What's the slope of the line through (1,3) and (-2,-3)
Answer:
m = 2
The slope of the line through (1, 3) and (-2, -3) is 2!
The formula to find the slope is attached below.
Hope I was of help. Have a good new year!
A customer's entire breakfast bill is $8. If the customer pays the server for the entire bill plus a 25% tip, what is total amount the customer pays?
A. $6
B. $10
C. $20
D. $32
Answer:
10
Step-by-step explanation:
I am confused on how to solve this. NOTE: the lower limit for the second function is (-6) NOT 6. Wouldn't let me type it in correctly.[tex]\int\limits^6_3 {|x-4|} \, dx + \int\limits^0_6 {\sqrt{36-x^2} } \, dx[/tex]
I think how you approach this depends on your knowledge of calculus.
If you don't know how to compute definite integrals yet, but you do know that they represent signed areas under curves, then you can plot both curves |x - 4| and √(36 - x ²), then recognize that the areas represented by these integrals are areas of geometric shapes. (See attached images)
First integral: if you plot |x - 4| on the interval [3, 6], you'll see that the integral corresponds to the area of two triangles. One of them has base = height = 1, and the other has base = height = 2. Then
[tex]\displaystyle\int_3^6|x-4|\,\mathrm dx=\frac12\times1\times1+\frac12\times2\times2=\frac52[/tex]
Second integral: if [tex]y=\sqrt{36-x^2}[/tex], then [tex]x^2+y^2=6^2[/tex], meaning this curve is the upper half of a circle with radius 6. On the interval [-6, 0], the area amounts to 1/4 of the total area of such a circle, so that
[tex]\displaystyle\int_{-6}^0\sqrt{36-x^2}\,\mathrm dx=\frac{\pi\times6^2}4=9\pi[/tex]
* * *
If you already know a few things about calculus and integration, you can compute these areas directly.
First integral:
[tex]\displaystyle\int_3^6|x-4|\,\mathrm dx=\int_3^4(4-x)\,\mathrm dx+\int_4^6(x-4)\,\mathrm dx[/tex]
[tex]\displaystyle\int_3^6|x-4|\,\mathrm dx=\left(4x-\frac{x^2}2\right)\bigg|_{x=3}^{x=4}+\left(\frac{x^2}2-4x\right)\bigg|_{x=4}^{x=6}[/tex]
[tex]\displaystyle\int_3^6|x-4|\,\mathrm dx=\left(\left(4\times4-\frac{4^2}2\right)-\left(4\times3-\frac{3^2}2\right)\right)+\left(\left(\frac{6^2}2-4\times6\right)-\left(\frac{4^2}2-4\times4\right)\right)[/tex]
[tex]\displaystyle\int_3^6|x-4|\,\mathrm dx=\frac52[/tex]
Second integral:
Substitute x = 6 sin(t ) and dx = 6 cos(t ) dt, then
[tex]\displaystyle\int_{-6}^0\sqrt{36-x^2}\,\mathrm dx=\int_{-\frac\pi2}^0\sqrt{6^2-(6\sin(t))^2} (6\cos(t))\,\mathrm dt[/tex]
[tex]\displaystyle\int_{-6}^0\sqrt{36-x^2}\,\mathrm dx=36\int_{-\frac\pi2}^0\cos (t) \sqrt{1-\sin^2(t)} \,\mathrm dt[/tex]
[tex]\displaystyle\int_{-6}^0\sqrt{36-x^2}\,\mathrm dx=36\int_{-\frac\pi2}^0\cos (t) \sqrt{\cos^2(t)} \,\mathrm dt[/tex]
[tex]\displaystyle\int_{-6}^0\sqrt{36-x^2}\,\mathrm dx=36\int_{-\frac\pi2}^0\cos (t) |\cos(t)| \,\mathrm dt[/tex]
For t ∈ [-π/2, 0], cos(t ) > 0, so |cos(t )| = cos(t ) :
[tex]\displaystyle\int_{-6}^0\sqrt{36-x^2}\,\mathrm dx=36\int_{-\frac\pi2}^0\cos^2(t)\,\mathrm dt[/tex]
Recall the half-angle identity,
cos²(t ) = (1 + cos(2t )) / 2
[tex]\displaystyle\int_{-6}^0\sqrt{36-x^2}\,\mathrm dx=18\int_{-\frac\pi2}^0(1+\cos(2t))\,\mathrm dt[/tex]
[tex]\displaystyle\int_{-6}^0\sqrt{36-x^2}\,\mathrm dx=18\left(t+\frac{\sin(2t)}2\right)\bigg|_{t=-\frac\pi2}^{t=0}[/tex]
[tex]\displaystyle\int_{-6}^0\sqrt{36-x^2}\,\mathrm dx=18\left(\left(0+\frac{\sin(2\times0)}2\right)-\left(-\frac\pi2+\frac{\sin\left(2\times\left(-\frac\pi2\right)\right)}2\right)\right)[/tex]
[tex]\displaystyle\int_{-6}^0\sqrt{36-x^2}\,\mathrm dx=9\pi[/tex]
The graph of a linear function iS shown.
Which word describes the slope of the line?
positive
negative
zero
undefined
Find the slope on the line.
Answer: -2 is the slope
(0,0) (1,4) (rise over run) *Y2 - Y1/X2 - X1*
X1= 0
Y1= 4
X2= 1
Y2= 2
2-4= -2
1-0= 1
-2/1= -2
the slope is -2
1. Luis went to the bank. He deposited
$20 into his savings account and
withdrew $40 from his checking
account. Write integers to describe
both transactions.
54 1/2-42 3/4
45 3/8- 13 3/4
Answer:
11 3/4
31 5/8
Step-by-step explanation:
1. 54 1/2 - 42 3/4
= 109/2 -171/4
= 218-171/4
= 47/4
= 11 3/4
2. 45 3/8 - 11 3/4
= 363/8 -55/4
= 363-110/8
= 253/8
= 31 5/8
PLS help i've been trying this for an hour i still don't get it
PLS HELP
WILL GIVE BRAINIEST
The points plotted below are on the graph of a polynomial. Which of the
following x-values is the best approximation of a root of the polynomial?
Check all that apply.
A. X-1.1
B. X= 4.3
C. x=2.4
D. X=6
E.X=1
Answer:
I don't know the answer but have a site that helps me with math, its called
Step-by-step explanation:
Just check it out
John is comparing his workers’ production for the day. The ratios of items produced to time in hours are shown. Worker Items Production Ratio James 12 : 3
Charlie 7 : 2 Michael 14 : 2 Fred 16 : 4 Which two workers have equivalent ratios?
Whats 4 5/6 + 5 7/8 thank you for answering
Answer:
4 5/6 + 5 7/8= 10 17/24
Step-by-step explanation:
pretty sure I answered this exact question like minutes ago
Answer: 257/24, or 10 and 17/24.
Step-by-step explanation:
First, we need to turn the fractions into improper fractions and then find the common denominator.
4 and 5/6 = 29/6
5 and 7/8 = 47/8
The common denominator is 24. Now, we convert the fractions and add. Hope this helps!
Patty's pet puppy, Oreo, liked to lie down on a small carpet by the door. The
carpet was 1 { feet long and 3 feet wide. What is the perimeter of the
carpet?
Can someone please help meee
Answer:
20
Step-by-step explanation:
Because this angle is 90 and we have 70
What is the slope and y-intercept of the line whose equation is y + 4x =
8?
Answer:
The slope is -4 and the y-intercept is 8.
Step-by-step explanation:
y+4x=8
y=8-4x
y=-4x+8
y=mx+b where m=slope and b=y-intercept.
Hello!
The equation of this line is written in slope-intercept form (y=mx+b)
Where
m is the slope
b is the y-intercept
m is 4
b is 8
Hope it helps!
If you have any questions, feel free to ask! :)
~An excited gal
[tex]MagicalNature[/tex] here to help
You roll a number cube twice. What is the probability of rolling a 2 first and then rolling an odd number?
A) 1/12
B) 1/36
C) 1/4
D) 1/9
А_______is part of the population chosen to
represent the entire group.
Answer:
mean.
Step-by-step explanation:
since this is a math question i'm assuming you want a mathematical term. the mean of a set of data represents the entire set of data.
factorise ab+cb+ad+cd
Answer:
ab=a×b
cb=c×b
ad=a×d
cd=c×d
Answer:
well the factor: Add and subtract the second term to the expression and factor by grouping. (a+c)(b+d)
Step-by-step explanation:
Hope this is helpful! God Bless you !
Prove that the recurring decimal 0.43333... has the value 13/30
Answer:
0.43ᵣ = 0.1 + 0.33ᵣ = 1/10 + 1/3 = 3/30 + 10/30 = 13/30
The expression 0.43333... is equivalent to the fraction number 13/30. And it is proved below.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
x = 0.43333......
Multiply the equation by 10 on both sides, then we have
10x = 10 × 0.43333......
10x = 4.33333...... ...1
Multiply the equation by 100 on both sides, then we have
100x = 100 × 0.43333......
100x = 43.33333...... ...2
Subtract equation 1 from equation 2, then we have
100x - 10x = 43.3333.... - 4.3333.....
90x = 39
x = 39 / 90
x = 13 / 30
The expression 0.43333... is equivalent to the fraction number 13/30. And it is proved below.
More about the Algebra link is given below.
https://brainly.com/question/953809
#SPJ2
There has been a great deal of controversy over the last several years regarding what types of surveillance are appropriate to prevent terrorism. Suppose a particular surveillance system has a 96% chance of correctly identifying a future terrorist and a 99.8% chance of correctly identifying someone who is not a future terrorist. If there are 1,000 future terrorists in a population of 200 million, and one of these 200 million is randomly selected, scrutinized by the system, and identified as a future terrorist, what is the probability that he/she actually is a future terrorist
Answer:
0.9976 = 99.76% probability that he/she actually is a future terrorist
Step-by-step explanation:
Conditional Probability
We use the conditional probability formula to solve this question. It is
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
In which
P(B|A) is the probability of event B happening, given that A happened.
[tex]P(A \cap B)[/tex] is the probability of both A and B happening.
P(A) is the probability of A happening.
In this question:
Event A: Person identified as a future terrorist
Event B: Person is actually a future terrorist.
Probability that a person is identified as a future terrorist:
96% of [tex]\frac{1000}{200000000}[/tex]
100 - 99.8 = 0.2% of [tex]\frac{200000000-1000}{200000000}[/tex]
So
[tex]P(A) = 0.96\frac{1000}{200000000} + 0.002\frac{200000000-1000}{200000000} = 0.002[/tex]
Probability of being identified and being a future terrorist:
100 - 99.8 = 0.2% of [tex]\frac{200000000-1000}{200000000}[/tex]
[tex]P(A \cap B) = 0.002\frac{200000000-1000}{200000000} = 0.00199999[/tex]
What is the probability that he/she actually is a future terrorist
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.00199999}{0.00200479} = 0.9976[/tex]
0.9976 = 99.76% probability that he/she actually is a future terrorist
Before dividing, decompose 420 to make it easier to divide by 4.
true or false help please pre cal
Answer:
True
Step-by-step explanation:
Hi, which one is the correct answer? thank you
Answer:
Step-by-step explanation:
tan B=372/279=(31×12)/(31×9)=12/9=4/3
Plz help I will give you 40 points and Brainly
Answer:
D) {-5,1}
R) {-4,7}
x (-31/11,0)
y (0,31/6)
Hope this helped! Have a nice day! Plz mark as brainliest!!! :D
-XxDeathshotxX
Simplify the expression 10 + 2(n + 5) + 4n
Answer:
6n + 20
Step-by-step explanation:
10 + 2n + 10 +4n
6n +20
Answer:
[tex]10 + 2n + 10 + 4n \\ 6n + 20 \\ 2(3n + 10)[/tex]
How many chicks hiding? Explain how you know.
If h(x) = sqrt 7 + 6f(x), where f(3) = 7 and f '(3) = 4, find h'(3).
Answer:
we should find the value of h(3) and do invers
Help me please i will give brainliest
Answer:
1. C. x^8
2. C. 3^9
3. D. 12x^7
Step-by-step explanation:
1.
x^6 * x^2 = x^(6 + 2) = x^8
Answer: C. x^8
2.
3^2 * 3^3 * 3^4 = 3^2 + 3 + 4) = 3^9
Answer: C. 3^9
3.
3x^2 * 4x^5 = 3 * 4 * x^2 * x^5 = 12x^(2 + 5) = 12x^7
Answer: D. 12x^7
The number 7,945 rounded to the nearest hundred is 7,950.
True
False
Answer:
false, it would be 8,000
I don't understand this math problem, please help
Answer/Step-by-step explanation:
1. <A = <B (alternate angles theorem)
90° = 2x (substitution)
Divide both sides by 2
90/2 = 2x/2
45 = x
x = 45
2. <3 = <5 (corresponding angles theorem)
½x = 60 (substitution)
Multiply both sides by 2
x = 60*2
x = 120
3. Based on supplementary bangle theorem, sum of supplementary angles = 180°. Therefore:
m<LFG + m<ABC = 180°
2.5x + x + 33 = 180 (substitution)
Add like terms
3.5x + 33 = 180
3.5x = 180 - 33
3.5x = 147
x = 147/3.5
x = 42
3a. m<LFG = 2.5x
Plug in the value of x
m<LFG = 2.5(42)
m<LFG = 105°
3b. m<ABC = x + 33
Plug in the value of x
m<ABC = 42 + 33
m<ABC = 75°
Can someone help with these questions?
¿Alguien puede ayudar con estas preguntas?
9514 1404 393
Answer:
63/94$6857.14Step-by-step explanation:
a) The fraction is ...
2(5 1/4)/(15 2/3) = (21/2)/(47/3) = 63/94
Two streamers will require 63/94 of the original material.
__
b) $4800 is 70% of Sara's salary, so that salary is ...
4800 = 0.70s
4800/0.70 = s = 6857.14
Sara's salary is about $6857.14.