Let a and b be the zeroes of x² + kx + 12 such that |a - b| = 1.
By the factor theorem, we can write the quadratic in terms of its zeroes as
x² + kx + 12 = (x - a) (x - b)
Expand the right side and equate the coefficients:
x² + kx + 12 = x² - (a + b) x + ab
Then
a + b = -k
ab = 12
The condition that |a - b| = 1 has two cases, so without loss of generality assume a > b, so that |a - b| = a - b.
Then if a - b = 1, we get b = a - 1. Substitute this into the equations above and solve for k :
a + (a - 1) = -k → 2a = 1 - k → a = (1 - k)/2
a (a - 1) = 12 → (1 - k)/2 • ((1 - k)/2 - 1) = 12
→ (1 - k)²/4 - (1 - k)/2 = 12
→ (1 - k)² - 2 (1 - k) = 48
→ (1 - 2k + k²) - 2 (1 - k) = 48
→ k² - 1 = 48
→ k² = 49
→ k = ± √(49) = ±7
what is the x-coordinate of R' ?
Answer:
3
Step-by-step explanation:
Answer:
12
The x-axis is the horizontal one. The full coordinate is (12, 0), which the x-coordinate (or x-intercept) is 12.
Whoever helps gets BRAINLIEST
The answer D. 275
Hope this helps :)
Whats The Answer Marking Brainliest, Please explain your answer:D...
.
Answer:
C. 12x
Each box has 12 envelopes.
The number of total envelopes will be the number of envelopes in a box multiplied by the number of boxes. The number of boxes is unknown, so it is replaced by the variable. This gives us 12x
In a basketball tournament, team A scored 6 more points than 3 times as many points as team B scored. Team C scored 45 more points than team B scored. The combined scores for all three teams was 476 points. Which statement about the number of points is true? Team A scored 85 points. Team A scored 255 points. Team C scored 261 points. Team C scored 130 points.
Answer:
"Team C scored 130 points."
Step-by-step explanation:
Let x represent how many points team B scored.
Team A: 3x + 6
Team B: x
Team C: x + 45
Total: 476 points
476 = (x) + (3x + 6) + (x + 45)
476 = x + 3x + 6 + x + 45
476 = 5x + 51
425 = 5x
x = 85
Team A:
3(85) + 6
= 261 pts
Team B:
= 85 pts
Team C:
(85) + 45
= 130 points
Answer:
Team c 130
Step-by-step explanation:
The lunch special at a diner offers you a choice of 5 sandwiches, 2 salads, 3 soups, 6 drinks, and 2 desserts. How many different meals are possible if you choose one item from each category?
Answer:
360
Step-by-step explanation:
there are 360 different meal combos possible if you choose 1 of each because 5×2×3×6×2 is 360
A plane travels 3,625.26 miles in 6.9 hours. What is the plane’s unit rate?
Represent this situation with a fraction.
a. Represent this situation using the same units.
b. Estimate the quotient.
c. Express the divisor as a whole number.
d. Use the division algorithm to find the quotient.
e. Use multiplication to check your work
Answer:
The correct answers are:
a) 3625.26 miles OVER 6.9 miles
b) 36252.6 tenths miles÷ 69 tenths hours
c) 3500 miles over 7 hours = 500 miles over hours
d) 3625.26 miles 10 over 6.9 hours 10 = 36252.6 miles over 69 hours
e) 525.4 miles/h
Step-by-step explanation:
Brainliest please?
Let r = unit rate of the plane
r = (3,625.26 miles)/(6.9 hours)
You now have the correct fraction set up to answer a through e.
Take it from here.
1. 6x+4x−1=2(5x+4)
2. 48x+43=47x+43
3. 2(3x+8)=2x+16+4x
4. 0.4(5x−15)=2.5(x+3)
5. 3(4x+2)=20x−9x+2
Answer:
1 . -9 = 0
2 . x = 0
3 . 0 = 0
4 .x = -27
5 . x = -4
Step-by-step explanation:
At an end- of-season sale, a kid's pool was on sale for $168 . A sign advertised that this was 20% off the original price. What was the original price?
Answer: $134.40
Step-by-step explanation: Just find 80% of 168. That is because 100 - 20 is 80. The question says 20% OFF.
Ms. D's 4th period geometry class has both freshman and sophomores. There are 27 kids in the class and it has twice as many freshman as sophomores. How many freshman are in the class?
let x=
let y=
What is the answer??
Answer:
letter C is the right answer
2. Use the distributive property to evaluate the expression.
A) 4(x-2)
B) 3(y+9)
C) -2(3-r)
Answer:
a) 4x-8
b) 3y + 27
c) -6 + 2r
Step-by-step explanation:
Here, we want to use the distributive property to evaluate the given expressions
Mathematically, the distributive property is;
(a + b) * c = (a * c) + (b * c)
So we use this on each of our questions;
a) 4(x-2)
= (4 * x) - (4 * 2) = 4x-8
b) 3(y + 9)
= (3 * y) + (3 * 9)
= 3y + 27
c) -2(3-r)
= (-2 * 3) - (-2 * r)
= -6 + 2r
Mass = 10 g
Density = Mass/volume
Volume of a cube = (side length)3
Now that you have the side length, determine the volume. Then use the density formula to calculate the density of the material. Record your observations by selecting the data table icon.
You may use a calculator for this section.
Measurement1.7 cm
FIRST ANSWER GETS BRAINLIEST
Answer:Hello! Here we have a cube, with a mass of 10g and a side length of 2.5cm.
First we want to determine the volume.
The volume of a cube, is equal to his cubic side length, where L is the side length:
So
So the volume of the cube is 15.625 cubic centimeters.
Now we want to calculate te density of the material, as you know:
This means that the density is 0.64 grams per cubic centimeter.
Step-by-step explanation:
Answer:
2
Step-by-step explanation:
1. Determine the value: V=L^3
so, (1.7)^3= 4.913
2. Calculate the density: mass divided by volume
10 divided by 4.913= 2.0
Answer: 2
Solve: |11x + 10| = 22
To solve the equation |11x + 10| = 22, we need to consider two cases: one where the expression inside the absolute value is positive and one where it is negative.
Case 1: (11x + 10) is positive:
In this case, the equation becomes 11x + 10 = 22. Solving for x, we subtract 10 from both sides, resulting in 11x = 12. Dividing by 11 gives x = 12/11.
Case 2: (11x + 10) is negative:
Here, the equation becomes -(11x + 10) = 22. Simplifying, we have -11x - 10 = 22. Adding 10 to both sides gives -11x = 32. Dividing by -11 yields x = -32/11.
Thus, the solution set for the given equation is x = 12/11 and x = -32/11, representing the two possible values of x that satisfy the equation |11x + 10| = 22.
For more such questions on equation
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solve 2x^2+9x-7=0
Give your solutions correct to 3 significant figures.
Answer:
X = -1 or X = -3.5
Step-by-step explanation:
2x^2 + 9x + 7 = 0
ac = 14
b = 9
find a two numbers which when you multiply you get 14 and add you get 9.
so it will 2 and 7. (they replace b which is 9x)
therefore: 2x^2 + 2x + 7x + 7 = 0
find common factors using each 2 from the four.
2x( x + 1) + 7 (x+1) = 0
so it will be (2x + 7) (x+1) = 0
find x,
i) 2x +7 = 0
x= -3.5
ii) x + 1 = 0
x = -1
pls help 7th grade math. what is the value of (-4)^2+6÷(3+4)(2)-5?
A Disney world
B the legend of zelda breath of the wild
C Christmas tree
D ELMER'S glue
Answer:
a carrot
Step-by-step explanation:
(-4)^2+6÷(3+4)(2)-5? x 2 +1(2) x 8 equals carrot
Answer:
Mario odyssey
Step-by-step explanation:
The clock below shows what time mason mom drops him off for practice . what time did mason mom drop him off
Answer:
where is the clock?
Step-by-step explanation:
I WILL GIVE BRAINLIEST TO WHOEVER ANSWERS FIRST!!!
Choose one of the following.
Parallel lines have ____________________.
A. one solution
B. 10 solutions
C. infinitely many solutions
D. no solution
D. no solution
Because they never found each other, the point they cross on is the solution.
Answer: D
Step-by-step explanation: it just is
Eva paid $16 for some notebooks and a backpack . She paid $1.25 for 5 notebooks.how much did she pay for her backpack ?write the equation
Answer:
10 dollars ALSO CAN SOMEONE PLEASE ANSWER MY QUESTION
Step-by-step explanation:
1.25 times 5=6
16-6=10
Answer:
$9.75
Step-by-step explanation:
Notebooks - $1.25 each
Number of notebooks bought - 5
Total money spent - $16
5 * 1.25 = 6.25
16 - 6.25 = 9.75
$9.75
Mrs. stone is three times older than her younger daughter, Joyce, but only two times older than her older daughter, Alex. how old is Mrs. stone now, if 9 years ago Alex was two times older than Joyce?
Answer:
54
Step-by-step explanation:
RSM homework lol
made equation, then solved it.
hope this helps!
Write and solve an equation for seven less than fou
times a number is 29.
help> ?????? pleaes asdfdfffffffff
Answer:
37.9701
Step-by-step explanation:
I only know the first one?? I'm really sorry cacsknak ik i said id help, but :( it's hard, and i never learned how to do the bottom two.
The longest leg of a right triangle is 12 inches. The hypotenuse is 3 inches longer then twice the shortest leg. How long is the shortest leg and the hypotenuse of the triangle.
Answer:
Shortest Leg: 5 inches, Hypotenuse: 13 inches
Step-by-step explanation:
A right triangle follows the pythagorean theorem, a^2+b^2=c^2. C is the hypotenus. A combination found using this is 5, 12, and 13. To double check this, we know that the hypotenus is 2x+3, where x is the smallest leg.
John has $190 in his savings account. He earns 10% in interest per year.
What will John’s saving account balance be at the end of the year?
Answer:
1,900
Step-by-step explanation:
Determine the quadrant point
Answer:
I think b
Step-by-step explanation:
Determine the intercepts of the line
Answer:
Step-by-step explanation:
y-intercept: (0 , 2.5)
x-intercept: (3.5 , 0)
8x – 12y = 48
Find the x-intercept and y-intercept
Answer:
my answer came out to x = 6 + 1.5y
Step-by-step explanation:
Which of the following values does not satisfy the inequality X - 7 > 12?
A 11
B 33
C 22
D 44
Answer:
We conclude that when we put x = 11, it does not satisfy the inequality.
Hence, option (A) is correct.
Step-by-step explanation:
Given the inequality
x - 7 > 12
Any value which makes the inequality FALSE would be the value that not satisfy the inequality.
Putting x = 11 in the inequality
x - 7 > 12
11 - 7 > 12
4 > 12
FALSE!
Reason: 4 can not be greater than 12
Putting x = 33 in the inequality
x - 7 > 12
33 - 7 > 12
26 > 12
TRUE!
Reason: 26 is indeed greater than 12
Putting x = 22 in the inequality
x - 7 > 12
22 - 7 > 12
15 > 12
TRUE!
Reason: 15 is indeed greater than 12
Putting x = 44 in the inequality
x - 7 > 12
44 - 7 > 12
37 > 12
TRUE!
Reason: 37 is indeed greater than 12
Therefore, we conclude that when we put x = 11, it does not satisfy the inequality.
Hence, option (A) is correct.
Answer:
11
Step-by-step explanation:
On Wednesday mornings, admission to the park swimming pool is $3.00 per adult and $2.00 per child. Which expression can be used to find the cost of admission to the pool for a group of adults (a) and children (c)?
A. 3ac
B.5+ac
C. 3a+2c
D. 2(3)+ac
WILL GIVE BRAINLIEST I NEED THIS FAST
Answer:
C.) 3a + 2c
Step-by-step explanation:
$3 per adult (a)
$3(a)
+
$2 per child (c)
$2(c)
Answer:
C. 3a+2c
Step-by-step explanation:
It is 3 $ for a adult hence the 3a and 2$ for a child hence 2c
solve each system of equation by elimination
{y=-x+1
{y= 4x-14
Answer:
(3, -2)
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightEquality Properties
Algebra I
Solving systems of equations using substitution/eliminationStep-by-step explanation:
Step 1: Define Systems
y = -x + 1
y = 4x - 14
Step 2: Rewrite Systems
y = 4x - 14
Multiply everything by -1: -y = -4x + 14Step 3: Redefine Systems
y = -x + 1
-y = -4x + 14
Step 4: Solve for x
Elimination
Combine equations: 0 = -5x + 15Isolate x term: -15 = -5xIsolate x: 3 = xRewrite: x = 3Step 5: Check
Define equation: y = -x + 1Substitute in x: y = -3 + 1Add: y = -2Evaluate the expression below
if a = -8, b = 17, and c = 21
a2 –(b+c)
Answer:
-54
Step-by-step explanation:
first fill in the numbers
next do the parentheses 17 + 21=38
then find -8×2 which equals -16
then subtract -16 from 38 and get -54
The value of the expression a² - (b + c) at a = -8, b = 17, and c = 21 will be 26.
What is the value of the expression?When the relevant factors and natural laws of a mathematical model are given values, the outcome of the calculation it describes is the expression's outcome.
Making anything easier to accomplish or comprehend, as well as making it less difficult, is the definition of simplification.
The expression is given below.
⇒ a² - (b + c)
The value of the expression at a = -8, b = 17, and c = 21 will be
⇒ a² - (b + c)
⇒ (-8)² - (17 + 21)
⇒ 64 - 38
⇒ 26
The value of the expression a² - (b + c) at a = -8, b = 17, and c = 21 will be 26.
More about the value of expression link is given below.
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