If your car gets 34 miles per gallon of gas and you have traveled 153 miles, how many gallons of gas have you used?

In rectangle ABCD, AC = -x + 21, BP = -9x + 19, and DP = -y + 5. Find the value of y.

creativ13 [48]

Answer:

y=-5

Step-by-step explanation:

see the attached figure to better understand the problem

we know that

The diagonals of a rectangle are equal and bisect each other

so

$BP=\frac{1}{2}AC$

$DP=BP$

step 1

Find the value of x

$BP=\frac{1}{2}AC$

substitute the given values

$(-9x+19)=\frac{1}{2} (-x+21)$

solve for x

Multiply by 2 both sides

$-18x+38=-x+21$

$18x-x=38-21\\17x=17\\x=1$

step 2

Find the value of y

$DP=BP$

we have

$BP=-9x+19$

$DP=-y+5$

substitute

$-y+5=-9x+19$

substitute the value of x

$-y+5=-9(1)+19\\-y+5=10\\y=5-10\\y=-5$

5 0

3 years ago

Last month Kim trained 3 times as many dogs as cats.

Lisa [10]

Answer:

8

Step-by-step explanation:

dog=3x

cat=x

3x+x=32

4x=32

4/4

32/4

x=8

3(8)=24

x=8

So she trained 24 dogs and 8 cats

6 0

3 years ago

The first four terms of a sequence are shown below: 9, 5, 1, â’3 Which of the following functions best defines this sequence? f(

matrenka [14]

The function that best defines this arithmetic sequence is:

$f(n) = f(n - 1) - 4, f(1) = 9$

<h3>What is an arithmetic sequence?</h3>

In an <em>arithmetic sequence,</em> the <u>difference between consecutive terms is always the same</u>, called common difference d.

The recursive function that defines the sequence is:

$f(n) = f(n - 1) + d$

$f(1) = f_0$

In which $f_0$ is the first term.

In this problem, the sequence is: {9, 5, 1, -3}

Each term is the previous term subtracted by 4, hence $d = -4$ .

The first term is 9, hence $f_0 = 9$ .

Hence, the function is:

$f(n) = f(n - 1) - 4, f(1) = 9$

You can learn more about arithmetic sequences at brainly.com/question/6561461

5 0

2 years ago

Read 2 more answers

Using the Two Tangent Theorem

Brums [2.3K]

Answer:44

Step-by-step explanation:

4 0

3 years ago

Read 2 more answers

Find the perimeter and the area of each shape. Give your answer as a completely simplified exact value in terms of π (no approxi

nydimaria [60]

Answer:

Circumference: 12π + 8 cm,

Area: 48 ( cm )^2

Step-by-step explanation:

This figure is composed of circles, squares, and semicircles. As you can see, the squares indicate that each semicircle should have ( 1 ) the same area, and ( 2 ) the same length ( circumference ). It would be easier to take the circumference of the figure first, as it is composed of arcs part of semicircles the same length.

Circumference of 1 semicircle = $\frac{1}{2}$ ( πd ) = $\frac{1}{2}$ π( 4 ) = 2π ( cm )

Circumference of Figure (composed of 6 semicircles + 2 sides of a square),

We know that 6 semicircles should be 6 $*$ 2π, and as the sides of a square are equal - if one side is 4 cm, the other 3 are 4 cm as well. Therefore the " 2 sides of a square " should be 2

Circumference of Figure = 6 $*$ 2π + 2 = 12π + 8 ( cm )

_____________

The area of this figure is our next target. As you can see, it is composed of 3 semicircles, and the area of 3 semicircles subtracted from the area of 3 squares. Therefore, let us calculate the area of 1 semicircle, and the area of 1 square first.

Area of 1 semicircle = 1/2π $r^2$ = 1/2π $(2)^2$ = 2π ( cm ),

Area of 1 square = ( 4 cm )( 4 cm ) = 16 ( $cm^2$ )

So, the area of the figure should be the following -

Area of Figure = 3 $*$ 2π + 3( 16 - 2π ) = 48 ( cm )^2

3 0

3 years ago