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Given the functions f(x) = x² – 8 and g(x) = 4-x, determine the equation for the combined function
y=f(x) - g(x).
Answer:
[tex]y=x^2+x-12[/tex]
Step-by-step explanation:
f(x) = x² – 8 and g(x) = 4-x
y=f(x) - g(x)
y=(x² – 8) - (4-x)
[tex]y=x^2-8-4+x\\y=x^2+x-12[/tex]
Find parametric equations for the tangent line to the curve with the given parametric equations at the specified point. Illustrate by graphing both the curve and the tangent line on a common screen. x=t, y=e^-t, z=2t-t^2; (0, 1, 0)
Answer:
[tex]x = t[/tex]
[tex]y = 1 - t[/tex]
[tex]z = 2t[/tex]
Step-by-step explanation:
Given
[tex]x=t[/tex]
[tex]y=e^{-t}[/tex]
[tex]z=2t-t^2[/tex]
(0, 1, 0)
The vector equation is given as:
[tex]r(t) = (x,y,z)[/tex]
Substitute values for x, y and z
[tex]r(t) = (t,\ e^{-t},\ 2t - t^2)[/tex]
Differentiate:
[tex]r'(t) = (1,\ -e^{-t},\ 2 - 2t)[/tex]
The parametric value that corresponds to (0, 1, 0) is:
[tex]t = 0[/tex]
Substitute 0 for t in r'(t)
[tex]r'(t) = (1,\ -e^{-t},\ 2 - 2t)[/tex]
[tex]r'(0) = (1,\ -e^{-0},\ 2 - 2*0)[/tex]
[tex]r'(0) = (1,\ -1,\ 2 - 0)[/tex]
[tex]r'(0) = (1,\ -1,\ 2)[/tex]
The tangent line passes through (0, 1, 0) and the tangent line is parallel to r'(0)
It should be noted that:
The equation of a line through position vector a and parallel to vector v is given as:
[tex]r(t) = a + tv[/tex]
Such that:
[tex]a = (0,1,0)[/tex] and [tex]v = r'(0) = (1,-1,2)[/tex]
The equation becomes:
[tex]r(t) = (0,1,0) + t(1,-1,2)[/tex]
[tex]r(t) = (0,1,0) + (t,-t,2t)[/tex]
[tex]r(t) = (0+t,1-t,0+2t)[/tex]
[tex]r(t) = (t,1-t,2t)[/tex]
By comparison:
[tex]r(t) = (x,y,z)[/tex] and [tex]r(t) = (t,1-t,2t)[/tex]
The parametric equations for the tangent line are:
[tex]x = t[/tex]
[tex]y = 1 - t[/tex]
[tex]z = 2t[/tex]
Solve for 2.
Your answer must be simplified.
x + 5<-4
WALLAHI HELP ME PLEASE I BEG ANYONE THIS IS HARD
Answer:
D.(-3,-7)
Step-by-step explanation:
5x+8=-5x-22
5x+8+5x=-22
10x+8=-22
10x=-22-8
10x=-30
x=-30/10
x=-3
y=5x+8 x=-3
y=5(-3)+8
y=-7
How do i solve for x if (x+1)/(x+1)= 1/2?
Answer:
x= -1
Step-by-step explanation:
Given data
We have the expression as
(x+1)/(x+1)= 1/2
let us first cross multiply
2(x+1)=(x+1)
2x+2=x+1
collect like terms
2x-x=1-2
x= -1
Hence the value of x=-1
plz help find the volume of the cylinder plz
Answer:
V = 12π in³
General Formulas and Concepts:
Symbols
π (pi) ≈ 3.14Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightGeometry
Volume of a Cylinder Formula: [tex]\displaystyle V = \pi r^2h[/tex]
r is radiush is heightStep-by-step explanation:
Step 1: Define
Radius r = 2 in
Height h = 3 in
Step 2: Find Volume
Substitute in variables [Volume of a Cylinder Formula]: V = π(2 in)²(3 in)[Volume] Evaluate exponents: V = π(4 in²)(3 in)[Volume] Multiply: V = π(12 in³)[Volume] Multiply: V = 12π in³Imagine pls helpppppppp!!!!!!
Answer:
169,000
Step-by-step explanation:
Answer:
Step-by-step explanation:
This is exponential growth of form
y=ar^x where y is final amount, a=initial amount, r=common ratio or rate and x=time
y=130000(1.03^10)
y=174709
Mrs. Java invests $4000 at 10% annual return and $6000 al 12% annual return. How much should she invest at 15% return so that her total annual retum is 13% of the total amount she has invested?
Answer:
Step-by-step explanation:
Interpreting as: 6000
Input:
6000
Number line:
Number line
Number name:
six thousand
Roman numerals:
\!\(\("V"\)\&_\)M
Binary form:
1011101110000_2
Prime factorization:
2^4×3×5^3
Residues modulo small integers:
m | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9
6000 mod m | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 6
Properties:
6000 is an even number.
6000 is a number that cannot be written as a sum of 3 squares.
6000 has the representation 6000 = 3^5 5^2 - 75.
6000 divides 49^10 - 1.
Character code 6000:
| Tagbanwa letter sa
Unicode: U+1770 (decimal: 6000)
Mathematica: \:1770
(Tagbanwa)
A small rectangular tray measures 16 cm by 18 cm. How long is the diagonal?
Answer:
24.1cm
Step-by-step explanation:
A new microwave costs $126.99 at Walmart. How much sales tax would
you pay if the tax rate is 7%?*
$135.88
$8.89
$135.87
$8.88
Answer:
135.87
Step-by-step explanation:
7% of 126.99 is 8.8893
add 126.99 to 8.8893
you get ~135.87
Answer:
8.89
Step-by-step explanation:
Take the cost of the item times the tax rate to find the amount of tax
126.99 * 7%
Change to decimal form
126.99 * .07
8.8893
Round to the nearest cent
8.89
13x² -7x -8 how to solve this
Answer:
132x-8
Step-by-step explanation:
I think I might be wrong, but hopefully this is helpful, and yet I still find this confusing.
It's a simplification I don't know if you needed that.
What is the value of (f-g)(7)?
f(x)=2+x;g(x)=x^2+5
(f-g)(7)=[1]
Answer:
Alright so on this type of problem you just perform the operation they ask for, which in this case is subtraction.
Your first step will be to set up the problem:
f(x) - g(x)
Next you will substitute in your values:
(2x + 1) - (x2 - 7)
The easiest way to do the subtraction problems is to distribute your negative into your second set of parenthesis, so your expression would become:
2x + 1 - x2 + 7
Then combine your like terms:
2x - x2 + 8
Lastly put your expression in standard form (highest exponent to lowest)
-x2 + 2x + 8
Hope this helped!
Step-by-step explanation:
Can anyone help to answer my previous questions?
Step-by-step explanation:
Umm I can try. c:
I'll see....
A. 78
B. 87.5
C. 100
please answer will give brainliest!!!!!!!
Answer: 100
Mode is simply the number which appears most often.
100 is the only number that appears more than once
1a)Every morning, Jim goes for a morning walk. His normal walking speed is 3 1/2 km per hour, and he walks
a total distance of 10 km every day. How much time does he take to cover one km?
minutes
Answer
17 1/7
1b)How much time does it take him to complete his morning walk?
9514 1404 393
Answer:
17 minutes 8.6 seconds (17 1/7 min)2 hours 51 minutes 26 seconds (2 h 51 3/7 min)Step-by-step explanation:
The relationship between time, speed, and distance is ...
time = distance/speed
__
a) For 1 km, the time in hours is ...
time = (1 km)/(3.5 km/h) = 1/3.5 h = 2/7 h
In minutes, that is ...
(60 min/h)(2/7 h) = 120/7 min = 17 1/7 min . . . . time for 1 km
__
b) The time for 10 km is 10 times the time for 1 km, so will be ...
(10)(2/7 h) = 20/7 h = 2 6/7 h
In hours and minutes, that is 2 hours and (6/7)(60 min) = 360/7 min = 51 3/7 min.
The time for 10 km is 2 hours 51 3/7 minutes.
Find the missing side length of the triangle 10m 7.5m
Answer:
c = 12.5
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightEquality Properties
Multiplication Property of Equality Division Property of Equality Addition Property of Equality Subtraction Property of EqualityTrigonometry
[Right Triangles Only] Pythagorean Theorem: a² + b² = c²
a is a leg b is another leg c is the hypotenuseStep-by-step explanation:
Step 1: Identify
Leg a = 7.5
Leg b = 10
Hypotenuse c = c
Step 2: Solve for c
Substitute in variables [Pythagorean Theorem]: 7.5² + 10² = c²Rewrite: c² = 7.5² + 10²Evaluate exponents: c² = 56.25 + 100Add: c² = 156.25[Equality Property] Square root both sides: c = 12.5can someone help me with this simple 8th grade worksheet
3. Jenny bought 7 jackets and 10 winter hats. The jackets cost $8 dollars each, and the winter hats cost $4 each. Write an equation to show the total cost c, in dollars, of the items Jenny bought.
Answer:
7(8)+10(4)=c
Step-by-step explanation:
Hope this helped!
Which of the following systems has an infinite number of solutions?
A. x+y=1 and x−y=1
B. x+y=1 and x+y=−1
C. x+y=1 and −x−y=−1
D. x+y=1 and x+y=2
Answer:
C. x+y = 1 and -x-y = -1
Step-by-step explanation:
Remember that if a system of equations has an infinite number of solutions, then the resulting equation from using the first step of the elimination method would have no variables and would be true.
1) Let's try canceling out the equations in option C, x+y =-1 and -x-y =-1. Add the two equations together. (Work shown in attached picture.)
2) All of the terms cancel out with each other, leaving only a true statement of 0 = 0. Thus, option C is the answer.
Sam purchased 2 pairs of sneakers for $225 in
total. His father receives a military discount of
23%. How much were the price of the sneakers
after the discount?
Once the discount was deducted they added 7%
in sales tax. What was the final cost for the
sneakers?
help pleaseeee giving 100 points
Answer:
173.25
173.25+7=
$180.25
Step-by-step explanation:
Answer:
$185.38 i beileve. I took the discount out then added the tax
15 is ___% of 60 HELP YALL
Answer:
25
Step-by-step explanation:
Answer:25%
Step-by-step explanation:
1 + 1 + 23 + 77 +109 + 4568+ 32?
Answer:
4811?
Step-by-step explanation:
sorry if incorrect
In the coordinate plane, what is the distance between (-2, 5) and (8, 5) ?
Suppose that a survey was taken of 320 people and each person was asked if they approved or disapproved of the president's actions during the government shutdown. One hundred eighty people said that they approved. Which of the following statements correctly describes how the confidence interval for the population proportion of people that approved the President's actions during the government shutdown?
A) There are not 15 successes and 15 failures. A confidence interval can be computed by adding 2 successes and 2 failures.
B) There are not 15 successes and 15 failures. A confidence interval can be computed by adding 4 successes and 5 failures.
C) There are not 15 successes and 15 failures. A confidence interval can not be done.
D) There are at least 15 successes and 15 failures. A large sample confidence interval for the population proportion can be computed (phat +/- z * sqrt(p*(1-p)/n) with no additional values added.
Answer: I believe it’s C
Step-by-step explanation: I hope i’m right
find the GCF 40,50,60
Answer:
10
Step-by-step explanation:
Which equation is correct?
75 × 4 = 70 + 5 × 4
75 × 4 = 70 × 4 + 5 × 4
75 × 4 = 700 × 4 + 5 × 4
75 × 4 = 70 × 4 + 5
In a survey of 3417 adults aged 57 through 85 years, it was found that 80.3% of them used at least one prescription medication. C
a. How many of the 3417 subjects used at least one prescription medication?
Answer:
2743.851 adults aged 57 through 85 years used at least one prescription medication.
Step-by-step explanation:
I did this on a calculator so yeah...
nesecito ayuda para hacer el ejercico es para hoy!!!!! Un número se multiplica por 37 y al sumar los productos parciales resulta 7890. ¿Cuál es la suma de cifras del número
The slope of the line that passes through the point (2,4) and (3,8) is
Hi! Your answer is m = 4 or slope is 4.
Make sure to read an explanation for a better and clear understanding to your problem.
Any questions about my answer and explanation can be asked through comments! :)
Step-by-step explanation:
To find a slope of a line with given two coordinate points, we can do by using rise over run or slope formula which is:
[tex]\large\boxed{m=\frac{y_2-y_1}{x_2-x_1}}[/tex]
The boxed formula is the slope formula. The changes of y over the changes of x. This can be called "rate of change".
From (2,4) and (3,8). We substitute the given coordinate points in the formula.
[tex]\huge{m=\frac{8-4}{3-2}}\\\huge{m=\frac{4}{1}}\\\huge{m=4}[/tex]
Hence, the slope is 4.
Additional Note
m-term comes from y = mx+b where m is defined as slope in slope-intercept form. Therefore, m = slope.Hope this helps!
Line A has a slope of -4/3. Line B is perpendicular to Line A. What is the slope of Line B?
Answer:
The answer is 3/4
Step-by-step explanation:
If two lines in perpendicular, then the slope has a relation as slope1 * slope2 = -1. Then if line 1 has slope -4/3 then -4/3 * x = -1, then x = 3/4 which is the slope for the second line.