1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
olchik [2.2K]
3 years ago
14

Josh estimates the height of his desk. what is the reasonable estimate?

Mathematics
1 answer:
Galina-37 [17]3 years ago
8 0
<span>The complete question includes these choices: A)1 foot B)2 feet C)5 feet D)9 feet The correct answer is B) 2 feet, approx. 24 inches; most standard desks have a height between 28'' to 30''. The answer A is too low, C and D are too much, the perfect answer would be at least 3-4 feet, but as this question proposes only these answers, the nearest estimating value is B)2 feet. </span>
You might be interested in
Help me on these questions
mojhsa [17]

Answer:

a) The equation is (y - 1)² = -8 (x - 4)

b) The equation is (x - 1)²/25 + (y - 4)²/16 = 1

c) The equation of the ellipse is (x - 3)²/16 + y²/4 = 1

Step-by-step explanation:

a) Lets revise the standard form of the equation of the parabola with a

   horizontal axis

# (y - k)² = 4p (x - h), (h , k) are the coordinates of its vertex and p ≠ 0

- The focus of it is (h + p , k)

* Lets solve the problem

∵ The focus is (2 , 1)

∵ focus is (h + p , k)

∴ h + p = 2 ⇒ subtract p from both sides

∴ h = 2 - p ⇒ (1)

∴ k = 1

∵ It opens left, then the axis is horizontal and p is negative

∴ Its equation is (y - k)² = 4p (x - h)

∵ k = 1

∴ Its equation is (y - 1)² = 4p (x - h)

- The parabola contains point (2 , 5), substitute the coordinates of the

 point in the equation of the parabola

∴ (5 - 1)² = 4p (2 - h)

∴ (4)² = 4p (2 - h)

∴ 16 = 4p (2 - h) ⇒ divide both sides by 4

∴ 4 = p (2 - h) ⇒ (2)

- Use equation (1) to substitute h in equation (2)

∴ 4 = p (2 - [2 - p]) ⇒ open the inside bracket

∴ 4 = p (2 - 2 + p) ⇒ simplify

∴ 4 = p (p)

∴ 4 = p² ⇒ take √ for both sides

∴ p = ± 2, we will chose p = -2 because the parabola opens left

- Substitute the value of p in (1) to find h

∵ h = 2 - p

∵ p = -2

∴ h = 2 - (-2) = 2 + 2 = 4

∴ The equation of the parabola in standard form is

  (y - 1)² = 4(-2) (x - 4)

∴ The equation is (y - 1)² = -8 (x - 4)

b) Lets revise the equation of the ellipse

- The standard form of the equation of an ellipse with  center (h , k)

 and major axis parallel to x-axis is (x - h)²/a² + (y - k)²/b² = 1  

- The coordinates of the vertices are (h ± a , k )  

- The coordinates of the foci are (h ± c , k), where c² = a² - b²  

* Now lets solve the problem

∵ Its vertices are (-4 , 4) and (6 , 4)

∵ The coordinates of the vertices are (h + a , k ) and (h - a , k)  

∴ k = 4

∴ h + a = 6 ⇒ (1)

∴ h - a = -4 ⇒ (2)

- Add (1) and (2) to find h

∴ 2h = 2 ⇒ divide both sides by 2

∴ h = 1

- Substitute the value of h in (1) or (2) to find a

∴ 1 + a = 6 ⇒subtract 1 from both sides

∴ a = 5

∵ The foci at (-2 , 4) and (4 , 4)

∵ The coordinates of the foci are (h + c , k) , (h - c , k)

∴ h + c = 4

∵ h = 1

∴ 1 + c = 4 ⇒ subtract 1 from both sides

∴ c = 3

∵ c² = a² - b²

∴ 3² = 5² - b²

∴ 9 = 25 - b² ⇒ subtract 25 from both sides

∴ -16 = -b² ⇒ multiply both sides by -1

∴ 16 = b²

∵ a² = 25

∵ The equation of the ellipse is (x - h)²/a² + (y - k)²/b² = 1

∴ The equation is (x - 1)²/25 + (y - 4)²/16 = 1

c) How to identify the type of the conic  

- Rewrite the equation in the general form,  

 Ax² + Bxy + Cy² + Dx + Ey + F = 0  

- Identify the values of A and C from the general form.  

- If A and C are nonzero, have the same sign, and are not equal  

 to each other, then the graph is an ellipse.  

- If A and C are equal and nonzero and have the same sign, then

 the graph is a circle  

- If A and C are nonzero and have opposite signs, and are not equal  

 then the graph is a hyperbola.  

- If either A or C is zero, then the graph is a parabola  

* Now lets solve the problem

∵ x² + 4y² - 6x - 7 = 0

∵ The general form of the conic equation is

   Ax² + Bxy + Cy² + Dx + Ey + F = 0  

∴ A = 1 and C = 4

∵ If A and C are nonzero, have the same sign, and are not equal  to

  each other, then the graph is an ellipse.

∵ x² + 4y² - 6x - 7 = 0 ⇒ re-arrange the terms

∴ (x² - 6x ) + 4y² - 7 = 0

- Lets make x² - 6x completing square

∵ 6x ÷ 2 = 3x

∵ 3x = x × 3

- Lets add and subtract 9 to x² - 6x to make the completing square

 x² - 6x + 9 = (x - 3)²

∴ (x² - 6x + 9) - 9 + 4y² - 7 = 0 ⇒ simplify

∴ (x - 3)² + 4y² - 16 = 0 ⇒ add 16 to both sides

∴ (x - 3)² + 4y² = 16 ⇒ divide all terms by 16

∴ (x - 3)²/16 + 4y²/16 = 1 ⇒ simplify

∴ (x - 3)²/16 + y²/4 = 1

∴ The equation of the ellipse is (x - 3)²/16 + y²/4 = 1

5 0
3 years ago
Pls help! I don’t understand bc I’m not smart-
Ipatiy [6.2K]

Answer:

78.5 m²

Step-by-step explanation:

The formula to find the area of a quarter of a circle: \frac{1}{4} * \pi * r^{2}, where r is the radius (diameter ÷ 2) and the \pi is alterable.

1) Substitute the given values into the formula.

= \frac{1}{4} * 3.14 * 10^{2}

2) Solve it.

= \frac{1}{4} * 314

= 78.5

3) Round it off to the nearest tenth. In this case, it has already been rounded off.

8 0
2 years ago
HELP ASAP PLZZ
Nonamiya [84]

Answer:

The Answer is A. 2/5

Step-by-step explanation:

The way i Divide fractions is by if you take the second fraction and swap the numbers around, you can do 7/24 TIMES 48/35. then you multiply the numbers NOT in a crossway like 7 times 35 butin a straight way so its 7 times 48. Doing so will get you 336/840. I simplified this answer by 6 and got 56/140 then i simplified it again by 4 to get 14/35 and once more i simplified it by 7 to get 2/5.

4 0
3 years ago
What would be the value of x in x+5=-3x-9
9966 [12]
-3 because it shows the value right there
4 0
3 years ago
Read 2 more answers
can someone please help me with number 12? there’s only two options and you can see them in the picture.
nataly862011 [7]

Answer:

B)

Step-by-step explanation:

Because it can't be a because if you wanna get P it is 20/16 not 1 /12

7 0
2 years ago
Other questions:
  • Hannah has 11 toothpicks that are the same length.Name the types of triangles and quadrilaterals Hannah can make if she uses onl
    8·2 answers
  • What does 3+x equal?
    9·1 answer
  • 20-23 only please?????
    8·1 answer
  • What is another word for rotation?<br><br> A. Slide<br><br> B. Turn<br><br> C. Fall<br><br> D. Flip
    9·2 answers
  • Find the definite integral from 0 to 1/16 of arcsin(8x)/sqrt(1-64x^2)dx
    13·1 answer
  • Just need help with number 1. Thanks!
    14·2 answers
  • 2/3 if a book read and 4/5 of a book read. Who read more and how much mire
    7·1 answer
  • At a fundraiser, a school group charges $6 for tickets for a "grab bag." You choose one bill at random from a bag that contains
    13·2 answers
  • Please help asap<br> which inequality is represented by this graph
    5·1 answer
  • Select the correct answer from each drop-down menu.
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!