We want to find the solutions for the following system
[tex]\begin{cases}y=10 \\ 3x+4y=19\end{cases}[/tex]We already know the value for the y variable, if we substitute this value on the second equation it is possible to find the x value.
[tex]\begin{gathered} 3x+4\cdot(10)=19 \\ 3x+40=19 \\ 3x=19-40 \\ 3x=-21 \\ x=\frac{-21}{3} \\ x=-7 \end{gathered}[/tex]And those are the results for our system
[tex]\begin{cases}x=-7 \\ y=10\end{cases}[/tex]eekkea dasd. dkksalaq'w
Rewrite the following expression as a single logarithm: 2log(x+3) + 3log(x - 7) - Slog(x - 2) + 2log(x) 3 log (x+3)(x-7) 12(3-2) 5 A. 5 log (x + 3)?(x - 2) (1-7712 B. 3 (1 +31°160 – 7) log O c. (x-2)-5-1 p2(x+3)*(1-73 log OD. (r-2) 5
Let's look at some logarithm properties,
[tex]\begin{gathered} p\log _b(M)=\log _b(M^p) \\ \log _b(\frac{M}{N})=\log _bM-\log _bN \\ \log _b(MN)=\log _bM+\log _bN \end{gathered}[/tex]We will use this properties to simplify and write the expression as a single logarithm.
The steps are shown below:
[tex]\begin{gathered} 2\log (x+3)+3\log (x-7)-5\log (x-2)+2\log (x) \\ =\log (x+3)^2+\log (x-7)^3-\log (x-2)^5+\log (x)^2 \\ =\log (\frac{(x+3)^2(x-7)^3(x)^2}{(x-2)^5}) \end{gathered}[/tex]The expression, as a single logarithm, is,
[tex]\log (\frac{(x+3)^2(x-7)^3(x)^2}{(x-2)^5})[/tex]From the answer choices, the correct answer is D.
Answer
D
how much money must be loaned to receive 15,000 if the money is loaned for 5 years at 12% interest
Step-by-step explanation:
i don't know if this is right
cos(theta) = - 3/4 and is in the 3rd quadrant, find the following:
Answer:
[tex]\begin{gathered} sin(\theta)=\frac{-\sqrt{7}}{4} \\ cos(\theta)=-\frac{3}{4} \\ tan(\theta)=\frac{\sqrt{7}}{3} \\ csc(\theta)=-\frac{4}{\sqrt{7}} \\ sec(\theta)=-\frac{4}{3} \\ cot(\theta)=\frac{3}{\sqrt{7}} \end{gathered}[/tex]Step-by-step explanation:
If theta is in the third quadrant, draw the diagram to easily identify the other trigonometric relations:
Solve for the missing leg of the triangle, using the Pythagorean theorem:
[tex]\begin{gathered} \text{ adjacent}^2+\text{ opposite}^2=\text{ hypotenuse}^2 \\ -3^2+\text{ opposite}^2=4^2 \\ \text{ opposite=}\sqrt{16-9} \\ \text{ opposite=}\sqrt{7} \end{gathered}[/tex]Therefore, for the trigonometric relationships:
[tex]\begin{gathered} \text{ sin\lparen}\theta)=\frac{opposite}{hypotenuse} \\ \text{ cos\lparen}\theta)=\frac{adjacent}{hypotenuse} \\ tan(\theta)=\frac{opposite}{adjacent} \\ csc(\theta)=\frac{hypotenuse}{opposite} \\ sec(\theta)=\frac{hypotenuse}{adjacent} \\ cot(\theta)=\frac{adjacent}{opposite} \end{gathered}[/tex]Now, substitute and solve for the relations:
[tex]\begin{gathered} sin(\theta)=\frac{-\sqrt{7}}{4} \\ cos(\theta)=-\frac{3}{4} \\ tan(\theta)=\frac{\sqrt{7}}{3} \\ csc(\theta)=-\frac{4}{\sqrt{7}} \\ sec(\theta)=-\frac{4}{3} \\ cot(\theta)=\frac{3}{\sqrt{7}} \end{gathered}[/tex]PLEASE HURRY ASAP PLEASE HURRY
The value of a stock decreases by an average of 10 dollars each week. Which of the following represents the total average decrease in the stock after 8 weeks?
The stock witness an total average decrease in stock of $80 in the 8 weeks
How to determine the total average decrease in the stockThe given parameters are:
Average decrease per week = 10 dollars
Also, we have the number of weeks to be
Number of Weeks = 8 weeks
So, the total average decrease in the stock is calculated using the following equation
Total = Average decrease per week x Number of weeks
Substitute the known values in the above equation
So, we have the following equation
Total = 10 x 8
Evaluate the products in the above equation
So, we have the following equation
Total = 80
Hence, the total average decrease in the stock is $80
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factor out 28p^5q^3+24p^3
Answer: 4p^3(7p^2q^3+6
Step-by-step explanation: Im pretty sure.
systems of equations
The solution to the system of equations in problem 13 is (0, -4).
The solution to the system of equations in problem 14 is (-6, -1).
In problem 13, the system of equations is:-5x-5y = 20x+6y = -24Simplify the first equation.x + y = -4x = -4-ySubstitute this value into the second equation.-4-y + 6y = -245y = -20y = -4x = -4-yx = -4-(-4)x = 0In problem 14, the system of equations is:-7x+12y = 30-3x+6y = 12Simplify the second equation.x-2y = -4x = 2y-4Substitute this value into the first equation.-7(2y-4)+12y = 30-14y + 28 + 12y = 30-2y = 2y = -1x = 2y-4x = 2(-1)-4x = -2-4x = -6To learn more about equations, visit :
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Find the value of x. Then find the measure of each labeled angle.
x= ____° (Simplify your answer.)
13x°= _____° (Simplify your answer.)
7x°= ____° (Simplify your answer.)
Answer:
13x + 7x = 180 (corresponding angles, sum of adjacent angles on a straight line=180)
20x = 180
x = 9
Substitute x into angle measures to find values.
13x° = 13(9)
= 117°
7x° = 7(9)
= 63°
which anwser shows the best approximation of [tex] \sqrt{42 } + \sqrt{63} [/tex]1. 10.22. 14.43. 14.84. 13.8
Quadrilateral ARMY is rotated 90° about the origin.
Draw the image of this rotation.
A 3,3
Y 5,1
M 7,5
R 5,7
The quadrilateral's image points will be A(3, 3) A'(-3, 3) R(5, 7) R'(-7, 5) M(7, 5) M'(-5, 7) Y(5, 1) Y' (-1, 5).
What do math quadrilaterals mean?
A polygon called a quadrilateral has four sides, four angles, and four vertices. Quadrilateral is a derivative of the Latin words quadri, which means four, and latus, which means side. A quadrilateral is shown in the above image as an example. quadrilateral pieces.If a point (x, y) is rotated 90 degrees counterclockwise with respect to the origin, the rotational rule is:
(x, y) → (-y, x) (-y, x)
Consequently, the image point's coordinates following rotation will be (-y, x).
According to this rule, the quadrilateral's image points will be A(3, 3) A'(-3, 3) R(5, 7) R'(-7, 5) M(7, 5) M'(-5, 7) Y(5, 1) Y' (-1, 5)
We may obtain the graph of the picture quadrilateral A'R'M'Y' by graphing the image points.
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6) What is the length of side x?
The given triangle is a right angled triangle. Therefore, by Pythagoras theoram,
[tex]\text{hypo}^2=base^2+altitude^2[/tex]From the figure,
[tex]\begin{gathered} x^2=2^2+5^2 \\ x^2=29 \\ x=\sqrt[]{29} \end{gathered}[/tex]Hence, Option D is the right answer.
9. After 25 minutes, an object accelerated from O km/hr to 50 km/hr south. What was the acceleration of the object? 2 km/hr south 2 km/hr/hr south 2 km/hr/s south 2 km/hr/min south
Acceleration is the rate of change of velocity.
Acceleration = change in velocity/change in time
Acceleration = (50 - 0)/(25 - 0)
Acceleration = 2 km/min South
5. Refer to Table 1. Suppose the government imposes a price ceiling of $5 on this market. What will be the size of
the shortage in this market?
0 units
2 units
8 units
10 units
There is no shortage of units in this market with a $5 price ceiling and the size of shortage is 0 units.
In mathematics, what is a data table?Tables are a good way to organize data by using rows and columns. Tables are a versatile organizational tool that can be used to communicate information on their own or in conjunction with another type of data representation (like a graph).Given: On this market, the government imposes a $5 price ceiling.
We need to find the size of the shortage in this market.
From the given table, we can see that the quantity demanded for $5 price ceiling is 4 units and the quantity supplied is 8 units.
So, the demand is satisfied and an extra 4 units are also provided.
Therefore, there is no shortage of units in this market a $5 price ceiling and the size of shortage = 0 units.
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A tank has 120 gallons of water and is being drained at a rate of 1/2
gallon each second. Another tank has 100 gallons of water and is being drained at a rate of 1/4
gallon each second. Which equation could be used to determine x, the number of seconds, when the two tanks have the same amount of water?
It will take 80 seconds for both tank 1 and tank 2 to have the same amount of water
Water in the tank 1 = 120 gallons
Drainage rate of tank 1 = 1/2 gallon each second
Water in tank 2 = 100 gallons
Drainage rate of tank 2 = 1/4 gallon each second
Let x represent the number of seconds it will take for both tanks to have the same amount of water
Formulating the equation we get the following:
Water in tank 1 - Drainage rate of tank 1*x = Water in tank 2 - Drainage rate of tank 2*x
120 - 1/2x = 100 - 1/4x
20 = 1/2x - 1/4x
20 = 1/4x
x = 80
So, it will take 80 seconds
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find the domain of (x). express your answer in interval notation.
so the domain is
[tex](0,\propto)[/tex]What is variable rate of change
Answer:
It is a rate of change that is not the same at all points - in time or space.
Step-by-step explanation:
Solve for x.
(8x - 34)
(5x + 2)°%
8x - 34 and 5x + 2 are corresponding angles and, by the Corresponding Angles Theorem, are congruent.
8x - 34 = 5x + 2
8x - 34 + 34 = 5x = 2 + 34
8x = 5x + 36
8x - 5x = 5x + 36 - 5x
3x = 36
3x/3 = 36/3
x = 12
Kevin, Mika, and Cheryl have a total of 45 people sponsoring them for a fun-raiser. Kevin has p people sponsoring him, MIka has one more than Kevin, and Cheryl has one more than MIka. Write and solve and equation to find the number of people sponsoring each person
The equation for the number of people sponsoring each person are; m = c + 3, p = c + 2.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Given that Kevin, Mika, and Cheryl have a total of 45 people sponsoring them for a fun-raiser.
Consider that Kevin has p people sponsoring him, Mika has one more than Kevin, and Cheryl has one more than Mika.
Kevin = p
MIka = m
Cheryl = c
Then m = 1 + p
c = 1 + m
Or
m = c - 1
Now solve both equation;
m = 1 + p = c - 1
p = c - 1 -1
p = c + 2
p = m -1
p = c + 2
Then m - 1 = c + 2
m = c + 3
Hence, the equation for the number of people sponsoring each person are; m = c + 3, p = c + 2.
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what is the equation of.the line+that+passes through (2,8) and has a slope of 3/2?
The line that passes through the point (2, 8) and has a slope of 3/2 is given by the equation y = (3/2)x + 10
What is equation of line passing through the point (x,y)?
(Y - Y1) = m(X - X1) is an equation for a line that passes through the point (x1, y1) and has a slope of m.
The line passing through points (2, 8) and having a slope of 3/2 is now a given.
Consequently, (x1,y1) equals (2, 8) and m = 3/2.
As a result, the line's equation is (y - y1) = m(x - x1).
When you combine (x1,y1) and m, you get (y - 8) = (3/2) (x - 2)
When we expand them, we obtain (y - 8) = (3/2) (x - 2)
y = (3/2)x + 5
Consequently, the equation y = (3/2)x + 5 describes the line that passes through the points (2, 8) and has a slope of 3/2.
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Mr. Stern owns an apartment building with 60 suites. He can rent all the suites if he charges a monthly rent of $200 per suite. At a higher rent, some suites will remain vacant. On the average, for each increase of $5, one suite remains vacant with no possibility of renting it. Determine the functional relationship between the total monthly revenue and the number of vacant units. What monthly rent will maximize the total revenue? What is the monthly revenue?
If Mr. Stern charges a monthly rent of $200, we still can rent all suites. An average increase of $5 in the monthly rent imply in the addition of one suite vacant.
Therefore, the total monthly revenue r in function of the number of vacant units v can be writen in the form:
[tex]\begin{gathered} r=(200+5v)\cdot(60-v) \\ r=-5v^2+100v+1200 \\ 0\leq v\leq60 \end{gathered}[/tex]The monthly rent m is given by:
[tex]m=200+5v[/tex]The value of v that maximize the total revenue r is the one found in the vertex of the parabola that represents r:
[tex]v_{\max }=-\frac{100}{2\cdot(-5)}=10[/tex]Therefore, the monthly rent that maximize the total revenue is m = 200 + 5*10 = $700
The monthly revenue with this monthly rent is:
[tex]r=-5\cdot10^2+100\cdot10+1200=\text{ \$1700}[/tex]
what is 4x-2=3(x-3)
4x -2 = 3(x-3)
4x - 2 = 3x - 9
bring like terms together
4x-3x = -9 +2
x = -7
In 2Use the formula t=kthat gives the time for a population, with a growth rate k, to double, to answer the following que0.0031The growth model A = 6 e describes the population, A, of a country in millions, t years after 2003.a. What is the country's growth rate?
We have an exponential function for the population A(t) and we have to find the growth rate.
[tex]A=6e^{0.003t}[/tex]This can be expressed as:
[tex]\frac{A(t+1)-A(t)}{A(t)}=\frac{A(t+1)}{A(t)}-1[/tex]For the exponential formula we get:
[tex]\begin{gathered} \frac{A(t+1)}{A(t)}-1 \\ \frac{6e^{0.003(t+1)}}{6e^{0.003t}}-1 \\ e^{0.003(t+1-t)}-1 \\ e^{0.003\cdot1}-1 \\ 1.003-1 \\ k=0.003 \end{gathered}[/tex]The growth rate is 0.003 or 0.3%.
We can calculate the time needed to double the population dividing ln(2) by the growth rate:
[tex]t=\frac{\ln (2)}{k}\approx\frac{0.693}{0.003}\approx231[/tex]Answer:
a) The growth rate is 0.003 or 0.3%
b) The number of years to duplicate the population is 231 years.
Find the indicated value. (Round your answer to eight decimal places.) 26!
The factorial expression 26! has a value of 4.032914600e+26
How to evaluate the expression?The expression is given as
26!
The above expression is a factorial expression
And the factorial of a number n where n >= 0 and n is not a decimal number is calculated using
n! = n x (n - 1) x (n - 2) x ..... x 1
This means that
n = 26
So, we have
26! = 26 x 25 x 24 x 23 x ..... x 1
Evaluate the products
26! = 4.0329146e+26
Approximate
26! = 4.032914600e+26
Hence, the value of the expression is 4.032914600e+26
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I only need the answer
THANK YOU!!
The value of C is 7.68 units and the value of angle A and B is 23° and 66° respectively.
As we can see,
This is a right angled triangle.
We can use Pythagoras theorem to find the value of third side,
It says, Square of hypotenuse side H is equal to square of Base side B plus square of Perpendicular side.
H² = P² + B².
The value of perpendicular here is 3.
The value of base here is 7.
Putting the values,
H² = (7)²+(3)²
H² = 49 + 9
H² = 58
H = √58
H = 7.68
Now, using trigonometric ratios,
For angle B,
Sin(B) = Perpendicular/Hypotenuse = P/H
Sin(B) = 7/7.68
Sin(B) = 0.91
Sin(66°) = 0.91
The value of B in degree is 66°.
For angle A,
Sin(A) = Perpendicular/Hypotenuse = P/H
Sin(A) = 3/7.68
Sin(A) = 0.39
Sin(23°) = 0.39
The value of A in degree is 23°.
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I only need the answer
THANK YOU!!
Cartesian coordinates are- 4.2426
The horizontal component of the Cartesian coordinate system is denoted by the letter x, whereas the vertical component is denoted by the letter y. In this coordinate system, equations for lines will need to include both the x and y variables.
Given
(r,θ) = (6,π/4)
x= r cosθ =6 x cos(π/4)
= 6√2 = 3√2
≈ 4.2426
y= r sinθ = 6 x sin(π/4)
= 6√2 = 3√2
≈ 4.2426
Hence the answer is 4.2426
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Suppose that R and S are points on the number line.
If RS 6 and R lies at -18, where could S be located?
==========================================================
Explanation:
Draw a vertical number line. Plot point R at -18 which is 18 units below 0.
Then move up 6 units to arrive at -12 which is one potential location of point S. The distance from R = -18 to R = -12 is RS = 6 units.
Now go back to point R = -18. This time move down 6 units to arrive at -24 as the other possible location of S.
See the diagram below.
The cost for Albert to play 2 games of laser tag is $18. Based on this relationship, which equation can be used to determine the total cost, y, in dollars, for Albert to play any number of games, x, of laser tag?
The equation that can be used to determine the total cost, y, in dollars for Albert to play any number of games, x, is Y = 18x/2 or 9x.
What is an equation?An equation is a mathematical statement expressing the equality that two values or expressions share.
Equations are generally represented using the equation sign (=).
The cost of 2 games of laser tag = $18
The cost of 1 game of laser tag = $9 ($18/2)
The cost of x laser tag games = $9x or 18x/2
Thus, we can represent the equation of the total cost as y = 9x.
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32
3 ÷ (z -
5
2
-)=2=÷(z+
3
2
+
3
Step-by-step explanation:
Consider the Cartesian equation,
2
x+3
=
4
y−5
=
2
z+6
Now,
a
=−3
i
+5
j
−6
k
b
=2
i
+4
j
+2
k
Vector equation,
r
=
a
+λ.
b
=−3
i
+5
j
−6
k
+λ(2
i
+4
j
+2
k
)
This is the required equation
help
A) What is true about each multiple of 3 other than that it is a multiple of 3?
B) What is true about each number with a factor of 7 other than that it is a factor of 7?
Every other multiple of 3 is even.
The answer is 7. Seven is a prime number, which means that its multiples are 1 and itself (7): 7 = 1 * 7
The digits in multiples of 3 add up to a multiple of 3 (36 = 3 + 6, 111 = 1 + 1 + 1, etc.) All EVEN multiples of 3 are also a multiple of 6 (the even multiples of 3 are the 6 “count by's”).
The answer is 7. Seven is a prime number, which means that its multiples are 1 and itself (7): 7 = 1 * 7. To find out which one is a factor of 7, we should divide each of them by 7. 1/7 will be a decimal number and 7/7 = 1, which is a whole number. Thus, 7 will be a multiple of 7 and also a factor of 7.
A whole number higher than 1 whose only elements are 1 and itself is referred to as a prime number. A whole number that may be split evenly into another number is referred to as a factor. 2, 3, 5, 7, 11, 13, 17, 19, 23 and 29 are the first few prime numbers. Composite numbers are those that have more than two components.
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Kubin Company’s relevant range of production is 18,000 to 22,000 units. When it produces and
sells 20,000 units, its average costs per unit are as follows:
Required:
1. Assume the cost object is units of production:
a. What is the total direct manufacturing cost incurred to make 20,000 units?
b. What is the total indirect manufacturing cost incurred to make 20,000 units?
2. Assume the cost object is the Manufacturing Department and that its total output is 20,000 units.
a. How much total manufacturing cost is directly traceable to the Manufacturing Department?
b. How much total manufacturing cost is an indirect cost that cannot be easily traced to the
Manufacturing Department?
3. Assume the cost object is the company’s various sales representatives. Furthermore, assume
that the company spent $50,000 of its total fixed selling expense on advertising and the
remainder of the total fixed selling expense comprised the fixed portion of the company’s
sales representatives’ compensation.
a. When the company sells 20,000 units, what is the total direct selling expense that can be
readily traced to individual sales representatives?
b. When the company sells 20,000 units, what is the total indirect selling expense that
cannot be readily traced to individual sales representatives?
4. Are Kubin’s administrative expenses always going to be treated as indirect costs in its internal
management reports?
For 18000 units the calculated sum is $150,000.
The following are the company's production and period costs:
The product costs $ 350,000 for 20,000 units.
20,000 units = $150,000 in cost period
The product costs $ 385,000 for 22,000 units.
18,000 units each period = $ 135,000
The corporation incurs two major costs while creating an item: production costs and period costs.
Production costs are expenses directly connected to the manufacturing process. These expenses include labor, raw materials, and overhead.
While period costs are expenses incurred for the company's activities such as administrative and selling/sales charges,1. The cost of making 20,000 units is
Existing unit manufacturing costs are as follows:
Direct labor costs $7.00. Manufacturing variable overhead of $4.00 Fixed manufacturing overhead of $1.50 $ 5.00
Total product cost per unit = $7.00 + $4.00 + $1.50 + 5.00 = $17.5
So, for 20,000 units, the calculation is: 20,000 x $17.5 = $350,000
The time required to produce 20,000 units is
Each unit's cost period is as follows:
$ 3.50 in fixed selling expenses, $ 2.50 in fixed administration expenses, and $ 1.00 in variable administrative expenses.
Total period cost per unit = $ 3.5+ $ 2.5+ $ 1.00+ $ 0.5 = $ 7.5
So, for 20,000 units, the calculation is: 20,000 x $ 7.5 = $150,000
The cost of making 22,000 units is
Existing manufacturing costs per unit: $ 17.5
So, for 20,000 pieces, the cost is 22,000 x $17.5 = $ 385,000
The total period cost / unit for generating 18,000 units is $ 7.5.
So, for 18,000 units, the calculation is: 18,000 x $ 7.5 = $ 135,000
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