Please help!!
Find the coordinates of the vertex of the following parabola algebraically. Write your
answer as an (x, y) point.
y = 4x + 56x + 192
Answers
Answer:
The vertex of the parabola = (-7 , -4)
Step-by-step explanation:
Step(i):-
Given that the parabola y = 4 x² + 56 x +192
y = 4 (x² + 14 x + 48 )
y = 4 ( x² + 2 × 7 (x) + 49-1)
y = 4 ( x² + 2 × 7 (x) + 49)- 4
we apply the formula
(a +b)² = a² + 2ab + b²
y = 4 ( x + 7 )² - 4
Step(ii):-
The general form of the parabola in algebraically
y = a ( x-h)² +k
The equation
y = 4 ( x + 7 )² - 4
y = 4 ( x-(-7))² - 4
The vertex of the parabola (h,k) = (-7 , -4)
Final answer:-
The vertex of the parabola = (-7 , -4)
Related Questions
In a triangle, the sum of the lengths of the
two shorter sides is 13 inches. What do
you know about the length of the third
side?
Answers
Answer:
The length of the third side is less than 13.
Step-by-step explanation:
In any given triangle the sum of any two sides is longer than the length of the third side.
This means that the length of the third side has to be less than 13, since that is the sum of the lengths of the two shorter sides.
Out of 180 students, 50 students play Piano, 68 play Guitar, and 59 play Flute
. Also 35 play Piano and Guitar, 40 play Guitar and Flute and 25 play Piano and Flute. 15
play all, Piano, Guitar and flute.
Draw a Venn diagram to represent this information.
Answers
Answer:
Step-by-step explanation:
A Venn diagram depicts the logical relationships between two or more sets of elements by using alternating circles or other shapes. They're often used to visually arrange information, showing how objects are similar and different. In the fields of mathematics and statistics, Venn diagrams, also known as "set diagrams" or "logic diagrams," are commonly used.
From the given information:
Since we are to represent the given question into a Venn diagram, the diagram is being attached in the image below.
From the image below, we represent:
P =students that played Paino
G = students that played guitar
F = students that played flute
P = 50
G = 68
F = 59
(PUG) -35
(PUF) = 59
(GUF) = 40
since the value of (PUGUF) is not given, we represent it with x.
See the attached image below for diagrammatic representation of the Venn diagram.
The population of China was about 1.39 billion in the year 2013with an annual growth rate of about 0.6\% . Find an equation P(t) that represents the growth function for China. Write your answer in the form a * (b) ^ 2 in billions Provide your answer below:
Answers
Answer: 1.39(1.006)^t
Step-by-step explanation:
The equation P(t) that represents the growth function for China is P(t) = 1.39 * ( 1.006)ⁿ.
What is a Function ?A statement that relates two unknown parameters such that one is dependent on the other is called a function.
It is given that
Initial population = 1.39 billion in 2013
Growth Rate = 0.6%
Let a represent the initial population
b is the growth rate
and 2 be the elapsed year from 2013
and let the population at any given year is P(t)
Then the equation formed is
P(t) = a * bⁿ
P(t) = 1.39 * ( 1.006)ⁿ
Therefore the equation P(t) that represents the growth function for China is P(t) = 1.39 * ( 1.006)ⁿ.
To know more about Function
https://brainly.com/question/21145944
#SPJ2
Cameron runs 2.4 miles 3 days a week. How many miles does he run total in one week?
Answers
Answer:
5.6
Step-by-step explanation:
2.4 / 3 = x / 7
2.4 x 7 = 16.8
16.8 ÷ 3 = 5.6
Which of the following statements are true about the function below? Select all that apply. f(x)=(x-4)^2-1
Answers
Answer:
the zero is at 4 (option 1)
and the minimum is -1 (option 2)
Step-by-step explanation:
the zero is at 4 (option 1)
and the minimum is -1 (option 2)
PLEASE please help me I can't deal with math anymore it's so confusing
Answers
If this is wrong I am sooo sorry it’s been a while since I have done these
PLEASE HELP FAST I WILL GIVE YOU BRAINLIEST
AABC - AQRS
Find the missing side length, n.
R
B.
12.5
5
2
А-
-C
4
10
n = [?]
Enter
Answers
Answer:
5
Step-by-step explanation:
yoy need to find hue multiplying factor, this is done by dividing one of the sides in QRS, by one in ABC. you can divide 10 by 4 to give you 2.5, and then multiply that by 2 to get 5
Shakira has 6 whole dollars, 3 hundredths of a dollar, and 7 tenths of a dollar. How much money does she have? What coins/bills does she have and how many of each? Answer in coins
Answers
Answer:
$6.73
Step-by-step explanation:
Since it says "answer in coins" she could have 24 quarters, 7 dimes, and 3 pennies.
I believe this correct but im not exactly sure
I hope this helps :)
Answer:
$6.73 || 26 quarters, 2 dimes, 3 pennies.
Step-by-step explanation:
If this isn't what you was asking sorry.
I will give the brainlist...plz help me.
Answers
Answer:
0.8,1.4
Step-by-step explanation:
0.8 is the biggest portion of the candy
Analyze the data represented in the graph and select the appropriate model. A) exponential B) linear C) none D) quadratic
Answers
Answer:
exponentialIt couldn’t be liner, liner is straight, the line is wriggly,, quadriceps obv no, so it has to be exponential.
Which equation represents the table of values (help for brainiest and 200+)
Answers
Answer: C)
Step-by-step explanation:
If you subtract .5 to y you get x
Answer:
the answer is B put the point 1 in the equation you will get 0 hence proved
Use an inverse trig function to find the missing angle measure. Round your answer to the nearest tenth (first decimal place)
Answers
Answer:
x° ≈ 51.1°
Step-by-step explanation:
In this geometry, you are given the side opposite the angle, along with the hypotenuse. The relevant trig relation is ...
Sin = Opposite/Hypotenuse
sin(x°) = 14/18
x° = arcsin(14/18) ≈ 51.0576°
x° ≈ 51.1°
Drew has two cats. One cat weighs 17 pounds, and the other one weighs 1212 pounds. Audrey’s dog weighs 33 pounds.
What is the difference in ounces between Audrey’s dog and the combined weights of Drew’s cats?
Enter your answer in the box.
Answers
Answer:
48 ounces.
Step-by-step explanation:
Steps:
Combine the weight of the cats.
12 (assuming it is a typo, 1212 pounds is a pretty big cat!) + 17 = 30 pounds
Convert to ounces.
33 pounds = 528 ounces
30 pounds = 480 ounces
Subtract the two/find the difference.
528 - 480 = 48.
The difference in ounces between Audrey's dog and the combined weights of Drew's cats is 48 ounces.
What is the area of this figure?
6mi
5mi
8mi
square miles
Answers
Answer:
6x5x8=240 square miles ([tex]240^2}[/tex])
Determine the measure of the missing angle in the figure below.
DRAG & DROP THE ANSWER
90
45
75
Missing angle:
Answers
Answer:
Step-by-step explanation:
what are three different whole numbers whose sum and product are equal?
A+B+C=D
AxBxC=D
Answers
Answer:
Answer: The whole numbers for which the products and sum are equal is 1, 2 and 3.
Step-by-step explanation:
Solution: To find the three whole numbers in such a way that their product and sum should be equal. Assume that the three numbers are x, y and z.
a triangle has two sides of lenghts 10 and 14 what value could the length of third side be, check all that apply.
Answers
Answer:
A 5
B 16
E 8
F 10
Step-by-step explanation:
g The pH measurements of water specimens from various locations along a given river basin are Normally distributed, with mean 8 and standard deviation 0.3. You take water specimens from four randomly selected locations on this river basin. What is the probability that the mean pH measurement of these four specimens is greater than 8.2
Answers
Answer:
0.0918 = 9.18% probability that the mean pH measurement of these four specimens is greater than 8.2
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
Mean 8 and standard deviation 0.3.
This means that [tex]\mu = 8, \sigma = 0.3[/tex]
Sample of 4:
This means that [tex]n = 4, s = \frac{0.3}{\sqrt{4}} = 0.15[/tex]
What is the probability that the mean pH measurement of these four specimens is greater than 8.2?
This is 1 subtracted by the pvalue of Z when X = 8.2. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{8.2 - 8}{0.15}[/tex]
[tex]Z = 1.33[/tex]
[tex]Z = 1.33[/tex] has a pvalue of 0.9082
1 - 0.9082 = 0.0918
0.0918 = 9.18% probability that the mean pH measurement of these four specimens is greater than 8.2
Jasmine has $4.90 in quarters, dimes, nickels, and pennies. She has 2 more dimes than
quarters. She has 3 more nickels than quarters. She has 4 more pennies than quarters. How
many quarters does Jasmine have? Note: A quarter is worth $0.25, a dime is worth $0.10, a
nickel is worth $0.05, and a penny is worth $0.01.
Answers
Answer:
11
Step-by-step explanation:
5. At Michael's store, a paint set is on sale for $39.99. The original price was
$66.65. What percent of the original price is the sale price?
PLS HURRY
Answers
around 50%
Step-by-step explanation:
because 30 of half of 60
Answer:
$ 26.66
Step-by-step explanation:
Minus the orignal price and the sale price and then you will get the answer
Drag the uses of computers into the order in which they were developed
Answers
Please help mee (don't send a link)
Answers
Answer:
a
Step-by-step explanation:
the sign flips when you divide or multiply one
Answer:
B.
Step-by-step explanation:
4x-8>(with a line underneath)12
-8 -8
4x>(with a line underneath)12
/4 /4
x>(with a line underneath)3
It stays the same because you aren't dividing or multiplying by a negative. Only a negative will cause you to flip the inequality sign.
In a random sample of 42 Democrats from one city, 10 approved of the mayor's performance. In a random sample of 58 Republicans from the city, 12 approved of the mayor's performance. Find a 90% confidence interval for the difference between the proportions of Democrats and Republicans who approve of the mayor's performance.
Answers
Answer:
The 90% confidence interval for the difference between the proportions of Democrats and Republicans who approve of the mayor's performance is (-0.1078, 0.1702).
Step-by-step explanation:
Before building the confidence interval, we need to understand the central limit theorem and subtraction of normal variables.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
Subtraction of normal variables:
When two normal variables are subtracted, the mean is the subtraction of the means while the standard deviation is the square root of the sum of the variances.
In a random sample of 42 Democrats from one city, 10 approved of the mayor's performance.
This means that:
[tex]p_D = \frac{10}{42} = 0.2381, s_D = \sqrt{\frac{0.2381*(1-0.2381)}{42}} = 0.0657[/tex]
In a random sample of 58 Republicans from the city, 12 approved of the mayor's performance.
This means that:
[tex]p_R = \frac{12}{58} = 0.2069, s_R = \sqrt{\frac{0.2069*(1-0.2069)}{58}} = 0.0532[/tex]
Distribution of the difference:
[tex]p = p_D - p_R = 0.2381 - 0.2069 = 0.0312[/tex]
[tex]s = \sqrt{0.0657^2+0.0532^2} = 0.0845[/tex]
Confidence interval:
We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1 - 0.9}{2} = 0.05[/tex]
Now, we have to find z in the Ztable as such z has a pvalue of [tex]1 - \alpha[/tex].
That is z with a pvalue of [tex]1 - 0.05 = 0.95[/tex], so Z = 1.645.
Now, find the margin of error M as such
[tex]M = zs[/tex]
[tex]M = 1.645*0.0845 = 0.139[/tex]
The lower end of the interval is the sample mean subtracted by M. So it is 0.0312 - 0.139 = -0.1078
The upper end of the interval is the sample mean added to M. So it is 0.0312 + 0.139 = 0.1702
The 90% confidence interval for the difference between the proportions of Democrats and Republicans who approve of the mayor's performance is (-0.1078, 0.1702).
an item is regularly priced at 29. Joe bought it at a discount of 45% off the regular price.
Answers
Answer:
$13.05
Step-by-step explanation:
The prize will be $13.05 after the discount.
29x45%=13.05
OR
29x0.45=13.05
X = {0, 10, 100, 1000}
Y = {100, 1000}
Answers
Answer:
What is The question?
Step-by-step explanation
I will help
Can someone please help me :(
Answers
Answer:
3 ^7
Step-by-step explanation:
7 goes in the box
you could do 5 + 2 and that is 7
Answer:
pretty sure you're supposed to put 7 in the box bc when multiplying numbers with exponents you add the exponents
Step-by-step explanation:
sorry if I'm mistaken
A rectangle has side lengths of (3x+6) inches and (2x-4) inches. Write an expression to represent the perimeter of the rectangle. Then find the value of x if the perimeter is 94 inches.
Answers
2 (3x+6) + 2 (2x+4)=94
6x+12+4x+8=94
10x+20=94
10x=74
X=74/10
X=37/5
What is the slope of the line?
x+ 3y = 10
Answers
Answer:
-1/3
Step-by-step explanation:
Answer:
-1/3
Step-by-step explanation:
Hi,
x + 3y = 10
3y = 10 - x
y = -1/3x + 10/3
Your slope is -1/3
I hope this helps :)
Hi here equation everybody please help thanks
Answers
Answer: 2(3x+1)
Step-by-step explanation:
2(3x+1) ==> 2(3x)+2(1)
6x+2
Answer:
2(3x + 1)
Hope that helps! :)
Step-by-step explanation:
If 4% of a number equals 3, find 8% of that number.
Answers
Answer:
I beleive your answer would be 6
8% of 75 is 6 and 4% of 75 is 3