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2 years ago

What is the slope of the line through (3, 2) and (-3,4)?

Mathematics

1 answer:

alukav5142 [94]2 years ago

8 0

Step-by-step explanation:

the slope of a line is the ratio y/x.

that means, when going from one point to the other, how many units y changes, when x changes a certain number of units.

the sign indicates the direction of the change (+ for larger and - for smaller).

so, here x changes by 6 units (from -3 to 3), and y changes by -2 units (from 4 to 2).

therefore, the slope is

-2/6 = -1/3

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VERY URGENT.

NemiM [27]

Answer:

(1)Base Area= 81 square yards.

(2)

3 ft long and 16 ft wide

6 ft long and 8 ft wide
24 ft long and 2 ft wide

(3)Height=12 Units

Step-by-step explanation:

Question 1

Volume of the rectangular prism=2,592 cubic yards.

Height of the rectangular prism=32 yards

Volume of a rectangular prism =lbh (where lb is the Base Area)

Therefore:

lbh=2592

32lb=2592

lb=2592/32=81

Base Area= 81 square yards.

Question 2

Volume of the rectangular prism=432 cubic feet.

Height of the rectangular prism=9 feet

Volume of a rectangular prism =lbh (where lb is the Base Area)

Therefore:

lbh=432

9lb=432

lb=432/9=48

Base Area= 48 square yards.

Any dimension whose product is 48 is a possible choice.

They are:

3 ft long and 16 ft wide
6 ft long and 8 ft wide
24 ft long and 2 ft wide

Question 3

Volume of the rectangular prism=960 cubic units.

Base Area of the rectangular prism, lb=80 Square Units

Volume of a rectangular prism =lbh (where lb is the Base Area)

Therefore:

lbh=960

80h=960

h=960/80=12

Height= 12 units.

4 0

4 years ago

Consider the following. f(x) = x5 − x3 + 6, −1 ≤ x ≤ 1 (a) Use a graph to find the absolute maximum and minimum values of the fu

kykrilka [37]

ANSWER

See below

EXPLANATION

Part a)

The given function is

$f(x) = {x}^{5} - {x}^{3} + 6$

From the graph, we can observe that, the absolute maximum occurs at (-0.7746,6.1859) and the absolute minimum occurs at (0.7746,5.8141).

b) Using calculus, we find the first derivative of the given function.

$f'(x) = 5 {x}^{4} - 3 {x}^{2}$

At turning point f'(x)=0.

$5 {x}^{4} - 3 {x}^{2} = 0$

This implies that,

${x}^{2} (5 {x}^{2} - 3) = 0$

${x}^{2} = 0 \: or \: 5 {x}^{2} - 3 = 0$

$x = - \frac{ \sqrt{15} }{5} \: or \: x = 0 \: \: or \: x =\frac{ \sqrt{15} }{5}$

We plug this values into the original function to obtain the y-values of the turning points

$( - \frac{ \sqrt{15} }{5} , \frac{1}{125} ( 6 \sqrt{15} +750)) \:and \: (0, - 6) \: and\: ( \frac{ \sqrt{15} }{5} , \frac{1}{125} ( - 6 \sqrt{15} +750))$

We now use the second derivative test to determine the absolute maximum minimum on the interval [-1,1]

$f''(x) = 20 {x}^{3} - 6x$

$f''( - \frac{ \sqrt{15} }{5} ) \: < \: 0$

Hence

$( - \frac{ \sqrt{15} }{5} , \frac{1}{125} ( 6 \sqrt{15} + 750))$

is a maximum point.

$f''( \frac{ \sqrt{15} }{5} ) \: > \: 0$

Hence

$( \frac{ \sqrt{15} }{5} , \frac{1}{125} (- 6 \sqrt{15} + 750))$

is a minimum point.

$f''(0) \: =\: 0$

Hence (0,-6) is a point of inflexion

4 0

3 years ago

A student says that a correlation coefficient of −0.93 indicates that the two quantities of a data set have a weak correlation.

zloy xaker [14]

Answer:

Step-by-step explanation:

Recall that correlation coefficients range from -1 to +1. So, -0.93 is a strong negative relationship. Two interpretations: 1) the correlation is actually very strong, and 2) the correlation is negative. When the correlation is negative, the dependent variable DECREASES when the independent variable INCREASES.

8 0

3 years ago

cuharra studied Monday and Tuesday for her math test she spent a total of 120 minutes studying. she spend an extra 15 minutes on

Mariulka [41]

135? is what i think

5 0

3 years ago

Match each fraction with the equivalent fraction on the right

Nikolay [14]

Answer:

3/4 - 6/8

1/3 - 2/6

1/2 - 5/10

3/5 - 6/10

1/4 - 2/8

3 0

3 years ago

Read 2 more answers