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3 years ago

Simultaneous equations, any method

Mathematics

1 answer:

oee [108]3 years ago

8 0

This is the method of substitution

And also an example of how it works

Hope this helps :))

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IB QUESTIONS:

enyata [817]

Step-by-step explanation:

Using SOHCAHTOA

$\tan = \frac{opposite}{adjacent} \\ \tan {31}^{0} = \frac{450}{x} \\ \tan {31}^{0} = 0.6009 \\ 0.6009 = \frac{450}{x} \\ cross \: multiply \\ 0.6009x = 450 \\ divide \: both \: sides \: by \: 0.6009 \\ x = \frac{450}{0.6009}x \\ = 748.9$

Second Question Explanation:

a. The base angles of an isosceles triangle are equal so angle ABC is also 32°

but the sum of angles in a triangle = 180° therefore

let angle CAB be x

${32}^{0} + {32}^{0} + {x}^{0} = {180}^{0} \\ 64 + x = 180 \\ {x}^{0} = 180 - 64 \\ {x}^{0} = {116}^{0}$

b. If you share a triangle in half you get 2 right angles so I'll use SOHCAHTOA to find the length AB

First the base of the right angled triangle will be 20/2 = 10

$\cos = \frac{adjacent}{hypotenuse} \\ \cos {32}^{0} = \frac{10}{ab} \\ \cos32 = 0.8480 \\ 0.8480 = \frac{10}{ab} \\ ab = \frac{10}{0.8480} \\ line \: ab = 11.8$

c. To find the are we'll need to get the height first

using the right angled triangle With base 10cm and hypotenuse 11. 8 to find the height we'll use the Pythagorean theorem

${(11.8)}^{2} = {x}^{2} + {10}^{2} \\ 1324.24 = {x}^{2} + 100 \\ {x}^{2} = 139.24 - 100 \\ {x}^{2} = 39.24 \\ \sqrt{ {x}^{2} } = \sqrt{39.24} \\ x = \sqrt{39.24 } \\ x = 6.3$

now to find the area

$area \: of \: triangle = \frac{1}{2} \times base \times height \\ = \frac{1}{2} \times 20 \times 6.3 \\ \frac{20 \times 6.3}{2} \\ = \frac{126}{2} \\ 63 {cm}^{2}$

4 0

3 years ago

Xavier and Ava are employees for a company. Xavier is making a salary of $42,700.

MrMuchimi

$62,342 is the salary earned by Ava.

Step-by-step explanation:

step 1 :

Xavier's salary = $42,700

step 2 :

Ava's salary = 46% higher than Xavier salary.

= 100% of Xavier salary + 46% of Xavier salary

= 146% of Xavier salary

step 3 :

Ava is earning a salary = (146/100) $\times$ 42,700

= 146 $\times$ 427

= 62,342

∴ Ava is earning a salary of $62,342.

7 0

3 years ago

People were asked if they were considering changing what they eat. 29% said yes

RUDIKE [14]

In this problem, you need to figure out whats 23% of 29% to find the percentage of the total group becoming vegetarians.

In order to do this, you can convert the percentages to decimals and multiply.

.23 x .29 = .0667 or 6.67%

6.67% of the total group are considering becoming vegetarians.

6 0

3 years ago

Read 2 more answers

there are 98515 trees at Washington Park. if there are 85 aceres of land and the trees are spread out evenly how many trees are

Vlada [557]

There are 1159 trees per acre because 98515/85 = 1159

6 0

3 years ago

Heather drove a constant rate

mrs_skeptik [129]

Answer:

cool