A student writes an incorrect step while checking if the sum of the measures of the two remote interior angles of triangle ABC below is equal to the measure of the exterior angle.

Step 1: m∠x + m∠y + m∠z = 180 degrees (sum of angles of a triangle)
Step 2: m∠w − m∠z = 90 degrees (corresponding angles)
Step 3: Therefore, m∠x + m∠y + m∠z = m∠w + m∠z
Step 4: So, m∠x + m∠y = m∠w

In which step did the student first make a mistake and how can it be corrected? (5 points)

a
Step 1; it should be m∠x + m∠y + m∠z = 180 degrees (sum of corresponding angles)

b
Step 2; it should be m∠w + m∠z = 180 degrees (supplementary angles)

c
Step 1; it should be m∠x + m∠y + m∠z = 90 degrees (corresponding angles)

d
Step 2; it should be m∠w + m∠z = 90 degrees (alternate exterior angle)

On solving the provide question, based on the congruent triangles properties, we got to know that x= 76° and 90°.

Congruent triangles are two triangles that are identical in terms of their size and form. The two congruent triangles remain congruent whether you rotate, flip, or flip one of them. If two triangles have the same number of sides, then their angles and congruence must match.

As a result, we can determine that two triangles are congruent if all three of their sides are equal. We also understand that if there is a side, an angle between the sides, and a third side that is congruent, the three sides are congruent. which means sides, corners, and sides.

For green -

=> x = 76° ( both side are same)

For orange -=> x = 90°

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Answer:

2x - 10y = - 40

Step-by-step explanation:

x - 3y = -14

x - 7y = -26

2x - 10y = - 40

The additive inverse of 7/8 is -7/8.

This can be seen when using the additive inverse formula. The additive inverse formula states that if a number is denoted as x, then the additive inverse would be -x. Therefore, when applied to 7/8, it would be -7/8. This can also be seen when adding the two numbers together. When 7/8 is added to -7/8, the sum is 0. This can be seen in the calculation below:

7/8 + (-7/8) = 0

7/8 - 7/8 = 0

0/8 = 0

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By combining the like terms from the given expression we get 2y-13

what is an algebraic expression ?

Algebraic expression can be defined as the combination of  constants , variables and operators.

Algebraic expressions are the concept of expressing numbers using letters or alphabets without specifying their real values. The basics of algebra taught us a way to specific an unknown value the usage of letters which includes x, y, z, and many others. those letters are called here as variables. An algebraic expression may be a combination of each variables and constants. Any value this is positioned before and increased through a variable is a coefficient.

Given ,

The expression ,

=y-9+y-4

=y+y-(9+4)

=2y-13

Hence , By combining the like terms from the given expression we get 2y-13.

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3.52bags will be filled completely with 7/8 lb of granola and 1/4 lb of granola

Word Problems are mathematical problems that are delivered in ordinary words, instead of mathematical symbols. Part of the problem with dealing with word problems that they first need to be translated into mathematical equations, and then the equations need to be solved.

To get the number of bags, we simplify and use the quotient, that is:

We divide the quantity of granola over the number of bags

=(7 / 8 pounds) / (1 / 4 pounds)

=0.88/0.25

= 3.52 bags

Hence, The number of bags that will be filled completely is 3.52 bags

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Annie loved the first novel she read by Danielle Steel. Ms. Steel has just published a new novel, and it got great reviews. Therefore, it is likely that Annie would like that novel too which means that the argument is inductive and it is a weak one.

This is a type of argument which is characterized by the arguer believing that the truth of the premises provides only good reasons to believe the conclusion is probably true.

In this scenario since Annie liked the author's previous books and the new one had great reviews then it is probably true that she would also like it and it is a weak one because assuming the premises are true,then it is probable for the conclusion to be false.

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The probability that a randomly selected bird is a parakeet given that it is green is 54.1%.

The area of mathematics known as probability explores potential outcomes of events, along with the likelihoods and distributions of those occurrences.

Simply put, probability measures how probable something is to occur. We can discuss the probabilities of various outcomes, or how likely they are, whenever we are unsure of how an event will turn out. Statistics is the study of events subject to probability.

Probability is a measure of the likelihood that an event will occur or the likelihood that something will happen. The likelihood that the coin will land with the heads side up after being tossed into the air is described using the word probability.

Let,

A be the  Parakee

B be the Green

To find the probability that a randomly selected bird is a parakeet given that it is green.

That means P(A|B)

The number of birds that are both parakeet and green is n(A∩B)=20

The number of birds that are green is n(B)=37

Hence, using the conditional probability formula P(A∣B) = [tex]\dfrac{n(A\bigcap B}{n(B)}[/tex]

P(A∣B) = [tex]\dfrac{n(A\bigcap B)}{n(B)}[/tex]

P(A∣B) = 20/37

P(A∣B) = 20/37 × 100%

P(A∣B) = 54.1%

Thus, the probability that a randomly selected bird is a parakeet given that it is green is 54.1%.

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You are  57 years old if 400 reduced by one half must subtracted from 257 is your age in the given arithmetic problem.

Mathematical arithmetic, which includes operations on numbers, is its foundation. Addition, subtraction, multiplication, and division are among these operations. The foundation of the subject "Maths" is laid by one of the crucial branches of mathematics: arithmetic.

Despite the fact that the subject involves numerous other modified operations, addition, subtraction, division, and multiplication are the three basic operations under the heading of arithmetic.

Let your age be x

[tex]$x=257-400\frac{1}{2}[/tex]

x = 257 - 200

x = 57

Hence, your age is 57 years old.

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Step-by-step explanation:

Given equations are

2x+3y=13 ....(1)

4x+y=11 .....(2)

multiply the equation (2) by 3, we get

⇒12x+3y=33 .....(3)

Subtract equation (1) from (3) to eliminate y, we get

12x+3y=33

2x+3y=13

− − −

10x=20

⇒x=2

Put this value in equation (1), we get

⇒2(2)+3y=13

⇒4+3y=13

⇒3y=9

⇒y=3

∴ the solution is x=2,y=3.

Michael and Ashley bought same amount of turkey and ham.

Linear equations are equation involving one or more expressions including variables and constants and the variables are having no exponents or the exponent of the variable is 1.

Linear equations may include one or more variables.

Michael and Ashley each buy x pounds of turkey and y pounds of ham.

Michael purchased from store A.

Cost of turkey per pound at store A = $3

Cost of ham per pound at store A = $4

Michael spends $18 at store A.

3x + 4y = 18

Ashley purchased from store B.

Cost of turkey per pound at store B = $4.50

Cost of ham per pound at store B = $6

Ashley spends $27 at store B.

4.5x + 6y = 27

We get two linear equations,

3x + 4y = 18

4.5x + 6y = 27

Multiplying the first equation throughout with 4.5 and the second equation throughout with 3, we get,

13.5x + 18y = 81

13.5x + 18y = 81

Since both the equations coincide, Michael and Ashley bought same amount of Turkey and Ham.

Hence Michael and Ashley bought same amount of turkey and ham.

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The perimeter of a triangle is about 18.77 inch and the area of a triangle is about 18 [tex]inch^{2}[/tex] .

What is triangle ?

A triangle is a three-sided polygon with three straight sides. The three sides of a triangle are called edges, and the three angles of a triangle are called vertices. The sum of the three angles of a triangle is always 180 degrees.

Have given ,

length of triangle [tex]4\frac{1}{5} ,4\frac{2}{7}[/tex],

perimeter of a triangle = [tex]4\frac{1}{5} +2*4\frac{2}{7}+6[/tex] = 18.77 inch.

Area of a triangle =  [tex]\frac{1}{2}*2*4\frac{1}{5}*4\frac{2}{7}[/tex]

⇒ 18 [tex]inch^{2}[/tex].

Hence , The perimeter of a triangle is about 18.77 inch and the area of a triangle is about 18 [tex]inch^{2}[/tex] .

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The rectangle flooring needs to be installed in his rectangular laundry room, which has dimensions of = 12 * 12 and a floor area of = 144 ft2.

A rectangle is a polygon with four right angles in Euclidean plane geometry. You may also refer to it as an equiangular quadrilateral, meaning that all of its degrees are comparable. A straight angle could also be present in the parallelogram. Rectangles with four evenly sized sides are called squares. Four 90-degree vertices with equal parallel sides make up a quadrilateral with the outline of a rectangle. As a result, it's also known as a georeferencing rectangle. A rectangle is also referred to as a parallelogram since its opposite sides remain parallel and equal.

given

are of floor = 12 * 12

= 144 ft2

The rectangle flooring needs to be installed in his rectangular laundry room, which has dimensions of = 12 * 12 and a floor area of = 144 ft2.

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A 1/3 scale factor is a constant of dilation that is used to change the size of a figure by a factor of 1/3. A dilation is a transformation that changes the size of a figure while preserving its shape.

In a dilation, the scale factor is multiplied by the coordinates of each point on the figure to determine the new coordinates of the dilated figure. If the scale factor is 1/3, then the coordinates of each point on the figure will be multiplied by 1/3, meaning that each point on the figure will be moved one-third as far from the origin as it was before the dilation.

The result of this is that the dilated figure will be smaller than the original figure and will have a scale factor of 1/3. It's important to note that if the scale factor is less than 1, the dilation will reduce the size of the figure and if the scale factor is greater than 1, the dilation will increase the size of the figure.

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The ordered pairings where the regions overlap are the answers to the linear inequality system (yellow).

The unitary technique is sometimes useful for multiplying and dividing by fractions because it makes sense immediately and can be done mentally if the numbers add up. This makes it a good method for defending or explaining frequently employed written fractional algorithms, like division by a fraction. The unitary technique has a formula that involves finding the value of a single unit, multiplying it by the quantity of units, and then finding the desired value.

given

Assume that y is the number of necklaces and x is the number of bracelets.

Up to (less than or equal to) 60 pieces (bracelets and necklaces) can be produced by Olivia each week:

x+ y ≤60

Up to (less than or equal to) 40 bracelets can be made by Olivia each week:

x≤40(2)

Up to (less than or equal to) 40 necklaces can be created by Olivia each week.

y≤40(3)

Olivia aims to sell at least 30 products per week, preferably more.

x+y≥30(4)

It is possible to write x+y60 as yx+60 with a boundary of y=x+60. Since is used, we shade below the line and draw the line as solid. (red)

The vertical boundary of x40 is defined by x=40. Because is employed,, after which we darken the line's left side and draw the line as solid. (orange)

The horizontal boundary of y40 is defined by y=40. Because is utilized, we shade below the line and draw a solid line over it. (green)

The expression x+y30 can be written as yx+30 has a limit of y=x+30.

Because is utilized, we shade above the line and draw the line as a solid. (blue)

The ordered pairings where the regions overlap are the answers to the linear inequality system (yellow).

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Answer:1/15

Step-by-step explanation
formula = y2-y1/x2-x1;

x1=7;y1=5; x2=-8;y2=4
4-5/-8-7=-1/-15
=1/15

There are about 1,000 times as many fourth graders in the US as there are in Washington DC.

what is an algebraic expression ?

Algebraic expression can be defined as the combination of  constants , variables and operators.

​We write 4 thousand as 4,000

We write 40 thousand as 40,000

We write 400 thousand as 400,000

The value of each place is ten times the value of the place immediately to the right.

So:

40,000 is 10 times 4,000

400,000 is 10 times 40,000.

4,000,000 is 10 times 400,000.

Thus, 400,000 = 10 *40,000, and there are about 10 times as many fourth graders in Texas as there are in Mississippi.

Also, 4,000,000 = 10* 400,000, and there are about 10 times as many fourth graders in the US as there are in Texas.

Finally, to go from 4,000 to 4,000,000, we have to multiply by 10 three times. We see that

10*10*10 = 10 * 100 = 1000

Hence, there are about 1,000 times as many fourth graders in the US as there are in Washington DC.

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When Dante deposits $300 to create a savings account, $385 will be available in the account after 4 years.

aggregate attempting to determine the whole amount, time, or quantity. The amount at hand or under consideration is very active. the overall outcome, significance, or import. a third accounting, the principal, and the interest. There are word forms for quantities, amounting, and amounted. adaptable noun A thing's quantity is how much of it there is, how much you have, how much you need, or how much you can get. He needs that much money to make ends meet.

given

A= P( 1- rt )

A = 275 ( 1+ 300 )

A = 275( 1.4 )= $385

When Dante deposits $300 to create a savings account, $385 will be available in the account after 4 years.

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The solution to the system of linear equations x 3y =- 2 is (x, y) = (6, -2).

The solution to the system of linear equations x 3y =- 2 can be found by using a method such as substitution or elimination.

One possible method is substitution, where we solve one equation for one variable in terms of the other, and then substitute that expression into the other equation.

For example, we can solve the equation x + 3y = -2 for x in terms of y: x = -3y - 2. Then we can substitute this expression into the second equation: -3y - 2 + 3y = -2, which simplifies to y = -2.

Then we can substitute this value back into the first equation to find x: x = -3(-2) - 2 = 6.

So the solution to the system of linear equations x 3y =- 2 is (x, y) = (6, -2).

In conclusion, The system of linear equations x + 3y = -2 can be solved by using the method of substitution. By solving one equation for one variable in terms of the other, and substituting that expression into the other equation, we find that the solution to the system is (x, y) = (6, -2).

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Answer:

because it has many factors other than 1 and 18

At a 10% annual growth rate, the cash equals Rs. 3,600 in two years. ​ Rs. 3960.

The principal is the sum you borrowed and are required to repay, while the interest is what you pay. For the majority of borrowers, the total monthly payment you make to your mortgage company includes additional expenses like homeowners taxes and homeowner's insurance that may be placed in an escrow account.

According to the given information:

here principal(P)=3600, R=10%, n= 2 year

amount A=p(1+R/100)ⁿ

3600(1+10/100)²

3600*11/10

=3690

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The solution is [tex](27^2)^{ 1/5}[/tex] express as [tex]145 \frac{4}{5}[/tex] in simplest radical form.

A radical in mathematics is the opposite of an exponent, which is denoted by the symbol "√" and is also referred to as the root. It can either be a square root or a cube root, and the number before the symbol or radical is regarded as an index number or degree. This number cancels the radical and is represented as a whole number by an exponent.

step1:

extract form

27² =729

729/5= decimal form=145.8

step 2:

729/5=145.8

mixed form:

[tex]145 \dfrac{4}{5}[/tex]

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The dimensions of the parallelogram to the nearest hundredth of an inch are 6.54 in and 3.06 in.

A Parallelogram is a flat shape with opposite sides parallel and equal in length.

properties of Parallelogram

Trigonometry would be used to determine the base and the length of the parallelogram.

Base: cos 40 = adjacent /hypotenuse

0.7660 = adjacent / 4

adjacent = 4 x 0.7660

adjacent  = 3.06 inch

Length = area/base

Length= 20/3.06

Length= 6.54 in

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The quotient of 3÷8 is 0.375

The number 3 is called the numerator or dividend, and the number 8 is called the denominator or divisor.

The quotient of 3 and 8, the ratio of 3 and 8, as well as the fraction of 3 and 8 all mean (almost) the same:

3 divided by 8, often written as 3/8.

The result of 3/8 is a terminating decimal with 3 digits to the right of the decimal point.

3 divided by 8 in decimal = 0.375

3 divided by 8 in fraction = 3/8

3 divided by 8 in percentage = 37.5%

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x=2 is value of x does the function f(x).

An easy definition of a function?

As a set of inputs with one output for each, a function is defined as a relationship between them.

                     In plain English, a function is an association between inputs in which each input is connected to precisely one output. a unique relationship in which each input only results in one outcome. Where x is the input value, it is frequently expressed as "f(x)". as in f(x) = x/2 ("f of x equals x divided by 2") Each input "x" yields a single output "x/2," indicating that it is a function: • f(2) = 1.

X f(x) g(x)

1    6   6

2  12 16

3  18 30

4  24 48

We can see from this table that f(x) is greater than g(x) starting from x=2

Therefore I think x=2 is your answer.

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The perimeter of a concave polygon may be calculated by summing the lengths of all its sides.

A perimeter is a closed path that surrounds, encompasses, or outlines a two-dimensional shape or a one-dimensional length. The perimeter of a circle or ellipse is its circumference. The perimeter calculation has a variety of practical applications. The perimeter of an object is the distance surrounding it. Your house, for example, has a fenced-in yard. The perimeter of the barrier is its length. A perimeter is the distance between the edges of a two-dimensional form. It is sometimes defined as the total of the object's side lengths. The perimeter of a shape is the algebraic sum of its side lengths. We have equations for the various forms in geometry.

Here,

The perimeter of a concave polygon may be calculated by summing the lengths of all its sides.

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The Output Variable is Total cost represented by c(m).

The range of values that we are permitted to enter into our function is known as the domain of a function. The x values for a function like f make up this set (x). A function's range is the collection of values it can take as input. After we enter an x value, the function outputs this sequence of values.

Given:

A website charges $3 for each movie you download.

They also charge a one-time sign-up fee of $14.99.

So, the input variable will be m which shows the number of movies.

and, the output variable will be c which shows the total cost.

Then, the equation models the cost c(m), is c(m)=3m+14.99

Now, putting the values for m = 0, 1, 2, ....

c(0)= 4.99, c(1)= 17.99, c(2)= 20.99

Hence, the output variable is total cost.

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Answer: 1. 55 sq inches

Step-by-step explanation:

add me and mark me brainlyest pls

Answer:

15.5 inches

Step-by-step explanation:

10cm = 3.93701 inches

3.93701 x 3.93701 = 15.50004774

15.50004774 to the nearest tenth is 15.5

Option (i) , (ii) and (iii) all represents quadratic equations as all of them is of degree 2 and coefficient of degree 2 is non-zero.

Having the form a[tex]x^2[/tex] + bx + c = 0, quadratic equations are 2nd degree algebraic expressions. The meaning of the term "quad," is square, comes the word "quadratic." A quadratic equation is a "equation of degree 2," to put it another way.

Option i

3x^2-5x+9=x^2-7x+3

so the coefficent of degree 2 is 3-1 which is 2 which is non - zero value so this expression is a quadratic equation.

Option ii

x+ [tex]\frac{1}{x}[/tex] =1

=> [tex]x^2[/tex] -x +1=0

so the coefficent of degree 2 is 1 which is non - zero value so this expression is a quadratic equation.

Option iii

[tex]x^2[/tex] -3x=0

so the coefficent of degree 2 is 1 which is non - zero value so this expression is a quadratic equation.

so all the 3 option represents a quadratic equation.

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