T/F cast iron exhibits a yield plateau similar to mild steel when tested under tension.

The equation that she can use as statement 5 is c) (3x + 24): 51 = 3x: 85.

To prove that x = 12, Dora must first prove that the segments ST and RQ are parallel. This can be done by showing that the angles formed by their intersection are congruent.

Since the angles, QRT and STP are congruent (statement 2) and the angles SPT and QPR are congruent (statement 3), the Triangle-Angle Angle Similarity Postulate can be applied to show that triangle SPT is congruent to triangle QPR (statement 4).

Now, the corresponding sides of the two triangles must be in proportion in order to prove that x = 12. For this, Dora can use the equation (3x + 24) : 51 = 3x : 85 (statement 5). This equation states that the ratio of the lengths of the corresponding sides of the two triangles is equal to the ratio of 3x to 51 and 3x to 85, respectively.

Since the ratio of the sides of the two triangles must be equal, then 3x + 24 must be equal to 85 and 3x must be equal to 51. Solving for x, we get x = 12, proving that if segment ST is parallel to segment RQ, then x = 12.

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The complete question

Look at the figure shown below. Dora is writing statements as shown to prove that if segment ST is parallel to segment RQ, then x = 12.

1.Segment ST is parallel to segment QR

Given

2.Angle QRT is congruent to angle STP

Corresponding angles formed by parallel lines and their transversal are congruent.

3.Angle SPT is congruent to angle QPR

Reflexive property of angles.

4.Triangle SPT is congruent to triangle QPR

Angle-Angle Similarity Postulate

5.?Corresponding sides of similar triangles are in proportion.

Which equation can she use as statement 5?

(3x + 24) : 3x = 85 : 51

(3x + 24) : 81 = 3x : 51

(3x + 24) : 51 = 3x : 85

34 : 24 = 3x : 51

Answer:

1.5 on edg

Step-by-step explanation:

When two triangles are similar, the reduced ratio of any two corresponding sides is called the scale factor of the similar triangles. In Figure 1, Δ ABC∼ Δ DEF. Figure 1 Similar triangles whose scale factor is 2 : 1. The ratios of corresponding sides are 6/3, 8/4, 10/5.

the solutions for a system of equations is where the graphs of each equation meet or intersect.

for the picture above with two parallel lines, well, the lines are parallel and apart from each other, that means they never meet or intersect, and since they never intersect, they have no solution.

Answer: 2 and 5.

Step-by-step explanation: We can use algebra to solve for the original numbers. Let's call the smaller number "a" and the larger number "b". From the information given, we know that:

x = b + a^2

y = b - a

The volunteer tells the magician that x = 9 and y = 3. So we can use these values to create a system of equations:

b + a^2 = 9

b - a = 3

To solve for the original numbers, we can first add the two equations together to eliminate b:

a^2 + 2a + 2 = 12

a^2 + 2a = 10

a^2 + 2a - 10 = 0

(a + 5)(a - 2) = 0

This tells us that the two solutions for a are -5 and 2. But since a is a positive integer, we know that it must be 2.

We can now substitute this value of "a" back into the original equations to find "b":

b + a^2 = 9

b + 2^2 = 9

b + 4 = 9

b = 5

So the original numbers are 2 and 5.

The value of the equation is P ( 4 , 4 ) , where P is the point of intersection of the equations

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the first equation be represented as A

Now , the value of A is

4x - 2y = 8  

Adding 2y on both sides of the equation , we get

2y + 8 = 4x

Subtracting 8 on both sides of the equation , we get

2y = 4x - 8   be equation (1)

Now , let the second equation be represented as B

Now , the value of B is

y = ( 3/2 )x - 2

On simplifying the equation , we get

2y = 3x - 4   be equation (2)

Now , subtracting equation (2) from equation (1) , we get

4x - 8 - ( 3x - 4 ) = 0

4x - 8 - 3x + 4 = 0

x - 4 = 0

Adding 4 on both sides of the equation , we get

x = 4

Substitute the value of x = 4 in equation ( 1 ) , we get

2y = 8

y = 4

So , the value of x = 4 and y = 4

The equations are plotted on the graph and the point of intersection is the solution to the equation , P ( 4 , 4 )

Hence , the equations are solved

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not sure if you need the solution too but if you do it’s (3,-2)

The new coordinates of the polygon are J'(-5/2, 3/2), K'(1, 3/2), L'(1, -3/2), M'(-5/2, -3/2).

Transformation is the movement of a point in the coordinate plane. Types of transformation are reflection, rotation, translation and dilation.

Dilation is the enlargement or reduction in the size of a figure by a scale factor.

Given the coordinates of polygon J(-5, 3), K(2, 3), L(2, -3), M(-5, -3). For a dilation with a scale factor of 1/2, the new coordinates are:

J'(-5/2, 3/2), K'(1, 3/2), L'(1, -3/2), M'(-5/2, -3/2).

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Answer:

25%

Step-by-step explanation:

percent change = (new value - old value)/(old value) × 100%

percent change = (20 - 16)/(16) × 100%

percent change = 25%

Answer:

r

Step-by-step explanation:

e

Note that the question is about numbers in multiples of 6 or which can be divided equally by 6. Thus the likely number of people who must show up to practice so that the coach can make these teams are 6, 12, 18, 24, 30, 36, 48, and so on. The bottom line is that the number must be a common multiple of 6.

One way to show that each of the numbers above will equal an exact team of 6 without anyone left off is by dividing each by 6. If we get an integer, then we are correct. Thus:

Hence, the above Common Multiples are correct.

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Constant of proportionality from side lengths in the original figure to side lengths in the scaled copy = 2/11

Proportion is a mathematical comparison between two numbers.  According to proportion, if two sets of given numbers are increasing or decreasing in the same ratio, then the ratios are said to be directly proportional to each other. Proportions are denoted using the symbol  "::" or "=".

Given,

f is the length of side of original figure

And s be the side of copied figure

f ∝ s

⇒ f = ks       --------(a)

where k is constant of proportionality

Proportion between side of original figure and its copy is such that

s = (11/2)f

f = (2/11)s      -----------(b)

comparing equation (a) and (b)

k = 2/11

Hence, 2/11 is constant of proportionality from side lengths in the original figure to side lengths in the scaled copy.

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Answer:

The answer is D!

The value of the upper quartile is 24.

This method is used to divide a data set into four equal parts and find the values of the quartiles.

To calculate the upper quartile, we first need to find the median (the middle value) of the data set.

This question involves the use of the quartile calculation method.

This can be done by arranging the data in numerical order and finding the middle value.

In this case, the median value is 20.

The upper quartile is then calculated by finding the median of the values above the median.

In this case, the values above the median are 22, 24, 28, and 30.

To find the upper quartile, we need to calculate the median of these values.

This is done by arranging the values in numerical order and finding the middle value, which is 24. Therefore, the upper quartile is 24.

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Makena deposited $0.70 per day.

In mathematics, the middle value—which is determined by dividing the sum of all the values by the total number of values—is the average value in a set of numbers. To calculate the average of a set of data, add up all the values and divide the result by the total number of values.

Given:

The savings account last month: $6.74, $5.21, $5.53, and $3.52.

Makena deposited $6.74,$5.21,$5.53 and $3.52 in her saving account.

To find the average amount she saves per day.

We add all the deposited savings

= ( 6.74 + 5.21 + 5.53 + 3.52)

= $21.031

Now, Makena Saved per day for the month = $21.031/30

                                                                        =$0.70

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The midpoint of a line segment with endpoints A(x1,y1) and B(x2,y2) is the point: M((x₁+x₂)/2,(y₁+y₂)/2)).

The midpoint formula is defined for the points in the coordinate axes. Let (x)1, (y)1, and (x)2, (y)2 be the endpoints of a line segment.

The midpoint is equal to half of the sum of the x-coordinates of the two points, and half of the sum of the y-coordinates of the two points.

The midpoint formula to calculate the midpoint of a line segment joining these points can be given as,

The midpoint is halfway between the two endpoints:

To calculate it:

Add both "x" coordinates, divide by 2

Add both "y" coordinates, divide by 2

M=(xA+xB/2,yA+yB/2)

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The probability of spinning an odd number, flipping heads, then spinning a yellow is of 1/9.

A probability is calculated as the division of the number of desired outcomes by the number of total outcomes.

The probabilities for each case in this problem are given as follows:

The events are independent, hence the probability is obtained multiplying each probability as follows:

p = 2/3 x 1/2 x 1/3 = 1/9.

The complete problem is given by the image shown at the end of the answer.

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Answer:

$3

Step-by-step explanation:

$13.99 is for one hour and one hour is for 3 children. This means they paid a total of 3 hours.

$13.99 * 3 = $41.97 for admission alone

Now our total is $50.97

Let's subtract that from admission to find sock price in total

$50.97-$41.97 = $9

Again, 3 children and each for a pair, so lets divide that $9 by 3 for each child.

$9/3 = $3

The lateral surface area of the cone is:

A = 84.3 in²

We know that for a cone of height H and a radius R, the lateral surface area is given by the formula:

A = pi*R*( √(H² + R²))

Where pi = 3.14

Here the height is 12 inches, and the diameter is 4.4 inches, then the radius is:

R = 4.4i/2 = 2.2 in

Then the lateral surface area is:

A = 3.14*2.2in*( √((12in)² + (2.2in)²))

A = 84.3 in²

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Answer:

----------------------------------

p is inversely proportional to the square of q:

p is 20 when q is 7, substitute:

Find the value of k:

Determine p when q is equal to 2:

Step 2 is the incorrect step and hence d is the correct answer.

The two angles are said to be adjacent angles when they share the common vertex and side. The endpoint of the rays, forming the sides of an angle, is called the vertex of an angle. Adjacent angles can be a complementary angle or supplementary angle when they share the common vertex and side.

Given here: m∠w + m∠z = 90 but this is not true because they are adjacent angles and they lie on a line so they must supplement each other.

m∠w + m∠z = 180

Hence, Step 2 is the incorrect step and hence d is the correct answer.

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Answer:

The length of the third side is 7.

Step-by-step explanation:

We can use the Pythagorean theorem to evaluate the length of the third side.

[tex]a^2+b^2=c^2[/tex]

Let the third side be [tex]a[/tex].

Lets solve for [tex]a.[/tex]

Subtract [tex]b^2[/tex] from both sides.

[tex]a^2=c^2-b^2[/tex]

Take the square root of both sides.

[tex]a=\sqrt{c^2-b^2}[/tex]

We are given

[tex]c=\sqrt{58} \\b=3[/tex]

Lets evaluate [tex]a[/tex].

[tex]a=\sqrt{(\sqrt{58} )^2-3^2}[/tex]

Simplify.

[tex]a=\sqrt{58-9}\\a=\sqrt{49} \\a=7[/tex]

Answer:

(5x - 3)(x - 3)

Step-by-step explanation:

Yes, the expression "5x^2 - 8x + 9" can be factored.

One way to factor it is to find the two numbers that multiply to give 9 (the constant term) and add to give -8 (the coefficient of x). These two numbers are 3 and -3.

We can use these two numbers to factor out the common factor (x - 3) from the expression:

5x^2 - 8x + 9 = (5x^2 - 8x) + 9

= (5x^2 - 8x + 9) - 9 + 9

= (5x^2 - 8x + 9) - (3x - 3x)

= (5x - 3)(x - 3)

So the fully factored form of the expression is (5x - 3)(x - 3)

So, (5x - 3) and (x - 3) are the factors of the expression "5x^2 - 8x + 9"

Base e used in exponential functions because base e is the base rate of growth shared by all continually growing processes which lets us take a simple growth rate.

In an exponential function, the base b is a constant. The exponent x is the independent variable in which the domain is the set of real numbers. There are two types of exponential functions, those are exponential growth and exponential decay. In the function f (x) = b^x when b > 1, the function represents exponential growth.

Base e allows us to take a simple growth rate, where all change occurs at the end of the year, and find the influence of compound, continuous growth, where every nanosecond or faster, we are growing slightly.

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Answer:

1) y=0.56x

2)y=5x

3)y= 0.25x

Step-by-step explanation:

1) 2.24/4 = $0.56 (Cost per carton)

2) 15/3=5 ( miles ran per hour)

3) 3/12 = 0.25 (cost per ounce)

Answer: 45 degrees

Step-by-step explanation:

By the inscribed angle theorem, the measure of an inscribed angle is half the measure of the intercepted arc. The measure of the central angle ∠POR of the intercepted arc ⌢PR is 90°. Therefore, m∠PQR=12m∠POR =12(90°) =45°.