The function g(x) = x³ - x² - 4x + 4 has zeros at 1, 2 and -2. The y intercept is at 4.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
The zeros of the function is at:
g(x) = 0, hence:
x³ - x² - 4x + 4 = 0
(x - 1)(x² - 4) = 0
(x - 1)(x + 2)(x - 2) = 0
x = 1, x = -2 and x = 2
The y intercept is at x = 0, hence:
g(0) = 0³ - 0² - 4(0) + 4 = 4
The function g(x) = x³ - x² - 4x + 4 has zeros at 1, 2 and -2. The y intercept is at 4.
Find out more on equation at: https://brainly.com/question/2972832
3827 x 8/8 lees than equal to or greater than 3827 asap
Answer:
It's equal to itself. Here are the two ways to do this problem. ↓
[tex](3,827 * 8) / 8 = 3,827[/tex][tex]3,827 * 100~percent(8/8) = 3,827[/tex]Please help! I cannot figure this out, I have no idea what to do.
3. First you should identify which line corresponds to which equation.
x + 2y = -8 ⇒ y = -x/2 - 4
is the line with slope -1/2 and intercept (0, -4), so the first inequality refers to the lower line in the graph.
For the inequality itself, the solution set that satisfies it is either the region above or below it. To decide which, pick any point in the plane and plug its coordinates into the inequality. The origin is a natural choice, since it's not on the line and working with 0s is easy.
In the first inequality, we have
x = 0 and y = 0 ⇒ 0 + 2•0 = 0 < -8
which is not true. So (0, 0) is not in the solution set, and it stands to reason that any point in the same region will not be a solution. In other words, the region above the line x + 2y = -8 does not satisfy the inequality, while the one below it does.
In the second inequality,
x = 0 and y = 0 ⇒ 2•0 + 0 = 0 ≥ -1
which is true. This means the region containing (0, 0) above the upper line solves the second inequality.
The solution to the system of inequalities is then the intersection of these two regions. (See attached; I've labeled the solution to the first inequality in blue, the solution to the second one in red, and the solution to both in green.)
All this work is kind of overkill for this particular question, though. All you really need to do is check if the given point satisfies the inequalities:
• (-5, 5) :
x = -5 and y = 5 ⇒ -5 + 2•5 = 5 < -8 ⇒ NO
• (2, -5) :
x = 2 and y = -5 ⇒ -2 + 2•5 = 8 < -8 ⇒ NO
• (-4, -6) :
x = -4 and y = -6 ⇒ -4 + 2•(-6) = -16 < -8 ⇒ MAYBE
x = -4 and y = -6 ⇒ 2•(-4) + (-6) = -14 < -8 ⇒ YES
• (5, -7) :
x = 5 and y = -7 ⇒ 5 + 2•(-7) = -9 < -8 ⇒ MAYBE
x = 5 and y = -7 ⇒ 2•5 + (-7) = 3 < -8 ⇒ NO
4. x is the number of candy boxes with chocolates and y is the number of boxes without chocolates. Each of the x boxes cost $27.50, so if you have x boxes, their total cost is $27.5x. Each of the y boxes cost $25.00, so y boxes cost $25y. The sponsor doesn't want to order more than 100 boxes total, so
x + y < 100
but wants to raise at least $2000, so
27.5x + 25y ≤ 2000
Now do the same thing as before; plug in the listed x- and y-coordinates and pick the point that satisfies both inequalities. You will find that (50, 30) is the correct choice.
5. Consult the "overkill" part of problem 3. The line y = -3x + 6 has a negative slope, so it's the downward sloping one. Check if the origin satisfies the inequality:
x = 0 and y = 0 ⇒ 0 ≤ -3•0 + 6 ⇒ 0 ≤ 6 ⇒ YES
This means Regions II and III solve the first inequality.
Do the same with the other inequality:
x = 0 and y = 0 ⇒ 0 ≥ 1/2•0 + 1 ⇒ 0 ≥ 1 ⇒ NO
This tells us that Regions I and II solve the second inequality.
The intersection of these regions is of course Region II.
6. One of the plotted lines is apparently y = x + 4, which has a positive slope, so this must be the upper line. The shaded region below it corresponds to the solution of either y < x + 4 or y ≤ x + 4 and we eliminate B.
The other line has negative slope, which eliminates A and D since
3x - 4y = 20 ⇒ y = 3/4x - 5
has positive slope. This leaves D.
Help help help help math math
Answer:
x> 2
Step-by-step explanation:
Multiply by 6
2x6=12
5x+2>12
Move the 2 and make it subtraction
5x>12-2
Subtract 12-2=10
5x>10 divide by 5
X>2
For the 50 students in an art contest, there will be 1 prize for first-place, 1 prize for second-place, and 3 prizes for honorable mention. What is the probability of winning a prize?
Step-by-step explanation:
there are 50 students and 5 prizes (1 + 1 + 3).
so, already in natural language we would say "there is 1 prize for every 10 students".
formally, remember the rule of probability : desired outcomes over total possible outcomes.
this is here
5/50 = 1/10 = 0.1
your can see it also this way :
if there was only 1 prize, each student would have a chance of 1/50 of winning.
now there are 5 prizes, which gives everybody 5 times the chance of winning. which is then 5×1/50 = 5/50 = 0.1
Find the equation of a line that passes through the points (-4,-2) and (6, 3).
Answer:
[tex]y = \frac{x}{4} [/tex]
Step-by-step explanation:
we find the slope which also represented as m by the formula
[tex] m = \frac{(y2 - y1)}{(x2 - x1)} [/tex]
where from point (-4, -2) the x1 is -4 and the y1 is -2 and also from point (6, 3) the x2 is 6 and the y2 is 3.
so we substitute
[tex] \frac{(3 - ( - 2))}{(6 - ( - 4))} = \frac{(3 + 2)}{(6 + 4)} = \frac{5}{10} = \frac{1}{2} [/tex]
[tex]m = \frac{1}{2} [/tex]
after we have the slope, we calculate the equation of the line by using the formula
[tex](y - y1) = m(x - x1)[/tex]
but for now, we only have y1, m and x1 so can substitute
[tex](y - ( - 2)) = \frac{1}{2} (x - ( - 4))[/tex]
we have to get rid of the fraction 1/2 so we multiply it through by the denominator 2
[tex]2(y + 2) = 2 \times \frac{1}{2}(x + 4) [/tex]
we get
[tex]2(y + 2) = 1 \times (x + 4)[/tex]
so now we expand the brackets
[tex]2y + 4 = x + 4[/tex]
we make y stand alone by grouping liked terms.
[tex]2y = x + 4 - 4[/tex]
we get
[tex]y = \frac{x}{4} [/tex]
Find the reciprocal of 6.
Answer:
1/6
Step-by-step explanation:
6 = 6/1
Therefore, reciprocal= 1/6
Answer:
1/6
Step-by-step explanation:
Multiply: (x−4)(x+5)
Simplify and write your answer in Standard Form.
HINT
Standard Form: ax2+bx+c
Answer:
x^2 + x -20
Step-by-step explanation:
First, Multiply
(x)(x) + (x)(5) + (-4)(5) + (-4)(x)
Second, Add The Like Terms Together
X^2 + x + -20
Answer: Its x^2 + 9x -20
Step-by-step explanation:
I did the test and got it wrong
Please solve with explanation high points
Answer:
k = 0, k = 4
Step-by-step explanation:
Given equation:
[tex]y=x^2+kx+3k+4x+4[/tex]
Rearrange into standard form [tex]ax^2+bx+c[/tex]:
[tex]\implies y=x^2+kx+4x+3k+4[/tex]
[tex]\implies y=x^2+(k+4)x+(3k+4)[/tex]
Therefore:
[tex]a=1, \quad b=(k+4), \quad c=(3k+4)[/tex]
If the vertex lies in the x-axis, then the quadratic has one (repeating) root at (x, 0). Therefore, we can use the discriminant to find the values of k.
Discriminant
[tex]b^2-4ac\quad\textsf{when}\:ax^2+bx+c=0[/tex]
[tex]\textsf{when }\:b^2-4ac > 0 \implies \textsf{two real roots}[/tex]
[tex]\textsf{when }\:b^2-4ac=0 \implies \textsf{one real root}[/tex]
[tex]\textsf{when }\:b^2-4ac < 0 \implies \textsf{no real roots}[/tex]
Therefore, set the discriminant to zero and solve for k:
[tex]\implies (k+4)^2-4(1)(3k+4)=0[/tex]
[tex]\implies k^2+8k+16-12k-16=0[/tex]
[tex]\implies k^2-4k=0[/tex]
[tex]\implies k(k-4)=0[/tex]
[tex]\implies k=0, k=4[/tex]
So the vertex lies in the x-axis when k = 0 or k = 4
A temperature of 35 degrees Fahrenheit is as cold as a temperature of -35 degrees Fahrenheit.
Answer:yes
Step-by-step explanation:
Triangle ABC is similar to triangle XYZ. Find side a.
Answer:
If ABC and XYZ are two similar triangles, then by the help of below-given formulas, we can find the relevant angles and side lengths. ∠A = ∠X, ∠B = ∠Y and ∠C = ∠Z AB/XY = BC/YZ = AC/XZ
Tanya is training a turtle for a turtle race. For every 3 of an hour that the turtle is crawling, he can travel 25 of a mile. At what unit rate is the turtle crawling? A 7 of a mile per hour 75 B. of a mile per hour C 37 } miles per hour D. 7 of a mile per hour
Answer:
D. but there should be an 8.33
Step-by-step explanation:
The answer should be 8.33 but in here it only says 7 which is the closest because the unit rate would be 8.33 miles an hour.
Help help help math math math
4x + 8 > -x - 7
4x + x > - 7 - 8
5 x > - 15
x > -3
x > -3
↪explanation4x + 8 > -x - 7
4x + x > -7 - 8
5x > -15
5x ÷ 5 > -15 ÷ 5
x > -3
☆...hope this helps...☆
Add the mixed numbers.
6 1/12
+ 3 1/3
The sum is ___
Answer:
9 5/6
Step-by-step explanation:
6 1/2 + 3 1/3
= (6 + 3) + (1/2 + 1/3)
= 9 + 1 * 3/ 2 * 3 + 1 * 2/ 3*2
= 9 + 3/6 + 2/6
= 9 + 3+2/6
= 9 + 5/6
= 9 5/6
Hey there!
6 1/12 + 3 1/3
= 73/12 + 10/3
= 73/12 + 40/12
= 73 + 40 / 12 + 0
= 113 / 12
= 9 5/12
Therefore, your answer is:
• 113/12
OR
• 9 5/12
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
Sawyer is 6 years older than his sister.
This year, Sawyer is also three times as
old as his sister. How old is Sawyer now?
Sawyer is 9 yrs old and his sister is 3 yrs old
hope it really helps...
Mr. and Mrs. Doran have a genetic history such that the probability that a child being
born to them with a certain trait is 0.61. If they have four children, what is the
probability that at most two of their four children will have that trait? Round your
answer to the nearest thousandth.
Using the binomial distribution, it is found that there is a 0.011 = 1.1% probability that exactly one of their four children will have that trait.
For each children, there are only two possible outcomes, either they have the trait, or they do not. The probability of a children having the trait is independent of any other children, hence, the binomial distribution is used to solve this question.
Binomial probability distribution
[tex]P(X=x)=C_{n,x.}p^x.(1-p)^{n-x}[/tex]
[tex]C_{n,x}=\frac{n!}{x!(n-x)!}[/tex]
The parameters are:
x is the number of successes.n is the number of trials.p is the probability of a success on a single trial.In this problem:
85% probability of a children having the trait, hence [tex]p=0.85[/tex].They have four children, hence [tex]n=4[/tex]The probability is P(X = 1), hence:
[tex]P(X=x)=C_{n,x.}p^x.(1-p)^{n-x}[/tex]
[tex]P(X=1)=C_{4,1*}(0.85)^1.(0.15)^3=0.011[/tex]
0.011 = 1.1% probability that exactly one of their four children will have that trait.
A similar problem is given at https://brainly.com/question/24863377
add the following integers {3 +(-7)}+(-6)
Answer:
-10
Step-by-step explanation:
Answer:
-10
Step-by-step explanation:
(3+(-7))+(-6)
=3-7+-6
=3-7-6=-10
What is 2/3 - 5/6 divided by 3/4
The following are ages of 16 of the signers of the Declaration of Independence.
43, 62, 35, 45, 42, 46, 39, 31, 60, 37, 39, 47, 35, 36, 35, 40
Send data to calculator
Find 10th and 75th percentiles for these ages.
(a)
The 10th
percentile: 0
(b)
The
75th
percentile: 0
Х
5
?
V
Playing with Numbers
5. Test the divisibility of the following numbers by 8:
(iii) 36712
Answer:
Last 3 digits 712 is divisible by 8 so 36712 is divisible by 8
Step-by-step explanation:
A naval engineer uses the function, P, to analyze the effects of water pressure on submarines. The
function P(d) measures the pressure exerted by water, where d represents the depth of water in
meters. Which of the following would be a possible domain?
A
d is the set of all integers.
B
d is the set of all integers where d > 0.
d is the set of all rational numbers.
D
d is the set of all rational numbers where 0 sds depth of sea floor).
994
Answer:
the correct answer is D.
Step-by-step explanation:
d is the set of all rational numbers where (0 ≤ d ≤ depth of seafloor).
i just took the test on math nation and got it correct.
hope this helped! :)
How many milliliters are in 5 liters?
500 mL
5,000 mL
50,000 mL
50 mL
Answer:
5,000 is the correct answer
Estimate the answer to
(
9.51
×
10
3
)
×
(
8.57
×
10
4
)
Give your answer in standard form.
Step-by-step explanation:
9.51 x 10^3 * 8.57 x 10^4 = ~~ 10000 * 90000 = 900, 000,000 est
Question was changed.....so answer was edited
The model represents an equation. What value of x makes the equation true?
A) 29/8
B) 29/2
C) − 29/2
D) − 29/8
Answer:
A) 29/8
Step-by-step explanation:
Identify the blocks. As you can see there are 5 x blocks on the left, and 9 -1 blocks on the left. On the right there are 3 -x blocks and 20 1 blocks. With this, form the equation.
5x - 9 = -3x + 20
Add 3x to both sides.
8x - 9 = 20
Add 9 to both sides.
8x = 29
Divide both sides by 28 to get:
x = 29/8.
You have two part-time jobs making $11 an hour mowing lawns and $8 an hour washing cars. You want to make at least $150 a week but work less than 20 hours per week. Write a system to represent this situation..
the area of a parallelogram measures 171 cm the base of the parallelogram is 18 cm in length which of the following best represents the height of the parallelogram A. 11cm B. 9.5 C. 13.5 D. 8cm give step by step explanation
Answer:
A=bxh
171 cm=18cmxh
h=171/18
= 9.5 cm
which is B no.
Write 0.000299 in scientific notation
Answer:
0.000299 in scientific notation
2.99 × 10-4
Step-by-step explanation:
To convert 0.000299 into scientific notation also known as standard form, follow these steps:
Move the decimal 4 times to right in the number so that the resulting number, m = 2.99, is greater than or equal to 1 but less than 10
Since we moved the decimal to the right the exponent n is negative
n = -4
Write in the scientific notation form, m × 10n
= 2.99 × 10-4
Answer:
0.000299
2.99 × 10^-4.
Step-by-step explanation:
The following list shows how many brothers and sisters some students have:
3
,
4
,
4
,
5
,
5
,
2
,
5
,
4
,
6
,
3
,
6
,
5
,
3
State the mode.
Answer:
5
Step-by-step explanation:
So we have the set of numbers: 3,4,4,5,5,2,5,4,6,3,6,5,3.
Mode just means the most repeated number so let's sort them into groups.
(2) (3,3,3) (4,4,4) (5,5,5,5) (6,6).
the most repeated number is 5 which we see in the sequence about 4 times.
Math test Farley easy
Answer:
417.831823 [tex]in^{2}[/tex]
Step-by-step explanation:
surface area of cone ;
[tex]=\pi r^{2}+\pi rl\\ =\pi (7^{2}) +\pi (7)(12)=417.831823 in^{2}[/tex]
Answer:417.831823
Step-by-step explanation:
The probability that a couple will havenbaby boys in a row is given by the formula
2
Find the probability that a couple will have Sbaby boys in a row.
Answer:The probability that a couple will havenbaby boys in a row is given by the formula2Find the probability that a couple will have Sbaby boys in a row.
The probability that a couple will havenbaby boys in a row is given by the formula2Find the probability that a couple will have Sbaby boys in a row.
Step-by-step explanation:The probability that a couple will havenbaby boys in a row is given by the formula2Find the probability that a couple will have Sbaby boys in a row.
is your correct answer
Espanol
- 9
1
2
P4
8
3
5
6
A triangle is placed in a semicircle with a radius of 3 yd, as shown below. Find the area of the shaded region.
Use the value 3.14 for it, and do not round your answer. Be sure to include the correct unit in your answer.
Answer: 5.13 square cm
Step-by-step explanation: