complete the factoring , if needed solve the polynomial any quality using a sign chart (x+3)(x^2-8x+15)<0

Noah will need a tether of 55 inches to secure it to the ground using Pythagorean theorem.

Let's say the side length of the square rain cover is x inches. Then, the diagonal length of the rain cover (the hypotenuse of the right triangle formed by the rain cover and the ground) is x√2 inches. To secure the rain cover to the ground with a tether, we need a right triangle with legs that are the same length as the sides of the rain cover and a hypotenuse that is 55 inches long.

Using the Pythagorean theorem, we can solve for x:

\(x^{2}\) + \(x^{2}\) = \(55^{2}\)

2\(x^{2}\) = 3025

\(x^{2}\) = 1512.5

x ≈ 38.94

So, if the rain cover is a square with side length of approximately 38.94 inches, Noah will need a tether of 55 inches to secure it to the ground.

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If cholesterol level were changed to being measured in grams instead of milligrams, the correlation between fat content and cholesterol level would not be affected.

This is because correlation is a measure of the strength and direction of the linear relationship between two variables, and converting the units of measurement does not change the underlying relationship between the variables. So, the correlation coefficient of 0.75 would remain the same whether cholesterol level is measured in milligrams or grams.

The correlation between fat content and cholesterol level for the 20 different brands of American cheese slices is 0.75. If you change the measurement of cholesterol level from milligrams to grams (1 gram = 1000 milligrams), it will not affect the correlation. The correlation coefficient will remain 0.75, as it is unit-less and only represents the strength and direction of the relationship between the two variables.

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ΔBCA Is-congruent-to ΔBFA can be proved by using property of congruence and third angle theorem.

Corresponding angles are any two angles that are both on the same side of a transversal that cuts two lines, as well as on the same side of the transversal.

If and only if two angles have equal measurements, they are said to be congruent. If and only if two segments have equal amounts of each, they are congruent. If and only if all of the corresponding angles and sides are congruent, two triangles are said to be congruent.

Because the corresponding angles have the same measure in degrees, we may determine that angle CBA is congruent to angle FBA and that angle CAB is congruent to angle FAB (as evidenced in the given equation). By using the reflexive property of congruence (more precisely, the Third Angle Theorem), we can see that angle BCA and angle BFA are congruent. As a result, since the two triangles share a line segment, we may say that triangle BCA is congruent to triangle BFA since a pair of corresponding angles and the included side are equal (AB).

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ΔBCA Is-congruent-to ΔBFA can be proved by using property of congruence and third angle theorem.

What is corresponding angel?
Corresponding angles are any two angles that are both on the same side of a transversal that cuts two lines, as well as on the same side of the transversal.

What is the property of congruence?
If and only if two angles have equal measurements, they are said to be congruent. If and only if two segments have equal amounts of each, they are congruent. If and only if all of the corresponding angles and sides are congruent, two triangles are said to be congruent.

Because the corresponding angles have the same measure in degrees, we may determine that angle CBA is congruent to angle FBA and that angle CAB is congruent to angle FAB (as evidenced in the given equation). By using the reflexive property of congruence (more precisely, the Third Angle Theorem), we can see that angle BCA and angle BFA are congruent. As a result, since the two triangles share a line segment, we may say that triangle BCA is congruent to triangle BFA since a pair of corresponding angles and the included side are equal (AB).

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Option (d) is correct i.e., y | −5 ≤ y ≤ −1 , for this we have to know the concept of range and coordinates.

In mathematics, a function's range can refer to one of two closely related ideas: The function's codomain a    representation of the action A binary relation f between two sets P and Q is a function if there is exactly one y in Q such that f connects x to y for every x in P .

In geometry, a coordinate     system is a method for determining how to place points or other geometrical     objects on a manifold, such Euclidean space, uniquely using one or more numbers, or coordinates.

The range of a function is the    set of all values that f can produce for all the x-axis in the domain.

If we are given the graph, in order to find     the range, we project the graph into the y-axis.     Informally, we draw the "shadow" of the graph into the y axis as in the FIGURE attached.

Option (d) is   correct i.e., y | −5 ≤ y ≤ −1 .

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the rate of change of the radius at the instant the volume equals 36π cm³ is 7 / (36π) cm/sec.

The volume V of a sphere with radius r is given by the formula V = (4/3)πr³. We are given that the rate of change of the volume is 7 cm³/sec. Differentiating the volume formula with respect to time, we get dV/dt =(4/3)π(3r²)(dr/dt), where dr/dt represents the rate of change of the radius with respect to time.

We are looking for the rate of change of the radius, dr/dt, when the volume equals 36π cm³. Substituting the values into the equation, we have: 7 = (4/3)π(3r²)(dr/dt)

7 = 4πr²(dr/dt) To find dr/dt, we rearrange the equation: (dr/dt) = 7 / (4πr²) Now, we can substitute the volume V = 36π cm³ and solve for the radius r: 36π = (4/3)πr³

36 = (4/3)r³

27 = r³

r = 3  Substituting r = 3 into the equation for dr/dt, we get: (dr/dt) = 7 / (4π(3)²)

(dr/dt) = 7 / (4π(9))

(dr/dt) = 7 / (36π)

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A baseball bat strikes a ball with an average force of 2.0 x 104 Newtons. if the bat stays in contact with the ball for a distance of 5.0 x 10-3 meter , then the kinetic energy will be 2× 10^2 J

kinetic energy of an object is the energy that it possesses due to its motion. It is defined as the work needed to accelerate a body of a given mass from rest to its stated velocity. Having gained this energy during its acceleration, the body maintains this kinetic energy unless its speed changes.

In classical mechanics, the kinetic energy of a non-rotating object of mass m traveling at a speed v is 1/2 mv²

Favg= -1/2 MV2

Favg = -1 2 ( 5.0 x 10-3)^2

Favg = - 1/2 ×25 × 10 ^-6

Favg = 2× 10^2 J

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Answer:

Step-by-step explanation:

We all know that the inner degrees of a pentagon add up to 540°

thus we can use the following equation to solve for x:

33+140+2x+x+x+75=540

173+4x+75=540

248+4x=540

4x=540-248

4x=292

x=292/4

x=73

Thus, the answer is 73 degrees

Answer:

\(x=73\)

Step-by-step explanation:

The sum of all interior angles of a pentagon is 540°.

\(33+140+2x+x+x+75=540\)

Add all like terms.

\(33+140+4x+75=540\)

\(4x+248=540\)

Subtract 248 on both sides.

\(4x=540-248\)

\(4x=292\)

Divide 4 on both sides.

\(x=292/4\)

\(x=73\)

Answer:

\(x=2\sqrt{2}\), \(x=-2\sqrt{2}\), \(x=4i\), \(x=-4i\)

Step-by-step explanation:

\(x^4+11x^2=3x^2+128\)

First, we subtract 128 from both sides:

\(x^4+11x^2-128=3x^2\)

Then, we subtract \(3x^2\) from both sides:

\(x^4+8x^2-128=0\)

Rewrite the equation:

\(u^2+8u-128=0\)

Insert and solve:

\(u^2+8u-128=0\\u=8,u=-16\\x^2=8:x=2\sqrt{2},x= -2\sqrt{2} \\x^2=-16:x=4i,x=-4i\)

Please give Brainliest

Answer:

A is the answer to the question

Step-by-step explanation:

4*6=24

5*8=40

The number of houses in Adenta can be determined by finding the least common multiple (LCM) of the number of copies of graphics and the number of copies of time. In this case, the LCM of 26 and 24 is 312, so there are 312 houses in Adenta.

To find the number of houses in Adenta, we need to find the LCM of the number of copies of graphics (26) and the number of copies of time (24).

Step 1: Find the prime factorization of each number:

26 = 2 * 13

24 = 2^3 * 3

Step 2: Identify the common prime factors and their highest powers:

2^3 * 3 * 13

Step 3: Multiply the common prime factors with their highest powers:

2^3 * 3 * 13 = 8 * 3 * 13 = 312

Therefore, the LCM of 26 and 24 is 312, which means there are 312 houses in Adenta. Each house received at least a copy of both newspapers, with a total of 26 copies of graphics and 24 copies of time being delivered.

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7^(3/5) * 7^(1/5) is equivalent to (7^3)^(1/5) * (7^1)^(1/5), which is equivalent to 343^(1/5) * 7^(1/5) = 343^(1/5) * (7^(1/5))^1 = 343^(1/5) * 7.

When you see an expression like 7^(3/5) * 7^(1/5), it is helpful to think about the properties of exponents. One property is that when you have the same base raised to different exponents, you can multiply the exponents. So, for example, 7^3 * 7^1 = 7^(3+1) = 7^4.

Another property is that when you have a base raised to a power, and then that result is raised to another power, you can multiply the exponents. So, for example, (7^3)^2 = 7^(3*2) = 7^6.

Using these properties, we can simplify the original expression as follows:
7^(3/5) * 7^(1/5) = (7^3)^(1/5) * (7^1)^(1/5) = 343^(1/5) * 7^(1/5) = 343^(1/5) * (7^(1/5))^1 = 343^(1/5) * 7

So, 7^(3/5) * 7^(1/5) is equivalent to 343^(1/5) * 7

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Answer:

y = x + 2

Step-by-step explanation:

slope = 1

y = mx + b

4 = 1(2) + b

2 = b

y = x + 2

Answer:

x = 10

Step-by-step explanation:

When any 2 lines are parallel to each other and a transversal intersects both the lines , then THE INTERIOR ALTERNATIVE ANGLES ARE ALWAYS EQUAL.

According to the question , m || n & t is transversal. So, the interior alternative angles will be equal.

\( = > 8x + 10 = 6x + 30\)

\( = > 8x - 6x = 30 - 10\)

\( = > 2x = 20\)

\( = > x = \frac{20}{2} = 10\)

Answer:

The value of X is 10.

Step-by-step explanation:

solution

(8x+10)=(6x+30) (alternate angle)

8x-6x=30-10

2x=20

X=20/2

X=10

Answer:

What is the payrate?

Step-by-step explanation:

Answer:

Rosa spend altogether Is 8.64

Step-by-step explanation:

Answer:

8.64

Step-by-step explanation:

u add 6.75 + 1.89.

=8.64

Answer:

The formula we use to calculate simple interest is I=Prt I = P r t . To use the simple interest formula we substitute in the values for variables that are given, and then solve for the unknown variable. It may be helpful to organize the information by listing all four variables and filling in the given information.

Fig. 2.6 alone does not provide sufficient information to calculate the percent elongation of materials. Percent elongation is a measure of the increase in length of a material after it has been subjected to a tensile load, and is calculated by dividing the increase in length by the original length and multiplying by 100.

Fig. 2.6 shows stress-strain curves for different materials, which provide information about the relationship between stress and strain for those materials. While the curve shape can provide some insight into the behavior of the material under load, it does not provide information about the original length or the change in length of the material, which are necessary to calculate percent elongation.

In order to calculate percent elongation, additional information about the material's original length and the change in length after a tensile load is required. This information can be obtained through laboratory testing or from material specifications provided by the manufacturer.

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Answer:

n = 3.02

Step-by-step explanation:

12.65 - n = 9.63

- n = 9.63 - 12.65

- n = - 3.02

-n/-1 = -3.02/-1

n = 3.02

Answer:

3.02

Step-by-step explanation:

Answer:

Step-by-step explanation:

I hope you want the area.

Area = L * W

L = 24x^3

W = 5x^2

Area = 24x^3 * 5x^2

Area = 120 * x^(3 + 2)

Area = 120 * x^5

Note

When you multiply numbers or letters that have powers, if the base for both of them is the same, the powers are added.

The above answer is an example x^2 * x ^3 are letters (x) that are raised to the 2nd power and the 3rd power. You add the powers.

Numbers can do the same thing

64 * 8 = 256

The statistical control chart is discussed below.

Given is the statistical control chart.

Therefore, the statistical control chart is discussed above.

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Answer:

3 is the gradient.

Step-by-step explanation:

take coordinates through which the line is passing through like

( 0 , -2 )  and ( 6 , 16 )

to find slope/ gradient = ( y2 - y1 )/ ( x2 -x1 )

                                     = ( 16 - -2 ) / ( 6 - 0 )

                                     =  3

to confirm, let me find the equation as well:

y - 16 = 3 ( x - 6 )

y - 16  = 3x - 18

y = 3x - 2

below for visual check. its true and matches. { confirmed }

Take two points

Slope

Answer:

\(y=\left \{ {{x < N:x+N}}\right\}\)

\(y=\left \{ {{x > = N:Nx-N}}\right\}\)

Step-by-step explanation:

N stands for a number. I can't read the numbers in the photo.

In brackets start with the if statement and then use a ":" and then write the function.

I tried to make out the numbers. DOUBLE-CHECK! Here is a photo.

Step-by-step explanation:

the process is show in the above picture.

The following are the respective measures of angles and lengths of the rectangle ABCD:

m∠1 = 49°, m∠2 = 41°, m∠3 = 41°, m∠ADC = 90°, AB = 6.9, BD = 10, and CE = 5.

Considering the triangle AEB, angles A and B are base angles of a the isosceles triangle AEB so;

2(m∠ABE) + 98 = 180° {sum of interior angles of a triangle}

m∠ABE = (180 - 98)/2

m∠ABE = 41°

m∠1 = 90° - 41° {complementary angles of a rectangle}

m∠1 = 49°

angles m∠2 and m∠BAC are alternate angles and are equal so;

m∠2 = 41°

m∠ADC is one of the four interior angles of a rectangle so m∠ADC = 90°

Considering the right triangle ∆ABD and the tangent of angle B = 41°, we can solve for the length of AB as follows:

tan 41° = 6/AB {opposite/adjacent}

AB = 6/tan41° {cross multiplication}

AB = 6.9022.

m∠3 and m∠ABD are alternate angles so;

m∠3 = 41°

lines AC and BD are diagonals of the rectangle and they bisect each other, since EB = 5 then;

BD = 2 × 5 = 10

CE = 5

Therefore, the following are the respective measures of angles and lengths of the rectangle ABCD:

m∠1 = 49°, m∠2 = 41°, m∠3 = 41°, m∠ADC = 90°, AB = 6.9, BD = 10, and CE = 5.

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Answer:

u would have to move 52 lawns

Step-by-step explanation:

844.00 - 70 = 774

774 / 15 = 51.6

The solution to the given differential equation is:

y(x) = a_0 (1 - x^2/4 + x^4/36 - x^6/576 + ...) where a_0 is an arbitrary constant.

To solve the given differential equation (1 + x^3)y'' + 4xy' + y = 0, we can use the method of power series. We will assume that the solution y(x) can be expressed as a power series:

y(x) = ∑[n=0 to ∞] a_nx^n

where a_n are the coefficients of the series.

First, let's find the first and second derivatives of y(x):

y' = ∑[n=0 to ∞] na_nx^(n-1)

y'' = ∑[n=0 to ∞] n(n-1)a_nx^(n-2)

Substituting these derivatives into the given differential equation, we get:

(1 + x^3)∑[n=0 to ∞] n(n-1)a_nx^(n-2) + 4x∑[n=0 to ∞] na_nx^(n-1) + ∑[n=0 to ∞] a_nx^n = 0

Now, let's re-index the sums to match the powers of x:

(1 + x^3)∑[n=2 to ∞] (n(n-1)a_n)x^(n-2) + 4x∑[n=1 to ∞] (na_n)x^(n-1) + ∑[n=0 to ∞] a_nx^n = 0

Let's consider the coefficients of each power of x separately. For the coefficient of x^0, we have:

a_0 + 4a_1 = 0   -->   a_1 = -a_0 / 4

For the coefficient of x, we have:

2(2a_2) + 4a_1 + a_0 = 0   -->   a_2 = -a_0 / 4

For the coefficient of x^2, we have:

3(2a_3) + 4(2a_2) + 2a_1 + a_0 = 0   -->   a_3 = -a_0 / 12

We observe that the coefficients of the odd powers of x are always zero. This suggests that the solution is an even function.

Therefore, we can rewrite the solution as:

y(x) = a_0 (1 - x^2/4 + x^4/36 - x^6/576 + ...)

The solution is a linear combination of even powers of x, with coefficients determined by a_0.

In summary, the solution to the given differential equation is:

y(x) = a_0 (1 - x^2/4 + x^4/36 - x^6/576 + ...)

where a_0 is an arbitrary constant.

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Answer:

4) x = 110° & y = 70°

Step-by-step explanation:

The correct option is a) (x + y) (y + z). Given the output function F in sum-of-minterms form as F = (0, 1, 2, 3, 7), we need to determine the corresponding Boolean expression for the output function.

A 3x8 decoder has three input variables (x, y, z) and eight output variables, where each output variable corresponds to a unique combination of input variables. The output variables are typically represented as minterms.

Let's analyze the given output function F = (0, 1, 2, 3, 7). The minterms represent the outputs that are equal to 1. By observing the minterms, we can deduce the corresponding Boolean expression.

From the minterms, we can see that the output is equal to 1 when x = 0, y = 0, z = 0 or x = 0, y = 0, z = 1 or x = 0, y = 1, z = 0 or x = 0, y = 1, z = 1 or x = 1, y = 1, z = 1.

By simplifying the above conditions, we get (x + y) (y + z), which is the Boolean expression corresponding to the given output function F.

In summary, the correct option is a) (x + y) (y + z).

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