The function is f(x) = x³ − 4x² + 2.
How to find the slope?The slope of a line or straight object is the ratio of how much amount of rise occurs in correspondence to the increment in the run.
Find the difference between the y coordinates, Δy is change in y.Find the difference between the x coordinates, Δx is change in x.Divide Δy by Δx to find slope.As,
Slope = rise/ run
Given:.
f(x) = x³ − 4x² + 2
As a line passing through the same point that f(x) passes through at x = 3 with a slope equal to the limit.
Then the slope of the function is given by the differentiation.
slope= d/dx [f(x)]
slope= d/dx ( x³ − 4x² + 2)
slope= 3x² - 8x
slope= 3* 3* 3 -8*3
slope= 27-24
slope= 3
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Write (b^3)^2 without exponents
Answer:
(b)(b)(b)(b)(b)(b)
Step-by-step explanation:
[tex](b^3)^2=b^6[/tex]
(b)(b)(b)(b)(b)(b)
Answer:
Step-by-step explanation:
(b^3)^2
= b^(3*2)
= b^6
= b*b*b*b*b*b.
Complete part (a) and part (b) given the following system of equations x-y=0 2x + 3y = -5 Solve this system graphically.
Answer:
(-1, -1)
Step-by-step explanation:
x - y = 0 ------> x = y
2x + 3y = -5
2(y) + 3y = -5
5y = -5
y = -1
x - (-1) = 0
x = -1
The solution to this system is (-1, -1). To solve graphically, plot both functions and you will see that they intersect at (-1, -1).
I hope this helps!
Katie baked a cake. Her brother ate 1/8 of the cake, her father ate 1/4 of the cake, and her mother ate 1/8 of the cake. How much is left?
Answer:
1/2
Step-by-step explanation:
hope this helps and have a nice day!
Solve for x: 3 (square root2-2x)+1=13
Answer:
x=7
Step-by-step explanation:
3√(2-2x) + 1 = 13
subtract 1 from both sides
3√(2-2x) = 12
Divide 3 from both sides
√2-2x= 4
square both sides
2-2x = 16
subtract 2 from both sides
2x= 14
x=7
(-24uy^2+19u^3y^5)/(-3u^3y^5)
Simplify
Answer:
8/(u^2y^3) -19/3
Step-by-step explanation:
The relevant rules of exponents are ...
(a^b)/(a^c) = 1/a^(c-b)
a^0 = 1
__
Your expression can be simplified like this:
[tex]\dfrac{-24uy^2+19u^3y^5}{-3u^3y^5}=\dfrac{24uy^2}{3u^3y^5}-\dfrac{19u^3y^5}{3u^3y^5}=\boxed{\dfrac{8}{u^2y^3}-\dfrac{19}{3}}[/tex]
Which will usually always be a higher amount?
A. Compound interest
B. Time
C. Debit
D. Simple interest
PLEASE HELP!!!!! I"LL MARK AS BRAINLIEST!!!Tom conducted a drawing competition at school. He bought 5 boxes of colored pencils and spent $5.25 on drawing paper. However, more contestants entered than he expected, and he had to buy 2 more boxes of colored pencils. The total cost of the paper and pencils was $82.95. Identify the equation and solution that would help to find the cost of each box of pencils.
A. 5x + 2x + 5.25 = 11.10; $82.95
B. 5x − 2x + 5.25 = 82.95; $11.10
C. 5x − 2x + 5.25 = 82.95; $1.11
D. 5x + 2x + 5.25 = 82.95; $11.10
HELP QUICK PLEASE!!!
Answer:
19
please make this answer brainliest If I helped you!
Answer:
c=19
Step-by-step explanation:
110-91=19
129-110=19
148-129=19
4x19 = 76 (91-76=15)
76+15 =91
5x19= 95 ( 110-95=15)
95+15= 110
6x19 = 114 (129-114 =15)
114+15=129
7x19=133 ( 148-133 =15)
133+15 = 148
Cole is buying a pair of sneakers. The expression shown represents the sales tax on the price of the sneakers, p.
0.045p
Write an expression in terms of p to represent the total amount Cole spends on the pair of sneakers, including tax.
By direct addition, we will see that the expression is:
T = 1.045*P.
What expression represents the total price of the sneakers?
We know that the price of the sneakers is P. We also know that the expression which represents the taxes of the sneakers is 0.045*P.
Now, we can assume that the total price of the sneakers will be the price plus the correspondent tax, then we can write:
T = P + 0.045*P = (1 + 0.045)*P = 1.045*P
This is the expression that represents the total amount Cole spends on the pair of sneakers.
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Nathaniel had $40 to spend on 9 beakers for his science class. After buying them, Nathaniel had $4 left. How much did each of the beakers cost?
Answer:
each baker cost $4
Step-by-step explanation:
4 times 9 is 36, and that leaves 4
Q10. Consider the following algorithm:
g_1 = 9
g_2 = 5
Git
For k starting at 0 and ending with 8:
gk = (k-1)*gk-1 + gk-2
What is the last term, 8, of the recursive sequence generated as a result of
executing this algorithm?
Answer:
61,940
Step-by-step explanation:
For a recursive sequence of reasonable length, it is convenient to use a suitable calculator for figuring the terms of it. Since each term not only depends on previous terms, but also depends on the term number, it works well to use a spreadsheet for doing the calculations. The formula is easily entered and replicated for as many terms as may be required.
__
The result of executing the given algorithm is shown in the attachment. (We have assumed that g_1 means g[-1], and that g_2 means g[-2]. These are the starting values required to compute g[0] when k=0.
That calculation looks like ...
g[0] = (0 -1)×g[-1] +g[-2} = (-1)(9) +5 = -4
The attachment shows the last term (for k=8) is 61,940.
Simplify the polynomial then evaluate for x=-1 3x^2-4+2x-1+x^2
Answer:
-3
Step-by-step explanation:
Simplified polynomial: 4x^2 + 2x - 5
Plug in -1: 4(-1)^2 + 2(-1) - 5
= -3
1 Whatis the value ofthe expression y 1/2 +z)+6 ( 2 + when y= 2 and 7 = 3 ? 4
.A) 57/8
.B) 19/2
.C) 17/2
.D) 22/3
30 BRAINLY points plus user!!!
2(1/2+3/4)+6=
17/2 or 8.5
The answer is C
Answer:
Option C
Step-by-step explanation:
Given:
[tex]y = 2[/tex]
[tex]z = \dfrac{3}{4}[/tex]
Substitute the values into the expression:
⇒ y(1/2 + z) + 6
⇒ 2(1/2 + 3/4) + 6
Make common denominators in the parenthesis:
⇒ 2(1/2 + 3/4) + 6
⇒ 2(2/4 + 3/4) + 6
Simplifying the expression:
⇒ 2(5/4) + 6
⇒ 2 × 5/4 + 6
**Keep in mind that multiplication first, then addtion
⇒ 10/4 + 6
Make common denominators:
⇒ 10/4 + 24/4
⇒ 34/4
Simplify the fraction:
⇒ 17/2 (Option C)
y = x^2 + 8x + 10
Vertex:
Axis of Symmetry:
Y-intercept:
The vertex of the function is (-4, -6), the axis of symmetry is x= -4 and the y-intercept is (0, 10).
What is the function?Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.
The given function is y=x²+8x+10.
Rewrite in vertex form and use this form to find the vertex (h, k).
(-4, -6)
The axis of symmetry is x= -4
To find the x-intercept, substitute in 0 for y and solve for x. To find the y-intercept, substitute in 0 for x and solve for y.
x-intercept(s): (-4+√6, 0), (-4-√6, 0)
y-intercept(s): (0, 10)
Therefore, the y-intercept is (0, 10).
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Making auto parts A grinding machine in an auto
parts plant prepares axles with a target diameter
p = 40.125 millimeters (mm). The machine has
some variability, so the standard cleviation of tlic
diameters is a = 0.002 mm. The machine operator
inspects a random sample of 4 uxles cach hour for
quality control purposcs and records llic sample
mcan diameter 1. Assuming that the process is work-
ing properly, what are the mean and standard devia I
fion of the sampling distribution of ? Explain.
Answer: See below
Step-by-step explanation:
Mean:
Since the sample is taken from a large population it follows the central limit theorem, which states that the sample mean is approximately equal to the population mean.
Therefore: [tex]\bold{\bar{X}=\mu=40.125}[/tex]
Standard Deviation:
Again by central limit theorem the standard deviation of the sample is calculated as:
[tex]S=\frac{\sigma}{\sqrt{n}}[/tex]
Since n=4, therefore
S = 0.001
Find the area and the circumference of a circle with radius 9 ft.
Use the value 3.14 for pie, and do not round your answers. Be sure to include the correct units in your answers.
Answers:
Area = 254.34 square feet
Circumference = 56.52 feet
=========================================================
Work Shown:
Area = pi*(radius)^2
A = pi*r^2
A = 3.14*9^2
A = 254.34 square feet
----------------
Circumference = 2*pi*(radius)
C = 2*pi*r
C = 2*3.14*9
C = 56.52 feet
The two results are approximate since pi = 3.14 is approximate.
1st area of circle:
[tex]\bold{\ area \ of \ circle \ : \pi r^2}[/tex]
[tex]\hookrightarrow \sf (3.14)(9)^2[/tex]
[tex]\hookrightarrow \sf 254.34 \ ft^2[/tex]
2nd circumference of circle:
[tex]\bold{circumference \ of \ circle \ : \ 2\pi r}[/tex]
[tex]\hookrightarrow \sf 2(3.14)(9)[/tex]
[tex]\hookrightarrow \sf 56.52 \ ft[/tex]
area of circle = 254.34 ft²circumference of a circle = 56.52 ftA student performed the following steps to find the solution to the equation x^2 + 14x + 40 = 0. Where did the student go wrong?
Step 1. Factor the polynomial into (x + 4) and (x + 10)
Step 2. x + 4 = 0 or x + 10 = 0
Step 3. x = -4 or x = 10
A. In step 3
B. The student did not make any mistakes, the solution is correct
C. In step 1
D. In step 2
Answer:
A. in Step 3
Step-by-step explanation:
It is factored correctly. Then separated into two smaller equations correctly. But in solving x + 10 = 0, there is an error.
x + 10 = 0
Add -10 to both sides.
x = -10
So, the error is in step 3.
Answer:
A . In Step 3.
Step-by-step explanation:
In step 3 the student went wrong
x = 4 or x = -10 is correct
( if x + 10 = 0, then x = -10)
5>x/5
Show all work in steps
Answer:
[tex]\boxed{\sf{x < 25}}[/tex]Step-by-step explanation:
To find the value of x, isolate it on one side of the equation.
5>x/5First, you have to switch sides.
→ x/5<5
Then, you multiply by 5 from both sides.
→ 5x/5<5*5
Solve.
Multiply the numbers from left to right.
→ 5*5=25
→ x<25
Therefore, the solution is x<25, which is our answer.I hope this helps you! Let me know if my answer is wrong or not.
Answer:
25 > x
Step-by-step explanation:
[tex]5 > \frac{x}{5}[/tex]
To find the value of x, you have to multiply both sides by 5.
[tex]5*5 > \frac{x}{5}* 5[/tex]
[tex]25 > \frac{5x}{5}[/tex]
[tex]25 > x[/tex]
$600 invested at 6% compounded annually for six years
Answer:
The final balance is $851.11.
The total compound interest is $251.11.
Step-by-step explanation:
I will give Brainliest! :<
This meal costs $75.00.
Fatima used a 20% off coupon and then tax was added.
The total after the coupon and tax was $75.00.
What was the tax rate?
Submit and EXPLAIN, please!
Answer:
25 %
Step-by-step explanation:
75 - 20% = 60
60 + 60 (x) = 75 where x = tax rate
x = .25 or 25 %
Write an equation in slope-intercept form of the line shown.
An equation is
Answer:
y = 3/4x - 1
Step-by-step explanation:
m = (1-4)/(4-8) = -3/-4 = 3/4
b = (0, -1)
y = mx + b
y = 3/4x - 1
BRAINLIEST please if this helps!Business mathematics.
Mr Kula opens a shopfront where he will lend money to anyone ( without security) if they are willing to pay his interest rate of 2% per week compounded daily. The first customer borrows $5000 to buy a used car, but is unable to pay Mr Kula back for 12 weeks. How much will the customer have to pay back at this time?
Answer:
$6200
Step-by-step explanation:
2% of $5000 = $100
So that's a hundred dollars per week
12 weeks x $100 = $1200
$5000 (The original amount the first customer borrowed)
+ $1200 (The interest rate)
= $6200
(P.S. Please give me a brainliest if you can)
if the cos 30° = sqrt 3/2, then sin 60° =
a. 0
b. 1/2
c. sqrt of 3 /2
d. 1
Answer:
C
Step-by-step explanation:
it's well known that the value of sin60 is sqrt 3/2
it's also the same as cos 30
Simplify the expression. –(3)–4
a)12
b)[tex]-\frac{1}{81}[/tex]
c)81
d)[tex]\frac{1}{81}[/tex]
Answer:
Answer is {C}
Step-by-step explanation:
I am a polygon that has two pairs of opposite sides that are parallel what am I
A Parallelogram because it is a quadrilateral with 2 pairs of parallel sides!
please help me Find m< G
Answer:
70°
Step-by-step explanation:
All angles in a kite equal 360°.∠F≅∠H. 360-(90+90+110) will get you the answer.
What's the difference between arithmetic and geometrical sequence with examples please.
Answer:
An arithmetic sequence has a constant difference between each consecutive pair of terms. This is similar to the linear functions that have the form y=mx+b. A geometric sequence has a constant ratio between each pair of consecutive terms. This would create the effect of a constant multiplier.
-- Credit -- libretexts
Hope this helps! Please let me know if you need more help or think my answer is incorrect. Brainliest would be MUCH appreciated. Have a wonderful day!
Answer:
An arithmetic sequence is a sequence with the difference between two consecutive terms constant. The difference is called the common difference. A geometric sequence is a sequence with the ratio between two consecutive terms constant. This ratio is called the common ratio.
Step-by-step explanation:
Matthew plays basketball for his high school. On average, he scores 33 points per game, with a standard deviation of 2 points. What percentage of basketball games will result in Matthew scoring less than 27 points?
Note: Assume that a Normal model is appropriate for the distribution of points.
Matthew will score less than 27 points in about 0.15% of his basketball games.
=======================================================
Explanation:
mu = 33 = population mean
sigma = 2 = population standard deviation
Let's find the z score when x = 27
z = (x - mu)/sigma
z = (27-33)/2
z = -6/2
z = -3
A score of 27 points is exactly three standard deviation units below the mean of 33 points.
Now refer to the Empirical Rule chart shown below. Notice that roughly 99.7% of the entire population is within 3 standard deviations of the mean. This is the span from z = -3 to z = 3.
That leaves about 100% - 99.7% = 0.3% left over for the two tails combined.
One tail has about (0.3%)/2 = 0.15% of the total area, and therefor about 0.15% of the total games will have Matthew scoring less than 27 points. This is an estimate of course.
To get a more accurate answer, you can use a Z table to find that
[tex]P(Z < -3) \approx 0.00135 \approx 0.135\%[/tex]
which isn't too far off from the 0.15%
Answer:
I believe is the correct answer
Step-by-step explanation:
a
Directions: Type the correct answer in each box. Spell all words correctly, and use numerals instead of words for numb
For this problem any non-integer answers should be entered as fractions in simplest form using / as the fraction bar(s).
A spinner has five colored sections of different sizes. Felicia spins the arrow on the spinner and records the color of the section it
lands on in the table below.
Complete the statements based on the given table.
The experimental probability of landing on orange is__
The experimental probability of landing on___is 1/5
The experimental probability of landing on a color that is not blue is___
Answer:
1/3, Yellow, 3/4
Step-by-step explanation:
All the numbers add up to 60, so using fractions
Red is 11/60
Green is 2/60
Yellow is 12/60
Blue is 15/60
Orange is 20/60
Finding The probability of w/o blue is subtracting 15 from 60 which ends as 45/60, and simplifying that would be 3/4
The probabilities by subject of on-time assignment submission and on-time arrival in class are given in the table. Subject On-time Assigment Submission On-time Arrival in Class Physics 89.7% 82.3% Math 88.2% 88.7% Chemistry 89.4% 83.1% Biology 90.1% 82.4% Total 88.5% 84.7% What is the probability of on-time arrival in class given that the subject is biology? A. 90.1% B. 88.5% C. 84.7% D. 82.4% E. insufficient data
The probability of on-time arrival in class given that the subject is biology is, 82.4%.
What is mean by Probability?The term probability refers to the likelihood of an event occurring. Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one.
Given that;
The probabilities by subject of on-time assignment submission and on-time arrival in class are given in the table.
Here, the table is,
Subject: On-time Assignment: On-time Arrival to Class:
PHYSICS 89.7% 82.3%
MATH 88.2% 88.7%
CHEMISTRY 89.4% 83.1%
BIOLOGY 90.1% 82.4%
TOTAL 88.5% 84.7%
Now, from table;
The probability of on-time arrival in class given that the subject is biology is, 82.4%.
Hence, the probability of on-time arrival in class given that the subject is biology is, 82.4%.
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