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
finlep [7]
3 years ago
13

The vertex of this parabola at (-5,-2). When the c - value is -4 the y-value is 2 what is the coefficient of the squared express

ion in the parabolas equation. ( to answer gets brainliest )

Mathematics
1 answer:
Andre45 [30]3 years ago
3 0

Answer:

4

Step-by-step explanation:

The vertex formula of a quadratic equation is:

●y= a(x-h)^2 +k

(h,k) are the coordinates of the vertex

Here: h = -5 and k= -2

y is 2 and x is -4

● 2 = a (-4-(-5))^2 + (-2)

● 2 = a (-4+5)^2 -2

● 2 = a *1^2 -2

● 2 = a -2

● 4 = a

You might be interested in
Use the given graph to determine the period of the function. 1 & 2 plz
White raven [17]
The period of the function is that distance where the function becomes equal again.
 We have then:
 Part 1:
 The period of the function is:
 T = 3
 Part 2:
 The period of the function is:
 T = 4
 Answer:
 
The period of functions 1 and 2 respectively are:
 
T = 3
 
T = 4
6 0
3 years ago
If UV = 6 and TV = 12, what is TU?
love history [14]

Answer:

TU = 6

Step-by-step explanation:

Using the Segment Addition Postulate, we know that TU + UV = TV, and since UV = 6 and TV = 12, we know that TU + 6 = 12, therefore, TU = 6.

3 0
3 years ago
What is 1/4 of 2,800
scZoUnD [109]

Answer:

700

Step-by-step explanation:

2800/4=700

5 0
3 years ago
What is all of the surface area and volume of this Castle? Find the surface area and volume of all the figures below, then out o
motikmotik

Answer:

Step-by-step explanation:

There are a few formulas that are useful for this:

  • lateral area of a pyramid or cone: LA = 1/2·Ph, where P is the perimeter and h is the slant height
  • lateral area of a cylinder: LA = π·dh, where d is the diameter and h is the height
  • area of a rectangle: A = lw, where l is the length and w is the width
  • volume of a cone or pyramid: V = 1/3·Bh, where B is the area of the base and h is the height
  • volume of a cylinder or prism: V = Bh, where B is the area of the base and h is the height

You will notice that for lateral area purposes, a pyramid or cone is equivalent to a prism or cylinder of height equal to half the slant height. And for volume purposes, the volume of a pyramid or cone is equal to the volume of a prism or cylinder with the same base area and 1/3 the height.

Since the measurements are given in cm, we will use cm for linear dimensions, cm^2 for area, and cm^3 for volume.

___

The heights of the cones at the top of the towers can be found from the Pythagorean theorem.

  (slant height)^2 = (height)^2 + (radius)^2

  height = √((slant height)^2 - (radius)^2) = √(10^2 -5^2) = √75 = 5√3

The heights of the pyramids can be found the same way.

  height = √(13^2 -2^2) = √165

___

<u>Area</u>

The total area of the castle will be ...

  total castle area = castle lateral area + castle base area

These pieces of the total area are made up of sums of their own:

  castle lateral area = cone lateral area + pyramid lateral area + cylinder lateral area + cutout prism lateral area

and ...

  castle base area = cylinder base area + cutout prism base area

So, the pieces of area we need to find are ...

  • cone lateral area (2 identical cones)
  • pyramid lateral area (2 identical pyramids)
  • cylinder lateral area (3 cylinders, of which 2 are the same)
  • cutout prism lateral area
  • cylinder base area (3 cylinders of which 2 are the same)
  • cutout prism base area

Here we go ...

Based on the above discussion, we can add 1/2 the slant height of the cone to the height of the cylinder and figure the lateral area of both at once:

  area of one cone and cylinder = π·10·(18 +10/2) = 230π

  area of cylinder with no cone = top area + lateral area = π·1^2 +π·2·16 = 33π

  area of one pyramid = 4·4·(13/2) = 52

The cutout prism outside face area is equivalent to the product of its base perimeter and its height, less the area of the rectangular cutouts at the top of the front and back, plus the area of the inside faces (both vertical and horizontal).

  outside face area = 2((23+4)·11 -3·(23-8)) = 2(297 -45) = 504

  inside face area = (3 +(23-8) +3)·4 = 84

So the lateral area of the castle is ...

  castle lateral area = 2(230π + 52) +33π + 504 + 84 = 493π +692

  ≈ 2240.805 . . . . cm^2

The castle base area is the area of the 23×4 rectangle plus the areas of the three cylinder bases:

  cylinder base area = 2(π·5^2) + π·1^2 = 51π

  prism base area = 23·4 = 92

  castle base area = 51π + 92 ≈ 252.221 . . . . cm^2

Total castle area = (2240.805 +252.221) cm^2 ≈ 2493.0 cm^2

___

<u>Volume</u>

The total castle volume will be ...

  total castle volume = castle cylinder volume + castle cone volume + castle pyramid volume + cutout prism volume

As we discussed above, we can combine the cone and cylinder volumes by using 1/3 the height of the cone.

  volume of one castle cylinder and cone = π(5^2)(18 + (5√3)/3)

  = 450π +125π/√3 ≈ 1640.442 . . . . cm^3

 volume of flat-top cylinder = π·1^2·16 = 16π ≈ 50.265 . . . . cm^3

The volume of one pyramid is ...

  (1/2)4^2·√165 = 8√165 ≈ 102.762 . . . . cm^3

The volume of the entire (non-cut-out) castle prism is the product of its base area and height:

  non-cutout prism volume = (23·4)·11 = 1012 . . . . cm^3

The volume of the cutout is similarly the product of its dimensions:

  cutout volume = (23 -8)·4·3 = 180 . . . . cm^3

so, the volume of the cutout prism is ...

  cutout prism volume = non-cutout prism volume - cutout volume

  = 1012 -180 = 832 . . . .  cm^3

Then the total castle volume is ...

  total castle volume = 2·(volume of one cylinder and cone) + (volume of flat-top cylinder) +2·(volume of one pyramid) +(cutout prism volume)

  = 2(1640.442) + 50.265 +2(102.762) +832 ≈ 4368.7 . . . . cm^3

4 0
3 years ago
A flagpole casts a shadow 16.60 meters long Tim stands at a distance of 12.45 meters from the base of the flagpole such that the
coldgirl [10]
This problem is solely on right triangles, wherein the Pythagorean theorem may be applied. We must first find the angle of elevation of the flagpole using Tim's height and the difference between the shadow of the flagpole and Tim's distance from the flagpole. Therefore tan a = 1.65/(16.6-12.5) where a=21.68 degrees. We use this angle to determine the height of the flagpole. tan 21.68 = x/ 16.6 where x=height of flagpole=6.6 meters.
6 0
3 years ago
Other questions:
  • Grover decides to swim downstream to search for new bones. He can swim 30 miles down stream in 3 hours. To return home swimming
    8·1 answer
  • Find the function rule.
    7·1 answer
  • What is the square root of 144
    7·2 answers
  • 2. The area of the rectangle is 224 square inches. The length of the rectangle is 14
    14·1 answer
  • Select each transformation that carries a square onto itself.
    8·1 answer
  • What is the length of AB?
    10·2 answers
  • Because the three sides are congruent, what foes that make each angle measure according to the equilateral triangle theorem.
    11·2 answers
  • If x is a number, which expression represents the statement below? 4 less than the product of 2 and a number
    10·1 answer
  • Write the system and
    6·1 answer
  • K4. The speed of a vehicle is 75 km hrl. Write the unit of the given speed as a fraction using a positive exponent​
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!