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3 years ago

You are told that an is an arithmetic sequence with a7=31 and a15=63. What is a19?

Mathematics

2 answers:

nikdorinn [45]3 years ago

3 0

Answer:

a19= 83.6

Step-by-step explanation:

sveticcg [70]3 years ago

3 0

A19 is 79.

So if you know that a7 is 31 and a15 is 63, then all you have to do is find how many sequences come in between the two and divide the difference to find the rate of change.

So, 15-7=8, there are 8 steps before a7 reaches a15.

Next, you subtract 63-31 to find how much is separating the two. So 63-31= 32.

Finally, you divide 32 by 8 to get 4 because that’s the rate of change. So every time the sequence goes up by 4.

Since a15 is 63 all you have to do is multiply 4 times 4 because a15 is 4 sequence numbers away from a19. And so 63+ 16 (4*4)= 79.

A19 is 79, I hope this helps!

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I NEED URGENT ASSISTANCE

Nata [24]

Answer:

8 C sometimes

9 64x^8 y^11

10 c 1.28r^2/ t^9

Step-by-step explanation:

Algebraic Operations

Some basic rules must be fresh in our minds when trying to simplify complex algebraic expressions. For example, the power rule respect to the product or quotient:

$\displaystyle \left(\frac{x^n.y^m}{z^p}\right)^q= \frac{x^{qn}.y^{qm}}{z^{qp}}$

$\displaystyle \frac{x^n.x^q}{x^p}= x^{n+q-p}$

$\displaystyle x^{-n}=\frac{1}{x^n}$

Let's face the questions at hand

8. A number is raised to a negative exponent is negative?

Following the expressions recalled above, let's pick the expression

$\displaystyle 3^{-2}=\frac{1}{3^2}=\frac{1}{9}$

This is a negative power resulting in a positive number

Now we pick

$\displaystyle (-2)^{-3}=\frac{1}{(-2)^3}=-\frac{1}{8}$

This time, the negative power leads to a negative result, so it doesn't matter the sign of exponent to determine the sign of the result

Answer: C sometimes

9 simplify(4xy^2)^3(xy)^5

$(4xy^2)^3(xy)^5=4^3x^3(y^2)^3x^5y^5$

$=64x^3y^6x^5y^5$

$=64x^8y^{11}$

10 simplify(2t^-3)^3(0.4r)^2

$(2t^{-3})^3(0.4r)^2=2^3(t^{-3})^30.4^2r^2$

$=8t^{-9} 0.16 r^2$

$=1.28t^{-9} r^2$

$\displaystyle \frac{1.28 r^2}{t^9}$

7 0

3 years ago

Tyler had $65.40 in his checking account. Then he wrote checks on the account for $20.38, $11.48, and $19.50. What is the balanc

andrew-mc [135]

money going out (20.38+11.48+19.50) =51.36

balance - out = new balance

65.40-51.36 =

14.04

new balance = 14.04

4 0

3 years ago

1 point

photoshop1234 [79]

Answer:

Step-by-step explanation:

done it

5 0

3 years ago

Help me please asap I need to know fully how to solve this problem

vivado [14]

Consider the absolute value, because we only worry about the quadrant later.

$\text{Consider: } sin(A) = |-\frac{\sqrt{3}}{4}|$
$sin(A) = \frac{\sqrt{3}}{4}$

Thus, we know that the hypotenuse has a length of 4 units, and the side opposite the angle, A is √3, because this is the nature of the sine function in relation to its triangular component.

The missing side can be found using Pythagoras' Theorem:
4² - (√3)² = x²
16 - 3 = x²
13 = x²
x = √13

$\therefore tan(A) = \pm \sqrt{\frac{3}{13}}$

Since angle A is in the third quadrant, the tangent function will produce a positive angle.

$tan(A) = \sqrt{\frac{3}{13}}$
$\text{Rationalise the denominator: } \frac{\sqrt{3}}{\sqrt{13}} \cdot \frac{\sqrt{13}}{\sqrt{13}}$

$tan(A) = \frac{\sqrt{39}}{13}$