[tex]\begin{cases} x = -4\implies &x+4=0\\ x=-2\implies &x+2=0\\ x=1\implies &x-1=0 \end{cases}\qquad \implies (x+4)(x+2)(x-1)=\stackrel{y}{0}[/tex]
now, that's the equation or polynomial in factored form, hmmm we also know that it has a y-intercept of -11, namely, when x = 0 y = -11, well let's plug in a factor to it, that will reflect those values, namely say hmmm factor "a", so
[tex](x+4)(x+2)(x-1)=y\qquad \stackrel{\textit{adding "a" factor for vertical shift}}{a(x+4)(x+2)(x-1)}=y \\\\\\ \stackrel{\textit{we know that when x = 0, y = -11}}{a(0+4)(0+2)(0-1)=-11}\implies -8a=-11\implies a=\cfrac{-11}{-8}\implies a = \cfrac{11}{8} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\mathbb{FOIL}}{\cfrac{11}{8}(x^2+6x+8)}(x-1)=y\implies \cfrac{11}{8}(x^3+6x^2+8x-x^2-6x-8)=y \\\\[-0.35em] ~\dotfill\\\\ ~\hfill \cfrac{11}{8}(x^3+5x^2+2x-8)=y~\hfill[/tex]
How do I multiply a fraction and a whole number? Please explain step by step to get marked
Any whole number can be written as a fraction. All we do is place the number over 1.
For example, the whole number 7 is the same as the fraction 7/1.
If we wanted to multiply the whole number 7 with the fraction 2/3 then...
[tex]7 * \frac{2}{3}\\\\\frac{7}{1} * \frac{2}{3}\\\\\frac{7*2}{1*3}\\\\\frac{14}{3}\\\\[/tex]
In the jump from the second step to the third step, we multiply straight across. The numerators multiply together. The denominators multiply together. The fraction 14/3 cannot be reduced because 14 and 3 don't have any factors in common other than 1.
What is the 18th term to the sequence 14,18,22
What does the transformation f(x)↦f(x+5)–1 do to the graph of f(x)?
Answer:
Every f(x) shall decrease to 5 times the previous value.
What number is the opposite of
3/11
O A. - 3/11
O B. -11/3
C. 11/3
O D. 1/3
Answer:
I believe the answer is A.
The dean of a business college in the Midwest claims that he can correctly identify whether a student is a finance major or a music industry management major by the way the student dresses. Suppose in actuality that he can correctly identify finance majors 84% of the time, while 16% of the time he mistakenly identifies a music industry management major as a finance major. Presented with one student and asked to identify the major of this student (who is either a finance or music industry management major), the dean considers this to be a hypothesis test with the null hypothesis being that the student is a finance major and the alternative that the student is a music industry management major. Which of the following statements illustrates a Type I error?
a. Saying that the student is a finance major when in fact the student is a music industry management major.
b. Saying that the student is a music industry management major when in fact the student is a music industry management major.
c. Saying that the student is a finance major when in fact the student is a finance major.
d. Saying that the student is a music industry management major when in fact the student is a finance major.
Using error concepts, it is found that the option that represents a Type I error is:
d. Saying that the student is a music industry management major when in fact the student is a finance major.The definitions of each type of error are as follows:
A Type I error happens when a true null hypothesis is rejected. A Type II error happens when a false null hypothesis is not-rejected.
In this problem, the Hypothesis are:
Null: Student is a finance major.Alternative: Student is a music industry management major.By the definition of a Type I error, in this problem, it would consist in saying that a finance major student is a music industry management major student, hence option d is correct.
You can learn more about Type I and II errors at https://brainly.com/question/25225353
2. Mark works as a consultant for a computer firm. His weekly income is $425. His
monthly expenses are $1,266. How much does he have left for variable expenses?
(Hint: There are four pay periods in one month.)
Hi there, I hope you understand my answer and that it is correct :)
So, First we multiply $425 by 4 because there are approximately 4 weeks in every month, so as shown [tex]425*4=1,700[/tex]
____________________________________________________________
Next We subtract the answer, which we got to be 1,700 from 1266.
[tex]1700 - 1266=434[/tex]
____________________________________________________________
Answer : $434 left to spend :)
Solve the following compound inequality: 4 less-than-or-equal-to x + 4 less-than-or-equal-to 12. a. 0 less-than-or-equal-to x less-than-or-equal-to 8 c. 8 less-than-or-equal-to x less-than-or-equal-to 16 b. x less-than-or-equal-to 8 d. no solution Please select the best answer from the choices provided A B C D
Answer:
A. 0 <= x <= 8
Step-by-step explanation:
4 <= x + 4 <= 12
Remove 4 from all sides
4 - 4 <= x + 4 -4 <= 12 - 4
0 <= x <= 8
mom left $5.00 for his 7 children. how much did each child receive
a.0.17
b.0.70
c.17
d.71
please answer it correctly.
Answer:
.71
Step-by-step explanation:
Answer:
B. 0.70
Step-by-step explanation:
Just divide the total amount of money by the total amount of people.
5/7=0.71428...
if you round up correctly, you get 0.70; thus, it is B.
Also, his is for he, mom is a she, so use her instead of his...
Jacob sells lemonade at a park. His cost to sell the lemonade is a one-time fee for the table,
plus a fixed cost to make each cup of lemonade. The line shows the total cost, y, for 3 cups
of lemonade.
v
Cost of Selling Lemonade
Use
y
A
y
60
50
40
Cost ($)
30
20
10
→ X
0
10
50
20
30
40
Number of Cups
Answer:y=12 x=00
Step-by-step explanation:
you can not
The required equation that represents the graph is y = x + 30
What is a linear equation?A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. The variables in the preceding equation are y and x, and it is occasionally referred to as a "linear equation of two variables."
The standard linear equation is given as y = mx + b
Where,
m is the slope
b is the y-intercept
Using the coordinates (20, 50) and (40, 70)
Get the slope of the line:
m = 70-50/40-20
m = 20/20
m = 1
Since the line cuts the y-axis at y = 30, hence the y-intercept is 30.
Therefore, the Required equation that Shows the graph is y = x + 30
Learn more about linear equations here:
brainly.com/question/13763238
#SPJ2
Sketch the region enclosed by the given curves. Decide whether to integrate with respect to x or y. Then find the area of the region y=4x^2, y=x^2 + 3
Answer:
Step-by-step explanation:
integrate with respect to x
Area is symmetric so will be twice the integral from zero to 1
( I cannot seem to figure out how to make the lower limit negative in this editor)
[tex]A = 2\int\limits^1_0 {(x^2 + 3) - 4x^2} \, dx[/tex])
[tex]A = 2\int\limits^1_0 {-3x^2 + 3} \, dx[/tex]
[tex]A = 6\int\limits^1_0 {-x^2 + 1} \, dx[/tex]
A = 6(-⅓x³ + x)[tex]\left \| {{x=1} \atop {x=0}} \right.[/tex]
A = 6((-⅓(1)³ + (1)) - (-⅓(0)³ + (0)))
A = 6(⅔)
A = 4 units²
Classify the Triangle by its sides and angles. 140° Right Scalene Right Isosceles Equilateral Obtuse Isosceles Acute Isosceles Obtuse scate Acute Scalene
Answer: Obtuse Isosceles.
Explanation: Two angles are congruent, which means the triangle is isosceles. One angle is over 90°, which means the triangle is obtuse.
If
you
invest $100 in an index fund that earns an average annual rate of
return of 12.3% compounded monthly. You make a regular monthly
contributions of $25, how much will your investment be worth in 52 years?
Answer Interest rate = 12.3%
The compound interest formula is given by:
Where
A = Future amount
P = Present amount (Principal amount)
r = Interest rate in decimal form
n = No. of times compounded per year
t = time in years.
We can say that if:
Present amount = P
Future amount = 3P
r = 12.3/100 = 0.123
n = 1
t = ?
Substitute the values in the formula of compound interest:
Taking log on both sides.
Round off to nearest option
t ≅ 9 years
Which relationships have the same constant of proportionality between y and x as the following table?
y
4
32
7
56
8 64
Choose 3 answers:
Answer:
A,C and D are the answers.
Step-by-step explanation:
I did it on Khan Academy and got it right.
Question:
Goofy Unlimited Lighting sells a 12 pack of lightbulbs for $8.40. Daisy Luminous Lighting sells a pack of 19 lightbulbs for
$15.35. Which store has the better deal. (3 points - 1 point showing the correct proportional relationship, 1 point
showing the unit rate, 1 point for identifying the store name)
es 0)
balo
Answer:
Goofy unlimited lighting 12 pack of light bulbs
Step-by-step explanation:
12 = 8.40/12 = .70 cents
19 = 15.35 = .81 cents
The bed of Jerry's pickup truck is 6 feet long. On
a scale model of the truck, the bed is 1/4 inch
What is the scale of the model?
6 ft
Answer:
1:4
Step-by-step explanation:
(1/4 in : 6 ft)
1/4 in : 6 (12 in)
1/4 in : 72 in
divide each side by 1/4
288/72 simplified is ...
1 : 4
⦁ Solve for x: 3|x – 7| = 15
SHOW WORK
[tex]3|x-7| = 15\\\\\implies |x-7| =\dfrac{15}3\\\\\implies |x -7| = 5\\\\\implies x -7 = 5 ~~ \text{or}~ x - 7 = -5\\\\\implies x = 12 ~~\text{or}~~ x = 2[/tex]
I'll give brainliest to the right answer!!!
Find three consecutive odd integers such that the difference of twice the second and the first is 11.
Answer:
7, 9, 11
Step-by-step explanation:
question: Find three consecutive odd integers such that the difference of twice the second and the first is 11.
make the 3 consecutive odd intergers x, y, and z.
numbers are consective (come right after another) AND odd, meaning you would add 2 every time. therefore:
x+2=y
y+2=z
given that: "difference of twice the second and the first is 11."
difference means subtraction
second number is the variable y
first number is the variable x
2y-x=11
----------------
3 equations:
2y-x=11
x+2=y
y+2=z
----------solve by substitution
x+2=y
x =y-2 into 2y-x=11
2y-(y-2)=11
2y-y+2=11
y=9
second number is 9
-----
numbers are 7, 9, 11
Help help help help math math
Answer:
umm i think its A/B
Step-by-step explanation:
Answer:
√49 < √56 < √64
Step-by-step explanation:
√56 = 7.4833....
7x7 = 49
8x8 = 64
√49 < √56 < √64
What is the value of x
Answer:
5"
root4square+3square=root25
=5
Find the exact value.
[tex]\text{Given that,}\\\\\cot A = -\dfrac{9}{\sqrt{40}}\\\\\\\implies \tan A = -\dfrac{\sqrt{40}}9\\\\\\\implies \tan^2 A = \dfrac{40}{81}\\\\\\\implies \sec^2 A -1 = \dfrac{40}{81}\\\\\implies \sec^2 A = 1 + \dfrac{40}{81}\\\\\implies \sec^2 A = \dfrac{121}{81}\\\\\implies \sec A = \pm \sqrt{\dfrac{121}{81}}= \pm\dfrac{11}{9}\\\\\\\text{Since the angle A is in quadrant II, the value of sec A will be negative.}\\\\\\\text{Hence,}~ \sec A=-\dfrac{11}{9}[/tex]
how much time should be allowed for a 392-km car trip if the car will be traveling at 120km/h
Answer:3hrs 16min
Step-by-step explanation:
392/120 = 49/15 hours = 3 hours + 4/15 hours = 3 hours + 4/15 x 60 min = 3 hours + 16 min
#10) Mrs. Sommer states that angle I is 65 degrees. Is she correct? why or why not
Answer: Mrs. Somner is correct.
Step-by-step explanation: In a triangle, the angles add up to 180 degrees. Since we know that Triangle ABC is equal to Triangle RST, we can assume that their angle values are equal as well. Angle A is 41 degrees, and Angle B is 74 degrees. This adds up to 115 degrees. If we subtract 115 from 180, we get 65. Therefore, Mrs. Somner is correct.
Graph the following features: Y-intercept = 1 Slope 3/2
Really need help pls ty
Answer:
1: Yes, because 20 divided by 5 is 4, meaning that he would have 16 dollars left
2: They are at each exibit for 51 min
Hope this helps: :)
Please help me solve
Answer:
i think t = 24
Step-by-step explanation:
68°+(5t-8)° = 180°
5t-8 = 180-68
5t-8 = 112
5t = 120
t = 120/5
t = 24
Multiply and write in standard form:
(2x)(x^2 - 6x + 3)
Show all work for full credit.
2x(x2-6x+3)
4x^3-12x^2+6x
Given f(x) = x + 2, describe how setting k = 4 affects the slope and y-intercept of the graph of g compared to the graph of f.
g(x) = (4x) + 2
g(x)=4(x+2)
Answer:
g(2)=(4x) +2=7y
g(3)=4(x+2)
What is an equation of the line that passes through the points (-4, -5) and (-2, -6)?
Answer: [tex]y=-\frac{1}{2}x-7[/tex]
Ok done. Thank to me :>
Triangle DNO has vertices at D(5, 8), N(– 3, 10), and O(– 3, 6). If vertex D is translated 4 units to the right, the best name for Triangle DNO is:
Answer Choices:
a. Scalene
b. Isosceles
c. Equilateral
d. Right
e. none of these
Using distance between two points to find the lengths of the edges of the triangle, the correct option is:
b. Isosceles
The distance between two points, [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex], is given by:
[tex]d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex]
Vertex D is translated 4 units to the right is (9,8).
The lengths of the edges are:
[tex]DN = \sqrt{(9 - (-3))^2 + (8 - 10)^2} = \sqrt{12^2 + 2^2} = \sqrt{148}[/tex]
[tex]DO = \sqrt{(9 - (-3))^2 + (8 - 6)^2} = \sqrt{12^2 + 2^2} = \sqrt{148}[/tex]
[tex]NO = \sqrt{(-3 - (-3))^2 + (10 - 6)^2} = \sqrt{0^2 + 4^2} = 4[/tex]
Two edges of the same length, hence, it is an isosceles triangle, given by option b.
You can learn more about distance between two points at https://brainly.com/question/18345417
Plz I need help
......................
Answer:
B. (0, -4) and (4, -4)
Step-by-step explanation:
The solutions are the points of intersection of the circle and the parabola.
(0, -4) and (4, -4)