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4 years ago

Find the value of each variable in each parallelogram.

Mathematics

1 answer:

svp [43]4 years ago

4 0

Answer:

a=109° b=71°

Step-by-step explanation:

All the angles in a parallelogram add up to 360. There are a few rules:

The opposite angles are congruent.

Consecutive angles are congruent.

We can apply these rules here.

71 is opposite to b

and a is consecutive to 71 so we can put together these equations.

180=71+a

71=b

we can simplify to get the answers

the end

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Which equation below best models the line of best fit for the data?

Zarrin [17]

Answer:

y=-2x-20y=−2x−20

Step-by-step explanation:

best models the line of best fit for the data

6 0

3 years ago

One number is times a first number. A third number is 100 more than the first number. If the sum of the three numbers

icang [17]

When a number is 3 times a first number. A third number is 100 more than the first number and the sum of the three numbers is 450, the numbers are 70, 170 and 210.

<h3>How to calculate the numbers?</h3>

Let the first number = x

Second number = 3x

Third number = x + 100

Sum = 450

The numbers will be:

x + 3x + x + 100 = 450

5x + 100 = 450

5x = 450 - 100

5x = 350

Divide

x = 350 / 5

x = 70

First number = 70

Second number = 3x = 3 × 70 = 210

Third number = x + 100 = 70 + 100 = 170

Therefore, the numbers are 70, 170 and 210.

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One number is 3 times a first number. A third number is 100 more than the first number. If the sum of the three numbers is 450 , find the numbers.

8 0

1 year ago

Sarah is carrying out a series of experiments which involve using mcreasing amounts of a chemical. In the

Marianna [84]

Sarah is carrying out a series of experiments which involve using increasing amounts of a chemical. In the first experiment she uses 6g of the chemical and in the second experiment she uses 7.8 g of the chemical

(i)Given that the amounts of the chemical used form an arithmetic progression find the total amount of chemical used in the first 30 experiments

(ii)Instead it is given that the amounts of the chemical used for a geometric progression. Sarah has a total of 1800 g of the chemical available. Show that the greatest number of experiments possible satisfies the inequality: $1.3^N \leq 91$ and use logarithms to calculate the value of N.

Answer:

(a)963 grams

(b)N=17

Step-by-step explanation:

(a)

In the first experiment, Sarah uses 6g of the chemical

In the second experiment, Sarah uses 7.8g of the chemical

If this forms an arithmetic progression:

First term, a =6g

Common difference. d= 7.8 -6 =1.8 g

Therefore:

Total Amount of chemical used in the first 30 experiments

$S_n=\dfrac{n}{2}[2a+(n-1)d] \\S_{30}=\dfrac{30}{2}[2*6+(30-1)1.8] \\=15[12+29*1.8]\\=15[12+52.2]\\=15*64.2\\=963$ grams$

Sarah uses 963 grams in the first 30 experiments.

(b) If the increase is geometric

First Term, a=6g

Common ratio, r =7.8/6 =1.3

Sarah has a total of 1800 g

Therefore:

Sum of a geometric sequence

$S_n=\dfrac{a(r^N-1)}{r-1} \\1800=\dfrac{6(1.3^N-1)}{1.3-1} \\1800=\dfrac{6(1.3^N-1)}{0.3}\\$Cross multiply\\1800*0.3=6(1.3^N-1)\\6(1.3^N-1)=540\\1.3^N-1=540\div 6\\1.3^N-1=90\\1.3^N=90+1\\1.3^N=91$