Answers
1. The solution to the quadratic equation, x² - 14x + 49 = 40, is x = 13.32 and x = 0.68
2. The solution to the quadratic equation, x² - x = 12, is x = -3 and x = 4
3. i. The factors of 2x² - 15x - 8 = 0 are (2x +1) and (x - 8)
ii. The x-intercepts of 2x² - 15x - 8 = 0 are x = -1/2 and x = 8
Solving Quadratic equationsFrom the question, we are to solve the given quadratic equation by completing the square.
The given equation is
x² - 14x + 49 = 40
Solving the equation
x² - 14x + 49 = 40
x² - 14x = 40 - 49
x² - 14x = -9
Multiply the coefficient of x by 1/2 square and add to both sides
x² - 14x + (-7)² = -9 + (-7)²
(x - 7)² = -9 + 49
(x - 7)² = 40
x - 7 = ±√40
x = 7 ± √40
x = 7 ± 6.32
x = 7 + 6.32 OR 7 - 6.32
x = 13.32 OR 0.68
Solving x² - x = 12 by factoring
x² - x = 12
x² - x - 12 = 0
x² -4x + 3x - 12 = 0
x(x - 4) + 3(x - 4) = 0
(x + 3)(x - 4) = 0
x + 3 = 0 OR x - 4 = 0
x = -3 OR x = 4
Determining the factors of 2x² - 15x - 8 = 0
2x² - 15x - 8 = 0
2x² - 16x + x - 8 = 0
2x(x - 8) + 1(x - 8) = 0
(2x + 1)(x - 8) = 0
The factors are (2x +1) and (x - 8)
Determining the x-intercepts
(2x + 1)(x - 8) = 0
2x + 1 = 0 and x - 8 = 0
2x = -1 and x = 8
x = -1/2 and x = 8
Hence, the x-intercepts are -1/2 and 8
Learn more on Solving Quadratic equations here: https://brainly.com/question/19614080
#SPJ1
Related Questions
Scores on a statistics final in a large class were normally distributed with a mean of 79 and a standard deviation of 12. Use the TI-84 PLUS calculator to answer the following. Round the answers to at least two decimals. (a) Find the 36th percentile of the scores. (b) Find the 70th percentile of the scores. (c) The instructor wants to give an A to the students whose scores were in the top 12% of the class. What is the minimum score needed to get an A
Answers
Answer:
a) The 36th percentile of the scores is of 74.68.
b) The 70th percentile of scores is 85.3.
c) The minimum score needed to get an A is 93.1.
Step-by-step explanation:
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.
Mean of 79 and a standard deviation of 12.
This means that [tex]\mu = 79, \sigma = 12[/tex]
(a) Find the 36th percentile of the scores.
This is X when Z has a pvalue of 0.36. So X when Z = -0.36.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]-0.36 = \frac{X - 79}{12}[/tex]
[tex]X - 79 = -0.36*12[/tex]
[tex]X = 74.68[/tex]
The 36th percentile of the scores is of 74.68.
(b) Find the 70th percentile of the scores.
This is X when Z has a pvalue of 0.7, so X when Z = 0.525.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]0.525 = \frac{X - 79}{12}[/tex]
[tex]X - 79 = 0.525*12[/tex]
[tex]X = 85.3[/tex]
The 70th percentile of scores is 85.3.
(c) The instructor wants to give an A to the students whose scores were in the top 12% of the class. What is the minimum score needed to get an A?
The 100 - 12 = 88th percentile, which is X when Z has a pvalue of 0.88, so X when Z = 1.175.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]1.175 = \frac{X - 79}{12}[/tex]
[tex]X - 79 = 1.175*12[/tex]
[tex]X = 93.1[/tex]
The minimum score needed to get an A is 93.1.
Please help I need this due in 3 minutes!
Answers
Answer: you just add 700 and 750 which will give us 1,450
Step-by-step explanation:
write an expression based on description; use grouping symbols
1:The sum of 11 and n decreased by 9
2:The product of y less than 16 and 5
Answers
Answer:
it's your answer and make me barinly least
How do you refer 2ml of blue and 6ml of green in batches
Answers
Answer:
8ml
Step-by-step explanation:
Zane is putting the strings on 5 harps. Each harp has 48 strings.
How many strings does Zane need for all 5 harps?
Answers
Answer:
Zane needs 240 strings for 5 harps.
Step-by-step explanation:
All you have to do is multiply
48 * 5 = 240
So, the answer is 240
Hope this helps! :)
what is the probability if you randomly select comedy book replace it and another comedy book?
(if your going to answer pls explain )
Answers
Jake tossed a paper cup 50 times and recorded how it landed. The table shows the results:
Position Open Side Up Closed Side Up Landing on Side
Number of Times Landed in Position 3 7 40
Based on the table, determine the experimental probability of each outcome (landing open side up, landing closed side up, and landing on its side). Show your work. (10 points)
TIMED PLS HELP ME IM BEGGING
Answers
Answer:
4 cm
Step-by-step explanation:
Cylinder Volume formula:
V = πr²h
Given:
V = 240π
h = 15
Finding r:
V = πr²h
240π = πr²(15)
r² = 240π/15π
r² = 16
[tex]\sqrt{r^2} =\sqrt{16}[/tex]
r = 4
Answer:
4 cm
Step-by-step explanation:
TTr^2h = 240TTcm^3(the TT cancel out)r^2 x 15 = 240cm^3(divide both sides by 15)r^2 = 16(square root both sides)r = 4cmCould someone explain to me how to solve any one of these problems so that I could solve the rest of them on my own? I already know the asymptote and the y-intercept, but I'm unsure of how to find the maximum/minimum.
Answers
Answer:
what in the world is this
Answer: Maybe asymptote means the lowest number and y-intercept means the second lowest and minimum means medium and maximum means the highest number.
I'm sorry if this doesn't help but i'm still in 3rd grade.
help! help! please help
Answers
Answer:
to answer this i am gonna need the rise and run or the y2 -x2/ y1-x1 and then i well come back and edit this to the right answer
Step-by-step explanation:
Which statement best explains whether △ABC is similar to △DEF?
A) The triangles are not similar because 613≠820.
B) The triangles are similar because 613=820.
C) The triangles are similar because 820=1025.
D) There is not enough information to determine whether the triangles are similar.
Answers
A). They are not similar, because 6/13 is not equal to 8/20
For triangles to be similar, the ratios of sides need to be the same (shortest to shortest, middle to middle, longest to longest). The shortest sides are 6 and 13, respectively, the middle ones are 8 and 20. Because 6/13 is not equal to 8/20, the triangles are not similar.
The statement best explains whether △ABC is similar to △DEF is (A) The triangles are not similar because 613≠820.
What are similar triangles?Similar triangles are triangles that have similar corresponding side lengths
The corresponding sides of the triangles are:
Triangle A Triangle B
6 13
8 20
10 25
Calculate the ratios
Ratio = 6/13
Ratio = 8/20
The ratios are not equal.
Hence, the triangles are not similar
Read more about similar triangles at:
https://brainly.com/question/14285697
f(x) = 3x – 5
g(x) = –6x2 + 6x + 2
Find: f(x) · g(x)
Answers
Answer:
f(x) = 3x - 5
g(x) = 6x^2 + 2x
Find: g(f(x))
method: for each x in g, substitute (3x-5)
g[f(x)]=6(3x-5)^2+2(3x-5)
=6(9x^2-30x+25)+6x-10
=54x^2-180x+150+6x-10
Step-by-step explanation:
A parent believes the average height for 13-year-old girls differs from that of 13-year-old boys. The difference in the height between girls and boys using a 95% confidence interval is estimated to be 0.26 to 0.41 inches. Based on the results, is there a significant difference between the true mean height of 13-year-old girls and boys
Answers
Answer:
There is 0.15 difference so yes
Step-by-step explanation:
Help fast i will make you the brainly thing if you get it right Which situation can be represented by the expression 3+(-7).
Choose 1 answer:
A Afootball team lost 3 yards on one play. The team gained 7 yards on the next play.
B
A football team gained 3 yards on one play. The team lost 7 yards on the next play.
A football team gained 3 yards on one play. The team gained 7 yards on the next play.
Answers
Answer:
I think it's B
Step-by-step explanation:
3 + (-7)
= 3 - 7
it's 3 - 7 because the positive and negative cancel each other out. A good example to think of intergers is with money, ex: If I borrow $7 from you and the next day I pay back $3, how much money do I still owe you?
(I'm not 100% sure)
What is the median for the data set below? 2 10 6.5 8.8 3 6 4.0 12.5
Answers
Answer:
Hi! The answer to your question is 6.25
Step-by-step explanation:
☆*: .｡..｡.:*☆☆*: .｡..｡.:*☆☆*: .｡..｡.:*☆☆*: .｡..｡.:*☆
☆Brainliest is greatly appreciated!☆
Hope this helps!!
- Brooklynn Deka
one of your friends is heading north for a holiday and the oter friend is heading south. if their destinies are 1029 miles apart and one car is traveling at 45 miles per hour and the other at 58 mile sper hour how many hours before the 2 cars pass eacother
Answers
Answer: 1029 + 45 + 58 + 2 = 1134
Step-by-step explanation: If you read the problem it has a key word how many so all you have to do is add.
The ring Zp^3 has exactly____maximal ideals
Answers
A dice is rolled 50 times.
The score of each throw is recorded in the table below.
Score
1
2
3
4
5
6
Frequency
12
9
5
13
3
8
12
a) The relative frequency of scoring a 1 was calculated as = 0.24
50
Work out the relative frequency, as a decimal, of throwing a 2.
I
[1]
b) How many times would you expect to roll a 5 when
this dice is thrown 3000 times?
[2]
c) How many times would you expect to roll a 5 when
a fair dice is thrown 3000 times?
+
[2]
Answers
Solve for x to the nearest degree.
Answers
Answer: 22 degrees
Step-by-step explanation:
[tex]sin^{-1}[/tex]([tex]\frac{7}{19}[/tex])= 21.62 nearest degree= 22
In the image below the area of the shaded sector is
Answers
Answer:
area = 471 ft²
Step-by-step explanation:
area of full circle = π30² = 2826 ft²
(60°/360°)(2826) = 471 ft²
k is decreased by 20
Answers
decreased means to take away/subtract, “k” is being subtracted by 20, therefore k-20
Hope this helps! have a wonderful day!
If you put two straight angles together, you get an angle that is 360°. You can think of this
angle as turning all the way around so that you are facing the same direction as when you
started the turn.
380
Answers
Answer:
what is your question?
Step-by-step explanation:
Helppppp !!! Quick I’ll mark u brainlist
Answers
Answer:
it is b approximately 163 yards
Calculate the slope of a line that goes through points (3, 4) and (0, 0).
Question 5 options:
3/4
3
4
4/3
Answers
Answer:
4/3
Step-by-step explanation:
0-4/0-3
-4/0-3
-4/-3
4/3
Answer:
Step-by-step explanation:
3\4
can someone please help me i’ll give you brainliest
Answers
Answer:
1/9
Step-by-step explanation:
Answer:
C. 1/9
Step-by-step explanation:
What is the surface area of this rectangular prism i-ready
Answers
Answer:
290 in²
Step-by-step explanation:
Using the net of the box given, we can see that there are 4 equal rectangles and 2 equal squares that make up the prism.
Area of the 4 rectangles = 4(60) = 240 in²
Area of the 2 squares = 2(25) = 50 in²
Therefore,
Surface Area of the prism = 240 + 50 = 290 in²
Answer:
The surface area of this prism is 290(in)²
Step-by-step explanation:
The surface area of a box is equal to the sum of the areas of each side of the box.
[tex]2 \times (lenght) \times (widht) + 2 \times (lenght) \times (height) + 2 \times (widht) \times (height)[/tex]
Substitute the values of the length l=5, the width w=5, and the height h=12 into the formula.
[tex]2 \times 5 \times 5 + 2 \times 5 \times 12 + 2 \times 5 \times 12[/tex]
Simplify each term.
[tex]50 + 120 + 120[/tex]
Simplify by adding numbers.
[tex]290(in)^{2} [/tex]
Hence, The surface area of this rectangular prism is 290in².
Discuss the various factors which lead to the formation of droughts
Answers
Step-by-step explanation:
Below average rainfall in a region for several months
Not enough rain to be absorbed into the ground before evaporating
Cutting down trees and overuse of land
Hot dry air masses blown into a region by westerly winds
Human activities that deplete the water table faster than it can be replaced
Rewrite 24 + 48 using GCF and the distributive property.
a: 12(3+1)
b: 24(1+2)
c: 3(12+6)
d: 5(2+3)
Answers
solve -5 √x =-15
A. X= -9
B. X= -7
C. X= 9
D. X= 7
Answers
You would then get (square root)x=3 since the negatives would cancel out
Then you square both sides
You will be left with (x)*2=(3)*2
Your answer will be C. X=9
Hope that helped!
The answer is C
solve for x:
(1/x) + (1/2x) = 18
Answers
Answer:
/sorry/
Step-by-step explanation:
How to solve your problem
(1)+(12⋅)=18
\frac{x}{(\frac{1}{x})}+(\frac{1}{2} \cdot x)=18
(x1)x+(21⋅x)=18
Solve
1
Combine multiplied terms into a single fraction
(1)+(12)=18
\frac{x}{(\frac{1}{x})}+(\frac{1}{2}x)=18
(x1)x+(21x)=18
(1)+(12)=18
\frac{x}{(\frac{1}{x})}+(\frac{1x}{2})=18
(x1)x+(21x)=18
2
Multiply by 1
3
Eliminate redundant parentheses
Solution
(1)+2=18
Help if you can please
Answers
Answer:
10 coconut cupcakes
Step-by-step explanation: so, here is what we do since there is 8 cupcakes sold and 4 of them are coconut cupcakes we divide. this is hard to explain but we know that 8 divided by 4 is 2 so we have to multiply to 20 so like 2 times 10 which gives us 20. then we use the answer that we got from multiplying which is 10 as our answer if that makes sense.