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2 years ago

The vertex angle of isosceles triangle is 110 degrees. what are the measures of the base angles

Mathematics

1 answer:

dalvyx [7]2 years ago

3 0

Answer:

35°

Step-by-step explanation:

The base angles of an isosceles triangle are congruent , then

base angles = $\frac{180-110}{2}$ = $\frac{70}{2}$ = 35°

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Given the sequence 1/2 ; 4 ; 1/4 ; 7 ; 1/8 ; 10;.. calculate the sum of 50 terms

miv72 [106K]

Hint :-

Break the given sequence into two parts .
Notice the terms at gap of one term beginning from the first term .They are like $\dfrac{1}{2},\dfrac{1}{4},\dfrac{1}{8}$ . Next term is obtained by multiplying half to the previous term .
Notice the terms beginning from 2nd term , $4,7,10,13$ . Next term is obtained by adding 3 to the previous term .

Solution :- 

We need to find out the sum of 50 terms of the given sequence . After splitting the given sequence ,

$\implies S_1 = \dfrac{1}{2},\dfrac{1}{4},\dfrac{1}{8}$ .

We can see that this is in Geometric Progression where 1/2 is the common ratio . Calculating the sum of 25 terms , we have ,

$\implies S_1 = a\dfrac{1-r^n}{1-r} \\\\\implies S_1 = \dfrac{1}{2}\left[ \dfrac{1-\bigg(\dfrac{1}{2}\bigg)^{25}}{1-\dfrac{1}{2}}\right]$

Notice the term $\dfrac{1}{2^{25}}$ will be too small , so we can neglect it and take its approximation as 0 .

$\implies S_1\approx \cancel{ \dfrac{1}{2} } \left[ \dfrac{1-0}{\cancel{\dfrac{1}{2} }}\right]$

$\\\implies \boxed{ S_1 \approx 1 }$

$\rule{200}2$

Now the second sequence is in Arithmetic Progression , with common difference = 3 .

$\implies S_2=\dfrac{n}{2}[2a + (n-1)d]$

Substitute ,

$\implies S_2=\dfrac{25}{2}[2(4) + (25-1)3] =\boxed{ 908}$

Hence sum = 908 + 1 = 909

7 0

2 years ago

A freezer is shaped like a rectangular prism. It has a length of 8 feet and a height of 3 feet. The volume is 54 cubic feet. Fin

yarga [219]

Well the formula:

V = Bh
54= 3*w*8
54= 24w
24w=54
w= 54/24
w= 2.25

4 0

2 years ago

4. What is the formula for distance?

hichkok12 [17]

Answer:

b) d=rt

Step-by-step explanation:

5 0

2 years ago

The actual distance between two villages is 120 km. On a map of the area, 0.5 cm represents 2 km. What is the actual distance be

otez555 [7]

If .5cm is 2km, then 1 cm is 4 km, and therefore 120/4 is 30, so 30 centimeters on the map

6 0

2 years ago

Read 2 more answers

Alden is registering for classes next semester. he uses the quantitative reasoning process to decide between two teachers, dr. a

Volgvan

Based on quantitative reasoning, Alden should take the classes from Dr. Baeno in his next semester.

Quantitative Reasoning Behind Choosing Dr. Baeno

Alden talked to 17 friends that previously took course from Dr. Alvarez.

Eight out of 17 friends recommended Dr. Alvarez.

∴ The fraction of his friends in favor of Dr. Alvarez = 8/17

Also, Alden talked to 18 friends who took course from Dr. Baeno.

Eleven out of 18 friends recommended Dr. Baeno.

∴ The fraction of his friends in favor of Dr. Baeno = 11/18

Making Comparison

Now, since we know that,

11/18 > 8/17

The capacity for using knowledge and mathematics to address problems in the real world is known as quantitative reasoning.

Hence, applying quantitative reasoning, we can infer that it is more favorable for Alden to take classes from Dr. Baeno.

Learn more about quantitative reasoning here:

brainly.com/question/15566375

#SPJ4

4 0

2 years ago