1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
otez555 [7]
3 years ago
6

The length of the shorter base in an isosceles trapezoid is 4 in, its altitude is 5 in, and the measure of one of its obtuse ang

les is 135°. Find the area of the trapezoid.

Mathematics
1 answer:
siniylev [52]3 years ago
5 0
The sum of angles in any quadrilateral, including trapezoid, is 360⁰. 
Because we have <span>an isosceles trapezoid, we have 2 angles with measure 135⁰,
and we have 2 equal acute angles with measure x⁰.
So, we can find value of acute angle,
135*2 +2x =360⁰
270+2x=360
2x=360-270
2x=90
x=45⁰

So, acute angles in trapezoid = 45⁰.
From triangle ABC,
angle ACB =90⁰
angle A=45⁰,
so angle ABC= 180-(90-45)=45⁰
Triangle ABC is isosceles triangle,so |AC| = |CB|= 5 in.

So, longer base AA' = 5+4+5= 14 in

Now, we can find area of trapezoid.
shorter base = 4 in
longer base = 14 in
altitude =h = 5 in
Area of trapezoid =(1/2)(base1+base2)*h
Area of trapezoid = (1/2)(4+14)*5= 9*5=45 in²
Answer is 45 in².
</span>

You might be interested in
Four friends purchase a pineapple for $2.89 and 18.4 pounds of peaches. The peaches cost $1.75 per pound. The friends share the
umka21 [38]

Answer: $3.00

Step-by-step explanation:

7 0
2 years ago
Read 2 more answers
Evaluate this expression for a = 3 and b = 4.
ahrayia [7]

Answer:

14

Step-by-step explanation:

a = 3

b = 4

b(a + 4)-3(3 + 2)+3 - 2\\a = 3,b=4\\4(3+4)-3(5)+3 - 2\\4(7)-15+3 - 2\\28-14\\\\14

8 0
3 years ago
A rectangular prism with a square base has a volume of 120 cubic feet. The base is 8 feet on each side. What is the height of th
Lelechka [254]

15feet

Step-by-step explanation: 120/8=15

pls give brainliest

3 0
3 years ago
You are given the following sequence:
borishaifa [10]
<h2>                     Question No 1</h2>

Answer:

7.5 is the 4th term of the sequence 60, 30, 15, 7.5, ... .

In other words:   \boxed{a_4=7.5}

Step-by-step explanation:

Considering the sequence

60, 30, 15, 7.5, ...

As we know that a sequence is said to be a list of numbers or objects in a special order.

so

60, 30, 15, 7.5, ...  

is a sequence starting at 60 and decreasing by half each time. Here, 60 is the first term, 30 is the second term, 15 is the 3rd term and 7.5 is the fourth term.

In other words,

a_1=60,

\:a_2=30,

a_3=15, and

a_4=7.5

Therefore, 7.5 is the 4th term of the sequence 60, 30, 15, 7.5, ... .

In other words:   \boxed{a_4=7.5}

<h2>                       Question # 2</h2>

Answer:

The value of a subscript 5 is 16.

i.e. When n = 5, then h(5) = 16

Step-by-step explanation:

To determine:

What is the value of a subscript 5?

Information fetching and Solution Steps:

  • Chart with two rows.
  • The first row is labeled n.
  • The second row is labeled h of n. i.e. h(n)
  • The first row contains the numbers three, four, five, and six.
  • The second row contains the numbers four, nine, sixteen, and twenty-five.

Making the data chart

n                  3         4         5         6

h(n)               4         9         16       25

As we can reference a specific term in the sequence by using the subscript. From the table, it is clear that 'n' row represents the input and and 'h(n)' represents the output.

So, when n = 5, the value of subscript 5 corresponds with 16. In other words: When n = 5, then h(5) = 16

Therefore, the value of a subscript 5 is 16.

<h2>                         Question # 3</h2>

Answer:

We determine that the sequence 33, 31, 28, 24, 19, … is neither arithmetic nor geometric.

Step-by-step explanation:

Considering the sequence

33, 31, 28, 24, 19, …

Lets calculate the common difference 'd' to determine if the sequence is Arithmetic or not.

\mathrm{Compute\:the\:differences\:of\:all\:the\:adjacent\:terms}:\quad \:d=a_{n+1}-a_n

d = 31 - 33 = -2

d = 28 - 31 = -3

d = 24 - 28 = -4

d = 19 - 24 = -5

As the common difference 'd' is not constant. It means the sequence is not Arithmetic.

Lets now calculate the common ratio 'r' to determine if the sequence is Geometric or not.

\mathrm{Compute\:the\:ratios\:of\:all\:the\:adjacent\:terms}:\quad \:r=\frac{a_n}{a_{n-1}}

\frac{31}{33}=0.93939\dots ,\:\quad \frac{28}{31}=0.90322\dots ,\:\quad \frac{24}{28}=0.85714\dots ,\:\quad \frac{19}{24}=0.79166\dots

The ratio is not constant. It means the sequence is not Geometric.

From the above analysis, we determine that the sequence 33, 31, 28, 24, 19, … is neither arithmetic nor geometric.

<h2>                         Question # 4</h2>

Answer:

We determine that the sequence -99, -96, -92, -87, -81... is neither arithmetic nor geometric.

Step-by-step explanation:

From the description statement:

''negative 99 comma negative 96 comma negative 92 comma negative 87 comma negative 81 comma dot dot dot''.

The statement can be translated algebraically as

-99, -96, -92, -87, -81...

Lets calculate the common difference 'd' to determine if the sequence is Arithmetic or not.

\mathrm{Compute\:the\:differences\:of\:all\:the\:adjacent\:terms}:\quad \:d=a_{n+1}-a_n

-96-\left(-99\right)=3,\:\quad \:-92-\left(-96\right)=4,\:\quad \:-87-\left(-92\right)=5,\:\quad \:-81-\left(-87\right)=6

As the common difference 'd' is not constant. It means the sequence is not Arithmetic.

Lets now calculate the common ratio 'r' to determine if the sequence is Geometric or not.

\mathrm{Compute\:the\:ratios\:of\:all\:the\:adjacent\:terms}:\quad \:r=\frac{a_n}{a_{n-1}}

\frac{-96}{-99}=0.96969\dots ,\:\quad \frac{-92}{-96}=0.95833\dots ,\:\quad \frac{-87}{-92}=0.94565\dots ,\:\quad \frac{-81}{-87}=0.93103\dots

The ratio is not constant. It means the sequence is not Geometric.

From the above analysis, we determine that the sequence -99, -96, -92, -87, -81... is neither arithmetic nor geometric.    

<h2>                      Question # 5</h2>

Step-by-step explanation:

Considering the sequence

12, 22, 30, 36, 41, …

\mathrm{Compute\:the\:differences\:of\:all\:the\:adjacent\:terms}:\quad \:d=a_{n+1}-a_n

22-12=10,\:\quad \:30-22=8,\:\quad \:36-30=6,\:\quad \:41-36=5

As the common difference 'd' is not constant. It means the sequence is not Arithmetic.

\mathrm{Compute\:the\:ratios\:of\:all\:the\:adjacent\:terms}:\quad \:r=\frac{a_n}{a_{n-1}}

\frac{22}{12}=1.83333\dots ,\:\quad \frac{30}{22}=1.36363\dots ,\:\quad \frac{36}{30}=1.2,\:\quad \frac{41}{36}=1.13888\dots

The ratio is not constant. It means the sequence is not Geometric.

From the above analysis, we determine that the sequence 12, 22, 30, 36, 41, … is neither arithmetic nor geometric.                  

8 0
2 years ago
PLS HELP WILL MARK BRAINLIEST TO BEST ANSWER
butalik [34]
I believe 504,000 seconds
6 0
3 years ago
Read 2 more answers
Other questions:
  • 4100 grams because 1 kilogram would = 100 grams
    11·1 answer
  • A concrete pillar has the shape of a cylinder. It has a radius of 4 meters and a height of 7 meters. If concrete costs $94 per c
    5·1 answer
  • What is 2 x 10 to the -6th power?
    10·2 answers
  • 3/7 of the coins in a box are nickels. The rest are pennies . If there are 48 pennies how many coins are there altogether?
    10·1 answer
  • Translate the following phrase into an algebraic expression. Do not simplify. Use the variable names "x" or "y" to describe the
    8·1 answer
  • N +-6 = 11<br> Please answer!
    7·2 answers
  • Plz help me am dam at math I will gave Brainliest
    8·2 answers
  • I’ll give brainliest
    6·1 answer
  • PLEASE HELP! I’ll give brainliest (no links please)
    6·1 answer
  • A drawing of a rectangular room has dimensions of 12 inches by 6 inches. If the scale is 2 inches : 4 feet, find the area of the
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!