In the first quadrant, you start at (6, 3)
and move 2 units left
What point will you end up on?

Answer:

[tex]x^2-8x+12[/tex]

Step-by-step explanation:

Knowing both intercepts we can write the equation in factored form:

[tex](x-2)(x-6)[/tex]

Now use distributive property to find the equation in standard form:

[tex](x-2)(x-6)\\x^2-6x-2x+12\\x^2-8x+12[/tex]

Given the data in the table, the slope, y-intercept and equation of the table are 1/3, (0,-2), and y = (1/3)x - 2 respectively.

Given that;

x           y

-3        -3

0         -2

3         -1

6         0

9         1

Slope m = rise/run = (y₂ - y₁)/(x₂-x₁)

Using the, the points (-3,-3) and (0,-2) from the table

Slope m = rise/run = (y₂ - y₁)/(x₂-x₁)

Slope m = rise/run = ((-2) - (-3)) / ( 0 - (-3) )

Slope m = 1/3

To determine the y-intercept b, use the formula for equation of line.

y = mx + b

Substitute in Point( -3,-3 ) and m = 1/3 and solve for b

y = mx + b

-3 = (1/3)(-3) + b

-3 = -3/3 + b

-3 = -1 + b

b = -3 + 1

b = -2

Hence the y-intercept in point form is (0,-2)

The equation of the line in slope-intercept form will be;

y = mx + b

y = (1/3)x + (-2)

y = (1/3)x - 2

Given the data in the table, the slope, y-intercept and equation of the table are 1/3, (0,-2), and y = (1/3)x - 2 respectively.

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Step-by-step explanation:

I can't draw here, but I can tell and explain to you what happens to the points (incl. N).

remember the slope of lines, and what happens when we have to create a perpendicular slope (90°) ?

x and y in the slope ratio y/x go upside down and the sign flips (that means it flips for one of them).

a rotation by 90° follows the same principles.

x and y trade places, and for one of them the sign flips.

the only "difficult" trick is to determine, if the sign of x or of y flips.

let's look at N first.

N = (-5, -4)

the rotation counterclockwise takes it over into the 4th (bottom right) quadrant, where x values are positive.

aha, so the sign of x flips after x and y trade places, and we get

N' = (4, -5)

now for the other points

X = (-3, -2)

the same principle as for N

X' = (2, -3)

B = (-4, 1)

this is now moving from the 2nd (where y values are positive) to the 3rd quadrant (where x and y are negative).

so, again the sign of x flips after x and y trade places

B' = (-1, -4)

with the new coordinates of the points you can now easily draw the new triangle'.

Answer:

50 I think

Step-by-step explanation:

30% of 500 is 150 so we have 150 red balls

40% of 500 is 200 so we can assume 50 balls were taken out

The following system of equations is solved to find how many minutes of each exercise type she should do now:

In which a is the amount of calories lost per minute running, and b is the amount of calories lost per minute jogging.

A system of equations is when two or more variables are related, and equations are built to find the values of each variable.

For this problem, the variables are given as follows:

She still wants to exercise for 40 min every other day, hence:

x + y = 40.

She wants to burn 460 calories during each session, hence:

ax + by = 460.

In which a is the amount of calories lost per minute running, and b is the amount of calories lost per minute jogging. (the problem is incomplete and I couldn't find it anywhere, hence I am speaking into general terms).

Then the following system of equations is solved to find how many minutes of each exercise type she should do now:

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Answer:

He has to pay $223.68 after 6 months

Step-by-step explanation:

I don't know if I understood you right but I think you meant how much does he have to pay in 6 months. That would be 37.28x6=223.68

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. (x+4)⁸ is expanded as x⁸ + 32x⁷ + 448x⁶ + 3584x⁵ + 17920x⁴ + 57344x³ + 114688x² + 131072x + 65536

The Binomial theorem tells us how to expand expressions of the form (a + b)ⁿ, for example, (x + y)⁷. The larger the power is, the harder it is to expand expressions like this directly.

The total number of terms in the expansion of (x+y)ⁿ are (n+1).

The sum of exponents of x and y is always n.

nC₀, nC₁, nC₂,….., nCₙ are called binomial coefficients and also represented by C₀, C₁, C₂, ….., Cₙ

The binomial coefficients which are equidistant from the beginning and from the ending are equal.

i.e. nC₀ = nCₙ, nC₁ = nCₙ₋₁ , nC₂ = nCₙ₋₂ ,….. etc.

Let the expression be (x + 4)⁸

Use the binomial expansion theorem to find each term. The binomial theorem states

(a+b)n=n∑k=0nCk⋅(an−kbk)(a+b)n=∑k=0n⁡nCk⋅(an-kbk).

8∑k=08!(8−k)!k!⋅(x)8−k⋅(4)k∑k=08⁡8!(8-k)!k!⋅(x)8-k⋅(4)k

Expand the summation

8!/(8−0)!0!.(x)⁸⁻⁰⋅(4)⁰+8!/(8−1)!1!(x)⁸⁻¹⋅(4)¹+…+8!/(8−8)!8!(x)⁸⁻⁸⋅(4)⁸

Simplify the exponents for each term of the expansion.

1⋅(x)⁸⋅(4)⁰+8⋅(x)⁷⋅(4)1+…+1⋅(x)⁰⋅(4)⁸¹⋅(x)⁸⋅(4)⁰+8⋅(x)⁷⋅(4)¹+…+1⋅(x)⁰⋅(4)⁸

Simplify the polynomial equation, we get

x⁸ + 32x⁷ + 448x⁶ + 3584x⁵ + 17920x⁴ + 57344x³ + 114688x² + 131072x + 65536

Therefore, by expanding the binomial equation, we get

(x + 4)⁸ =  x⁸ + 32x⁷ + 448x⁶ + 3584x⁵ + 17920x⁴ + 57344x³ + 114688x² + 131072x + 65536

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The coordinates of A are (3, 5).

According to the section formula-

If a point (x , y) divides a line in the ratio of m : n, where the two endpoints of the line are (x1, y1) and (x2, y2), then-

x = (nx1 + mx2)/ (m + n)

and y = (ny1 + my2)/ (m + n)

Here, M (4,6) is the midpoint of AB and B is (5,7)

Let the coordinates of A be (x2, y2)

Therefore,

x1 = 5, y1 = 7

x = 4, y = 6

Since, midpoint divides a line segment into two equal halves, m : n = 1 : 1

Now, substituting the values in the section formula we get-

4 = (5 + x2)/2

4 × 2 = 5 + x2

8 = 5 + x2

5 + x2 = 8

x2 = 8 - 5

x2 = 3

and 6 = (7 + y2)/2

6 × 2 = 7 + y2

12 = 7 + y2

7 + y2 = 12

y2 = 12 - 7

y2 = 5

Thus, the coordinates of A are (3, 5).

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Answer: The dimensions are 8 and 28

Answer:

The answer is 7

Step-by-step explanation:

The formula is y=mx+b so m=10 and b=7

Answer:

Hope this helps :)

The y-intercept is 7.

Step-by-step explanation:

This is because the in the slope-intercept form, y = mx + b, so the b in this case is 7.

Answer:

J.o.i.n p.l.z pqp-yuth-ygd

The original price based on the gift card of $15 and discount of 30% is $55.50

What deductions are taken from the original price?

In order to arrive at the total cost before taxes, the gift card of $15 was first of all deducted from the original price before grossing up to 100% since the total cost before taxes represents 70% after the gift card has been deducted

original price(total cost before taxes+gift card)/(1-discount rate)

total cost before taxes=$23.85

gift card=$15

discount rate=30%

original price=($23.85+$15)/(1-30%)

original price=$55.50

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Based on the given equation which has been solved in the table (see attachment), we know that: D. the subtraction property of equality was not applied to solve this equation.

An equation can be defined as a mathematical expression which shows that two (2) or more thing are equal.

The subtraction property of equality states that the two (2) sides of an equation would still remain equal even when the same number has been subtracted from both sides of an equality.

Based on the given equation which has been solved in the table (see attachment), we can reasonably and logically deduce that the subtraction property of equality wasn't applied to solve this equation.

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[tex] \bold \implies{ \bold{The \: correct \: option \: is \: c) \: sin \: 141° < 0}}[/tex]

[tex] \bf \longrightarrow \tan141\degree = - \frac{b}{a} < 0 \\ \\ \bf \longrightarrow \sin141\degree = \frac{b}{c} > 0 \\ \\ \bf \longrightarrow \cos141 \degree = - \frac{a}{c} < 0[/tex]

=========================================================

Explanation:

We'll use Heron's Formula.

When given the three sides a,b,c, the area of the triangle is

[tex]A = \sqrt{s(s-a)(s-b)(s-c)}[/tex]

where s = (a+b+c)/2 is the semi-perimeter, aka half the perimeter.

Let's compute the value of s first

s = (a+b+c)/2 = (8+9+3)/2 = 20/2 = 10

Then we can say,

[tex]A = \sqrt{s(s-a)(s-b)(s-c)}\\\\A = \sqrt{10(10-8)(10-9)(10-3)}\\\\A = \sqrt{140}\\\\A \approx 11.8321595661992\\\\A \approx 11.83\\\\[/tex]

The triangle has area of roughly 11.83 square meters.

The inverse function of f(x) is; f-¹(x) = x³ + 5

To find the inverse of the function;

We should represent f(x) as y.

Now we have;

By taking the cube of both sides;

y³ = x - 5

By solving for x;

x = y³ + 5

By swapping x and y; we have;

y = x³ + 5

f-¹(x) = x³ + 5.

The inverse function of f(x) is; f-¹(x) = x³ + 5.

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The domain of the function is (0,∞) , {x|x>0}

and the range is  (₋∞, ∞) ,  {y|y ∈ R}

Given the function is y = log₅x

A function's domain and range are its constituent parts. A function's range is its potential output, whereas its domain is the set of all possible input values. Range, Domain, and Function. A is the domain and B is the co-domain if a function f: A B exists that maps every element of A to an element in B. 'b', where (a,b) R, provides the representation of an element 'a' under a relation R. The set of images is the function's range. In general, a function's domain and range are denoted as follows: Range(f) = f(x): x domain(f) and domain(f) = f(x): x R

hence we get the domain and range as (0,∞) , {x|x>0} and  (₋∞, ∞) ,  {y|y ∈ R} respectively.

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Kyra wants the total length of the tree to the nearest inch it will be 193.68 inches.

The measurement couldn't have been added earlier because they're in different units

Kyra measures 4 feet. This in centimeters will be:

= 4 × 30.48 = 121.92 cm

Tai measures 3.5 yards. This in centimeters will be:

= 91.44 × 3.5

= 320.04 cm

Rodney measures 50 centimeters.

Therefore, the addition will be:

= 121.92 cm + 320.04 cm + 50cm

= 491.96 cm

The total length in inches will be:

1 inch = 24 cm

= 491.96 / 2.54

= 193.68 inches.

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The given function y=4(0.2) ^x+1 is a exponential function because value of x could be any number. Whenever we have a degree of x in terms of y then it is a part of exponential function.

In the biological sciences, exponential functions are frequently used to simulate the evolution of a particular quantity over time, such as population size. Experimental data graphs are typically created with the quantity on the y-axis and the time on the x-axis.

Exponential functions play a key role in economic analysis of growth and decay. Examples include investment values that rise by a fixed percentage each period, business sales that rise by a fixed percentage each period, models of economic expansion, or models simulating the spread of an epidemic.

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The required statement is proved.

Given y = ax² ₊ bx ₊ c, which is the general formula of quadratic form)

vertex = (-b/2a , 4ac ₋ b²/4a) which is the quadratic vertex formula

according to y = ax² ₋ 2px ₊ ap² ₊ q

therefore, a = a

b = ₋2xp

c = ap²₊q

⇒ (₋(₋2p/2a , 4a× (ap² ₊ q)₋ (2ap)²/4a)

⇒ (p , 4a²p² ₊ 4aq ₋ 4a²p²/4a)

⇒ (p , 4aq/4a)

⇒ (p,q)

hence we proved the quadratic equation .

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Answer: (x−3)(3x−8)

Step-by-step explanation:(x−3)(3x−8)

Apply the distributive property by multiplying each term of x−3 by each term of 3x−8.

3x

2

−8x−9x+24

Combine −8x and −9x to get −17x.

3x

2

−17x+24

Two identical figures with all sides of equal length = Both are square

Solution :

The perimeter of a square is defined as the total length that its boundary covers. The perimeter of any closed geometrical shape is calculated by finding the distance around that shape. For a square, the perimeter can be calculated by finding the sum of all the sides. Since all four sides are equal, it is four times the length of each side of a square. Let us learn about perimeter of square in detail in this article.

Derivation of Perimeter of Square Formula

The perimeter of the square is defined as the total length of the boundary of a square. In order to calculate the perimeter of the square, we will find the sum of all of its sides. Since all sides of a square are equal for a square, with each side measuring "s" units, perimeter will thus be given as,

Perimeter of square = s + s + s + s

⇒ Perimeter of square = 4s, where "s" is the side length of the square.

Squares :

A square is a special kind of rectangle (an equilateral one) and a special kind of parallelogram (an equilateral and equiangular one). A square has four axes of symmetry, and its two finite diagonals (as with any rectangle) are equal. Bisection of a square by diagonal results in two right triangles.

The formula for the perimeter of a square is,

P = Side + Side + Side + Side. Or,

P = 4 × Side.

two identical figures with all sides of equal length the combined perimeter of the figure is 80centimeters

2(4*side ) = 80

8*side = 80

side = 10

length of one side =10

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Answer:

Step-by-step explanation:

30.466666.999

2.81*10^4

the number of times you move the decimal adds to the exponent

The value of x based on the equation illustrated as BM=x+7,DM=2x+3 is 10.

It should be noted that an equation is used to show the relationship that exists between rte variables.

The expression given are

BM=x+7

DM=2x+3

Equate both equations

x + 7 = 2x - 3

Collect like terms

2x - x = 7 + 3

x = 10

Therefore, the value of x is 10.

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Answer:

P = 4s

Step-by-step explanation:

All the numbers in column P are equal to 4 times the numbers in column s