The sum of the measures of two angles is 107.3º. One angle has a measure of 51º. What is the measure of the second angle?

Point M is the midpoint between points A and B. If A(-7, 2) and B(-1,-4) find the location of M.

rjkz [21]

Answer:

M(-4, -1)

Step-by-step explanation:

M = (A +B)/2

M = ((-7, 2) +(-1, -4))/2 = (-8, -2)/2 = (-4, -1)

The location of M is (-4, -1).

4 0

3 years ago

Ms. Jimenez surveyed 430 men and 200 women about their vehicles. Of those surveyed, 160 men and 85 women said that they own a wh

Neko [114]

Answer:

3/7

Step-by-step explanation:

430 +200 = 630 (630 people in all)

430-160 =270 (270 men NO WHITE CAR)

270/630 = 3/7

5 0

3 years ago

Please help!! Find the domain and range of the following function ƒ(x) = 5|x - 2| + 4

blagie [28]

Answer:

There are no restrictions on x, so the domain is (-∞,∞)

When x = 2, 5|x - 2| = 0, so the range is [4,∞)

Step-by-step explanation:

6 0

3 years ago

2(x+6)=3(x+1) Solving equations with variables on both sides. ;)

N76 [4]

Step-by-step explanation:

2(x+6)=3(x+1)

2x+12=3x+3

collect the like terms

2x + 3x = 3+12

x=15/5=3

or

2x-3x = 3-12

= -9

5 0

3 years ago

Rectangle 1 has length x and width y. Rectangle 2 is made by multiplying each dimension of Rectangle 1 by a factor of K, where k

STALIN [3.7K]

$\bold{\huge{\underline{\pink{ Solution }}}}$

<h3>Given :- </h3>

Rectangle 1 has length x and width y
Rectangle 2 is made by multiplying each dimensions of rectangle 1 by a factor of k
Where, k > 0

<h3>Answer 1 :-</h3>

Yes, The rectangle 1 and rectangle 2 are similar .

<h3>According to the similarity theorem :-</h3>

If the ratio of length and breath of both the triangles are same then the given triangles are similar.

Let's Understand the above theorem :-

The dimensions of rectangle 1 are x and y

Now, 

Rectangle 2 is made by multiplying each dimensions of rectangle 1 by a factor of k .

Let assume the value of K be 5

Therefore, 

The dimensions of rectangle 2 are

$\sf{ 5x \:and \:5y }$

Now, The ratios of dimensions of both the rectangle :-

$\bold{Rectangle 1 = Rectangle 2}$

$\bold{\dfrac{ x }{y}}{\bold{ = }}{\bold{\dfrac{5x}{5y}}}$

$\bold{\blue{\dfrac{ x }{y}}}{\bold{\blue{ = }}}{\bold{\blue{\dfrac{x}{y}}}}$

From above, 

We can conclude that the ratios of both the rectangles are same

Hence , Both the rectangles are similar

<h3>Answer 2 :- </h3>

Here, 

We have to proof that, the

Perimeter of rectangle 2 = k(perimeter of rectangle 1 )

In the previous questions, we have assume the value of k = 5

<h3>Therefore, </h3>

According to the question,

Perimeter of rectangle 1

$\sf{ = 2( length + Breath) }$

$\bold{\pink{= 2( x + y ) }}$

Thus, The perimeter of rectangle 1

Perimeter of rectangle 2

$\sf{ = 2( length + Breath) }$

$\sf{ = 2(5x + 5y) }$

$\sf{ = 2 × 5( x + y) }$

$\bold{\pink{= 10(x + y) }}$

Thus, The perimeter of rectangle 2

According to the given condition :-

Perimeter of rectangle 2 = k( perimeter of rectangle 1 )

Subsitute the required values,

$\sf{ 2(x + y) = 10(x + y)}$

$\bold{\pink{2x + 2y = 5(2x + 2y) }}$

From Above, 

We can conclude that the, Perimeter of rectangle 2 is 5 times of perimeter of rectangle 1 and we assume the value of k = 5.

Hence, The perimeter of rectangle 2 is k times of rectangle 1

<h3>Answer 3 :</h3>

Here, 

We have to proof that ,

The area of rectangle 2 is k² times of the area of rectangle 1.

That is, 

Area of rectangle 1 = k²( Area of rectangle)

<h3>Therefore, </h3>

According to the question,

Area of rectangle 1

$\sf{ = Length × Breath }$

$\sf{ = x × y }$

$\bold{\red{= xy }}$

Area of rectangle 2

$\sf{ = Length × Breath }$

$\sf{ = 5x × 5y }$

$\bold{\red{ = 25xy }}$

According to the given condition :-

Area of rectangle 1 = k²( Area of rectangle)

$\sf{ xy = 25xy }$

$\bold{\red{xy = (5)²xy }}$

From Above, 

We can conclude that the, Area of rectangle 2 is (5)² times of area of rectangle 1 and we have assumed the value of k = 5

Hence, The Area of rectangle 2 is k times of rectangle 1 .

7 0

2 years ago