Complete the square
to find the vertex
of this parabola.
2.
х
- 16 Y-4 x-12=0
Answers
Answer:
Vertex coordinates; (h,k) = (2, -1)
Step-by-step explanation:
Vertex form of a parabola is;
y = a(x - h)² + k
Now, we are given;
x² - 16y - 4x - 12 = 0
Rearranging, we have;
x² - 4x = 16y + 12
Let's complete the square on the left hand side;
First add square of half of the coefficient of x to both sides;
x² - 4x + (-½ × 4)² = 16y + 12 + (-½ × 4)²
x² - 4x + 4 = 16y + 12 + 4
LHS can be expressed as;
(x - 2)² = 16y + 16
16y = (x - 2)² - 16
Divide both sides by 16 to get;
y = (1/16)(x - 2)² - 1
Comparing this with y = a(x - h)² + k, we have;
a = 1/16
h = 2
k = -1
(h,k) = (2, -1)
Related Questions
¿En què situaciones usamos los nùmeros enteros positivos y negativos, escribe 2 ejemplos de cada uno? Por favor para ahora hocino me jalan :(
Answers
Respuesta:
Los enteros positivos, o números enteros, se utilizan de muchas maneras durante la vida diaria. Los números de carretera se contabilizan junto con los límites de velocidad de la carretera. Los enteros se utilizan para comprender qué velocidad conducir en una carretera determinada. Los números en los relojes se utilizan para entender la hora y para configurar las alarmas del reloj. Hay números en edificios y casas para identificar direcciones y números para los niveles de piso dentro de los edificios. Los mapas utilizan enteros para proporcionar dirección e información. Los enteros negativos pueden ser menos obvios para su uso en la vida cotidiana. Algunos ejemplos de uso negativo de enteros incluyen las lecturas del termómetro, manteniendo la puntuación en un juego de hockey, altitud y bancos. Aunque todos estos ejemplos utilizan enteros positivos, también utilizan enteros negativos. Un termómetro utiliza negativo enteros para representar temperaturas por debajo de cero. En hockey, cuando el otro equipo anota en la línea del primer equipo, es un menos, pero cuando el primer equipo anota, es un plus. La altitud que está por debajo del nivel del mar está representada con números negativos. Los bancos y las cooperativas de crédito representan débitos con enteros negativos y créditos con enteros positivos.
I’m asking again bc I really need a answer ;_;
If the measure of angle 6 is 123 degrees, what is the measure of angle 1?
Answers
Answer:
57 because 6 is 123 and so is 4 so 180 - 123 and you get 57.
Answer:
The measure of angle one is 57.
Step-by-step explanation:
The 2 angles are supplementary, which means that they add up to 180 degrees.
180-123=57
Find the size of the angle a.
a=
Answers
a=72
Step-by-step explanation:
2a+a+2a=360 (being complete turn )5a=360a=360/5a=72what is the vaule form this plz give me the answer
Answers
Answer:
what's the question ????
Olivia’s makes $825 per week at her job at Target. She is paid an additional $15.00 for every hour of overtime she works. Olivia’s goal was to make at least $900 on her paycheck. How much overtime would she have to work to accomplish her goal?
Write, solve and graph the inequality.
Answers
Answer:
Step-by-step explanation:
900-825=75
75/15=5
5 hours extra
Ann works in a supermarket for $10.00 per hour. If her pay is increased to $12.00, then what is her percent increase in pay? Show your work.
Answers
Answer:
20% increase in her pay
Step-by-step explanation:
It's 20% increased, because it increased by $2, $2 goes into $10 5 times, and if you were to put that into percentages 2 is a fifth of 10 so that would 20%, because 20 is a fifth of 100.
Answer:
It's 20% increased,
Step-by-step explanation:
because it increased by $2, $2 goes into $10 5 times, and if you were to put that into percentages 2 is a fifth of 10 so that would 20%, because 20 is a fifth of 100.
change 64/11 into a mixed number
Answers
Answer:
5 9/11
Step-by-step explanation:
how can i solve that equation by factoring
Answers
Answer:
y = ( x + 3 )( x + 5 )
Step-by-step explanation:
N/A
Answer:
[tex]y = {x}^{2} + 8x + 15 \\ factors \: = 3 \: and \: 5 \\ y = {x}^{2} + 3x + 5x + 15 \\ y = x(x + 3) + 5(x + 3) \\ y = (x + 5)(x + 3) \\ either \: (x + 5) = 0 \: or \: (x + 3) = 0 \\ x = - 5 \: and \: - 3[/tex]
Geometry: CC 2015 > Chapter 9: Chapter 9 Test > Chapter Test 9
Answers
Answer:
ohk where is test
Step-by-step explanation:
and question
Please help! And serious answers please
Answers
Answer:
I think it is 10
Step-by-step explanation:
Well, there are 2 segment of 4 and 1 segment of 3, meaning it is about 10 away. (rounding to the nearest tenth)
A building in the shape of a cube has a width of 30 ft., a length of 30 ft., and a height of 30 ft. An architect wants to build a scale model of the building that is 10% smaller in volume. What is the height of the new building?
Answers
Answer:
Step-by-step explanation:
The height of the scale model is 13.92 feet. (Rounding to the nearest hundredth).
Step-by-step explanation:
These are the measurements of the real building:
Height = 30 feet
Width = 30 feet
Length = 30 feet
Volume of the real building = 30 * 30 * 30 = 27,000 cubic feet
These are the measurements of the scale model:
Volume of the scale model = 10% of 27,000 cubic feet
Volume of the scale model = 0.1 * 27,000 = 2,700 cubic feet
Height = ∛ 2,700 = 13.92 feet (Rounding to nearest hundredth)
Width = ∛ 2,700 = 13.92 feet (Rounding to nearest hundredth)
Length =∛ 2,700 = 13.92 feet (Rounding to nearest hundredth)
The height of the scale model is 13.92 feet.
Answer:
28,96 ft (round to the nearest hundreds)
Step-by-step explanation:
1) find the volume of the first cube
V = side^3 = 30^3 = 27000 ft^3
2) find the 10% of 27000
27000 / 0,1 = 2700
3) find the volume of the second cube
V = 27000- 2700 = 24300 ft^3
4) find the height
height = ∛24300 = 28,96 ft (round to the nearest hundreds)
what is 7 divided by 80?
Answers
Answer:
7 divided by 80 is 0.0875 .
Answer:
0.0875 as a decemial or 7/80 as a fraction
Step-by-step explanation:
Isaac chose A as the correct answer. How did he get that answer?
Answers
Step-by-step explanation:
Simplify the expression
For what value of n does (1/36)n=216
Answers
Answer:
(1/36)^n=216
(1/2^2 * 3^2)^n=216
n=-3/2
Step-by-step explanation:
I'm smart
I NEED HELP ASAP WITH EXPLANATION PLEASE!!!!!!!!!$!_!$!
which equation can you use to solve for m?
1) 5m = 105
2) 5m + 105 = 90
3) 5m + 105 = 180
4) 5m + 105 = 360
Answers
Answer:
(3) 5m+ 105 = 180
Step-by-step explanation:
180 - 105 = 5m
A golf driving range charges a flat fee of $20 to practice and then $5.75 for a buckets of balls. Write an equation that models the charges (C) in terms of the number of bucket of balls (b) that you use
Answers
Answer:
A
Step-by-step explanation:
Flat fee is $20 [initial cost]
Each bucket of ball is $5.75
b is the number of buckets and c is the total cost
To get total cost, we add the flat fee with the bucket fee. Bucket fee is $5.75 multiplied by the number of buckets, which is b.
So, we have:
cost = $20 + $5.75b
In equation it is:
Choice A is right.
What is the quadratic regression equation that fits these data?
Number of seconds Height (in feet)
0,11 1,13 2,13 3,15 4,9 5,1
Answers
Answer:
Step-by-step explanation:
do you know the answer?
The mean (average) number of albums released by the four artists is 7 albums. Calculate the mean absolute deviation (MAD) of the data shown in the display below.
Answers
Answer:
I'm sorry I dint understand the question very well
Simplify 4p+3q-3p-3q
Answers
Answer:
4p+3q-3p-3q
=4p-3p+3q-3q
=p+3q-3q
=p
Step-by-step explanation:
Eva buys a piece of red fabric that is 5.6 meters long and a piece of yellow fabric that is 2.8 meters long. How long are the two pieces of fabric together in millimeters?
Answers
Answer:
Total length of fabric pieces is 8400 mm.
Step-by-step explanation:
Eva buys a piece of red fabric of length = 5.6 meters
Since, 1 meter = 1000 mm
Therefor, 5.6 meter = 5.6 × 1000
= 5600 mm
Similarly, length of yellow fabric piece = 2.8 meters
≈ 2.8 × 1000 mm
≈ 2800 mm
If these pieces are joined together, total length of the fabric pieces
= 5600 + 2800
= 8400 mm
Therefore, total length of fabric pieces is 8400 mm.
Answer:
above is right
Step-by-step explanation:
n a family vacation, Amy’s dad drove the car at a constant speed and traveled 585 miles in 13 hours. At this rate, how long would it have taken the family to travel 810 miles? What was the car’s rate of speed
Answers
Answer: 18 hours
Step-by-step explanation:
Amy's dad drove the car at a constant speed and travel 585 miles in 13 hours , using proportion . Find out how long would it have taken the family to travel 810 miles . Let x -----> the time in hours to travel 810 miles! Hope this helps! Good luck!
Answer: It would take them 18 hours, and the car was going 45 miles per hour.
Step-by-step explanation:
To find how fast the car was going, I divided 585÷13.
To find how many hours it would take, I divided 810÷45.
Hope I helped! May I have brainliest?
Amelia received $4.15 in tips from one table. All of her tips were in quarters, dimes and nickels. There were five less dimes than quarters and three more nickels than twice the number of quarters. How many dimes did she have?
Answers
Step-by-step explanation:
received $4.15 in tips from one table. All of her tips were 4.1500in quarters, dimes and nickels. There
Please help!!! Im trying to bring my math grades up!!!
What is the area of a circular pool with a diameter of 20 feet? Use 3.14
for pi and round your answer to the nearest hundredth.
Answers
Answer:
314
Step-by-step explanation:
To find the area of a circle using the diameter, use this formula:
[tex]A=\frac{1}{4}\pi d^2[/tex]
Substitute the diameter and the value of pi:
[tex]A = \frac{1}{4}*(3.14) * (20)^2[/tex]
[tex]A = 0.785 * 400[/tex]
A = 314
The product of two numbers is 323 and the difference between them is 2. What are the two numbers?
Answers
Answer:
17 and 19
Step-by-step explanation:
17 * x = 323
x = 323 / 17
x = Second number = 19.
Step-by-step explanation:
323
2
=16×2=32
=3×1=3
=3
=16
=16,3
Help! I will give brainliest to the best answer.
The high jumper set a new personal record when she cleared 5 feet 8 inches. How can we find how many inches high 5 feet 8 inches is?
Answers
Answer:
60 inches = 5 feet.
Step-by-step explanation:
12 inches in one foot, 12 x 5 = 60, meaning it would be 68 inches high
Solve: 5x2 + 25x = 0. (2 points)
Answers
Answer:
=−5
Step-by-step explanation:
Find 30% decrease from 95
68.40
63.20
66.50
Answers
Answer:
66.50
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Which of the following examples has a unit rate of 30 meters per second? Select all that apply. A) 90 meters in 5 seconds B) 90 meters in 3 seconds C) 120 meters in 6 seconds D) 150 meters in 5 seconds E) 240 meters in 6 seconds
Answers
The following examples have a unit rate of 30 meters per second:
B) 90 meters in 3 seconds.
D) 150 meters in 5 seconds.
What is division?The division in mathematics is one kind of operation. In this process, we split the expressions or numbers into the same number of parts.
Given:
We have the unit rate of 30 meters per second.
A) 90 meters in 5 seconds.
The unit rate = 90/5 meters per second.
The unit rate = 18 meters per second.
B) 90 meters in 3 seconds.
The unit rate = 30 meters per second.
C) 120 meters in 6 seconds.
The unit rate = 20 meters per second.
D) 150 meters in 5 seconds.
The unit rate = 30 meters per second.
E) 240 meters in 6 seconds.
The unit rate = 40 meters per second.
Therefore, B and D have the unit rate of 30 meter per second.
To learn more about the division;
https://brainly.com/question/13263114
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What is the factorization of the trinomial below?
x² - 6x + 5
A. (x+4)(x-2)
B. (X - 5)(x - 1)
C. (x+5)(x - 1)
D. (x-4)(x - 2)
Answers
Answer:
B)
Step-by-step explanation:
Find the length of AB
Answers
Answer:
35.6 units
Step-by-step explanation:
By intersecting chords theorem:
10*x = 16*16
10x = 256
x = 256/10
x = 25.6
AB = 10 + x
AB = 10 + 25.6
AB = 35.6