Spencer wrote the following paragraph proof showing that rectangles are parallelograms with congruent diagonals. Quadrilateral R E C T is shown with right angles at each of the four corners. Segments E R and C T have single hash marks indicating they are congruent while segments E C and R T have two arrows indicating they are parallel. Segments E T and C R are drawn. According to the given information, quadrilateral RECT is a rectangle. By the definition of a rectangle, all four angles measure 90°. Segment ER is parallel to segment CT and segment EC is parallel to segment RT by the ________________. Quadrilateral RECT is then a parallelogram by definition of a parallelogram. Now, construct diagonals ET and CR. Because RECT is a parallelogram, opposite sides are congruent. Therefore, one can say that segment ER is congruent to segment CT. Segment TR is congruent to itself by the Reflexive Property of Equality. The Side-Angle-Side (SAS) Theorem says triangle ERT is congruent to triangle CTR. And because corresponding parts of congruent triangles are congruent (CPCTC), diagonals ET and CR are congruent. Which of the following completes the proof? Alternate Interior Angles Theorem Converse of the Alternate Interior Angles Theorem Converse of the Same-Side Interior Angles Theorem Same-Side Interior Angles Theorem

Answer: C

Step-by-step explanation:

(x - y)²

we want (8)², so need: x - y = 8

There are many options that satisfy x - y = 8  but of the options provided to you, 10 - 2 is the only one that works.

A) 2 - 6 = -4

B) 64 - 0 = 64

C) 10 - 2 = 8

D) 8 - 64 = -56

37 and 38

consecutive integers have a difference of 1 between them

let n and n + 1 be the consecutive integers, then

n + n + 1 = 75 ( subtract 1 from both sides )

2n = 74 ( divide both sides by 2 )

n = [tex]\frac{74}{2}[/tex] = 37

the integers are 37 and 37 + 1 = 38

Ok so logically it would be the blue which is consistently low and unlike the others doesn't get any spikes of interst so BLUE.

For this one, I would go with D.

D makes the most sense, giving that there is two sets of each and, that it is just a shorter way to say "add all the sides."  

B and C would only give us half or part of the perimeter and then A does not make much sense.

D would be the answer through process of elimination.

The equation is r(x) = 10x - 0.025x² where x is measured in thousands of toys produced, and r(x) is measured in thousands of dollars.

For maximum r, r'(x) = 0

It becomes: r'(x) = [tex]10-0.025\times2x=0[/tex]

= [tex]10-0.5x=0[/tex]

[tex]x=\frac{10}{0.05}[/tex]

x= 200

Hence, r(200) = [tex]10\times200-0.025\times200^{2}[/tex]

Solving it we get,

r(200) = 1000

Hence, maximum revenue is $1000.

You multiply fractions simply by multiplying numerators and denominators with each other:

[tex] -\dfrac{1}{4} \times \left(-\dfrac{6}{11}\right) = \dfrac{1 \times 6}{4 \times 11} = \dfrac{6}{44} = \dfrac{3}{22} [/tex]

Answer:

The graph in option (c) is the correct answer.

Step-by-step explanation:

The line corresponding to the inequality [tex]x+y<1[/tex] represents the dashed line and the line corresponding to the inequality [tex]2y\geq x-4[/tex] represents the solid line.

In order to figure out the correct shaded region, we test one point from each of the four possible regions and figure out the point at which both the inequalities bold true. The region containing that point would be the correct shaded region.

Let us test the point (0,0).

First inequality [tex]0+0<1[/tex], that is, [tex]0<1[/tex] holds true.

The second inequality [tex]2(0)\geq 0-4[/tex] that is, [tex]0\geq -4[/tex] as well holds true.

Since both the inequalities hold true at point (0,0), therefore, region  containing origin is the correct answer. Thus, the correct answer is forth option. Since the options are not labeled, I have attached the correct graph with my solution in order to make sure you get the correct answer.

It is 165 degrees celcius

ANSWER

The possible rational roots are [tex]\pm3[/tex]  and [tex]\pm\frac{1}{3}[/tex]

EXPLANATION

According to  the rational roots theorem, the possible rational roots of

[tex]9x^3+14x^2-x+18=0[/tex]

is given by all the possible factors of [tex]18[/tex] which are

[tex]\pm1,\pm2,\pm3,\pm6,\pm9,\pm18[/tex]

expressed over all the possible factors of the coefficient of the highest degree of the polynomial which is  [tex]9[/tex] which are

[tex]\pm1,\pm3,\pm9[/tex]

in their simplest form.

One of this possible ratios are [tex]\pm9[/tex] from the factors of 18, over [tex]\pm3[/tex] from the factors of 9.

This will give us

[tex]\frac{\pm9}{\pm3} =\pm3[/tex].

Another possible rational root is

[tex]\pm \frac{1}{3}[/tex].

Hence the correct options are

A and C.

Secrete: Check if the denominator is a factor of 9 and the numerator is also a factor of 18, then these are the correct answers.

The possible rational roots of the polynomial 9x^3+14x^2-x+18=0, according to the Rational Root Theorem, are ±3 and ±1/3. The other given options, ±1/18 and ±1/2, do not meet the criteria set by the theorem.

The question asks for the possible rational roots of the polynomial 9x^3+14x^2-x+18=0 according to the Rational Root Theorem. The Rational Root Theorem states that if a polynomial has a rational root p/q, where p and q are integers and q is not zero, then p is a factor of the constant term and q is a factor of the leading coefficient.

The constant term here is 18 and its factors are ±1, ±2, ±3, ±6, ±9, and ±18. The leading coefficient is 9 and its factors are ±1, ±3, and ±9. According to the theorem, we divide each factor of the constant term by each factor of the leading coefficient to determine the potential rational roots:

±1/1, ±1/3, ±1/9

±2/1, ±2/3, ±2/9

±3/1, ±3/3, ±3/9

±6/1, ±6/3, ±6/9

±9/1, ±9/3, ±9/9

±18/1, ±18/3, ±18/9

Out of the list, the values that match the options given in the question are ±3 and ±1/3. The other options, ±1/18 and ±1/2, are not rational roots because 1/18 is not a factor of 9 (leading coefficient), and 2 is not a factor of 18 (constant term) when considering the reduced form.

Always remember (y2-y1)/(x2-x1) for finding slope

So (-3)-4 / 1-1=

-7 / 0

So undefined

Answer:

Step-by-step explanation:

(g/h)(t) = g(t) / h(t)

              =( t³-5t² ) /(t+5) we cannot simplify this further so

(g/h)(t) = ( t³-5t² ) /(t+5)

               =

Answer:

The awnser is C and trust me

Step-by-step explanation:

After translating the statement into an inequality and simplifying, we find that the solution to 'The sum of a number and twenty is greater than four times the number decreased by one' lies in the set of numbers that is less than 7.

The question asks us to solve an inequality. Let's take the given statement: 'The sum of a number and twenty is greater than four times the number decreased by one'. We can translate that into an inequality as follows: x + 20 > 4x - 1, where x stands for the unknown number.

Now, let's simplify the inequality: we subtract x from both sides to get 20 > 3x - 1, and then add 1 to both sides, yielding 21 > 3x. Lastly, divide each side by 3 for the final inequality x < 7.

So the solution to the inequality means any number less than 7, when added to 20, is greater than four times the number minus one.

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Answer:

B.Triangle ACD is congruent to triangle ABD

Step-by-step-explanation:

We are given that AC is congruent to segment AB

We have to prove that angle ABD is congruent to angle ACD

When triangle ACD is congruent to triangle ABD

Then ,Angle ACD is congruent to angle ABD

Angle ADC is congruent to angle ADB

Angle CAD is congruent to angle DAB

Segment CD congruent to segment BD

Because when two triangles are congruent then sides and length of a triangle congruent to its corresponding sides and angles of other triangle .

Therefore,Triangle ACD is congruent to triangle triangle ABD is used to prove that angle ABD is congruent to angle ACD.

Hence, option B is true.

Construction of an angle congruent to a given angle.

Congruent angles are two or more angles that are identical to each other. Thus, the measure of these angles is equal to each other.

For two angles to be congruent their measurements must be equal.

Therefore, we can conclude that the construction above is angle congruent to a given angle.

Learn more about congruent angles here

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An angle congruent to a given angle construction is illustrated in the figure. Option B is the right choice.

Congruent angles share an identical measure, establishing equality between their angular dimensions.

In the realm of geometry, the fundamental criterion for angles to be considered congruent is that their measurements are precisely equal. This equality in angular magnitude implies that the angles exhibit indistinguishable orientations and positions.

Consequently, when engaging in geometric constructions, if a constructed angle aligns in measurement with a given angle, it is deemed congruent to the specified angle.

This fundamental concept is pivotal in geometric reasoning and problem-solving, providing a basis for establishing equivalences between angles and facilitating precise angular constructions. In summary, congruent angles signify an equality in measurement, forming a cornerstone in geometric analyses and constructions.

Option B is the right choice.

For similar question on congruent

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in 40 minutes it will be 12:10

You seem to be missing some information here.

Complex conjugate example:

2 - 16i >> 2 + 16i

Are you sure this is the entire question?

For this case we have a complex number of the form:

[tex]a + (b) (i)\\[/tex]

Where:

Thus, given 1-8i, its complex conjugate is given by:

[tex]1 + 8i\\[/tex]

On the other hand, the product of both is given by:

[tex](1 + 8i) (1-8i) =\\\\(1 ^ 2-8i + 8i-64 (i ^ 2)) =\\\\1-64 (-1) =\\\\1 + 64 = 65\\[/tex]

Answer:

Conjugate complex: [tex]1 + 8i\\[/tex]

Product: 65

Answer:

A. The check may not have been cashed or deposited yet.

Step-by-step explanation:

Our bank statements contains all our transactions like the debits or withdrawals, credits or deposited amounts and checks deducted etc.

And all the transactions are ordered date wise.

So, if a check was skipped on a bank statement, that means the check has not been cashed yet.

Answer:

A for plato

Step-by-step explanation:

See the attached picture for the solution:

Answer:

76=R

R=76

180-76-38=66

Step-by-step explanation:

0.25 = [tex]\frac{1}{4}[/tex]

1.25 = 1 [tex]\frac{1}{4}[/tex] = [tex]\frac{5}{4}[/tex]

there are 5 quarters thus each person woud get one quarter

  11 = -3k - 22 - 8k

  11 = -11k - 22         added like terms (-3k and -8k)

+22         +22

33 = -11k

[tex]\frac{33}{-11} = \frac{-11k}{-11}[/tex]

 -3 = k

Answer: k = -3

y = -x - 6

the equation of a line in ' slope- intercept form ' is

y = mx + c ( m is the slope and c the y-intercept )

y = - x is in this form with m = - 1 and c = 0

note that parallel lines have equal slopes thus

the partial equation is y = - x + c

To find c substitute ( - 8, 2 ) into the partial equation

2 = 8 + c ⇒ c = 2 - 8 = - 6

y = - x - 6 ← is the equation of the parallel line

The correct answer would be A.  13/3 Divided by -5/6

The total answer would be negative 5 1/5

because you do 4x3+1=13 over the denominator that is already there so 13/3 then you do KCF a.k.a keep change and flip you keep 13/3 change the division sign into multiplication sign then you flip the -5/6 to -6/5 then multiply straight across and reduce this is the way my teacher taught me how to remember - to positive kind of things:

when a negative thing or bad thing happens to a good person is that good or bad in this case thats bad because if you think about it if a bad thing happend to someone you care about that would be bad. then that same idea goes for each pattern another example could be a good thing (+) happens to a good person (+) it is good (+)

(+) (+)=+

(-) (-)=+

(+) (-)= -

(-) (+)= -

Hope this helps. Have a good day! :)

And Whats the question here?!?!

When dividing a positive number by a negative number, the result is negative.

A better estimation would be -3.

Solution:

As the two numbers [tex]15 \frac{1}{3} {\text{and} -4\frac{2}{3}[/tex] are mixed fractions.

[tex]15 \frac{1}{3}= \frac{46}{3} \\\\ -4\frac{2}{3}= \frac{-14}{3}[/tex]

Now,  [tex]\frac{ \frac{46}{3}}{\frac{-14}{3}}[/tex] = - 3

Ankur's answer= 3

The mistake he has committed , while dividing two fractions , he must have forgot that one of the fraction which is in the denominator bears negative sign  before it.

So, [tex]\frac {+}{-}= -[/tex].

Ankur forgot to put negative sign before 3.

So, The correct option which describes ankur's error is : Ankur found that the quotient of a positive number and a negative number is positive.

Option 3 is right choice.

Answer: 10 & 16

Step-by-step explanation:

The slope-point form of a line:

[tex]y-y_0=m(x-x_0)[/tex]

We have

[tex]m=\dfrac{3}{4}\\\\(4,\ 1)\to x_0=4,\ y_0=1[/tex]

Substitute:

[tex]y-1=\dfrac{3}{4}(x-4)[/tex]

The slope-intercept form:

[tex]y=mx+b[/tex]

Solve for y:

[tex]y-1=\dfrac{3}{4}(x-4)\qquad|\text{use distributive property}\\\\y-1=\dfrac{3}{4}x-3\qquad|\text{add 1 to both sides}\\\\y=\dfrac{3}{4}x-2[/tex]

Answer: D.

Answer: The correct statements are 0.75 (x,y) = (0.75x, 0.75y) , LM is parallel to L'M' and "the vertices of the image are closer to the origin than those of the preimage".

Explanation:

It is given that the triangle ABC was dilated according to the rule DO,0.75 (x,y)

DO, 0.75(x,y) represents the rule of dilation. Where both x- and y-coordinates are multiplied by 0.75 the dilation is about the origin has a scale factor of 0.75. The  notation for this dilation would be,

[tex](x,y)\rightarrow (0.75x,0.75y)[/tex]

Therefore, the first statement is true.

Since both x- and y-coordinates are multiplied by 0.75, therefore the sides of image and preimage are parallel but the sides of image are 0.75th of the side of preimage.

Therefore, the second statement "LM is parallel to L'M'" is true but the third and fifth statement is false.

The scale factor is 0.75 which is less than 1, so the vertices of the image are closer to the origin than those of the pre-image.

Therefore, the forth statement "The vertices of the image are closer to the origin than those of the pre-image"  is true.

Answer: 124

Step-by-step explanation: