Answer:
x = 61/2 = 30.5 = 60 1/2
Step-by-step explanation:
We have:
[tex]\frac{5}{6}x+\frac{1}{12}=15+\frac{1}{3}+\frac{1}{3}x[/tex]We have to find the Least Common Multiple to solve this question:
[tex]\begin{gathered} \frac{2\cdot5x+1=12\cdot15+4+4x}{12} \\ \frac{10x+1=180+4+4x}{12} \\ 10x+1=180+4+4x \\ 10x-4x=180+4-1 \\ 6x=183 \\ x=\frac{183}{6} \\ x=\frac{61}{2}=30.5=30\frac{1}{2} \end{gathered}[/tex]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
find the domain of (x). express your answer in interval notation.
so the domain is
[tex](0,\propto)[/tex]please show me how to graph 4x + 5y = -40
Plot the points (0, -8), (1, -8.8) and (2, -9.6) on the graph. Therefore, the graph for the given equation is plotted below.
The given equation is 4x + 5y = -40.
What is the graph?Graph is a mathematical representation of a network and it describes the relationship between lines and points. A graph consists of some points and lines between them. The length of the lines and position of the points do not matter.
Put x=0, 1, 2, 3, 4, 5,.....in the given equation and solve for y
When x=0, 4(0)+5y=-40
⇒ 5y=-40
⇒ y=-8
When x=1, 4(1)+5y=-40
⇒ 5y=-44
⇒ y=-8.8
When x=2, 4(2)+5y=-40
⇒ 5y=-48
⇒ y=-9.6
Plot the points (0, -8), (1, -8.8) and (2, -9.6) on the graph
Therefore, the graph for the given equation is plotted below.
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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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Identify two segments that are marked congruent to each other on the diagrambelow. (Diagram is not to scale.)
Step 1:
What are congruences?
Congruent triangles are triangles that have the same size and shape. This means that the corresponding sides are equal and the corresponding angles are equal.
Step 2:
JH is congruent to HI
Final answer
JH is congruent to HI
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.
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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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°
eekkea dasd. dkksalaq'w
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
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.
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
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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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
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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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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factor out 28p^5q^3+24p^3
Answer: 4p^3(7p^2q^3+6
Step-by-step explanation: Im pretty sure.
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]
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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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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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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Taylor works on an art project that uses rectangular pieces of paper the first rectangle has length 3/8 inches in width 3 in.
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:
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.
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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px+5=7x–q please help me
Answer:
Step-by-step explanation:
Simplifying
px + 5 = -4x + q
Reorder the terms:
5 + px = -4x + q
Reorder the terms:
5 + px = q + -4x
Solving
5 + px = q + -4x
Solving for variable 'p'.
Move all terms containing p to the left, all other terms to the right.
Add '-5' to each side of the equation.
5 + -5 + px = q + -5 + -4x
Combine like terms: 5 + -5 = 0
0 + px = q + -5 + -4x
px = q + -5 + -4x
Reorder the terms:
px = -5 + q + -4x
Divide each side by 'x'.
p = -5x-1 + qx-1 + -4
Simplifying
p = -5x-1 + qx-1 + -4
Reorder the terms:
p = -4 + qx-1 + -5x-1
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]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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which anwser shows the best approximation of [tex] \sqrt{42 } + \sqrt{63} [/tex]1. 10.22. 14.43. 14.84. 13.8
The two ways we can measure the SPREAD of a distribution:a. mean and quartilesb. median and standard deviationc. mean and mediand.quartiles and standard deviation
In statistics, there are ways of analyzing data and these include measures of "central tendency" and "measures of dispersion."
This question is focused on "measures of dispersion," that is, an analysis of how well the data set is being spread away from the centre. The centre is most commonly denoted as the mean (average), and the SPREAD is an analysis of how farther away the observed data is from the centre.
The Mean, Median and Mode are basically measures of "central tendency" and therefore, options A, B and C do not measure the SPREAD of a distribution.
The Quartiles and Standard deviation actually measure how well (either very close or very far) the data set move away from the distribution.
The Quartiles basically examine the data set from all four quarters of the entire set, the 1st, 2nd, 3rd and 4th quarters. This measure of spread measures how well the data is from the distribution depending on which quartile it falls. The Standard deviation measures how far the mean deviates (or drifts away) from the data set.
The correct answer therefore is option D.