To go on a summer trip, Kareem borrows 400$. He makes no payments until the end of 4 years when he pays off the entire loan. The lender charges simple interest at an annual rate of 6%.
If a system of two linear equations has no solutions, which of the following statements describes the graph of the two corresponding lines in the xy-plane?
a. The lines are coinciding
b. The lines intersect at only one point
c. The lines are parallel
d. The lines are perpendicular
Explain why you picked your answer:
From the linear equation, the option that describes the graph of the two corresponding lines is C. The lines are parallel.
Based on the complete information, it should be noted that the lines are not coinciding and they don't intersect at only one point.
Rather, it can be deduced that the graph of the two corresponding lines in the xy-plane are parallel.
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The temperature at the point (x, y, z) in space is given by T ( x, y, z) = x + yz. A fly is at the point (1, 2, 1). In what direction should he begin to fly to cool off as quickly as possible. Your answer should be a unit vector in the requested direction.
Answer:
[tex]u= -\frac{1}{\sqrt{6}} ,-\frac{1}{\sqrt{6}} ,-\frac{2}{\sqrt{6}}[/tex]
Step-by-step explanation:
From the question we are told that
Temperature is given [tex]T ( x, y, z) = x + yz.[/tex]\
A fly is at (1,2,1)
Generally the direction of fly is given by
[tex]\triangleT(x,y,z) =(1,z,y)\\[/tex]
[tex]v= \triangleT(1,2,1)\\v=(1,1,2)[/tex]
Mathematically solving for the vector direction
[tex]|v|=\sqrt{1^2+1^2+2^2}[/tex]
[tex]|v|=\sqrt{6}[/tex]
[tex]u=- \frac{v}{|v|}[/tex]
[tex]u= -\frac{1}{\sqrt{6}} ,-\frac{1}{\sqrt{6}} ,-\frac{2}{\sqrt{6}}[/tex]
Therefore this the direction which should be taken to cool down soonest
Salena has twice as many DVDs as Jolene,and Jolene has one third as many as Brodie.What fraction of the total DVDs has Salena?
Answer:
let jolene's dvd be x
2x+x+3x= total dvds = 6x
2x/6x=1/3
Salena has 1/3 of the total dvds
Use proportional reasoning to determine the value of a in the proportion shown below.
a=1
a=25
a=10
a=15
Answer: a = 10
Step-by-step explanation:
3/5 = a + 5/25
Multiply both sides by 25 to get rid of it:
3/5 * 25 = 25(a + 5) /25
15 = a + 5
a = 15 - 5
a = 10
Over the period of a year, Sam's net worth increased. Which of the following could be true?
a. Sam's assets and liabilities decreased by the same amount.
b. Sam's assets and liabilities increased by the same amount.
C. Sam's assets increased by more than his liabilities.
d. Sam's assets decreased by more than his liabilities.
Please select the best answer from the choices provided
A
B
D
Mark this and retun
Save and Exit
Submit
Please give me the answer to this it's due at 8:00
Answer: 20
Step-by-step explanation:
Answer:
Each metal sheet costs 18 dolares per square foot
Step-by-step explanation:
7.6x−2.3x= $95.40
simplify
5.3x = $95.40
/5.3
x = 18
The price of a video game was reduced from 60 to 45 . By what percentage was the price of the video game reduced
Answer:
The price was reduced from $60 to $45 - So the price was reduced by $15. $15 is what percent of the original price of $60? Percentages can be expressed as fractions or decimals. For example, 30% is the same as 0.30 or 30/100.
Convert the expression to exponential form
4.4.4.4.4
Answer:
4^5 (the 5 is the exponent)The exponential form of expression is 4⁵.
What is exponential form?To grow at an ever-increasing rate is referred to as exponential growth. On the other hand, it is a mathematical expression with one or more exponents in mathematics. As a result, we call it an exponential form.
We can say that something might grow at an exponential rate if it grows faster and faster as the thing being discussed gets bigger.
Given expression
4.4.4.4.4
Writing a number as the product of its prime factors is the very first step in expressing it in exponential form.
number is in factors
4 x 4 x 4 x 4 x 4
a numerical term that has been increased to certain powers of its prime factors
= 4⁵
where 5 is exponent.
Hence the exponential form is 4⁵.
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HELP EDG 2020!!!!
Which half of the unit circle satisfies the trigonometric inequality cos Ø >0? Assume that ø is the angle made by the
positive x-axis and a ray from the origin.
O the top half
O the bottom half
O the right half
O the left half
Answer:
the right half
Step-by-step explanation:
We know that cosine is a pair function.
This means that:
Cos(a) = Cos( -a)
We also know that:
Cos(pi) = 0
then:
Cos(-pi) = 0
pi and -pi are located in the y-axis, so from this we can know that the cosine function will be always positive on the right side, or in the left side, we can discard the other two options.
Now, we also know that cos(0) = 1.
And:
-pi < 0 < pi
So the two zeros are at the y-axis, and we know that cos(0) is positive (the angle 0 would be on the positive side of the x-axis, at the right), then all the right side must be positive.
Then the correct option is:
the right half
Answer:
C - The right half
Step-by-step explanation:
Just took the quiz on edge
find the zeros of the function: f(x)=3x^2-5x+3
Answer:
x = 5 ± i √ 11 /6
Step-by-step explanation:
The roots (zeros) are the x values where the graph intersects the x-axis. To find the roots (zeros), replace y with 0 and solve for x .
i need help with a function
Answer:
one: 9
Two: D
Step-by-step explanation:
One
The symbol used is x≥8 so 8 is included in the function part. That would mean that F(x) = 9
Two
The value you need to use is -4x + 3. That's because -2≤x and the symbol ≤ makes - 2 inclusive.
-4(-2) + 3 = 8 + 3 = 11
3a
The function is decreasing over -4x + 3
It goes from 11 to -29 roughly. That means it's going from a positive to negative number. Definitely decreasing
3b
The function is a constant when x≥8. The value of the function is 9 no matter what x is.
3c
The function is increasing from - 2x to 8 which is going from -9 to 11
please help!!!! find x and y
9514 1404 393
Answer:
(x, y) = (10, 2)
Step-by-step explanation:
The upper angle marked with an expression in x and y is supplementary to the angle marked 70°. The lower angle marked with an expression in x and y is an alternate interior angle with respect to the one marked 70°, is equal to that. This gives the two equations in x and y:
6x +10y +30 = 110
4x +10y +10 = 70
Subtracting the second equation from the first gives ...
2x +20 = 40
x +10 = 20 . . . . . divide by 2
x = 10 . . . . . . . . . subtract 10
Substituting into the second equation gives ...
4(10) +10y +10 = 70
4 + y + 1 = 7 . . . . . . . . divide by 10
y = 2 . . . . . . . . . . . . . . subtract 5
The values of x and y are 10 and 2, respectively.
Answer:
9514 1404 393
Step-by-step explanation:
Please help me asap
Answer:
She walked 1.5 miles, then 0.75 miles. Hence 1.5 + 0.75= 2.25 or 2 and 1/4 a mileIs (1, 3) a solution to the system of equations listed below? (1 point) y= 6x -3 y = x - 2
Answer:
The solution for given system of equation is: [tex]x=\frac{1}{5}\:and\:y=\frac{-9}{5}[/tex] and ordered pair is: [tex]\mathbf{(\frac{1}{5},\frac{-9}{5})}[/tex]
So, (1,3) is not solution to the given system of equations.
Step-by-step explanation:
we can solve the system of equations to find the value of x and y and then verify if (1,3) is a solution or not.
The system of equation given is:
[tex]y=6x-3\\y=x-2[/tex]
Solving:
Let:
[tex]y=6x-3--eq(1)\\y=x-2--eq(2)[/tex]
Put value of y from equation 2 into equation 1
[tex]y=6x-3\\Put\:y=x-2\\x-2=6x-3\\x-6x=-3+2\\-5x=-1\\x=\frac{-1}{-5}\\x=\frac{1}{5}[/tex]
Now, put value of x in equation 2 to find value of y
[tex]y=x-2\\Put\:x=\frac{1}{5} \\y=\frac{1}{5} -2\\y=\frac{1-2*5}{5} \\y=\frac{1-10}{5}\\ y=\frac{-9}{5}[/tex]
So, the solution for given system of equation is: [tex]x=\frac{1}{5}\:and\:y=\frac{-9}{5}[/tex] and ordered pair is: [tex]\mathbf{(\frac{1}{5},\frac{-9}{5})}[/tex]
So, (1,3) is not solution to the given system of equations.
need the answer pleas thx1
Answer:
n = 1.42857
Step-by-step explanation:
if a2 is -140 then somewhere between is -100. 3/7 is equal to 0.42857142857 in which it is 3/7 from -70 to -140 in a number range of 1 to 2. 1.42857142857 is your best bet as your answer.
what’s the correct answer, please
Answer:
D?
Step-by-step explanation:
What is the sum of the fractions? Use the nurnber line and equivalert fractions to help find the answer.
o-1
o
Answer:
-3/4
Step-by-step explanation:
-5/4 + 2/4 = -3/4
Hope this helps :)
Calculate the federal income taxes. In 1980, the federal income tax was 14 percent on incomes between $2,300 and $3,400 per year, 16 percent
on incomes between $3,400 and $4,400 per year, and 21 percent on incomes between $8,500 and 10,800 per year. In 1980, you made $3,000.
What was your income tax this year?
O $42.00
O $420
$480
$630
Answer: 420
Step-by-step explanation: 14 percent of 3000 is 420
Correct Answer: $420
Help me solve please
Which of the following ratios are equivalent to 124:20? plsss anwer right asap plss im wasted all my points !!!!!!!!!!!!:(
Answer:
It is 31:5
Step-by-step explanation:
Hope this helped have an amazing day!
please help with this question i have 1 hour to finish this test
Answer:
29
Step-by-step explanation:
2x - 14 = x + 15
2x - x = 15 + 14
x = 29
check
44 = 44
Answer:
pretty sure it's 29
Step-by-step explanation:
equation: 2x-14=x+15
how to solve: add 14 to both side, and subtract x from both sides. The equation will then be x=29.
I might be wrong tho.
is -12•(-8) negative vaule
Answer:
Yes i think its -96,
if thats what your asking
what expression is d squared
The first five terms of a sequence are 7, 10, 13, 16, and 19.
Which of the following functions define this sequence for all integers n ≥ 1?
Answer:
Option B is correct
For , the function for the given sequence is defined as;
Step-by-step explanation:
An arithmetic sequence is a sequence in which the difference between each consecutive term is constant.
An explicit formula for this arithmetic sequence given by;
where a represents first term
Since, the given sequences; 7 , 10 , 13 , 16 and 19
⇒ common difference(d) = 3 and a = 7
Since.
10 -7 = 3
13- 10 = 3 ....
The function which defined this sequence is;
using distributive property:
therefore, the function for the given sequence for all integers is;
Help? ^-^ WILL GIVE BRAINLIEST!
What is the slope of a line through (1, 3) and (-2, 2)?
Answer:
The slope of the line is [tex]\frac{1}{3}[/tex]
Step-by-step explanation:
The Slope of a Line
Suppose we know a line passes through points A(x1,y1) and B(x2,y2). The slope can be calculated with the formula:
[tex]\displaystyle m=\frac{y_2-y_1}{x_2-x_1}[/tex]
It's given the points (1,3) and (-2,2). Let's calculate the slope:
[tex]\displaystyle m=\frac{2-3}{-2-1}[/tex]
Calculating:
[tex]\displaystyle m=\frac{-1}{-3}[/tex]
[tex]\displaystyle m=\frac{1}{3}[/tex]
The slope of the line is [tex]\frac{1}{3}[/tex]
A researcher wishes to determine whether the rate of water flow (in liters per second) over an experimental soil bed can be used to predict the amount of soil washed away (in kilograms). In this study, the explanatory variable is the
A. amount of eroded soil.
B. rate of water flow.
C. depth of the soil bed.
D. size of the soil bed.
E. None of the above.
Answer:
B. rate of water flow.
Step-by-step explanation:
Given that in a research study the explanatory variable is a form of a variable that is independent and it is used by the researcher to make predictions or analyze variations in other variables known as response variables.
Hence, in this case, the Explanatory variable is the "rate of water flow" because it is the variable researcher wishes to utilize in predicting the amount of soil washed away.
i need help with this question
9514 1404 393
Answer:
11/20
Step-by-step explanation:
It is appropriate to "invert and multiply".
[tex]\dfrac{5}{20}\div\dfrac{5}{11}=\dfrac{5}{20}\times\dfrac{11}{5}=\dfrac{5\times11}{5\times20}=\boxed{\dfrac{11}{20}}[/tex]
PLEASE I NEED HELP WITH MATH HOMEWORK
Answer:
x=59
Step-by-step explanation:
3x+3=180
3x=177
x=59
Evaluate the surface integral S F · dS for the given vector field F and the oriented surface S. In other words, find the flux of F across S. For closed surfaces, use the positive (outward) orientation. F(x, y, z) = y i + (z − y) j + x k S is the surface of the tetrahedron with vertices (0, 0, 0), (8, 0, 0), (0, 8, 0), and (0, 0, 8)
Answer:
[tex]\dfrac{-8^3}{6}[/tex]
Step-by-step explanation:
According to the divergence theorem;
The flux through the surface S is given by the formula:
[tex]\iint _S F.dS = \iiint_E \ div (F) \ dV[/tex]
where the vector field is:
F = [tex]\langle y,z-y,x \rangle[/tex]
Then the divergence of the vector field is:
[tex]div (F) = \bigtriangledown.F = \Bigg [ \dfrac{\partial (y)}{\partial x} + \dfrac{\partial (z-y)}{\partial (y)}+ \dfrac{\partial (x)}{\partial (z)} \Bigg ][/tex]
= 0 - 1 + 0
= -1
Thus, the flux through the surface of the tetrahedron is:
[tex]\iint_S . FdS = \iiint _E(-1) \ dV \\ \\ = - \iiint_E \ dV[/tex]
To determine the volume of the tetrahedron with vertices O(0,0,0), A(8,0,0), B (0,8,0) & C(0,0,6)
The equation of the plane P moving through the vertices A, B and C is:
[tex]P = \dfrac{x}{8}+ \dfrac{y}{8}+ \dfrac{z}{8} = 1[/tex]
x + y + z = 8
Range:
For z: 0 ≤ z ≤ 8 - x - y
For y: 0 ≤ y ≤ 8 - x
For x; 0 ≤ x ≤ 8
Thus;
[tex]\iiint_E \ dV = \int ^8_0 \int ^{8-x}_{0} \int ^{8-x-y}_{0}[/tex]
[tex]\int ^8_0 \int ^{8-x}_{0} [z] ^{8-x-y}_{0} \ dydx = \int ^8_0 \int ^{8-x}_{0} \ (8 -x-y) \ dy dx[/tex]
[tex]\int ^8_0 [ (8-x)^2 - \dfrac{(8-x)^2}{2} ] dx = \dfrac{1}{2} \int ^8_0 (8-x)^2 \ dx[/tex]
i.e.
[tex]= \dfrac{1}{2} [ \dfrac{(8-x)^3}{(-1)^3}]^8_0[/tex]
[tex]= \dfrac{-1}{6}[(8-8)^3-(0-8)^3][/tex]
[tex]= \dfrac{-8^3}{6}[/tex]
This question is based on the Gauss Divergence theorem. Therefore, the surface integral [tex]\int\limits {F.dS}[/tex] is -85.33.
Given:
F(x, y, z) = y i + (z − y) j + x k S in outward orientation.
Tetrahedron with vertices (0, 0, 0), (8, 0, 0), (0, 8, 0), and (0, 0, 8).
We have to evaluate the surface integral [tex]\int\limits {F.dS}[/tex] .
According to the Gauss divergence theorem ,
The flux through the surface S is given by the formula:
[tex]\int\int _s F.dS = \int \int \int_e div (F)\; dV[/tex]
Where the vector field is:
F = ( y, z-y, x )
Therefore, the divergence of the vector field is:
[tex]div(F) = \bigtriangledown .F = ( \dfrac{\partial( y)}{\partial (x)} + \dfrac{\partial(z-y)}{\partial(y)} + \dfrac{\partial(x)}{\partial(z)} )\\\\div(F) = \bigtriangledown .F = 0-1+0=-1[/tex]
Thus, the flux through the surface of the tetrahedron is:
[tex]\int\int _s F.dS = \int \int \int_e (-1)\; dV = -\int \int \int_e \; dV[/tex]
Now, determine the volume of the tetrahedron with vertices O(0,0,0), A(8,0,0), B (0,8,0) & C(0,0,6).
The equation of the plane P moving through the vertices A, B and C is:
[tex]P = \dfrac{x}{8} +\dfrac{y}{8} +\dfrac{z}{8} = 1[/tex]
x + y + z = 8
Range:
For z: 0 ≤ z ≤ 8 - x - y
For y: 0 ≤ y ≤ 8 - x
For x; 0 ≤ x ≤ 8
Thus,
[tex]\int\int\int_e dV = \int\limits^8_0\int\limits^{8-x} _ 0 \int\limits^{8-x-y}_0 \; dzdxdy\\= \int\limits^8_0\int\limits^{8-x} _ 0 [z]\limits^{8-x-y}_0 dx \\= \int\limits^8_0\int\limits^{8-x} _ 0 (8-x-y) dy dx\\= \int\limits^8_0 [ 8y-xy-\dfrac{y^{2} }{2} ]\limits^{8-x}_ 0 dx\\= \int\limits^8_0 ([ 8-x]^{2} - \dfrac{ [ 8-x]^{2}}{2} ) dx\\= \dfrac{1}{2} [\dfrac{(8-x)^{3} }{(-1)^{3} } ] \limits^8_0\\=\dfrac{-8^{3} }{6} \\\\= -85.33[/tex]
Therefore, the surface integral [tex]\int\limits {F.dS}[/tex] is -85.33.
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