Question 4(Multiple Choice Worth 2 points)
(Linear Relationships MC)
Which linear equation shows a proportional relationship?
Oy=-2x-
Oy=²x-1
Oy = 4x+6
Oy=2x

Answer:

6 1/2

Step-by-step explanation:

The difference between 13 9/20 and 6 7/8 can be found by converting both fractions to decimals and subtracting the two values.

13 9/20 can be expressed as a decimal as 13.45.

6 7/8 can be expressed as a decimal as 6.875.

So, the difference between 13 9/20 and 6 7/8 can be expressed as:

13.45 - 6.875 = 6.575

So the reasonable difference between 13 9/20 and 6 7/8 is 6.575.

The value of x is equal to 16

Pythagorean theorem, the well-known geometric theorem that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse (the side opposite the right angle)—or, in familiar algebraic notation, a² + b² = c².

Given here: A right angle triangle

let the triangle be ABC with AC as the hypotenuse and AB is the perpendicular and BC is the base of the triangle. And D be a point on AC with AD=32 and DC=8 .Clearly the perpendicular using the pythagoras theorem

AB=[tex]\sqrt{x^2+32^2}[/tex]

Now in triangle BDC we have BC= [tex]\sqrt{x^2+64}[/tex]

Again a triangle ABC we have

AC²=BC²+AB²

[tex]40^2=x^2+64+x^2+32^2\\2x^2=40^2-32^2-64\\2x^2=512\\x^2=256\\x=16[/tex]

Thus x is equal to 16

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Step-by-step explanation:

[tex]3x - \frac{8}{2} = x - 6[/tex]

[tex] \frac{8}{2} = 4[/tex]

[tex]3x - 4 + 4 = x - 6 + 4[/tex]

[tex]3x = x - 6 + 4[/tex]

[tex]3x - x = - 6 + 4 - x[/tex]

[tex]3x - x = - 6 + 4[/tex]

[tex]2x = - 2[/tex]

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

[tex]x = - 1[/tex]

An equation for the total cost, y, in terms of the number of kites purchased, x, is y = 2x + 20.

In order to write a linear equation to describe this situation, we would a assign variable to the number of kites purchased and the total cost respectively, and then translate the word problem into a linear equation as follows:

Since Wendy charges $2 per kite and a flat rate of $20 for shipping, a linear equation that models the total cost is given by:

y = 2x + 20

When x = 4, the total cost for Wendy kites is given by:

y = 2(4) + 20

y = $28.

When x = 7, the total cost for Wendy kites is given by:

y = 2(7) + 20

y = $34.

When x = 10, the total cost for Wendy kites is given by:

y = 2(10) + 20

y = $40.

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Zeke's average speed in mph for the first 20 minutes was 3 mph.

To find Zeke's average speed in mph for the first 20 minutes, divide the distance traveled by the time it took him to travel that distance:

1.0 mile / 20 minutes = 0.05 miles per minute

Since there are 60 minutes in an hour, to convert minutes per mile to miles per hour, multiply by 60:

0.05 miles per minute * 60 minutes per hour = 3 mph

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Answer:

34/50 or 68% or 0.68

Step-by-step explanation:

S= {16, 12, 22}

16 + 12 + 22 = 50

50 - 16 = 34

34/50

or

68%

or

0.68

Answer:

14

Step-by-step explanation:

14 divided by -2 = -7

The first three triangles are similar triangles as their corresponding sides are in same proportion but the last triangle with side lengths 4, 6, and 8 does not belong to the first three.

Similar triangles are two triangles that have the same shape, but not necessarily the same size. This means that corresponding angles of the two triangles are equal, and corresponding sides are in proportion.

The base lengths 12, 6, and 18 of the first three triangles corresponds in proportion but does not for the last triangle with 8.

The side 6, 3, and 9 corresponds in proportion but does not for the side 4 of the last triangle

And lastly, the side 8, 4, and 12 of the first three triangles corresponds in proportion but does not for the last triangle with side length 6.

Therefore, the first three triangles are similar triangles as their corresponding sides are in same proportion but the last triangle with side lengths 4, 6, and 8 does not belong to the first three.

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Answer:

as 92 is 2 std deviaiton above mean ; th

Step-by-step expla

The coordinates of A', B', C' and D' are obtained as follows:

A dilation happens when the coordinates of the vertices of an image are multiplied by the scale factor, changing the side lengths of a figure.

Hence the coordinates of the dilated figure are obtained multiplying it's respective coordinates on the original figure by the scale factor.

The problem is incomplete, hence the answer was given in general terms.

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The total distance covered while swimming and running for a total of 3 hours is 45 kilometers.

In mathematics, the term "total" refers to the sum of two or more values. It is used to describe the combined or complete amount of a quantity. The total can be calculated by adding together all the individual values in a set or series.

The distance x can be calculated by using the formula:

distance = rate * time

For swimming, the rate is 5 kilometers per hour, and the time is t₁. So, the distance covered while swimming is:

d₁ = 5 * t₁

For running, the rate is 20 kilometers per hour, and the time is t2. So, the distance covered while running is:

d₂ = 20 * t2

The total time for swimming and running is 3 hours, so:

t₁ + t₂ = 3

The total distance covered while swimming and running is x, so:

x = d₁ + d₂

Substituting the values of d₁ and d₂, we get:

x = 5 * t₁ + 20 * t₂

Now, substituting the value of t₁ + t₂ = 3, we get:

x = 5 * t₁ + 20 * (3 - t₁)

Expanding the equation, we get:

x = 5 * t₁ + 60 - 20 * t₁

Combining the like terms, we get:

x = -15 * t₁ + 60

Substituting the value of t₁ = 3 - t2, we get:

x = -15 * (3 - t2) + 60

Expanding the equation, we get:

x = 45 - 15 * t₂

Now, we have to find the value of t₂ such that x is maximum.

Taking the derivative of x with respect to t₂, we get:

dx/dt₂ = -15

So, t₂ is a decreasing function of x. Hence, when t₂ is maximum, x is also maximum.

As t₂ cannot be negative, the maximum value of t₂ is 0. Hence,

t₂ = 0

Substituting the value of t₂ = 0 in the equation x = 45 - 15 * t₂, we get:

x = 45

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If you draw 2 cards, the probability of drawing 1 heart and 1 non-heart card are: 26/676.

It's crucial to keep in mind that your chances may change depending on the particular rules of the card game you're playing. B. The quantity of cards in the deck, the number of cards drawn, and whether or not the cards drawn after play were replaced.

A regular deck of 52 cards has a chance of producing exactly one heart depending on how many cards are drawn.

The likelihood of drawing a heart if you only draw one card is 13/52, or 1/4.

The probabilities of getting a card with a heart and a non-heart are:

(13/52) × (39/51) + (39/52) × (13/51) = 26/676

And if more cards are drawn, the odds of drawing exactly one heart are different.

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Answer:

Step-by-step explanation:

15+.31x ≤ 93

Answer:

Below

Step-by-step explanation:

Volume of a cylinder :    Find the area of the end....then multiply by height

Volume = pi r^2     *   h

                 3.14 (6)^2  mm)   *  6 mm = 678.24 mm^3

A graph of the solution (4, 4) for the system of linear equations is shown in the image attached below.

In Mathematics, the x-intercept can be defined as the point at which the graph of a function crosses the x-coordinate (x-axis) and the value of "y" or y-value is equal to zero (0).

In this context, we would replace the y-value of the first equation 4x - 2y = 8 with zero (0) as follows;

4x - 2(0) = 8

4x = 8

x = 2 ⇒ (2, 0).

For the y-intercept of the first equation 4x - 2y = 8, we would substitute the x-value with zero (0) as follows;

4(0) - 2y = 8

2y = -8

y = -4 ⇒ (0, -4).

For the y-intercept of the first equation y = 3x/2 - 2, we would substitute the x-value with zero (0) as follows;

y = 3(0)/2 - 2

y = -2 ⇒ (0, -2).

Based on the graph shown in the image attached below, we can logically deduce that the solution to this system of linear equations is at the point of intersection of the lines on the graph representing each of them, which lies in Quadrant I and it is equal to the ordered pair (4, 4).

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The total value of the loan in simple interest is $59,625, which is the lowest amount and hence is the best option.

Simple interest is defined as the interest obtained over the principal amount on a certain rate.

Compound interest is defined as the amount of interest which has been calculated on the principal amount and the amount accumulated over the previous period.

Principal amount, P = $50,000

Rate of interest, r = 5.25% = 0.0525

Time,t = 3 years 8 months = 3 + 0.6667 years = 3.6667 years

Part A :

For simple interest, total amount is,

A = P (1 + rt) = 50,000 ( 1 + (0.0525 × 3.6667 ))

                   = $59,625

Part B :

For compounded interest. total amount is,

A = P (1 + [tex]\frac{r}{n}[/tex])^(nt), where n is the number of times compounding is done in an year.

Here, n = 4, since compounding is quarterly

A = 50,000 [ 1 + [tex]\frac{0.0525}{4}[/tex]] ^(4 × 3.6667)

   = $60,537.9639 ≈ $60,537.96

Part C :

For continuously compounded interest, final amount is,

A = P [tex]e^r^t[/tex]

   = 50,000 [tex]e^{0.0525*3.6667[/tex]

   ≈ 60,613.83

Part D :

The option of simple interest is best for the small business owner since the total value of the loan is lowest for it.

Hence the value of the loan for simple interest is $59,625, value of the loan when compounded quarterly is $60,537.96 and the value of the loan when continuously compounded is 60,613.83. Simple interest is the best option since the value of the loan is lowest for it.

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Answer:

Similar by AA/SAS

Step-by-step explanation:

20.8/8 = 23.4/9 = 2.6

So, the bottom of the smaller triangle is parallel the bottom of the larger one (Thales' theorem)

So, corresponding angles are equal and hence, they are similar by AA similarity.

Note: As sides are given, similarity can also be proven by SAS.

The median daily electricity use is 1 kW-hr than the average (arithmetic mean) daily electricity use.

The median is the middle value of a set of data when the data is arranged in order. If there is an odd number of observations, the median is the middle value. If there is an even number of observations, the median is the average of the two middle values.

The data in ascending order is : 19 24 27 29 31

The median of the data is 27.

The mean, or average, is calculated by summing all the values in a set of data and dividing by the total number of observations.

Average of the data is

= ( 19 + 24 + 27 + 29 + 31)/ 5

= 26

The difference is therefore

= 27 - 26

= 1

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The correct option for the true proportion is  AB/EF = CD/GH (option D)

Two figures are called similar if they have equal corresponding angles and their side are in same  ratios,

Given that, there are two similar polygons, ABCD and EFGH, we need to find the true proportion for the side of the polygons,

We know that, similar figure have equal ratios of the corresponding sides,

Therefore, we get,

AB/EF = CD/GH = BC/FG = AD/EH

From the options given, the true proportion is

AB/EF = CD/GH (option D)

Hence, the correct option for the true proportion is  AB/EF = CD/GH (option D)

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Answer: One Half

Step-by-step explanation: 3 is half of 6 and  I took the test ;)

The given expression 5 subtracted from three times any number is written as 3x - 5

Algebra is the system of computation using letters or other symbols to represent numbers.

5 subtracted from three times any number.

Let

the unknown number= x

(3 × x) - 5

= 3x - 5

Therefore, 3x - 5 is the algebraic representation of the expression.

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If twice Brittany's age is less than the age of Abraham Lincoln when he died, then the answers are;

2b < 56

n = b - 2

b = n + 2

b < 28

n = b - 2 < 26

Yes, Brittany could be 27 years old and Nate 26

Let Brittany's age = b

Twice Brittany's age = 2 × b = 2b

Lincoln's age = 56

Inequality to represent Brittany's age: 2b < 56

b < 56/2 = 28

Nate's age = n

in terms of Brittany's age: n = b - 2

Isolating b: b = n + 2

Substituting b: b < 28

Solving for b: b < 28 and n = b - 2 < 26

Could Brittany be 27 years old and Nate 26? Yes, Brittany could be 27 years old and Nate 26 as both are within the range defined by the inequality (b < 28 and n < 26).

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The complete question is:

Twice Brittany’s age is less than the age of Abraham Lincoln when he died. President Lincoln was 56 years old at the time of his death. Write an inequality to represent Brittany’s age, b. Brittany’s brother, Nate, is two years younger than Brittany. Write an equation for Nate’s age, n, in terms of Brittany’s age, b. Rewrite the expression from Part B to get the variable b alone on one side of the equation. (This is also called isolating b.) Substitute the value of b from Part C into the inequality you found in Part A. Solve the inequalities from parts A and D for the variables b and n, respectively. Could Brittany be 27 years old and Nate 26? Why or why not?

The distance between the two corners of the garden is approximately equal to 3 units.

Mathematically, the distance between two (2) points that are on a coordinate plane can be calculated by using this formula:

Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]

Where:

x and y represents the data points (coordinates) on a cartesian coordinate.

Substituting the given parameters into the distance formula, we have the following;

Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]

Distance = √[(5 - 8)² + (-3 - (-2))²]

Distance = √[(-3)² + (-3 + 2)²]

Distance = √[(-3)² + (-1)²]

Distance = √(9 + 1)

Distance = √10

Distance = 3.1623 ≈ 3 units.

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Answer:

3239609472 Km

Step-by-step explanation:

Answer:

16

Step-by-step explanation:

You need to find 25% of 64.

To find a percent of a number, multiply the percent by the number.

25% of 64 = 25% × 64

To multiply a percent by a number, change the percent to a decimal by dividing the percent by 100. Move the decimal point two places to the left.

25% × 64 = 0.25 × 64 = 16

The value of the standard deviation depends on the value of the mean.

As per the given data, we have to determine that the value of the standard deviation depends on the value of the mean

Yes, the value of the standard deviation depends on the value of the mean.

Because you have to know the mean to calculate the standard deviation.

The size of the standard deviation of a data set depends on what the mean is because the calculation of the mean is essential for calculating Standard Deviation.

The standard deviation determines how much the values deviate from the mean.

Besides, Standard deviation in simple terms means the deviation of data from the Mean.

The most popular way to assess dispersion is standard deviation, which is based on all values. As a result, even a small change in one value can modify the standard deviation's value.

Hence, Standard Deviation depends on the Mean.

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So y = 2x + 2 is the equation of a line parallel to line ef and includes point (0, 2).

In its most basic form, an equation is a mathematical statement that indicates that two mathematical expressions are equal. 3x + 5 = 14, for example, is an equation in which 3x + 5 and 14 are two expressions separated by a 'equal' sign.

Here,

Since line ef has a slope of 2, any line parallel to it will also have a slope of 2. The equation of a line in slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept. To find an equation of a line parallel to line ef that contains point (0, 2), we need to find its y-intercept.

We can use the point-slope form of a line to find the equation of the line: y - y1 = m(x - x1)

Plugging in the point (0, 2) and the slope of 2, we get:

y - 2 = 2(x - 0)

y - 2 = 2x

y = 2x + 2

So, the equation of a line parallel to line ef and containing point (0, 2) is y = 2x + 2.

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The option that would give the most money after 2 years would be Option 1.

The amount that Option 1 would give after 2 years is:

= Amount invested x ( 1 + rate / number of periods ) ^ number of periods in quarters

= 1, 000 x ( 1 + 12 % / 4 ) ⁴ ˣ ²

= $ 1, 267

The amount Option 2 would give after 2 years with continuous compounding is:

= Amount to invest x e ^ ( rate  x number of periods)

= 1, 000 x e ^ ( 6 % x 2 years )

= $1, 127 .50

Option 1 is the better option.

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The expression is solved with x = 6 to 62

Algebraic expressions are simply described as expressions that are composed of variables, coefficients, terms, factors and constants.

They are also composed of mathematical operations

From the information given, we have that;

1/2 x + 7.5 (x) + 11.4 + 2.6

Now, expand the bracket

1/2x + 7.5x + 11.4 + 2.6

Substitute the value of x as 6 , we get;

1/2(6) + 7.5(6) + 11.4 + 2.6

Multiply the values

3 + 45 + 11.4 + 2.6

Add the values

62

Hence, the value is 62

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Answer:

14

Step-by-step explanation:

8/9 = 0.888888888......

<5 round down

[tex]\geq[/tex]5 round up

8/9 = 0.888888888....

larger than 0.5

the answer is 14