If cos A = 3/√13 and angle A is not in quadrant I, determine the exact value of sin A.
Answers
To determine the exact value of sin A we get -2/√13
What is determinant?
the determinant is a scalar of value that is a function of to the entries of a square matrix. It is allows characterizing of some properties of to the matrix and the linear map of represented by the matrix.
It is a scalar value which is associated with the square matrix.
Sol-Cos A =3/√13
angle A is not in quadrant I
So angle A is in quadrant IV
Thus,
Sin A =-√(√13)^2-3^2/√13
=-√13-9/√13
=-√4/√13
=-2/√13
Thus the answer is -2/√13.
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Related Questions
A college conducted a survey of randomly selected freshmen about their choice of major. The table shows the results of the survey. KS
Answers
ONLY F is correct;
Here, we want to select the correct inference from the data presented
f) We want to comapre the number of English freshmen and the undecided
Both have a count of 50; we can see that these values are equal and thus, we conclude that these two are equal
This makes the inference correct
g) Here, we want to compare Education freshmen to science freshmen or others
From the question, the number of education freshmen is 60
The number of science or others is (30+25) = 55
The number for education is greater and not less
This makes this option or inference incorrect
h) Here, we want to comapre Business/Education and Science/Engineering
Business OR Education is = 45 + 60 = 105
Science OR Engineering is = 35 + 40 = 75
Business/Education is greater and this makes this option or inference wrong
j) Here, we want to compare Business and English
Business is 45
English is 50
We can see that English is greater and this makes the inference/option wrong
Solve for x. 8x-2x+7>21+10
Answers
Answer: [tex]x > 4[/tex]
Step-by-step explanation:
[tex]8x-2x+7 > 21+10\\\\6x+7 > 31\\\\6x > 24\\\\x > 4[/tex]
Hannah is saving money to buy some lirns. She invests $290 in a savings account that earns 7.6% interest, compounded annually. How much money will she have in her account after 2 years? Answer in dollars and round to the nearest cent.
Answers
Principal amount, P= $290.
Rate, r = 0.076
Time, t = 2
Therefore, the total amount in her account after 2 years is
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]Hence,
[tex]\begin{gathered} A=290(1+0.076)^2 \\ =335.755 \end{gathered}[/tex]Therefore, the amount is 335.80 dollars.
That is, 335 dollars and 80 cents.
write an equation of each parabola in vertex form. Vertex (3,-2) Point (2,3)
Answers
The equation of Parabola in the vertex form with vertex (3,-2) and point(2,3) is y = 5(x-3)² - 2 .
The equation of parabola with vertex (h,k) is denoted by the equation
y = a(x-h)² + k
In the question ,
it is given that
the vertex of the Parabola is (3,-2) and the point is (2,3)
So, the equation of the parabola with vertex (3,-2) will be
y = a(x-3)² - 2
Since the point (2,3) lies on the parabola ,
So, 3 = a(2-3)² - 2
3 + 2 = a*(-1)²
5 = a
Substituting a in the equation y = a(x-3)² - 2 ,
we get
y = 5(x-3)² - 2
Therefore , The equation of Parabola in the vertex form with vertex (3,-2) and point(2,3) is y = 5(x-3)² - 2 .
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Maria is at the top of a cliff and sees a seal in the water. If the cliff is 40 feet above the water, Marla's eye-level is 5.5 feet, and the angle of depression is 52°, what is the horizontal distance from the seal to the cliff, tothe nearest foot?
Answers
SOLUTION
Let us make a diagram to interpret the question
from the diagram above, we can make the right-angle triangle as follows
So we can use SOHCAHTOA to solve this. The opposite side to the angle 52 degrees is 45.5 ft, this is gotten by adding the height of the cliff to Maria's height from her feet to her eyes.
The adjacent side is d, that is the distance from the seal to the cliff, so we have
[tex]\begin{gathered} TOA\text{ tan}\theta\text{ = }\frac{opposite}{adjacent} \\ tan52\degree=\frac{45.5}{d} \\ cross\text{ multiply, we have } \\ tan52\degree d=45.5 \\ d=\frac{45.5}{tan52} \\ d=35.54849 \end{gathered}[/tex]Hence the answer is 36 foot to the nearest foot
Applying the product rule to expression \left(3^3\div 3^4\right)^5gives us Answer raised to the power of Answerdivided by Answer raised to the power of AnswerSimplify that into a reduced fraction.The numerator is AnswerThe denominator is Answer
Answers
Given the expression
[tex](3^3\div3^4)^5[/tex]Using product rule
[tex]\begin{gathered} (3^3\div3^4)^5=(\frac{3^3}{3^4})^5 \\ =(3^{3-4})^5=(3^{-1})^5 \\ =3^{-1\times5}=3^{-5} \end{gathered}[/tex]Where
[tex]3^{-5}=\frac{1}{3^5}=\frac{1}{243}[/tex]Hence, answer is 1/243
[tex](3^3\div3^4)^5=\frac{1}{243}[/tex]The numerator is 1
The denominator is 243
A) 14x + 7y > 21 B) 14x + 7y < 21 C) 14x + 7y 5 21 D) 14x + 7y 221match with graph
Answers
As all the options are the same equation
so, we need to know the type of the sign of the inequality
As shown in the graph
The line is shaded so, the sign is < or >
The shaded area which is the solution of the inequaity is below the line
So, the sign is <
So, the answer is option B) 14x + 7y < 21
Question 5The table below shows the coordinates of a figure that was transformed.Pre-ImageImageA(5,2)B(6, 1)A'(0,0)B'(1, -1)C'(-1,3)C(4,5)Which is a correct description of the transformation?
Answers
You have the following A, B and C points, which are transformed to the points A', B' and C', jus
find the height of the trapezoidA=80 CM2 7Cm9CM
Answers
The area formula for trapezoids is
[tex]A=\frac{(B+b)h}{2}[/tex]Where B = 9 cm, b = 7 cm, and A = 80 cm2. Let's replace these dimensions to find h
[tex]\begin{gathered} 80=\frac{(9+7)\cdot h}{2} \\ 160=16h \\ h=\frac{160}{16} \\ h=10 \end{gathered}[/tex]Hence, the height is 10 cm.can you help me? on this math problem. (in the pic)
Answers
Given:
(x, y) ==> (1, -6)
m = 5
To write the equation, use the slope intercept form:
y = mx + b
where m is the slope and b is the y-intercept.
To solve for b, substitue 1 for x, -6 for y, and 5 for m in the equation.
Thus we have:
y = mx + b
-6 = 5(1) + b
-6 = 5 + b
Subtract 5 from both sides:
-6 - 5 = 5 - 5 + b
-11 = b
The y-intercept is -11.
Therefore, the equation of the line in slope-intercept form is:
y = 5x - 11
ANSWER:
y = 5x - 11
1. The equations y = x2 + 6x + 8 and y = (x + 2)(x+4) both define thesame quadratic function.Without graphing, identify the x-intercepts and y-intercept of the graph.Explain how you know
Answers
Given the quadratic equation
[tex]y=x^2\text{ +6x + 8}[/tex](1) x-intercepts are -2 and -4 is the points that pass through the x-axis
when y = 0
[tex]\begin{gathered} y\text{ = 0 } \\ x^2\text{ + 6x + 8 = 0} \\ x^2+2x\text{ +4x +8 = 0} \\ (x\text{ + 2)(x +4)=0} \\ x\text{ +2 = 0 or x +4 =0} \\ x\text{ = -2 or x = -4} \end{gathered}[/tex](11) y-intercepts = 8 is the points that pass through the y axis when x = 0
[tex]\begin{gathered} y=x^2\text{ +6x +8} \\ \text{when x = 0} \\ y=0^2\text{ +6(0) +8} \\ \text{y = 8} \end{gathered}[/tex]
Linda's medicine bottlesays "If you will be driving, then youshould not take this medicine." What arethe inverse, converse, and thecontrapositive of this statement?
Answers
For two statements p and q, and the compounded statement "If p, then q", we have the following definitions for the inverse, converse, and contrapositive of this compounded statement:
inverse: If not p, then not q.
converse: If q, then p.
contrapositive: If not q, then not p.
So, for the presented statement, i. e., "If you will be driving, then you should not take this medicine" we have:
p: you will be driving
q: you should not take this medicine
Notice that:
not p: you will not be driving
not q: you may take this medicine
Then, using the above definitions, we write:
inverse: If you will not be driving, then you may take this medicine.
converse: If you should not take this medicine, then you will drive.
contrapositive: If you may take this medicine, then you will not be driving.
Find the reference angle for the given angles 745 degree.
Answers
Maisa,. let's recall the formula for calculating the reference angle when the angle is > 360 degrees:
Reference angle = Given angle - 360
Reference angle = 745 - 360
Reference angle = 385
It's still higher value than 360, therefore we subtract 360 again.
Reference angle = 385 - 360
Reference angle = 25 degrees
A building worth $829,000 is depreciated for tax purposes by its owner using the straight-line depreciation method.
The value of the building, y, after x months of use, is given by y=829,000-2700x dollars. After how many years will
the value of the building be $699,400?
Answers
The value of the building would be $699,400 in 4 years.
What will be the value of the building?Depreciation is the when the value of an asset reduces as a result of wear and tear. Straight line depreciation is a method used in depreciating the value of an asset linearly with the passage of time.
The equation that can be used to determine the value of the building with a straight line depreciation is:
Value of the asset = initial value of the asset - (number of months x deprecation rate)
y = 829,000 - 2700x
The first step is to determine the number of months it would take for the building to have a value of $699,400.
$699,400 = 829,000 - 2700x
829,000 - 699,400 = 2,700x
129,600 = 2,700x
x = 129,600 / 2,700
x = 48 months
Now convert, months to years
1 year = 12 months
48 / 12 = 4 years
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How do I find x I know you separate the shapes but I got it wrong…
Answers
Let's find this length first
6√2 is the hypotenuse, then
[tex]\begin{gathered} (6\sqrt{2})^2=6^2+y^2 \\ \\ y^2=(6\sqrt{2})^2-6^2 \\ \\ y^2=36\cdot2-36 \\ \\ y^2=36 \\ \\ y=\sqrt{36}=6 \end{gathered}[/tex]Then we can find x because
[tex]\begin{gathered} x^2=y^2+12^2 \\ \\ x^2=6^2+12^2 \\ \\ x^2=36+144 \\ \\ x^2=180 \\ \\ x=\sqrt{180} \\ \\ x=6\sqrt{5} \end{gathered}[/tex]The length of x is
[tex]x=6\sqrt{5}[/tex]I need help figuring out which of the following statements is false
Answers
EXPLANATION
We can first array the sets in order to match the terms:
X= {15, 22, 33, 44, 89, 165, 1025}
Y= {-5, 15, 33, 88, 99, 150, 160, 1025}
We can see that the common terms are {15,33,1025}, thus the third statement is true.
Now, we can check if the second statement is true or false.
If we put both sets together from smaller to greater and using just one common term, we get the following expression:
X U Y = {-5, 15, 22, 33, 44, 89, 99, 150, 160, 165, 1025}
In conclusion, the second statement is also true.
you have torn a tendon and is facing surgery to repair it. the surgeon explains the risks to you: infection occurs in 3% of such operations, the repair fails in 17%, and both infection and failure occur together in 2%. what percentage of these operations succeed and are free from infection? give your answer as a whole number.
Answers
Our required probability is 99.82% or a 100%
%, which is a relative figure used to denote hundredths of any quantity. Since one percent (symbolized as 1%) is equal to one hundredth of something, 100 percent stands for everything, and 200 percent refers to twice the amount specified. percentage.
What is the definition of percentage in statistics?
Percentages. The use of percentages to express statistics is one of the most popular. The word "percent" simply refers to "per hundred," and the sign for percentage is %. By dividing the whole or whole number by 100, one percent (or 1%) is equal to one hundredth of the total or whole.
Given that P(operational infection occurs at a 3% rate)
P(operational repair failures) = 17%
P(infection and failure happen simultaneously) = 2%
The first thing we'll discover is that P(infection or failure) is given by 0.03 + 0.17 - 0.02 = 0.18 = 0.18%.
Therefore, the probability that these procedures will be successful and infection-free is given by 100 - 0.18 = 99.82%.
Consequently, 99.82% of a probability is needed.
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if [tex] \sqrt{ \times } [/tex]is equal to the coordinate of point D in the diagram above, then X is equal to:
Answers
11)
The number line is divided into 5 equal intervals. if the fourth segment is 7, then we would find the distance between each segment
The distance between the fourth segment and the first segment is 7 - - 1 = 8
Since we are considering the distance between segment 1 and segment 4, the distance between each segment would be
8/4 = 2
Thus,
point D = 7 + 2 = 9
If
[tex]\begin{gathered} \sqrt[]{x\text{ }}\text{ = D, then} \\ \sqrt[]{x}\text{ = 9} \\ \text{Squaring both sides of the equation, we have} \\ x=9^2 \\ x\text{ = 81} \end{gathered}[/tex]Option E is correct
Find the percent increase in volume when 1 foot is added to each dimension of the prism. Round your answer to the nearest tenth of a percent.7 ft10 ft86 ft
Answers
Solution
Step 1
The volume of a triangular prism = Cross-sectional area x Length
Step 2
[tex]\begin{gathered} Cross\text{ sectional area = area of the triangle} \\ Base\text{ = 6ft} \\ Height\text{ = 7ft} \\ Cross\text{ sectional area = }\frac{1}{2}\times\text{ 7 }\times\text{ 6 = 21 ft}^2 \\ Volume\text{ = 21 }\times\text{ 10 = 210 ft}^3 \end{gathered}[/tex]Step 3:
When 1 foot is added to each dimension of the prism.
The new dimensions becomes Base = 7, Height = 8 and length = 11
[tex]\begin{gathered} \text{Cross-sectional area = }\frac{1}{2}\text{ }\times\text{ 7 }\times\text{ 8 = 28 ft}^2 \\ Length\text{ = 11 ft} \\ Volume\text{ = 28 }\times\text{ 11 = 308 ft}^3 \end{gathered}[/tex]Step 4
Find the percent increase in volume
[tex]\begin{gathered} \text{Percent increase in volume = }\frac{308\text{ - 210}}{210}\text{ }\times\text{ 100\%} \\ \text{= }\frac{98}{210}\text{ }\times100 \\ \text{= 46.7} \end{gathered}[/tex]Final answer
46.7
Score: U OQuestion Help3.3.29CeringritdA train travels 140 km in the same time that a plane covers 630 km. If the speed of the plane is 30 km per hr less than 5 times the speed ofTrain140the train, find both speeds.Planey 630The train's speed is km per hr
Answers
Notice that the time for both trips is the SAME but not known (let's use the letter T to address this unknown).
We also assign St to the speed of the train, and Sp to the speed of the plane.
Then, the relationship between the speeds according to the information they provide, is given by the equation:
Sp = 5 * St - 30
we also know that the train covers 140 km in the time T, Then according to the formula for speed (distance divided by time) we can say:
St = 140 km / T, therefore T = 140 km / St
We do something similar with the information on the distance covered by the plane:
Sp = 630 km / T which solving for T gives:
T = 630 km / Sp
Now we equal the expressions for T (since that time is the SAME as we noticed before, and get:
630 km / Sp = 140 / St
we corss-multiply to get the speeds in the numerator:
630 St = 140 Sp
ANd we use the very first equation we wrote (Sp = 5 * St - 30)
to replace Sp in terms of St:
630 St = 140 (5 St - 30)
Now use distributive property on the right to eliminate the parenthesis:
630 St = 700 St - 4200
add 4200 to both sides, and subtract 630 St from both sides :
4200 = 700 St - 630 St
4200 = 70 St
divide both sides by 70 to isolate St completely:
St = 4200 / 70
St = 60 km/h (this is the speed of the train)
Now we can find the value of the speed of the plane, using the first equation again:
Sp = 5 * St - 30 = 5 (60) - 30 = 300 - 30 = 270 km/h
Then the speed of the plane is: 270 km/h
The transformation T-2,3 maps the point (7,2) onto the point whose coordinates are
Answers
we know that
the rule of the translation in this problem is 2 units at left and 3 units up
so
(x,y) ------> (x-2,y+3)
Apply the rule
(7,2) ------> (7-2,2+3)
(5,5)Dalia works mowing lawns and babysitting. She earns $8.40 an hour for mowing and $7.90 an hour for babysitting . How much will ahe earn for 7 hours of mowing and 1 hour of babysitting?
Answers
Given that she earns $8.40 an hour for mowing then for 7 hours of mowing, the amount earned
= 7 * $8.40
=$58.80
Furthermore, given that she earns $7.90 for baby sitting for an hour
Hence for mowing for 7 hours and baby sitting for 1 hour, the total amount she will earn
= $58.80 + $7.90
= $66.70
Virginia is going to visit 5 cities this summer. She will choose from 8 different cities and the order in which she visits the cities does not matter. How many different city combinations are possible for the summer travelling?
Answers
The price of Stock A at 9 A.M. was $15.21. Since then, the price has been increasing at the rate of $0.07 each hour. At noon the price of Stock B was $15.96. It begins to decrease at the rate of $0.15 each hour. If the two rates continue, in how many hours will the prices of the two stocks be the same?
Answers
The price of the two stocks will be same in 1 hours .
in the question ,
it is given that
the price of the stock A at 9 A.M is $15.21
price increases at the rate of 0.07 each hour .
so the price of the stock A at 12 P.M. is 15.21 + 0.21 = $15.42
and the price of the stock A after x hours from 12 P.M. is given by the equation
stock A = 15.42 + 0.07(x)
the price of stock B at 12 P.M. is $15.96
price decreases at the rate of 0.15 each hour .
the price of the stock B after x hours from 12 P.M. is given by the equation
stock B = 15.96 - 0.15(x)
since the price of the two stocks is same , we equate both the equations .
15.42 + 0.07(x) = 15.96 - 0.15(x)
15.42 + 0.07x = 15.96 - 0.15x
0.15x + 0.07x = 15.42 - 15.21
0.22x = 0.21
x = 0.9545
x ≈ 1
Therefore , The price of the two stocks will be same in 1 hours .
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find the unit price of a 3 pack of bottle juice for $6.75 fill in the amount per bottle of juice
Answers
EXPLANATION
Let's see the facts:
Unit price = $6.75
Number of packs = 3
The unit price is given by the following relationship:
[tex]\text{Unit price= }\frac{6.75}{3}=2.25\frac{\text{dollars}}{\text{pack}}[/tex]The unit price is 2.25 $/pack
Calculate the degree of the angles in the triangles below.
Answers
the sum of the internal angles of a triangle is equal to 180, then
[tex]\begin{gathered} 2x+7+5x+12=180 \\ 7x+19=180 \\ 7x+19-19=180-19 \\ 7x=161 \\ \frac{7x}{7}=\frac{161}{7} \\ x=23 \end{gathered}[/tex]so
answer:
angle 1 = 2x + 7 = 2(23) + 7 = 46 + 7 = 53°
angle 2 = 5x = 5(23) = 115°
angle 3 = 12°
A storm is moving at 30km/hr .it is 60 km away. What time will it arrive
Answers
From the information provided, the storm is travelling at a speed of 30km/hr. In other words, its travelling 30 kilometers every hour. If the storm is 60 kilometers away, then we have the following ratio;
[tex]undefined[/tex]Cai says you can divide both quantities in a ratio by the same non-zero number to find an equivalent ratio. Explain why cai is correct.
Answers
In this case, Cai is right.
Basically, Cai is right because a ratio is a fraction. So, if you divide the numerator and denomirator by the same number, the fraction won't be changed, in that case you would get an equivalent fraction.
For example, if we have 4/6, and we divide both numbers by 2, we get 2/3, these operations are valid because you are dividing both numbers by the same (2).
A 43-inch piece of steel is cut into three pieces so that the second piece is twice as long as the first
piece, and the third piece is three inches more than five times the length of the first piece. Find the
lengths of the pieces.
What is the length of the first piece?
Answers
The length of the first piece is 5 inches when a 43-inch piece of steel is cut into three pieces.
According to the question,
We have the following information:
A 43-inch piece of steel is cut into three pieces so that the second piece is twice as long as the first piece, and the third piece is three inches more than five times the length of the first piece.
Now, let's take the length of the first piece to be x inches (as shown in the figure).
Length of second piece = 2x inches
Length of third piece = (3+5x) inches
Now, we have the following expression for addition:
x + 2x + 3 + 5x = 43
8x+3 = 43
8x = 43-3
8x = 40
x = 40/8
x = 5 inches
Hence, the length of the first piece is 5 inches.
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I don’t know what im doing wrong. Can someone help?
Answers
We want to write
[tex]\frac{\sqrt[]{5}+1}{2}[/tex]as decimal, doing it on a calculator we have
[tex]\frac{\sqrt[]{5}+1}{2}=1.61803398875[/tex]But we only need three decimal places, then the result is
[tex]\frac{\sqrt[]{5}+1}{2}=1.618[/tex]
