Consider the following equations:

Which is a valid conclusion that can be drawn from these statements?

photoshop1234 [79]

Answer:

both statement have valid conclusions.

Step-by-step explanation:

A rhombus is a parallelogram with all sides equal.

A parallelogram has opposite angles congruent.

Therefore

both statements have valid conclusions.

5 0

3 years ago

Brian has a gift card with a $250 balance. He buys several video games that cost $33 each. After the purchases, his gift card ba

Leno4ka [110]

Answer: x=6.6969

Step-by-step explanation:

250-(33x)=29

-33x=-221

x=6.6969

5 0

3 years ago

Read 2 more answers

If sinA =3/5 and A+B =90 find cosB

-Dominant- [34]

$A+B=90^o\to B=90^o-A\\\\\cos B=\cos(90^o-A)=\cos90^o\cos A+\sin90^o\sin A\\\\=\cos A+1\cdot\dfrac{3}{5}=0+\dfrac{3}{5}=\dfrac{3}{5}\\\\\boxed{\cos B=\dfrac{3}{5}}$

$Used:\\\\\cos(x+y)=\cos x\cos y+\sin x\sin y\\\\\cos90^o=0,\ sin90^o=1$

Other method:

Look at the picture.

$\sin\theta=\dfrac{opposite}{hypotenuse}\\\\\sin A=\dfrac{3}{5}\to opposite=3\ and\ hypotenuse=5$

$\cos\theta=\dfrac{adjacent}{hypotenuse}\\\\adjacent=3\ and\ hypotenuse=5\to\cos B=\dfrac{3}{5}$

8 0

3 years ago

Tell me what each angle is in the following triangle: angle 1 is 8x, angle 2 is 2x+3, angle 3: 30 degrees. give me the two answe

9966 [12]

Answer: 117.6° ; 32.4° .
_________________________
Explanation:
_______________________________________________________
Note: ALL triangles, by definition, have exactly 3 (THREE) sides and exactly 3 (THREE) angles.
_____________________
We are given the following:
_______________________
We have a triangle.

Angle 1: m∡1 = (8x) ;

Angle 2: m∡2 = (2x + 3) ;

Angle 3: m∡3 = 30.
______________________________________
We are asked to find: "m∡1" and " m∡2" .
______________________________________
Note: In ALL TRIANGLES, the measurements of all THREE (3) angles ALWAYS add up to 180 degrees.
________________________________________
So, " m∡1 + m∡2 + m∡3 = 180 " .
________________________________________
Let us substitute our given values for the measurements in EACH of
the THREE (3) angles — on the left-hand side of the equation; then solve for "x" ; then substitute that solved value for "x" into the given expressions for BOTH "m∡1" AND "m∡2" ; to find the values for " m∡1" AND " m∡2 " ; which are the values asked for in this very question ;
___________________________________________

  m∡1 + m∡2 + m∡3 = 180 ;
___________________________________________
8x + (2x + 3) + 30 = 180 ;
___________________________________________
8x + 2x + 3 + 30 = 180 ;
___________________________________________
Combine the "like terms" on the 'left-hand side" of the equation; to simplify:
____________________________________________________________
+8x + 2x = +10x ;
___________________________________________
+3 + 30 = +33 ;
___________________________________________
Rewrite the entire equation, as:
___________________________________________
10x + 33 = 180 ;
___________________________________________
Now, subtract "33" from EACH SIDE of the equation:
___________________________________________
10x + 33 − 33 = 180 −<span> 33 ;
___________________________________________
to get:
___________________________________________
10x = 147 ;
____________________________________________
Now, divide EACH side of the equation by "10" ; to isolate "x" on ONE SIDE of the equation; and to solve for "x" :
____________________________________________
10x / 10 = 147 / 10 ;
____________________________________________
to get:
____________________________________________
x = 14.7 ;
___________________________________________
Now, given the following, we plug in our solved value, "14.7", for "x", into the expression given for "m</span>∡1" and "m∡2"; as follows:
________________________________________________

Angle 1: "(8x)" = 8*(14.7) = 117.6° ;
________________________________________________
Angle 2: "2x + 3" = 2*(14.7) + 3 = 29.4 + 3 = 32.4° ;
________________________________________________
These are the two answers; that is the 2 (TWO) values asked for in the question: 117.6° ; 32.4° .
<span>____________________________________</span><span>
Do they make sense? That is, do the measurements of ALL 3 (THREE) angles; that is, our two solved measurements added together, and then added to the value of the third angle (given: "m</span>∡3 = 30°); all add up to 180° ?
___________________________________________
Let us check:
_______________________________
m∡1 + m∡2 + m∡3 = 180 ;
_______________________________
Plugging in our solved values for "m∡1" and "m∡2" ; and our given value: "30" — for "m∡3 — does the equation hold true?
______________________________________________
→ 117.6 + 32.4 + 30 = ? 180 ??
______________________________________________
→ 117.6 + 32.4 = 150 ;   → 150 + 30 =? 180 ? Yes!
______________________________________________

4 0

4 years ago

Lesson 4-3 Dividing Mixed Numbers Practice and Problem Solving: A/B

muminat

Answer:

<h3>Reciprocals are: </h3>

1) 10 1/2 = 21/2

Reciprocal will be 2/21

2) 6 3/7 = 45/7

Reciprocal will be 7/45

3) 2 8/9 = 26/9

Reciprocal will be 9/26

4) 15 1/4 = 61/4

Reciprocal will be 4/61

5) 9 2/3 = 29/3

Reciprocal will be 3/29

6) 7 5/8 = 61/8

Reciprocal will be 8/61

<h3>Divide</h3>

7) 8/10 divide by 1 5/6

8/10 divide by 11/6

or 8/10 * 6/11

4/5* 6/11

24/55

8) 2 divides by 1 6/7

2 divides by 13/7

2 * 7/13

14/13

1 1/13

9) 3 3/5 divides by 2 1/4

18/5 divides by 9/4

18/5 * 4/9

8/5

1 3/5

10) 4 1/2 divides by 2 3/8

9/2 divides by 19/8

9/2 * 8/19

36/19

1 17/19

11) 5 5/6 divides by 3 1/6

35/6 divides by 19/6

35/6 * 6/19

35/19

1 16/19

12) 11/12 divides by 2 5/8

11/12 divides by 21/8

11/12 * 8/21

22/63

13) 1 9/13 divides by 3/8

22/13 divides by 3/8

22/13 * 8/3

176/39

4 20/39

14) 6 4/5 divides by 3 2/9

34/5 divides by 29/2

34/5 * 2/29

68/145

15) 9 2/3 divides by 6 8/9

29/3 divides by 62/9

87/62

1 25/69

<h3>Division problem</h3>

Width of patio = 5 2/3 feet

Area of patio = 36 5/6 sq. feet

Length will be: area /width

36 5/6 divides by 5 2/3

221/6 divides by 17/3

221/6 * 3/17

13/2

6 1/2 feet

Length is 6 1/2 feet, that means we can place the concrete patio on a 7 foot picnic table.

17) Area of mirror = 225 sq. inches

Width of mirror = 13 3/4 inches.

Length of mirror will be=area/ width

225 divides by 13 3/4

225 divides by 55/4

225 * 4/55

180/11

16 4/11

The width of mirror will be 16 4/11 feet. It is greater than 16 feet. Therefore mirror can't be fit in a space of 15 inches by 16 inches.

18) Total length of fabric = 16 1/5 yards

One fabric piece size= 5 2/5

Number of fabric pieces will be= total length/ 1 fabric length

16 1/5 divides by 5 2/5

81/5 divides by 27/5

81/5*5/27

3

There will be total 3 pieces of size 5 2/5 yards.

3 0

4 years ago