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3 years ago

Determine the intercepts of the line that passes through the following points.

Mathematics

1 answer:

aev [14]3 years ago

6 0

Slope-intercept form: y = mx + b (m is the slope, b is the y-intercept or the y value when x = 0 -- > (0 , y))

To find the slope (m), you use the slope formula and plug in 2 points.

$m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

(x₁ , y₁) = (1 , 20)

(x₂, y₂) = (5 , 10)

$m=\frac{10-20}{5-1}=\frac{-10}{4}=-\frac{5}{2}$

$y=-\frac{5}{2}x+b$ To find b, plug in a point into the equation (1,20)

$20=-\frac{5}{2}(1)+b$ Add 5/2 on both sides

$20+\frac{5}{2}=b$

$\frac{40}{2}+\frac{5}{2}=b$

22.5 = b

$y=-\frac{5}{2}x+22.5$

Your y-intercept is (0, 22.5) or (0, 45/2)

The x-intercept is the x value when y = 0 ---> (x, 0)

To find the x-intercept, set y = 0 in the equation

0 = -5/2x + 22.5

-22.5 = -5/2x Multiply -2/5 on both sides to get x by itself

9 = x

Your x-intercept is (9, 0)

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16x 2 + 8x - 15 Mathematics?

Gala2k [10]

If you're factoring, your answer is

(4x - 3)(4x + 5)

You'll work it out this way:

16x^2 + 8x - 15

Since there's no GCF here, you multiply the first and third terms, giving you -240. Your next step is to find two numbers that have a sum of 8 and a product of -240. These numbers are 20 and -12. Plug those in and you've got:

16x^2 + 20x - 12x - 15

From here you divide it into two binomials. These are (16x^2 + 20x) and (-12x - 15).
When you take out the greatest common factors (4x and -3), they become:

4x(4x + 5) - 3(4x + 5)

Then you group what's outside of the parentheses together (4x - 3)
And bring what's inside of the parentheses down (4x + 5).
This brings your answer to

(4x - 3)(4x + 5)

5 0

3 years ago

Help me, Thanks!!

Marrrta [24]

2.) dT/dt = -t^2 + 3t

dT = (-t^2 + 3t)dt

T = -t^3/3 + 3t^2/2 + C

at 4:00 AM

80 = -4^3/3 + 3*4^2/2 + C

C = 80 + 4^3/3 - 3*4^2/2

C = 77.33

T = -t^3/3 + 3t^2/2 + 77.33

at 8:00 AM

T = -8^3/3 + 3*8^2/2 + 77.33

T = 2.67 deg

5 0

2 years ago

Felicia bought 3 feet of ribbon for a project. she needs to cut the ribbon into 6 equal pieces. how long will each ribbon be?

anastassius [24]

3feer is 36 inches

36/6= 6 inches

6 0

2 years ago

Which of the following is an exponential equation?<br><br> y = mx + b<br> y = a(b^x)

Darina [25.2K]

Y = a(b^x)

y=mx + b is the equation of a line. It is a linear function because it has a constant rate of change.

y = a(b^x) is an exponential function because it has has an exponent and its rate of change is not constant

4 0

3 years ago

In October of 2012, Apple introduced a much smaller variant of the Apple iPad, known at the iPad Mini. Weighing less than 11 oun

sveticcg [70]

Answer:

a. $f_X(x) = \dfrac{1}{3.5}8.5$

b. the probability that the battery life for an iPad Mini will be 10 hours or less is 0.4286 which is about 42.86%

c. the probability that the battery life for an iPad Mini will be at least 11 hours is 0.2857 which is about 28.57 %

d. the probability that the battery life for an iPad Mini will be between 9.5 and 11.5 hours is 0.5714 which is about 57.14%

e. 86 should have a battery life of at least 9 hours

Step-by-step explanation:

From the given information;

Let X represent the continuous random variable with uniform distribution U (A, B) . Therefore the probability density function can now be determined as :

$f_X(x) = \dfrac{1}{B-A}A$

where A and B are the two parameters of the uniform distribution

From the question;

Assume that battery life of the iPad Mini is uniformly distributed between 8.5 and 12 hours

So; Let A = 8,5 and B = 12

Therefore; the mathematical expression for the probability density function of battery life is :

$f_X(x) = \dfrac{1}{12-8.5}8.5$

$f_X(x) = \dfrac{1}{3.5}8.5$

b. What is the probability that the battery life for an iPad Mini will be 10 hours or less (to 4 decimals)?

The probability that the battery life for an iPad Mini will be 10 hours or less can be calculated as:

F(x) = P(X ≤x)

$F(x) = \dfrac{x-A}{B-A}$

$F(10) = \dfrac{10-8.5}{12-8.5}$

F(10) = 0.4286

the probability that the battery life for an iPad Mini will be 10 hours or less is 0.4286 which is about 42.86%

c. What is the probability that the battery life for an iPad Mini will be at least 11 hours (to 4 decimals)?

The battery life for an iPad Mini will be at least 11 hours is calculated as follows:

$P(X\geq11) = \int\limits^{12}_{11} {\dfrac{1}{3.5}} \, dx$

$P(X\geq11) = {\dfrac{1}{3.5}} (x)^{12}_{11}$

$P(X\geq11) = {\dfrac{1}{3.5}} (12-11)$

$P(X\geq11) = {\dfrac{1}{3.5}} (1)$

$P(X\geq11) = 0.2857$

the probability that the battery life for an iPad Mini will be at least 11 hours is 0.2857 which is about 28.57 %

d. What is the probability that the battery life for an iPad Mini will be between 9.5 and 11.5 hours (to 4 decimals)?

$P(9.5 \leq X\leq11.5) =\int\limits^{11.5}_{9.5} {\dfrac{1}{3.5}} \, dx$

$P(9.5 \leq X\leq11.5) ={\dfrac{1}{3.5}} \, (x)^{11.5}_{9.5}$

$P(9.5 \leq X\leq11.5) ={\dfrac{1}{3.5}} (11.5-9.5)$

$P(9.5 \leq X\leq11.5) ={\dfrac{1}{3.5}} (2)$

$P(9.5 \leq X\leq11.5) =0.2857* (2)$

$P(9.5 \leq X\leq11.5) =0.5714$

Hence; the probability that the battery life for an iPad Mini will be between 9.5 and 11.5 hours is 0.5714 which is about 57.14%

e. In a shipment of 100 iPad Minis, how many should have a battery life of at least 9 hours (to nearest whole value)?

The probability that battery life of at least 9 hours is calculated as:

$P(X \geq 9) = \int\limits^{12}_{9} {\dfrac{1}{3.5}} \, dx$

$P(X \geq 9) = {\dfrac{1}{3.5}}(x)^{12}_{9}$

$P(X \geq 9) = {\dfrac{1}{3.5}}(12-9)$

$P(X \geq 9) = {\dfrac{1}{3.5}}(3)$

$P(X \geq 9) = 0.2857*}(3)$

$P(X \geq 9) = 0.8571$

NOW; The Number of iPad that should have a battery life of at least 9 hours is calculated as:

n = 100(0.8571)

n = 85.71

n ≅ 86

Thus , 86 should have a battery life of at least 9 hours

3 0

3 years ago