What is the the value of x? Enter uour answer in the box. 91°, 8x+3°,10x-4°

Mathematics

2 answers:

klemol [59]3 years ago

8 0

Answer:

The value of x is 5

Step-by-step explanation:

In triangle ABC

Using Angle Sum property of triangle to find the value of x.

Angle Sum property: The sum of all angles of a triangle is 180.

$\angle A+\angle B+\angle C=180^{\circ}$

$91^{\circ}+(10x-4)^{\circ}+(8x+3)^{\circ}=180^{\circ}$

$10x+8x+90=180$

$18x=180-90$

$x=5$

Hence, The value of x is 5

zzz [600]3 years ago

5 0

Answer:

x = 5 is the right answer.

Step-by-step explanation:

As we know sum of all angles in a triangle is 180°.Therefore in this question we will form an equation.

Sum of all the angles of a triangle = 180

91 + 10x - 4 +8x +3 = 180

90 + 18x = 180

18x + 90 - 90 = 180 - 90

18x = 90

x = 90÷18 = 5

Therefore x = 5 is the right answer.

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A series contains 18 numbers and has a sum of 4,185. The last number of the series is 275. What is the first number?

N76 [4]

If the series is made up of numbers in an arithmetic progression, you have

$\displaystyle\sum_{n=1}^{18}a_n=\sum_{n=1}^{18}(a_1+(n-1)d)=18a_1+153d=4185$

where $a_1$ is the first term and $d$ is the common difference between terms.

Since the last term in the series is $a_{18}=275$ , you have

$a_{18}=a_1+(18-1)d\implies a_1+17d=275$

Solve the system

$\begin{cases}18a_1+153d=4185\\a_1+17d=275\end{cases}$

and you'll find that the first term is $a_1=190$ (with $d=5$ ).