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2 years ago

Parallelogram P Q S R is shown. The length of P Q is (2 x + 5) centimeters and the length of R S is (4 x + 1) centimeters.

Mathematics

1 answer:

lisabon 2012 [21]2 years ago

8 0

Answer:

9 cm

Step-by-step explanation:

In a parallelogram, opposite sides are equal.

RS = PQ

4x + 1 = 2x + 5

Now, to find the value of x,

Step1. Subtract 1 from both sides

4x = 2x + 5 - 1

4x = 2x + 4

Step 2: Subtract 2x from both sides

4x - 2x = 4

2x = 4

Step 3: Divide both sides by 2

x = 4/2

x = 2

PQ = 2x + 5

= 2*2 + 5

= 4 + 5

PQ = 9 cm

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Find the slope between the two points given. Then, use the slope and one of the points to write the equation of the line in Slop

Anika [276]

Answer:

Equation: y=2x-1

Slope: 2

y-intercept: -1

Step-by-step explanation:

Hi there!

We are given the points (-1, -3) and (-2, -5). We need to find the slope, equation of the line, and the y intercept of the line

First, let's find the slope

The formula for the slope (m) calculated from two points is $\frac{y_2-y_1}{x_2-x_1}$ where ( $x_1$ , $y_1$ ) and ( $x_2$ , $y_2$ ) are points

We have everything we need for the formula, but let's label the values of the points to avoid any confusion

x1=-1

y1=-3

x2=-2

y2=-5

Now substitute into the formula (remember: the formula has SUBTRACTION):

m= $\frac{-5--3}{-2--1}$

simplify

m= $\frac{-5+3}{-2+1}$

add

m= $\frac{-2}{-1}$

divide

m=2

So the slope is 2

Now let's find the equation of the line

The question asks for it to be in slope-intercept form, which is y=mx+b, where m is the slope and b is the y intercept

We calculated the slope from earlier, so let's substitute that into the equation

y=2x+b

Now we need to find b

The equation will pass through both (-1, -3) and (-2, -5) so we can use either one of them to solve for b (doesn't matter which one)

Let's take (-1, -3) as an example

substitute -1 as x and -3 as y into the equation

-3=2(-1)+b

multiply

-3=-2+b

Add 2 to both sides

-1=b (the value of the y intercept!)

Substitute -1 as b into the equation

y=2x-1

We found everything needed for this problem

Hope this helps!

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3 years ago

The table of values represents an exponential function f(x).

Ostrovityanka [42]

Answer:

-3.98 (nearest hundredth)

Step-by-step explanation:

The average rate of change of function f(x) over the interval a ≤ x ≤ b is given by:

$\dfrac{f(b)-f(a)}{b-a}$

Given interval: -2 ≤ x ≤ 2

$\implies a = -2$

$\implies b = 2$

$\implies f(a) = f(-2)=16$

$\implies f(b) =f(2)= \dfrac{1}{16}$

Substituting the values into the equation:

$\begin{aligned}\implies \textsf{rate of change} & =\dfrac{\frac{1}{16}-16}{2-(-2)}\\\\ & = \dfrac{-\frac{255}{16}}{4}\\\\ & = -\dfrac{255}{64}\\\\ & = -3.98\: \sf (nearest\:hundredth)\end{aligned}$

7 0

2 years ago

If Jeremy drinks 1 1/2 quarts of coffee every 3 days, how many liters of coffee would Jeremy drink in 3 weeks? (1 quart = 0.946

Nostrana [21]

Answer:

9.93 liter approximately 10 liter

Step-by-step explanation:

3 days = 3/2 quart

3 week = 3/2/3 × 21 quarts

= 1/2×21

=21/2 quarts

now

1 quart = 0.946 liter

21/2 quart = 0.946×21/2 liter

21/2 quart = 9.93 liter

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2 years ago

What is the slope intercept form of the line that passes through the point (-2,-18) and has a slope of 1/4

mart [117]

Answer:

y=(1/4)x - 35/2

Step-by-step explanation:

y=mx+b

y=(x/4)+b plug in the slope (m)

-18=(-2/4)+b plug in x and y

b= -17 1/2= -35/2 solve for b

y=(1/4)x - 35/2 plug in m and b into the equation

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3 years ago

I have yet to understand this subject

Oliga [24]

the answer is -3/2 and -11/2

5 0

3 years ago