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3 years ago

8

What is the equation, in point-slope form, for a line that goes through (2, −6)(2, −6) and has a slope of −34−34 ?

1 answer:

Keith_Richards [23]3 years ago

8 0

The answer is the last one option: y+6=-34(x+2). I told you the reason in the other similar question.

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A right prism has height 7½ and triangular bases with sides of length 5, 12, and 13 What is the: Total Surface Area of the Prism

sdas [7]

Given:

A right prism has height 7½ and triangular bases with sides of length 5, 12, and 13.

To find:

The total surface area of the prism.

Solution:

We have,

Height of prism = 7½ = 7.5

Sides of triangular base are 5, 12, 13. These sides of Pythagorean triplets because

$5^2+12^2=13^2$

$25+144=169$

$169=169$

So, the base of the prism is a right triangle.

Area of a triangle is

$Area=\dfrac{1}{2}\times base \times height$

$A_1=\dfrac{1}{2}\times 5\times 12$

$A_1=30$

The area of the base is equal to the area of the top, i.e., $A_2=30$ sq units.

Perimeter of the base is

$P=5+12+13$

$P=30$

The curved surface area of the prism is

$CSA=\text{Perimeter of the base}\times \text{Height of the prism}$

$CSA=30\times 7.5$

$CSA=225$

Now, the total area of the prism is

$A=A_1+A_2+CSA$

$A=30+30+225$

$A=285$

Therefore, the total surface area of the triangular prism is 285 square units.

5 0

3 years ago

Use the Pythagorean Theorem to determine which of the following give the measures of the legs and hypotenuse of a right triangle

kakasveta [241]

The Pythagorean theorem states that the square of the hypotenuse is equal to the sum of the squares of the legs:

$c^2=a^2+b^2.$

The hypotenuse is the side with the greatest length.

Check all options:

1. c=5, a=3, b=4:

$5^2=25,\\3^2+4^2=9+16=25,\\5^2=3^2+4^2$ true.

2. c=14, a=4, b=11:

$14^2=196,\\4^2+11^2=16+121=137,\\14^2\neq 4^2+11^2$ false.

3. c=17, a=9, b=14:

$17^2=289,\\9^2+14^2=81+196=277,\\17^2\neq 9^2+14^2$ false.

4. c=16, a=8, b=14:

$16^2=256,\\8^2+14^2=64+196=260,\\16^2\neq 8^2+14^2$ false.

5. c=17, a=8, b=15:

$17^2=289,\\8^2+15^2=64+225=289,\\17^2=8^2+15^2$ true.

Answer: correct options are A and E.

4 0

3 years ago

Read 2 more answers

Imena's math test scores are 83, 93, 78, 89, and 83. She has one more math test this semester. What score most she get on the te

marshall27 [118]

87 is the median because 83 and 87's average is 85.

8 0

3 years ago

Read 2 more answers

Vanessa swims 7.25 feet below sea level. Her friend Emily swims 5.4 feet further down. How many feet did Emily swim down to?

grin007 [14]

B: 12.65 feet
if vanessa is already 7.25 feet down, and emily is 5.4 feet further, you would do 7.25+5.4 which is 12.65

8 0

2 years ago

Line ℓ1 has the equation

aleksley [76]

Answer:

$\sqrt{2}$ units

Step-by-step explanation:

The Line 1 has equation x + y = 5 ....... (1) , and

Line 2 has equation x + y = 3 .......... (2)

Now, we have to find the perpendicular distance between line 1 and line 2.

We can say that (3,0) is a point on line 2 as it satisfies the equation (2).

Now, the perpendicular distance from point (3,0) to the line 1 will be given by the formula

$\frac{|3 + 0 - 5|}{\sqrt{1^{2}+ 1^{2}}} = \frac{2}{\sqrt{2}} = \sqrt{2}$ units (Answer)

We know that the perpendicular distance from any external point ( $x_{1},y_{1}$ ) to a given straight line ax + by + c = 0 is given by the formula $\frac{|ax_{1} + by_{1} + c|}{\sqrt{a^{2} + b^{2}}}$ .

3 0

3 years ago