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2 years ago

What is the measure of j

Mathematics

2 answers:

siniylev [52]2 years ago

6 0

J=54
For future problems like this, when you have a triangle just remember that all three angles equal 180. In this problem you have vertical angles.

Effectus [21]2 years ago

5 0

Your answer is j= 54. J + 86 + 40 = 180

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Which of the following are possible explicit formulas for the nth term of the constant velocity sequence below? Check all that a

oksano4ka [1.4K]

We have an arithmetic progression:
Nth=an
an=a₁+(n-1)d
a₁ is the first term.
n=number of terms.
d=common difference

10,17,24,31...
a₁=10
d=a₂-a₁=17-10=7

Therefore:
Nth=an
an=a₁+(n-1)d
an=10+(n-1)7
an=10+7n-7
an=7n+3.

Therefore: the formula for the nth is, an=a+(n-1), in this case; an=7n+3,

To check:
a₁=7*1+3=10
a₂=7*2+3=17
a₃=7*3+3=24
a₄=7*4+3=31
a₅=7*5+3=38.......

8 0

2 years ago

Sum of positive roots of the equation (x2 - 12x + 35) (x2 + 10x + 24) = 504 is

Digiron [165]

Answer:

(3)11

Step-by-step explanation:

We are given that

$(x^2-12x+35)(x^2+10x+24)=504$

We have to find the sum of positive roots of the equation.

$x^2(x^2+10x+24)-12x(x^2+10x+24)+35(x^2+10x+24)=504$

$x^4+10x^3+24x^2-12x^3-120x^2-288x+35x^2+350x+840=504$

$x^4-2x^3-61x^2+62x+840-504=0$

$x^4-2x^3-61x^2+62x+336=0$

Factor of 336

2,3,4,6,8,7,

Let x=2

$2^4-2^4-61(2^2)+62(2)+336\neq0$

x=2 is not the root of equation

x=-2

$(-2)^4-2(-2)^3-61(-2)^2+62(-2)+336=0$

Hence x=-2 is the root of equation.

x+2 is a factor of equation.

x=3

$3^4-2(3^3)-61(3^2)+62(3)+336=0$

Therefore, x=3 is the root of equation.

$(x+2)(x-3)(x^2-x-56)=0$

$(x+2)(x-3)(x^2-8x+7x-56)=0$

$(x+2)(x-3)(x(x-8)+7(x-8))=0$

$(x+2)(x-3)(x-8)(x+7)=0$

$x-8=0\implies x=8$

$x+7=0\implies x=-7$

Positive roots are 3 and 8

Sum of positive roots=3+8=11

Option (3) is true.

4 0

2 years ago

Nathan flew 3,547 miles from Canada to California during the first part of his trip. He flew 2,567 miles from California to Hawa

AURORKA [14]

Difference in the number of miles Nathan flew between the first and second parts of his trip is 980 miles

<em><u>Solution:</u></em>

Given that Nathan flew 3,547 miles from Canada to California during the first part of his trip

He flew 2,567 miles from California to Hawaii during the second part of his trip

Therefore,

first part of his trip = 3547 miles

second part of his trip = 2567 miles

Difference in the number of miles Nathan flew between the first and second parts of his trip is given as:

difference = first part of his trip - second part of his trip

difference = 3547 - 2567 = 980

Therefore, the difference in number is 980 miles

4 0

2 years ago

Use the converse of the side-splitter theorem to determine if T R is parallel to R S. Which statement is true? Line segment TU i

kramer

Answer:

IM SORRY MI IM

Step-by-step explanation:

8 0

2 years ago

Read 2 more answers

The value of a car is 18,500. It loses 10.3% of its value every year. Find the approximate monthly decrease in value. Round your

valentina_108 [34]

Answer:

$158.8

Step-by-step explanation:

There are 12 months in 1 year.

If in 1 year, it looses value of 10.3%, so in a month it will loose value of:

10.3%/12 = 0.8583% per month

So, to find the decreased value (in dollars) per month, we got to find 0.8583% of 18,500 dollars.

First, we need to convert percentage to decimal by dividing by 100. Then we multiply that to 18,500 to get our answer. So:

0.8583% = 0.8583/100 = 0.008583

Now,

0.008583 * $18,500 = $158.7855

Rounded to nearest tenth (1 decimal pae) = $158.8

6 0

2 years ago