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3 years ago

ABCD is a rectangle. Find the length of each diagonal.ac=2(5a+1) bd=2(a+1).

1 answer:

7 0

Rectangle diagonals are equal.

2(5a+1) = 2(a+1)
10a + 2 = 2a + 2
10a -2a = 2 - 2
8a = 0
⇒ a = 0

AC = 2(5a+1) = 2(5 × 0 +1)= 2(0 + 1) = 2 × 1 = 2 
BD = 2(a+1) = 2(0 + 1) = 2 × 1 = 2

Ansver: AC = BD = 2

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Find the area of the trapezoid with a base of 19 inches, height 12.6 inches and base 29.2 inches

aksik [14]

Minor base: b=19 inches
Height: h=12.6 inches
Major base: B=29.2 inches

Area of the trapezoid: A
A=(b+B)h/2
Replacing the values:
A=(19 inches + 29.2 inches) (12.6 inches) / 2
A=(48.2 inches) (12.6 inches) / 2
A= (607.32 inches^2 ) /2
A= 303.66 inches^2

Answer: The area of the trapezoid is 303.66 square inches

3 0

3 years ago

Read 2 more answers

A circle has a radius of 5 in. A central angle that measures 150° cuts off an arc.

Slav-nsk [51]

Answer:

Part 1) The exact value of the arc length is $\frac{25}{6}\pi \ in$

Part 2) The approximate value of the arc length is $13.1\ in$

Step-by-step explanation:

step 1

Find the circumference of the circle

The circumference of a circle is equal to

$C=2\pi r$

we have

$r=5\ in$

substitute

$C=2\pi (5)$

$C=10\pi\ in$

step 2

Find the exact value of the arc length by a central angle of 150 degrees

Remember that the circumference of a circle subtends a central angle of 360 degrees

by proportion

$\frac{10\pi}{360} =\frac{x}{150}\\ \\x=10\pi *150/360\\ \\x=\frac{25}{6}\pi \ in$

step 3

Find the approximate value of the arc length

To find the approximate value, assume

$\pi =3.14$

substitute

$\frac{25}{6}(3.14)=13.1\ in$

7 0

3 years ago

How do you eliminate the parameter theta to find a Cartesian equation of the curve: x=sin(1/2 theta), y=cos(1/2 theta), 0 is les

kiruha [24]

The answer to the problem is as follows:

x = sin(t/2)
y = cos(t/2) 

Square both equations and add to eliminate the parameter t: 

x^2 + y^2 = sin^2(t/2) + cos^2(t/2) = 1 

The final step is translating the original parameter limits into limits on x and y. Over the -Pi to +Pi range of t, x varies from -1 to +1, whereas y varies from 0 to 1. Thus we have the semicircle in quadrants I and II: y >= 0.

6 0

3 years ago

Help What is the graph???

marin [14]

We are given

$y=\frac{x^2-4x+3}{x^2-9}$

Vertical asymptotes:

Firstly, we will factor numerator and denominator

we get

$y=\frac{(x-1)(x-3)}{(x-3)(x+3)}$

We can see that (x-3) is common in both numerator and denominator

so, we will only set x+3 to 0

and then we can find vertical asymptote

$x+3=0$

$x=-3$

Hole:

We can see that (x-3) is common in both numerator and denominator

so, hole will be at x-3=0

$x=3$

Horizontal asymptote:

We can see that degree of numerator is 2

degree of denominator is also 2

for finding horizontal asymptote, we find ratio of leading coefficients of numerator and denominator

and we get

y=1

now, we can draw graph

Graph:

6 0

3 years ago

Pick the expression that matches this description:

Katen [24]

Option C is correct because it is a trinomial with a leading coefficient of 3 and a constant term of -5

Step-by-step explanation:

We need to pick the expression that matches this description:

A trinomial with a leading coefficient of 3 and a constant term of -5

First lets explain the terms:

Trinomial: a polynomial having 3 terms

Leading coefficient: The constant value of variable having highest power

Constant term: Having no variable and value cannot be changed.

Now using these definitions, we can choose the correct option

Option A is incorrect because the expression has 2 terms

Option B is incorrect because it is a trinomial but the leading coefficient is -5 and not 3 constant term is 3 and not -5.

Option C is correct because it is a trinomial with a leading coefficient of 3 and a constant term of -5

Option D is incorrect because it is a trinomial but the leading coefficient is 3 but constant term is 1 and not -5.

So, Option C is correct.

Keywords: Algebra

Learn more about Algebra at:

#learnwithBrainly

6 0

2 years ago