The value of sin Y is 4/5. The correct option is B) 4/5
Calculating the value of the sine of an angleFrom the question, we are to determine the value of sin Y.
From the given information, we have that
sin X = 3/5
and
cos X = 4/5
Also,
We have that angle X and angle Y are complementary angles.
That is,
X + Y = 90°
From the Trigonometric ratios of complementary angles, we have that
sin Y = cos (90° - Y)
From X + Y = 90°
X = 90° - Y
Therefore,
sin Y = cos X
From the given information,
cos X = 4/5
Hence, sin Y = 4/5
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By completing the square , solve x^2+12x-c=0 where c is a positive constant.
Give your answers in surd form in terms of c.
You must show all your working.
The roots of [tex]x^{2}[/tex] +12x -c = 0 in surd form is -6 ± [tex]\sqrt{c + 36}[/tex]
What is a quadratic equation?A quadratic equation is an algebraic equation of the second degree in x. The quadratic equation in its standard form is ax2 + bx + c = 0, where a and b are the coefficients of [tex]x^{2}[/tex] and x respectively and c is the constant term.
[tex]x^{2}[/tex] + 12x - c = 0
taking c to the other side, we have
[tex]x^{2}[/tex] + 12x = c
adding the square of half the coefficient of x, which is 6
[tex]x^{2}[/tex] + 12x + [tex]6^{2}[/tex] = c + [tex]6^{2}[/tex]
The left side is now a perfect square which can be simplified as [tex](x + 6)^{2}[/tex]
So,
[tex](x + 6)^{2}[/tex] = c + 36
taking the square root of both sides, we have
x + 6 = [tex]\sqrt{ c + 36}[/tex]
Therefore,
x = -6 ±[tex]\sqrt{c + 36}[/tex]
In conclusion, the solution to the equation is x = -6 ±[tex]\sqrt{c + 36}[/tex]
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A popular resort hotel has 300 rooms and is usually fully booked. About 7% of the time a reservation is canceled before the 6:00 p. M. Deadline with no penalty. What is the probability that at least 285 rooms will be occupied? use the binomial distribution to find the exact value.
The probability that at least 285 rooms will be occupied is 0.0885
A popular resort hotel's reservation follows Normal distribution as size of sample is greater than 30 with mean np and standard deviation √npq
Given , Probability of cancelation : q = 7% = 0.07
Probability of no cancellation of room : p = 1 - q
p = 1 - 0.07
p = 0.93
here, Binomial distribution tends to normal
Sample size : n = 300
Mean = np
= 300 × 0.93
= 279
Standard deviation = [tex]\sqrt{npq}[/tex]
= [tex]\sqrt{(300)(0.93)(0.07)}[/tex]
= [tex]\sqrt{19.53}[/tex]
= 4.42
We have to find P(x ≥ 285)
subtracting 279 and dividing by 4.42 to each sides
P(x ≥ 285) = [tex]P(\frac{x - 278}{4.42} \geq \frac{285 - 278}{4.42} )[/tex]
= P(z ≥ 1.357) = 1 - P(z<1.357)
Using Z probability table ,
P(x ≥ 285) = 1 - (0.9115)
= 0.0885 is required probability
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(-20x)( 3xy-y/x^2 )( 3x/9x^2-3x )
When we simplify the given expression, the given expression equals to -20(3x-y)/x(3x-1)
Expression is a combination of variables, numbers and symbols (operations) which is defined according to some rules. We can apply any formula or solve the given expression according to the operations provided.
Given expression
-20x(3x-y/x^2)(3x/9x^2-3x)
Multiply each term with another term
= -20x × (3x-y)/x^2 × 3x/9x^2-3x
In first term and second term cancel x from numerator and denominators and from last expression take 3x common
= -20 × (3x-y)/x × 3x/3x(3x-1)
Cancel 3x from numerator and denominator in last term and we will get the final result.
= -20 × (3x-y)/x × 1/(3x-1)
= -20(3x-y)/x(3x-1)
The given question is incomplete, the complete question is
Simplify the following expression
(-20x)( 3xy-y/x^2 )( 3x/9x^2-3x )
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help meeeeeeeeeeeeeee pleaseeeeeee
Answer: Width = 4.7 meters, Length = 6.7 meters
Step-by-step explanation:
Let the width be [tex]w[/tex]. It follows that the length is [tex]w+2[/tex].
[tex]w(w+2)=32\\\\w^2+ 2w-32=0\\\\w=\frac{-2 \pm \sqrt{2^2 -4(1)(-32)}}{2(1)}\\\\w \approx 4.7 \text{ } (w > 0)\\\\\implies w+2 \approx 6.7[/tex]
A rectangular prism has a width of 4 cm, a height of 3 cm and a depth of 5 cm. What is the volume of the prism?
We have that the equation of the volume of a rectangular prism is:
[tex]V=w\cdot h\cdot d[/tex]in this case, we have the following information:
[tex]\begin{gathered} w=4\operatorname{cm} \\ h=3\operatorname{cm} \\ d=5\operatorname{cm} \end{gathered}[/tex]then, using the formula we have:
[tex]\begin{gathered} V=4\cdot3\cdot5=12\cdot5=60 \\ V=60\operatorname{cm}^3 \end{gathered}[/tex]therefore, the volume of the prism is 60 cm^3
Can you please help me out with a question
ame of the
GXIS.
4. Practice: Organizing Information (3 points)
Fill in the blanks.
The factory is operational for at most 12 hours a day. A reasonable domain for
the graph of daily energy use would be <__x___
A domain of the situation is given by:
The factory is operational for at most 12 hours a day.
[tex]0\leq x\leq12[/tex]Answer:
[tex]0\leqslant x\leqslant12[/tex]The price for five pounds of
candy is $8. How much does it cost for
one pound?
Answer:
1.60
8/5=1.60
Step-by-step explanation:
Answer: $1.60
Step-by-step explanation: Easy, just divide 8 by 5. 8/5 = 1.6
WILL GIV BRAINLIEST Fred spent $3.15 on 4 1/2 pounds of peanuts. How much did he pay for each pound of peanuts? write the number sentence that goes with the word problem. Then, write your answer.
Answer:
Fred paid 70 cents per pound.
Step-by-step explanation:
Let c = the cost of one pound of peanuts.
[tex]4.5c = 3.15[/tex]
[tex]c = .70[/tex]
Answer:0.7
Step-by-step explanation:
3.15÷4.5=0.7
Given ∠3≅∠13, which lines, if any, must be parallel based on the given information? Justify your conclusion. Responses a∥b, Converse of the Alternate Interior Angles Theorem a is parallel to b, , Converse of the Alternate Interior Angles Theorem c∥d, Converse of the Same-Side Interior Angles Theorem c is parallel to d, , Converse of the Same-Side Interior Angles Theorem c∥d, Converse of the Corresponding Angles Theorem c is parallel to d, , Converse of the Corresponding Angles Theorem not enough information to make a conclusion not enough information to make a conclusion Two horizontal, parallel lines, line c and line d, where line c is above line d. These lines are intersected by two diagonal parallel lines, line a and line b. Line a is to the left of line b. The angles created by each intersection are numbered. From top left, going clockwise, the angles where line a intersects line c are labeled eleven, ten, nine, and twelve. The angles where line b intersects line c are labeled seven, six, five, and eight. The angles where line a intersects line d are labeled fifteen, fourteen, thirteen and sixteen. The angles where line b intersects line d are labeled three, two, one and four.
The order of the arrangement of the angles in the question (see attached drawing based on a similar question on the website, created with MS Word) indicate that the angles ∠3 and ∠13 are congruent. The correct option is therefore;
a║b, Converse of the Alternate Interior Theorem
What are congruent angles?Congruent angles are angles that have the same measure.
The lines that must be parallel, such that ∠3 ≅ ∠13 is indicated by the definition of the relationship between ∠3 and ∠13 as follows;
Statement [tex]{}[/tex] Reason
1. ∠3 ≅ ∠13 [tex]{}[/tex] 1. Given
2. ∠3 and ∠13 are alt int. ∠s[tex]{}[/tex] between a and b 2. Definition
3. Line a is parallel to line b [tex]{}[/tex] 3. Conv of the alt int. ∠s theorem
The lines that must be parallel are line a and line bThe reason for the conclusion is based on the converse of the alternate interior angles theorem as follows;
Angle ∠3 and angle ∠13 are alternate interior angles, which are angles located on the inside and on the opposite sides of the common transversal of two lines.
The converse of the alternate interior angles theorem state that if the alternate interior angles formed between two lines, a and b and their common transversal are congruent, then the two lines, a and b are parallel (a ║ b).
The correct option is therefore;
a ║ b, Converse of the Alternate Interior Angles Theorem
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What is the area of the polygon?
A=
? square units
Answer:
30 square units.
Step-by-step explanation:
Divide the full polygon into two halves. The left half is 5 wide by 5 tall, making the area of the left 25 square units. The right half is 4 wide by 5 tall, and is perfectly cut in half. We can calculate the area normally, and then cut it in half: (5×4)/2 = 10 square units. Add the two polygons together, totalling 30 square units.
IS THE ANSWER 1, 3, 17, 57 or none of the aboveIf none of the above please write the correct answer!Please answer step by step explanation
ANSWER
None of the above.
EXPLANATION
We want to solve the equation given for x:
[tex]\sqrt[]{x-1+5}=9[/tex]First, simplify the radical:
[tex]\sqrt[]{x+4}=9[/tex]Now, find the square of both sides of the equation:
[tex]\begin{gathered} (\sqrt[]{x+4})^2=9^2 \\ x+4=81 \end{gathered}[/tex]Finally, simplify by subtracting 4 from both sides of the equation:
[tex]\begin{gathered} x=81-4 \\ x=77 \end{gathered}[/tex]Hence, the correct option is "None of the above".
V ABCD - EFGH. What is the value of k? Your answer may be exact or rounded to the nearest tenth. Note: Images are not to scale. A E 4 mm k 8 mm B 6 mm H D 6 mm F 8 mm 4 mm C С
Since rectangles ABCD and EFGH are similar, we can take the ratios of the corresponding sides of the rectangles
[tex]\frac{AB}{AD}=\frac{EH}{EF}[/tex][tex]\frac{8}{4}=\frac{k}{6}[/tex]cross multiplying
8 x 6 = 4 x k
48 = 4k
4k = 48
Divide both sides by 4
k = 48/4
k = 12
Charlie subtracts two polynomials, 5x^2 – 9x^2, and says that the difference proves that polynomials are not closed under subtraction.Kate argues that the difference does in fact show that polynomials are closed under subtraction. Who is correct? Type only 'Charlie' orKate' as your answer in the box.
Charlie
Here, we want to check if polynomials is closed under subtraction or not
To check this, we proceed either ways, if the answer is same, then it is closed. If otherwise, then it is not
We have;
[tex]\begin{gathered} 5x^2-9x^2=-4x^2 \\ \\ \text{And;} \\ \\ 9x^2-5x^2=4x^2 \end{gathered}[/tex]As we can see, both results are not equal
If subtraction was closed under polynomials, then the results of both should have been equal. This means Charlie is correct.
Please explain cos-cot equations. Then I would like to figure out the rest.If sin θ=3/5 and θ is in quadrant II, thencos(θ)=________ ;tan(θ)=________ ;cot(θ)=_________;sec(θ)=_________;csc(θ)=_________;Give exact values.
Remember that the sine of an angle in a right triangle is equal to the quotient between the side opposite to the angle and the hypotenuse of the triangle.
Since the sine of the given angle θ is equal to 3/5, we can represent θ as part of a right triangle whose hypotenuse has a measure of 5 and the side opposite to θ has a measure of 3:
The length of the side adjacent to θ must be equal to 4 in order to satisfy the Pythagorean Theorem:
[tex]3^2+4^2=5^2[/tex]On the other hand, the cosine of an angle is defined as the quotient between the side adjacent to the angle and the hypotenuse of the triangle. Then, the cosine of θ must be equal to 4/5:
[tex]\cos \theta=\frac{4}{5}[/tex]The rest of the trigonometric relations are defined in terms of the sine and the cosine as follows:
[tex]\begin{gathered} \tan \theta=\frac{\sin \theta}{\cos \theta} \\ \cot \theta=\frac{\cos \theta}{\sin \theta} \\ \sec \theta=\frac{1}{\cos \theta} \\ \csc \theta=\frac{1}{\sin \theta} \end{gathered}[/tex]Since sinθ=3/5 and cosθ=4/5, then:
[tex]\begin{gathered} \tan \theta=\frac{3}{4} \\ \cot \theta=\frac{4}{3} \\ \sec \theta=\frac{5}{4} \\ \csc \theta=\frac{5}{3} \end{gathered}[/tex]2. MGSE9-12.A.REI. 1 Which step in solving this equation is justified by the Distributive Property? Consider the sequence of steps to solve the equation: 6v + 3(v – 5) = 4v - (2v + 1) Given = 6v + 3(v — 5) = 4v - (2v + 1) Step 1 = 6 + 3x – 15 = 4y - (2v + 1) Step 2 => 6v + 3v – 15 = 4v – 2y = 1 Step 3 9v – 15 = 4y – 2y - 1 Step 4 => 9v - 15 -- 2v + 4y = 1 Step 5 =9v = 15 = 2y + 1 Step 6 3 7v - 15 =-1 Step 7 3 Tv = 14 Step 8 = v= 2 a. Step 1 b. Step 7 C. Step 5 d. Step 2
6v + 3(v – 5) = 4v - (2v + 1)
Given = 6v + 3(v — 5) = 4v - (2v + 1)
step 1
when you open the first parenthsesis in step 1
we have 6v + 3v - 15 = 4v - (2v + 1)
Then in step 2
we open the second parenthesis,
This gives;
6v + 3v - 15 = 4v - 2v - 1
Therefore; step 1 and step 2 justified the distributive property
anslating Triangle D. (2 pts.)Figure AFigure BSelect all the true statements.A. Figure A is congruent to Figure BB Figure B is a translation of Figure A.C. Triangle C is congruent to Triangle C.D. Triangle D'is congruent to Triangle D.
According to the problem, the transformation is a translation.
It is important to know that translations are rigid transformations, which means the figures won't change their shape or size. In other words, the images are congruent to the pre-images.
Hence, triangle C is congruent to triangle C', triangle D is congruent to triangle D', but the figures are not congruent because their shape is different.
Therefore, the right answers are B, C, and D.If the distance a runner travels is represented by d(h) = 2√h and the associated time is t(h) = 3√/4h, what is the runner's speed?
s(h) = h√3
s(h) =1/3
s(h) = 12h
s(h) = √ 2/h
Based on the given distance and time, the speed of the runner is s(h) = 8h/√3.
Relationship between time, distance and speed:
The relationship of speed with distance and time is written as,
Speed = Distance x Time
Which describes the distance travelled divided by the time taken to cover the distance will results the speed.
Given,
Here we need to find the runner's speed when the distance a runner travels is represented by d(h) = 2√h and the associated time is t(h) = 3√/4h.
We know that the formula to calculate the speed is,
Speed = Distance / Time
Here we have the value of
distance = d(h) = 2√h
time = t(h) = √3/4h
Now, we have to apply the values on the formula, then we get,
Speed = 2√h / √3/4h
Therefore, the speed of the runner is 8h/√3.
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please help asap if you help i'll give brainilist. Two pieces of metal measure one and one sixth yards and three twelfths yards each. Three times the amount of metal is needed for a project. How many total yards of metal is needed?
four and one quarter yards
four and one sixth yards
one and one quarter yards
one and ten eighteenths yards
Answer:
Step-by-step explanation:
four and one quarter yards. explanation: add 1 1/6 + 3/12 = 1 5/12. now, multiply that by 3.
Using the arithmetic operations the total yards of metal is needed 4(1/4).
What is arithmetic operation?The study and application of numbers in all other branches of mathematics is the focus of the branch of mathematics known as arithmetic operations. In essence, it consists of addition, subtraction, multiplication, and division operations.
According to the given:
First pieces of metal = 1 (1/6)
= 7/6
Then Second pieces of metal = 3/12
Adding both the pieces, we have
=7/6 + 3/12
= (14 + 3)12
= 17/12.
now multiply that by 3.
We get,
= (17/12)3
= 17/4
= 4(1/4)
Using the arithmetic operations the total yards of metal is needed 4(1/4).
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Use the diagram to the right to determine whether BC. DE. Justify your answer. AD = 15, DB = 12, AE = 10, and EC = 8. The cut part is BC (top to bottom)
Explanation:
AD = 15, DB = 12, AE = 10, and EC = 8
To determine if line BC is parallel to line DE, we will find the ratio of thier corresponding sides. if it is equal, they are parallelf
Find the exponential equation that goes through the points (-1, 2) and (2, 128) Bullet point 3
The general form of the exponential function is given by;
[tex]y=f(x)=ab^x[/tex]where a is the initial value and b is any value greater than 0.
If the exponential function goes through the points (-1, 2) and (2, 128) we have;
[tex]2=ab^{-1}\ldots\ldots\ldots\text{.}.1[/tex]And,
[tex]128=ab^2\ldots\ldots\ldots\text{.}.2[/tex]Divide [2] by [1] we have;
[tex]\frac{128}{2}=\frac{ab^2}{ab^{-1}}[/tex]Simplify
[tex]\begin{gathered} 64=\frac{b^2}{b^{-1}} \\ 64=b^2\div b^{-1} \\ 64=b^{2--1} \\ 64=b^{2+1} \\ 64=b^3 \end{gathered}[/tex]Find the cube-root of both sides
[tex]\begin{gathered} \sqrt[3]{64}=\sqrt[3]{b^3} \\ 4=b \\ \therefore b=4 \end{gathered}[/tex]Substitute the value of b = 4 in [2] we get;
[tex]\begin{gathered} 128=ab^2 \\ 128=a(4)^2 \\ 128=16a \\ \text{Divide both sides by 16} \\ \frac{128}{16}=\frac{16a}{16} \\ 8=a \\ \therefore a=8 \end{gathered}[/tex]Substitute the value of a and b in
[tex]f(x)=ab^x[/tex]then we have;
[tex]f(x)=8(4)^x[/tex]Therefore, the exponential function that goes through the points ( -1, 2) and (2, 128) is;
[tex]f(x)=8(4)^x[/tex]Determine the type of triangle that is drawn below.
⇒ ΔVWX is a Scalene triangle because all the sides and all the angle are not equal.
F(x)=2x and g(x)= sqrt(x+1)Find (fg)(x)
First, let us define what (fg)(x) is:
[tex](fg)(x)=f(x)\times g(x)[/tex]Given:
[tex]f(x)=2x[/tex][tex]g(x)=\sqrt[]{x+1}[/tex]So the solution to (fg)(x) will be:
[tex]\begin{gathered} =2x\times\sqrt[]{x+1} \\ =2x\text{ }\sqrt[]{x+1} \end{gathered}[/tex]What is the range of this relation?
Answer: (-9, -3, -2, 6, 8)
Step-by-step explanation:
Use the long division method to find the result when 6x4 +423-7x²+3x-7 is
divided by 2x2 + 2x-3. If there is a remainder, express the result in the form
q(x) +5(2).
Answer:−6x4−3x3−2x2−4x−7x2+3=−6x2−3x+16+5x−55x2+3.
Step-by-step explanation: −6x4−3x3−2x2−4x−7x2+3. The Long Division method: −6x2−3x+16
What is the value for y?
Answer:
28
Step-by-step explanation:
x - 5 = 34, meaning 39 = x
34 + 34 = 68
All triangles add up to 180
180 - 68 = 112
112/4 = 28
Determine whether a relation is a function.
Answer:
so i think id be no
Step-by-step explanation:
if each input value Leads to only one output value that Classify the Relationship as a Function tell me if im wrong
ABCD is a rhombus. Find xA) x = 3B) x = 10 D) x = 5C) x = 2
ANSWER
5
EXPLANATION
The given shape is a rhombus
The sum of interior angles of a rhombus add up to 360 degrees
The opposite angles of a rhombus are equal to each other.
hence, adding up all the interior angles, we have;
[tex]\begin{gathered} 9x+9x+135+135=360 \\ 18x+270=360 \end{gathered}[/tex]collecting like terms, we have;
[tex]\begin{gathered} 18x=360-270 \\ 18x=90 \\ x=\frac{90}{18} \\ x=5 \end{gathered}[/tex]Therefore the value of x is 5
a week before the election, based on a random sample of 1200 voters, the support rate for candidate a is 53%. can we assert, with 95% confidence, that candidate a is winning the election (in other words, his support rate is higher than 50%)?
With 95% confidence, candidate A can win the election within 50.18% and 55.82%.
Probability is the branch of discrete mathematics. It is used for calculating how likely an event is to occur or happen.
According to the question, n = 1200
The support rate for candidate A ([tex]p_{A}[/tex]) = 53% ≅ 0.53
So, [tex]z_{c}[/tex] for 95% confidence = 1.96
Confidence interval for [tex]p_{A}[/tex]
= ( [tex]p_{A}[/tex] ± [tex]z_{c}[/tex] ([tex]\sqrt{\frac{p_{A}( 1 - p_{A} ) }{n} }[/tex]) )
= ( 0.53 ± 1.96([tex]\sqrt{\frac{0.53(1-0.53)}{1200} }[/tex]) )
= ( 0.53 ± 1.96([tex]\sqrt{\frac{0.53*0.47}{1200} }[/tex]) )
= ( 0.53 ± 1.96([tex]\sqrt{\frac{0.2491}{1200} }[/tex]) )
= ( 0.53 ± 1.96([tex]\sqrt{0.0002075833}[/tex]) )
= ( 0.53 ± 1.96(0.014407751) )
= ( 0.53 ± 0.028239191 )
= ( 0.53 - 0.02823,0.53 + 0.02823 )
= ( 0.50177,0.55823 )
( 0.50177,0.55823 ) ≅ ( 50.18%,55.82%)
Candidate A can win the election between 50.18% and 55.82% with a confidence level of 95%.
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Given h(x) = 4x - 4, solve for x when h(x) = 0
Answer: 1
Step-by-step explanation:
Well, what they have asked is to find the zero of this equation, or the value of the variable when the equation is equal to 0.
So, h(x) = 4x-4 = 0
4x = 4
x = [tex]\frac{4}{4}[/tex]
x = 1