is equal to 1.609344 kilometers. Thus, to convert kilometers to miles, simply multiply the number of kilometers by 0.62137.

The number of kilometers between these two lighthouses is 219.2.

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Hi!

55<35+10x

Move 35 to the left, using the opposite operation:

55-35<10x

20<10x

Divide both sides by 10:

2<x

Since 2 is greater than x, x is less than 2:

x<2 (Answer)

Hope it helps!

Enjoy your day!

~Misty~

The Vickers hardness (HV) test calculates indentation diagonal length (d) when a load is applied to a material.

To determine d when a 0.700 kg load produces a Vickers HV of 650, use the formula: HV = 1.8544 * (F/d^2), where F is the force in Newtons (N) and d is in mm.
First, convert the load to Newtons: F = 0.700 kg * 9.81 m/s^2 ≈ 6.867 N. Next, rearrange the formula for d: d = √(1.8544 * F/HV). Substituting values: d = √(1.8544 * 6.867 N / 650) ≈ 0.044 mm.
So, the indentation diagonal length (d) is approximately 0.044 mm when a 0.700 kg load produces a Vickers HV of 650.

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