The equivalent inequality with x isolated in the left side is x<(L-Ky)/J
What is equivalent inequality?A positive number divided by both sides of an inequality results in an equal inequality. And if the inequality symbol is reversed, division on both sides of an inequality with a negative value results in an analogous inequality.
Following step by step process-
Jx+Ky<L (Given)
Subtracting Ky on both the side
Jx<L-Ky
Now dividing by J both side
x<(L-Ky)/J
Therefore, equivalent inequality with x isolated in the left side is x<(L-Ky)/J.
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The complete question is:
"Jx+Ky<L assume J<0
The equivalent inequality with x isolated in the left side is"
PLEASE HELP: Which of the following are identities? Check all that apply. A. (sin x + cos x)^2 = 1 + sin 2x B. sin 3x - sinx/ cos3x + cosx = tan xC. sin 6x = 2 sin3x cos3x D. sin 3x/sin x cos x = 4 cos x - sec x
All the options are correct
Explanations:A quick and smart way is to substitute a value for x in each of the options and verify if the right hand side equals the left hand side
Let x = 30
A) (sin x + cos x)² = 1 + sin 2x
(sin 30 + cos 30)² = 1.866
1 + sin 2(30) = 1.866
Therefore (sin x + cos x)² = 1 + sin 2x
B)
[tex]\begin{gathered} \frac{\sin3x-\sin x}{\cos3x+\cos x}=\tan x \\ \frac{\sin3(30)-\sin30}{\cos3(30)+\cos30}=0.577 \\ \tan \text{ 30 = 0.577} \end{gathered}[/tex]Therefore:
[tex]\frac{\sin3x-\sin x}{\cos3x+\cos x}=\tan x[/tex]C) sin 6x = 2 sin3x cos3x
sin 6(30) = 0
2 sin3(30) cos3(30) = 0
Therefore sin 6x = 2 sin3x cos3x
This can also be justified by sin2A = 2sinAcosA
D.
[tex]\frac{\sin3x}{\sin x\cos x}=\text{ 4}\cos x-\sec x[/tex][tex]\begin{gathered} \frac{\sin 3(30)}{\sin 30\cos 30}=\text{ 2.31} \\ 4\cos 30-\sec 30=\text{ }2.31 \end{gathered}[/tex]Options A to D are correct
I need help figuring out how to find sides a and b using the law of sine
Given the triangle ABC below.
a is the side facing b is the side facing
c is the side facing
We ara interested in calculating the value of side a and b.
To do this, we need to apply the "sine rule"
Sine rule state that
[tex]\frac{a}{\sin A}=\frac{b}{\sin B}=\frac{c}{\sin C}[/tex]Where
a is the side facing b is the side facing
c is the side facing
To calculate b,
B = 95 , b = ?
C = 48, c=100
[tex]\begin{gathered} \frac{b}{\sin B}=\frac{c}{\sin C} \\ \frac{b}{\sin 95}=\frac{100}{\sin \text{ 48}} \\ \\ b\text{ x sin48=100 x sin95} \\ b=\frac{100\text{ x sin95}}{\sin 48} \\ b=134.05 \end{gathered}[/tex]b = 134 ( to nearest whole number)
To calculate a:
A = 37, a = ?
C = 48, c=100
[tex]\begin{gathered} \frac{a}{\sin A}=\frac{c}{\sin C} \\ \frac{a}{\sin37}=\frac{100}{\sin 48} \\ a\text{ x sin48 = 100 x sin37} \\ a=\frac{100\text{ x sin37}}{\sin 48} \\ a=80.98 \\ \end{gathered}[/tex]a = 81 ( to the nearest whole number)
Alberto is saving money to buy a pair of shoes that cost $50 he has already saved $32 he still needs to save D dollars explain how to solve your equation to find how much money Alberto needs to save how much more does he need to save
This is the formula that represents how much money needs Alberto to buy a pair of shoes.
To solve this equation, first, subtract 32 to both sides of the equation:
[tex]32\text{ - 32 + x = 50 - 32}[/tex][tex]x\text{ = 50 - 32}[/tex][tex]x\text{ = 18}[/tex]Thus, he still needs to save $18 to buy the shoes.
A principal of $3100 is invested at 5.5% interest, compounded annually. How much will the investment be worth after 9 years? Round your answer to the nearest dollar.
Given:
[tex]\begin{gathered} \text{Principal(P)}=\text{ \$3100 } \\ r=5.5\text{ \%} \\ n=9 \end{gathered}[/tex][tex]Final\text{ amount=P(1+}\frac{r}{100})^n[/tex][tex]\begin{gathered} Final\text{ amount after 9 years=}3100(1+\frac{5.5}{100})^9 \\ =3100(1.6191) \\ =\text{ \$50}19.21 \end{gathered}[/tex]Therefore, the investment be worth after 9 years is $5019.21
Which of the following equations could you solve by first adding six and then dividing by negative three?
3x - 6 = -9
6 - 3x = -9
-3x - 6 = -9
x/-3 + 6 = -9
Answer:
-3x-6=-9
Step-by-step explanation:
[tex]-3x-6=-9[/tex]
[tex]+6[/tex] [tex]+6[/tex]
[tex]-3x = -3[/tex]
[tex]-3x/-3 = -3/-3[/tex]
[tex]x=1[/tex]
What is the area in square feet ( of the rectangle) of 4 3/4 feet and 6 4/5 feet
Recall the area of a rectangle is determined by the formula
[tex]\begin{gathered} A_{\text{rectangle}}=lw \\ \text{where} \\ l\text{ and }w\text{ are the dimensions of the rectangle} \end{gathered}[/tex]Given the following
w = 4 3/4 ft
l = 6 4/5 ft
Convert the following given into improper fraction first
[tex]\begin{gathered} w=4\frac{3}{4}\text{ ft}\Longrightarrow w=\frac{19}{4}\text{ ft} \\ l=6\frac{4}{5}\text{ ft }\Longrightarrow l=\frac{34}{5}\text{ ft} \end{gathered}[/tex]Next, substitute those values to the given formula for solving the area of the rectangle
[tex]\begin{gathered} A=lw \\ A=\frac{34}{5}\text{ ft}\cdot\frac{19}{4}\text{ft} \\ A=\frac{646}{20}\text{ ft}^2 \\ \text{Convert the final answer back into mixed fractions} \\ A=\frac{646}{20}\text{ ft}^2\Longrightarrow A=32\frac{3}{10}\text{ ft}^2 \\ \\ \text{Therefore, the area of the rectangle is} \\ 32\frac{3}{10}\text{ ft}^2 \end{gathered}[/tex]Alleen's bi-weekly gross pay is $829.70. She sees that $174.25 was deducted for taxes. What percent of Alleen's bi-weekly gross pay has been withheld for tax? Round to the nearest whole percent. (1 point)
O 21%
20%
2%
O 1%
Which choice is equivalent to the expression below?V-81A. 91B. AiC.D. -29E. -9SUBMIT
Given the expression:
[tex]\sqrt[]{-81}[/tex]As we know, there is no square root for the negative numbers
But, using the complex numbers:
[tex]i=\sqrt[]{-1}[/tex]So, the given expression can be written as:
[tex]\sqrt[]{-81}=\sqrt[]{-1}\cdot\sqrt[]{81}=i\cdot9=9i[/tex]So, the answer will be option A) 9i
Find the perimeter of the square.
Width = 4x
Length = 36 – 5x
Answer:
The perimeter of the square is 64 units===========================
GivenA square with dimensions:
Width = 4x,Length = 36 - 5x.To findThe perimeterSolutionSquare has all sides equal:
width = length4x = 36 - 5x4x + 5x = 369x = 36x = 4Each side is:
4*4 = 16 unitsPerimeter:
P = 4*16 = 64 unitsThe perimeter of the square is found as 64 units.
What is defined as the perimeter of the square?The perimeter of such a square is indeed the total length of all of its sides. As a result, we can calculate the perimeter of the a square besides adding its four sides.A square's sides are all equal. As a result, the perimeter of such a square is determined by multiplying the side of a square by four.For the given question,
The dimension of the square are given as;
Width = 4xLength = 36 – 5xFor square, as all sides are equal.
Then,
Width = Length
Put the values.
4x = 36 – 5x
9x = 36
x = 4
Put in dimensions.
Width = 4×4 = 16 unitsLength = 36 – 5×4 = 16 units.The perimeter of square is;
Perimeter = 4 × side
Perimeter = 4 × 16
Perimeter = 64 units.
Thus, the perimeter of the square is found as 64 units.
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In 1990, there were 1330 registered alpacas in the United States. By summer of 2000, there were 29,856. What was the percent of increase in registered alpacas?
answer - 214% increase
explanation
formula = big number - small number ÷ original number
29856 - 1330 = 28,526 ÷ 1330 = 21.45
21.45 to percent = 214% then if rounded to nearest
The beginning mean weekly wage in a certain industry is $789.35. If the mean weekly wage grows by 5.125%, what is the new mean annual wage? (1 point)O $829.80O $1,659.60O $41,046.20$43,149.82
Given:
The initial mean weekly wage is $ 789.35.
The growth rate is 5.125 %.
Aim:
We need to find a new annual wage.
Explanation:
Consider the equation
[tex]A=PT(1+R)[/tex]Let A be the new annual wage.
Here R is the growth rate and P is the initial mean weekly wage and T is the number of weeks in a year.
The number of weeks in a year = 52 weeks.
Substitute P=789.35 , R =5.125 % =0.05125 and T =52 in the equation.
[tex]A=789.35\times52(1+0.05125)[/tex][tex]A=43149.817[/tex][tex]A=43149.82[/tex]The new mean annual wage is $ 43,149.82.
Final answer:
The new mean annual wage is $ 43,149.82.
Using trigonometry functions find the value missing in the diagram round to the nearest whole number
Given a right angle triangle
As shown:
Given ∠58
the opposite side to the angle = 22
The adjacent side to the angle = x
So,
[tex]\begin{gathered} \tan 58=\frac{\text{opposite}}{\text{adjacent}} \\ \\ \tan 58=\frac{22}{x} \end{gathered}[/tex]solve for x:
[tex]x=\frac{22}{\tan 58}\approx13.747[/tex]round to the nearest whole number
So, the answer will be x = 14
Translate to an algebraic expression.10 more than dThe translation is
10 more than d is the same as d plus 10, so the algebraic expression is:
d + 10
Answer: d + 10
In each of the following problems, how do I graph the line with the given slope m and y-intercept b.
m=5/3,b=-4
The graph is shown the following slope intercept formula y = 5/3x -4.
What exactly is a slope?A line's slope can be used to determine how steep it is.The slope is calculated mathematically as "rise over run" (change in y divided by change in x).When a line's equation is expressed as y = mx + b, the slope-intercept representation of the equation is used.M displays the slope of the line.B is the value of b where the y-intercept is located (0, b).For instance, the slope and y-intercept of the equation y = 3x - 7 are 3 and 0, respectively.So, the slope-intercept formula: y = mx + b
Where, = 5/3x and b = -4.Now, substitute the values in the formula and graph the slope-intercept on the graph as follows:
y = 5/3x -4(Refer to the graph attached below )
Therefore, the graph is shown the following slope intercept formula y = 5/3x -4.
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Im just needing a little bit more help with these type of problems ;/
Answer:
Expected value = 2.21
Explanation:
The formula to obtain the expected value is given by:
[tex]E\mleft(X\mright)=\mu=∑xP\mleft(x\mright)[/tex]We will proceed to calculate the given scenario as given below:
[tex]\begin{gathered} E\mleft(X\mright)=\mu=∑xP\mleft(x\mright) \\ E(X)=(1\times0.31)+(2\times0.41)+(3\times0.07)+(4\times0.18)+(5\times0.03) \\ E(X)=0.31+0.82+0.21+0.72+0.15 \\ E(X)=2.21 \\ \\ \therefore E(X)=2.21 \end{gathered}[/tex]Therefore, the expected value of this scenario is 2.21
Fill In the proportion No explanation just need answer got disconnected from last tutor
Explanation
Since the given shapes are similar, which implies that they are proportional,
Therefore; we will have
Answer:
[tex]\frac{AB}{EF}=\frac{BC}{FG}[/tex]For the line that passes through Y(3,0), parallel to DJ with D(-3,1) and J(3,3), complete the following: Find the slope. Write an equation in point-slope form. Graph the line.Slope:Point-slope form:
I am going to graph the situation on an external graphing utility and show you the answer, it will take a
minute, stay with me.
[tex]m\text{ = }\frac{rise\text{ }}{\text{run}}=\frac{change\text{ in y}}{\text{change in x}}=\frac{3}{1}=3[/tex][tex]y\text{ = mx+b}\rightarrow\text{ b =-1}[/tex]So the equation of the line is.
[tex]y\text{ =3x -1}[/tex][tex]y\text{ -1 = m(3-0)}[/tex]find the perimeter of a garden that measures 6 feet by 3/4 foot?
The perimeter of a garden that measures 6 feet by 3/4 foot is 13.50 feet.
What is the perimeter?The perimeter of a rectangle is calculated thus:
Perimeter = 2(Length + Width)
From the information, we want to find the perimeter of a garden that measures 6 feet by 3/4 foot.
This will be illustrated thus:
Perimeter = 2(Length + Width)
Perimeter = 2(6 + 3/4)
Perimeter = 2(6 + 0.75)
Perimeter = 2(6.75)
Perimeter = 13.50
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What is the midpoint of the x-intercepts off(x) = (x – 4)(x + 4)?(0,0)(0,4)(–4,0)(2,0)
Given:
[tex]f(x)=(x-4)(x+4)[/tex]Required:
To find midpoint of intercepts.
Explanation:
We know that when y=0,x=4,-4
therefore x- intercept of the function are (4,0) and (-4,0)
We know that the midpoint of this intercept is at equidistance from both the graph, therefore the points from which graph is equidistance is at origin (0,0)
Required answer:
Hence the midpoint of the x- intercepts of f(x) will be at (0,0) or at the origin of the graph so option 1 is correct.
in the graph below line k,y = -x makes a 45 degree angle with the X and Y axes complete the following
The point with a coordinate of (2,5) will be translated into y=-x line.
The transformation for y=-x would be:
1. x'= -y
2. y'= -x
For x=2 and y=5 would be:
x'= -y
x'= -5
y'= -x
y'= -2
The translated coordinate would be: (-5, -2)
Is my answer correct help please
Answer:
No, the correct answer is C.
Step-by-step explanation:
Five less than a number m = m - 5. and not 5 - m, so false.
Use the given rounded values, the properties of logsand your knowledge of logarithmic functions to find thevalue of each log expression. Show your work.
We want to find the value for
[tex]\log _425[/tex]To do that, first let's rewrite this expression as
[tex]\log _425=\log _45^2[/tex]Using the following property
[tex]\log _ab^c=c\log _ab[/tex]We can rewrite our expression as
[tex]\log _45^2=2\log _45[/tex]Using the given value on the text, we get our answer
[tex]\log _425=2\log _45=2\cdot1.2=2.4[/tex]The side of a square lot is (5×-3) meters. How many meters of fencing materials are needed to enclose the square lot?
The length of the fencing will be the perimeter of the given square with side (5x - 3) thus (20x - 12) meters will be the fencing length.
What is a square?A square is a geometrical figure in which we have four sides each side must be equal and the angle between two adjacent sides must be 90 degrees.
As per the given,
Side of square = 5x - 3
The fencing around the square will cover the complete perimeter of the square.
Since the perimeter of the square = 4 × side
Therefore,
Length of fencing = 4 × (5x - 3)
Length of fencing = 20x - 12
Hence "The length of the fencing will be the perimeter of the given square with side (5x - 3) thus (20x - 12) meters will be the fencing length".
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The data for the production of number of components at an industry for three weeks are given below. Make a stem-and-leaf plot68, 91, 42, 85, 13, 96, 15, 46, 95, 46, 64, 18, 44, 83, 69
In a stem and leaf plot, the first digit is always the stem, while the other digits are the leaves.
For the data represented:
The stem = the first digit
The leaf = the second digit
In the plot:
13, 15, and 18 will be grouped together because they have the same stem (1)
42, 44, 46, 46 are grouped together because they have the same stem (4)
64, 68, 69 are grouped together because they have the same stem (6)
83, 85 are grouped together because they have the same stem (8)
91, 95 and 96 are grouped together because they have the same stem (9)
The stem-and-leaf plot is shown below:
At the farmer’s market, Joan bought apples at $1.20 per pound, cherries for $2.00 per pound and pears for $0.80 per pound. She bought a total of 9 pounds of fruit for $11.00. Joan bought twice as many pounds of apples than cherries. Let A be the weight of the apples, C be the weight of the cherries, and P be the weight of the pears. Formulate a system of equations to determine how many pounds of each type of fruit were bought. Do Not Solve.
We have here a case in which we need to translate a problem into algebraic expressions to solve a problem, and we have the following information from the question:
• We have that Joan bought:
0. Apples at $1.20 per pound
,1. Cherries at $2.00 per pound
,2. Pears at $0.80 per pound
• We know that she bought a total of 9 pounds of fruit.
,• We also know that she spent $11.00 for the 9 pounds of fruit.
,• Joan bought twice as many pounds of apples than cherries.
We need to label weights as follows:
• Weight of apples ---> A
,• Weight of cherries ---> C
,• Weight of pears ---> P
Now to find a system of equations to determine the number of pounds of each type of fruit was bought, we can proceed as follows:
1. We know that if we multiply the price of the fruit per pound by the weight in pounds, we will obtain the amount of money Joan spent in total. Then we have:
[tex]1.20a+2.00c+0.80p=11.00\rightarrow\text{ \lparen First equation\rparen}[/tex]2. We also know that the total weight of the fruits was equal to 9 pounds. Then we can translate it into an algebraic expression as follows:
[tex]a+c+p=9\rightarrow(\text{ Second equation\rparen}[/tex]3. And we know that Joan bought twice as many pounds of apples than cherries, and we can translate it as follows too:
[tex]\begin{gathered} 2a=c \\ \\ \text{ If we subtract c from both sides of the equation, we have:} \\ \\ 2a-c=c-c \\ \\ 2a-c=0\text{ \lparen Third equation\rparen} \end{gathered}[/tex]Now we have the following equations:
[tex]\begin{gathered} 1.20a+2.00c+0.80p=11.00 \\ \\ \begin{equation*} a+c+p=9 \end{equation*} \\ \\ \begin{equation*} 2a-c=0 \end{equation*} \end{gathered}[/tex]Therefore, we have that the correct option is the first option:
• 1.20a + 2.00c + 0.80p = 11.00
• a + c + p = 9
,• 2a - c = 0
[First option].
Mariana, who rents properties for a living, measures all the offices in a building she is renting. Size (square meters) Number of offices 60 3 70 2 98 5 X is the size of a randomly chosen office. What is the expected value of X? Write your answer as a decimal.
The expected value formula is
[tex]E=\Sigma x\cdot P(x)[/tex][tex]\begin{gathered} E=60\cdot\frac{3}{10}+70\cdot\frac{2}{10}+98\cdot\frac{5}{10} \\ E=18+14+49 \\ E=81 \end{gathered}[/tex]Hence, the expected value is 81.A rectangular room is 1.5 times as long as it is wide, and its perimeter is 26 meters. Find the dimension of the room.The length is :The width is :
The rectangular room is 1.5times as long as it is wide and its perimeter is 26m. Let "x" represent the room's width, then the length of the room can be expressed as "1.5x"
The perimeter of a rectangle is equal to the sum of twice the width and twice the length following the formula:
[tex]P=2w+2l[/tex]We know that:
P=26m
w=x
l=1.5x
Then, replace the measurements on the formula:
[tex]\begin{gathered} 26=2x+2\cdot1.5x \\ 26=2x+3x \end{gathered}[/tex]From this expression, you can calculate x, first, add the like terms:
[tex]26=5x[/tex]Second, divide both sides by 5 to determine the value of x:
[tex]\begin{gathered} \frac{26}{5}=\frac{5x}{5} \\ 5.2=x \end{gathered}[/tex]The width is x= 5.2m
The length is 1.5x= 1.5*5.2= 7.8m
A company has been forced to reduce its number of employees. Today the company has 29% fewer employees than it did a year ago. If there are currently355 employees, how many employees did the company have a year agoemployees?
to solve this, question, we would have to convert the percentage to fractions or decimals.
Let x represent the numbers of employees the had a year ago
[tex]\begin{gathered} \frac{29}{100}\times x=355 \\ 0.29x=355 \\ \text{divide both sides by the coefficient of x} \\ \frac{0.29x}{0.29}=\frac{355}{0.29} \\ x=1224.127 \\ x\approx1224 \end{gathered}[/tex]a year ago, the company had 1224 empolyees
Find the equation of the line passing through the points (3,-2) and (3, 4).The answer is x = 3. I'm just wondering how my textbook got to this solution.My work:y-y1=m(x-x1). m=y2-y1 / x2-x1. y=mx+bm=4--2 / 3-3 = 6/0 = 0. m=0.y--2=0(x-3) = y=0-2 y=-2 <<<
Given two points. we can find the equation of a line passing through the points
The formula to be used is:
[tex]\frac{y_2-y_1}{x_2-x_!}=\frac{y-y_1}{x-x_!}[/tex]where
[tex]x_1=3,y_!=-2,x_2=3,y_2=4[/tex][tex]\frac{4-(-2)}{3-3}=\frac{y-(-2)}{x-3}[/tex]=>
[tex]\frac{6}{0}=\frac{y+2}{x-3}[/tex]The next step is to cross multiply
[tex]6(x-3)=0(y+2)[/tex]=>
[tex]6(x-3)=0[/tex]Divide both sides by 6 and make x the subject
x=3
5+10+15+...+100 write the series using summation notation
The Solution.
To determine that the series is an arithmetic progression,
[tex]\begin{gathered} T_{2_{}}-T_1=T_3-T_2=d \\ \text{Where d = common difference} \end{gathered}[/tex][tex]d=10-5=15-10=5[/tex]The sum of n terms of an arithmetic progression is given as
[tex]\begin{gathered} S_n=\frac{n}{2}(a+l) \\ \text{Where S}_n=\sum ^{\square}_{\square} \\ n=n\text{ umber of terms}=\text{?} \\ a=\text{first term=5} \\ l=\text{last term=100} \end{gathered}[/tex]But we need to first find the number of terms (n), by using the formula below:
[tex]\begin{gathered} l=a+(n-1)d \\ \text{Where a = 5, l=100, d = 5 and n =?} \end{gathered}[/tex]Substituting the values, we get
[tex]\begin{gathered} 100=5+(n-1)5 \\ 100=5+5n-5 \\ 100=5n \\ \text{Dviding both sides by 5, we get} \\ n=\frac{100}{5}=20 \end{gathered}[/tex]Substituting into the formula for finding the sum of terms of the series, we get
[tex]\begin{gathered} S_{20}=\frac{20}{2}(5+100) \\ \text{ } \\ \text{ = 10(105) = 1050} \end{gathered}[/tex]Therefore, the correct answer is 1050.
