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lakkis [162]
3 years ago
6

Which answer gives statements that should be used to prove angles 4 and 6 are congruent?

Mathematics
1 answer:
Firdavs [7]3 years ago
5 0

Answer:

Angles 4 and 8 are congruent as corresponding angles; angles 8 and 6 are congruent as vertical angles.

Step-by-step explanation:

We know that in the given diagram

The vertical angles are the opposite angles formed when two line's meet like 8 , 6 in the given diagram.These angles are clearly equal.

The corresponding angles are the angles formed when a line meets two parallel line's Like angles 4 , 8 or 3 , 7 etc. These are also same because the cutting line makes equal angles with the two parallel line's .

So angle 4 and angle 8 are equal because they are corresponding angles and the angles 8 and angle 6 are equal because they are vertical angles.

Therefore angle 4 and angle 8 are equal.

You might be interested in
Four times the lesser of two consecutive even integers is 12 less than twice the greater number. Find the integers.
pashok25 [27]
Oh, this one lol. ok
you gotta read it like its a book.
4 x s(i picked that variable) which is 4s together

4s+12 (if they said'12 less than' then the 12 gotta be adding.)
then u have to divide it so its going to look like this:

4s+12= blah blah blah
'twice the greater number' means you gotta do this: 2(s+2)

so the problem is this: 4s+12=2(s+2)

now you solved it and the answer will beeeeee s=-4
7 0
3 years ago
In the diagram below of a parallelogram STUV, SV=x+3, VU 2x-1, and TU=4x-3. What is the length of SV?
Katena32 [7]

Answer:

SV=5\ units

Step-by-step explanation:

see the attached figure to better understand the problem

we know that

In a parallelogram opposites sides are parallel and congruent

so

In this problem

SV=TU ---> by opposite sides

substitute the given values

x+3=4x-3

solve for x

4x-x=3+3\\3x=6\\x=2

Find the length of SV

SV=x+3

substitute the value of x

SV=2+3=5\ units

5 0
3 years ago
Write number in two other forms 40,000+1,000+300+70+8
tankabanditka [31]
1.) 35,000+6,000+65+13
2.) 25,000+ 16,000+11,000+78
8 0
3 years ago
It is estimated that the average amount owed for student loans in 2010 was $25,250 per student.  If the interest rate for studen
Nostrana [21]
Given:
loan amount: 25,250
original interest rate: 3.4%
new interest rate: 6.8%
term: 10 years.

Assuming that simple interest formula is used.
I = P * r * t
I = interest
P = principal
r = interest rate
t = term/time

I = 25,250 * 3.4% * 10 years
I = 8,585

I = 25,250 * 6.8% * 10 years
I = 17,170

17,170 - 8,585 = 8,585 Additional interest paid using the new interest rate.

Using an online loan repayment calculator: Here are the following data:
Loan Balance:$25,250.00
Adjusted Loan Balance:$25,250.00Loan
Interest Rate:6.80%
Loan Fees:0.00%
Loan Term:10 years
Minimum Payment:$0.00
Monthly Loan Payment:$290.58
Number of Payments:120
Cumulative Payments:$34,869.23
Total Interest Paid:$9,619.23

<span><span>Loan Balance:$25,250.00
</span><span>Adjusted Loan Balance:$25,250.00
</span><span>Loan Interest Rate:3.40%
</span><span>Loan Fees:0.00%
</span><span>Loan Term:10 years
</span><span>Minimum Payment:$0.00</span>
<span>Monthly Loan Payment:$248.51
</span><span>Number of Payments:120</span>
<span>Cumulative Payments:$29,820.59
</span><span>Total Interest Paid:<span>$4,570.59</span></span></span>
6 0
3 years ago
(x+y)^2 (x2+2xy+y2) pleas show all work
lakkis [162]

Answer:

{x}^{4}+4{x}^{3}y+6{x}^{2}{y}^{2}+4x{y}^{3}+{y}^{4}x

​4

​​ +4x

​3

​​ y+6x

​2

​​ y

​2

​​ +4xy

​3

​​ +y

​4

​​  

Step-by-step explanation:

1 Use Square of Sum: {(a+b)}^{2}={a}^{2}+2ab+{b}^{2}(a+b)

​2

​​ =a

​2

​​ +2ab+b

​2

​​ .

({x}^{2}+2xy+{y}^{2})({x}^{2}+2xy+{y}^{2})(x

​2

​​ +2xy+y

​2

​​ )(x

​2

​​ +2xy+y

​2

​​ )

2 Expand by distributing sum groups.

{x}^{2}({x}^{2}+2xy+{y}^{2})+2xy({x}^{2}+2xy+{y}^{2})+{y}^{2}({x}^{2}+2xy+{y}^{2})x

​2

​​ (x

​2

​​ +2xy+y

​2

​​ )+2xy(x

​2

​​ +2xy+y

​2

​​ )+y

​2

​​ (x

​2

​​ +2xy+y

​2

​​ )

3 Expand by distributing terms.

{x}^{4}+2{x}^{3}y+{x}^{2}{y}^{2}+2xy({x}^{2}+2xy+{y}^{2})+{y}^{2}({x}^{2}+2xy+{y}^{2})x

​4

​​ +2x

​3

​​ y+x

​2

​​ y

​2

​​ +2xy(x

​2

​​ +2xy+y

​2

​​ )+y

​2

​​ (x

​2

​​ +2xy+y

​2

​​ )

4 Expand by distributing terms.

{x}^{4}+2{x}^{3}y+{x}^{2}{y}^{2}+2{x}^{3}y+4{x}^{2}{y}^{2}+2x{y}^{3}+{y}^{2}({x}^{2}+2xy+{y}^{2})x

​4

​​ +2x

​3

​​ y+x

​2

​​ y

​2

​​ +2x

​3

​​ y+4x

​2

​​ y

​2

​​ +2xy

​3

​​ +y

​2

​​ (x

​2

​​ +2xy+y

​2

​​ )

5 Expand by distributing terms.

{x}^{4}+2{x}^{3}y+{x}^{2}{y}^{2}+2{x}^{3}y+4{x}^{2}{y}^{2}+2x{y}^{3}+{y}^{2}{x}^{2}+2{y}^{3}x+{y}^{4}x

​4

​​ +2x

​3

​​ y+x

​2

​​ y

​2

​​ +2x

​3

​​ y+4x

​2

​​ y

​2

​​ +2xy

​3

​​ +y

​2

​​ x

​2

​​ +2y

​3

​​ x+y

​4

​​  

6 Collect like terms.

{x}^{4}+(2{x}^{3}y+2{x}^{3}y)+({x}^{2}{y}^{2}+4{x}^{2}{y}^{2}+{x}^{2}{y}^{2})+(2x{y}^{3}+2x{y}^{3})+{y}^{4}x

​4

​​ +(2x

​3

​​ y+2x

​3

​​ y)+(x

​2

​​ y

​2

​​ +4x

​2

​​ y

​2

​​ +x

​2

​​ y

​2

​​ )+(2xy

​3

​​ +2xy

​3

​​ )+y

​4

​​  

7 Simplify.

{x}^{4}+4{x}^{3}y+6{x}^{2}{y}^{2}+4x{y}^{3}+{y}^{4}x

​4

​​ +4x

​3

​​ y+6x

​2

​​ y

​2

​​ +4xy

​3

​​ +y

​4

​​  

7 0
3 years ago
Read 2 more answers
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