When will the tuition reach $20,000 according to the trendline?

At 88°F, a certain insect chirps at a rate of 64 times per minute, and at 97°F, they chirp 118 times per minute. Write an equati

Allushta [10]

Let " x " denotes the temperature in degree Fahrenheit .

Let " y " denotes the chirp rate per minute .

We have given that at 88 degree Fahrenheit , chirp rate is 64 times per minute and at 97 degree Fahrenheit , it is 118 times per minute .

We write this information in coordinate form ( x,y) .

We have ( x₁ ,y₁) = ( 88 , 64 ) and ( x₂ , y₂) = ( 97,118) .

y₂ - y ₁ 118 - 64 54

Slope , m = ---------------------- = --------------------- = -----------

x₂ - x₁ 97 - 88 9

Slope , m = 6 .

Equation of line in slope intercept form is

y = m x + b where ' m' is slope and ' b ' is intercept .

Plug value of m , we get

y = 6 x + b .

To find value of b , we put ( 88 , 64 ) in place of x and y .

Put x = 88 and y = 64 , we get

64 = 6 * 88 + b

64 = 528 + b

64 - 528 = b

- 464 = b

Thus we get b = - 464 .

So the equation become

y = 6 x - 464 .

Equation in slope intercept form representing the situation is

y = 6 x - 464 .

6 0

3 years ago

Find the measure of angle A. A 9x+6 4x + 6 m/A=

Likurg_2 [28]

Answer:

angle A=30°

Step-by-step explanation:

$9x + 6 + 4x + 6 + 90 = 180 \\ 13x + 102 = 180 \\ 13x = 180 - 102 \\ 13x = 78 \\ \frac{13x}{ 13} = \frac{ 78}{13} \\ x = 6 \\ 4x + 6 = a \\ 4(6) + 6 = a \\ 24 + 6 = a \\ 30 = a$

6 0

2 years ago

13. Find the measure of an angle if its measure is eight less than six times its complement.

tatiyna

For an instance, the measure of the angle is represented by y, and the measure of its complement is represented by x. We should write the expression for the problem.
⇒ We can express "eight less" as -8
⇒ We can express "six times its complement" as 6x
The first equation will be
y = 6x - 8

In the second equation, we will describe about the complementary angles. If they add up, the result is 90°. The second equation will be
x + y = 90

Using substitution method, we will find the value of x
x + y = 90
x + 6x - 8 = 90
7x - 8 = 90
7x = 90 - 8
7x = 82
x = 82/7

Using substitution method, we find the value of y
y = 6x - 8
y = 6(82/7) - 8
y = 492/7 - 8
y = $\frac{492}{7}- \frac{56}{7}$
y = $\frac{436}{7}$
y = 62.3
to the near whole number
y = 62

The measurement of the angle is 62°

5 0

4 years ago

If

sp2606 [1]

Answer:

51

Step-by-step explanation:

4x12-3x3+12

48-9+12=51

7 0

3 years ago

Solve the following exponential equations. (10^x)^2 − 2(10^x) − 1 = 0

Hunter-Best [27]

Answer:

x = log(1+√2) ≈ 0.38277569

Step-by-step explanation:

Let z = 10^x. Then the equation can be rewritten ...

z^2 -2z -1 = 0

z^2 -2z +1 -2 = 0 . . . . rewrite to a form with a square

(z -1)^2 = 2 . . . . . . . . . add 2

z -1 = ±√2 . . . . . . . . . . square root

z = 1 ± √2 . . . . . . . . . . add 1

From the definition of z, we know it must be positive, so the only viable solution here is ...

z = 10^x = 1+√2

x = log(1+√2)

x ≈ 0.38277569

6 0

3 years ago