Mary and Bart bought a house. They keep track of their house's value over the
years. Which equation represents the trend line for the data and can be used
to make predictions?

The distance between the points (-6, 7) and (-1, -5) is 13 units.

The complete velocity of an object, regardless of direction, is its distance.

Distance is the amount of space an object has traveled, regardless of where it began or concluded.

Knowing an object's distance from us allows us to calculate its true size.

Typically, the following formula is used to determine the distance between two points:

d=((x2 - x1)2 + (y2 - y1)2)

So, the following is the distance formula:

d=((x2 - x1)2 + (y2 - y1)2)

Points are: (-6, 7) and (-1, -5)

Now, put in the values in the above formula and calculate as follows:

d=((x2 - x1)2 + (y2 - y1)2)

d=((-1+6)2 + (-5-7)2)

d=√25+144

d=√169

d=13 units

Therefore, the distance between the points (-6, 7) and (-1, -5) is 13 units.

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Answer: 24%

Step-by-step explanation: 48 out of 200 is 24%, meaning that 48 is 24% of 200. To find our answer, we follow two simple steps before we add the percentage symbol, though there can be three steps if we have to round a decimal in a percentage to two digits after the decimal point.

Answer:24%

Step-by-step explanation:

The measure of ∠F is 57 degree.

A figure which is formed by two rays or lines that shares a common endpoint is called an angle. Degree is the unit of measure is used to measure the magnitude of an angle.  A triangle is a three-sided polygon that consists of three edges and three vertices. The most important property of a triangle is that the sum of the internal angles of a triangle is equal to 180 degrees.

cos F = (e² + g² - f²)/2eg

cos F = (2.6² + 8.3²- 7.2²)/2(2.6)(8.3)

  = 0.5516

∠F = arccos 0.5516

∠F = 57° (rounded to the nearest degree)

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Option C better choice, the measurement of the line segment RS is equal to x+5.which is difference of segment TR and TS.

A line segment is a part of a straight line that is bounded by two distinct end points and contains every point on the line that is between its endpoints. The length of a line segment is given by the Euclidean distance between its endpoints. A closed line segment includes both endpoints, while an open line segment excludes both endpoints.

There is a point S between the line segments T and R, measure of segment TR is 4x+1 and the measure of segment TS is 3x-4.

we shall find out the measure of RS.

so, length of RS is equal to difference of TR and TS.

Mathematically,

RS=TR-TS

RS=(4x+1) -(3x-4)

RS=4x+1-3x+4

RS=x+5

Hence the length of RS is equal to x+5.

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The surface area of a square pyramid with base length of 3 ft. and height of 6 ft. is 45 square ft. (option A)

The formula for the surface area of a square pyramid is given by:

A = a² + a  √(a² + 4h²)

Where:

A = surface area

a = base length

h = height of the pyramid

In the given problem, the side length of the base = W = L = 3 ft.

Hence,

a = 3 ft.

h = 6 ft.

Plug these parameters into the formula:

A = 3² + 3 x √(3² + 4x6²)

A = 9 + 3 x √153

A = 45 ft². (option (A)

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Answer:

(x+8)^2=40

Step-by-step explanation:

x^2+16x+24=0.

Well, to solve for this, you do:

1. (16/2)^2 to find what number should be in place of 24.

That, by the way, is 64.

2. There's no 64! We have to add 64-24 on both sides, which makes the equation

x^2+16x+64=40.

3. Since we know that (16/2)=8, using the completing the square formula, you know that it's going to be a variation of (x+8)^2 or (x-8)^2.

As we are adding for the middle term, it must be (x+8)^2.

4. Answer: (x+8)^2=40.

Sorry if this is too late :)

The rules of logarithms are as: 

1. Rule of product.

2. Rule of division.

3. The Power/Exponential Rule.

4. A new fundamental rule.

The alternate format for writing exponents is with logarithms. A number appears base-based logarithm is approximately equivalent to another number. A logarithm performs exponentiation's exact opposite function.

1. Rule of product: According to this rule, adding the individual logarithms of two logarithmic values results in the multiplication of those values.

[tex]Log_b (mn)= log_b m + log_b n[/tex]

2. Rule of division: The difference between each logarithm is equivalent to the division of two logarithmic values.

[tex]Log_b \left(\frac{m}{n}\right)= log_b m - log_b n[/tex]

3. The Power/Exponential Rule: According to the exponential rule, the exponent times the logarithm of m's logarithm is equivalent to m's logarithm with a reasonable exponent.

[tex]Log_b (m^n) = n log_b m[/tex]

4. A new fundamental rule:

[tex]Log_b m =\frac{log_a m}{log_a b}[/tex]

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No, Robert has traveled 1,000 meters (600 + 400), or 0.62 miles, by walking 400 meters to and from the store and 600 meters to and from the library.

Miles are used to measure distance. The distance is 1.609 kilometers equivalent. 1,760 yards make up one mile.

The Roman mille passus, sometimes known as the "thousand paces," was 5,000 Roman feet long and served as the model for the statute mile, which is 5,280 feet. Five Roman feet are equivalent to one Roman pace, which is the distance between the heel of one foot being elevated to the heel being laid down again following a step by the other foot.

Assumed distances from home to four different locations are as follows:

To school = 350 meters

To church = 240 meters

To store = 200 meters

To library = 300 meters

Therefore, for Robert to walk a mile, he needs to cover 1,609 meters.

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Answer:

c)   (0,6) and (-5,-9)

Step-by-step explanation:

if you graph the system you will get a line and a parabola

the two points at which they intersect will be (0,6) and (-5,-9)

The value of the slope indicates that the average cost of a haircut is increased by 2 US dollars each year.

What is the average cost?

We are aware that it is determined by the cost-to-production ratio. The sum of the fixed cost and the variable cost is referred to as the total cost, which is also known as the unit cost. As a result, Average Cost is calculated as Total Cost/Number of Units or (Fixed Cost + Variable Cost)/Number of Units.

Here, we have

In this case, we use the linear function y = 2x + 25, where x is the time after 1985, measured in years, and y is the average cost of a haircut. The slope of the model is m = 2 USD yr.

It means that the average cost of a haircut increased by 2 every year after 1985.

In 1985, y=0, and the cost is 25

In 1986, y=1, and the cost is 25+2 = 27

In 1987, y=2, and the cost is 25+4 = 29

and so on.

Hence, the value of the slope indicates that the average cost of a haircut is increased by 2 US dollars each year.

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1/2 is not a whole number.

We know that the whole numbers are numbers that include natural numbers and zero.

That is the set of whole numbers is denotes by W = N ∪ {0},

here N represents the set of natural numbers.

And we know that the natural numbers are nothing but the numbers which can be counted and start from 1 and ends at infinity.

i.e., the set of natural numbers N = {1, 2, 3, . . ., ∞}

and the set of whole numbers W =  {0, 1, 2, 3, . . ., ∞}

A set of whole numbers do not include fractions, decimals, or negative integers.

Here, 1/2 is a fraction (number of the form p/q where q ≠ 0)

So, given number 1/2 is not a whole number.

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Answer:

Step-by-step explanation:

Choose two pairs of data from the data table and calculate the slope (m = Δy/Δx):

(430 - 295) / (6 - 3) = 135/3 = 45

She adds 45 cards to the collection every week.  This is like finding the slope of the line you would graph using this data.  

To find how many cards she starts out with, use the point-intercept form

y - y1 = m(x - x1)    m = 45, use the point (3, 295)

y - 295 = 45(x - 3)

y - 295 = 45x - 135

y = 45x + 160   now the equation is in slope-intercept form y = mx + b

The y-intercept (b) is where x = 0.  So, she had 160 cards to start with.

The given point and parallel to the given line is: y - 5 = 0 (Slope is 0)perpendicular to the given line is: y - 5 = -1/6x (Slope is -1/6).

Slope-intercept is a form of linear equation which is written in the form y = mx + b, where m is the slope of the line and b is the y-intercept. This form of equation is useful for graphing linear equations, as it allows the user to quickly determine the slope and the y-intercept of the equation, which makes it much easier to plot on a graph. It is also helpful for solving linear equations, as the slope and the y-intercept can quickly be determined.

(a) The slope-intercept form of the equation of the line through the given point and parallel to the given line is y = 5. This is because the given line has a slope of 0 and the given point has a y-coordinate of 5, which is the same as the y-intercept of the parallel line.

(b) The slope-intercept form of the equation of the line through the given point and perpendicular to the given line is y = -6x + 5. This is because the given line has a slope of 0 and the line perpendicular to it has a slope of -1/0, which is -infinity. This means that the slope of the perpendicular line is -6 and its y-intercept is 5, which is the same as the given point's y-coordinate.

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The proof that the square root of 2 is irrational can be shown using proof by contradiction.

Assume that the square root of 2 is rational, meaning that it can be expressed as the ratio of two integers (p/q, where p and q are integers and q is not equal to zero).

This means that:

√2 = p/q, where p and q are integers and q is not equal to zero.

Squaring both sides of the equation:

2 = p^2/q^2

multiply both sides by q^2

2q^2 = p^2

Now, since p and q are integers, p^2 and q^2 are also integers.

Therefore, 2q^2 is an even integer.

However, if 2q^2 is an even integer, q^2 is also an even integer, which means that q is even.

Therefore, p and q have a common factor of 2. But, this contradicts the assumption that p and q have no common factors other than 1.

Therefore, our assumption that the square root of 2 is rational must be false.

Hence, we can conclude that the square root of 2 is irrational.

Answer:

To prove that the square root of 2 is irrational, we will use a proof by contradiction. Suppose that the square root of 2 is rational, which means that it can be expressed as a fraction a/b, where a and b are integers with no common factors. Then, we can square both sides of this equation to get:

2 = (a/b)^2 = a^2 / b^2

Multiplying both sides by b^2, we get:

2b^2 = a^2

This means that a^2 is an even number, because it is equal to 2 times b^2. Therefore, a must be an even number, because the square of an odd number is always odd. Let a = 2c, where c is an integer. Substituting this into the previous equation, we get:

2b^2 = (2c)^2 = 4c^2

Dividing both sides by 2, we get:

b^2 = 2c^2

This means that b^2 is an even number, and therefore b must also be an even number. However, this contradicts our original assumption that a and b have no common factors. Therefore, our assumption that the square root of 2 is rational must be false, and the square root of 2 is indeed an irrational number.

Answer:

For f(1), it's -14. For determining x, x = -1.

Step-by-step explanation:

For f(1), just plug in 1 to x. -6(1) is -6, + -8 is -14.

For determining x, if you plug in -1, you get -6(-1), which is +6. +6 -8 is -2.

Inconsistent Pair of Linear Equations is the type of system of linear equation which has no solution notice that the two lines are parallel and will never intersect.

What in mathematics is a linear equation?

A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept. Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.

What makes an equation linear?

When a linear equation is graphed, it always produces a straight line since each term in the equation has an exponent of 1. This is the basis for the term "linear equation" being used to describe it.

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Answer:

x=1

Step-by-step explanation:

If y=6x+1, we can substitute that into the original equation, so it would look like 3x+6x+1=10.

Now we just solve for x. Add 3x and 6x to get 9x, and subtract 1 from both sides of the equation, now we have

9x=9, divide both sides by 9 and we end up with x=1.

PS. sorry for the bad handwriting but i attached a photo of how i solved it.

The values of x that are solutions to the equation 10x²-64 36+6x² are x = 5, x = -5, x = -10, and x = 10.

Equation is a statement of equality between two expressions that states that they have the same value. Equations can be used to solve problems, model real world situations and describe relationships between different quantities. Equations can be expressed in many different forms, such as linear equations, quadratic equations, exponential equations and more. Equations are a powerful tool for understanding and describing the world around us.

The solutions to the equation 10x²-64 36+6x² are B. x = 5, C. x = -5, E. x=-10, and F. x= 10. These values represent the x-coordinates of the points in which the equation cuts the x-axis. The equation does not have a solution for x= -√√5 or x = √√√5, so these answers are incorrect.

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Answer:B

Step-by-step explanation: To solve this, we first need to find the ratio of concenrate to water for each mixture. A is 2:3.5, B is 5:8, and C is 0.5:2. Now, we can roughly estimate them. C is .25, B is around .6, and A is around .57. This means that B is the most lemony.

Answer:

3515.3443 grams

There are 20 non-negative integer solutions to the equation 2x1 + 2x2 + x3 + x4 = 12.

The number of non-negative integer solutions to the equation 2x1 + 2x2 + x3 + x4 = 12 is equivalent to the number of solutions to the equation x1 + x2 + x3 + x4 = 6, which is the number of ways to place 6 distinguishable balls into 4 distinguishable boxes. This is equivalent to the number of ways to choose 3 balls to not place in the first box, which is (6 choose 3) = 20. Therefore, there are 20 non-negative integer solutions to the equation 2x1 + 2x2 + x3 + x4 = 12.

The equation 2x1 + 2x2 + x3 + x4 = 12 is equivalent to the equation x1 + x2 + (x3/2) + (x4/2) = 6. The variables x1, x2, x3 and x4 are non-negative integers, thus (x3/2) and (x4/2) are also non-negative integers.

The number of solutions to x1 + x2 + (x3/2) + (x4/2) = 6 is equivalent to the number of ways to place 6 distinguishable balls into 3 distinguishable boxes. This is equivalent to the number of ways to choose 3 balls to not place in the first box, which is (6 choose 3) = 20.

Because each of x1 and x2 are integers and (x3/2) and (x4/2) are integers, it ensures x1, x2, x3, and x4 are also integers. Therefore, there are 20 non-negative integer solutions to the equation 2x1 + 2x2 + x3 + x4 = 12.

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Step-by-step explanation:

3√64/343

3√4^3/7^3

3√(4/7)^3

4/7

Answer:

4/7

Step-by-step explanation:

[tex]\sqrt[3]{\frac{64}{343} }[/tex]

[tex]\frac{\sqrt[3]{64}}{ \sqrt[3]{343} }[/tex]

[tex]\sqrt[3]{64}[/tex] = 4

[tex]\sqrt[3]{343}[/tex] = 7

[tex]\frac{4}{7}[/tex]

Answer:

C. Functional

Step-by-step explanation:

I hope I helped you,

Alex Martin :)

The area of the regular decagon is 496.7 squared unit.

In geometry, a decagon is a ten-sided polygon or 10-gon. The total sum of the interior angles of a simple decagon is 1440°. Regular decagon.

To calculate the area of the decagon, we use the formula below.

Formula:

Where:

Substitute these values into equation 1

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Answer:

Step-by-step explanation:

Firstly, divide the figure into 2

You will have a rectangle on the bottom and a triangle on top. Let's name your shapes by saying that the rectangle is FIG -1 and your triangle is FIG -2

FIG -1

b x h

8 x 11

88 cm^2

FIG -2

b x h / 2

7 x 11 / 2

77/2

38.5 cm^2

Total = 88 + 38.5

        = 126.5 cm^2  

The median weekly income for someone with a bachelor's degree is 1137.006

What is percentage ?

Percentage can be defined as the product of ratio of given value, total value and hundred.

The median weekly income for someone with a high school diploma was $629.00. If they continued their education and obtained abachelor's degree,

their median weekly income increased about 63.7%.

so we have to Determine the median weekly income for someone with a

bachelor's degree.

That is,

678x0.677=459.006

=459.006+678

=1137.006

Therefore, The median weekly income for someone with a bachelor's degree is 1137.006

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Answer:  (x*4) - 3= 11.   X = 3.5

Step-by-step explanation

(4x) - 3 = 11 or (x*4) - 3 = 11.

11 + 3 = 14

So then,

14 = x * 4 (or 4x)

14 / 4 = 3.5

so,

X = 3.5

The values of angles are  m∠1 = 39° and m∠2 = 51° from the given kite.

What is triangle ?

triangle can be defined in which it consists of three sides , three angles and sum of the angles is 180 degrees

Given figure is a kite.

The diagram is not drawn to scale.

We have to find the measure of angle 1 and 3 in the kite.

From the figure,

Kites have two sets of equivalent adjacent sides and one set up of congruent opposite angles.

So, sides AB and AD are equivalent adjacent sides.

m∠1 = 39°

AC and BD are diagonals.

Diagonals of a kite always meet at right angles.

Let the diagonals intersect at point O.

From right triangle AOB,

m∠1 + m∠2 + m∠O = 180°

39° + m∠2 + 90° = 180

m∠2 = 180° - 90° - 39°

m∠2 = 90° - 39°

m∠2 = 51°

Therefore, m∠1 = 39° and m∠2 = 51°.

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The answer is given below.

An inequality is a relation which makes a non-equal comparison between two numbers or mathematical expressions.

here, we have,

given that,

35z>34

=> z>34/35

=> z> 0.97

which is < 1

hence, The answer is given below.

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The phrase "inconsistent pair of linear equations" refers to a set of linear equations that cannot be solved.

What in mathematics is a linear equation?

A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept. Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.

What makes an equation linear?

When a linear equation is graphed, it always produces a straight line since each term in the equation has an exponent of 1. This is the basis for the term "linear equation" being used to describe it.

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