Determine if the lines through each set of ordered pairs are parallel, perpendicular, or neither. Explain your answer. Ordered pairs: (8, 3) (-2, 5) and (-2, -5) (-1, -10)

Answer: [tex]\frac{r^9}{r^3} = r^{9-3} = r^6[/tex]

We subtract the exponents when dividing terms with the same base.

The general rule is [tex]\frac{a^b}{a^c} = a^{b-c}[/tex]

Hii!

___________________________________________________________

[tex]\rightsquigarrow\circ\boldsymbol{Answer}\circ\leftharpoonup[/tex]

r^6

[tex]\rightsquigarrow\circ\boldsymbol{Explanation}\circ\leftharpoonup[/tex]

To simplify this we need to use the division property of exponents:

[tex]\large\boxed{\mathtt{\frac{x^m}{x^n} =x^{m-n}}}[/tex]. So if we divide two numbers with the same base, we subtract their exponents.

Let's apply this rule here.

[tex]\twoheadrightarrow\sf r^9\div r^3[/tex].

[tex]\bullet[/tex] Since these two numbers have the same base, we subtract their exponents

[tex]\twoheadrightarrow\sf r^6[/tex]

[tex]\bullet[/tex] Great job! We found the answer

--

Hope that this helped! Best wishes.

[tex]\textsl{Reach far. Aim high. Dream big.}\\\boldsymbol{-Greetings!-}[/tex]

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The solution to the complex inequality as in the task content is; -2 < x <= 1.

The inequality in discuss is; -5<4x+3 <= 7.

Hence, solving the inequalities separately; we have;

-5 < 4x +3

-8 < 4x

-2 < x

Also; 4x+3 <= 7

4x <= 4

x <= 1.

Ultimately, the solution to the inequalities is;

-2 < x <= 1.

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Answer:

-1 and -11

Step-by-step explanation:

"sum" means we're adding.

-1 + -11 = - 12

"product" means we're multiplying.

-1 × -11 = 11

Answer:

The vertex is the point of coordinates (-2 , 5)

Step-by-step explanation:

we notice that the equation of the parabola is given in vertex form :

y = -4(x + 2)² + 5

then

y = -4(x − (-2))² + 5

Therefore

The vertex of the graph is the point (-2 , 5)

The linear equation that represents the line that passes through the points (4,5) and (0,-3) is given by:

B. y = 2x - 3

A linear function is modeled by:

y = mx + b

In which:

The line passes through (0,-3), that is, when x = 0, y = -3, hence the y-intercept is of b = -3.

The slope is given by the change in y divided by the change in x, hence:

m = (5 - (-3))/(4 - 0) = 2

Hence the equation is:

y = 2x - 3.

Which means that option B is correct.

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The expression can be used to find the difference of the polynomials is [10m (–7m)] [(–6) 4]

Difference of polynomials

A polynomial is a function that has a leading degree of 3 and above.

Given the expression below

(10m – 6) – (7m – 4)

Expand

10m - 6 - 7m  + 4

Collect the like terms

10m - 7m - 6 + 4

Simplify

3m -2

Hence the expression can be used to find the difference of the polynomials is [10m (–7m)] [(–6) 4]

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Answer:

This situation of the recipe can be represented as y=x+5.5 and it is expected that x is ≥ 0 and y is ≥ 5.5.

What is the equation for this situation?

It is known the total amount of flour (y) is equivalent to the total amount of whole wheat flour (5.5) added to the total white flour (x). Therefore, the equation is:

y = x + 5.5

The possible values are

x = It is expected x is equalthan 0 or greater to it since the minimum amount of white flour that can be added is 0.

y = It is expected y is equal than 5.5 or greater to it since even if no

white flour is added the minimum total is 5.5.

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Step-by-step explanation:

This situation of the recipe can be represented as equation y = x+5.5 and it is expected that x is ≥ 0 and y is ≥ 5.5.

A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output.

For the given expression

y = x + 5.5

The possible values are

x = It is expected x is equal to 0 or greater to it

since the minimum amount of white flour that can be added is 0.

y = It is expected y is equal than 5.5 or greater to it since even if no

white flour is added the minimum total is 5.5.

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Answer:

17

Step-by-step explanation:

5x+5x+10=180

10x=170

x=17

Answer:

Answer is 17

Step-by-step explanation:

It is done in this step

5x +5x+10=180

10x=170

x=17

Proved Below

[tex]\Longrightarrow x-y = \sqrt{(x+y)^2-4xy}[/tex]

[tex]\Longrightarrow x-y = \sqrt{x^2+2(x)(y)+ y^2-4xy}[/tex]

[tex]\Longrightarrow x-y = \sqrt{x^2+2xy-4xy+y^2}[/tex]

[tex]\Longrightarrow x-y = \sqrt{x^2-2xy+y^2}[/tex]

[tex]\Longrightarrow x-y = \sqrt{(x-y)^2}[/tex]

[tex]\Longrightarrow x-y =x-y[/tex]

Let's check

x-y=√(x+y)²-4xy

Solve RHS

Hence proved

The point of intersection of two given equations is (0.333, 2.667).

Given that, equation with two variables are y = 8x and y = 2x + 2.

The given equations will intersect at some point where y is the same for both equations.

When you replace y in y = 2x + 2 with y = 8x, we get 8x = 2x + 2.

So, the solution of 8x = 2x+2 will satisfy both equations.

Now, we need to find the solutions to take the integer values of x between -3 and 3.

That is,

x = -3 , then 8(-3) = 2(-3) +2⇒-24 = -6+2

⇒-12 = -4    False.

similarly, for x = -2

8(-2) = 2(-2)+2

⇒-16 = -2   False

For, x = -1

8(-1) = 2(-1)+2

⇒-8= 0   False

For, x = 0

8(0) = 2(0)+2

⇒0= 2   False

For, x = 1

8(1) = 2(1)+2

⇒8= 4   False

For, x = 2

8(2) = 2(2)+2

⇒16 = 6   False

For, x = 3

8(3) = 2(3)+2

⇒24 = 8   False

Therefore, there is no solution to 8x = 2x +2 for the integers values of x between -3 and 3.

The equations can be solved graphically by plotting the two given functions on a coordinate plane and identifying the point of intersection of the two graphs.

The point of intersection is the values of the variables which satisfy both equations at a particular point.

Hence, you can see the graph as shown below, the point of intersection is (0.333, 2.667).

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The figure that shows the reflection of the letter Z is C

The figure shows the letter Z and four of its transformed images—A, B, C, and D

Which of the four images was formed by a reflection of the letter Z?

A   B   C    D

From the graph, see attachment, we have the following highlights:

The letter Z is in the second quadrant.

Also, B and D are letter Z.

So, they cannot represent the reflection

When reflected across the x-axis, the reflection is C

Hence, the figure that shows the reflection of the letter Z is C

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Answer:

29/10

Step-by-step explanation:

7/2+(-3/5)

7/2-3/5

35/10-6/10

29/10

The number of cows and ducks in the garden are 3 and 4 respectively.

Let the numbers of cows be x and the number of ducks is y.

Total number of legs=20

Total number of eyes=14

Linear equation for the total number of legs in the garden,

4x+2y=20 -(1)

Linear equation for the total number of eyes in the garden,

2x+2y=14 -(2)

Solve the system of the two linear equations to find the values of x and y.

Subtract equation (1) from equation (2), and we get,

2x=6

[tex]x=\frac{6}{2}\\[/tex]

x=3

Substitute the value of x in equation (1), and we get,

4(3)+2y=20

12+2y=20

2y=20-12

2y=8

[tex]y=\frac{8}{2}\\[/tex]

y=4

Number of cows=3

Number of ducks=4

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The number of peanuts ( x ) he could plant on 8,500 square meters of land = 95.6 kg

"It is a method of finding the value of a single unit, and based on that value we can find the required value."

For given question,

A farmer can plant 45 kg of peanuts on 4,000 square meters of land.

Using unitary method,

[tex]\frac{4000}{45}\\\\=88.8888 \\\\\approx 88.89[/tex]

This means, a farmer can plant 1 kg of peanuts on 88.89 square meters of land.

We need to find the number of peanuts ( x ) he could plant on 8,500 square meters of land.

Here, 1 kg = 88.89 square meters

          x kg = 8500 square meters

[tex]\Rightarrow x=\frac{8500}{88.89}\\\\ \Rightarrow x = 95.6~kg[/tex]

Therefore, the number of peanuts ( x ) he could plant on 8,500 square meters of land = 95.6 kg

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Answer:

y=-2/3x-13/3

Step-by-step explanation:

parralel line have the same gradient

y=mx+c is the general straight line equation

m represents the gradient

if the equation is y=-2/3x+3/2

m=-2/3

the coordinates (4,-7)

x=4

y=-7

substitute into equation

-7=-2/3×4+c

-7=-8/3+c

c=-7+8/3

c=-13/3

so the equation is :

y=-2/3x-13/3

Answer:

Step-by-step explanation:

Simplify the following expression:

Simplify the following expression:

7a + 5b - 2a + b =

5a + 6b

Answer:

[tex]x > - 3[/tex]

I hope this is helpful

Answer:

if a line is parallel they have the same slope

so the slope is 5

Hope This Helps!!!

Answer:

the answer to the question is C) 8

Answer:

x>0

Step-by-step explanation:

points exist on the right of the graph so the domain is x>0

We can actually deduce here the one that uses the reciprocal property to rewrite  [tex]\frac{x}{6} = \frac{28}{3\\}[/tex]  is: C. [tex]\frac{6}{x} = \frac{3}{28}[/tex].

A reciprocal of a number is defined as the number that when it is multiplied by the number, the result is 1. Thus, we deduce here that the product of a number and its reciprocal gives one.

Thus: x/6 x 6/x = 1

Also, if 28/3 x 3/28 = 1

Thus, we see that they use the reciprocal property.

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Answer:

Slope =  - 1

Step-by-step explanation:

The equation is in form [tex]y=mx+c[/tex], [tex]m[/tex] s the slope and [tex]c[/tex]  is the intercept on [tex]y[/tex] axis.

Hence, in [tex]y=-x+3[/tex] , slope is -1  and intercept on [tex]y[/tex] axis is 3.

The graph which resembles the graph of f(x)=[tex]2^{x}[/tex] but is reflected over the x-axis is g(x)=[tex]2^{x} +1[/tex]

Given Function f(x)=[tex]2^{x}[/tex].

We have to generate a function whose graph is similiar to the given function and is reflected over the x axis.

If we take first function g(x)=2x-1

put the value of x=-1 then the value of function g(x)=2*(-1)-1=-2-1=-3 means the value of y in this function will be negative means the graph will be under x-axis.

Taking second function g(x)=[tex]2^{x} +1[/tex]

for all the negative values of x it posses a positive value of y so the graph will be over the x axis.

Taking third function g(x)=-[tex]2^{x}[/tex]

In the above function for each value of x the function possess a negative value so the graph will be under x axis.

Taking fourth function g(x)=2x-1

For all values of x less than 1 the function becomes negative which takes graph below the x axis. First graph is for [tex]2^{x}[/tex] and the second is for [tex]2^{x} +1[/tex]

Hence the graph similar to [tex]2^{x}[/tex] and reflected over x axis is g(x)=[tex]2^{x} +1[/tex].

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Answer:

Step-by-step explanation:

In this figure of overlapping parallelograms, each angle is related to the others by several different theorems involving triangles, parallelograms, and parallel lines. That is, there are several different ways one can arrive at the answers to this question.

__

∠UTC ≅ ∠UDC = 180° -∠EDU . . . opposite angles of parallelogram; linear pair

∠UTC = 180° -125° = 55°

__

∠UCD ≅ ∠TBC = 180° -∠TBA . . . . corresponding angles; linear pair

∠UCD = 180° -110° = 70°

__

∠BCT ≅ ∠UTC = 55° . . . . alternate interior angles