What is the equation of the line that is parallel to the line y = -1/3x+4 and passes through the point (6,5)

The average rate of change of the function h(x) = x2 + 6x + 5 over the function -4 < x < 1 is 1

The given function is:

h(x)  = x² + 6x + 5

The average rate of a function h(x) over the interval a < x < b is given as:

\(\frac{dh}{dx}= \frac{h(b)-h(a)}{b-a}\)

For the rate of change of h(x)  = x² + 6x + 5 in the interval -4 < x < -1.

a  =  -4,  b =  -1

\(h(-1) = (-1)^2 + 6(-1)+5\\h(-1) = 1 -6+5\\h(-1) = 0\)

\(h(-4) = (-4)^2+6(-4)+5\\h(-4) = 16-24+5\\h(-4) = -3\)

\(\frac{dh}{dx}= \frac{h(-1)-h(-4)}{-1-(-4)} \\\frac{dh}{dx}= \frac{0-(-3)}{3} \\\frac{dh}{dx}= \frac{3}{3} \\\frac{dh}{dx}=1\)

The average rate of change of the function h(x) = x2 + 6x + 5 over the function -4 < x < 1 is 1

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Rectangle ABCD has sides AB equal in length to AD, and sides BC equal in length to CD. The diagonals of the rectangle form two congruent right isosceles triangles, BCD and ABD, with right angles at points B and D, respectively.

In rectangle ABCD with diagonal BD connecting points B and D, we are given that triangle BCD is a right isosceles triangle. This information allows us to make certain conclusions about the properties of rectangle ABCD.
Since triangle BCD is a right isosceles triangle, angle BCD is a right angle (90 degrees) by definition. This means that angle B in the rectangle is also a right angle, which confirms that ABCD is a rectangle as all four angles are 90 degrees. Additionally, in a right isosceles triangle, the two legs (BC and CD) are equal in length. This implies that the length of side BC is equal to the length of side CD in the rectangle.
The diagonal BD of rectangle ABCD also forms another right isosceles triangle, ABD. By symmetry, triangle ABD shares similar properties with triangle BCD. This means that the two legs (AB and AD) are equal in length, so the length of side AB is equal to the length of side AD.

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Answer:

Is there a graph involved because i don't know the lengths

Step-by-step explanation:

Answer:

false

Step-by-step explanation:

3(0) - 2(-5) = 10

the < says it cannot be equal

To provide a general real-valued solution to a linear system of differential equations, specific equations need to be provided. Without the specific equations, it is not possible to determine the exact solution.

In general, a linear system of differential equations can be written in matrix form as follows:

dY/dt = AY,

where Y is a vector of functions, t is the independent variable, and A is a constant matrix.

To solve this system, one can use methods such as matrix diagonalization, eigenvalues, and eigenvectors, or the method of variation of parameters. These methods allow you to find the general solution of the system, which represents a family of solutions that satisfy the given equations.

It is important to note that the specific form of matrix A and the initial or boundary conditions if provided, will determine the exact solution to the system of differential equations.

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Answer:

Step-by-step explanation:

The explicit rule for determining the nth term of a geometric sequence is expressed as Tₙ = arⁿ⁻¹ where;

a is the first term of the geometric sequence

r is the common ratio

n is the number of terms

If a geometric sequence has a common ratio of 2 and the 12th term is −12,288, then;

T₁₂ = ar¹²⁻¹

T₁₂ = ar¹¹

Given T₁₂ = -12,288 and r = 2, we can calculate the first term a

-12,288 = a2¹¹

a = -12,288/2¹¹

a =  -12,288/2048

a = -6

Since the explicit rule for determining the nth term of a geometric sequence is expressed as Tₙ = arⁿ⁻¹, then for the sequence given, the explicit rule will be;

Tₙ = -6(2)ⁿ⁻¹

Tₙ = -6 * 2ⁿ * 2⁻¹

Tₙ = -6 * 2ⁿ * 1/2

Tₙ = -3(2)ⁿ

Hence the explicit rule that describes this sequence is Tₙ = -3(2)ⁿ

Answer:

0.40 is the correct answer

Answer:

0.35

Step-by-step explanation:

Labeling systems exist to roughly categorize r values where correlation coefficients (in absolute value) which are ≤ 0.35 are generally considered to represent low or weak correlations, 0.36 to 0.67 modest or moderate correlations, and 0.68 to 1.0 strong or high correlations with r coefficients > 0.90 very high.

Answer:

2 and two fifths

Step-by-step explanation:

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Answer:

2 and 2/5

Step-by-step explanation:

The x-coordinates of the points of intersection of the given function graphs are;

1) x = 0 and x = 2

2) x = -1

3) x = 0

The point of intersection of a graph is defined as the point or coordinates where two lines or curves meet each other.

1) In the first graph, we are given the functions as;

f(x) = -³/₄x² + 3x + 1

g(x) = 2ˣ

Thus;

From the graph, f(x) = g(x) is at (2,4 and (0, 1)

2) In the first graph, we are given the functions as;

f(x) = x² + 4x + 2

g(x) = (¹/₂)ˣ + 1

Thus;

From the graph, f(x) = g(x) is at (-1. 3)

C) In the third graph, we are given the functions as;

f(x) = -⁷/₃x - 3

g(x) = 2ˣ - 4

Thus;

From the graph, f(x) = g(x) is at (0, -3)

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To find the y-coordinate of point P on the unit circle, given that its x-coordinate is 5/13, we can utilize the Pythagorean identity for points on the unit circle.

The Pythagorean identity states that for any point (x, y) on the unit circle, the following equation holds true:

x^2 + y^2 = 1

Since we are given the x-coordinate as 5/13, we can substitute this value into the equation and solve for y:

(5/13)^2 + y^2 = 1

25/169 + y^2 = 1

To isolate y^2, we subtract 25/169 from both sides:

y^2 = 1 - 25/169

y^2 = 169/169 - 25/169

y^2 = 144/169

Taking the square root of both sides, we find:

y = ±sqrt(144/169)

Since we are dealing with points on the unit circle, the y-coordinate represents the sine value. Therefore, the y-coordinate of point P is:

y = ±12/13

So, the y-coordinate of point P can be either 12/13 or -12/13.

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The real values of k for which there is precisely one real solution to the equation are as follows:

k = (20 + 10√3) / 2 and k = (20 - 10√3) / 2

these values are approximately equal to 15.85 and 4.15, respectively.

A quadratic equation requires both a real root and a complex root in order to have exactly one real solution. This is only possible if the equation's discriminant is equal to zero, which indicates that it is tangent to the parabola.

The discriminant of the equation {eq}(k - 5)x^{2} - kx + 5 = 0 {/eq} is given by:

b^2 - 4ac = k^2 - 20k + 25

In order for the discriminant to equal 0, we need:

k^2 - 20k + 25 = 0

This is a quadratic equation, and the quadratic formula can be used to find the value of k:

k = (20 ± √(20^2 - 4 * 25)) / 2

k = (20 ± √(400 - 100)) / 2

k = (20 ± √300) / 2

k = (20 ± 10√3) / 2

As a result, the real values of k for which there is precisely one real solution to the equation are as follows:

k = (20 + 10√3) / 2 and k = (20 - 10√3) / 2

Note that these values are approximately equal to 15.85 and 4.15, respectively.

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In a painting class, students will pick sets that show combinations of primary colors.

Primary colors are the basic colors from which all other colors can be created. In traditional color theory, the primary colors are red, blue, and yellow. When these colors are mixed together, they can produce a wide range of secondary and tertiary colors. To create a set of primary colors, students would choose combinations of red, blue, and yellow. For example, they might pick a set that includes pure red, pure blue, and pure yellow, allowing them to mix various shades and hues by combining these primary colors. By experimenting with different proportions and mixing techniques, students can create a vast array of colors using just the primary colors. Understanding the mixing of primary colors is fundamental in art, as it allows artists to achieve the desired color palette and effectively express their creative vision. By learning how primary colors interact and blend, students can develop a strong foundation in color theory and expand their artistic possibilities.

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The total number of red marbles in the vase are 10.

A ratio is described as a comparison between two amounts with the same unit to determine the amount of 1 quantity is contained in the other. Ratios are divided into two sorts.

The first is a part-to-part ratio, and the second is a part-to-whole ratio. The part-to-part ratio expresses the relationship between 2 separate entities or groupings.

Now, according to the question;

Let 'x' be the red marbles in the vase.

Let 'y' be the orange marbles in the vase.

The total number of marbles in the vase are 60

x  + y = 60 (equation 1)

The ratio of red marbles to orange ones is 1:5.

Thus, x/y = 1/5

cross multiplying;

5x = y

or y = 5x

substitute the value of y in equation 1;

x  + y = 60 (equation 1)

x  + 5x = 60

6x = 60

x = 10  (red marbles)

Thus, the number of red marbles in the vase are 10.

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The midsegment of AD (which in this case is DE) always generates two congruent parts (which in this case are AD and DB)

Answer:

Angles 1 and 2 are 115 degrees. Angles 3 and 4 are 65 degrees.

Step-by-step explanation:

7x - 4 + 3x + 14 = 180 (angles 1 and 3 form a straight line so they add to 180 degrees)

10x + 10 = 180

10x = 170

x = 17

m<1 = 7(17) - 4 = 115

m<3 = 3(17) + 14 = 65

Opposite angles are equivalent so m<2 = 115 and m<4 = 65.

If we denote the probability of hitting a bullseye on a dartboard with radius 12 inches as a function of the size of the bullseye, we can refer to this function as PS.

The function PS represents the probability of hitting the bullseye and is dependent on the size of the bullseye. The larger the bullseye, the higher the probability of hitting it, and vice versa. By adjusting the size of the bullseye, we can determine the corresponding probability of hitting it using the function PS.

It's important to note that without specific information about the relationship between the bullseye size and the probability, it's not possible to provide a specific mathematical expression or further details about the PS function. The function would need to be defined or provided to calculate the probability accurately.

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Answer:

BODMAS

Step-by-step explanation:

BODMAS is correct.

Brackets

Of

Division

Multiplication

Addition

Subtraction

Answer:

Step-by-step explanation:

Answer:

(199+0.32)minus 350

Step-by-step explanation:

199 is the cost plus fee per mile 0.32 subtract 350 to see if he can afford it

Answer:

59,049

Step-by-step explanation:

(3^5)^2 x 3^0

(243)^2 x 1

(243)^2

59,049

The range of values for x is x>2

2x-4>0

2x>4

x>4/2

x>2

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The rectangle which should go in position I is rectangle A.

We are given that;

The rectangles A,B,C and D with numbers

Now,

To take the same the number of side

If we take A on 1 place

F will be on second place

And  B will be on 4th place

Therefore, by algebra the answer will be rectangle A.

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Answer: y = 4x

Step-by-step explanation:

I would say y = 4x because all of these equations have a constant involved except for that.

The possible sets of intensities that fit the given pattern are options (d) 63%, 65%, 67%.

We can use the given pattern to determine the possible intensities for the fourth, fifth, and sixth visits:

Constant intensity for 3 visits: This means that the intensity will be the same for the first three visits. Let's call this intensity level "I".

Increasing intensity over 3 visits: This means that the intensity will increase for the next three visits. Let's call the new intensity levels "I + x", "I + 2x", and "I + 3x".

Decreasing intensity over 3 visits: This means that the intensity will decrease for the final three visits. Let's call the new intensity levels "I + 2x", "I + x", and "I".

Note that the intensity increases by the same amount "x" during the increasing intensity visits, and decreases by the same amount during the decreasing intensity visits.

Now, let's look at each answer choice:

a. 63%, 63%, 63%: This corresponds to a constant intensity throughout all 3 visits, which does not fit the pattern given in the question.

b. 66%, 69%, 72%: This corresponds to an increasing intensity, but the amount of increase is not specified. Therefore, we cannot determine if this fits the given pattern.

c. 66%, 62%, 58%: This corresponds to a decreasing intensity, but the amount of decrease is not specified. Therefore, we cannot determine if this fits the given pattern.

d. 63%, 65%, 67%: This corresponds to an increasing intensity, with a constant increase of 2% per visit. This fits the given pattern of increasing intensity over 3 visits.

e. 67%, 72%, 77%: This corresponds to an increasing intensity, with a constant increase of 5% per visit. This does not fit the given pattern of increasing intensity over 3 visits, as the increase is too large.

Therefore, the possible sets of intensities that fit the given pattern are options (d) 63%, 65%, 67%.

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Answer: He received $3.51 in change.

Step-by-step explanation:

To get the answer we can subtract the amount Felix paid ($20) by the cost of the dinner ($16.49).

It will look like this:

$20.00 - $16.49 = $3.51

Answer:3 dollars and 51 cents

Step-by-step explanation:

Answer:

Part 1) 30%

Part 2) 80 students

Part 3) 57 votes

Part 4) LaToya

Step-by-step explanation:

75 divided by 250 = 0.30 = 30%

32% = 0.32 and then 0.32 times 250 = 80 students

250 - 75 - 80 = 95 students that didn't vote for Carlos or LaToya. Then 0.60 times 95 = 57

LaToya had 80 votes, the most votes.