Horse = x = 1 head and 4 feet
Chicken =y = 1 head and 2 feet
Horse + chicken = x + y = 43 ( total heads)
Horse = 43 - y
4x + 2y = 122
4(43-y) + 2y = 122
Simplify:
172-4y + 2y = 122
Combine like terms
172-2y = 122
Subtract 172 from both sides
-2y = -50
Divide both sides by-2
Y = 25
X + y = 43
X + 25 = 43
X = 18
There are 18 horses and 25 chickens.
Determine the 1st and 2nd degree Taylor polynomials L(x,y) and Q(x,y) for
f(x, y) = tan^−1(xy) for (x, y) near the point (1,1).
Answer:
Step-by-step explanation:
[tex]f(x,y)=arctan(xy)\\\\\dfrac{ \partial f}{ \partial x}=\dfrac{y}{1+x^2y^2} \\\\\dfrac{ \partial f}{ \partial y}=\dfrac{x}{1+x^2y^2} \\\\\dfrac{ \partial ^2 f}{ \partial x^2}=\dfrac{-2xy^3}{(1+x^2y^2)^2} \\\\\dfrac{ \partial ^2 f}{ \partial y^2}=\dfrac{-2x^3y}{(1+x^2y^2)^2} \\\\\dfrac{ \partial ^2 f}{ \partial x\ \partial y}=\dfrac{1-x^2y^2}{(1+x^2y^2)^2} \\[/tex]
[tex]f(x,y)= f(1,1)+(x-1)\dfrac{\partial f}{\partial x} (1,1)+(y-1)\dfrac{\partial f}{\partial y} (1,1)+\dfrac{(x-1)^2}{2} \dfrac{\partial^2 f}{\partial x^2} (1,1)+(x-1)(y-1)\dfrac{\partial^2 f}{\partial x\ \partial y} (1,1)+\dfrac{(y-1)^2}{2} \dfrac{\partial^2 f}{\partial y^2} (1,1)+...\\\\=\dfrac{\pi}{4}+\dfrac{(x-1)}{2} +\dfrac{(y-1)}{2} -\dfrac{(x-1)^2}{4} +(x-1)(y-1)*\dfrac{0}{4}-\dfrac{(y-1)^2}{4} \\\\[/tex]
[tex]\boxed{f(x,y)=\dfrac{\pi}{4}+\dfrac{(x-1)}{2} +\dfrac{(y-1)}{2} -\dfrac{(x-1)^2}{4} -\dfrac{(y-1)^2}{4} }\\\\[/tex]
Find the equation of a line that contains the points (3,7) and (-6, 4). Write the equation in slope-intercept form, using
fractions when required.
Answer:
[tex]y=\frac{1}{3} x+6[/tex]
Step-by-step explanation:
[tex](3,7)(-6,4)[/tex]
Step 1. Find the slope (by using the slope-formula)
m = slope
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]m=\frac{4-7}{-6-3}[/tex]
[tex]m=\frac{-3}{-9}[/tex]
[tex]m=\frac{3}{9}[/tex]
[tex]m=\frac{1}{3}[/tex]
Step 2. Write the equation (using the slope and the points)
Here's how to do it:
Slope-intercept Formula [tex]y=mx+b[/tex] whrere m = slope and b = y-intercept
Plug in the slope into the Slope-intercept Formula
[tex]y=\frac{1}{3} x+b[/tex]
Find the y-intercept (b) by using a point and substituting their x and y values
[tex]y=\frac{1}{3} x+b[/tex]
Point: (3, 7)
[tex]7=\frac{1}{3} (3)+b[/tex]
[tex]7=1+b[/tex]
[tex]b=7-1[/tex]
[tex]b=6[/tex]
Step 3. Write the equation in Slope-intercept form
[tex]y=mx+b[/tex]
[tex]y=\frac{1}{3} x+6[/tex]
Select the correct answer.
Which statement best describes the zeros of the function () = (x-6)(X + 8x + 16)?
ОА.
The function has two distinct real zeros.
ОВ.
The function has three distinct real zeros.
OC. The function has one real zero and two complex zeros.
OD
The function has three complex zeros.
Answer:
So for the sequence to work, the 5,3=18 would have to be changed to 5,3=23 in which it now fits and works to solve for x which is 4. There was a pattern of the numbers 4 and 5 that surfaced as the difference between each pairings sum total. The difference between each sum was alternating between the numbers 4 and 5, which equal 9 when added together. Which also helped me to form a chart of sorts that makes sense. My answer is typed above, that is the most stable conclusion that I could come to to make sense of the pairings that were listed.
Answer: A (if i have well corrected)
Step-by-step explanation:
[tex]f(x)=(x-6)(x^2+8x+16)\ i\ suppose)\\\\f(x)=(x-6)(x+4)^2\\Sol=\{6;-4\}\\Answer \ A[/tex]
On my last birthday I weighed 180 pounds. One year later my weight was decreased by x pounds, write the expression that gives my weight one year later.
Which is the action to take?
A) Multiplication
B) division
C) subtraction
D) addition
Answer:
c
Step-by-step explanation:
The expression that gives my weight one year later is (180 pounds - x pounds). Hence the subtraction action that gives weight one year later.
Given that;
On my last birthday, I weighed 180 pounds.
And, One year later my weight decreased by x pounds.
Now the equation to represent the weighed after one year,
180 pounds - x pounds
Hence we can use the subtraction action that gives weight one year later.
Therefore, the correct option is C.
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Which features describe the graph? Select all that apply.
ту
14
-2
O
-2
domain: (-3,3]
Orange: (-3,4]
decreasing: (-1.4)
increasing: (-3,-1)
negative: (-3,-2), (2,5]
positive: (-2,2)
Answer:
Only Option III, IV, VI are correct
Step-by-step explanation:
Domain is the set of values of x at which the function is defined. f(x) has defined values from x>-3 to x<=4, so the domain is (-3,4). Incorrect.
Range of the function is the set of all defined values of it. Here all values with y=f(x)>-3 and y<=3 are defined. So the range is (-3, 3}.
Decreasing and increasing parts of the funtion are shown in the graph when the y value goes up (positive slope) and vice versa.
The negative part of the function should be (3,-2) and (2,4] since (4, 5] is not defined and there is no indication for its negative-ness.
let x^4+y^4=16 and consider y as a function of x. use the implicit differentiation to find y"
Answer:
[tex] \frac{dy}{dx} = - \frac{ {x}^{3} }{ {y}^{3} } [/tex]
Step-by-step explanation:
Differentiate both sides of the equation (consider y as a function of x).
[tex] \frac{d}{dx} ( {x}^{4} + {y}^{4} (x)) = \frac{d}{dx} (16)[/tex]
the derivative of a sum/difference is the sum/difference of derivatives.
[tex]( \frac{d}{dx} ( {x}^{4} + {y}^{4} (x))[/tex]
[tex] = ( \frac{d}{dx} ( {x}^{4} ) + \frac{d}{dx} ( {y}^{4} (x)))[/tex]
the function of y^4(x) is the composition of f(g(x)) of the two functions.
the chain rule:
[tex] \frac{d}{dx} (f(g(x))) = \frac{d}{du} (f(u)) \frac{d}{dx} (g(x))[/tex]
[tex] = ( \frac{d}{du} ( {u}^{4} ) \frac{d}{dx} (y(x))) + \frac{d}{dx} ( {x}^{4} )[/tex]
apply the power rule:
[tex](4 {u}^{3} ) \frac{d}{dx} (y(x)) + \frac{d}{dx} ( {x}^{4} )[/tex]
return to the old variable:
[tex]4(y(x) {)}^{3} \frac{d}{dx} (y(x)) + \frac{d}{dx} ( {x}^{4} )[/tex]
apply the power rule once again:
[tex]4 {y}^{3} (x) \frac{d}{dx} (y(x)) + (4 {x}^{3} )[/tex]
simplify:
[tex]4 {x}^{3} + 4 {y}^{3} (x) \frac{d}{dx} (y(x))[/tex]
[tex] = 4( {x}^{3} + {y}^{3} (x) \frac{d}{dx} (y(x)))[/tex]
[tex] = \frac{d}{dx} ( {x}^{4} + {y}^{4} ))[/tex]
[tex] = 4( {x}^{3} + {y}^{3} (x) \frac{d}{dx}(y(x))) [/tex]
differentiate the equation:
[tex]( \frac{d}{dx} (16)) = (0)[/tex]
[tex] = \frac{d}{dx} (16) = 0[/tex]
derivative:
[tex]4 {x}^{3} + 4 {y}^{3} \frac{dy}{dx} = 0[/tex]
[tex] \frac{dy}{dx} = - \frac{ {x}^{3} }{ {y}^{3} } [/tex]
write 45 as a product of prime numbers
Answer:
3²×5
Step-by-step explanation:
Product of its prime numbers its more like having the number in its simplest form by factorising it
13. State the restrictions
and then simplify
8x2 +14x-49 /
2x²+x-21
Answer:
Whenever the denom is 0, that's where it's undefined -- or in your case "restrictions"
So factoring 2x^2 + x - 21 gets you (x-3)(2x+7). That means 3 and -7/2 are the restricted values.
To simplify, I'm going to factor it. (Assuming what you wrote is 8x^2 for the numerator)
[(4x-7)(2x+7)] / (x-3)(2x+7)
You can cancel 2x+7 out,
so you get 4x-7/x-3
what is the arithmetic sequence of a1=228 n=28 sn=2982
Answer:
use the formula sn= n(a1+an)/2
Step-by-step explanation:
2982=28(228+an)/2
5964=28(228+an)
5964/28=228+an
213=228+an
an=-15(last term)
to find difference use formula
an = a+(n-1)d
-15=228+(28-1)d
-243=27d
d=-243/27
d=-9
arithmetic sequence can be found be keep on subtracting 9 from 228
hence the arithmetic sequence is
228, 219, 210, 201, 192, 183, 174........-15
(01.02 MC)
The distance, d(t), in feet, a bug has traveled is shown in the graph.
A coordinate plane with a function d of t consisting of a line starting at 0 comma 1 rising to 1 comma 2, a horizontal line from 1 comma 2 to 2 comma 2, a line falling from 2 comma 2 to 3 comma 1, and a line falling from 3 comma 1 to 6 comma 0.
Estimate the rate of change in the distance of the bug at time t = 4 seconds.
negative one third ft/s
the limit as t approaches 4 of the function d of t feet per second
d(4) ft/s
0.7 ft/s
When we have a given function f(x), the rate of change in a given value x₀ is given by:
[tex]\frac{df(x_0)}{dx} = \lim_{h \to 0} \frac{f(x_0 + h) - f(x_0)}{h}[/tex]
We will find that the rate of change at t = 4s is:
r = -1/3
Now we can't do this if we do not have the function and we only have a text description of the graph, but what we can do is find the average rate of change.
For a function f(x), the average rate of change in an interval (a, b) such that a < b is given by:
[tex]r = \frac{f(b) - f(a)}{b - a}[/tex]
Something really nice is that the average rate of change is equal to the exact rate of change if f(x) is a linear equation.
If we want to find the rate of change at t = 4, then we need to find the smallest interval that contains t = 4.
Here we know that the graph passes through the points:
(3,1) to (6, 0)
Because of the statement "a line falling from (3, 1) to (6, 0)" we know that in this segment we have a line, which implies that the average rate of change will be equal to the exact rate of change.
Using the equation of the average rate of change we get:
[tex]r = \frac{d(6) - d(3)}{6 - 3} = \frac{0 - 1}{3} = - 1/3[/tex]
Then the rate of change in the distance at the time t = 4s is -1/3.
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Write the following number in
scientific notation.
0.05796
[? ][ ]
Answer:
[tex]0.05796 = 5.796 \times {10}^{ - 2} [/tex]
I hope I helped you^_^
Answer:
Step-by-step explanation:
Scientific notation is always written as a number between 1 and 9.999999. The number after the decimal is shown by a power of 10.
so 0.05796 = 5.796 * 10^-2
which means that the decimal was moved to represent a number less than one. That's the point of the minus sign. The two comes from the number of places you have to shift the decimal to get a number between 1 and 10.
True or False
No links
Answer:
False
Brainliest, please!
Step-by-step explanation:
+ + = +
- - = +
+ - = -
- + = -
Answer:
False
Step-by-step explanation:
The question doesn't specify whether you are adding positive or negative integers. If you have add 2 positive integers, your answer will be positive. If you add 2 negative integers, the answer will be negative. Here is an example;
1 + 1 = 2
-1 + (-1) = -1 - 1 = -2
Best of Luck!
what is four fifteenths times two thirds?
Answer:
Try 0.17? I hope it's right
Answer:
2 10/15 or 2 2/3 (simplified)
Step-by-step explanation:
To Multiply we need to get the same denominator for each fraction:
2 x 5 =10
3 x 5 =15
10/15
4/15 x 10/15 (or) 4 x 10 = 40/15
40/15 (also) = 2 10/15
2 2/3 (simplified version of 2 10/15)
Hope This Helps! :)
Pls answer this question! I will mark as brainliest!!!
Answer:
1/8
Step-by-step explanation:
There is a 1/2 probability for each of the three flips to result in the desired outcome. To get 3 desired outcomes in a row, we multiply each of the probabilities together
(1/2)³ = 1/8
Answer: it is D) 2/3
What do these have in common??
Answer:
They can all be simplified to 2/3
need help in math!!!
Answer:
(3,15)
Step-by-step explanation:
Rule 1
5x = y
Rule 2
x+12 = y
Set them equal
5x = x+12
Subtract x from each side
5x-x = x+12-x
4x= 12
Divide by 4
4x/4 = 12/4
x=3
5x=y
5*3 = y
15 = y
The solution is (3,15)
Given rules
y=5xy=x+12Equate and solve
5x=x+124x=12x=3Opt ion B is correct as no other contains 3 as x
This car traveled 3 miles per 1 min. Tell me how far the car will travel at 6 mins. Use a table to show your work .
Answer:
min | miles
———|———
1 | 3
2 | 6
3 | 9
4 | 12
5 | 15
6 | 18
Step-by-step explanation:
try putting this into a T-chart like I kind of did here or some other kind of other table.
Integer rules:
When adding Integers with the same sign you
Add,subtract,multiply
them and keep the sign.
When adding integers with different signs you
Add,subtract,multiply
them and keep the sign of the bigger number.
To make subtracting integers easler, you can change all subtraction problems to
Word,multiplication,addition
problems.
SUBTRACT. -18- (-12)
O
30
O
6
Answer: -6
Step-by-step explanation:
-18 - (-12)
= -6
none of them
it's actually-6.
Which expression is equivalent to 6x+8 + x+15
There are 12 girls and 14 boys in class today. What is the ratio of girls
to boys? whats the answer
Answer:
12:14
Step-by-step explanation:
1.6 lbs. = __ gal
how many gallons are in 1.6lbs?
Find the area and the circumference of a circle with radius 7 ft.
Answer:
Area is 307.72 ft^2
Circumference is 43.96 ft
Step-by-step explanation:
Area is 2pir^2
Circumference is 2rpi
pi is about 3.14
A=2pi(7)^2
A= 98pi which is about 307.72 ft^2
C= 2(7)pi
C= 14pi which is about 43.96 ft
(I'm not sure whether they want the answer left in terms of pi or not)
-3x - 4 = 11 is which property of equality?
Answer:
x= _5 is the correct answer
2
1,0,0.2, 73, 7.9, 136
3
9.736
a. List all the natural numbers from the given set.
What numbers are natural today
Answer:
1,2,73,and 136
Step-by-step explanation:
hope this helps
mark me as brainliest plz
ANSWER PLEASE NO FAKE ANSWERS ILL GIVE BRAINLIEST: Jaxson did the following problem incorrectly. Choose the option that correctly identifies what Jaxson did
wrong
Jaxson's work: 8 3/5 + 7 1/8 = 15 4/3
1. Jaxson forgot to simplify his answer.
2. Jaxson should have changed the mixed numbers to improper fractions.
3. Jaxson added the denominators instead of finding a common denominator and leaving it alone,
4. Jaxson did not make a mistake. He did everything right.
Answer:
3. Jaxson added the denominators instead of finding a common denominator and leaving it alone
Step-by-step explanation:
8 3/5 + 7 1/8 = 15 4/3
Get a common denominator
8 3/5 *8/8 + 7 1/8 *5/5
8 24/40 + 7 5/40
15 29/40
12 63 x 42 is equivalent to 216 x 16. True or False?
Answer:
False
Step-by-step explanation:
63 x 42= 2646
216 x 16= 3456
have a great day
what is the ratio 0.6:2.4 written in simplest form
Answer:
1:4
Step-by-step explanation:
multiply both sides by 10 to get whole numbers which will be 6:24. then divide by the GCF which is 6 and you get 1:4
Find the area of the shaded region.
Step-by-step explanation:
find the area of the big semicircle and the small semicircle.minus the area of the small semicircle from the big semicircle.
now find the area of the other semicircle on top of the big semicircle.
add your results
area of semicircle=1/2(pir^2)
Note: Enter your answer and show all the steps you use to solve this problem in the space provided. 6 × 5 + 3 × 8
Make it simple, please
Answer:
54
Step-by-step explanation:
6x5=30
3x8=24
30+24=54