Find the number of possible outcomes for following situation.
Perry chooses from 6 colors and 2 seat designs for his new mountain bike.

By using the fact that the internal angles of a triangle always add up to 180°, we will see that x = 100°.

Remember that the sum of all the internal angles of a triangle is always equal to 180°.

On the image we can see two triangles, let's define the angle at the right as A. and the angle at the left as B

We can write:

A + B + x = 180°

And for the inner triangle the angles give:

A/2 + B/2 + 140° = 180°

So we have a little system of equations:

A + B + x = 180°

A/2 + B/2 + 140° = 180°

If we multiply the second equation by 2 we get:

A + B + 280° = 360°

With the first equation we can write:

A + B = 180° - x

And replace that in the above equation

(A + B) + 280° = 360°

180° - x + 280°  = 360°

Now we can solve this to get the value of x:

180° + 280° - 360° = x = 100°

We conclude that the measure of angle x is 100°

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Simplification of the each sum or difference of the given equation [tex]\frac{d-3}{2d+1}+\frac{d-1}{2d+1}[/tex] is equal to 2(d-2)/(2d+1). Restriction on the variables is given by d≠ (-1/2).

As given in the question,

Given equation is [tex]\frac{d-3}{2d+1}+\frac{d-1}{2d+1}[/tex]

Simplify it by taking least common multiple of the denominator,

[tex]\frac{d-3}{2d+1}+\frac{d-1}{2d+1}\\\\\\=\frac{d-3+d-1}{2d+1}\\ \\=\frac{2d-4}{2d+1}\\ \\=\frac{2(d-2)}{2d+1}[/tex]

Restriction on the variables is given by d≠ (-1/2).

Therefore, simplification of the each sum or difference of the given equation [tex]\frac{d-3}{2d+1}+\frac{d-1}{2d+1}[/tex] is equal to 2(d-2)/(2d+1).Restriction on the variables is given by d≠ (-1/2).

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The negative solution of the given statement is - 4.

A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.

Let the unknown number be 'n'.

∴ When 32 is subtracted from the square of a number, is n² - 32 and the result is 4 times the number which is equal to 4n,

So, n² - 32 = 4n.

n² - 4n - 32 = 0.

n² - 8n + 4n - 32 = 0.

n(n - 8) + 4(n - 9) = 0.

(n - 8)(n + 4) = 0.

n - 8 = 0 Or n + 4 = 0.

n = 8 Or n = - 4.

So, the negative solution is - 4,

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The required value of the constant of proportion is 5.

What is the constant of proportion?

A constant of proportion is illustrated as the ratio which relates two given quantities with each other in the relationship of proportion. Constant of proportion is also called constant of variation, rate of change, and constant ratio.

Solving for the value of constant of variation

When a quantity varies directly with others, then we have a relation, y = kx, where k is the constant of the proportion      —-- 1

Given the relation is y = 5x            —-- 2

On comparing both the equation 1 and 2, we have,

k = 5

Hence, the required value of constant of variation is 5.

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Answer: 1.) 4x+5

2.) 4

Answer:

Y=7x+1

Step-by-step explain

formula is y=mx+b

your slope is your M and the y-intercept is your B

Answer:

[tex]\{x \in \mathbb{R}|-4 \le x \le -8\}[/tex]

Step-by-step explanation:

According to the question, to calculate the probability of the event which states that the spinning a spinner whose number is from one-eight and it is not landing on the number 5.

Therefore, the numbers which are greater than five are (6,7,8).

And the spinner numbers are (1,2,3,4,5,6,7,8).

What is Probability?

The term probability means the study of the occurrence or the outcomes of the event. It is the measurement of the events that occurred during events. And many uncertain events cannot be measured.

Probability of spinning a number greater than 5 is:

P(E) = 3/8

And the probability of tossing a tail on a coin is: 1/2

Now, the total probability is: 3/8 [tex]\times[/tex] 1/2 = 3/16

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The volume of the original block and the volume of the wood removed as polynomials in factored form will be 2x³ + 15x² + 31x + 12 and (x + 2)(x + 1)(2x + 1).

Let the prism with a length of L, a width of W, and a height of H. Then the volume of the prism is given as

V = L x W x H

A carpenter hollowed out the interior of a block of wood as shown on the right.

The volume of the original block will be

V = (2x + 1)(x + 3)(x + 4)

V = (2x + 1)(x² + 7x + 12)

V = 2x³ + 14x² + 24x + x² + 7x + 12

V = 2x³ + 15x² + 31x + 12

The volume of the wood removed as polynomials in the factored form will be

V = (x + 2)(x + 1)(2x + 1)

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Answer:

13 inches

Step-by-step explanation:

Convert to improper fraction and multiply

13/4 x 4/1 (4's cancel out)

13

Answer: (7y+237) / 8 = x

Step-by-step explanation:

So your equation is:
(2y+50) + (7x-248) + (5y-17) + (x+44)
First thing to do is combine all the like terms. Lets start with y. So that would be 2y + 5y= 7y and 50 + -17 is 33. The new equation is:
(7y + 33) + (7x-248) + (x+44)

Now we will combine the x. We will do -248+44= -204
and 7x+x= 8x.
Now our new equation is:

(7y + 33) + (8x+-204)
Now we can subtract 33 from -204. That is 237.
Now we have 7y+237 = 8x
To isolate x we need to divide by 8. That will give us this:
(7y+237) / 8 = x

The equation of the line in point-slope form, which passes through the pair of points located at A(-3 , 12) and B(9 , -4), is y - 12 = -4/3(x + 3).

The equation of a line can be expressed in three different forms: standard form, slope-intercept form, and point-slope form.

The standard form of an equation of a line is expressed as ax + by = c, where a and b, if all possible must be integers, are the coefficients of variable x and y, respectively, and c is a constant. Meanwhile, slope-intercept form is given by the formula y = mx + b, where m is the slope of the line and b is the y- intercept. On the other hand, given the slope m and a point on the line (x , y), we can express the equation in point-slope form, (y - y1) = m(x - x1).

Getting the slope of the two points: A(-3 , 12) and B(9 , -4).

m = (y2 - y1)/(x2 - x1)

m = (-4 - 12)/(9 - -3)

m = -16/12

m = -4/3

Using the point slope form, plug in the values of the slope and Point A to set up the equation.

(y - y1) = m(x - x1)

where m = -4/3 and (x1 , y1) = A(-3 , 12)

(y - 12) = -4/3(x - -3)

y - 12 = -4/3(x + 3)

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When we divide [tex]\frac{pq}{p^{2} -q^{2} } +\frac{q}{q-p}[/tex]  by [tex](p-q) +\frac{4q^{2} -p^{2} }{q+p}[/tex] , we get simplified answer [tex]\frac{1}{3(q-p)}[/tex]

What are algebraic identities?

Algebraic identities are set of rules that are derived from binomial theorem and are used to solve algebraic expressions .

One such identity is [tex]a^{2} -b^{2} =(a+b)(a-b)[/tex]    ....(1)

We have to divide [tex]\frac{pq}{p^{2} -q^{2} } +\frac{q}{q-p}[/tex] by [tex](p-q) +\frac{4q^{2} -p^{2} }{q+p}[/tex], we get

=[tex]\frac{\frac{pq}{p^{2} -q^{2} } +\frac{q}{q-p}}{(p-q) +\frac{4q^{2} -p^{2} }{q-p}}[/tex]

=[tex]\frac{\frac{pq}{(p-q)(p+q) } +\frac{q}{q-p}}{\frac{(p-q)(p+q)+4q^{2} -p^{2} }{q+p}}[/tex]

=[tex]\frac{\frac{pq+q(-1)(p+q)}{(p-q)(p+q) } }{\frac{(p-q)(p+q)+4q^{2} -p^{2} }{q+p}}[/tex]

=[tex]\frac{\frac{pq-q^{2}-pq }{(p-q)(p+q) } }{\frac{p^{2} -q^{2} +4q^{2} -p^{2} }{q+p}}[/tex]

=[tex]\frac{\frac{-q^{2} }{(p-q)(p+q) } }{\frac{3q^{2} }{q+p}}[/tex]

[tex]\frac{-q^{2}(q+p) }{3q^{2} (p-q)(p+q) }=\frac{-1}{3(p-q)}\\ =\frac{1}{3(q-p)}[/tex]

On dividing [tex]\frac{pq}{p^{2} -q^{2} } +\frac{q}{q-p}[/tex] by [tex](p-q) +\frac{4q^{2} -p^{2} }{q+p}[/tex] and simplifying the answer we get [tex]\frac{1}{3(q-p)}[/tex].

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If Tamika receives 20 rewards points just for signing up and she earns 10.5 points for each visit to the movie theater and she needs 167 points for a free movie ticket, then an equation to determine x, the number of visits Tamika must make to earn a free movie ticket is 10.5x + 20 = 167 and the value of x is calculated to be 14.

The number of visits Tamika must make can be determined by using a linear equation with one variable.

As,

reward points for signing up = 20

points for each visit = 10.5

points needed for free movie ticket = 167

If we consider x to be the number of visits required, then the linear equation can be given as,

10.5x + 20 = 167

Solving for x,

10.5x = 167 - 20

10.5x = 147

x = 147/10.5 = 14

Hence, the number of visits Tamika must make to earn a free movie ticket is equal to 14.

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answer:

it would be negative.

explanation:

when you subtract a value from a value, the result will be left to the larger number. if you subtract a larger number from a smaller number, the value will move left but since the value subtracted is more than the number minus itself, you would be subtracting from 0, therefore resulting in a negative number.

The midpoint is at (0,0,0,)

In the given statement is

To find the midpoint of the line segment joining the pair of points

K(2,2,0) and L(-2,-2,0)

Midpoint:

The coordinates of the midpoint of a line segment are the average of the coordinates of the end points.

m = (A +B)/2

If we are given three points and we wish to find the midpoint of those points, we need to use the midpoint formula m =([tex]\frac{x_{1}+x_{2} }{2} , \frac{y_{1}+y_{2} }{2} , \frac{z_{1}+z_{2} }{2}[/tex])

where:

(x1 , y1 ,z1) are the coordinates of the first point:

(x2 , y2 , z2) are the coordinates of the second point:

Now, We are given the three points K(2,2,0) and L(-2,-2,0)

Solving for the midpoint , we have,

m = ([tex]\frac{2+(-2) }{2} ,\frac{2+(-2)_{} }{2} ,\frac{0+0}{2}[/tex])

m = (0 , 0 , 0)

Therefore, the midpoint is at (0, 0, 0,)

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Answer:

PLEASE READ! Is that 7 to the second power? if so, here is your answer: 49

Step-by-step explanation:

-439 is the value which is equivalent to (s circle t) (negative 7).

Given,

s(x) = 2 - x²

t(x) = 3x

We have to find the value which is equivalent to (s circle t) (negative 7)

That is,

(s circle t) (negative 7) : This is a notation for compound function.

A function that takes another function as an argument is referred to as a compound function.

s(t(-7)) is the alternative notation for this compound function, which means that the value obtained from the function t(-7) will be used in the function s. (x).

Now, let's calculate the value of t(-7):

That is,

t(x) = 3x

t(-7) = 3 × (-7) = -21

Next, apply the value of t(-7) for s(x)

That is,

s(x) = 2 - x²

s(t(-7)) = s(-21) = 2 - (-21)^2 = 2 - 441 = -439

That is, -439 is the value which is equivalent to (s circle t) (negative 7).

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Answer:

-14

Step-by-step explanation:

if you add negative fourteen by 8 you would get 6 and you keep the sign of the greater number

The numerical coefficient in -7yz²  from the expression 5x⁶+3xy-7yz²+2y/z   is  -7 .

A Numerical Coefficient in an Algebraic Expression is defined as the integer value which is written along with the variable .

For Example : the numerical coefficient in 7xy is 7 , and in -5x is -5 as 7 and 5 are the only numerical value along with the variable y and x respectively.

In the question ;

the given Algebraic Expression is 5x⁶+3xy-7yz²+2y/z  

the numerical coefficient in -7yz² is -7 , as -7 is the only  numerical value in -7yz² .

Therefore , the numerical coefficient in -7yz²  from the expression 5x⁶+3xy-7yz²+2y/z   is  -7 . the correct option is (d) -7 .

The given question is incomplete , the complete question is

In the expression 5x⁶+3xy-7yz²+2y/z  , which of the following choices is the numerical coefficient in -7yz²  ?

(a) 2

(b) 3

(c) 5

(d) -7

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The area of the triangle is mathematically given as

A=20.8cm

This is further explained below.

The region that is surrounded by the perimeter of the triangle, also known as the three sides of the triangle, is referred to as the area of the triangle.

The space that is encompassed by all three of a triangle's sides is referred to as the triangle's area.

It is computed with the assistance of a variety of formulae that differ according to the kind of triangle, and the results are represented in square units such as centimeters squared, inches squared, and so on.

Generally, the equation for Area the is mathematically given as

A = 1/2 * base * height

Therefore

A= 1/2 * 8 * 5.2

A=20.8cm

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Answer:

37777777777999999999999999

According to the question, to calculate the probability of the event which states that to draw a card from the standard deck but the condition is not getting the diamond.

The total number of the playing cards are [tex]52[/tex]

And total number of diamond cards are [tex]13[/tex]

Therefore, the total number of favorable outcomes in which diamond is not there is [tex]52-13 = 39[/tex]

As per question, the probability can be written as:

P(no diamond card) = [tex]\frac{39}{52} = \frac{3}{4}[/tex]

Hence, the probability of not getting a diamond card is [tex]\frac{3}{4}[/tex].

What is Probability?

The term probability means the study of the occurrence or the outcomes of the event. It is the measurement of the events that occurred during events. And many uncertain events cannot be measured.

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Answer:

       Co ordinate of A' = (1, -4)

       Co ordinate of B' = (3, 2)

       Co ordinate of C' = (4, -2)

Explanation:

The figure of the triangle is shown below.

 If we are finding image of the triangle about X-axis all the x -co-ordinates will remain same, but y co-ordinate will change it's sign.

So, co ordinate of A' = (1, -4)

       Co ordinate of B' = (3, 2)

       Co ordinate of C' = (4, -2)

If you want to buy as many bread rolls as possible from one shop, you should use Paul the baker's shop.

Peter:

Unit rate = $2.30 / 6

= $0.383 per pack of bread rolls

Paul:

Unit rate = $3.50 / 10

= $0.35 per pack of bread rolls

So,

Paul the baker bread rolls is cheaper than Peter the baker bread rolls.

Therefore, If you want to buy as many bread rolls as possible from one shop, you should use Paul the baker's shop.

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The difference between the sum of the measures of the interior angles in an octagon and the sum of the measures of the interior angles in a hexagon is 360°.

Interior angle refers to the angle inside a polygon that is formed by two of its adjacent sides. The sum of the measures of the interior angles of a polygon is given by the equation:

180°(n - 2)

where n is the number of sides

An octagon is a polygon that has 8 vertices and 8 sides. The sum of the measures of the interior angles of an octagon is:

180°(8 - 2) = 180°(6) = 1080°

On the other hand, a hexagon is a polygon that has 6 vertices and 6 sides. The sum of the measures of the interior angles of an octagon is:

180°(6 - 2) = 180°(4) = 720°

Subtracting the sum of the interior angles of the two polygons,

1080° - 720° = 360°

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