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3 years ago

A flagpole casts a shadow 15 feet long. At the same time of day, Mr. James, who is 6 feet tall, casts a shadow that

Mathematics

1 answer:

Yanka [14]3 years ago

7 0

Answer: the second bubble

Step-by-step explanation:

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What is the 21st term of the sequence with a1 = -6 and d = 4?

Nutka1998 [239]

Answer:

answer is 74

Step-by-step explanation:

-6+4 x 20

- 6+80=74

8 0

3 years ago

Read 2 more answers

Expand and simplify (2x−12) ^2

lubasha [3.4K]

Answer:

$\boxed{4x^{2} - 48x + 144}$

Step-by-step explanation:

Given expression:

(2x - 12)²

To simplify the expression, we will use the formula (a - b)² = a² - 2ab + b².

[Where "a and b" are the first and second term in (a - b)²]

$\rightarrowtail (2x - 12)^{2}$

In this case, the first term of (2x - 12)² is "2x" and the second term is "12".

$\rightarrowtail (2x)^{2} - 2(2x)(12) + (12)^{2} \ \ \ \ \ \ \ \ \ \ \ \ \ \ [\small\text{First term = a = 2x; Second term = b = 12]}$

Now, simplify the expression.

$\rightarrowtail (2x)^{2} - 2(2x)(12) + (12)^{2}$

$\rightarrowtail (2x)(2x) - (4x)(12) + (12)(12)$

$\rightarrowtail \boxed{4x^{2} - 48x + 144}$

4 0

3 years ago

Which of the following expressions are equivalent to -8/11-3/4-1/4.Choose 3 answers

Effectus [21]

Answer:

option a

option d

option e

Step-by-step explanation:

option a

$-\frac{8}{11}+( -\frac{3}{4})+( -\frac{1}{4})=-\frac{8}{11}-\frac{3}{4} -\frac{1}{4}$

option d

$-(\frac{8}{11}+\frac{3}{4}+\frac{1}{4})=-\frac{8}{11}-\frac{3}{4} -\frac{1}{4}$

option e

$-\frac{8}{11}-(\frac{3}{4}+\frac{1}{4})=-\frac{8}{11}-\frac{3}{4} -\frac{1}{4}$

4 0

3 years ago

A parabola has a focus of F(2, -0.5) and a directrix of y=-1.5 P(x,y) represents any point on the parabola, while D(x, -1.5) rep

prohojiy [21]

The sketch of the parabola is attached below

We have the focus $(a,b) = (2, -0.5)$
The point $P(x,y)$
The directrix, c at $y=-1.5$

The steps to find the equation of the parabola are as follows

Step 1
Find the distance between the focus and the point P using Pythagoras. We have two coordinates; $(2, -0.5)$ and $(x,y)$ .
We need the vertical and horizontal distances to find the hypotenuse (the diagram is shown in the second diagram).
The distance between the focus and point P is given by
$\sqrt{ (x-a)^{2}+ (y-b)^{2} }$

Step 2
Find the distance between the point P to the directrix $c$ . It is a vertical distance between y and c, expressed as $y-c$

Step 3
The equation of parabola is then given as
$\sqrt{ (x-a)^{2}+ (y-b)^{2} }$ = $y-c$
$(x-a)^{2}+ (y-b)^{2}= (y-c)^{2}$ ⇒ substituting a, b and c
$(x-2)^{2}+ (y--0.5)^{2} = (y--1.5)^{2}$
$(x-2)^{2}+ (y+0.5)^{2}= (y+1.5)^{2}$ ⇒Rearranging and making $y$ the subject gives

$y= \frac{ x^{2} }{2} -2x+1$

7 0

4 years ago

Height: 15 ft <br> area: 285 square feet <br><br> find the missing dimension for the triangle

seraphim [82]

A=1/2 B×h
285=1/2×B×15
B=38 feet, so the base of the triangle is 38 feet. Hope it help!

4 0

3 years ago