Use A quadratic function to find two real numbers with a sum of 11 and a product of -42
Answers
9514 1404 393
Answer:
+14, -3
Step-by-step explanation:
If x represents one of the numbers, then the equation can be written as ...
x(11 -x) = -42
x^2 -11x -42 = 0 . . . . quadratic equation whose solutions are the numbers
__
If we are to solve this by factoring, we look for factors of -42 that have a sum of 11 (the original problem). The factorization in integers can be any of ...
-42 = 42(-1) = 21(-2) = 14(-3) = 7(-6)
The sums of these factor pairs are 41, 19, 11, 1. Clearly the numbers we're interested in are 14 and -3.
__
There are ways to solve quadratics that don't involve searching for integer factors by trial and error. A graphical solution is attached. The quadratic formula can also be used.
The solution to ax^2+bx+c = 0 is ...
x = (-b±√(b^2-4ac))/(2a)
Then the solution to our quadratic is ...
x = (-(-11)±√((-11)^2-4(1)(-42)))/(2(1)) = (11±√289)/2 = (11±17)/2
x ∈ {-3, 14}
_____
Additional comment
When the solutions are integers, sometimes the easiest way to find them is to look for the factors of the product that have the correct sum. If the numbers are such that finding factor pairs is difficult or tedious, the more direct approach of graphing or using the quadratic formula may be preferred.
Related Questions
Find f(5) for f(x)=1/4(2)^x
O A. 4
O B. 32
C. 2
O D. 8
Answers
Answer:
D. 8
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
FunctionsFunction NotationStep-by-step explanation:
Step 1: Define
f(x) = 1/4(2)ˣ
f(5) is x = 5 for function f(x)
Step 2: Evaluate
Substitute in x [Function]: f(5) = 1/4(2)⁵Exponents: f(5) = 1/4(32)Multiply: f(5) = 8Can someone please tell me what 597 ➗ 5 is
Answers
Answer:
119.4
Step-by-step explanation:
Big Brain Dude <:
Use the normal distribution and the given sample results to complete the test of the given hypotheses. Assume the results come from a random sample and use a 5% significance level.
Test H0: p = 0.25 vs Ha: p < 0.25 using the sample results p(hat) = 0.15 with n = 102
Round your answer for the test statistic to two decimal places, and your answer for the p-value to three decimal places.
Answers
Answer:
Test statistic = - 2.33
Pvalue = 0.010 (3 decimal places)
Step-by-step explanation:
Given :
H0: p = 0.25 vs Ha: p < 0.25
Phat = 0.15
Sample size, n = 102
α = 0.05
The test statistic :
(Phat - p) / (√p(1 - p) /n)
1 - p = 1 - 0.25 = 0.75
(0.15 - 0.25) / (√0.25(0.75) /102)
-0.1 / √0.0018382
-0.1 / 0.0428742
Test statistic = - 2.33
The Pvalue using the test statistic score obtained :
P(Z < - 2.33) = 0.0099031 = 0.010
Pvalue < α ; Reject H0
In 2002, the manufacturers of M&M's surveyed people from around the world and asked them to vote for a new color: purple, aqua, or pink. In the United States, 42% of those who voted said purple, 37% said aqua, and 19% said pink. What's the probability that a randomly picked survey respondent from the United States preferred purple or pink?
Answers
Answer:
don't know
Step-by-step explanation:
dont know...........
Which expression is equivalent to (see the picture)
A. 20x-21y +14
B. 20x + 11y + 14
C. 20x - 11y + 6
D. 20x + 21y +6
Answers
What is the midpoint of a line segment with endpoints at (2, 3) and (4,5)
Answers
Answer:
(3, 4)
Step-by-step explanation:
First, find the x coordinate of the midpoint by finding the average of the two x values:
(2 + 4) / 2
6 / 2
= 3
Find the y coordinate of the midpoint by finding the average of the two y values:
(3 + 5) / 2
8 / 2
= 4
So, the x coordinate of the midpoint is 3 and the y coordinate is 4.
The midpoint is (3, 4)
500 meters to kilometers
Answers
If f(x) = x and g(x) = vx, what is f(g(x) when x = -3?
Answers
Answer:
f(g(x) = -3v
Step-by-step explanation:
Consider the points plotted on the number line shown below
Answers
Point C is at 2.25 so that’s true
Point A is -1.25 and Point D is 4, so point A is less than point D.
They all look true to me
1 1/4 X 5 3/4 = _________________
Answers
Answer:
7 1/8
Step-by-step explanation:
Hope this helps
Answer: 7.1875
Step-by-step explanation:
First you would multiply the two numbers which are 1 1/4 and 5 3/4 then you would simplify that because you would get 115/16 then when you simplify you get 7.1875
Please help and explain ( Brainliest for answer!)
Answers
Answer:
AD = 3
Step-by-step explanation:
Pythagoras theorem formula: a² + b² = c² (c being the hypotenuse, the longest side of the triangle).
Using this formula, you can easily say that c²-b²=a². c=5, b=4, making the equation 5² - 4² = a ².
Expanding the formula, you'll get 25 - 16 = a².
25 - 16 = 9.
This means that 9 = a².
To find a, you need to root 9. Using a calculator, you'll know that this number is 3, meaning that AD = 3.
A recipe calls for 72 fluid ounces of light whipping cream. If Anthony has 4.5 pints of whipping cream in his refrigerator, does he have enough for the recipe ? PLEASE ANSWER IMMEDIATELY PLEASE
Answers
Answer:
Yes, he has enough
Step-by-step explanation:
1 pint = 16 onces
4.5 * 16 = 72
Yes, he has enough
how many times does 48 go into 123
Answers
Answer:
48 goes into 123 about 2.5625 times.
Step-by-step explanation:
To determine how many times does 48 go into 123, the following mathematical calculation must be performed, by which 123 will be divided by 48 to obtain said number of times:
123/48 = X
2.5625 = X
Therefore, 48 goes into 123 about 2.5625 times.
Which equation of a line is parallel to the graph of y = 3x -5 and passes through the point
(1,5)?
Answers
order the following list of numbers from least to greatest
Answers
Answer:
The answer is D
29/3 = 9.6 (.6 is repeating)
√94 = 9.69
49/5 = 9.8
9.8 (.8 is repeating)
Enter the value of p so that the expression 4 (n+8) is equivalent to (n+p)4
Answers
The triangle represents a scale drawing that was created by using a factor of One-half. A triangle with sides lengths of 5 inches. Which is true of the measures of the sides of the original triangle? Each side of the original triangle is One-half the length of each side of the scale drawing. Each side of the original triangle is 2 times the length of each side of the scale drawing. Each side of the original triangle is the same length as each side of the scale drawing. Each side of the original triangle is 2 inches shorter than the scale drawing.
Answers
Answer:
Step-by-step explanation:
C
Answer:
D (Each side of the original triangle is 2 times the length of each side of the scale drawing.)
Step-by-step explanation:
I did it on Edge 2021.
A runner can run 5 miles in 26 minutes at this rate how many miles can he run and 41.6 minutes?
Answers
Answer:
8 miles
Step-by-step explanation:
Given: A runner can run 5 miles in 26 minutes, 41.6 minutes = ___
To find: At this rate, how many miles can he run and 41.6 minutes?
Solution: If the runner ran 5 miles in 26 minutes, to find how far he ran in 41.6 minutes, set up a fraction:
let x be the variable
[tex]\frac{26}{5} = \frac{41.6}{x}[/tex]
Apply fraction cross multiply;
[tex]26x=5\cdot \:41.6[/tex]
[tex]26x = 208[/tex]
Divide both sides by 26
[tex]\frac{26x}{26}=\frac{208}{26}[/tex]
Simplify
[tex]x = 8[/tex]
Then, at the rate, the runner ran 8 miles 41.6 minutes
41.6 min / 5 miles = 8.32 miles
round off = 8 miles
The runner will run 8 miles total and 41.6 minutes
Which expression is equivalent to
Answers
Answer:
x^6
Step-by-step explanation:
A box contains 3 defective batteries and 7 good ones. You reach in and pull out three
batteries. What is the expected number of defective batteries?
Answers
Answer:
The expected number of defective batteries to be pulled out is 0.9, which rounded to the nearest integer gives a total of 1, that is, 1 of the 3 batteries is expected to be defective.
Step-by-step explanation:
Given that a box contains 3 defective batteries and 7 good ones, and I reach in and pull out three batteries, to determine what is the expected number of defective batteries, the following calculation must be performed:
3 + 7 = 100
3 = X
10 = 100
3 = X
3 x 100/10 = X
300/10 = X
30 = X
3 x 3/10 = X
0.9 = X
Therefore, the expected number of defective batteries to be pulled out is 0.9, which rounded to the nearest integer gives a total of 1, that is, 1 of the 3 batteries is expected to be defective.
Please help what does A equal
Answers
Answer:
a = 23 degrees (brainliest?)
Explanation:
supplementary line is 180 degrees
180 - 157 = 23
If OB = 6 and AB = 8, then EA
Answers
Answer:
what is that means i think it's better to ask by take a picture
Owen follows the rule "divide by 2" to write the pattern below. He will write two
more numbers to complete the pattern. Which statement is true?
Grace
800, 400, 200, 100, 0, 0
Every number in the pattern will have a 0 or a 5 in its ones place.
Every number in the pattern will have a 0 or a 5 in its tens place.
Every number in the pattern will have a 0 in its ones place.
Every number in the pattern will have a 0 in its tens place.
Done -
Answers
Answer:tbh
Step-by-step explanation:
and\
Which equation represents the relationship between x and y?
X y
1 4
2 5
3 6
4 7
Answers
Answer:
0 and 3, right? like look how everything else is set up
Step-by-step explanation:
1 4
2 5
3 6
4 7
they all add one to each number every problem. So subtract 1 from both and that should be your answer.
Help Help Help Help Help Help Help Help!!!!
Answers
Answer:
option c is the correct answer
What’s the answer (no link I give brainly)
Answers
Answer:
the answer is A
Step-by-step explanation:
I had the same question and I got it correct
Please help me with this answer
Answers
9514 1404 393
Answer:
x = 12∠H = 94°Step-by-step explanation:
The marked angles are supplementary, so ...
(5x +26)° +(8x -2)° = 180°
13x = 156 . . . . . . . . . . . . . . divide by °, subtract 24
x = 12 . . . . . . . . . . . divide by 13
∠H = (8x -2)° = (8·12 -2)°
∠H = 94°
Marta walked at 4.7 miles per hour for 0.83 hours. How far did she walk?
Answers
4
The portable basketball hoop shown is made so that BA= AS = AK. The measure of BSK is 76. What is m(angle)AKB?
Answers
Answer:
have you found the answer
An article reports on an experiment in which each of five groups consisting of six rats was put on a diet with a different carbohydrate. At the conclusion of the experiment, the DNA content of the liver of each rat was determined (mg/g liver), with the following results:
Carbohydrate xi.
Starch 2.58
Sucrose 2.63
Fructose 2.13
Glucose 2.41
Maltose 2.49
Assuming also that Σ Σ xij^2 = 185.4, does the data indicate that true average DNA content is affected by the type of carbohydrate in the diet? Construct an ANOVA table and use a 0.05 level of significance.
Answers
Answer:
H0 is rejected, Hence the true average DNA content is affected by the type of carbohydrate in the diet between samples
Step-by-step explanation:
A B C D E
2.58 2.63 2.13 2.41 2.49
∑A=2.58 ∑B=2.63 ∑C=2.13 ∑D=2.41 ∑E=2.49
A² B² C² D² E²
6.6564 6.9169 4.5369 5.8081 6.2001
∑A²=6.6564 ∑B²=6.9169 ∑C²=4.5369 ∑D²=5.8081 ∑E²=6.2001
Calculations
Group A B C D E Total
N n1=1 n2=1 n3=1 n4=1 n5=1 n=5
∑xi T1=2.58 T2=2.63 T3=2.13 T4=2.41 T5=2.49 ∑x=12.24
∑x²i 6.6564 6.9169 4.5369 5.8081 6.2001 ∑x²=30.1184
Mean xi 2.58 2.63 2.13 2.41 2.49 Total2.448
Σ Σ xij^2 = 185.4 given
Let k = the number of different samples = 5
n=n1+n2+n3+n4+n5=1+1+1+1+1=5
Overall ˉx=12.24/5 =2.448
∑x=T1+T2+T3+T4+T5=2.58+2.63+2.13+2.41+2.49=12.24----1
Correction Factor=(∑x)²/n=12.242/5=29.9635--------(2)
∑T²i/ni=(2.582/1+2.632/1+2.132/1+2.412/1+2.492/1)=30.1184------(3)
∑x²=∑x²1+∑x²2+∑x²3+∑x²4+∑x²5
=6.6564+6.9169+4.5369+5.8081+6.2001=30.1184-------(4)
ANOVA:
Step-1 : sum of squares between samples
SSB=(∑T2i/ni)-(∑x)2/n
=(3)-(2)
=30.1184-29.9635
=0.1549
Step-2 : Total sum of squares
SST=SSB-CF
= 185.4-2.488
=182.952
Step-3 : Sum of Squares Within Samples
SSW=∑x²-(∑T²i/ni)=SST- SSB=
= 182.952-0.1549=182.7971
Step-4 : variance between samples
MSB=SSB/k-1
=0.1549/4
=0.0387
Step-5 : variance within samples
MSW=SSW/n-k
=182.7971/5-5
=36.55942
Step-6 : test statistic F for one way ANOVA test
F=MSB/MSW
=0.0387/36.55942 = 0 .001058
ANOVA table
Source Sums Degrees Mean
of Variation of Squares of freedom Squares
SS DF MS F
B/w samples SSB = 0.1549 k-1 = 4 MSB = 0.0387 0.001
Within samples SSW = 0 n-k = 0 MSW = 36.55942
Total SST = 0.1549 n-1 = 4
H0 : The true average DNA content is not affected by the type of carbohydrate in the diet between samples
Ha : The true average DNA content is affected by the type of carbohydrate in the diet between samples
F(4,0) at 0.05 level of significance =0.5
As calculated F=0.001 >0.5
So, H0 is rejected, Hence the true average DNA content is affected by the type of carbohydrate in the diet between samples