Given:
The given quadratic polynomial is :
[tex]x^2-x-12[/tex]
To find:
The quadratic polynomial whose zeroes are negatives of the zeroes of the given polynomial.
Solution:
We have,
[tex]x^2-x-12[/tex]
Equate the polynomial with 0 to find the zeroes.
[tex]x^2-x-12=0[/tex]
Splitting the middle term, we get
[tex]x^2-4x+3x-12=0[/tex]
[tex]x(x-4)+3(x-4)=0[/tex]
[tex](x+3)(x-4)=0[/tex]
[tex]x=-3,4[/tex]
The zeroes of the given polynomial are -3 and 4.
The zeroes of a quadratic polynomial are negatives of the zeroes of the given polynomial. So, the zeroes of the required polynomial are 3 and -4.
A quadratic polynomial is defined as:
[tex]x^2-(\text{Sum of zeroes})x+\text{Product of zeroes}[/tex]
[tex]x^2-(3+(-4))x+(3)(-4)[/tex]
[tex]x^2-(-1)x+(-12)[/tex]
[tex]x^2+x-12[/tex]
Therefore, the required polynomial is [tex]x^2+x-12[/tex].
Seven gallons of a sugar solution was mixed with 4 gallons of a 80 percent sugar solution to make an 72 percent sugar solution. Find the percent concentration of the first solution. (a) 70% (b) 61% (c) 69% (d) 67%
Answer:
67%
Step-by-step explanation:
Let the percentage of the first solution = x
7 gallons + 4 gallons = 11 gallons
Our system of equation is
Seven gallons of a sugar solution was mixed with 4 gallons of a 80 percent sugar solution to make an 72 percent sugar solution.
7 gallons × x % + 4 gallons × 80% = 72% × 11 gallons
= 7x + 3.2 = 7.92
Collect like terms
7x = 7.92 - 3.2
7x = 4.72
x = 4.72/7
x = 0.6742857143
Converting to percentage
0.6742857143 × 100
= 67.42857143%
Approximately, the percent concentration of the first solution is 67%
I would really like help for this, if anyone is willing to help me.
Answer:
It's bc
Step-by-step explanation:
Given y varies inversely as x, and y = 5 when x = 9. Write the inverse function
Answer:
y = 45/x
Step-by-step explanation:
Given y varies inversely as x, then;
y = k/x
If y = 5 when x = 9
5 = k/9
k = 5*9
k = 45
Substitute into the formula above;
y = k/x
y = 45/x
Hence the required inverse function is y = 45/x
please help this answer is very important
Answer:
option 4
2
Step-by-step explanation:
1 Litre = 1000 mililitre
so,
2 litres = 2000 mililitres
it took samatha 325 minutes to cook an 18 lb turkey.How many minutes per pound did it take to cook the turkey ?
Answer:
Below.
Step-by-step explanation:
325/18
= 18.055... minutes
= 18 minutes to nearest minute.
Can someone explain to me what 8√42 ÷ 2√7 is?
Answer:
Step-by-step explanation:
8√42 ÷ 2√7 is 8√42/2√7 in a fraction form
you want to take the square root out of the denominator, and so you would multiply the denominator by the numerator and itself.
8√42/2√7 * 2√7/2√7 = 4√6
What are the solutions of the equation 3x^2 +13x=10 ?
PLS HELP ITS TIMED TYSM!!!
HELP 5TH GRADE ,]\\ MADEGVGUGU MATH
Answer:
i think base. i might be wrong.
Step-by-step explanation:
Answer:
Its period................
Enter an expression equivalent to (2x^2- 4x + 5) + (x^2+ 3x – 7) using the fewest possible number of terms.
The black trapezoid is a dilation of the green trapezoid. What is the scale factor of the dilation?
A) 1/5
B) 1/3
C) 3
D) 5
============================================================
Explanation:
We're told that "The black trapezoid is a dilation of the green trapezoid". This means the black trapezoid is the image, while the green one is the preimage. In other words, the green is the "before" and the black is the "after". The mapping is [tex]\text{green} \to \text{black}[/tex] because of the ordering [tex]\text{preimage} \to \text{image}[/tex]
Since the green figure (preimage) is larger than the black figure (image), the scale factor must be some value k such that 0 < k < 1. That narrows the answer choices between A and B.
Focus on the green trapezoid. The bottom left corner is at (-10,0). The bottom right corner is at (5,0). The distance between these two points is 15 units.
Using the same idea, the distance along the bottom edge of the black trapezoid is 3 units. We can count out the spaces along the bottom, or we can note the two bottom corners are at (-2,0) and (1,0).
------------------------------
So far we found:
The bottom edge of the green trapezoid is 15 unitsThe bottom edge of the black trapezoid is 3 unitsThese two edges correspond to one another. We divide the values to get the scale factor. We divide the image length over its corresponding preimage length.
scale factor = (image length)/(preimage length)
scale factor = 3/15
scale factor = 1/5
14. Twelve more than seven times a number equals the number less six
Answer:
The number is -3.
Step-by-step explanation:
Set up an equation:
Variable n = number
12 + 7n = n - 6
Assuming the question is solve for n, isolate the variable:
Subtract n from both sides:
12 + 6n = -6
Subtract 12 from both sides:
6n = -18
Divide by 6 on both sides:
n = -3
Check your work:
12 + 7(-3) = -3 - 6
12 - 21 = -3 - 6
-9 = -9
Correct
Identify the graphed linear question.
A. y=5x+2
B. y=5x-2
C. y= -5x+2
D. y= -5x-2
Answer:
The answer is: y= -5x-2
Step-by-step explanation:
I hope it help.
Jose is trying to pick out an outfit for the first day of school. He can choose from 2 pairs of pants, 6 t-shirts, and 3 pairs of shoes. How many different outfits does Jose have to choose from?
Jose has to choose from 36 different ways.
What is the Combination?The various ways in which objects from a set may be selected, generally without replacement to form subsets is known as combination.
For the given situation,
Pairs of pants = [tex]2[/tex]
T-shirts = [tex]6[/tex]
Pairs of shoes = [tex]3[/tex]
The formula to find the number of ways using combination = [tex]nC_{r}[/tex]
Number of ways of picking the outfit = [tex](2C_{1}) (6C_{1}) (3C_{1} )[/tex]
⇒ [tex](2)(6)(3)[/tex]
⇒ [tex]36[/tex]
Hence we can conclude that Jose has to choose from 36 different ways.
Learn more about combinations here
https://brainly.com/question/13003667
#SPJ2
There are 20 marbles in the box. 4 marbles are black, 6 marbles are blue, 10 are red. What is the probability of drawing a black OR a red marble?
Answer:
7/10 or 70% or 0.7
Step-by-step explanation:
4 black, 10 red
10+4=14
now you put it over the total marbles
14/20=7/10
i don't know how your teacher wants you to give the answer but it is 7/10 or 0.7 or 70%
Alyssa is getting gas for her car. Her car's 15-gallon tank has 15 of a tank of gas left. If gas costs $2.699 per gallon, how much will she pay for gas, rounded to the nearest cent?
Answer: $32.39
Step-by-step explanation:
The car's tank has a capacity of 15 gallons and has only 1/5 of a tank left which means that the quantity left is:
= 1/5 * 15
= 3 gallons
If Ayssa is going to fill up the tank, the number of gallons needed is:
= 15 - 3
= 12 gallons
Gas is $2.699 per gallon so cost is:
= 12 * 2.699
= $32.39
What is the value of y-x?
A. 20
B. 30
C. 45
ASAP
-will mark brianist
Answer:
20-12
35-21
40-24
Step-by-step explanation:
You times both numbers by the same value
Answer:
1st is 12
2nd is 35
3rd is 40
Step-by-step explanation:
Which expression is equivalent to the one below? 6÷9 A. 9.1/6 B. 6.1/9 C. 54 D. 9/6
Answer:
None
Step-by-step explanation:
6÷9=0.666...
9.1÷6=1.5166..
6.1÷9=0.6777...
54 is 54
9÷6=1.5
So none are equal
Answer:
the answer is 6 × 1/9
Step-by-step explanation:
6÷ 9 = 0.666
9 × 1/6 = 1 1/2
6 × 1/9 = 2/3 same as 0.666
54 = 54
9/6 = 1.5
PLEASE ANSWER EEEEEEEEEEEEEEEEEEE
Answer:
5 x 4 x 3 = 60
Step-by-step explanation:
Do - H x L x W
H is 5
L is 4
W is 3
3x+2y=12 2x-3y=21 elimination please solve with answer and steps
Answer:
(6,-3)
or
x=6 y= -3
Step-by-step explanation:
Taking a quick look at this question we notice that we simply cannot add/subtract the two equations and eliminate a variable
What we can do is mulitply an equation to make the above true
let's try to get the first equation to have a 3y, and we can do this by multiplying it by 1.5 (this is legal because we do it to both sides)
So our new first equation is
1.5(3x+2y)=12*1.5
which simplifies to
4.5x+3y=18
We then add the two equatiosn
(4.5x+3y)+(2x-3y)=18+21
6.5x=39
x=6
Now that we know x we can plug that in and solve for y
3(6)+2y=12
18+2y=12
-6=2y
y= -3
NO LINKS!
Select the correct answer from each drop-down menu.
Consider the end behavior of the function
g(x) = | x-2 | -3
As x approaches negative infinity, f(x) approaches
[BLANK] infinity
Options :
Negative, Positive
As x approaches positive infinity, f(x) approaches [BLANK] infinity
Options :
Negative, Positive
Answer: negative, positive
Step-by-step explanation:
FOR PLATO!
Positive
Positive
Find x.
A. 4/6
B. 6
c. 4√3
D.3/2
Last year, a population of rabbits had 20 births, 10 deaths, 15 individuals immigrate, and 15 individuals emmigrate.
What is the change in population size for the rabbits that year?
Answer:
+10
Step-by-step explanation:
35 - 25 = 10. I got 35 because 20 + 15 from the bunnies immigrating and 25 from the deaths and bunnies emmigrating out of the population.
Colin invests £1100 into his bank account. He receives 5% per year simple interest. How much will Colin have after 6 years? Give your answer to the nearest penny where appropriate.
Answer:
Step-by-step explanation:
P = £1100
r = 5%
t = 6 years
I =P*r*t
[tex]I =1100*\frac{5}{100}*6\\\\I=11*5*6\\\\I = 330[/tex]
Amount = P + I = 1100 + 330 = £1430
Help me plssssssssssss.
Answer:
5
Step-by-step explanation:
If Johnny borrowed $1,300 for 5 years on a 7% interest rate, how much interest will Johnny have to pay total?
Answer:
฿₹Ø: 1391 US$
Step-by-step explanation:
yeah please help me I’ll give brainliest if correct
Answer:
p=20
6p=120
Step-by-step explanation:
Answer:
A: 6p = 120
Solution:
6 / p = 120 / 6
p = 20
dont forget to five-star and heart! ;)
Identify the volume and surface area of the sphere in terms of π.
The figure shows a sphere. The sphere has a radius of 9 centimeters.
V = 972π cm3; S = 324π cm2
V = 243π cm3; S = 324π cm2
V = 972π cm3; S = 162π cm2
V = 243π cm3; S = 162π cm2
Answer:
Volume is: 972 and Surface area is 324
Step-by-step explanation:
How to get the volume is 9^3
That is 729
Times 4/3
972.
The surface area is 4 times 9^2
324.
You dont use the pie.
If (X+2,4) and (5,y-1 are equal ordered pairs ,Find the value of X and y
Answer:
x = 3, y = 5
Step-by-step explanation:
Since the ordered pairs are equal, then equate the x and y coordinates
x + 2 = 5 ( subtract 2 from both sides )
x = 3
y - 1 = 4 ( add 1 to both sides )
y = 5