Write an equation in slope-intercept form for the line that passes through the given point and is parallel to the given equation.

5x+2y=10
and passes through (-6, 7)

Answer:

1/2y+1/2a=x

Divide both sides by2, then but the a value on the other side.

Counterexample

A counterexample is an example that meets the mathematical statement's condition but does not lead to the statement's conclusion. It is used to check the validity of an argument.

We have been given the conjecture:-

"For every integer n, [tex]n^3[/tex] is positive."

We have to show that the conjecture is false by finding a counterexample.

Let us take an integer n = - 5

Finding its cube we, get

[tex]n^3[/tex] = -125

We know that,

-125 is not positive, it is negative.

Hence, the conjecture "For every integer n, [tex]n^3[/tex] is positive." is proven wrong by finding a counterexample which states otherwise.

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In 400 minutes, it will reach the destination.

What is distance?

Distance is a measurement of how far apart two objects or points are, either numerically or occasionally qualitatively. Distance can refer to a physical length in physics or to an estimate based on other factors in everyday language (e.g. "two counties over"). The term is also frequently used metaphorically to refer to a measurement of the amount of difference between two similar objects (such as statistical distance between probability distributions or edit distance between strings of text) or a degree of separation, as spatial thinking is a rich source of conceptual metaphors in human thought (as exemplified by distance between people in a social network). The concept of a metric space is used in mathematics to formalise the majority of these notions of distance, both literal and figurative.

Distance is equal to speed × time. Time is equal Distance/Speed.

we have given, d(t)=340-0.85t

where, t is the time and d(t) is the distance.

when t = 0 we get,

d(t)=340

If we set d(t)=0 we get, 0= 340- 0.85t

add with 0.85t on both side

0.85t=340

t= 340/0.85

t= 400 minutes

Hence, the time taken to reach the destination is 400 minutes.

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Answer:

x=10.50

Step-by-step explanation:

14 =  5

________
29.40 = x

cross multiply - 29.40 x 5 = 147

Then u would divide like this

14/14=1      147/14=10.5

Answer:

The third one (the elliptical shape) is not a function

Step-by-step explanation:

Every x value of a function must be paired to a single y value.  One really easy way to tell of a graph is a function is called the "vertical line test."  This says that if a vertical line drawn anywhere in the graphed area passes through more than one point, it is not a function.

The graph represents the solution set of y > -2x - 2 and y ≤ x + 4 is graph (a)

Inequality expressions are mathematical statements that are represented by variables, coefficients and operators where the opposite sides are not equal

The system of inequalities is given as

y > -2x - 2

y ≤ x + 4

Next, we plot the system of inequalities on a graph (see attachment)

From the attached graph, we have both lines of the graph intersect at (-2, 2)

Also, we can see that the graph has two lines (one shaded and one closed line)

By comparing the attached graph and the graphs in the list of options, we can see that the graph represents the solution set of the system of inequalities is graph (a)

Hence, the graph represents the solution set of the system of inequalities is graph (a)

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Answer:

3 × 5 = 15

Step-by-step explanation:

5 is the common number

Angles of a polygon add to 360 degrees. To find the measure of each exterior angle of a regular n-gon. divide 360 by n.

nswer

First image

Angle ABC covers around the inside and outside of the circle.

Second image

Angle x l

hird image

Angle DBE l

ngle of arc DE l

ngle of arc AC l

ourth angle

ll the angles at U lie inside the circle.

ngle 78° l

ngle 114° l

ope this Helps!!!

Answer:

48

Step-by-step explanation:

Step-by-step explanation:

1.

200 - 7/21 = (200×21 - 7)/21 = (4200 - 7)/21 =

= 4193/21 = 599/3 = (199×3 + 2)/3 =

= 199 2/3

we could have seen that 7/21 = 1/3.

so, then this problem was

200 - 1/3 = (200×3 - 1)/3 = 599/3 = 199 2/3

(see above)

2.

50 - 4/7 = (50×7 - 4)/7 = (350 - 4)/7 =

= 346/7 = (49×7 + 3)/7 = 49 3/7

3.

24 1/4 - 20 3/5 = (24×4 + 1)/4 - (20×5 + 3)/5 =

= 97/4 - 103/5

to calculate this we need to bring both fractions to the save denominator. the LCM (lowest common multiple) of 4 and 5 is 20.

so,

97/4 - 103/5 = (97×5)/(4×5) - (103×4)/(5×4) =

= 485/20 - 412/20 = 73/20 =

= (3×20 + 13)/20 = 3 13/20

4.

10 5/8 - 6 4/9 = (10×8 + 5)/8 - (6×9 + 4)/9 =

= 85/8 - 58/9

the LCM of 8 and 9 is 72.

85/8 - 58/9 = (85×9)/(8×9) - (58×8)/(9×8) =

= 765/72 - 464/72 = 301/72 =

= (4×72 + 13)/72 = 4 13/72

5.

6 1/2 - 5 3/4 = (6×2 + 1)/2 - (5×4 + 3)/4 =

= 13/2 - 23/4

the LCM of 2 and 4 is 4.

13/2 - 23/4 = (13×2)/(2×2) - 23/4 =

= 26/4 - 23/4 = 3/4

Answer:

Image result for kumon level C

This award is presented to a student who has completed Level C10 or higher during or before their 1st-grade year. Math Level C covers multiplication and division.

Step-by-step explanation:

The total cost for the items which the Tiny family purchased is $41.6 × 10⁻⁶ while their change is equal to $45.84 × 10⁻⁵.

An expression can be defined as a mathematical equation which is used to show the relationship existing between two or more variables and numerical quantities.

In order to determine the total cost, we would add all of the costs incurred by Tiny family as follows:

Total cost = 1.3 × 10⁻⁵ + 2.1 × 10⁻⁵ + 7.6 × 10⁻⁶

Total cost = (1.3 + 2.1) × 10⁻⁵ + 7.6 × 10⁻⁶

Total cost = 3.4 × 10⁻⁵ + 7.6 × 10⁻⁶

Total cost = $41.6 × 10⁻⁶

Next, we would calculate the change as follows:

Change = Amount paid - Total cost

Change = $5.0 x 10⁻⁴ - $41.6 × 10⁻⁶

Change = $45.84 × 10⁻⁵

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Answer:

30.375

Step-by-step explanation:

this is a geometric sequence, meaning it has a common growth factor

to find the growth factor, you divide a term by the previous term (example: 9/6)

so for this problem:

9/6 = 1.5

6/4 = 1.5

so 1.5 is the common growth factor

then you just multiply so:

9 • 1.5 = 13.5

13.5 • 1.5 = 20.25

20.25 • 1.5 = 30.375

4, 6, 9, 13.5, 20.25, and 30.375

so 30.375 is your 6th term

hope this helps :)

The rule of g(x) after the transformation is g(x) = 3(x + 4)^2 + 3(x + 4)

The function is given as

f(x) = x^2 + x

The transformations are given as:

The rule of the above transformations are :

When the above transformations are combined, we have

This means that

g(x) = 3f(x + 4)

So, we have

g(x) = 3(x + 4)^2 + 3(x + 4)

Hence, the function g(x) is g(x) = 3(x + 4)^2 + 3(x + 4)

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Answer:(3,1)

Step-by-step explanation:

Because you cant have (1,3) and (3,1).

Answer:

(2,3)

or (2,2) if the function does not need to be continuous.

Step-by-step explanation:

For a set of points to be considered a function, it must be true that for every X value, you have only a single Y value solution.

In other words, looking through your points listed, you would remove any point where an X value appears twice with different Y values.

[tex](X,Y)\\(-1,0)\\(1,3)\\(2,2) < -\\(2,3) < -\\(3,1)\\\\[/tex]

Notice the two points with arrows, both have 2 as their X value, but different Y values. Removing either one of them would make this a function. Although, by removing (2,3) the function has the potential to also be continuous, because having two of the same Y value for different X values would cause a piece-wise function which is generally non-continuous.

The length of the square collage will be 63in.

In the question, It is stated that a photo collage is made by arranging 7 square shaped photos in a row. The arrangement is done in such a way that it forms a rectangle. The total area of the collage is 567 square inches. We have to find out the length of the Collage.

Given that, the photos arranged are of square shape then their length and breadth must be equal. So,

Side of square photo: x

Now, seven photos were arranged, So,

Length of collage = 7x

Breadth of collage = x

We know the Area of the Rectangle is Length*Breadth

Putting Area A = 567, l = 7x, and b = x, we get:

=> Area = l*b

=> 567 = 7x*x

=> 567 = 7x²

=> x² = 81

=> x = 9

We get x = 9, We know length = 7x so l = 63in

Hence, the Length of the Collage will be 63 inches.

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Answer: [tex]x^4 +2x^3 -14x^2 +210x+1025[/tex]

Step-by-step explanation:

By the conjugate root theorem, -4+5i is also a root.

[tex]f(x)=a(x+4-5i)(x+4+5i)(x+5)^2\\\\=a(x^2 -8x+41)(x+5)^2\\\\ =a(x^2 -8x+41)(x^2 +10x+25)\\\\=a(x^4 +2x^3 -14x^2 +210x+1025)[/tex]

Answer:

7 hours

Step-by-step explanation:

each day she practices 1 hour and there are 7 days in a week so 7 hours by the end of the week

Answer:

type in english

Step-by-step explanation:

english please

The function of both burger king and mcdonalds cost are respectively; C(n) = 0.75(1.15)ⁿ and C(n) = 2.5 + 0.25n

The formula for the nth term of an arithmetic sequence is given as;

aₙ = a + (n - 1)d

where;

a is first term

n is position of term

d is common difference

For McDonald's, we are told that the initial price is $2.50 and the common difference is $0.25. Thus, the function will be;

C(n) = 2.5 + 0.25n

where n is number of years after 1998

We are told that the cost in burger king increases by 15% each year. Thus, using formula for geometric progression, the function is;

C(n) = 0.75(1 + 0.15)ⁿ

C(n) = 0.75(1.15)ⁿ

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Answer:

56

Step-by-step explanation:

3m + 72 = 4y - 56

3(8) + 72 = 4y - 56

24 + 72 = 4y - 56

96 = 4y - 56

4y = 152

y = 38

3(8) + 72 = 4y - x

24 + 72 = 152 - x

96 = 152 - x

-56 = -x

x = 56

Value of x when y = 17 for the quadratic function f(x) = x² + 6x + 10 is -7 and 1. That is option E.

Given, y=17 :

17 = x² + 6x + 10

Move 17 to RHS (right-hand side) :

0 = x² + 6x - 7

Using the Middle Splitting method:

0 = x² + (7x - 1x) - 7

0 = x(x + 7) - 1(x+7)

0 = (x - 1) (x + 7)

Now, equate both the equations (x-1) and (x+7) separately with 0.

The first value of x is

(x - 1) = 0

x = 1

The second value of x is

(x + 7) = 0

x = -7

∴ The values of x are -7 and 1. According to the question, that is option E.

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5. The value of x = 15

6. The converse that must be used is: C. Same-side exterior ∠s converse.

7. The proof is completed in the explanation part.

8. Slope of AB = 7/4; Slope of CD = -4/7, they are perpendicular.

The same-side exterior angles theorem states that same-side exterior angles that are on the same side of a transversal are supplementary to each other. Its converse states that if same-side interior angles are supplementary, then the lines they lie on are parallel to each other.

5. 10x - 22 + 3x + 7 = 180 [same-side exterior angles theorem]

13x - 15 = 180

13x = 180 + 15

13x = 195

x = 15

6. The converse that must be used to show that lines y and x are parallel to each other is: C. Same-side exterior angles converse.

7.

Statements                                      Reasons                                            

1. ∠6 ≅ ∠8                                       1. Given

2. y║z                                              2. Corresponding ∠s converse

3. ∠2 and ∠3 are supplementary  3. Same Side Interior ∠s

8. Given:

A(-3, 8)

B(1, 15)

C(10, -9)

D(3, -5)

Slope = change in y / change in x

Slope of AB = (8 - 15)/(-3 - 1) = -7/-4 = 7/4

Slope of CD = (-9 -(-5))/(10 - 3) = -4/7

-4/7 is the negative reciprocal of 7/4. Perpendicular lines have slope that are negative reciprocals of each other.

Therefore, CD and AB are perpendicular.

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The equation of the line that is parallel to y = 2/3x + 19 and passes through (-9, 4) is: y = 2/3x + 10.

Two lines that are parallel have equal slope (m).

In the slope-intercept form of the equation of  given line, y = mx + b:

Given:

A point (-9, 4)

Equation, y = 2/3x + 19.

The slope (m) = 2/3.

The line that passes through (-9, 4) and is parallel to y = 2/3x + 19 would also have a slope (m) = 2/3.

Substitute (x, y) = (-9, 4) and m = 2/3 into y = mx + b to find the value of b:

4 = 2/3(-9) + b

4 = -6 + b

4 + 6 = b

b = 10

To write the equation, substitute m = 2/3 and b = 10 into y = mx + b:

y = 2/3x + 10.

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Applying the rules for the constant, logarithm and exponents, the derivative of the given function is of:

f'(x) = 3/x - 6x² - 8/(x^5).

The function is given by:

f(x) = √2^3 + ln(x^3) - 2x^3 - log_3(729) - 2/x^4

The derivative of a sum is the sum of the derivatives, hence:

f'(x) = (√2^3)' + (ln(x^3))' - (2x^3)' - (log_3(729))' - (2/x^4)'

The derivative of a constant is of zero, hence:

Hence:

f'(x) = (ln(x^3))' - (2x^3)' - (2/x^4)'.

The derivative of the logarithm is given by:

ln(h(x))' = (1/h(x)) x h'(x).

Hence:

(ln(x^3))' = 3x²/x³ = 3/x.

The derivative of the power of x is given by:

[x^n]' = nx^(n-1).

Hence:

Hence the derivative of the function is given by:

f'(x) = 3/x - 6x² - 8/(x^5).

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The total amount contact paper required will depend on total surface area of the box which will be 778 square inches.

As per the question statement, we are given a box with dimensions

(18in x 1ft 1in x 5 in) and we are supposed to find the total amount contact paper required to cover it.

The total amount contact paper required to cover it will depend on the total surface area of the box.

Given length(L) = 18 inches

Given width(W) = 1 ft 1 in = 13 inches

Given height(H) = 5 inches

Total Surface Area of the box is given by the formula

Area = 2(LW + WH + HL)

Area = 2(18*13 + 13*5 + 5*18)

Area = 2*389

Area = 778 square inches

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