Answer:
the equations are dependent; both describe the line y = 2x -6
Step-by-step explanation:
Remove the common factor of 5 from the first equation and you have ...
2x -6 = y
Subtract 6 from the second equation and you have ...
2x -6 = y
The two equations are the same, so describe the same line. The solution set is all points on that line. The equations are dependent, and have an infinite number of solutions.
Solve the initial-value problem. x' + 2tx = 5t, x(0) = 8 x(t) =
Multiply both sides of the ODE
[tex]x'+2tx+5t[/tex]
by [tex]e^{t^2}[/tex]:
[tex]e^{t^2}x'+2te^{t^2}x=5te^{t^2}[/tex]
Now the left side can be condensed as the derivative of a product:
[tex]\left(e^{t^2}x\right)'=5te^{t^2}[/tex]
Integrate both sides, then solve for x :
[tex]e^{t^2}x=\dfrac52e^{t^2}+C[/tex]
[tex]\implies x(t)=\dfrac52+Ce^{-t^2}[/tex]
Given that x(0) = 8, we find
[tex]8=\dfrac52+Ce^0\implies C=\dfrac{11}2[/tex]
so that the particular solution to this IVP is
[tex]\boxed{x(t)=\dfrac{5+11e^{-t^2}}2}[/tex]
Solve for the variables: 3x-4y=17 x-4y=3
Answer:
[tex]3x - 4y = 17ndx - y = 3 \\ 3x - x - 4y + 44y = 17 - 3 \\ 3x - x = 17 - 3 \\ 2x = 17 - 3 \\ 2x = 14 \\ x = 7 \\ \\ 7 - 4y = 3 \\ - 4y = - 4 \\ y = 1[/tex]
Answer:
x = 7
y = 1
Step-by-step explanation:
3x - 4y = 17
x - 4y = 3
Solve x in the second equation.
x = 3 + 4y
Put x as 3 + 4y in the first equation and solve for y.
3(3 + 4y) - 4y = 17
9 + 12y - 4y = 17
9 + 8y = 17
8y = 17 - 9
8y = 8
y = 8/8
y = 1
Put y as 1 in the second equation and solve for x.
x = 3 + 4(1)
x = 3 + 4
x = 7
Help!!! Type SSS, SAS, ASA,
AAS, or HL to justify
why the two larger
triangles are congruent.
DB = CA
its congruent by HL or RHSaxiom
Answer:
HL
Step-by-step explanation:
[tex] In\: right \triangle 's DAB \: \&\: CBA\\
\angle DAB \cong \angle CBA... (each 90\degree) \\ hypotenuse \: DB \cong hypotenuse \: CA. (given) \\
side AB \cong side BA.. (common) \\
\therefore \triangle DAB \cong \triangle CBA.. (By \: RHS\: or \: HL \: Postulate) [/tex]
Solve for w. 5w + 9z = 2z + 3w
Answer:
w = -7z/2
Step-by-step explanation:
Our goal is to isolate w
1. subtract 3w from both sides to get 2w+9z = 2z
2. Subtract 9z from both sides to get 2w = -7z
3. Divide both sides by 2 to get w = -7z/2
We cannot simplify further, so this is our answer.
If (x^2 – 4) = (x + 2) = x - 2, which polynomial should fill in the blank below?
Hey there! :)
Answer:
2nd choice. (x - 2)
Step-by-step explanation:
Given in the question:
(x²-4) ÷ (x + 2) = x-2
This is an example of difference of squares.
We can rearrange the equation by multiplying both sides by (x+2) to become:
(x² - 4) = x - 2 (x + 2)
Therefore, the binomial that must be multiplied by (x+2) is the second choice, x-2.
Answer: B
Step-by-step explanation:
HELP ON THIS QUESTION PLEASE
Answer:
slope is m=1. y-intercept is -1
Answer:
Slope is 1 and intercept is -1. Slope can be found by taking the rise and run of 2 points on a graph. and intercept is just when x = 0
The height of the triangle is
The base of the triangle is
The area of the triangle is
Answer:
The height of triangle is 12cm.
The base of triangle is 25 cm.
The area of triangle is 150cm².
Step-by-step explanation:
Given that the area of triangle is Area = 1/2×base×height. So you have to substitute the values into the formula :
[tex]area = \frac{1}{2} \times base \times height[/tex]
[tex]let \: base = 25 \\ let \: height = 12[/tex]
[tex]area = \frac{1}{2} \times 25 \times 12[/tex]
[tex]area = \frac{1}{2} \times 300[/tex]
[tex]area = 150 \: {cm}^{2} [/tex]
Help me Please, i will give you branliest
Answer:
35/42 = b/7 and b= 35/6
Step-by-step explanation:
Our base is unkhown so it will be the variable in our equation :
Let A be the area , h the height and b the base A = b*h 35/42 = b/7 this is the equation , let's solve it (35*7)/42 = b (35*7)/ 7*6 =b 35/6 = bso b is 35/6 cm
What is the answer? X=
Answer:
5
Step-by-step explanation:
[tex] \because \triangle ACB \cong \triangle DCE... (given) \\
\therefore \angle A \cong \angle D... (c.a.c.t)\\
\therefore m\angle A = m\angle D\\
\therefore 50\degree = 10x\\\\
\therefore x = \frac{50\degree}{10}\\\\
\huge \orange {\boxed {\therefore x = 5\degree}} [/tex]
Does this table represent a function? Why or why not?
х
y
0
4
7
8
5
5
8
8
10
9
A. No, because two of the y-values are the same.
B. Yes, because there are two x-values that are the same,
C. Yes, because every x-value corresponds to exactly one y-value.
D. No, because one x-value corresponds to two different y-values.
Answer:
no because one x value corresponds to two different y values
Which shapes have the same volume as the given rectangular prism?
base area = 50 cm^2
Answer:The first one
Step-by-step explanation:
V rectangular prism = Area of the base *5
whats the square root of 83
Answer:
9.110434
Step-by-step explanation:
√83 ≈ 9.110434
Identify the parent function that can be used to graph the function/(x) = 471-3.
a. f(x) = x
c. f(x) = x
b. f(x) - [x]
d. f(x) -11
What would be the slope of the positions (3,3) and (4,5)
Answer:
m = 2
Step-by-step explanation:
Slope Formula: [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Simply plug our coordinates into the slope formula and solve for m:
m = (5 - 3)/(4 - 3)
m = 2/1
m = 2
Answer:
2Step-by-step explanation:
Let the points be A and B
A( 3 , 3 ) -----> ( x1 , y1 )
B(4 , 5 ) ------>( x2 , y2 )
Now,
finding the slope,
Slope =[tex] \frac{y2 - y1}{x2 - x1} [/tex]
[tex] = \frac{5 - 3}{4 - 3} [/tex]
[tex] = \frac{2}{1} [/tex]
[tex] = 2[/tex]
Hope this helps...
Good luck on your assignment..
520 after a 30% increase
Answer:
676
Step-by-step explanation:
Convert the percentage to a decimal.
30% = 0.3
Multiply the number by the decimal.
520 × 0.3 = 156
Add this number by the number given.
520 + 156 = 676
Write a number with 2 decimal places, that is bigger than 4 and 1/5 but smaller than 4.25?
Answer: 4 wholes and 1/5 is 4.20 and you need something greater than that but less than 4.25 which still has only 2 decimals.
Pls help me with my geometry guys
Answer:
(1,1)
Step-by-step explanation:
x=1
y=1
6(1) + 1=7
6+1=7
Answer:
x=1, y=1
Step-by-step explanation:
Micah mixed 5 ounces of yellow paint with 11 ounces of blue paint. What is the ratio of blue paint to the total amount of paint that Micah used? Write the ratio using a colon and no spaces.
Answer: 11:16
Step-by-step explanation: 11 ounces of blue paint: the total number ounces of paint (adding blue and yellow)
Answer:
5:16
Step-by-step explanation:
The amount of blue paint is 5 oz
The total amount of paint is 16 oz
Make these numbers a ratio of blue to total
A girl loves to receive mail, but only 5% of the family's letters are addressed to her. The recipient of each letter is independent of all other letters. Find the mean number of letters received by other members of the family prior to her receiving her second letter.
Answer:
Negative Binomial
Step-by-step explanation:
The girl receives only 5% of mail which are addressed to her. Rest of 95% mails belong to other family members.
P (X) = 5%
P (X) = 95 / 5
P (X) = 19
The family receives 19 mails out of which only 5% will address the girl. The all other mails belong to the other family members.
Evaluate. Write your answer as a fraction or whole number without exponents. 9^–3 =
Answer:
[tex]\frac{1}{9^3}[/tex] or [tex]\frac{1}{729}[/tex]
Step-by-step explanation:
When we have an exponent that is a negative, it is the same thing as 1 over the positive exponent. So, we move 9^-3 into 1/9^3 and then we evaluate the exponent to get our answer.
write the number name for 6782163 in international system
Answer:
Six Million Seven Hundred Eighty Two Thousand one hundred sixty three
Step-by-step explanation:
Hope it helps...Pls Mark as Brainliest!!
Answer:
Six Million Seven Hundred Eighty Two Thousand One Hundred and Sixty Three.
Step-by-step explanation:
6, 782, 163
I NEED HELP PLEASE ASAP!!!
Answer:
see below
Step-by-step explanation:
There are a couple of ways to go about this.
The general form of a conic equation is ...
Ax^2 +Bxy +Cy^2 +Dx +Ey +F = 0
For AC > 0, this is the equation of an ellipse or circle. (AC < 0, hyperbola; AC = 0, parabola)
So, from the coefficients of the given equation, AC = 2·5 = 10, you know the equation is of an ellipse.
__
The rotation matrix for Cartesian coordinates tells you ...
x = x'·cos(θ) +y'·sin(θ)
y = -x'·sin(θ) +y'·cos(θ)
For θ = 45° the values of these trig functions are all (√2)/2. That is, there is no way to get coefficients in the rotated equation that involve √3. This eliminates choice 2.
The only remaining viable choice is choice 4.
__
If you like, you can substitute for x and y using the above relations. You will find that the result differs from any of the answer choices. The rotated figure will have the equation ...
[tex]5x^2-6xy+9y^2+10\sqrt{2}x+2\sqrt{2}y-80=0[/tex]
For example, the x and y terms become ...
[tex]6x-4y=6(x'\cos{(45^{\circ})}+y'\sin{(45^{\circ})})-4(-x'\sin{(45^{\circ})}+y'\cos{(45^{\circ})})\\\\=10x'\dfrac{\sqrt{2}}{2}+2y'\dfrac{\sqrt{2}}{2}\\\\\text{Multiplying this by 2 gives $\dots$}\\\\10x'\sqrt{2}+2y'\sqrt{2}[/tex]
Note that this is not the 10√2x' -10√2y' shown in choice 4.
__
Another way to look at this is to look at the angle of rotation relative to alignment with the x- and y-axes. That angle α is given by ...
cot(2α) = (A -C)/B
For the original ellipse, the rotation angle is ...
α = arccot((2 -5)/2)/2 ≈ -16.85°
For the transformed ellipse of choice 4, the rotation angle is ...
α = arccot((9 -5)/6)/2 ≈ 28.15°
This is 45° more*, as it should be, indicating choice 4 is the better of the offered choices.
__
If you do the angle calculation for the 2nd answer choice, you will find it has no relation to a 45° rotation of the original ellipse.
_____
* While the computed rotation angle is as expected, the fact that the x^2 and y^2 coefficients have been swapped means that the long and short axes of the ellipse have been swapped. That is, the long axis of the ellipse has been rotated 45° in the wrong direction by the equation given in the answer choices. The second attachment shows the original ellipse (red), the properly rotated ellipse (dashed red) and the ellipse of choice 4 (blue).
Robert uses a wheelbarrow to haul wood from the back yard to his neighbor's house located 9 meters away. If he takes two breaks evenly when pushing the wheelbarrow to its destination, at which distance will he reach his first break?
Robert has 36 pieces to take, but can only take 9 each time. What distance in meters will he travel to move all the wood?
Answer:
3 meters
63 meters
Step-by-step explanation:
In order for his two breaks to occur after even distances, simply divide his total path in three:
[tex]B = \frac{9}{3}\\ B=3\ meters[/tex]
He will reach his first break after 3 meters.
If he can only take 9 pieces at a time the number of trips required is:
[tex]n=\frac{36}{9}\\ n=4[/tex]
Note that he will have to back to the back yard for the first three trips (traveling back the 9 meters path). The total distance traveled is:
[tex]d= 3*(9+9)+9\\d=63\ meters[/tex]
He will travel 63 meters.
How many square feet of outdoor carpet will we need for this hole?
Answer:
9.
Step-by-step explanation:
You would have to find the area of the triangle which is 1/2(bh) which would give you 9. So you would 9 feet of outdoor carpet. Which is actually already given to you as the area inside the triangle.
Answer:
9
Step-by-step explanation:
I finally got it!
please simplify this
Answer:
(√77) / 22
Step-by-step explanation:
To rationalize the fraction we must multiply the entire fraction by √11 / √11. Note that the 2 is not important because it's not a radical. This gives us √77 / 22.
Are 2b+ b and 3b equivalent expressions?
Answer:
yes
Step-by-step explanation:
2b+b=3b because2+1 = 3
Answer:
the answer is yes
Step-by-step explanation:
yes it is equivalent expression because 2b+b and 3b have the same value and length or numerator which equals yes.
Work out percentage change to 2 decimal places when price of 97 is decreased to 90
Answer:
7.22?
Step-by-step explanation:
What is 4 2/3 ÷ 1 1/5
Answer:
3 8/9
Step-by-step explanation:
1.) Convert each fraction from a mixed number to a improper fraction (to do that multiply the denominator with the whole number then add the numerator, the improper fraction denominator will remain the same as the mixed number denominator):
14/3 ÷ 6/5
2.) Solve
a. To divide the fractions, Flip the reciprocal, and multiply the fractions
14/3 x 5/6
b. Check if you can reduce the numbers, which you can 14 and 6 can be both divided by 2:
7/3x5/3
c. Multiply fractions (simply by multiplying across):
35/9
3.) Simplify numbers into mixed fraction (or decimal):
3 8/9
The average college major requires 34 credit hours to complete, with a standard deviation of 3 hours. A college's academic advisors conduct a study to see how many credit hours a sample size of 50 students will need to take to complete their majors. They calculate:μx= μ = 34and σx= μ /√n =34/√50=4.81What did they do wrong?
The question is incomplete! Complete question along with answer and step by step explanation is provided below.
Question:
The average college major requires 34 credit hours to complete, with a standard deviation of 3 hours. A college's academic advisors conduct a study to see how many credit hours a sample size of 50 students will need to take to complete their majors.
They calculate:
μx = μ = 34
σx = μ/√n = 34/√50 = 4.81
What did they do wrong?
Answer:
The sample mean will be the same as the population mean
μx = μ = 34
Whereas the standard deviation of the sample would be
σx = σ/√n
σx = 3/√50
σx = 0.424
Therefore, the college's academic advisors wrongly calculated the standard deviation of the sampling distribution.
Step-by-step explanation:
From the given information we know that,
The population mean is
μ = 34 credit hours
The population standard deviation is
σ = 34 credit hours
The college's academic advisors take a sample size of 50 students so
sample size = n = 50
Since the sample size is quite large then according to the central limit theorem,
The sample mean will be the same as the population mean
μx = μ = 34
Whereas the standard deviation of the sample would be
σx = σ/√n
σx = 3/√50
σx = 0.424
Therefore, the college's academic advisors wrongly calculated the standard deviation of the sampling distribution.
Evaluate the following:
Answer:
csc∅ = 25/7
sec∅ = 25/24
cot∅ = 24/7
Step-by-step explanation:
Cosecant (csc) is 1/sin∅ or hypotenuse over opposite
Secant (sec) is 1/cos∅ or hypotenuse over adjacent
Cotangent (cot) is 1/tan∅ or adjacent over opposite