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3 years ago

13

The two parallelograms in the sketch below are congruent. Which sequence exhibits their congruence? A reflection across the y-ax

is followed by a translation 10 units left A reflection across the x-axis followed by a translation 10 units up A reflection across the y-axis followed by a translation 10 units right A reflection across the x-axis followed by a translation 10 units left

2 answers:

Oxana [17]3 years ago

4 0

A reflection across the y-axis followed by a translation 10 units right

BartSMP [9]3 years ago

3 0

A reflection across the y-axis followed by a translation 10 units right

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Given: △ABC, AB=5 square root 2 <br><br>m∠A=45°, m∠C=30°<br><br>Find: BC and AC

hichkok12 [17]

Answer:

Part a) $BC=10\ units$

Part b) $AC=13.66\ units$

Step-by-step explanation:

step 1

Find the length side BC

Applying the law of sines

we know that

$\frac{AB}{sin(C)}=\frac{BC}{sin(A)}$

we have

$AB=5\sqrt{2}\ units$

$A=45^o$

$C=30^o$

substitute

$\frac{5\sqrt{2}}{sin(30^o)}=\frac{BC}{sin(45^o)}$

solve for BC

$BC=\frac{5\sqrt{2}}{sin(30^o)}(sin(45^o))$

$BC=10\ units$

step 2

Find the measure of angle B

we know that

The sum of the interior angles in a triangle must be equal to 180 degrees

so

$m\angle A+m\angle B+m\angle C=180^o$

substitute the given values

$45^o+m\angle B+30^o=180^o$

$75^o+m\angle B=180^o$

$m\angle B=180^o-75^o$

$m\angle B=105^o$

step 3

Find the length side AC

Applying the law of sines

we know that

$\frac{AB}{sin(C)}=\frac{AC}{sin(B)}$

we have

$AB=5\sqrt{2}\ units$

$A=45^o$

$B=105^o$

substitute

$\frac{5\sqrt{2}}{sin(30^o)}=\frac{AC}{sin(105^o)}$

solve for AC

$AC=\frac{5\sqrt{2}}{sin(30^o)}(sin(105^o))$

$AC=13.66\ units$

4 0

3 years ago

If 12 was added to one-third of a certain number to get 35. What is this number? *

PolarNik [594]

12+(1/3)x=35
(1/3)x=23
x=7.6666

3 0

3 years ago

Which of the following is a solution to the equation c+(4-3c)-2=0

Marysya12 [62]

So, what you need to do is take away the parenthesis so you can combine like terms:
c+4-3c-2=0
Add 4 and -2: 4+-2=2
Add c and -3c: c+=3c=-2c

Now you have:
2-2c=0

Add the -2c to the other side so we can work on getting c alone:
2=2c

Divide by 2 so c will now be alone:
c=1
The answer is C

Hope this helps :)

7 0

3 years ago

In the 1st generation, there are 8 raccoons in a forest.

Talja [164]

Answer:

$a(n)=8.3^{n-1}$

Choice D is correct

Step-by-step explanation:

The sequence representing the number of raccoons;

8, 24, 72

is simply but a geometric sequence with first term 8 and common ratio 3.

The formula for the n-th term of a geometric sequence with first term x and common ration r is;

$a(n)=xr^{n-1}$

In the given case, x = 8 and r = 3

We substitute these values in the above formula;

$a(n)=8.3^{n-1}$

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3 years ago

(-5q squared p) cubed

EleoNora [17]

$(-5q^{2} p)^3\\-125q^6p^3$

Final answer: $-125p^3q^6$

7 0

4 years ago

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