Are ∠2 and ∠5 vertical angles? Explain your reasoning.

The equation of the straight line is  y = 7/4 x .

A straight line is an endless, one-dimensional shape with no breadth. It is made up of two connected points on either side of a point that are connected indefinitely. A straight line has no curvature. It could be horizontal, vertical, or inclined.

A straight line's equation is of the form y = mx + c, where m denotes the slope and c the y-intercept.

The concept of a line is strongly tied to how the geometry is described given the range of geometries in contemporary mathematics.

For instance, in analytic geometry, a line in the plane is typically defined as the set of points whose coordinates fulfil a particular linear equation, but in a more abstract setting, such as incidence geometry,

The given points for the line is given by (0, 0) and (4, 7)

Now let us calculate the slope of the line:

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

Substituting the values we get the slope of the line is

m =  7/4

Now we will use the equation :

y-y₁=m(x-x₁)

y-0 = 7/4(x-0)

or, y = 7/4 x

Therefore the equation of the required line is y = 7/4 x

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Answer:

11 3/8.

Step-by-step explanation:

3 1/2 * 3 1/4

= 7/2 * 13/4

= 91/8

= 11 3/8.

Answer:

Your answer is 39.8

You basically add all the numbers and divide by how many numbers there are.

The factors are (x + 4), (x + 5) & (x - 4) and the solution is x = -4,  = -5 and x = 4

The given parameters are

f(x) = x^3 + 5x^2 - 16x - 80

x = -4 is a root

To set up the synthetic division, we start by writing out the coefficient of each term

So, we have

-4 |  1    5    -16    -80

Bring down the first coefficient

-4 |  1    5    -16    -80

      1

Multiply by -4

So, we have

-4 |  1    5    -16    -80

           (-4)

      1

Add

-4 |  1    5    -16    -80

           (-4)

      1     1

Multiply by -4

So, we have

-4 |  1    5    -16    -80

           (-4)  (-4)

      1     1

Add

So, we have

-4 |  1    5    -16    -80

           (-4)  (-4)

      1     1     -20

Multiply by -4

-4 |  1    5    -16    -80

           (-4)  (-4)    80

      1     1     -20

Add

So, we have

Multiply by -4

-4 |  1    5    -16    -80

           (-4)  (-4)    80

      1     1     -20    0

This means that,

Quotient = x^2 + x - 20

Remainder = 0

Expand x^2 + x - 20

x^2 + x - 20 =x^2 + 5x - 4x - 20

Factorize

x^2 + x - 20 = (x + 5)(x - 4)

Recall that the initial root is

x = -4

Rewrite as

x + 4 = 0

So, we have the complete factor to be

f(x) = (x + 4)(x + 5)(x - 4)

Set to 0

(x + 4)(x + 5)(x - 4) = 0

Solve for x

x = -4,  = -5 and x = 4

Hence, the factors are (x + 4), (x + 5) & (x - 4) and the solution is x = -4,  = -5 and x = 4

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The Subject formula for r= 3t/ ( t- 1)

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given:

t= r/r-3

Now, writing the above equation for r

tr - 3t = r

tr - r= 3t

r( t - 1)= 3t

r= 3t/ ( t- 1)

Hence, the Subject formula for r= 3t/ ( t- 1)

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The answer is x = [tex]\frac{1}{25}[/tex].

5√x + 7 = 8

⇒ 5√x = 8 - 7

⇒ 5√x = 1

⇒ √x = [tex]\frac{1}{5}[/tex]

Squaring both sides, we get,

⇒ x = [tex]\frac{1}{25}[/tex]

Answer) x = [tex]\frac{1}{25}[/tex]

         An extraneous solution refers to the roots of the transformed equation. This root is not the root of the original equation, as the original equation has been transformed to create another equation from which the answer has been found. The original equation has been excluded from the domain of the function.

         In the given equation, I have tried to take the equation in the value of x, and hence, after squaring the value, the root has been found.

         Since the square root function is used, we get a single value for the variable x.

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Total number of muffins you would have to sell to make at least $ 250.00 in sales is 100 muffins.

The sales amount can be find by the total sales. That is , if there are n products to sell and selling amount is x rs. then we can easily find the total sales by multiplying them and by this total sales we can easily find the number of items sold per units and vice versa.

In the question given,

amount (A) = $ 250.00

Now take any of two values from table ,

Choose any two points and calculate the slope:

slope = [tex]\frac{50 - 20}{20 - 8}[/tex] =  2.5

thus, y = 2.5x

we can also write this as,

A = 2.5 m , where m is number of muffins

Therefore, m = 250 / 2.5 = 100

Hence, Total number of muffins to sell are 100 .

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The complete question is:

In a bake sale, you recorded the number of muffins sold and the amount of sales in a table as shown.

a. What is a function that relates the sales and the number of muffins?

b. How many muffins would you have to sell to make at least $ 250.00 in sales?

The slope of the line with equation - 6y = 2x + 7 is - 1/3.

The slope of a line is the rise-to-run ratio or the rise divided by the run. It gives information about a line's slope in the coordinate plane.

The general equation of a straight line is y = mx +c where m is the slope of the line.

Now,

Consider the equation of the line,

- 6y = 2x + 7

Dividing each side of the equation by 6.

( - 6y/ 6 ) = ( 2x / 6 ) + ( 7/6 )

- y = x/ 3 + 7/ 6

Multiplying each side of the equation by - 1,

- y × - 1 = x/ 3 × -1 + 7/ 6 × - 1

y = - x/3 - 7/6

y = - (1/3) × (x) - 7/6

Now comparing the equation with the general equation y = mx + c.

We get, the slope of the line as:

m = - 1/3

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The result of simplifying each number 16¹.⁵ using the exponent rules is 2⁽²⁰⁾

To solve this exercise we have to resolve algebraic operations following the exponent rules.

16¹.⁵

Base= 16=  2⁴

The base number 16 is the same as: 2⁴, then we get:

(2⁴)¹.⁵

Using the power of a power rule that indicates that: the exponent result will be the multiplication of these exponents, we have:

4⁽⁴*¹*⁵⁾

4⁽⁴*⁵⁾

2⁽²⁰⁾

In mathematics an exponent is the number of time that a number, called (base) is multiplied by itself. It is also called, power or index.

Example: 3² = 3*3 = 9

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So, the correct equation is equivalent to the x + 9 = ±5. The third option is correct.

What is the quadratic equation?

It is a polynomial that is equal to zero. Polynomial of variable power 2, 1, and 0 terms are there. Any equation having one term in which the power of the variable is a maximum of 2 then it is called a quadratic equation. The general form of the quadratic equation is ax² + bx + c.

Given

(x + 9)² = 25 is a quadratic equation.

How to find the equation results from taking the square root of both sides?

(x + 9)² = 25 is a quadratic equation.

Taking square root on both sides.

(x + 9) = √25

(x + 9) = ±5

So, the equation is equivalent to the x + 9 = ±5.

Thus, the third option is correct.

The number of girls and boys in the senior class is 240 and 150 respectively.

let

1/3x + 1/2y = 205

1/2x + y = 370

From (2)

y = 370 - 1/2x

1/3x + 1/2y = 205

1/3x + 1/2(370 - 1/2x) = 205

1/3x + 185 - 1/4x = 205

1/3x - 1/4x = 205 - 185

(4x-3x) / 12 = 20

x/12 = 20

x = 20 × 12

x = 240

1/2x + y = 370

1/2(240) + y = 370

120 + y = 370

y = 370 - 120

y = 150

Therefore, the number of girls and boys in the senior class is 240 and 150 respectively.

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The linear function on a coordinate plane passes through (minus 5, 4), (0, 2), and (5, 0) to form a blue shaded portion at the top.

Option (c) is correct.

The relation between two expressions that are not equal, employing a sign such as ≠ ‘not equal to’, > ‘greater than’, or < ‘less than’.

Given:

The given inequality is

y< - 2/5x + 2

According to given question we have

The  inequality is

y< - 2/5x + 2

To solve the inequation by putting the value of

At x=0

y< - 2/5x + 2

y<-2/5*0+2

y<2

The points are (0,2).

At x= 5

y< - 2/5x + 2

y<-2/5*5+2

y<-2+2

y<0

The points are (5,0).

At x= -5

y< - 2/5x + 2

y<-2/5*-5+2

y<2+2

y<4

The points are (-5,4).

Therefore, the linear function on a coordinate plane passes through (minus 5, 4), (0, 2), and (5, 0) to form a blue shaded portion at the top.

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Answer: The linear function on a coordinate plane passes through (minus 5, 4), (0, 2), and (5, 0) to form a blue shaded portion at the top.

Option (c) is correct.

What is inequality?

The relation between two expressions that are not equal, employing a sign such as ≠ ‘not equal to’, > ‘greater than’, or < ‘less than’.

Given:

The given inequality is

y< - 2/5x + 2

According to given question we have

The inequality is

y< - 2/5x + 2

To solve the inequation by putting the value of

At x=0

y< - 2/5x + 2

y<-2/5*0+2

y<2

The points are (0,2).

At x= 5

y< - 2/5x + 2

y<-2/5*5+2

y<-2+2

y<0

The points are (5,0).

At x= -5

y< - 2/5x + 2

y<-2/5*-5+2

y<2+2

y<4

The points are (-5,4).

Therefore, the linear function on a coordinate plane passes through (minus 5, 4), (0, 2), and (5, 0) to form a blue shaded portion at the top.

Step-by-step explanation:

Answer:

28

Step-by-step explanation:

If 1/6 of the markers are red (8) then 8 * 6 = 48 meaning Oona has 48 markers, 8 of them being red.

1/4 of 48 is 12, so 12 yellow markers

If the rest are blue, then 8+12 = 20 and 48-20=28

There are 28 blue markers

The answer to the expression is   [tex]= x^{2}[/tex]

The phrase simplifies manner to make something simpler to do or recognize. So, by decreasing or simplifying the fractions method we make the fraction as simple as feasible. We do this by dividing the numerator and the denominator with the aid of the most important range that could divide into both numbers precisely.

The only form is likewise known as the decreased form of a fraction. for instance, ¾ is the most effective shape of a fraction that has a not unusual thing equal to 1. but 2/4 is not the most effective form, because 2/four can in addition be simplified and written as ½.

Step one is to perceive a common issue between the denominator and numerator. The denominator and numerator are each divided by the commonplace thing. The department operation is repeated until there are not any extra elements. The fraction is said to be simplified if no greater factors go out.

apply exponent rule [tex](a^{b} )^{c} = a^{bc}[/tex]

assuming a≥ 0

[tex]x^{1/5} . 10[/tex]

[tex]\frac{1}{5} .10 =2[/tex]

[tex]= x^{2}[/tex]

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The value of constant  variation is √16.

A mathematical constant is a significant integer that has a steady value and is specified by a precise definition.

relationship between two variables in mathematics that may be represented by an equation where the product of their products equals a constant

Inverse variation is y = k. 1/x

given y = √18

x = √2

So, √8 = k. 1/√2

So, the value of k = √16

We can conclude that the value of constant variation is √16

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The median rating assigned by the agents is  mathematically given as

X=4.35

This is further explained below.

Generally,4.35 is the middle rating that the agents have given the product.

In light of the fact that an airline requested that its agents rate the level of convenience offered by 114 flights departing from one of its hub locations on a scale ranging from 1 to 7, the following graph has to be evaluated in order to discover what the median rating that the agents gave was:

X=(8 x 1 + 11 x 2 + 19 x 3 + 17 x 4 + 23 x 5 + 25 x 6 + 11 x 7) / 114

X=(8 + 22 + 57 + 68 + 115 + 150 + 77) / 114

X=497/114

X=4.35

In conclusion, 4.35 is the median rating that the agents have given the product.

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Answer:lm

Step-by-step explanation:

Answer:

f(1) = 1 , f(-2) = -5, f(5) = 9

Step-by-step explanation:

f(x) = 2x-1

then,

f(1) = 2×1-1

= 2-1

= 1

f(-2) = 2×(-2)-1

= -4-1

= -5 ( when sign is both negative the values are added but sign is kept negative)

f(5) = 2×5-1

= 10-1

= 9

The simplified form of the expression which is as described by the word phrase given in the task content is; 83.4.

In order words, when the sum of 5.5 and 4.3 all divided by the quantity 4 end quantity times the quantity 2 minus 6 end quantity squared plus 5 is being simplified, it gives 83.4

According to the task content, it follows that the expression given by the word phrase and required to be simplified is;

{(5.5 + 4.3)/4} × (2-6)² + 5.

Hence, it follows from PEMDAS guidelines that the parentheses be solved first as follows;

{(9.8)/2} × (-4)² + 5

= 4.9 × 16 + 5

Hence, by multiplying first, we have;

= 78.4 + 5

= 83.4.

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The simplified form of the expression which is as described by the word phrase given in the task content is; 83.4.

In order words, when the sum of 5.5 and 4.3 all divided by the quantity 4 end quantity times the quantity 2 minus 6 end quantity squared plus 5 is being simplified, it gives 83.4

What is the simplified form of the word phrase given in the task content?

According to the task content, it follows that the expression given by the word phrase and required to be simplified is;

{(5.5 + 4.3)/4} × (2-6)² + 5.

Hence, it follows from PEMDAS guidelines that the parentheses be solved first as follows;

{(9.8)/2} × (-4)² + 5

= 4.9 × 16 + 5

Hence, by multiplying first, we have;

= 78.4 + 5

= 83.4.

After solving the given inequality the answer is logx+5log₁₀(x-1) ≥ 3.

So,

Given: logx+5 log(x-1) ≥ 3

logx+5 log(x-1) ≥ 3 ⇒ logx+5log₁₀(x-1) ≥ 3

Therefore, after solving the given inequality the answer is

logx+5log₁₀(x-1) ≥ 3.

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In the given function if csc = 13/5 then:

So,

cscθ = 13/5 ⇒ 1/sinθ = 13/5

When both sides are flipped:

Tangent is found by knowing that 13 is the hypotenuse because it is the longest side, and 5 is "opposite," so 12 is "adjacent."

And because cosine is adjacent/ hypotenuse, the equation is:

Secθ is the inverse of cos theta, so it is as follows:

So, (B) sin= 5/13 and (D) tan=5/12 are correct.

Therefore, in the given function if csc = 13/5 then:

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The result of simplifying the expression  y⁵/₇ / y³/₁₄  using the exponent rules is [tex]\sqrt{}[/tex](y)

To solve this exercise we have to resolve algebraic operations following the exponent rules.

[(y)⁵/₇] / [(y)³/₁₄]

Using the quotient that indicates that: the exponent result will be the subtraction of these exponents, we have:

(y)⁵/₇ ⁻ ³/₁₄

(y) ⁽¹⁰⁻³⁾/¹⁴

(y) ⁽⁷/¹⁴)

(y) ¹/²

As we have a fractional exponent, you must convert the exponent to root:

[tex]\sqrt{}[/tex](y)

In mathematics an exponent is the number of time that a number, called (base) is multiplied by itself. It is also called, power or index.

Example: 3² = 3*3 = 9

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1 yard is added to the field position on average for each running play.

In plain English, an average is a single number chosen to represent a group of numbers; it is often the sum of the numbers divided by the number of numbers in the group. For instance, based on the information provided, the average of the digits 2, 3, 4, 7, and 9 is 5.

Detailed explanation:

A data set's average can be calculated by:

Average = sum of data values/ total number of values

Given: The total number of plays =6

Sum of the change in field position resulting from each play is given by :-

sum =-3+2+(-1)+(-2)+(-3)+(1)

         =-6

Now, the average change in field position per running play is given by :-

Average = sum/total plays

               =-6/6

               =-1

Hence, the average change in field position per running play is -1 yard per play.

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Combining the like terms, the equivalent expressions are given as follows:

To add or subtracted symbolic expressions, in which the terms are accompanied by letters, we combine the like terms, that is, we add or subtract terms that have the same letter.

One example is:

a + b + 3a + 20b = 4a + 21.

As 1 + 3 = 4, 1 + 20 = 21.

Hence the equivalent expressions for the first space is:

-15a - 3b + 16a + 4b = a + b.

For the second space, it is:

2a - 4b - 3a + 6b + 6 = -a + 2b + 6.

For the third space, it is:

2a + 2b - 6a -3 - 2b + 6 = -4a + 3.

For the fourth space, it is:

3a - 6b - 6 + 2a + 6b + 2 = 5a - 4.

For the fifth space, it is:

3a + 4a + 2b - 4 - 5b - 10 = 7a + 7b - 14.

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Answer:

The inequality that describes the problem for the given equation that is 12 + x ≤ 21 is x = 9.

Step-by-step explanation:

It is given that a shuttle bus to Willow Creek Mall has enough seats for 21 people to ride. Right now, there are 12 people on the bus.

It is further provided that,  let x represent how many more people can ride on the bus and we need to find which inequality describes the problem for the given equation that is 12 + x ≤ 21.

Now,

based on the above-mentioned conditions it can be formulated that;

=> 12 + x = 21

After rearranging the terms;

=> x = 21 - 12

=> x = 9

Therefore, the inequality that describes the problem for the given equation that is 12 + x ≤ 21 is x = 9.

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[tex]\begin{array}{ccll} miles&gallons\\ \cline{1-2} 350 & 20\\ 875& g \end{array} \implies \cfrac{350}{875}~~=~~\cfrac{20}{g} \\\\\\ \cfrac{2}{5}=\cfrac{20}{g}\implies 2g=100\implies g=\cfrac{100}{2}\implies g=50[/tex]