Step-by-step explanation:
f(x) = x³ + 3x² - x - 3 = x²(x + 3) - (x + 3)
= (x² - 1)(x + 3) = (x + 1)(x - 1)(x + 3).
The roots of f(x) are x = -3, -1 and 1.
=> The new roots are x = -5, -3 and -1.
=> g(x) = (x + 5)(x + 3)(x + 1) = x³ + 9x² + 23x + 15.
Grinnell Glacier in Glacier National Park in the US covered about 142 acres in 2007 and was shrinking at a rate of about 4.4% per year.3 (a) Write a formula for the size, , of the Grinnell Glacier, in acres, as a function of years since 2007. (b) Use the model to predict the size of the glacier in the year 2020. (c) According to the model, how many acres of ice were lost from the glacier between 2007 and 2010
Answer:
Step-by-step explanation:
Glacier National park has the area in year 2007 = 142 acres
It's shrinking at a rate = 4.4% per year
a). Since, shrink in the size of the glacier is an exponential process,
Therefore, formula for the size of the glacier in 'n' years,
A = 142(1 - 0.044)ⁿ
A = 142(0.956)ⁿ
b). Difference between year 2007 and 2020 = 13 years
By substituting n = 13 years in the formula,
A = 142(0.956)¹³
= 79.11 acres
Therefore, size of the glacier in year 2020 = 79.11 acres
c). Difference between year 2007 and 2010 = 3 years
By substituting n = 3 years in the formula,
A = 142(0.956)³
A = 124.07 acres
Loss of the ice from the glacier = 142 - 124.07
= 17.93 acres
Therefore, loss of the ice from the glacier in 3 years = 17.93 acres
3. The radius of a circle is 14 yds. What is the area? Use 3.14 as pi.
answer gets brainliest
Answer: I'm just answering so if only one person answers then u can give the other person brainliest.
Step-by-step explanation: Also if nobody is answering u might want to repost this question
Answer:
153.86 yds. sq.
Hope this helps you!
Step-by-step explanation:
6 batteries cost 29 dollars what is the unit rate?
Answer:
Step-by-step explanation:
In a unit rate, the denominator is always 1. So, to find unit rate, divide the denominator with the numerator in a way that the denominator becomes 1. For example, if 50km is covered in 5.5 hours, the unit rate will be 50km/5.5 hours = 9.09 km/hour
Answer:
[tex]\large \boxed{\sf{4.83 \ dollars/battery}}[/tex]
Step-by-step explanation:
Unit rate is a ratio that compares two measurements.
Denominator is 1
[tex]\displaystyle \sf \frac{29\ dollars}{6\ batteries}=4.83\ dollars/battery[/tex]
Mr. Starnes and his wife have 6 grandchildren: Connor, Declan, Lucas, Piper, Sedona, and Zayne. They have 2 extra tickets to a holiday show, and will randomly select which 2 grandkids get to see the show with them. Find the probability that at least one of the girls (Piper and Sedona) get to go to the show.
Answer:
the probability that at least one of the girls (Piper and Sedona) get to go to the show is 0.533
Step-by-step explanation:
The computation of the probability that have at least one of the girl get to go is shown below;
[tex]= \frac{^2C_1 \times ^4C_1}{^6C_2} \\\\= \frac{8}{15}\\\\= 0.53333[/tex]
Hence, the probability that at least one of the girls (Piper and Sedona) get to go to the show is 0.533
So the same is relevant
Probability that at least one of the girls (Piper and Sedona) get to go to the show = 1/5
The number of grandchildren = 6
The number of girls = 2
Two grandkids out of 6 are to be selected
Number of ways of choosing 2 grandkids out of 6 is 6C2
[tex]6C2=\frac{6!}{(6-2)!2!} \\\\6C2=\frac{6!}{4! \times 2!} \\\\6C2 = 15[/tex]
Number of ways of selecting 2 grandkids out of 6 = 15 ways
Number of ways of selecting 1 out of the two girls =2C1
[tex]2C1= 2[/tex]
Number of ways of selecting 1 out of the two girls = 2 ways
Number of ways of selecting of selecting both girls =2C2
Number of ways of selecting of selecting both girls = 1 way
Probability of selecting 1 out of the two grandkids = 1/15
Probability of selecting both girls = 2/15
Probability that at least one of the girls (Piper and Sedona) get to go to the show = 1/15 + 2/15
probability that at least one of the girls (Piper and Sedona) get to go to the show = 3/15
Probability that at least one of the girls (Piper and Sedona) get to go to the show = 1/5
Learn more here: https://brainly.com/question/20709225
Kayla went shopping for a new pair of sneakers. The listed price of the pair of sneakers was $20, but the price with tax came to $21.80. Find the percent sales tax.
Hello!
[tex]\large\boxed{9 \%}[/tex]
To find the percent tax, use the equation:
[tex]\text{ \% tax} = \frac{\text{ price after - initial price}}{\text{initial price}}[/tex]
Substitute in the given values:
[tex]\text{ \% tax} = \frac{\text{ 21.80 - 20}}{\text{20}} \\\\\text{ \% tax} = \frac{1.80}{20} = 0.09[/tex]
Multiply by 100 to find the percent tax:
[tex]0.09 * 100 = 9\%[/tex]
Answer: Its 9%
Step-by-step explanation:
_____indicates the level
of uncertainty that people can
tolerate to work efficiently without
experiencing undue stress
Select one:
a. Tolerance for ambiguity
b. Risk propensity
c. Workahollism
d. Authoritaritznism
= Tolerance for ambiguity
Step-by-step explanation:
indicates the level
of uncertainty that people can
tolerate to work efficiently without
experiencing undue stress
HHHEEEELLLLLP!!!!!!!!
Compare these rational numbers. Which of the following are true?
In which step did the veterinarian make the first error?
Step 1
Step 2
Step 3
Step 4
Answer:step 3 Step-by-step explanation: because it is right and i took the test edge 2021
helppppppppppppppppppppppppppppppppjhfyigcusfdcusVCOUVc
Answer:
use the app called msthway
The diagram shows a right-angled triangle,
Calculate the value of x.
Answer:
x = 12
Step-by-step explanation:
[tex]90 + 3x + 16 + 2x + 14 = 180 [/tex]
[tex]5x + 120 = 180[/tex]
[tex]5x = 180 - 120[/tex]
[tex]5x = 60[/tex]
[tex]x = \frac{60}{5} = 12[/tex]
Answer:
x = 12°
Step-by-step explanation:
[tex](3x + 16) + 90 + (2x + 14) = 180 \\ 3x + 2x = 180 - 16 - 90 - 14 \\ 5x = 60 \\ x = \frac{60}{5} \\ x = 12[/tex]
The table shows the regular price and percent of discount for four items. Write the correct sale price for each item. Round to the nearest cent if necessary.
Answer:
Step-by-step explanation:
A. $154.20 * 0.65 = $100.23
B. $91.96 * 0.70 = $64.37
C. $47.60 * 0.75 = $35.70
D. $84.60 * 0.80 = $67.68
I will give brainiest to whoever answers correctly !!
Answer:
the material when you get a chance can you send me the material
matt would like to share 5/8 of a pound with 4 with his 3 friends how many pound of chocolate will each of the 4 people receive
C - -1
D - 3/4
Can someone please help? I’ll give you brainliest.
Answer:
Step-by-step explanation:
The answer is (A)
Express the integral as a limit of Riemann sums. Do not evaluate the limit. (Use the right endpoints of each subinterval as your sample points.)
int 1 between 5 x/2+3^3*dx
Answer:
[tex]\mathbf{4 \lim \limits _{n \to \infty} \sum \limits ^n_{i=1} \Big ( \dfrac{n(n+4i)}{2n^3 +(n+4i)^3} \Big )}[/tex]
Step-by-step explanation:
Given integral:
[tex]\int ^5_1 \dfrac{x}{2+x^3} \ dx[/tex]
[tex]\mathbf{Using \ Riemann \ sums; \ we \ have: }[/tex]
[tex]\int ^b_a \ f(x) \ dx = \lim_{n \to \infty} \sum \limits ^n_{i =1} \ f( a + i \Delta x) \Delta x[/tex]
[tex]here; \ \Delta x = \dfrac{b-a}{n}[/tex]
∴
[tex]\int ^5_1 \dfrac{x}{2+x^3} \ dx = f(x) = \dfrac{x}{2+x^3}[/tex]
[tex]\implies \Delta x = \dfrac{5-1}{n} =\dfrac{4}{n}[/tex]
[tex]f(a + i \Delta x ) = f ( 1 + \dfrac{4i}{n})[/tex]
[tex]f( 1 + \dfrac{4i}{n}) = \dfrac{n^2 ( n+4i)}{2n^3 + (n + 4i)^3}[/tex]
[tex]\lim_{n \to \infty} \sum \limits ^n_{i=1} \ f(a + i \Delta x) \Delta x = \lim_{n \to \infty} \sum \limits ^n_{i=1} \Big ( \dfrac{n^2(n+4i)}{2n^3 +(n+4i)^3} \Big )\dfrac{4}{n}[/tex]
[tex]\mathbf{= 4 \lim \limits _{n \to \infty} \sum \limits ^n_{i=1} \Big ( \dfrac{n(n+4i)}{2n^3 +(n+4i)^3} \Big )}[/tex]
solve for x: x/-5+6≤2
Answer:
x ≥ 20
Step-by-step explanation:
hope this helps!
Answer:
x>= 20 or 20≤x
Step-by-step explanation:
Isolate x
Subtract 6 from both sides:
x/-5<=-4
Multiply both sides by -5, and switch the inequality sign bc u multiplied by a negative number:
x>= 20
PLEASE HELP!! WILL GIVE 200 POINTS PLUS BRAINLY!!!
Question2. Eric is observing the velocity of a runner at different times. After one hour, the velocity of the runner is 5 km/h. After three hours, the velocity of the runner is 3 km/h.
Part A: Write an equation in two variables in the standard form that can be used to describe the velocity of the runner at different times. Show your work and define the variables used. (5 points)
Part B: How can you graph the equations obtained in Part A for the first 5 hours? (5 points)
Question 3. The graph shows the functions f(x), p(x), and g(x):
Graph of function g of x is y is equal to 2 multiplied by 0.85 to the power of x. The straight line f of x joins ordered pairs minus 7, 3 and minus 3, minus 2 and is extended on both sides. The straight line p of x joins the ordered pairs 4, 1 and minus 3, minus 2 and is extended on both sides.
Part A: What is the solution to the pair of equations represented by p(x) and f(x)? (3 points)
Part B: Write any two solutions for f(x). (3 points)
Part C: What is the solution to the equation p(x) = g(x)? Justify your answer. (4 points)
Question 4. The coordinate plane below represents a town. Points A through F are farms in the town.
graph of coordinate plane. Point A is at negative 3, negative 4. Point B is at negative 4, 3. Point C is at 2, 2. Point D is at 1, negative 2. Point E is at 5, negative 4. Point F is at 3, 4.
Part A: Using the graph above, create a system of inequalities that only contains points A and E in the overlapping shaded regions. Explain how the lines will be graphed and shaded on the coordinate grid above. (5 points)
Part B: Explain how to verify that the points A and E are solutions to the system of inequalities created in Part A. (3 points)
Part C: Chickens can only be raised in the area defined by y < −2x + 4. Explain how you can identify farms in which chickens can be raised. (2 points)
Question 5. Tom has taken out a loan for college. He started paying off the loan with a first payment of $200. Each month he pays, he wants to pay back 1.2 times the amount he paid the month before, Explain to Tom how to represent his first 30 payments in sequence notation, Then explain how to find the sum of his first 30 payments, using complete sentences,
https://brainly.com/question/11874728 here is the answer! pls give brainliest
Answer:
Slope intercept form: The straight line equation is given by:
, .....[1] where m is the slope of the line.
(A)
Let x represents the number of hours and y represents the velocity of the runner.
As per the statement: After one hour, the velocity of the runner is 5 km/h. After three hours, the velocity of the runner is 3 km/h.
we have two points as (1, 5) and (3, 3)
Calculate first slope.
Formula for slope(m) is given by;
Then substitute the given values we get;
Now, substitute the value of m = -1 and (1, 5) in equation [1] we have;
Using distributive property:
Add both sides by 5 we get;
or
Therefore, an equation in two variables in the standard form that can be used to describe the velocity of the cyclist at different times is,
(B)
x y = 6 -x
1 5
2 4
3 3
4 2
5 1
Now, plot these points on the graph for the first 5 hours as shown below in the attachment.
Slope intercept form: The straight line equation is given by:
, .....[1] where m is the slope of the line.
(A)
Let x represents the number of hours and y represents the velocity of the runner.
As per the statement: After one hour, the velocity of the runner is 5 km/h. After three hours, the velocity of the runner is 3 km/h.
we have two points as (1, 5) and (3, 3)
Calculate first slope.
Formula for slope(m) is given by;
Then substitute the given values we get;
Now, substitute the value of m = -1 and (1, 5) in equation [1] we have;
Using distributive property:
Add both sides by 5 we get;
or
Therefore, an equation in two variables in the standard form that can be used to describe the velocity of the cyclist at different times is,
(B)
x y = 6 -x
1 5
2 4
3 3
4 2
5 1
Now, plot these points on the graph for the first 5 hours as shown below in the attachment.
Step-by-step explanation:
If Fred drives 50 miles per hour in his car, and this relationship Is graphed, which ordered palr would not be on the graph? (0,0) (4, 200) (2, 100) (5,300)
Answer:
The last one: 5,300
Step-by-step explanation:
200/4=50
100/2=50
300/5=60 when it supposed to be 50 since the graphing is 50mph
Hope this helps
(2,3)
(3,2)
(3,4)
(3,-2)
Answer:
(3,2)
Step-by-step explanation:
Right now point A is at the coordinates (3,2)
When you reflect the shape at line x = 3, point A is at the same x-axis, in which your supposed to reflect it on.
So when you reflect the shape, point A wont move, it will stay in the same colinear and coplanar plane which is (3,2)
use a number line to show the following operations (a) -5+7-2 (b) -4×3 (c) 3.5+4.5
Hey there!
• A.
–5 + 7 – 2 = ?
–5 + 7 = 2
2 – 2 = 0
Answer: 0 ☑️
• B.
–4 * 3 = ?
“Guide”
• Negative & Negative = Positive
• Positive & Positive = Positive
• Negative & Positive = Negative
• Positive & Negative = Negative
• So, in this particular equation your answer will most likely have a NEGATIVE result because you have a NEGATIVE number & a POSITIVE number!
–4 * 3 = –12
Answer: –12 ☑️
• C.
3.5 + 4.5 = ?
5 + 5 = 10
• CARRY your 1
3 + 4 + 1 = ?
3 + 4 = 7
7 + 1 = ?
Answer: 8 ☑️
You basically had to do ORDER OF OPERATIONS / PEMDAS
(Parentheses, Exponents, Multiplication, Division, Addition, and Subtraction)
Good luck on your assignment and enjoy your day!
~LoveYourselfFirst:)
Pls help extra points and mark brainlist
Rana and Josie are cooking food for a party they need to cut up the food so people can share your she makes two small pepperoni pizzas there are four people who was share the pizza how much will each person get
Answer:
sdfshefvhwedsbdhcfbHISE
Step-by-step explanation:
FSDSd
Which is the graph of y= -x + 2?
Answer:
Its A
Step-by-step explanation:
y intercept equal 2 so it must intersect at 2 on the y axis and it must go down because its a negative function
Convert each of these fractions into a percent.
a. 3/20 -
b. 1/20 -
c. 12/50 =
d. 80/200 =
e. 8/25 =
f. 8/10 =
g. 16/400 =
h. 24/300 =
i. 3/5 =
j. 3/2 =
k. 45/500 =
I. 30/25 =
Answer:
15%
5%
24%
40%
32%
80%
32%
54%
60%
66%
9%
89%
Step-by-step explanation:
Given the function g(x)=41x^3+a for some constant a, which describes the inverse function g^-1(x)
Answer:
[tex]g^{-1}(x)=\sqrt[3]{\frac{x-a}{41}}[/tex]
Step-by-step explanation:
The inverse of a function has [tex]x[/tex] and [tex]y[/tex] values switched from the original function. Therefore, simply switch [tex]x[/tex] and [tex]y[/tex] and isolate [tex]y[/tex] to get your inverse function:
Original function: [tex]g(x)=41x^3+a[/tex]
Switching [tex]x[/tex] and [tex]y[/tex], then isolating [tex]y[/tex]:
[tex]x=41y^3+a,\\x-a=41y^3,\\\frac{x-a}{41}=y^3,\\y=\sqrt[3]{\frac{x-a}{41}}[/tex].
Therefore, the inverse of the [tex]g(x)=41x^3+a[/tex] is:
[tex]\fbox{$g^{-1}(x)=\sqrt[3]{\frac{x-a}{41}}$}[/tex].
Find the Volume of the Grain Silo shown below that has a diameter of 20ft and a height of 40ft. Round your answer to the nearest hundredth . The top shape is a hemisphere and the bottom is a cylinder .
9514 1404 393
Answer:
14,660.77 ft^3
Step-by-step explanation:
The volume of a hemisphere-topped cylinder is given by the formula ...
V = πr^2(2/3r +h)
where r is the radius and h is the height of the cylindrical section. Of course, the radius is half the diameter, so this silo has a volume of ...
V = π(10 ft)^2(20/3 +40 ft) = 14,660.77 ft^3
__
Additional comment
The volume is 14,653.33 ft^3 if you use 3.14 for π.
Answer:14,660,77ft
Step-by-step explanation:
most of the time we ____ energy but it is everywhere around us
Answer:
waste
Step-by-step explanation:
Try to think of something that doesn't involve energy and you won't get very far. Even thinking—even thinking about energy!—needs some energy to make it happen. In fact, everything that happens in the world uses energy of one kind or another. But what exactly is energy?
Energy is a bit of a mystery. Most of the time we can't see it, yet it is everywhere around us. Revving car engines burn energy, hot cups of coffee hold energy, street lights that shine at night are using energy, sleeping dogs are using energy too—absolutely everything you can think of is using energy in one way or another. Energy is a magical thing that makes other things happen. Everything in the world is either energy or matter ("stuff" around us) and even matter, when you really get down to it, is a kind of energy!
PLEASE ANSWER THIS QUESTION FOR ME I WILL GIVE YOU BRAINLEST PLZ
Answer:
43/13 or 1.0769 = 1
Step-by-step explanation:
9y+3-4x-2y-3x-5 combine like terms
Answer:
7y-7x-2
Step-by-step explanation:
9y+3-4x-2y-3x-5
7y-7x-2
that a lot of points thx :)
you just add the numbers of the like terms togehter
Answer:
7y-2-7x
Step-by-step explanation:
Place these numbers in order from small to big. 35% , 36/100, 4/25, 0.85, 2.6, 0.1
Answer:
0.1, 4/25, 35%, 36/100, 0.85, 2.6
Step-by-step explanation: