what is an equation of the line that passes through the points (5,-6) and (-5,-2)

Answer:

[tex] \sf {\large{4\pi }}[/tex]

Step-by-step explanation:

Circumference of a circle ⭕ = [tex] 2 \pi r [/tex]

Where,

r = d/2

d means diameter

r = 4/2 = 2

So, substitute to equation C = 2πr

C = 2πr

C = (2r)π

C = (2•2)π

C = 4π

Slope of one of the dotted lines: -1/3

Slope of the line of reflection:​ 3

From given figure, we can observe that the line of reflection passes through points (2, 8) and (0, 2)

We need to find the slope of the line of reflection and any dotted line.

Using the formula of slope, the slope of the line of reflection would be,

m1 = (y2 - y1)/(x2 - x1)

m1 = (2 - 8)/(0 - 2)

m1 = -6 / (-2)

m1 = 3

The dotted lines are perpendicular to the line of reflection.

Let m2 be the slope of any dotted line.

We know that the product of slopes of any perpendicular lines is -1.

so, m1 * m2 = -1

3 * m2 = -1

m2 = -1/3

So, the slope of dotted any line = - 1/3

Therefore,  Slope of one of the dotted lines: -1/3

Slope of the line of reflection:​ 3

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Answer:

  28.  Correctly used

  30.  Incorrectly used

Step-by-step explanation:

You want to know if the word "function" is correctly used in the following cases:

28. The sales tax on a purchased item in a given state is a function of the selling price.

30. A function pairs each chaperone on a school trip with 10 students.

There is exactly one value of sales tax associated with any given selling price. This means the ordered pair (selling price, sales tax) will be unique for any given selling price. Hence, the relation between selling price and sales tax is a function. The word function is used correctly in describing this relation.

There are 10 different students associated with any given chaperone. This means there will be multiple (chaperone, student) ordered pairs for any given chaperone: (c1, s1), (c1, s2), ..., (c1, s10), (c2, s11), (c2, s12), ..., (c2, s20), .... The relation between chaperones and students is not a function. The word function is used incorrectly in describing this relation.

The perimeter of a rectangular garden with width w = 4x - 6 and length l = 2x + 4 is given by: 2w + 2l = 2(4x - 6) + 2(2x + 4) = 8x - 12 + 4x + 8 = 12x - 4

Answer: option B

Answer:

x = -7

Step-by-step explanation:

Hi!

Ok we know a few things here :

x + 37 + x + 67 + 90 = 180

2x + 104 = 90

2x = -14

x = -7

Hope this helps!

Have a great day! :)

The Markup percentage based on cost if the wholesaler paid $780 for the guitar is 79%

Given,

The cost price of the guitar = $780

The selling price of the guitar = $1396.20

We have to find the markup percent based on the cost;

Markup percentage;

The gross profit of a unit, which is its sales price less its cost to produce or acquire for resale, is divided by the unit's cost to determine the markup %.

Markup percent = (Selling price - cost price) / cost price x 100

= (1396.20 - 780) / 780 x 100

= 616.20 / 780 x 100

= 0.79 x 100

= 79%

That is,

The Markup percentage based on cost if the wholesaler paid $780 for the guitar is 79%

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The Explicit Formula is a(n) = 27×[tex](\frac{2}{3})^n^-^1[/tex]

Given,

The first four terms are 27, 18, 12, 8.

Find the common ratio:

To do this, let that ratio = r,

and write and solve 27r = 18.  Thus, r = 2/3.

The general explicit formula for this sequence is:

a(n) = a(1)*(2/3)^(n - 1),

or, since a(1) = 27,

a(n) = 27×[tex](\frac{2}{3})^n^-^1[/tex]

Hence, The Explicit Formula is a(n) = 27×[tex](\frac{2}{3})^n^-^1[/tex]

What is Explicit formula For sequence?

The explicit formula for an arithmetic sequence is an = a + (n - 1)d, and any term of the sequence can be computed, without knowing the other terms of the sequence. In general, the explicit formula is the nth term of arithmetic, geometric, or harmonic sequence.

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The Pythagorean Theorem states that the squares on the hypotenuse of a right triangle, or, in standard algebraic notation, a² + b² = c².

The Pythagorean Theorem states that the squares on the hypotenuse (the side across from the right angle) of a right triangle, or, in standard algebraic notation, a² + b² = c².

The Pythagorean theorem, sometimes known as Pythagoras' theorem, is a fundamental relationship between a right triangle's three sides in Euclidean geometry. According to this statement, the areas of the squares on the other two sides add up to the size of the square whose side is the hypotenuse.

First use the Pythagorean theorem. a² + b² = c²

then take the first derivative of it to get

2a(a') + 2b(b') = 2c(c')

Now figure out how far the train is after 4 seconds

6(4)=24

70² + 24² = c²

c = 74

Now plug in the variables you know

2(70)0 + 2(24)6 = 2(74)c' and solve for c' or the rate of change of c.

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Answer:

5x-4

Step-by-step explanation:

1st , 3rd & 5th choices

Step-by-step explanation:

perpendicular line would have a slope that is a

negative reciprocal

so if the slope is 3 then a perpendicular line would have a slope of -1/3

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

make the line look like y = mx + b

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

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

y = 1/3x + 2/3 + 3/3

y = 1/3x + 5/3

m = 1/3

perpendicular line has a slope of

m = -3

For the given function

The sum of all angles = 360°

So,

So, the difference between x and y will be:

So, the answer will be:

∠x is 91° smaller than ∠y

Question: Write the system of linear equations represented by the augmented matrix to the right use W, X, Y and Z for the variables :

Solution:

An augmented matrix is equivalent to a system of linear equations. In this case, the given matrix is represented by the following system of linear equations:

-1 w - 3x +5y +2z = 13

0w + 1x + 3y + 0z = 10

0w + 0x +y - 1z = 3

1w - 3x + 0y + 0z = -2

this is equivalent to:

w - 3x +5y +2z = 13

x + 3y = 10

y - z = 3

1w - 3x = -2

So that, the correct answer is:

w - 3x +5y +2z = 13

x + 3y = 10

y - z = 3

1w - 3x = -2

Answer:

2 times 1/4 = 1/2 or 0.5

Step-by-step explanation:

Step 1: Setup

First of all, note that 2 is the same as 2/1 since 2 divided by 1 is 2. Therefore, start by setting up the problem like this:

2/1 x 1/4

Step 2: Multiply

Multiply the numerators together (2 x 1 = 2) and multiply the denominators together (1 x 4 = 4) and make it into one fraction like so:

2/4

Step 3: Minimize

The greatest common factor of 2 and 4 is 2. Minimize the fraction by dividing the numerator and the denominator by its greatest common factor to get the answer as follows:

1/2

Based on the percentage of games played at home by the team, and the percentage win rate, the probability that the team wins is 63.05%

First, find the probability that the team wins playing at home:

= Percentage win rate at home x Percentage played at home

= 83% x 65%

= 53.95%

Then find the probability of winning away:

= Percentage win rate away x Percentage played away

= 26% x (1 - 65%)

= 9.1%

The probability the team wins is:

= 53.95 + 9.1

= 63.05%

In conclusion, the probability of the team winning at home and the probability of them winning away, can be summed up to find the probability of the team winning which is 63.05%.

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The △ABE is congruent to △CDE (△ABE ≅ △CDE) under AAA, ASA, SSS, and SAS conditions.

So, △ABE ≅ △CDE:

Therefore, the △ABE is congruent to △CDE (△ABE ≅ △CDE) under AAA, ASA, SSS, and SAS conditions.

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The value of interior angle is 60.

What is triangle?

A triangle is a simple polygon with 3 sides and 3 interior angles. It is one of the basic shapes in geometry in which the 3 vertices are joined with each other and it is denoted by the symbol.

What is interior angle?

In a triangle, there are three interior angles at each vertex. The sum of those interior angles is always 180°. The bisectors of these angles meet at an point known as incenter. As the sum of interior angles of a triangle is 180°, there is only one possible right angle or obtuse angle possible in each triangle.

The sum of interior angle is 180

Given angles is 30, 90, x.

Therefore, sum is given by

90 + 30 + x = 180

120 + x = 180

x = 180-120

x = 60

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We are told that Julia keeps 255 masks on the wall and 45 on the display case, this means in total the number of masks she has is

The number of masks Julia keeps on the wall is 255 masks; therefore, the percentage of fo masks on the wall is

Hence, Julia keeps 85% of her mask collection on her wall.

The slope of the line that is parallel to 8x + 9x = 3 is: -8/9.

If two lines are parallel to each other, their slope values is equal to each other. This means the value of "m" in their equation expressed in slope-intercept form as y = mx + b, is the same.

Given the equation of a line in standard form as, 8x + 9y = 3, rewrite this in slope-intercept form:

8x + 9y = 3

8x + 9y - 8x = -8x + 3 [subtraction property of equality]

9y = -8x + 3

9y/9 = -8x/9 + 3/9 [division property of equality]

y = -8/9x + 1/3

The slope of the equation is -8/9. Therefore, the slope of the line that is parallel to the equation 8x + 9y = 3 will also be: -8/9.

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The equations of each of the given lines are:

Line a is: x = -4

Line b is: x = 4

Line c is: y = 4

Line d is: y = -2

Line e is: y = -¾x + 1

If we determine the slope value, m, and the y-intercept value, b, the equation of a line can be written as y = mx + b in slope-intercept form by plugging in the values of the determined variables.

For a vertical line, the equation is expressed as x = b, where b is the x-intercept of the line.

For a horizontal line, the equation would be y = b, where b is the line's y-intercept value.

Equation of line a (vertical line):

The x-intercept is -4. This means that, the equation of line a is: x = -4

Equation of line b (vertical line):

The line's x-intercept is 4. To write the equation of the line, substitute the value of the x-intercept into x = b.

Therefore, the equation of line b is: x = 4

Equation of line c (horizontal line):

The y-intercept (b) = 4. Substitute the b = 4 into y = b.

The equation of line c is: y = 4

Equation of line d (horizontal line):

y-intercept (b) = -2. Substitute b = -2 into y = b.

Equation of line d is: y = -2

Equation of line e:

Slope (m) = rise/run = -3/4

y-intercept (b) = 1

To write the equation of the line, substitute m = -¾, and b = 1 in the equation y = mx + b

y = -¾x + 1

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We can see the next function:

And we need to translate this function 5 units down, which results in the function g(x).

To find the rule for g(x), we can follow the next steps:

1. We know that the general rule for a function translated k units down is given by:

2. Then if we translate the original function by 5 units down, we will have that:

3. Therefore, g(x) will be:

Hence, in summary, we have that the rule for g(x) is g(x) = 3x + 4 (option A).

Answer:

[tex] {2x}^{2} + 7[/tex]

so hope it helps

Step-by-step explanation:

that is not mathematics, and I am not sure, if you listed everything, but the result to such a loop is

25811

because it first prints the Imuran content of c (2).

then it increases the content of c by 3. c is now 5

then it checks that 5 is still smaller than 12 (yes it is), and it prints 5.

then it prints 8. then 11. and then c becomes 14 and is therefore larger than 12. and the loop ends.

I don't know what your particular print command does, but I assume it is just a basic "bring the parameter to output". in that case it will write all numbers right after the previous number.

hence : 25811

A painter has three partially filled paint cans.

The first contains 1 7/8 gallons

The second contains 1 1/5 gallons

The third contains 1 3/4 gallons

The total amount of paint is the sum of these paint cans.

Now let us add these mixed fraction numbers

As you can see, 4.825 is closest to 5.

Therefore, the correct option would be D

Answer:

height = 12

Step-by-step explanation:

try and use the formula to plug it in and solve for x.

The absolute value function graphed in this problem is given as follows:

A. y = |x - 5| - 4.

An absolute value function of vertex (h,k) is defined as follows:

y = a|x - h| + k.

The leading coefficient a does not influence the vertex of the absolute value function.

The vertex of the graph is the turning point, hence it is given as follows:

(5, -4).

Hence, considering a leading coefficient 1, h = 5 and k = -4, the equation is given as follows:

y = |x - 5| - 4.

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Answer:

The equation is an example of the associative property of addition.

Step-by-step explanation:

Associative property of addition: changing the grouping of addends does not change the sum.

For example: A+(B+C) = (A+B)+C.

Answer:

The 40 lb bag is cheaper by $4

Step-by-step explanation:

10 x 4 = 40

7 x 4 = 28

If you bought the 10 lb bag 4 times, you'd spend more money than just buying the 40 lb bag once.

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If you rent an apartment that cost $1000 per month during the first year, but the rent is set to go up 8% per year, the the rent amount  of the apartment during the 5th year of living in the apartment is $1469.32

The initial rent amount = $1000

The percent of rent increase each year = 8%

Time period = 5 years

Here we can use the compound interest equation

A = [tex]P(1+\frac{r}{100})^t[/tex]

Substitute the values in the equation

The rent amount  of the apartment during the 5th year of living in the apartment = [tex]1000(1+\frac{8}{100})^5[/tex]

= $1469.32

Hence, if you rent an apartment that cost $1000 per month during the first year, but the rent is set to go up 8% per year, the the rent amount  of the apartment during the 5th year of living in the apartment is $1469.32

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Answer:

D

Step-by-step explanation: