Solve the given equation by completing the square.
x^2 + 8x = 38
Fill in the values of a, b, and cto complete the solutions.
Answers
Answer:
Step-by-step explanation:
[tex]x^2+8x=38\\\\x^2+8x-38=0\\\\\Delta=8^2+4*38=216=6^3\\\\x=\dfrac{-8-6\sqrt{6} }{2} \ or\ x=\dfrac{-8+6\sqrt{6} }{2}\\\\x=-4-3\sqrt{6} \ or\ x=-4+3\sqrt{6}\\\\a=-4\\b=3\\c=6\\[/tex]
Related Questions
Tom makes a bet with his friend Bob. Bob wagers $100, but Tom decides to make him a deal. If Bob wins, Tom will pay him $100. If Tom wins, Bob will instead pay $1 for the first day, then every day for 10 days he must match the total amount paid so far.
For the first day, Bob will pay $1. The second day, he will pay an additional dollar, since he has only paid $1 thus far. The third day he will pay $2, the fourth $4, and so on.
If Bob has a 75% chance to win, which of the following is the closest to the amount of money Tom will make on average with this bet?
Possible Answers:
A. -$25
B. $50
C. $0
D. $25
E. $100
Answers
Answer:
B
Step-by-step explanation:
Find the GCF of 8 and 12. WIll give brainliest for the best and most clear answer. :)
Answers
Answer:
GCF = 4
Step-by-step explanation:
The factors of 8 are: 1, 2, 4, 8
The factors of 12 are: 1, 2, 3, 4, 6, 12
The greatest common factor is 4.
I hope this helps :).
Answer:
4
Step-by-step explanation:
8 = 2 * 2 * 2
12 = 2 * 2 * 3
Since 2 times 2 is common in both the numbers,
Greatest Common Factor = 2 * 2 = 4
[tex]\rule[225]{225}{2}[/tex]
Hope this helped!
~AH1807Peace!a tank is 4÷5 full of water. after drawing off 190 litees of water,it is just 1÷6 full. what is the capacity of the tank
Answers
Hey there! I'm happy to help!
Let's have the capacity be c. The tank is currently at 4/5c. We subtract 190 and then we are at 1/6c. Let's set this up as an equation and solve it.
4/5c-190=1/6c
We want to get the c all by itself to see the capacity of the tank. Let's get all of the c values on the left side of the equation and the numbers on the right by using inverse operations.
4/5c-190=1/6c
Add 190 to both sides.
4/5c=1/6+190
Subtract 1/6 from both sides.
19/30c=190
Divide both sides by 19/30.
c=300
So, the capacity of the tank is 300 liters of water.
Have a wonderful day and keep on learning! :D
6. Teri estimates that it will cost $200,000 to send his daughter to a private college in 16
years. He currently has $125,000 to deposit in an account. What simple interest rate
would
he need so that $125,000 grows info $200,000 in 16 years? Round to the nearest
percent.
How do I solve this?
Answers
The simple interest rate need by Teri will be 4%.
Step-by-step explanation:
Given:
Teri has $125,000 to deposit in his accounts so that he gets $200,000 in 16 years along with the simple interest.
To find:
The simple interest rate needed to grow $125,000 into $200,000 in 16 years.
Solution:
The principle amount Teri has = P = $125,000
The total amount Teri wants to have in 16 years = A = $200,000
The simple interest that will Teri earn = S.I
[tex]S.I= A - P =\$200,000-$125,000=\$ 75,000[/tex]
The rate of interest per year = R
The time for which money is deposited = T = 16 years
The simple interest is calculated by the formula:
[tex]S.I=\frac{P\times R\times T}{100}\\\$75,000=\frac{\$125,000\times R\times 16}{100}\\R=\frac{$75,000\times 100}{$125,000\times 16}=3.75\% \approx 4\%[/tex]
The simple interest rate need by Teri will be 4%.
Learn more about Simple interest here:
https://brainly.com/question/19222840
#learnwithbrainly
Simple interest rate (R) is 3.75%
Given:
Amount deposit as saving (P) = $125,000
Number of year (n) = 16 year
Amount needed (A) = $200,000
Find:
Simple interest rate (R)
Computation:
Amount of interest (I) = A - P
Amount of interest (I) = 200,000 - 125,000
Amount of interest (I) = 75,000
So,
I = (P)(R)(T)
75,000 = (125,000)(R)(16)
75,000 = 2,000,000(R)
R = 75,000 / 2,000,000
R = 0.0375
Simple interest rate (R) = 3.75%
Learn more:
https://brainly.com/question/22004878?referrer=searchResults
geometry #1 please will give brainliest
Answers
Step-by-step explanation:
If two lines, segments, or rays intersect at right angles, then they are perpendicular. If two angles are complementary, then their measures add up to 90 degrees. If two angles' measures add up to 90 degrees, then they are complementary. If two angles are supplementary, then their measures add up to 180 degrees.
Reorder the numbers and combine like terms to simplify. 4.5 + 2 1/2 + 6.0 - 5 1/2
A. 8.5
B. 7.5
C. -7.5
D. 7m
Answers
Answer: B
Step-by-step explanation:
4.5+6=10.5
2 1/2 - 5 1/2 = 2.5 - 5.5 = -3
10.5 - 3 = 7.5
Jade purchased a game controller for $14.65 including tax. How much did she get from a twenty-five dollar bill?
Answers
Answer:
$5.35
Step-by-step explanation:
20-14.65=5.35
So the question is "Write down four common multiples of 2 and 3"
Step by step explaination :(
Answers
Answer:
The common multiples of 2 and 3 are 6,12,18,24
Multiples of 2: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24...
Multiples of 3: 3, 6, 9, 12, 15, 18, 21, 24, 27...
Common multiples of 2 and 3 include 6, 12, 18, and 24.
step by step
6x+1<9-2x
2x-1 less than or equal to 5x+20
3-(2x-7) less than or equal to 34-6x
Answers
Answer:
6x+1<9-2x
6x+2x<9-1
8x<8
x<1
2x-1 ≤ 5x+20
2x-5x≤20+1
-3x≤21
x≥-7
3-(2x-7) ≤ 34-6x
3-2x+7 ≤ 34-6x
-2x+6x ≤ 34-3-7
4x ≤ 24
x ≤ 6
Solve for X: -2x - 4 > 7
(9th grade Algebra 1)
Answers
Answer:
x is less than -6
Step-by-step explanation:
Add 4 to both sides
-2x is greater than 12
Divide both sides by -2 and don't forget to change the sign
x is less than -6
Answer:
x < - 6
Step-by-step explanation:
Given
- 2x - 4 > 8 ( add 4 to both sides )
- 2x > 12
Divide both sides by - 2, reversing the symbol as a result of dividing by a negative quantity.
x < - 6
Please help I will mark brainlyest thank you
Answers
Answer:
3
Step-by-step explanation:
the reason being, is that three is the most repeated number (it is repeated 6 times!)
hope this helps!!
Answer:
The Tables Mode is: 3
Step-by-step explanation:
Mode is the number in a table or set of data that appears most. In this case, there are 6 number 3's, 4 number 6's, and 3 number 0's. But the number with the most is 3. So that is your answer.
Hope this helped! Let me know if you have any questions! :)
A puppy gained 1/2 ounce in weight every day. At this rate, how long did it take the puppy to gain 16 ounces?
Answers
Answer:
It took 32 days into the puppy was 16 ounces
Step-by-step explanation:
i hope this was helpful
Answer:
32 days to gain 16 ounce
Step-by-step explanation:
I. If y = [tex]\frac{1}{2}x[/tex]
when y is total weight, x is day
Perform 16 = 1/2x
16 * 2 = x
x = 32
Can someone plzzz explain.
Why do you only need a single counterexample to show that a conditional statement is false?
Answers
Answer:
For a conditional (if-then) statement, a counterexample must be an instance which satisfies the hypothesis , but not the conclusion .
Step-by-step explanation:
Joey’s brother is 4 years younger than twice his age. If the sum of their ages is 8. How old is Joey?
Answers
1,7,5,3,6,2
J+B=8
J=6
Joey is 6
A plane traveled 1000 miles each way to Albuquerque and back. The trip there was with the wind. It took 10 hours. The trip back was into the wind. The trip back took 20 hours. What is the speed of the plane in still air? What is the speed of the wind?
Answers
100 mph going there, 50 coming back
Write 81 in exponential form
Answers
Answer:
3 exponent 4
Step-by-step explanation:
[tex]\huge\text{Hey there!}[/tex]
[tex]\bullet\rm{\ Exponential\ form \ is \ basically \ a \ number \ that \ is \ expressed \ within \ the \ exponent.}[/tex]
[tex]\star\rm{\ Example: a^b, whereas\ \underline{a} \ is \ the \ \bold{base} \ \& \ \underline{b} \ is \ the \ \bf exponent}[/tex]
[tex]\huge\boxed{\square }\huge\textsf{ Answering your question }\huge\boxed{\square{}}[/tex]
[tex]\large\boxed{= 81}[/tex]
[tex]\large\boxed{= 3 \times3 \times 3 \times3}[/tex]
[tex]\large\boxed{= 9\times9}[/tex]
[tex]\large\boxed{= \bf 3^4}[/tex]
[tex]\huge\boxed{\mathsf{\rm Answer: \mathsf{3^4}}}\huge\checkmark[/tex]
[tex]\large\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
Your college professor tells you he will give you a 30%-30%-40% split on grades between homework, quizzes, and test. However which ever category you have the highest average and will be able to 40% category. What will your final grade be if your homework average of 62, your quiz average is 93, and your test average 60?
Answers
Here we want to calculate percentages of different values to find your final grade, we can conclude that your final grade will be 73.8
We know that:
you have an average of 62 in homework
you have an average of 93 on quiz
you have an average of 60 on test.
Your final grade will be a 30%-30%-40% of the above average scores, such that the 40% will be of the highest average.
We can see that the highest one is on quiz, then your final grade will be:
the 40% of your average quiz grade plus the 30% of your average homework grade plus the 30% of your average test grade.
This will be:
[tex]g = \frac{40 \%}{100 \%}*93 + \frac{30 \%}{100 \%}*62 + \frac{30 \%}{100 \%}*60\\\\g = 0.4*93 + 0.3*62 + 0.3*60 = 73.8[/tex]
We can conclude that your final grade will be 73.8
If you want to learn more, you can read:
https://brainly.com/question/19179977
please help me with this ixl it would be much appreciated
Answers
Answer:
q=2,6
r=8,6
s=8,10
t=2,10
Answer:
Q= (-2, -6)
R= (-8, -6)
S= (-8, -10)
T= (-2, -10)
Step-by-step explanation:
Since the rotation is 180 degrees, change all of the numbers to the opposites/negatives.
Then, since the rotation is counterclockwise, switch all of the x and y values.
I hope this helps!
pls ❤ and mark brainiest pls!
How many solutions does the system have?
8x + 2y = 14
82 + 2y = 4
Answers
you can solve the equestion by many rules , but in my point of view the easiest rule is subtraction/addition and subtition method .
Ans X=11.5
Y = -39
8x+2y=14 eqn.......1
82+2y=4 eqn .......2
2y= -78 (4-82)
y = - 39
putting value of y in eqn ..1
we get,
8x+ 2×(-39) =14
8x= 14+78
8x=92
x = 92÷8
x=11.5
it's a subtition method..
1. The volume of a cube is 27 cubic inches. How long is its side? 3
Answers
If I'm not wrong, it should be 27cm^3. Hope this helps!!
Answer:
3
Step-by-step explanation:
[tex]\sqrt[3]{27}[/tex]
A new cars salesperson, sold an average of $32,130 per day for the first 4 days she worked. The next 5 days she worked, she sold an average of $31,173. How much did she sell on average per day over the entire time she worked??
Answers
Answer:
$31,598.33
Step-by-step explanation:
she worked 4+5=9 days.
due the total average we need the total of sales and divide it by the length of the observation period (9 days).
how much did she sell in total on the first 4 days ?
well, the average times 4 = 32130×4 = $128520
how much did she sell in total during the following 5 days ?
31173×5 = $155865
so, the daily average is
($128520 + $155865) / 9 =$284385 / 9 = $31,598.33
Help ASAP
What are the correct notations for the following number line? (Select all that Apply)
Answers
Answer:
the first, third and fourth options are correct
The function fis defined by f(x) = 5^x. What is the value of f(3)?
O 15
O 25
O 53
O 125
Answers
Answer:
125
Step-by-step explanation:
If the function is f(x) = 5^x and you need to know the value of f(3), you just need to put 3 in place of x:
f(3) = 5^3 = 5•5•5 = 125
Hello! I’ll take any help !!
Answers
Answer:
√73
Step-by-step explanation:
a^2+b^2=c^2
8^2+3^2=c^2
64+9=c^2
√73 =√c^2
√73 =c
can someone answer these 2 questions
Answers
Explanation:
1).
a. f(1) = 2(1)^2 - 3(1) + 1
= 2 - 3 + 1
= 0
b. g(2) = 4(2) - 2
= 8 - 2
= 6
c. f(-3) = 2(-3)^2 - 3(-3) + 1
= 2(9) + 9 + 1
= 28
d. f(-4) = 2(-4)^2 - 3(-4) + 1
= 2(16) + 12 + 1
= 45
2).
When x = -8
y = -3/4x + 2
= -3/4(-8) + 2
= 6 + 2
= 8
When x = -4
y = -3/4(-4) + 2
= 3 + 2
= 5
When x = 0
y = -3/4(0) + 2
= 2
When x = 4
y = -3/4(4) + 2
= -3 + 2
= -1
Which table has a constant of proportionality between y and 2 of 0.3?
Choose 1 answer:
х
y
6
2.
А
12
4
30
10
х
у
3
1.8
B
7
4.2
9
5.4
T
y
4
1.2
с
8
2.4
13
3.9
Answers
Answer:
C
Step-by-step explanation:
y=kx or xy=k are true such that k=0.3
in C, 1.2=4*0.3, 2.4=8*0.3, and 3.9=13*0.3, so C follows this rule
Write an equation that represents the line.
Use exact numbers.
Answers
Answer:
5y=4x+2
Step-by-step explanation:
First the slope, the slope is 4/5. Using the slope intercept form, the line of equation is y-2=(4/5)(x-2), 5y-10=4x-8, 5y=4x+2
5. Mrs. Perkins hosts a birthday party for her son and 7 guests. She orders 2 cookies and a
cupcake for each child. The cost of the cupcake is $2.75, and the total bill is $46.00. What is the
cost of a cookie?
Answers
Answer:
Below.
Step-by-step explanation:
In total there are 8 kids. Each cupcake is 2.75 so 8x2.75= 22 now the total is 46.00 So? 46-22 = 24. 24 divided by 2 = 12.
I Divided by 12 because they said cost of each individual cookie.
Answer:
$1.375
Step-by-step explanation:
7guests + 1son = 8children
8 (children) x 2.75 (dollars-per-cupcake) = 22
46 (total cost) - 22 (dollars spend on cupcakes) = 24
24 (left) / 16 (number of cookies needed (each child gets two)) = 1.375
how do i find the slope
Answers
Hi, I'm happy to help!
To find the slope, you need to use the slope formula, where m is the slope:
m=[tex]\frac{y_{2}-y_{1 } }{x_{2} -x_{1} }[/tex]
Slope means rise over run, or how much the line rises per the amount the line moves forward. This equation shows the movement from the y points to show rise, over the difference in the x points to show run.
Now, to find the slope we insert our values, starting with our second y point:
m=[tex]\frac{2-y_{1 } }{x_{2} -x_{1} }[/tex]
Now insert our first y point:
m=[tex]\frac{2-4 }{x_{2} -x_{1} }[/tex]
Now we insert our second x point:
m=[tex]\frac{2-4 }{-3 -x_{1} }[/tex]
And finally our first x point:
m=[tex]\frac{2-4 }{-3 -3 }[/tex]
Now, we solve:
m=[tex]\frac{-2 }{-6}[/tex]
So, our slope is -2/-6, to simplify it, we remove both negatives because they cancel each other out.
m=[tex]\frac{2 }{6}[/tex]
Now, we simplify our fraction by dividing the top and bottom by 2:
m=[tex]\frac{1}{3}[/tex]
So, our slope is 1/3. This means that for every 1 unit the line rises, it goes to the right 3 units. The y-intercept is where the line hits the y axis.
If the question is asking for slope intercept form for the equation, you use y=mx+b
y represents any y coordinate on your line, m represents your slope (1/3), x represents any x coordinate on your line, and b represents your y-intercept (3).
If you were to insert these values, you would get:
y=[tex]\frac{1}{3}[/tex]x+3
You use this to find what a y coordinate would be so you can draw your line.
For the next equation we do the same thing:
m=[tex]\frac{y_{2}-y_{1 } }{x_{2} -x_{1} }[/tex]
Insert our values:
m=[tex]\frac{4-1}{2-(-4)}[/tex]
Get rid of the double negative:
m=[tex]\frac{4-1}{2+4}[/tex]
Solve:
m=[tex]\frac{3}{6}[/tex]
Simplify:
m=[tex]\frac{1}{2}[/tex]
Now that we know our slope, let's plug it in to our slope intercept form equation.
y=[tex]\frac{1}{2}[/tex]x+3
I hope this was helpful! Keep learning! :D
Hellpp pleaseeeeeeee
Answers
Answer:
4th option
Step-by-step explanation:
The translation shifts Δ ABC → Δ A'B'C'
Consider the x- coordinates of A and A'
A has x- coordinate 1
A' has x- coordinate - 3
Then 1 to - 3 is a shift of 4 units left
Answer:
4 units lefts
Step-by-step explanation:
First you have to take 2 similar points, we will take A' and A and counts the squares between them. Since the dashed A is the new translation, we know the translation is left, all we do now is count the squares which is 4.