Answers
18. x = y = -3
21. y was substituted into the wrong equation. The solution is (x, y) = (2, 1).
Step-by-step explanation:18. Adding y to the first equation transforms it to ...
... x = y
Then you can substitute for either variable in the second equation.
... 2y -5y = 9 . . . . . substitute for x
... -3y = 9 . . . . . . . . simplify
... y = -3 . . . . . . . . . divide by the coefficient of y
.. x = -3 . . . . . . . . . x and y have the same value
___
21. The first equation is being used to find an expression for y in terms of x. If you substitute that expression back into the same equation, it will tell you nothing you didn't already know. (Here, it is telling you 5 = 5.) The expression is only useful if you substitute it into a different equation. Here, it needs to be substituted into the second equation:
... Step 2: 3x -2(-2x+5) = 4 ⇒ 7x -10 = 4 . . . . . substitute for y in the second eqn
... Step 3: 7x = 14 . . . . . add 10
... Step 4: x = 2 . . . . . . . divide by 7
... Step 5: y = -2·2 +5 = 1 . . . . . find the value of y from x using the expression from step 1. Now, you know the solution is (x, y) = (2, 1).
_____
The attached graph shows the solution to the problem of 21.
Related Questions
The expression 700(1.005644)4x shows the quarterly interest rate Letrice earns after x years. Which expression shows the x isolated in the exponent in an equivalent form?
Answers
Answer:
[tex]700(1.022768)^x[/tex]
Step-by-step explanation:
We have been give an expression [tex]700(1.005644)^{4x}[/tex] that shows the quarterly interest rate Letrice earns after x years.
We can find an equivalent expression with x isolated by using exponent properties.
Since power rule of exponents states that an exponent raised to another exponent can be simplified by multiplying the exponents
So using power rule of exponents we can write our expression as:
[tex]700((1.005644)^4)^x[/tex]
Now let us simplify our expression.
[tex]700(1.0227678485832441)^x[/tex]
Upon rounding to 6 decimal places we will get,
[tex]700(1.022768)^x[/tex]
Therefore, the expression [tex]700(1.022768)^x[/tex] shows the x isolated in the exponent in an equivalent form.
Should I round 13.9876652 to 14 or 13.99?
Answers
Answer:
14.
Unless your assignments tells you not to round to whole numbers or to round to the nearest decimal places, then 13.99. But, in most cases, you'd round to 14.
write a quadratic function whose graph has the given characteristics x-intercepts: -4,2 point on graph (0,-9)
Answers
y = (9/8)(x +4)(x -2)
Step-by-step explanation:When the x-intercepts are "a" and "b", you know factors of the function are (x-a) and (x-b). So, we can write the function as ...
... y = k(x -(-4))(x -2) = k(x +4)(x -2) . . . . . for some scale factor k
We can find k using the given point.
... -9 = k(0 +4)(0 -2) = -8k
Dividing by -8 gives ...
... 9/8 = k
The desired function is ...
... y = (9/8)(x +4)(x -2)
... = (9/8)(x² +2x -8)
Find the value of x that makes the equation true.
x/9 = -6
A. -54
B. -48
C. 54
D. 48
Answers
x/9 = -6
Solve for X by multiplying both sides by 9:
x = -6 * 9
x = -54
[tex]9\frac{x}{9}=-54[/tex]
The nines on the left hand side and it it
[tex]x=-54[/tex]
What is the effect on the graph of the function f(x)=x when f(x) is replaced with -1/2f(x)?
Answers
Answer:
For negative sign , the graph reflects over x -axis and for 1/2 there will be a vertical compression
Step-by-step explanation:
Parent function is f(x)= x
We need to find the effect of the graph when f(x) is replaced with -1/2f(x)
When negative sign is multiplied outside f(x) like -f(x), then there will be a reflection over x-axis
When negative sign is multiplied inside f(x) like f(-x) then there will be a reflection over y-axis
When a number is multiplied outside f(x) then there will be a vertical stretch or compression
Here 1/2 is multiplied outside f(x). [tex]\frac{1}{2}[/tex] is less than 1 so there will be a vertical compression
For negative sign , the graph reflects over x -axis and for 1/2 there will be a vertical compression
PLEASE HELP ASAP: highest amount of points
for my career development
you are paid a salary of $23,000 annually, you pay 12% in taxes. What is your net pay biweekly?
Answers
Answer:
$778.46 is the bi-weekly net pay
Step-by-step explanation:
Net pay is the gross pay minus taxes
Net pay = gross pay - gross pay * tax rate
Simplifying this equation by factoring out gross pay
Net pay = gross pay (1- tax rate)
Substituting this in
Net pay = gross pay (1- tax rate)
We know the
hours worked = 23000
tax rate = .12
Net pay = 23000 (1- .12)
Net pay = 23000 (.88)
Net pay = 20240
But this is per year, and we want it bi weekly
There are 52 weeks in a year, divide by 2 (bi weekly)= 26
So divide 20240 by 26, so you get paid every 2 weeks.
$20240/26 = 778.46 (we round to the nearest cent)
i will give brainliest thanks
Answers
Answer:
The correct answer is A which is
[tex]\:<\:1[/tex]
Step-by-step explanation:
The angle of elevation from the submarine to the boat is [tex]\:<\:1[/tex].
This is the angle through which an observer from the submarine will raise the head before seeing the boat.
See diagram in the attachment for illustration.
a model is made of a car. please help.
Answers
Answer:
10.8 : 1
Step-by-step explanation:
In raw terms the ratio of car length to model length is ...
... 9 ft : 10 in
As a pure number this will be ...
... 108 in : 10 in = 10.8 : 1
How would the expression x3 - 64 be rewritten using difference of cubes? A. (x + 4)(x2 - 4x - 16) B. (x - 4)(x2 + 4x + 16) C. (x + 4)(x2 - 4x + 16) D. (x - 4)(x2 + 16x + 4)
Answers
Answer:
B. (x - 4)(x2 + 4x + 16)
Step-by-step explanation:
a3 – b3 = (a – b)(a2 + ab + b2)
substitute a=x n b=4 (cuz 64=4x4x4)
x3 - 64 = (x-4)(x2+4x+4x4)
= (x - 4)(x2 + 4x + 16)
The expression rewritten using difference of cubes as (x - 4)(x^2 + 4x + 16). Option b is correct.
Expansion of x^3 - 64 to be determine.
Difference of cube = [tex]a^3-b^3=(a-b)(a^2+ab+b^2)[/tex]
Here,
[tex]=x^3 - 64 \\=x^3-4^3[/tex]
a =x ; b = 4, put a and b in below equation,
[tex]a^3-b^3=(a-b)(a^2+ab+b^2)[/tex]
[tex]x^3-4^3=(x-4)(x^2+4x+16)[/tex]
Thus, the expression rewritten using difference of cubes as (x - 4)(x^2 + 4x + 16).
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PLZ help on 1 and 2 ASAP have to turn in homework now.
Answers
the rhombus, m<1 = 168. what are m<2 and m<3?
Answers
Answer:
∠2 = 168°
∠3 = 6°
Step-by-step explanation:
Opposite angles of a rhombus are congruent, so ∠2≅∠1 = 168°.
∠3 is the base angle of the isosceles triangle with an apex angle of 168°. Hence it will be (180° -168°)/2 = 6°.
Write an equation for the line
Answers
y = 1/9x + 3 5/9
Step-by-step explanation:The slope between the two marked points is ...
... m = (change in y)/(change in x)
... = (4 -3)/(4 -(-5))
... m = 1/9
Then the point-slope equation for the line with slope m through point (h, k) can be written as ...
... y = m(x -h) +k
... y = 1/9(x -(-5)) +3 . . . . . m = 1/9, (h, k) = (-5, 3)
... y = 1/9x + 3 5/9 . . . . . . simplify
The table of values below represent an exponential function. Write an exponential equation that models the data.
x y
-2 21
-1 14.7
0 10.29
1 7.203
2 5.0421
a. y = 21(0.7) b. y = 14.7(1.7) c. y = 10.29(0.7) d. y = 10.29(1.3)
Answer: c
Answers
y = 10.29·0.7^x . . . . . selection c seems the closest
Step-by-step explanation:For most any exponential function, the exponential multiplier will be 1 when x=0, so the y-intercept is the overall multiplier for the function.
The values decrease as x increases, so the base of the exponential term must be less than 1.
These considerations narrow your choice to C.
... y = 10.29·0.7^x
_____
If you actually want to determine the equation, you can do it several ways. One is to make use of the exponential regression function of your graphing calculator. (See attached). Another is to take the logarithms of the y-values and find a best-fit line through them.
_____
Comment on the answer choices
You may notice that none of the offered answers appears to be anything but the product of two numbers. There are no x-variables involved, and no exponents indicated. Cutting and pasting answers like this does not work.
Answer:
c
Step-by-step explanation:
How many years will it take you to double your money if; Round off your answers to one decimal place. 1) Your ROI or rate of return is 4%? years. 2) Your ROI is 10%? years. 3) Your ROI is 13%? years.
Answers
Assuming the return is compounded annually, the multiplier each year for rate "r" is (1+r). Then the multiplier for "t" years is (1+r)^t. We want this to be 2.
... 2 = (1+r)^t
... log(2) - t·log(1+r)
... log(2)/log(1+r) = t
The attachment shows the rounded calculator result for r={4%, 10%, 13%}.
You can calculate the years it would take to double your investment using the 'Rule of 72', by dividing 72 by your rate of return. Thus, with an ROI of 4%, 10%, and 13%, it would take roughly 18.0, 7.2, and 5.5 years respectively to double your investment.
Explanation:The time it takes to double your money can be calculated using the 'Rule of 72'. This rule states that if you divide 72 by the rate of return, you get the number of years it will take to double your money. So, for your situation:
1) With an ROI of 4%, it will take 18.0 years (72 divided by 4).
2) With an ROI of 10%, it will take 7.2 years (72 divided by 10).
3) With an ROI of 13%, it will take 5.5 years (72 divided by 13). Remember, this is an approximation and actual results may vary due to compounding frequency and timing of deposits and withdrawals. This rule is a simple way to estimate the effects of compound interest.
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Classify the following as Linear or Quadratic. Then identify the quadratic, linear, and constant terms.
x + 2x(x-3)
Answers
Answer:
This is quadratic since it has an x^2
The quadratic term is 2x^2, the linear term is -5x and the constant term is 0
Step-by-step explanation:
x + 2x(x-3)
Distribute the 2x
x + 2x^2 -6x
Combine like terms
2x^2 -5x
This is quadratic since it has an x^2
The quadratic term is 2x^2, the linear term is -5x and the constant term is 0
Answer:
quadratic, 2, -5, 0
Step-by-step explanation:
x + 2x(x-3)
= x + 2x^2 - 6x
= 2x^2 - 5x
so the eqn is quadratic
the quadratic term is 2,
the linear term is -5, and
the constatnt term is 0
Max delivers 8520 pieces of mail in one year. If he delivers the same number of pieces of mail each month, about how many pieces of mail does he deliver in two months? Explain your steps
Answers
Answer:
1420 pieces of mail he delivered in 2 months.
Step-by-step explanation:
If he delivered the same amount each month, you would divide 8520 by 12 (number of months in a year). Then once you divide it, the number you get is 710 now multiply 710 by 2 (because they ask how many he delivered in 2 months). And the answer would be 1420
Answer:
Max delivers 1420 in two Months because 8520 divided by 12 is 710 and thats just one month so 710 x 2 = 1420.
Step-by-step explanation:
are theese rational
11/12 times 9/22
x + (-2x)
Answers
Answer:
11/12 times 9/22 - rational
x + (-2x) unknown
Step-by-step explanation:
11/12 is a rational number (the ratio of integers)
9/22 is a rational number (the ratio of integers)
11/12 * 9/22 is a rational number
The product of 2 rational numbers is rational
x+-2x = x but we do not know if x is rational or irrational , so we cannot say if it is rational or not. If x is rational, the sum is rational. If r is irrational, the sum is irrational.
Select all radical expressions that are equivalent to 5 2/3
Answers
Answer:
1 and 3
Step-by-step explanation:
(5^(1/3))^2 = 5^(2/3)(5^2)^(1/2) = 5^(2/2) = 5(5^2)^(1/3) = 5^(2/3)(5·3)^(1/2) = 5^(1/2)·3^(1/2)(5^(1/2))^3 = 5^(3/2)(5·2)^(1/3) = 5^(1/3)·2^(1/3)___
Applicable rules are ...
[tex]\sqrt[n]{x^{m}}=x^{\frac{m}{n}}\\\\(x^{b})^{c}=x^{bc}\\\\(ab)^{c}=a^c\cdot b^c[/tex]
Determine the slope of the line that is perpendicular to the line y = -7x - 12.
Select one:
A. 17
B. −3
C. −7
D. −12
Answers
Answer:
1/7th
Step-by-step explanation:
To find the perpendicular slope find the negative reciprocal
e.i. 1/3 would be -3/1 or -3
The slope of the line perpendicular to y = -7x - 12 is 1/7.
Explanation:The slope of a line perpendicular to another line is the negative reciprocal of the slope of the original line.
The given line has a slope of -7, so the slope of the line perpendicular to it would be the negative reciprocal of -7, which is 1/7.
Therefore, the slope of the line that is perpendicular to the line y = -7x - 12 is 1/7.
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Solve the inequality for b.
Answers
Answer:
-2 ≥ b
Step-by-step explanation:
10 ≤ -2 ( 9 + 12b ) / 3
10 ≤ -2 ( 3 + 4b )
-10 ≥ 2 ( 3 + 4b )
-10 ≥ 6 + 8b
-16 ≥ 8b
-2 ≥ b
What adds to 5 minus negative 2 gives you the result 6?
Answers
-1
Step-by-step explanation:You apparently want to find the value of x such that ...
... x + 5 -(-2) = 6 . . . . . . the problem statement
... x + 5 + 2 = 6 . . . . . . . simplify signs
... x +7 = 6 . . . . . . . . . . . perform the addition
... x = 6 -7 = -1 . . . . . . . subtract 7 from both sides of the equation, evaluate
-1 adds to 5 - (-2) to give the result 6.
A company estimates its total profit (profit = total revenue minus total cost) as P(x) = 2x5 − 3x4 − 5x2 − 2, where P is in thousands of dollars and x is the number of years elapsed since the company was founded. How many times can the total profit become exactly zero? Hint: Use Descartes's rule of signs.
A.
2 or 0
B.
5 or 3 or 1
C.
3 or 1
D.
1
Answers
Answer:
D. 1
Step-by-step explanation:
The signs of the terms are +---, so there is 1 change of sign. That means there is 1 positive real root. Profit is zero exactly one time.
Brenda has 5/6 of a pie to divide evenly among 4 people. How much pie will each person get?
Answers
Brenda has 5/6 of a pie to divide evenly among 4 people. The poundage each person will get is computed by dividing 5/6 by 4, resulting in 5/24 of the pie per person.
Explanation:To find out how much pie each person will get, we need to divide Brenda's portion of the pie by the number of people. Brenda has 5/6 of a pie, and there are 4 people. So, if we divide 5/6 by 4, we'll get the amount of pie per person.
This can be represented by the following math equation: 5/6 ÷ 4 = x, where x is the amount of pie each person gets. You do this by performing the division as if it were a multiplication but flipping the second fraction, so it turns into
5/6 * 1/4 = 5/24. Therefore, each person will get 5/24 of the pie.
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The perpendicular bisectors of two sides of a triangle meet at point that belongs to the third side. Prove that this is a right triangle.
Answers
The point of intersection of the perpendicular bisectors of a triangle is the circumcenter, the center of the circle that contains the three triangle vertices.
If that center is on one side, that side must be a diameter of the circle. The diameter cuts the circle into two arcs, each of which measures 180°.
The third vertex of the triangle and its two legs form an inscribed angle that subtends an arc of 180°. The measure of that angle is half the measure of the arc, so the angle measures 90° and is a right angle.
A triangle with a right angle is a right triangle. QED
Please help. Accuplacer question.
Answers
Answer:
D. 6
Step-by-step explanation:
The system can be solved by subtracting double the second equation from the first:
... (4x +3y) -2(2x +y) = (20) -2(7)
... y = 6 . . . . . . . . . for solution (x, y) = (a, b), this tells you b=6.
Putting this into the second equation gives ...
... 2x +6 = 7
... 2x = 1
... x = 1/2
The solution is (x, y) = (a, b) = (1/2, 6). b = 6.
Given: The coordinates of triangle PQR are P(0, 0), Q(2a, 0), and R(2b, 2c). Prove: The line containing the midpoints of two sides of a triangle is parallel to the third side. As part of the proof, find the midpoint of PQ
Answers
To find the midpoint of PQ in the given triangle PQR, we use the midpoint formula, which states that the coordinates of the midpoint are the average of the x-coordinates and the average of the y-coordinates of the given points.
Explanation:To prove that the line containing the midpoints of two sides of a triangle is parallel to the third side, we need to show that the slope of the line is equal to the slope of the third side. Let's find the midpoint of PQ first.
The coordinates of P and Q are P(0, 0) and Q(2a, 0). The midpoint formula is given by:
Midpoint of PQ = ( (x1 + x2) / 2 , (y1 + y2) / 2 )
Substituting the values, we get Midpoint of PQ = ( (0 + 2a) / 2 , (0 + 0) / 2 ) = (a , 0)
Therefore, the midpoint of PQ is (a , 0).
In the figure on the right, STWC space is a square centered at the origin with side length 2a What are the coordinates of the vertices?
Answers
D. S(-a, -a), T(-a, a), W(a, a), Z(a, -a)
Step-by-step explanation:Point S is in the 3rd quadrant, where both coordinates are negative. That eliminates choices A and B.
The distance between points is 2a, so the distance from a corner point to either axis is "a". That is, the magnitude of any coordinate value is "a", not "2a." That eliminates choice C.
Remaining is the correct choice: D.
I am a rectangle. One of my sides is 8 centimeters long. Another side is 6 centimeters long. What is my area?
Answers
Answer:
48
Step-by-step explanation:
To get the area of a rectangle or square, its only one step, really.
The formula for a rectangle is A=x*y, where x and y are the two side lengths of the rectangle.
Answer:
48
Step-by-step explanation:
8*6=48
Tim ran 5 miles in 35 minutes. Dan rund 7 miles in 70 minutes. If they are running a marathon 26 miles, who will finish first?
Answers
Answer:
they will tie
Step-by-step explanation:
if you divied 7 in to 70 you get 7 and if you divied 5 into 35 it 7
It takes both of them 7 mins to complet a mile
Please help with this question:)
Answers
Answer:
x=1
Step-by-step explanation (this way is not the shortest one):
if 2x-3>0, then the equation 2x-3=2x-1 has no roots.
if 2x-3<0 (x<1,5), then the equation 3-2x=2x-1 has one root, x=1