angles formed by a transversal worksheet answer key

For making sandwiches 5 hours and delivering for 4 hours, Eric earns a total of $53.

We know that the expression that represnets how much Eric saves for working s hours making sandwiches and d hours in delivery is:

(1/2)*(10s + 14d)

Now we want to see how much he earns for making sandwiches 5 hours and delivering for 4 hours, then we need to evaluate in:

s = 5

d = 4

Replacing that we will get:

(1/2)*(10*5 + 14*4) = 53

He makes 53 dollars.

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The total cost to download 30 songs is $40.7.

An expression is combination of variables, numbers and operators.

Given that a music app charges $2 to download the app plus $1.29 per song download

This data can be written in the form of expression

2+1.29x

Here x is the number of songs.

We have to find the total cost to download 30 songs

2+1.29(30)

2+38.7

40.7

Hence, the total cost to download 30 songs is $40.7.

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The sum of interior angles of a triangle is 180°.

Angle sum property of a triangle:

The sum of interior angles of a triangle is 180°.

One exterior angle of a triangle is equal to the sum of the other two angles in the triangle.

The exterior angle is obtained by extending the side of the triangle. Since it is a straight line, the angle is 180°.

Here, ∠CBD =180°   Linear pair

∠ACD = ∠BAC +∠ABC

The formula to find the sum of interior angles of a regular polygon is

(n-2)180°, where n is the number of sides of the polygon.

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From the proof below, the reason why ΔMKO ≅ ΔMLO is; SAS Congruency Postulate

From the triangle construction, we can see that;

MN bisects ∠KML

Thus;

∠KMO ≅ ∠LMO

Similarly, since KM, ML and KL were drawn with length AB, then it means that; KM ≅ ML ≅ KL

Similarly, MO ≅ MO by reflexive property of congruence

Thus, we conclude that ΔMKO ≅ ΔMLO by SAS Congruency Postulate

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Rodney's family can save $ 20 by purchasing a family pass instead of 4 individual passes.

To find the saving in the given problem, calculate the money that can be spent by purchasing a family pass and by purchasing 4 individual passes and find the difference between them.

Here we have

Rodney's family is thinking about buying a family pass to a gym. The pass is $60 for a family of 4. Individual passes are $20 each.  

If Rodney's family buys a family pass then the cost = $ 60

If they buy Individual passes, then the total cost = 4 × $ 20 = $ 80

Difference between two costs = $ 80 - $ 60 = $ 20

Therefore,

Rodney's family can save $ 20 by purchasing a family pass instead of 4 individual passes.

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The  3 examples of quadratic equations written in standard form is:

(1) a[tex]x^2[/tex] + bx + c = 0

(2) a[tex](x - h)^2[/tex] + k = 0

(3) a (x - p)(x - q) = 0

a[tex]x^2[/tex] + bx + c = 0 is the quadratic equation's standard form, where 'a' is the leading coefficient and a non-zero real number. Due to the word "quad" meaning "square," this equation, whose degree is 2, is referred to as "quadratic." A quadratic equation can be expressed in other ways in addition to the usual form.

Vertex Form: a[tex](x - h)^2[/tex] + k = 0

Intercept Form: a (x - p)(x - q) = 0

[tex]ax^2 + bx + c = 0[/tex], where a 0 and a, b, and c are real numbers, is the conventional form of a quadratic equation with a variable x.

a is the [tex]x^2[/tex] coefficient, b is the x coefficient, c is the constant.

In this case, b and c might either be zeros or non-zero values.

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"Study smart one triangle has vertices a,b, and c. another has vertices t, r, and i, are the 2 triangles similar?"

It is not possible to determine if the two triangles are similar based on the information provided.

In order for two triangles to be similar, they must have the same shape but not necessarily the same size. The sides of the two triangles must be in proportion and corresponding angles must be congruent.

Similarity between two triangles can be determined by using the criterion of AAA similarity or SAS similarity, which states that two triangles are similar if:

without knowing the measures of the angles and sides of the triangles, it is impossible to determine if the two triangles are similar.

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The equation for the given scenario is 4x-22.20=1.90. Therefore, option B is the correct answer.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

Given that, Rhyan bought four tire patches. Rhyan paid using a gift card that had $22.20 on it. After the sale, Rhyan’s gift card had $1.90 remaining.

Let cost of each tire be x.

Now, the equation is 4x-22.20=1.90

Therefore, option B is the correct answer.

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"Your question is incomplete, probably the complete question/missing part is:"

To prepare for his mountain biking trip, Rhyan bought four tire patches. Rhyan paid using a gift card that had $22.20 on it. After the sale, Rhyan’s gift card had $1.90 remaining. Which equations could you use to find the price of one tire patch? Select all that apply.

4x – 1.9 = 22.2

4x – 22.2 = 1.9

4x + 1.9 = 22.2

4x + 22.2 = –1.9

22.2 – 4x = 1.9

6. The correct option is (a) a critical value of za/2

7. The correct option is (c) 6627

6. In this case, since the population standard deviation is unknown and the sample size is relatively small (n = 9), a margin of error should be calculated using a critical value of ta/2. This is because when the population standard deviation is unknown and the sample size is small, the t-distribution should be used to calculate the margin of error, as it takes into account the additional uncertainty that arises from estimating the population standard deviation from the sample. The t-distribution is more forgiving for small sample sizes, and it gets closer to the normal distribution as the sample size increases.

7. To construct a 90% confidence interval estimate of the mean of the population, we can use the following formula:

Mean ± (t*critical value) * (standard deviation/√n)

Where t*critical value is the critical value of t-distribution with n-1 degrees of freedom at a 90% level of confidence, and standard deviation is the standard deviation of the sample, and n is the sample size.

To find the critical value of t-distribution with 14 degrees of freedom at a 90% level of confidence, we can use a t-table or a calculator.

For the given sample, the standard deviation is 345, the mean is 6784 and n=15. Plugging these values in the above formula gives:

6784 ± (t*critical value) * (345/√15)

As we are using 90% level of confidence, t*critical value is approximately 1.76

So the 90% Confidence interval estimate of the population mean is (6784 - (1.76345/√15) , 6784 + (1.76345/√15) ) = 6627.22 or 6940.77 .

As, 6940 is not an option given, we consider 6627 as the correct answer.

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Mendelian genetics uses probability pedigrees and chi-square statistics to study the patterns of inheritance of traits. Probability pedigrees are diagrams to calculate chance of inheritance, while chi-square statistics is a test to compare observed data to expected results.

Mendelian genetics is the study of inheritance patterns of traits from parent to offspring. It is based on the work of Gregor Mendel, a 19th century monk and scientist who studied the inheritance of traits in pea plants. Probability pedigrees are diagrams that can be used to calculate the chance of a certain trait being passed down from generation to generation. These diagrams represent the relationships between family members, and the likelihood of a trait being inherited from a parent. Chi-square statistics is a statistical test used to compare observed data to expected results. This is often used to determine the likelihood that an observed trait is inherited from a parent. The chi-square test is used to measure the amount of deviation from the expected, and can help to identify patterns of inheritance. By using probability pedigrees and chi-square statistics, researchers can gain a greater understanding of the patterns of inheritance in a population. This knowledge can be used to develop strategies to prevent or treat diseases that have a genetic component.

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Answer:

x = 12.5

Step-by-step explanation:

Because it is a straight line, the total angle is 180

you already know that one angle is 130 so take 180 - 130 and you get 50

now you know 4x = 50

divide by 4 from both sides

x = 12.5

The system of equations that pass through the given point are mentioned below -

{y = 4x + 9  &  y = - 3x - 5}

and

{y = 2x + 5  &  y = 5x + 11}

Given is the coordinate point (- 2, 1) on the cartesian system.

The system of equations that will satisfy the point (- 2, 1) will be such that the Left hand side {L.H.S} and right hand side {R.H.S} of both the equations will be equal.

y = 4x + 9    &    y = - 3x - 5

For the point (- 2, 1), we can write -

y = 4x + 9

1 = 4 x - 2 + 9

1 = 9 - 8

1 = 1

and

y = - 3x - 5

1 = -3 x -2 - 5

1 = 6 - 5

1 = 1

y = 2x + 5    &    y = 5x + 11

For the point (- 2, 1), we can write -

1 = 2 x - 2 + 5

1 = - 4 + 5

1 = 1

and

y = 5x + 11

1 = 5 x - 2 + 11

1 = 1

Therefore, the system of equations that pass through the given point are mentioned below →

{y = 4x + 9  &  y = - 3x - 5}

and

{y = 2x + 5  &  y = 5x + 11}

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Answer:

1. y=4x+9  2. y=2x+5  3. y=3x+7

  y=-3x-5      y=5x+11      y=-x-1

Step-by-step explanation:PLATO

all 3 of those are the answers, i got it right!

Answer:

Point Form:

(−2,2)

Equation Form :x=−2,y=2

Step-by-step explanation:

:)

No problem at all! Getting on it now.

So if you want to eliminate variables, do this.  :)

-3x + 2y = 10
6x + 6y = 0

Maybe something you didn't know is that you can multiply one set by a number.  Watch this!

2(-3x + 2y) = 2(10)
6x + 6y = 0  [You don't have to multiply this set by 2.]

-6x + 4y = 20
6x + 6y = 0
Set it up like addition!

0x + 10y = 20

= 10y = 20

So you found what y is, after you divide 10y by 10 and 20 by 10.  Y = 2!  Then use substitution to put it back in and find x.

-3x + 2(2) = 10
6x + 6(2) = 0

So -3x + 4 = 10.  Subtract 4 from both sides to cancel it out.  This is now -3x = 6.  Divide -3x by -3 and 6 by -3 to get x = -2.  Yay!!

The values are (-2, 2).  :)  If you graph it out, you can even see that that is where the lines intersect!!

(attached file)
How cool is that!

Answer:

Step-by-step explanation:

For (a), draw a horizontal line that crosses 1600 on the y-axis and the graph.

For (b), find the x coordinates of the point that makes the y coordinates 1600. So the coordinates would be (420,1600) which means that he needs to sell 420 boxes.

For (c), mark the spot between 360 and 480 and write 420 under it.

From $1786 Bill Dupp’s Lumber Yard delivered 620 cubic feet of sand.

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

Given, Bill Dupp’s Lumber Yard charges $2.80 for each cubic foot of sand delivered, plus $50 to deliver the sand.

Let, 'x' be the number of cubic foot of sand delivered.

Therefore,

2.80x = 50 + 1786

2.80x = 1786 - 50.

2.80x = 1736.

x = 1736/2.80.

x = 620 cubic foot of sand.

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The range of the given function is expressed as;

{4, 7, 10, 13}

In mathematics, the range of a function is defined as the set of all possible output values for every possible input value.

Now, in this question, we given;

Function; f(x) = 3x + 7

Domain = {-1, 0, 1, 2}

To find the range. we will plug in each of the domain values for x in the given function to get;

when x = 1;

f(1) = 3(1) + 7

f(1) = 10

When x = 2;

f(2) = 3(2) + 7

f(2) = 13

When x = 0;

f(0) = 3(0) + 7

f(0) = 7

When x = -1;

f(1) = 3(-1) + 7

f(1) = 4

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Distributing to create an equivalent expression with fewest symbols possible will result to 24m - 28

According to the Distributive Law, multiplying a number by a collection of numbers is equivalent to performing each multiplication independently.

In mathematics, the law linking the operations of multiplication and addition is known as distributive law, sometimes known as distributive property. It is symbolically expressed as a(b + c) = ab + ac.

For the problem the law is applied as follows

(6m - 7 )* 4

multiplying each term

24m - 28

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Answer: X is equal to 62

Answer:

just need points and the anser would be

Step-by-step explanation:

6

If Trevon sold  8 apple pies and 6 blackberry pies for a total of $150 and  Jack sold 6 apple pies and 12 blackberry pies for a total of $210 , then the cost each of one apple pie is $9  and one blackberry pie is $13   .

For Trevon :

he sold 8 Apple Pies and 6 Black Berry Pies ,

the amount Trevon gets is = $150  ;

For Jack :

he sold 6 Apple Pies and 12 Black Berry Pies ,

the amount Trevon gets is = $210  ;

let the cost for 1 Apple Pies is = $x  ;  and

let the cost for 1 Blackberry Pies is = $y  .

the given situation can be represented in equation as :

[tex]8x + 6y = 150[/tex]  and [tex]6x+12y = 210[/tex] ;

On solving the two equations ,

we get , the values as x = 9 and y = 13   .

Therefore , the cost of apple pies is $9 and cost of blackberry pie is $13  .

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(1,6), (1, 3), (5, 3) is  the transformation for the coordinates of the vertices of the given pairs of triangles.

The triangle's vertices' coordinates are (x1,y1), (x2,y2), and (x3,y3). The line that connects the first two is split in the ratio l:k, and the line that runs from the division point to the opposing angular point is divided in the ratio m:k+l.

Determine the coordinates of each of the triangle's vertices in step one. Step 2: Add the horizontal translation value to each vertex's x-coordinate and the vertical translation value to each point's y-coordinate to translate each.

We are aware that the distance between the two points (x 1, y 1) and (x 2, y 2) is given by the formula

d = [tex]\sqrt{}[/tex](x 2 x 1 ) 2 +(y 2 y).

(1,6), (1, 3), (5, 3) is  the transformation for the coordinates of the vertices of the given pairs of triangles.

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The answers of the equations are (x,y) = ((11/3),(8/3)), x = -4 & y = -9/2 and x = -16/7 & y = 4/7.

1. To solve the system of equations using the substitution method, we can solve one of the equations for one of the variables and substitute that into the other equation.

3x - 4y = -5

-x + 2y = 3

Solving the first equation for x:

3x = 4y - 5

x = (4/3)y - (5/3)

Substituting this into the second equation:

-((4/3)y - (5/3)) + 2y = 3

-y + 2y = 3 + (5/3)

y = (8/3)

Now we can substitute this back into the first equation to find x:

3x = 4((8/3)) - 5

3x = 16 - 5

3x = 11

x = (11/3)

So the solution to the system is (x,y) = ((11/3),(8/3))

2. 3x-4y=9

-3x+2y=-9

multiply the first equation by -3 and add it to the second equation:

-9x + 12y = -27

-3x+2y=-9

-9x+14y=-36

x = -4

y = -9/2

3. x+6y=2

5x+4y=36

multiply the second equation by -1 and add it to the first equation:

x+6y=2

-5x-4y=-36

-4x+2y=-34

x = -17/2

y = 17

5x-2y=6

-3x+y=2

multiply the first equation by -3 and add it to the second equation:

-15x+6y=-18

-3x+y=2

-18x+7y=-16

x = -16/7

y = 4/7

Therefore, The answers of the equations are (x,y) = ((11/3),(8/3)), x = -4 & y = -9/2 and x = -16/7 & y = 4/7.

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Answer:

[tex]\angle I \cong \angle F[/tex]

Step-by-step explanation:

The angles included between the pairs of sides with proportional side lengths must be congruent to prove similarity by SAS.

The slope and y-intercept of 3x - 2y = 5 is 3/2 and -5/2 respectively.

In the given question, we have to find the slope and y-intercept of 3x-2y=5.

The general equation of line is y = mx + c, where m is the slope of line and c is the y-intercept of line.

The given equation of line is 3x - 2y = 5.

To find the slope and y-intercept we first isolate the y.

Subtract 5 on both side, we get

3x - 2y - 5 = 0

Add 2y on both side, we get

2y = 3x - 5

Divide by 2 on both side, we get

y = [tex]\frac{3}{2}x-\frac{5}{2}[/tex]

On comparing the equation by y = mx + c, we get

m = 3/2 and c = -5/2

Hence, the slope and y-intercept of 3x - 2y = 5 is 3/2 and -5/2 respectively.

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The complete question is:

What is the slope and y-intercept of 3x - 2y = 5?

Answer: The answer you chose was correct

Step-by-step explanation:

Angle y = 60 + 65 = 125 degrees

Person B will be rated the highest on their eligibility for a home loan. The solution is obtained using debt-to-income ratio.

What is debt-to-income ratio?

Lenders use the debt-to-income (DTI) ratio, which measures what proportion of your gross monthly income is utilised to pay your debts each month, to assess your risk of borrowing.

Now, let's evaluate the debt-to-income ratio of all persons.

Person A

Home value= $95,000

Income= $46,000

Savings= $20,000

Recurring Debt= $310

Debt-to-income ratio = 310/46000 = 0.007

Person B

Home value= $107,000

Income= $53,000

Savings= $13,910

Recurring Debt= $198

Debt-to-income ratio = 198/53000 = 0.004

Person C

Home value= $120,000

Income= $58,000

Savings= $18,000

Recurring Debt= $265

Debt-to-income ratio = 265/58000 = 0.005

Person D

Home value= $128,000

Income= $60,000

Savings= $19,200

Recurring Debt= $400

Debt-to-income ratio = 400/60000 = 0.007

Hence, Person B will be rated the highest on their eligibility for a home loan because his debt-to-income ratio is the lowest.

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The different ways to arrange the pens for the horses and cows in the barn is,

''They could have six pens in each row, with room for people to walk around them. They could also have ten pens in each row, with room for the animals to move around.''

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

We know that;

The planners of the county fair can arrange the pens for the horses and cows in the same barn in a few different ways. They could have six pens in each row, with room for people to walk around them. They could also have ten pens in each row, with room for the animals to move around.

Hence, The different ways to arrange the pens for the horses and cows in the barn is,

''They could have six pens in each row, with room for people to walk around them. They could also have ten pens in each row, with room for the animals to move around.''

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The slope of the horizontal line y = -2 is 0.

This is because the line is always at a constant y-value of -2 and does not have any change in x-value.

The slope of a line is the ratio of the change in the y-value to the change in the x-value.

For a horizontal line, the y-value remains constant and there is no change in the x-value, so the slope of the line is 0. This means that the line is always at the same y-value and does not move when the x-value changes.

Therefore, we can conclude that the slope of the horizontal line y = -2 is 0 since the line is always at a constant y-value of -2 and does not have any change in the x-value.

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The present value of the painting is 1287 pounds.

The English term "percentage" originates from the Latin phrase "per centum," which means "by the hundred." Percentages are fractions with a denominator of 100. In other words, it is a connection where it is always assumed that the value of the entire is 100. You may determine a percentage in one of two ways:

1. Adopt a unified perspective.

2. by setting the denominator of the fraction to 100.

According to the question,

1300 × (1 - 1%)

Rewrite the expression as

1300 × ((100 - 1)/100)

= 1300 × (99/100)

= 13 × 99

= 1287

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Therefore , the solution of the given problem of unitary method comes out to be 1. x*0.14 = y , 2.£3.22 and 37 apples.

To accomplish a task through using unitary procedure, multiply the number of a tiny slice by two after first determining its size. The unit technique, to put it simply, is used to isolated a programmed object from either a specific set or set of sets. For illustration, 40 pens would cost 400 pounds ($1.01), or Rs. It's feasible that one nation will have complete control over the technique used to do this. Almost all living things have a unique characteristic. It can integrate and reciprocate in equal measure (mathematics, algebra).

Here,

Given :

Cost of one apple : 1.68/12

=> £0.14

a) let number of apple be x

where y is the total cost

=> x*0.14 = y

b) 23*0.14 = 3.22

=> £3.22

c) £5.18 = 0.14*x

=> 5.18/0.14 =x

=> 37 apples

Therefore , the solution of the given problem of unitary method comes out to be 1. x*0.14 = y , 2.£3.22 and 37 apples.

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