Determine the relationship between The two triangles on whether or not they can be proven to be congruent

Answer:

[tex]\boxed {\boxed {\sf y= -7x -30}}[/tex]

Step-by-step explanation:

We are asked to find the equation of a line,  given a point and a slope.

We can use the point-slope formula:

[tex]y-y_1= m(x-x_1)[/tex]

In this formula, (x₁, y₁) is the point and m is the slope. This line has a slope of -7 and passes through the point (-5,5). Therefore:

Substitute the values into the formula.

[tex]y-5= -7 (x- -5)[/tex]

[tex]y-5= -7(x+5)[/tex]

We want to give the answer in slope-intercept form, or y=mx+b. We must isolate the variable y.

First, distribute the -7 on the right side of the equation. Multiply each term inside the parentheses by -7.

[tex]y-5= (-7*x) + (-7*5)\\y-5 = (-7x) + (-35) \\y-5= -7x -35[/tex]

5 is being subtracted from y. The inverse operation of subtraction is addition. Add 5 to both sides of the equation.

[tex]y-5+5 =-7x -35 +5 \\y= -7x -35 +5 \\y= -7x +30[/tex]

The equation of the line is y= -7x+30.

Step-by-step explanation:

Camilla started her collection with 20 buttons, meaning that this number is a constant, and that it will not change: (+20)

She then collects 5 buttons per month. Month is represented by the variable, x (given by the question), and there are 5 per month (so you multiply).

Set the equation:

Total pins = Amount of pins per month x amount of months + Amount of pins started.

y = 5x + 20

In this case, plug in the amount of months (x) to obtain your total (y):

When x = 0, y = 20

y = 5(0) + 20

y = 0 + 20

y = 20

When x = 1 , y = 25

y = 5(1) + 20

y = 5 + 20

y = 25

When x = 2, y = 30

y = 5(2) + 20

y = 10 + 20

y = 30

When x = 3, y = 35

y = 5(3) + 20

y = 15 + 20

y = 35

When x = 4, y = 40

y = 5(4) + 20

y = 20 + 20

y = 40

~

Note: This is a linear graph, so you can choose any of these given points (and more if you want to plot more). I would choose two that aren't too close to each other, unless you want a really small graph size.

Answer:

(-1,1)

Step-by-step explanation:

Im pretty sure the answer to A'' would be the inverse of A, as the triangle was mirrored on the opposite quadrant of the graph. (The inverse or opposite  of (1,-1) would be (-1,1) ).

Hope this helped!

Answer:

50%

Step-by-step explanation:

shaded area = 2/4

shaded area as a percentage ;

     2 / 4 x 100

  = 1 / 2 x 100

  = 1 / 1 x 50

  = 50%

The sample mean of the random sample is 50

The margin of error (E) is the amount of error allowed in the random sample.

The confidence interval (CI) is given by:

CI = μ ± E = (μ - E, μ + E)

Given a confidence interval of (38.02, 61.98), hence:

μ - E = 38.02     (1)

μ + E = 61.98     (2)

Hence solving equations 1 and 2 simultaneously gives:

μ = 50, E = 11.98

Hence the sample mean of the random sample is 50

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Answer:

-60

Step-by-step explanation:

Any number within the absolute value sign is always positive.

−|60|  

- x 60  Negative sign times 60

=-60

Hope this helps :)

Answer:

17504.40

Step-by-step explanation:

You take 17100 x 2.4% and get 410.40

add 17100 and 410.40 and get 17504.40

Answer:

40

Step-by-step explanation:

Answer:

1/4 in decimal form is 0.25. You can convert any fraction into a decimal by just diving the numerator by the denominator.

Every time you see a fraction sign basically “—“ it jsut means divide by.

Now you can just divide. 1/4= 0.25

now we Increase which just means add

2.75+0.25 =3

Answer:

Step-by-step explanation:

Begin by finding a common denominator in the numerator of that rational expression. The common denominator is 3(x+2):

[tex]\frac{\frac{(3)1}{(3)x+2} -\frac{(x+2)1}{3(x+2)} }{x-1}[/tex] which simplifies to

[tex]\frac{\frac{3}{3x+6} -\frac{(x+2)}{3x+6} }{x-1}[/tex] which simplifies further to

[tex]\frac{\frac{3-x-2}{3x+6} }{x-1}[/tex] and

[tex]\frac{\frac{1-x}{3x+6} }{x-1}[/tex]  Bring up the lower fraction and flip it and multiply:

[tex]\frac{1-x}{3x+6}*\frac{1}{x-1}[/tex]  In order to make the 1-x into x-1, multiply the numerator of that fraction on the left by -1 to get:

[tex]-\frac{x-1}{(3x+6)(x-1)}[/tex] and now the x-1 terms cancel out, leaving us with:

[tex]-\frac{1}{3(1)+6}=-\frac{1}{9}=-.1111[/tex]

[tex]\lim \limits_{n \to \infty} ~\dfrac{8n}{3n^2 +5} \\\\\\=8\lim \limits_{n \to \infty} ~ \dfrac{\tfrac n{n^2}}{\tfrac{3n^2}{n^2} + \tfrac 5{n^2}}\\\\\\=8 \lim \limits_{n \to \infty} ~\dfrac{ \tfrac 1n}{ 3 + \tfrac 5{n^2}}}\\\\\\=8 \cdot \dfrac{ 0}{3 +0} = 8 \cdot 0 = 0[/tex]

We want to evaluate the limit of [tex]\frac{8n}{3n^{2}+5}[/tex] as n tends toward infinity (+∞)

The limit of this expression is the same as the limit of [tex]\frac{8n}{3n^{2}}[/tex]

But this last expression can be simplified, we can remove one n up and down which gives us : [tex]\frac{8}{3n}[/tex]

We know the limit of this one, it is simply Zero 0, by definition of the class lesson.

So to conclude the limit of [tex]\frac{8n}{3n^{2}+5}[/tex] as n tends toward infinity is 0.

Good Luck

[tex]2v - 3u\\\\=2<3,7> - 3<-5,4>\\\\=<6,14>-<-15,12>\\\\=<6+15, 14-12>\\\\=<21,2>[/tex]

Answer:

Step-by-step explanation:

Answer:

7 Decenas = 70 Unidades espero que te ayude

Step-by-step explanation:

Answer:

c :)

Step-by-step explanation:

i guessed and got it right <3

Answer:

B= (-1,0,1)

Step-by-step explanation:

because -1 is not a whole number.

Answer:

B = {-1, 0, 1)

Step-by-step explanation:

The answer is B = {-1, 0, 1) because -1 is not a whole number.

Hope this helps :)

Line m and line l are parallel as m∠2 = m∠3

An equation is an expression that shows the relationship between two or more variables and numbers.

Two angles are said to be supplementary if they add up to 180 degrees.

m∠1 + m∠2 = 180° (Given)

m∠1 + m∠3 = 180° (sum of angles on a straight line)

Hence:

m∠1 + m∠2 = m∠1 + m∠3

m∠2 = m∠3

Line m and line l are parallel as m∠2 = m∠3

Find out more on Equation at: https://brainly.com/question/2972832

=====================================================

Explanation:

Refer to the dice chart below. It represents all possible ways to roll two dice and sum up the face values.

According to the table, there are...

There are A+B+C+D = 1+2+3+4 = 10 instances where we get a sum between 2 and 5. The table shows 6*6 = 36 sums total. This means there are 36-10 = 26 sums where they are between 6 and 12, aka "the sum being greater than 5".

Those 26 sums are what we focus on. Out of those 26 items, four of them are sums of "9".

The probability we want is therefore 4/26 = 2/13

The probability that the sum of the dice is 9, given that the sum is greater than 5 is 0.154

See attachment for the sample space of a roll of two dice.

From the attached sample space,

Represent the events that a sum is greater than 5 with A, and a sum is greater than 5 is 9 with B.

So, we have:

[tex]n(A) = 26[/tex]

[tex]n(A\ n\ B) = 4[/tex]

The probability that the sum of the dice is 9, given that the sum is greater than 5 is then calculated using:

[tex]Pr = \frac{n(A\ n\ B)}{n(A)}[/tex]

This gives

[tex]Pr = \frac{4}{26}[/tex]

[tex]Pr = 0.154[/tex]

Hence, the probability is 0.154

Read more about probability at:

https://brainly.com/question/251701

Answer:

y = -1/4x + 2

Step-by-step explanation:

1. First you find m. Because the line is slanting downwards, you know it is negative. Then you can find the number by looking at the rise over run (rise/run). We can go up 1 (rise) and then to the side 4 (run). We go to the right side 4 because that is where the line intersects with up 1. So because the rise goes over the run, the number would be 1/4. But remember that it is negative so m = -1/4

2. Now we have to find c. For this you just have to go up or down the y-axis until you find the point where it intersects with the line. On this graph it intersects on positive 2. So c = + 2

Answer:

Range: {-5, 19, 31}

Step-by-step explanation:

Given the linear function, f(x) = 2x + 1, and the domain, {-3, 9, 15}.

In order to determine the range of the given linear function, simply substitute each domain value as inputs into the function.

f(x) = 2x + 1

f(-3) = 2(-3) + 1

f(-3) = -6 + 1

f(-3) = -5

f(9) = 2x + 1

f(9) = 2(9) + 1

f(9) = 18 + 1

f(9) = 19

f(15) = 2x + 1

f(15) = 2(15) + 1

f(15) = 30 + 1

f(15) = 31

Therfore, the range of the function is: {-5, 19, 31}.

Answer:     3 :3 :3

                 $8.88

Step-by-step explanation:

Answer:

10.446

Step-by-step explanation:

Answer:

48

Step-by-step explanation:

212 + 163 = 375    <---- These are the students

423 - 375 = 48     <----- These are the teachers

Answer:

42

Step-by-step explanation:

168 factors into

2•2•2•3•7

two of the 2's make a perfect square

(2•2)•2•3•7

   2²•2•3•7

as none of the product of the remaining factors makes a perfect square

2•3 = 6,  2•7 = 14,  3•7 = 21

we need to multiply the remaining factors together to find another perfect square

   2²•(2•3•7)²

2•3•7 = 42

42(168) = 7056 = 84²

=======================================================

Explanation:

Your teacher wants you to use the angle-angle-side congruence theorem, which abbreviates to AAS. Note in the diagram that we have two pairs of angles marked.

So we have the info about the angles being congruent, and that takes care of the two "A"s in AAS.

We just need a pair of sides to be congruent. Specifically, we need the pair of sides that are not between the angles mentioned for either triangle. If we went for this option, then we'd go for ASA instead of AAS. The order is important.

So we have two possible answers

If either of those were given to us, then we can use the AAS theorem.  Unfortunately PR = UT isn't listed, but QR = ST is listed. So this is why choice B is the answer.

Side note: Both QR and ST are opposite the double arc angle.

Answer:

QR≅ST

Step-by-step explanation:

With AAS congruence, you need 2 angles and a non-included side. On ΔPQR, that could be either PR or QR. PQ is the included side as it is between the angles, and therefore cant be used for this congruence theorem.

As said above, it can be either PR or QR, but it has to be QR in this case as there is no answer option for PR.

On the other triangle, the corresponding side is ST. ∠S and ∠Q are corresponding, and US is the included side, so that leaves only ST.

Finally, the information you need to prove that the triangles are congruent is QR≅ST.

Answer:

The answer is 24 with remainder of 1

Step-by-step explanation:

First, solve the problem by seeing what number gives you 4 when multiplied by 2. That would be 2 (2x2=4)

you subtract 4 by 4 to get zero and bring down the nine

Then you see which number would get you close to nine without overlapping when multiplied by two. That would be 4 (2x4=8)

your answer would be 24 then you subtract 9 by 8 to get a remainder of 1

Answer:

Part A would be C because divided 30 by 5 to get the unit rate.

Part B would be B

Answer:

C). −30÷5

B). –$6

Step-by-step explanation:

Answer:

d. It does, the points shown on the line would be part of y = −2x.

is the answer let me know if this helped

Step-by-step explanation:

Answer:

d

Step-by-step explanation:

hope i helped

as there are 30 children and from 30 children 2 will be picked (which will than be 2/30)

but if we simplify that by 2, than that will lead to the ANSWER OF: 1/15