What is the intermediate step in the form (x+a)^2=b as a result of completing the square for the following equation? x^2+16x=14x+191
Answers
The given expression is
x^2 + 16x = 14x + 191
The first step is to subtract 14x from both sides of the expression. Thus, we have
x^2 + 16x - 14x = 14x - 14x + 191
x^2 + 2x = 191
To complete the square, we would add the square of half the coefficient of x to both sides of the equation. The coefficient off x is 2. Half of 2 is 1. Thus, we have
x^2 + 2x + 1^2 = 191 + 1^2
(x + 1)^2 = 191 + 1
(x + 1)^2 = 192
Thus, the intermediate step is (x + 1)^2 = 192
Related Questions
Consider the linear function that is represented by the equation y = negative 10 x + 6 and the linear function that is represented by the equation y minus 36 = 8 (x minus 4). Which statement is correct regarding their slopes and y-intercepts?
Answers
Answer: The function that is represented by the equation y = negative 10 x + 6 has a steeper slope and a greater y-intercept.
Step-by-step explanation: I took the unit test on edge hoped this helped <3
We want to compare the slopes and y-intercepts of two given linear functions.
The comparations that we can make are:
The first line has a larger y-intercept.The second line has a larger slope.The general linear function in the slope-intercept is:
y = a*x + b
where a is the slope and b is the y-intercept.
Here, the two given lines are:
y = -10*x + 6
(here we can see that the slope is -10 and the y-intercept is 6).
The other line is:
y - 36 = 8*(x - 4)
Writing this in the slope-intercept form we get:
y = 8*x - 8*4 + 36
y = 8*x - 32 + 36
y = 8*x + 4
Then the slope is 8 and the y-intercept is 4.
Then the comparations that we can make are:
The first line has a larger y-intercept.The second line has a larger slope.If you want to learn more, you can read:
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f(x)=2x-8 and g(x)=1/2x+4
compose the two given functions and simplify
Answers
Composing f(x)=2x-8 and g(x)=1/2x+4 results in the identity function, f(g(x)) = x.
How to compose f(x)=2x-8 and g(x)=1/2x+4To compose the two functions, we substitute g(x) into f(x) in place of x:
f(g(x)) = 2(g(x)) - 8
= 2(1/2x + 4) - 8
= x + 8 - 8
= x
Therefore, composing the two functions results in the identity function, f(g(x)) = x.
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If x = 36 and y = 40 and “x varies directly as y”, then find “x” when y = 80.
Answers
Answer:
x= it will be 76
PLS HELP ASAP
100 points and brainliest for 1st answer
answers for both questions pls
Answers
The gradients are -5 and -0.25
How to determine the gradientsGraph 1
From the question, the points are given as
(0, -5) and (-1, 0)
The gradient of the line is then calculated using the following slope equation
Gradient = (y₂ - y₁)/(x₂ - x₁)
Substitute the known values in the above equation
So, we have the following equation
Gradient = (0 + 5)/(-1 - 0)
Evaluate
Gradient = -5
For the second grah, we have
Gradient = (2 - 1)/(-1 - 3)
Gradient = -0.25
Hence, the slope of the second line is -0.25
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Which of the following shows the numbers in order of least to greatest? 0.9, -1.2, -1.3, 0.8
A. -1.3, -1.2, 0.8, 0.9
B. -1.2, -1.3, 0.8, 0.9
C. 0.8, 0.9, -1.2, -1.3
D. 0.9, 0.8, -1.2, -1.3
Answers
Answer: A
Step-by-step explanation:
Since -1.3 is the least, it comes first in least to greatest. The biggest negative numbers are the least.
Answer:
A. -1.3, -1.2, 0.8, 0.9
Step-by-step explanation:
If you know how the -'s are on the number line then you know that the further left you go the less they are so the further right you go on the number line the greater they get. So thats how i got my answer. Hope it helped you.
-7 = p/4
Please help
Answers
-7(4)=p.
-28=p.
B is a subset of A g Let set A = {a, b, c} and let set B = {b, c, d}
a. True
b. False
Answers
Answer:
False
Step-by-step explanation:
A subset is a set whose elements belong to another set
If B is a subset of A, B would contain elements of A
For example, A = {a, b, c} and if B is a subset of A , B = { a, b}
Based on the scatter plot above, describe the relationship between the moves and the score of the Solitaire game.
Answers
Answer:
The moves and score have an inverse linear relationship. The more moves the person makes, the lower their score. The less moves the person makes, the lower their score.
Step-by-step explanation:
Kiran left his house at time zero and drove to the store, which is 3 blocks away, at a speed of 1 block per minute. Then he stopped and went into the store for 2 minutes. From there, he drove in the same direction at a speed of 1 block per minute until he got to the bank, which is 3 blocks away from the store. He stopped at the bank for 4 minutes. Then he drove home at a speed of 2 blocks every minute. Make a graph of showing the humber of blocks away from home that Kiran is a minutes after he leaves his house, until he gets back home.
Answers
we can see that Kiran is farthest from home (6 blocks away) at time 5, when he reaches the bank. He spends the most time away from home (9 minutes) during his entire journey.
How to make graph?
To make a graph showing Kiran's distance from home over time, we can use the following steps:
Divide the journey into three parts: from home to store, from store to bank, and from bank to home.
Calculate the time taken for each part of the journey based on the distance and speed.
Use a coordinate system to plot Kiran's distance from home on the y-axis and time on the x-axis.
Plot the points corresponding to Kiran's position at different times for each part of the journey.
Connect the dots to form a continuous line.
Let's go through each part of the journey in more detail:
Home to store: Kiran is driving at a speed of 1 block per minute, and the distance is 3 blocks. Therefore, he reaches the store in 3 minutes.
Store to bank: After spending 2 minutes at the store, Kiran continues driving at a speed of 1 block per minute, and the distance is 3 blocks. Therefore, he reaches the bank in 5 minutes.
Bank to home: After spending 4 minutes at the bank, Kiran drives at a speed of 2 blocks per minute, and the distance is 6 blocks. Therefore, he reaches home in 9 minutes.
To plot the graph, we can use a coordinate system where the x-axis represents time in minutes and the y-axis represents Kiran's distance from home in blocks. We can label the points on the graph corresponding to Kiran's position at different times, as follows:
At time zero, Kiran is at home, which is 0 blocks away from home.
At time three, Kiran reaches the store, which is 3 blocks away from home.
At time five, Kiran reaches the bank, which is 6 blocks away from home (3 blocks from the store plus 3 blocks from home).
At time nine, Kiran reaches home again, which is 0 blocks away from home.
To create the graph, we can plot these points and connect them with a line, as shown in the attached image.
Graph showing Kiran's distance from home over time
From the graph, we can see that Kiran is farthest from home (6 blocks away) at time 5, when he reaches the bank. He spends the most time away from home (9 minutes) during his entire journey.
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You have three dice: one red (R), one green (G), and one blue (B).? When all three dice are rolled at the same time, calculate the probability of the following outcomes:! a. 1 (R), 1 (G), 1 (B) _________? b. odd (R), even (G), any number (B) _________ c. 6 or 5 (R), 4 or 3 (G), 1, 2 or 3 (B) _________ ? d. No fives at all_________? e. A different number on each dice_________!
Answers
The probability of rolling 1 (R), 1 (G), 1 (B) is 1/216, odd (R), even (G), any number (B) is 1/36, 6 or 5 (R), 4 or 3 (G), 1, 2 or 3 (B) is 1/18, no fives at all is 125/216, and a different number on each dice is 1/6.
a. The probability of rolling 1 (R), 1 (G), 1 (B) is 1/216. This is because there are 6 faces on each die, and 6 x 6 x 6 = 216 total possible outcomes. Since there is only one way to roll the dice and get 1 (R), 1 (G), 1 (B), the probability of this outcome is 1/216.
b. The probability of rolling odd (R), even (G), any number (B) is (3/6) x (3/6) x (1/6) = 1/36. This is because there are 3 odd numbers on the red die, 3 even numbers on the green die, and 6 numbers on the blue die, thus making the total number of outcomes (3/6) x (3/6) x (6/6) = 1/36.
c. The probability of rolling 6 or 5 (R), 4 or 3 (G), 1, 2 or 3 (B) is (2/6) x (2/6) x (3/6) = 1/18. This is because there are 2 faces with a 6 or 5 on the red die, 2 faces with a 4 or 3 on the green die, and 3 faces with a 1, 2, or 3 on the blue die, thus making the total number of outcomes (2/6) x (2/6) x (3/6) = 1/18.
d. The probability of rolling no fives at all is (5/6) x (5/6) x (5/6) = 125/216. This is because there are 5 faces on each die that do not have a 5, thus making the total number of outcomes (5/6) x (5/6) x (5/6) = 125/216.
e. The probability of rolling a different number on each dice is (6/6) x (5/6) x (4/6) = 1/6. This is because there are 6 different numbers on the red die, 5 different numbers on the green die, and 4 different numbers on the blue die, thus making the total number of outcomes (6/6) x (5/6) x (4/6) = 1/6.
In conclusion, the probability of rolling 1 (R), 1 (G), 1 (B) is 1/216, odd (R), even (G), any number (B) is 1/36, 6 or 5 (R), 4 or 3 (G), 1, 2 or 3 (B) is 1/18, no fives at all is 125/216, and a different number on each dice is 1/6.
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The integrated curriculm mode, sometimes referred to as integrative teaching, is both a method of teaching and a way of organising the teaching programme so that many subject areas and skills provided in the curriculum can be linked to one another. Provide an example of how you, as the teacher, could use the content in Social Sciences as a vehicle for mathematical skills development.
Answers
The teacher can thus use social sciences as a vehicle to develop mathematical skills by facilitating the development of skills such as data interpretation and analysis.
As an instructor, I would use social sciences to develop mathematical skills in the following manner:Consider a social science topic like demography. In this case, a teacher could use mathematics to assist students in interpreting population statistics.
Teachers might guide students to gather information about population size, growth rate, and geographical distribution from various countries and then use statistics to analyze the data.
For example, a teacher could give students graphs or charts to help them understand population growth rates. They can be asked to make comparisons and identify trends.
In this way, students' understanding of the population is improved, as is their mathematical reasoning.Aside from using mathematics to interpret population statistics,
the teacher can also incorporate mathematical skills development in social sciences by using methods that involve understanding and analysis of data. In other words, students learn how to use data to reach conclusions and make decisions.
They learn how to interpret data and how to extract information from it.This method of teaching creates opportunities for the use of the same skills in different contexts and areas of learning.
It enables students to see connections between subjects and fosters an integrated approach to learning.
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People use water to cook, clean, and drink every day. An estimate of 34.6% of the water used each day is for drinking. If a family uses 69.2 gallons of water a day for drinking, how many gallons do they use every day?
Answers
The number of gallons that they use every day will be 200 gallons.
What is the percentage?The amount of any product is given as though it was a proportion of a hundred. The ratio can be expressed as a quarter of 100. The phrase % translates to one hundred percent. It is symbolized by the character '%'.
The percentage is given as,
Percentage (P) = [Final value - Initial value] / Initial value x 100
People use water to cook, clean, and drink every day. An estimated 34.6% of the water used each day is for drinking. If a family uses 69.2 gallons of water a day for drinking.
Then the total amount of water is given as,
⇒ 69.2 / 0.346
⇒ 200 gallons
The number of gallons that they use every day will be 200 gallons.
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Can you please find and solve the unknown variable.
Answers
The value of x is; x = 3.14
Here, we have,
from the given diagram, we get,
there is a right angle triangle.
we have to find the value of x.
we know that,
Let the angle be θ , such that
cos θ = base / hypotenuse
here, we get,
cos 17 = 3/x
so, we have,
0.956 = 3/x
so, x = 3.14
Hence, The value of x is;x = 3.14
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Dhara will be 26 years old when she graduates. If her mean bi-weekly wage over her career is $1,875.00, what will her lifetime earnings be when she retires at the age of 65?
Answers
Dhara's Lifetime earnings when she retires at the age of 65 is; $1,901,250
How to find the lifetime earnings?The first thing we will do here is to find the difference between Dhara's current age and the age he will be when he retires. Thus;
Difference in age = 65 - 26
Difference in age = 39 years old
Bi- weekly wage = 52 weeks/2
Bi- weekly wage = 26 paychecks per annum
Thus;
Lifetime earnings = $1875.00 × 26 paychecks per annum × 39
Lifetime earnings = $1,901,250
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What is the opposite of the number located at point d.
Answers
Answer:
-7
Step-by-step explanation:
The number located at point D is 7, And the opposite of 7 is -7.
what is the surface area for this figure
Answers
The surface area of the triangular prism is 313.47 cm².
Given is a triangular prism, we need to find the surface area,
A triangular prism is a 3D shape with two identical faces in the shape of a triangle connected by three rectangular faces. The rectangular faces are referred to as the lateral faces, while the triangular faces are called bases. The bases are also called the top and the bottom (faces) of the prism.
Triangular Prism Meaning: A triangular prism is a 3D polyhedron with three rectangular faces and two triangular faces. The 2 triangular faces are congruent to each other, and the 3 lateral faces which are in the shape of rectangles are also congruent to each other. Thus, a triangular prism has 5 faces, 9 edges, and 6 vertices. Observe the following image of a triangular prism in which l represents the length of the prism, h represents the height of the base triangle, and b represents the bottom edge of the base triangle.
so, the surface area of a triangular prism =
perimeter × length + 2 × base area
So,
SA = (4.5+7.2+9) × 8.1 + 2 × 8.1 × 9
= 167.67 + 145.8
= 313.47
Hence the surface area of the triangular prism is 313.47 cm².
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A photographer charges a sitting fee of $15, and charges $4 for each 5-in. by 7 in.photograph the customer orders. The linear function c = 15 + 4 n can be used to calculate the customer’s cost (c) based on the number of photographs (n) purchased. Determine the cost of 6 photographs.
a.
$24
b.
$39
c.
$114
d.
$25
Answers
Answer:
I am pretty sure it is C
Answer:
It is B.
Step-by-step explanation:
I got it right on edge.
please help for 100 points and brainlist quickly
Answers
Answer:
1)36.3
2) yards
3)B, D, F
4)Sorry, but I can't see!
5)B.
Btw, I'm just copying my sister's answers, she gave me permission. XD
Have a nice day!
Answer:
1)36.3
2) yards
3)B, D, F
4)Sorry, but I can't see!
5)B.
Gave my sister permission, she's too lazy to answer the questions.
Cindy gave away 12% of her lollipop and is now left with 220 lollipops. Calculate the number of lollipops Cindy had ?
Answers
Answer:
The answer would be 250.
Step-by-step explanation:
Cindy started off with 250 lollipops, gave away 30 (which is 12% of 250) and stayed with 220.
250-30=220
Due in 5 mins!! FIND THE MISSING LENGTHS!!!!!
Answers
Sqrt(169) = 13
So x = 13
c = 1/2 ab^2
Solve for b
Answers
Answer:
b= √2ca /a
Step-by-step explanation:
it was a question on my test yesterday
Find the area of the surface with parametric equations
\(x=u^2, y = uv, z = \frac{1}{2} v^2\\0\leq u\leq 2, 0\leq v\leq 3\)
Answers
This can be rounded to the nearest tenths place, giving us a final answer of V = 4πSin in3, rounded to the nearest tenths place.
What is area?Area is the size of a two-dimensional surface or shape. It is usually measured in square units such as square feet, square meters, or acres. Area can be used in a variety of ways, such as for measuring the size of a garden or calculating the amount of paint needed for a wall. Area can also be used to measure the area of a circle, triangle, or other shapes. Area is an important concept in mathematics, as it is used in a variety of formulas and equations.
The volume of a cylinder is calculated by multiplying the base area with the height. The base area is calculated by multiplying pi (π) with the square of the radius. Therefore, the volume of a cylinder with a height of h and a base radius of r is calculated by the formula V = πr2h. In this case, the height is h = Sin and the base radius is r = 2in. Applying these values to the formula, we get V = π(2in)2(Sin) = 4πSin in3. This can be rounded to the nearest tenths place, giving us a final answer of V = 4πSin in3, rounded to the nearest tenths place.
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This can be rounded to the nearest tenths place, giving us a final answer of V = 4mSin in³,
What is area?
Area is the size of a two-dimensional surface or shape. It is usually measured in square units such as square feet, square meters, or acres. Area can be used in a variety of ways, such as for measuring the size of a garden or calculating the amount of paint needed for a wall. Area can also be used to measure the area of a circle, triangle, or other shapes. Area is an important concept in mathematics, as it is used in a variety of formulas and equations.
The volume of a cylinder is calculated by multiplying the base area with the height. The base area is calculated by multiplying pi (n) with the square of the radius.
Therefore, the volume of a cylinder with a height of h and a base radius of r is calculated by the formula V = mr²h.
In this case, the height is h Sin and the base radius is r = 2in. Applying these values to the formula, we get V = π(2in)²(SinA) = 4πSinA in³.
This can be rounded to the nearest tenths place, giving us a final answer of V = 4mSinA in³, rounded to the nearest tenths place.
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Is this correct?
Answers
Answer:
B
Step-by-step explanation:
Yes.
Providing FI is a straight line, then FGH + HGI = 180. The angles are supplementary.
If one of them is 89 then the other one must be 180 - 89 = 91
B is the correct answer.
a tree nursey planted 72 trees last year. if 2/9 of them were oak trees, what number of trees were oak trees
Answers
Answer:
16 are oak trees
Step-by-step explanation:
2/9 of 72=
16
thus making the answer 16 oak trees
Answer:
Hi there!
Your answer is:
16 of the trees are Oak trees!
Step-by-step explanation:
72÷ 9= 8
8× 2= 16
Check your work!
16× 4 + (16/2) should equal 72!
and it does!
Hope this helps
Based on the plot, approximately how many practice puzzles
per week do members solve if they finish the contest puzzle
in one hour?
a 6
b 10
c 4
d 2
Answers
Based on the plot, the number of practice puzzles per week that members solve if they finish the contest puzzle
in one hour is c 4
How to explain the scatterplotThe line of best fit for the scatter plot shows that there is a positive correlation between the number of practice puzzles solved per week and the time it takes to solve a contest puzzle. This means that as the number of practice puzzles solved per week increases, the time it takes to solve a contest puzzle decreases.
If a member finishes a contest puzzle in one hour, they are on the line of best fit. This means that they solve approximately 4 practice puzzles per week.
The other options are incorrect. Option a is too high, option b is too low, and option d is not on the line of best fit.
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One pound of ground beef costs $3.99. Five pounds of ground beef costs $17.45. How much cheaper is the ground beef per pound if you buy in bulk?(HOW DID YOU GET YOUR ANSWER PLEASE SHOW YOUR WORK. DO NOT BOTHER ANSWERING YOU DO NOT HAVE PROF AND HAVE SHOWN YOUR WORK!!)
A. 48.14
B. 22.36
C. 192
D. 4.15
E. .50
F. 0
G. .251
H. 1.25
I. -135
Answers
Step-by-step explanation:
Ok, so, to find this, remember- to find the true price of an item, remember the equation (PRICE DIVIDED BY QUANTITY), this will give you true price. So, for the individual, its $3.99 for one pound. In bulk, to find the true price, do price divided by quantity. $17.45/5= 3.45. So thats the better deal. Anyways, to find out how much cheaper it is, subtract 3.45 from 3.99. The answer is .54, however, since you need to round to the nearest tenth place, the answer would be .50
Joey opened a bank account 5 years ago with $100.
Today he has $1,000 in the account.
What is the percentage of increase?
_____%
Answers
There are 3 types of PercentProblems.
a) Number compared to the Base is unknown: x/100 = ?/b
b) Base Number is unknown: a/?= x/100
c) Percent is unknown: a/b = ?/100
Solve the following percent problems using the appropriate percent equation. Describe
the steps used to calculate each answer.
1) What distance is 24% of 710 miles?
2) 62 hours is what percent of 3 days?
3) 16% of what number is 8?
Answers
Answer:A. x= .100
Step-by-step explanation:because of the distance in miles
There are 3 feet in a yard. How many yards,
as a mixed number, will you drive until you
reach this exit?
EEXIT ¹,000
FEET
Answers
The number of yards, as a mixed number, will you drive until you reach this exit is 333 1/3 yards
How to determine the number of yards to drive?From the attached figure, we have:
Exit = 1000 feet
From the question, we have
3 feet = 1 yard
So, the number of yards is
Number of yard =Exit/3 yards
This gives
Number of yard = 1000/3 yards
Evaluate the quotient
Number of yard = 333 1/3 yards
Hence, the number of yards, as a mixed number, will you drive until you reach this exit is 333 1/3 yards
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Line DCE is parallel to line AB
a) Find the size of angle ABC
b) Find the size of angle DCA
c) Calculate the size of angle ACB
Answers
Answer:
Angle DCA = Angle CAB. (Alternate Interior Angle)
Angle DCA = 68°
Angles(DCA + ACB + BCE) = 180°. (Linear Pair)
Angle ACB + 68° + 33° = 180°
Angle ACB = 79°
Therefore,
Angle ABC = 33°. (Alternate Interior Angle)