Answer:
Step-by-step explanation:
Starting from tan x, you can find sec x, because of the trigonometric identity 1 + tan2 x = sec2 x.
1 + (-4/3)2 = 1 + 16/9 = 25/9 = sec2 x.
So sec x = ±√(25/9) = ±5/3. But since x is in Quadrant II, sec x has to be negative. That's because sec x has the same sign as cos x, because sec x = 1 / cos x. We know that cos x is negative is Quadrant II, therefore so is sec x. So sec x = -5/3.
Since sec x and cos x are reciprocals of each other, cos x = 1/sec x = -3/5.
Now use the identity sin2 x + cos2 x = 1, to find sin x:
sin2 x + (-3/5)2 = 1
sin2 x + 9/25 = 1
sin2 x = 16/25
sin x = ±4/5
Again, we know that sin x is positive in Quadrant II, so sin x = 4/5.
Now that we know sin x and cos x, we can use the double angle formulas to find sin 2x and cos 2x.
sin 2x = 2 sin x cos x = 2 (4/5) (-3/5) = -24/25
cos 2x = cos2 x - sin 2 x = (-3/5)2 - (4/5)2 = 9/25 - 16/25 = -7/25
Finally use the identity tan x = sin x / cos x to find tan 2x:
tan 2x = sin 2x / cos 2x = (-24/25) / (-7/25) = -24/-7 = 24/7
ATTACHMENTS OBJECTIVES A banana is 7 inches long. How many slices of banana can be cut from the 7-inch piece if each piece is 1/2 long? inch sation to solve and check your solution. Submission VIEW GRADE DETAILS M 9
As the banana is 7 inches long and each piece is 1/2 inches you divide 7 into 1/2 to find how many slices of banana can be cut:
Division of fractions:
[tex]\frac{\frac{a}{b}}{\frac{c}{d}}=\frac{a\cdot d}{b\cdot c}[/tex]Yo have: 7/1 divided into 1/2:
[tex]\frac{\frac{7}{1}}{\frac{1}{2}}=\frac{7\cdot2}{1\cdot1}=14[/tex]Then, in a banana of 7inches you can cut 14 slices of 1/2inchA single fair die is tossed. Find the probability of rolling a number greater than 5
Using the probability concept, the odds of rolling a number greater than 5 is 1 :5
What is probability ?
probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur or how likely it is that a proposition is true . the probability of an event is a number between 0 and 1 , where ,roughly speaking ,0 indicates impossibility of the event and 1 indicates certainty.
The odd of a particular experiment is defined thus :
Number of possible outcomes greater than 5 : number of possible below or equal to 5
Sample space = {1, 2, 3, 4, 5, 6}
Outcomes greater than 5 = {6} = 1
Outcomes below or equal to 5 = {1, 2, 3, 4, 5} = 5
The odds equals to 1 : 5
to know more about probability and numerical, click here :
https://brainly.com/question/28868231
#SPJ9
3. Which of the following equations would be a parabola with vertex (2,-3) that opendownwards? Select ALL.a.h.y = -2(x - 2)2 – 3i.y = (-x + 2)2 + 3C.y = -(x - 2)2 – 3b. y = -(x + 2)2 – 3y = -(x - 2)2 + 3d. y=-(x + 2)2 +3y = -(x - 2)3 +3f. y = -(x - 2)3 – 3y=-{(x - 2)2 - 3j. y = (-x - 2)2 – 3k. y = (-x + 2)2 – 3: نه1. y = (-x - 2)2 – 3m. y =} (x - 2)2 – 3g.n.y = 2(x - 2)2 - 3
Solution:
Given:
[tex]\text{Parabola with vertex (2,-3) that open downwards}[/tex]The equation of a parabola in vertex form is given by;
[tex]\begin{gathered} y=a(x-h)^2+k \\ \\ \text{where;} \\ (h,k)\text{ is the vertex} \\ \\ \text{Hence,} \\ h=2 \\ k=-3 \end{gathered}[/tex]Hence, the equation of the parabola is;
[tex]\begin{gathered} y=a(x-2)^2-3 \\ \\ \text{For the parabola to open downwards, then;} \\ a<0 \\ a\text{ must be negative} \end{gathered}[/tex]Hence, from the options, the equations that have a as negative and in the form gotten above will be selected.
Therefore, the equations of a parabola with vertex (2,-3) that open downwards are;
[tex]\begin{gathered} y=-2(x-2)^2-3 \\ \\ y=-(x-2)^2-3 \end{gathered}[/tex]PLEASE HELP
What is the value of x?
Answer: x = 50
Step-by-step explanation:
The two angles are opposite each other, meaning that they are equivalent.
So, we can set them equal to each other and then solve for x.
2(x + 10) = 3x - 30
2x + 20 = 3x -30
x = 50
Answer:
x = 50
Step-by-step explanation:
Since the two angles are opposite each other, you know that they are equal.
Set both equations equal to each other to isolate x:
2(x + 10) = 3x - 30
Distribute 2 on the left side
2x + 20 = 3x - 30
Subtract 2x from both sides
20 = x - 30
Add 30 to both sides
50 = x
6) Paul bought and sold a computer
He wrote his business activity as
follows:
cost price of computer = $1064
5 marked price of computer = $1399
Anscount on marked price
(if paid in cash)
Calculate.
5%
The selling price, if paid
Cash.
"1) The profit or loss as a percent.
of the cost price
The profit percentage of the computer sold by Paul is 31.5%
What is profit?It should be noted that profit simply means the gain that's derivd from selling a particular product.
In this case, the cost price of computer is $1064 and the marked price of computer is $1399.
The profit percentage will be:
= Profit / Cost price × 100
= (1399 - 1064) / 1064 × 100
= 335/1064 × 100
= 31.5%
Learn more about profit on
brainly.com/question/1078746
#SPJ1
Write rules for the composition of translations.
Answer: gurl you think i know
Step-by-step explanation:
find the perimeter of ABC with vertices A(-4,4), B(5,-6) and C(7,-9)
Answer:
The answer is maybe about around 26
Step-by-step explanation:
Please correct me if I am wrong, but I hope this helped.
Evaluate the expression for the given variable.9 - k ÷ 3/4 k=2/3
We are given the following expression:
[tex]9-k\div\frac{3}{4}[/tex]We are also given that k is equal to 2/3. So, we can substitute that into the expression:
[tex]9-\frac{2}{3}\div\frac{3}{4}[/tex]Due to order of operations, we have to do the division first, and then do the subtraction. To do division with fractions, we keep the first fraction the same and take the reciprocal of the second fraction. Then, we can multiply the two fractions. Let's do that:
[tex]9-(\frac{2}{3}\div\frac{3}{4})=9-(\frac{2}{3}*\frac{4}{3})=9-\frac{8}{9}[/tex]Now, we can do the subtraction:
[tex]9-\frac{8}{9}=\frac{81}{9}-\frac{8}{9}=\frac{73}{9}[/tex]Therefore, our answer is 73/9
Are these lines parallel or not: L1: (1,2), (3,1), and L2: (0,-1), (2,0)
First find the slope of the first line
L1
m = ( y2-y1)/(x2-x1)
m = ( 1-2)/(3-1)
= -1/2
Now find the slope of the second line
L2
m= ( y2-y1)/(x2-x1)
= ( 0 - -1)/(2 -0)
= (0+1)/(2-0)
= 1/2
Parallel lines have the same slope
These lines do not have the same slope, they are different by a negative sign.
These lines are not parallel.
Deborah bought a yard of ribbon for $14.76. How much did Deborah pay per inch? (1 yard = 3 feet.)
$0.41
$0.49
$1.23
$4.92
Answer:
$0.41 per inch
Step-by-step explanation:
Deborah bought a yard of ribbon for $14.76. How much did Deborah pay per inch? (1 yard = 3 feet.)
$0.41
$0.49
$1.23
$4.92
paid $14.76 for 1 yard or 3 feet. Solve for per foot:
$14.76 / 3 = $4.92 per foot
There are 12 inches per feet. Solve per inch:
$4.92 / 12 = $0.41 per inch
what is 338.8882 rounded to the nearest thousandth
Answer:
338.8882 rounded to the nearest thousandth is 338.888
hope it helps, mark as brainliest please :D
A firefighter has an annual income of $46,870. The income tax the firefighter has to pay is 16%. What is the amount of income tax in dollars and cents that the firefighter has to pay? (TEKS 7.13A-S)
amount of income tax:
[tex]Tax=46,870\times0.16=7499.2[/tex]Answer:
$7499.2
On a piece of paper, graph yz 2x - 3. Then determine which answer choicematches the graph you drew.ABсD(2, 1)(2, 1)(2, 1)((2, 1)(0-3)0,-3)(0-3)(0-3)A. Graph DOB. Graph BO C. Graph AD. Graph
The graph says
[tex]y\ge x-1[/tex]The upper section of the graph will be shaded since y is greater than or equals to x - 1.
The answer is A . Graph A
the quotient of two numbers is -1 their difference is 8 what are the numbers
Let the two numbers be represented with x and y.
Quotient of two numbers = -1:
[tex]\frac{x}{y}=-1\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\text{.}.(1)[/tex]Difference of two numbers = 8:
[tex]x\text{ - y = 8}\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots(2)[/tex]From the first equation, make x the the subject.
Thus, we have:
x = -y
Substitute -y for x in equation 2:
-y - y = 8
-2y = 8
Divide both sides by -2:
[tex]\begin{gathered} \frac{-2y}{-2}=\frac{8}{-2} \\ \\ y\text{ = -4} \end{gathered}[/tex]Now, substitute -4 for y in equation 2:
x - y = 8
x - (-4) = 8
x + 4 = 8
Subtract 4 from both sides:
x + 4 - 4 = 8 - 4
x = 4
Therefore,
x = 4 and y = -4
Thus, the numbers are 4 and -4
ANSWER:
4 and -4
A toy costs 35 000 lndonesian rupiah (Rp).
The conversion rate is Rp 1000 = 5$0.145 598.
Without using a calculator, estimate the price of
the toy in S$.
here is your answer I hope this helps
Is z(x) = 1 + 6x^2 + 4x a quadratic function? I don't believe it's linear or constant, just wanted to make sure.
Given function is
[tex]z(x)=1+6x^2+4x[/tex]In the given function, the maximum power of x is 2 and it is of the form
[tex]ax^2+bx+c[/tex]Therefore, it is a quadratic function.
two debt payments, the first for $800 due today and the second for $600 due in nine months with interest at 10.5% compound monthly, are to be settled by a payment of $800 six months from now and a final payment in 24 months. Determine the size of the final payment if money is now worth 9.5% compounded quarterly.
Given:
First payment = $800 due today
Second payment = $600 in 9 months
Interest rate = 10.5% compounded monthly
The interest is to be settled in a payment of $800 in 6 months and a final payment in 24 months.
Let's determine the final payment if the money is now worth 9.5% compounded quarterly.
Apply the compound interest formula:
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]Let x represent the initial amount of debt.
Thus, we have the equation:
[tex]\begin{gathered} (x-800)(1+\frac{0.105}{12})^{12\ast\frac{9}{12}}=600 \\ \\ (x-800)(1.00875)^9=600 \\ \\ (x-800)(1.08156)=600 \\ \\ x-800=\frac{600}{1.08156} \\ \\ x=1340.44 \end{gathered}[/tex]For the amount due in six months, we have:
[tex]\begin{gathered} A=1340.44(1+\frac{0.095}{4})^{4\ast\frac{6}{12}}_{} \\ \\ A=1340.44(1.02375)^2 \\ \\ A=1404.87 \end{gathered}[/tex]Hence, the amount which is due after 6 months will be:
$1404.87 - $800 = $604.87
Now, let's find the payment due in 24 months.
Number of months remaining = 24 - 6 = 18 months.
Hence, we have:
[tex]\begin{gathered} A=604.87(1+\frac{0.095}{4})^{4\ast\frac{18}{12}} \\ \\ A=604.87(1.02375)^6 \\ \\ A=696.35 \end{gathered}[/tex]Therefore, the final payment if the money is now worth 9.5% compounded quarterly is $696.35
ANSWER:
$696.35
Justin earns a base salary of $1500 per month at
the jewelry shop. He also earns a 3% commission
on all sales. If Just sold $82,975 worth of jewelry
last month, how much would he make for the
month including his base salary and commission?
8)
He make $84475 for the month including his base salary and commission.
Define commission.The percentage or fixed payment attached to a specific volume of sales is known as the commission rate. For illustration, a fee can be $30 for each sale or 6% of sales. The payment that is either a fixed amount or a percentage of a sale is the commission rate. When they make a sale, people in commission-based professions like insurance brokers, real estate agents, and automobile salespeople get compensated. A business pays its employees according to the revenue they bring in through a commission structure. An employee receives a commission when they conduct business or provide a service, according to the definition of commission.
Given,
Salary = $1500
Commission = 3%
Sales = $82975
= 1500 + 82975 + [tex]\frac{3}{100}[/tex]
= 84475.03
84475(approximately)
He make $84475 for the month including his base salary and commission.
To learn more about commission, visit:
https://brainly.com/question/20987196
#SPJ13
A laptop computer is purchased for $2100. Each year, its value is 75% of its value the year before. After how many years will the laptop computer be worth$300 or less?
SOLUTION:
After the first year, the price of the laptop computer is;
[tex]P_1=0.75\times2100=1575[/tex]After the second year, the price of the laptop computer is;
[tex]P_2=0.75\times1575=1181.25[/tex]After the third year, the price of the laptop computer is;
[tex]P_3=0.75\times1181.25=885.94[/tex]After the fourth year, the price of the laptop computer is;
[tex]P_4=0.75\times885.94=664.45[/tex]After the fifth year, the price of the laptop computer is;
[tex]P_5=0.75\times664.45=498.34[/tex]After the sixth year, the price of the laptop computer is;
[tex]P_6=0.75\times498.34=373.75[/tex]After the seventh year, the price of the laptop computer is;
[tex]P_7=0.75\times373.75=280.32[/tex]CORRECT ANSWER: 7 years
A grocer wants to mix two kinds of nuts. One kind sells for $2.00 per pound, and the other sells for $2.90 per pound. He wants to mix atotal of 16 pounds and sell it for $2.50 per pound. How many pounds of each kind should he use in the new mix? (Round off the answersto the nearest hundredth.)
Let
x -----> pounds of one kind of nuts ($2.00 per pound)
y ----> pounds of other kind of nuts ($2.90 per pound)
we have that
2x+2.90y=2.50(16) ------> equation 1
x+y=16-----> x=16-y -----> equation 2
solve the system of equations
substitute equation 2 in equation 1
2(16-y)+2.90y=40
solve for y
32-2y+2.90y=40
2.90y-2y=40-32
0.90y=8
y=8.89
Find out the value of x
x=16-8.89
x=7.11
therefore
the answer is
7.11 pounds of one kind of nuts ($2.00 per pound)8.89 pounds of other kind of nuts ($2.90 per pound)Which equation represents a line that is perpendicular to the line represented by
y=2/3x+1?
1) 3x+2y=12
2) 3x-2y=12
3) y=3/2x+2
4) y= -2/3x+4
Answer: (1)
Step-by-step explanation:
Perpendicular lines have slopes that are negative reciprocals. So, since the slope of the given line is 2/3, the slope of the line we want to find is -3/2.
Rearranging equations 1 and 2 into slope intercept form,
[tex]3x+2y=12 \implies 2y=-3x+12 \implies y=-\frac{3}{2}x+6\\\\3x-2y=12 \implies 2y-3x=-12 \implies 2y=3x-12 \implies y=\frac{3}{2}x-6[/tex]
From this, we see that equation 1 is the answer.
1260/27 as a mixed number
For each expression, combine like terms and write an equivalent expression with fewer terms.a. 4x+3xb. 3x+5x-1c. 5+2x+7+4xd. 4-2x+5xe. 10x-5+3x-2
To simplify the expressions you have to combine the like terms.
This means that you'll solve the operations between the terms that have the same variables, for example x + 2x=3x
Or the terms that have no variables and are only numbers, for example 4+5=9
a. The expression is
[tex]4x+3x[/tex]Both terms have the same variable "x", so you can add them together. To do so, add the coefficients, i.e. the numbers that are being multiplied by x
[tex]4x+3x=(4+3)x=7x[/tex]And you get that the simplified expression is 7x
b. The expression is
[tex]3x+5x-1[/tex]In this expression you have two types of terms, the x-related terms and one constant. In this case you have to solve the operation for the x-related terms together and leave the constant as it is
[tex](3x+5x)-1=(3+5)x-1=8x-1[/tex]The simplified expression is 8x-1
The width of a Rectangle is 3.6 inches and the perimeter is 72 inches. What is the length of the rectangle?
We know that
• The width of the rectangle is 3.6 inches.
,• The perimeter is 72 inches.
The perimeter formula for a rectangle is
[tex]P=2(w+l)[/tex]Where P = 72, w = 3.6, and we have to solve for l.
[tex]\begin{gathered} 72=2(3.6+l) \\ \frac{72}{2}=3.6+l \\ 36=3.6+l \\ l=36-3.6 \\ l=32.4 \end{gathered}[/tex]Therefore, the length of the rectangle is 32.4 inches.In the following figure PR is perpendicular to QS. PR= 14cm, QR=15 cm and QS =12 cm. What is the perimeter of PQR?
A quarterback completed 19 out of 30 attempts to pass the football.What was his percent of completion
The percentage of completion is 63.34%.
Rectangle ABCD is graphed in the coordinate plane. The following are the vertices of the
rectangle: A(-8,-6), B(-3,-6), C(-3,-4), and D(-8,-4).
Given these coordinates, what is the length of side AB of this rectangle?
The length of side AB of this rectangle is = 5 units
what is rectangle ?
A shape with four straight sides and four angles of 90 degrees ( right angle ) . two of the sides are longer than the other two . a rectangle with four sides of equal length is square .
we could use distance formula to find the length
A (-8,-6) ; B (3 , -6 )
distance =(( X2 - X1 )^2 +( Y2 - Y1 ) ^2 ) ^1/2
AB = (( -3+8)^2+(-6-[-6]^2)^1/2
AB= 5^2
AB = 5 units .
To know more about square and rectangle click here :
https://brainly.com/question/28868826
# SPJ13
To draw a graph for y = 3/4x + 7, a person can draw a point at x of 0 and y of ___, a second point by going up 3 and over ___, and then draw a line through the points.
To draw a graph for y = 3/4x + 7, a person can draw a point at x of 0 and y of y = 7, a second point by going up 3 and over y = 10, and then draw a line through the points.
How to know if a point lies in the graph of a function?
All the points (and only those points) which lie on the graph of the function satisfy its equation. Thus, if a point lies on the graph of a function, then it must also satisfy the function.
Given that:
y = 3/4x + 7
At x = 0
y = 7.
Going over by 3 then,
7 + 3 = 10.
So, now y = 10
10 = 3/4x +7
3/4x = 10-7
3/4x = 3
x = 4.
Now,
To draw a graph of 3/4x + 7, a person can draw c point x of 0 and y of 7, a second point by going over 3 and up 4.
Thus, for drawing the graph for y = 3/4x + 7, a person can draw a point at x of 0 and y of 7, a second point by going over 3 and up 10 and then draw a line through the points.
To know more about points lying on graph of a function
Refer this link:
brainly.com/question/24361987
#SPJ1
Move numbers to the blanks to rewrite each square root. [tex] \sqrt{ - 4} = [/tex][tex] \sqrt{ - 5 = } [/tex]answers:[tex]2i[/tex][tex] - 2[/tex][tex]4i[/tex][tex] \sqrt{5i} [/tex][tex] - \sqrt{5} [/tex][tex]i \sqrt{5} [/tex]
We have 2 expressions:
[tex]\begin{gathered} a)\text{ }\sqrt[]{-4} \\ b)\sqrt[]{-5} \end{gathered}[/tex]Case a.
We can rewrite our square root as
[tex]\sqrt[]{-4}=\sqrt[]{-1\times4}=\sqrt[]{-1}\times\sqrt[]{4}[/tex]but by definition
[tex]\sqrt[]{-1}=i[/tex]which is the imaginary number. So, our square root is equal to
[tex]\sqrt[]{-4}=\sqrt[]{4}i[/tex]which corresponds to option 3.
Case b.
Similarly,
[tex]\sqrt[]{-5}=\sqrt[]{-1}\times\sqrt[]{5}[/tex]and the answer is
[tex]\sqrt[]{-5}=i\sqrt[]{5}[/tex]which corresponds to option 6
Solve form. 2m - p = 11f
ANSWER
[tex]m=\frac{11f+p}{2}[/tex]EXPLANATION
We want to solve for m in the equation:
[tex]2m-p=11f[/tex]This means that we want to make m the subject of formula.
That is:
[tex]\begin{gathered} \text{Add p to both sides of the equation:} \\ 2m-p+p=11f+p \\ 2m=11f+p \\ \text{Divide both sides by 2:} \\ \frac{2m}{2}=\frac{11f+p}{2} \\ m=\frac{11f+p}{2} \end{gathered}[/tex]That is the answer.