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3 years ago

Find the slope of the line through each pair of points. 6. * (4, 10), (0, 3)

Mathematics

1 answer:

lidiya [134]3 years ago

5 0

Answer:

Slope: 1.75

Step-by-step explanation:

Slope = (3-10) / (0-4)

= -7 / -4

= 1.75

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Two shapes are shown below, one isosceles triangle and one rectangle. The dimensions can be represented by algebraic expressions

liberstina [14]

Answer:

Perimeter of Isosceles Triangle = 16 units

Step-by-step explanation:

Area of rectangle is given by the formula;

Area = 1/2 × base × height

From the diagram, base = 6x - 6 and height = 6x - 8

Thus,Area = 1/2 × (6x - 6) × (6x - 8)

Area = (3x - 3)(6x - 8) = 18x² - 42x + 24

Secondly, area of rectangle is given by;

Area = length x breadth

So, area of rectangle in question = (6x - 9)(3x - 2) = 18x² - 39x + 18

We are told both the area of the triangle and the rectangle are the same, so let's equate both areas;

18x² - 42x + 24 = 18x² - 39x + 18

18x² will cancel out and rearranging, we have;

24 - 18 = 42x - 39x

6 = 3x

x = 6/3

x = 2

Plugging 2 for x for the height and base of the triangle, we have;

base = 6(2) - 6 and height = 6(2) - 8

Base = 6 and height = 4

So,let's find the slant height of the isosceles triangle.

Dividing the base by 2,we have; 6/2 = 3

So,using Pythagoras theorem, let the slant height be h, so we have;

h² = 3² + 4²

h² = 9 + 16

h² = 25

h = √25

h = 5

2 slant sides of isosceles triangle are the same. So perimeter = 5 + 5 + 6 = 16 units

8 0

3 years ago

The potential energy, P, in a spring is represented using the formula P = kx2. Lupe uses an equivalent equation, which is solved

ella [17]

Original equation is $P=kx^{2}$

So, $kx^{2} =P$ and

$k=\frac{P}{x^{2} }$

If we compare this equation with the given options, we can easily find that this matches with the last one $k=\frac{p}{2x^{2} }$ with P = p/2.

Hence, correct option is $k=\frac{p}{2x^{2} }$ .

4 0

3 years ago

Read 2 more answers

Subtract 3/y-2 - 1/y+3

Helen [10]

To subtract fractions, we need a common denominator.

$\frac{3}{y-2}$ - $\frac{1}{y+3}$

the common denominator will be (y-2)(y+3)

$\frac{3(y+3)-1(y-2)}{(y-2)(y+3)}$
$\frac{3y + 9 - y + 2}{(y-2)(y+3)}$
$\frac{2y + 11}{(y-2)(y+3)}$

The answer above will be the simplified form.

3 0

3 years ago

Solve the equation √x-6 +2=6

Dovator [93]

Answer:

x = 22

Step-by-step explanation:

$\sqrt{x-6}$ + 2 = 6 ( subtract 2 from both sides )

$\sqrt{x-6}$ = 4 ( square both sides to clear the radical )

x - 6 = 4² = 16 ( add 6 to both sides )

x = 22

8 0

2 years ago

Thirty adults were asked how many pets they have had over their lifetime. the results are shown in the histogram below. a bar gr

Savatey [412]

Using the concepts of the mean and of the median, it is found that the correct option is given by:

both in the interval 6–10.

<h3>What are the mean and the median of the data-set?</h3>

The mean is the <u>sum of all observations divided by the number of observations</u>.

The median is the measure that separates the bottom half of the variable from the upper half, that is, the 50th percentile.

To calculate the mean from the histogram, we take the midpoint of each interval and calculate the weighed mean, hence:

$M = \frac{14(3) + 9(8) + 5(13) + 2(18)}{30} = 7.17$

The median is in the interval in which the 30/2 = 15th measure is, which is also in the interval 6-10, as the interval 1-5 had 14 adults, and after interval 6-10, there are 23 adults.

Hence, the correct option is given by:

both in the interval 6–10.

More can be learned about the mean and the median of a data-set at brainly.com/question/24732674

4 0

2 years ago