at a point on the ground 15 ft from the tree, the distance to the top of the tree is 1 ft more than 2 times the height of the tree. find the height of the tree.

Answers

Answer 1

Answer: Let's say the tree is of height h. The point 15 ft away, the base of the tree, and the height of the tree form a right triangle, where the length of the sides are h, 2h + 1, and 15 (see attached image).

Using the Pythagorean theorem, $h^2+ 15^2 = (2h +1)^2$

Simplifying it down, we get $3h^2+4h-224=0$

We can use the quadratic formula to solve this, where the solutions are $(-4 \pm √(4^2 - 4 * 3 * (-224)) )/(2*3) = (-4 \pm √(2704) )/(6) = (-4 \pm 52)/(6)$

Therefore the answers are $- (56)/(6)$ or $(48)/(6) =8$

The answer is 8 since the height of the tree must be positive.

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What is the appropriate restriction on the literal equation ax+b=c if you intend to solve the equation for x?Please provide explanation. Thanks :)

Answers

Answer:

ax+b=c

Step-by-step explanation:

The appropriate restriction on the literal equation ax+b=c if you intend to solve for x is that a cannot be equal to zero. Otherwise, the equation becomes undefined and cannot be solved for x.

Answer:

Step-by-step explanation:To solve the literal equation ax + b = c for x, you would typically want to isolate x on one side of the equation. The appropriate restriction in this case is that 'a' should not be equal to 0, because if 'a' were equal to 0, you would have 0x + b = c, which simplifies to b = c. This would mean there's no 'x' variable to solve for, and the equation would have no solution or would be true for any value of 'c'. So, the restriction is that 'a' must be nonzero for the equation to be solvable for 'x'.

Mason gave the waiter a $14.58 tip, which was 15 percent of the dinner bill. What was the amount of the dinner bill before he added the tip?A.$9.72
B.$21.87
C.$97.20
D.$218.70

Answers

Answer:

C. $97.20

Step-by-step explanation:

Let the dinner bill be $x.

The tip given to the waiter is $14.58.

Also, it is given that the tip is 15% of the tip.

Thus we get the relation 15% of x = 14.58

i.e. 0.15x = 14.58

i.e. $x=(14.58)/(0.15)$

i.e. x = 97.20

Hence, the amount of dinner bill before the tip is added is given by $97.20

the answer is :

the amount of the bill before the tip = 14.58 *100 /15 = 97.20 $

Larry,Mary,and Terry each had a full glass of juice.Larry drank 3/4 of his.Mary drank 3/8of hers.Terry drank 7/10 of his.who drank less than 1/2 of their juice?

Answers

Answer: Marry drank less than half of her glass of juice.

Step-by-step explanation: Given that Larry, Mary and Terry each had a full glass of juice.Larry drank $(3)/(4)$ of his. Mary drank $(3)/(8)$ of hers and Terry drank $(7)/(10)$ of his.

We are to find who drank less than $(1)/(2)$ of their juice.

We have

Portion of the glass of juice that Larry drank

$=(3)/(4)>(2)/(4)\left(=(1)/(2)\right).$

Portion of the glass of juice that Mary drank

$=(3)/(8)<(4)/(8)\left(=(1)/(2)\right).$

Portion of the glass of juice that Terry drank

$=(7)/(10)>(5)/(10)\left(=(1)/(2)\right).$

Therefore, Marry drank less than half of her glass of juice.

Mary drank the least because when half of 8 is 4/8.

Naomi used 100 tiles to create a design. Blue tiles make up 1/2 of the design. Another 15 tiles are green, and 1/5 of the tiles are yellow. The rest of the tiles are red. How many red tiles did Naomi use in her design? A. 15 tiles
B. 25 tiles
C. 65 tiles
D. 85 tiles

Answers

Answer:

Naomi used 15 red tiles in her design.

Step-by-step explanation:

We need to add the total number of tiles that we know to find out the unknown value of red tiles. The blue tiles make up 1/2 of the design, or 50 tiles. Next we will add the green tiles, which Naomi used 15 of, as stated.

So far, we have figured out how many blue and green tiles we have. (50 blue, and 15 green, which is a total of 65).

Now we need to calculate the number of yellow tiles, which equal 1/5 of the design. 1/5 of 100 is 20.

Now we add all of our tiles that we already know. We have 50 red + 15 green + 20 yellow which = 85.

Now to find the unknown value of red tiles, we subtract our 85 other tiles from the 100 total tiles, and the ends us up with 15 red tiles.

Hope this helps!!

stay safe :0)

Bill measures the circumference of a circular fish pond to be 28 ft. What is the diameter of the fish pond, rounded to the nearest foot? Use 3.14 to approximate pi.

Answers

it would be 9 ft. using the knowledge of $\pi$ times the diameter ( $\pi$ equals aprox. 3.14) equal the circumference of a circle, and since we know the circumference, we need to divide that by $\pi$ to get the diameter.

equation: 28/3.14=8.913
rounding that would bring it to 9 ft.

What is 1/8 divided by 1/2

Answers

Solve using the KCF Method (Keep, Change, Flip)

1/8 / 1/2
1/8 stays the same
= 1/8 x 1/2
Change the division sign into multiplication
= 1/8 x 2/1
Flip 1/2 so it can be 2/1
= 2/8
Multiply as you would. (Numerator x Numerator, Denominator x Denominator)
= 1/4
Simplified

the answer would be 2\8 but you have to divide them by 2 and get 1\4 hope this helps

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