Answer:
Therefore,
[tex]BC=a=10\ units\\\\AC=b=13.66\ units[/tex]
Step-by-step explanation:
Consider a Δ ABC with
m∠ A = 45°
m∠ C = 30°
AB = c = 5√2
To Find:
BC = a = ?
AC = c = ?
Solution:
Triangle sum property:
In a Triangle sum of the measures of all the angles of a triangle is 180°.
[tex]\angle A+\angle B+\angle C=180\\\\45+30+\angle B=180\\\ttherefore m\angle B =180-75=105\°[/tex]
We know in a Triangle Sine Rule Says that,
In Δ ABC,
[tex]\frac{a}{\sin A}= \frac{b}{\sin B}= \frac{c}{\sin C}[/tex]
substituting the given values we get
[tex]\frac{a}{\sin 45}= \frac{b}{\sin 105}= \frac{5\sqrt{2} }{\sin 30}[/tex]
∴ [tex]\frac{a}{\sin 45}= \frac{5\sqrt{2} }{\sin 30}\\\\a=\sin 45\times \frac{5\sqrt{2} }{\sin 30}\\\\a=\frac{1}{\sqrt{2} }\times \frac{5\sqrt{2} }{0.5} \\\\\\a=\frac{5}{0.5} =10\\\therefore BC = a = 10\ units[/tex]
Similarly for 'b',
[tex]\frac{b}{\sin 105}= \frac{5\sqrt{2} }{\sin 30}\\\frac{b}{0.9659}= \frac{5\sqrt{2} }{0.5}\\\\b=0.9659\times \frac{5\sqrt{2} }{0.5}\\\\b=\frac{6.8301}{0.5} \\\\b=13.66\\\therefore AC = b =13.66\ units\\[/tex]
Therefore,
[tex]BC=a=10\ units\\\\AC=b=13.66\ units[/tex]
By using the Law of Sines, side BC of the triangle is found to be approximately 10 m, and AC is approximately 8.66 m. These calculations take into account the given lengths and angles of triangle ABC.
Explanation:To find the lengths of sides BC and AC in triangle ABC with given angles and side AB, we will employ trigonometry and the properties of triangles. Since the sum of the angles in any triangle is 180 degrees, we know that m∠B = 180° - 45° - 30° = 105°. With this information, we can use the Law of Sines, which states:
[tex]\(\frac{AB}{\sin(C)} = \frac{BC}{\sin(A)} = \frac{AC}{\sin(B)}\)[/tex]
From the given, AB = 5√2 m, m∠A = 45°, and m∠C = 30°, we know that:
[tex]\(\frac{5\sqrt{2}}{\sin(30°)} = \frac{BC}{\sin(45°)}\)[/tex]
[tex]Knowing \ that\ \(\sin(30 ) = 0.5\) and \(\sin(45) = \frac{\sqrt{2}}{2}\), we can find BC:[/tex]
[tex]BC = \(\frac{5\sqrt{2}}{0.5} \times \frac{\sqrt{2}}{2}\) = 5√2 \times \sqrt{2} = 10 m[/tex]
Now, to find AC, we set up the ratio:
[tex]\(\frac{5\sqrt{2}}{\sin(30°)} = \frac{AC}{\sin(105°)}\)[/tex]
Solving for AC, we get:
[tex]AC = 5\sqrt{2} \times \frac{\sin(105°)}{0.5}[/tex]
Since \(\sin(105°)\) is not a standard angle, we can use the sine sum identity where [tex]\(\sin(105) = \sin(60 + 45\),[/tex]which gives us:
[tex]AC = 10 \times (\(\frac{\sqrt{3}}{2}\times\frac{\sqrt{2}}{2} + \frac{1}{2}\times\frac{\sqrt{2}}{2}\)) = 10 \times (\(\frac{\sqrt{6} + \sqrt{2}}{4}\))[/tex]
AC ≈ 8.66 m
Which ordered pair belongs to the solution set of the equation y = x2 - 2x + 1?
A. (510)
B. (-1,3)
c. (1,2)
D. (3,4)
The correct ordered pair for the given equation is D. (3,4).
To find the correct ordered pair, we substitute the x-value from each pair into the equation and check if the resulting y-value matches the one in the ordered pair.
Substituting x = 5 into the equation gives us 52 - 2(5) + 1 = 25 - 10 + 1 = 16, which does not match the y-value of 10 in the ordered pair (5,10), so A is not correct.
Substituting x = -1 gives us (-1)2 - 2(-1) + 1 = 1 + 2 + 1 = 4, which does not match the y-value of 3 in (-1,3), so B is not correct.
Substituting x = 1 gives us 12 - 2(1) + 1 = 1 - 2 + 1 = 0, which does not match the y-value of 2 in (1,2), so C is not correct.
Finally, substituting x = 3 into the equation gives us 32 - 2(3) + 1 = 9 - 6 + 1 = 4, which matches the y-value in the ordered pair (3,4), making D the correct answer.
Therefore, the correct ordered pair is D. (3,4).
Use the graph shown to fill in the blank. When x = 1, then y = a0.
Explanation:
Step 1) Start at 1 on the horizontal x axis number line.Step 2) Draw a vertical line straight down until you reach point P that is marked in the attached image (see below). Point P is on the diagonal line.Step 3) From point P, move horizontally until you reach -2 on the vertical y axis number line.We started with x = 1 and ended up with y = -2. So the point (x,y) = (1,-2) is on the diagonal line. In other words, point P is located at (1,-2).
solve plzz!?!!?!?!?!?
Answer:
[tex]([7]x+[2])^2[/tex]
Step-by-step explanation:
Given:
[tex]49x^2+28x+4[/tex]
We need to factorize the given trinomial.
To solve the above expression we will Split the product of first term and third term to get the second term by either adding or subtracting.
So we get;
[tex]49x^2+14x+14x+4\\\\7x(7x+2)+2(7x+2)\\\\(7x+2)(7x+2)\\\\(7x+2)^2[/tex]
Hence Final Answer is:
[tex]([7]x+[2])^2[/tex]
Express the shaded Area as both a faction and a decimal
The shaded area's Fraction= 21/100 and Decimal = 0.21.
Step-by-step explanation:
When an area is divided into multiple smaller regions ( smaller squares ) is called parts.
In case of Squares, it can be divided into either rows or columns, sometimes both.
Form the given diagram, the square consists of 10 rows and 10 columns which makes 100 (10×10) parts in it.
One fraction is obtained by dividing it by the total number of parts.
In this square, 21 shaded fractions are given.
∴ The fraction of shaded Area = 21/100.
Decimal of shaded Area=0.21.
Jane is adding 3 1/4 + 2 7/8 using fraction strips.How can she rename the sum of the fraction parts of the problem? Explain your thinking
Answer:
3 1/4 + 2 7/8= 6 1/8
Step-by-step explanation:
1. Cross multiply 1/4 and 7/8 which equals 1 1/8.
2. 3+2+1(from cross multiplying)= 6
Answer: 6 1/8
Using fraction strips, the result of 3 1/4 + 2 7/8 is 6 1/8.
What is simplification?Simplifying procedures is one way to achieve uniformity in job efforts, expenses, and time. It reduces diversity and variation that is pointless, harmful, or unneeded. Parenthesis, exponents, multiplication, division, addition, and subtraction are all referred to as PEMDAS. The order of the letters in PEMDAS informs you what to calculate first, second, third, and so on, until the computation is finished, given two or more operations in a single statement.
Given, Jane is adding 3 1/4 + 2 7/8 using fraction strips.
Fraction strips are rectangular pieces (electronic or copied on paper strips) to represent different parts of the same whole. They can be cut apart and manipulated to see how various parts can be added together to make the whole or compare different fractional amounts for equivalency.
First, we will add fraction parts
=> 1/4 + 7 / 8
We can write 1/4 as 2/8 since they have the same values
=> 2/8 + 7/8
Since now the denominators are the same, therefore we can add the numerators directly. Hence, the sum of 2/8 and 7/8
=> 9/8
=> 8/8 +1/8
=> 1 + 1/8
Thus the sum = 3 + 2 + 1 + 1/8
Sum = 6 + 1/8
therefore, the sum of 3 1/4 + 2 7/8 using fraction strips is 6 1/8.
Learn more about Simplification here:
https://brainly.com/question/28996879
#SPJ5
If cosA = 3/5 and A ∈ (0,90), what is sin2A?
Answer:
[tex]\frac{24}{25}[/tex]
Step-by-step explanation:
Given
cosA = [tex]\frac{3}{5}[/tex] = [tex]\frac{adjacent}{hypotenuse}[/tex]
Then the opposite side using Pythagorean triple is 4, thus
sinA = [tex]\frac{4}{5}[/tex]
Using the trigonometric identity
sin2A = 2 sinAcosA, then
sin2A = 2 × [tex]\frac{4}{5}[/tex] × [tex]\frac{3}{5}[/tex]
= [tex]\frac{2(4)(3)}{5(5)}[/tex] = [tex]\frac{24}{25}[/tex]
Answer:
[tex]\sin(2A)=\frac{24}{25}[/tex]
Step-by-step explanation:
Double angle identity for sine is
[tex]\sin(2A)=2\sin(A)\cos(A)[/tex].
We know [tex]\cos(A)[/tex]. We now need to find [tex]\sin(A)[/tex] to find our answer.
Recall the following [tex]Pythagorean Identity[/tex]:
[tex]\sin^2(A)+\cos^2(A)=1[/tex].
Replace [tex]\cos(A)[/tex] with [tex]\frac{3}{5}[/tex]:
[tex]\sin^2(A)+(\frac{3}{5})^2=1[/tex]
[tex]\sin^2(A)+\frac{9}{25}=1[/tex]
Subtract [tex]\frac{9}{25}[/tex] on both sides:
[tex]\sin^2(A)=1-\frac{9}{25}[/tex]
[tex]\sin^2(A)=\frac{25}{25}-\frac{9}{25}[/tex]
[tex]\sin^2(A)=\frac{25-9}{25}[/tex]
[tex]\sin^2(A)=\frac{16}{25}[/tex]
Now to finally get the value of [tex]\sin(A)[/tex] take the square of both sides:
[tex]\sin(A)=\pm \sqrt{\frac{16}{25}}[/tex]
Since [tex]A[/tex] is in the interval [tex](0,90)[/tex], then [tex]\sin(A)>0[/tex].
[tex]\sin(A)=\sqrt{\frac{16}{25}}[/tex]
[tex]\sin(A)=\frac{\sqrt{16}}{\sqrt{25}}[/tex]
[tex]\sin(A)=\frac{4}{5}[/tex]
So let's finally find the numerical value of [tex]\sin(2A)[/tex].
[tex]\sin(2A)=2\sin(A)\cos(A)[/tex]
[tex]\sin(2A)=2\cdot \frac{4}{5} \cdot \frac{3}{5}[/tex]
[tex]\sin(2A)=\frac{2(4)(3)}{5(5)}[/tex]
[tex]\sin(2A)=\frac{24}{25}[/tex]
Side note:
If [tex]A[/tex] is between 0 and 90 degrees, then we are in the first quadrant.
If we are in the first quadrant, both [tex]x=\cos(A)[/tex] and [tex]y=\sin(A)[/tex] are positive.
y = − 1/3 x + 2
y = x + 2
What is the solution to the system of equations?
A) (0, 2)
B) (2, 0)
C) (-1, 3)
D) (0, -2)
Answer:
I think is d I need help please
Need help for this question
Answer:
For 0 hours = $40
For 1 hours = $75
For 2 hours = $110
For 3 hours = $145
For 4 hours = $180
For 5 hours = $215
Step-by-step explanation:
Given equation is:- [tex]C=35n+40[/tex]
where, C=Cost in dollars, n=hours.
Now, Amy charge $40 for service call and $35 for per hour service.
So,
For 0 hours:
[tex]C=35n+40[/tex]
[tex]C=(35\times 0)+40[/tex]
[tex]C=0+40[/tex]
[tex]C=40[/tex]
Therefore for 0 hours Amy charge $40.
For 1 hours:
[tex]C=35n+40[/tex]
[tex]C=(35\times 1)+40[/tex]
[tex]C=35+40[/tex]
[tex]C=75[/tex]
Therefore for 1 hours Amy charge $75.
For 2 hours:
[tex]C=35n+40[/tex]
[tex]C=(35\times 2)+40[/tex]
[tex]C=70+40[/tex]
[tex]C=110[/tex]
Therefore for 2 hours Amy charge $110.
For 3 hours:
[tex]C=35n+40[/tex]
[tex]C=(35\times 3)+40[/tex]
[tex]C=105+40[/tex]
[tex]C=145[/tex]
Therefore for 3 hours Amy charge $145.
For 4 hours:
[tex]C=35n+40[/tex]
[tex]C=(35\times 4)+40[/tex]
[tex]C=140+40[/tex]
[tex]C=180[/tex]
Therefore for 4 hours Amy charge $180.
For 5 hours:
[tex]C=35n+40[/tex]
[tex]C=(35\times 5)+40[/tex]
[tex]C=175+40[/tex]
[tex]C=215[/tex]
Therefore for 5 hours Amy charge $215.
what is the best approximation of the solution to the equations that these two lines represent
Answer: the answer would be c
Step-by-step explanation:
Kyle’s parents told him that for every 5 hours of homework or reading he completes, he will be able to play 3 hours of video games. His friend victor’s parents told their son that he can play 30 minutes for every hour of homework or reading time he completed. If both boys spend the same amount of time on homework and reading this week, which boy gets more time playing video games
Kyle will have more time to play video games
Solution:
From given question,
Kyle’s parents told him that for every 5 hours of homework or reading he completes, he will be able to play 3 hours of video games.
5 hours of homework = 3 hours of video games
Victor’s parents told their son that he can play 30 minutes for every hour of homework or reading time he completed.
1 hour of homework = 30 minutes of playtime
Suppose if victor spends 5 hours doing homework or reading, then he could play,
5 hours of victor homework = 30 minutes x 5 = 150 minutes of play
That is,
150 minutes = 120 + 30 = 2 hours 30 minutes
This 2 hours 30 minutes playtime of victor is less than kyle playtime (which is 3 hours )
So Kyle gets more play time
Eldar cooks lasagna and spaghetti using pesto sauce.
Let L represent the number of batches of lasagna and
S represent the number of batches of spaghetti that Eldar can cook with the amount of pesto sauce he has.
0.9
L
+
0.3
S
≤
6
0.9L+0.3S≤60, point, 9, L, plus, 0, point, 3, S, is less than or equal to, 6
Eldar cooks
4
44 batches of spaghetti. How many batches of lasagna can he cook at most with the remaining pesto sauce?
Answer:
He can cook 52 or less than 52 batches of lasagna.
Step-by-step explanation:
0.9L+0.3S≤60
Putting the value of s = 44
0.9L+0.3 (44) ≤ 60
0.9L+ 13.2 ≤ 60
0.9L ≤ 60 -13.2
L ≤ 46.8/0.9
L ≤ 52
Answer:
Eldar can cook 555 batches of lasagna at most.
Step-by-step explanation:
Mrs. Bollis has 26 yards of fabric to make costumes. Each costume requires 3 yards of fabric. How many costumes can Mrs. Bollis make? How many yards will she have left?
The required number of costume is 8 and remaining fabric is 2 yards.
What are arithmetic operations?The arithmetic operations are the fundamentals of all mathematical operations. The example of these operators are addition, subtraction, multiplication and division.
The total length of fabric is 26 yards.
And, the requirement for each costume is 3 yards.
Now, the number of costumes to be made and the remaining fabric are the quotient and remainder of the following expression,
26 ÷ 3
It gives the quotient and remainder as 8 and 2 respectively.
Hence, the number of costumes and the fabric left are given as 8 and 2 yards respectively.
To know more about arithmetic operation click on,
https://brainly.com/question/25834626
#SPJ2
A person is standing 50 ft from a statue. The person looks up at an angle of elevation of 8 degrees when staring at the top of the statue. Then the person looks down at an angle of 14 degrees when staring at the base of the statue. How tall is the statue to the nearest tenth of a foot?
The height of the statue is 19.5 feet.
Why?
We can solve the problem using trigonometric formulas. In this case, we are going to use the trigonometric formula of the tangent.
We know that the person is standing 50ft from the statue, so, it will be the base of the two triangles formed by both angles (elevation and depression)
Using the trignometric formula, we have:
First triangle:
[tex]tg(\alpha )=\frac{h_{1}}{base} \\\\tg(8\°)=\frac{h_{1}}{50ft}\\\\0.14*50ft=h_1\\\\h_1=7ft[/tex]
Second triangle:
[tex]tg(\alpha )=\frac{h_{2}}{base} \\\\tg(14\°)=\frac{h_{1}}{50ft}\\\\0.25*50ft=h_1\\\\h_1=12.5ft[/tex]
Now, the total height of the statue will be:
[tex]TotalHeight=h_1+h_2=7ft+12.5ft\\\\TotalHeight=19.5ft[/tex]
Have a nice day!
In this question, we utilize trigonometry to calculate the height of the statue. By using the tangent of the given angles and the known distance from the observer to the statue, we can find the lines of sight when looking up and down. Subtracting these two measurements gives us the height of the statue, which we find to be 5.2ft.
Explanation:This question is about applying trigonometry to find the height of an object, in this case, a statue. First, we need to find the height of the line of sight when the person looks up and when they look down. The height for the line of sight when looking up can be found using the formula for the tangent of an angle: tan(θ) = opposite side/adjacent side. Applying this formula, we find that the height of this line of sight is tan(8°) * 50ft = 7.1 ft. Similarly, when looking down, the height is tan(14°) * 50ft = 12.3 ft.
The height of the statue is the difference between these two heights. Therefore, we find: 12.3ft - 7.1ft = 5.2ft
This is a simple application of the concept of the tangent of an angle in a right triangle, a basic part of trigonometry.
Learn more about Trigonometry here:https://brainly.com/question/11016599
#SPJ11
Drag each expression to show whether it is equivalent to −2.6x−(−5.9x), −2.6x+(−5.9x), or neither. −2.6x−5.9x 5.9x+(−2.6x) 5.9x−(−2.6x) −5.9x+(−2.6x) −2.6x+5.9x −5.9x+2.6x −2.6x−(−5.9x) −2.6x+(−5.9x) Neither
Answer:
The 2 expressions are:
1) −2.6x−(−5.9x) = −2.6x + 5.9x
2) −2.6x+(−5.9x) = −2.6x - 5.9x
Options:
−2.6x−5.9x -> equivalent to 2nd expression
5.9x+(−2.6x) = −2.6x) + 5.9x -> equivalent to 1st expression
5.9x−(−2.6x) = 5.9x + 2.6x = 2.6x + 5.9x -> equivalent to neither expression
−5.9x+(−2.6x) = −5.9x − 2.6x = − 2.6x − 5.9x -> equivalent to 2nd expression
−2.6x+5.9x -> equivalent to 1st expression
−5.9x+2.6x = 2.6x − 5.9x -> equivalent to neither expression
While in Europe, if you drive 117 km per day, how much money would you spend on gas in one week if gas costs 1.10 euros per liter and your car's gas mileage is 42.0 mi/gal ? Assume that 1euro = 1.26dollars.
You would spend $63.58 on gas per week.
Step-by-step explanation:
Given,
Distance per day = 117 km
Distance in a week = 117*7 = 819 km
1 km = 0.6214 mile
819 km = 819*0.6214 = 508.93 miles
Car's mileage = 42.0 mi/gallons
Let,
x be the gallons for 508.93 miles
x gallons = [tex]\frac{508.93}{42}=12.12[/tex]
Therefore,
12.12 gallons of gas is needed for one week.
1 US gallon = 3.785 liters
12.12 gallons = 12.12*3.785
12.12 gallons = 45.87 liters
Cost of gas per liter = 1.10 euro
Cost of 45.87 liters = 1.10*45.87 = 50.457 euros
1 euro = $1.26
50.457 euros = 1.26*50.457 = $63.58
You would spend $63.58 on gas per week.
Keywords: multiplication, division
Learn more about division at:
brainly.com/question/1859222brainly.com/question/1993757#LearnwithBrainly
A hotel shuttle service charges $7.50 plus $0.85 per mile . A customer hires a shuttle for a ride to the airport and the total charge is $12.60 . Which equation can be used to determine the number of miles from the hotel to the airport ?
Answer:
6.40=$12.60
Step-by-step explanation:
First, make the equation following the problem.
$7.50 + $0.85 = $12.60
Then, find the number of miles.
$7.50 * $0.85 = $6.40
$6.40=$12.60
Don't need to solve it because it is asking for the equation.
This is a linear equation problem in Mathematics. The equation to find out the number of miles for the given total charge would be 7.50 + 0.85m = 12.60. Through algebraic manipulation, it is found that the shuttle travelled 6 miles.
Explanation:The subject of this question is in the field of Mathematics, specifically under linear equations in algebra. In this problem, the customer is charged a flat fee of $7.50 and then an additional $0.85 per mile. The total charge for this trip was $12.60, and we're tasked with finding the number of miles covered for this charge.
The equation to solve this problem would be 7.50 + 0.85m = 12.60, where 'm' represents the miles. We subtract 7.50 from both sides, then we get: 0.85m = 5.1. To solve for 'm', we divide both sides by 0.85, and we receive m = 6 miles.
Learn more about Linear equations here:https://brainly.com/question/32634451
#SPJ2
what does this expression represent?
12f + 24
A: twenty-four more than twelve times a number.
B: twelve time the difference of a number and twelve four.
C: twelve times the sun of a number plus twelve four.
D: twelve- four more than twelve plus a number.
Answer:
A
Step-by-step explanation:
12f means 12 x f
+24 means you add 24
Because of pedmas, you do the multiply first so its (12xf)+24
(Also twelve four isn't a number, so B and C don't make sense)
can someone please explain 10 3/4 - 6 4/4 ??
3 3/4 is the answer
10 3/4 --- 43/4
6 4/4--- 7 or 28/4
43/4- 28/4= 15/4
15/4 simplified is 3 3/4
Answer:
43/4 - 28/4 = (43 - 28)/4 = 15/4 or 3 3/4
Step-by-step explanation:
10 3/4 - 6 4/4 . The expression means we should find the difference between 10 3/4 and 6 4/4. The best approach to find the difference of this kind of fractions with whole number is by turning each to an improper fraction.
10 3/4 . This whole number fraction can be turn to an improper fraction as follows
10 × 4 + 3 = 43 then 43/4
6 4/4. 4 × 6 + 4 = 28/4.
Now , let's find the difference
The denominator is same, which is 4
43/4 - 28/4 = (43 - 28)/4 = 15/4 or 3 3/4
please solve this equation
Evaluate.
12.25 - 7 2/3 = 12 1/4 - 7 2/3 = 12 3/12 - 7 8/12 = 4 7/12
answer: B
HELP I WILL MARK YOU AS A BRAINLIEST!!
Nick bought raffle tickets to try to win a
prize. He paid $3.00 for 12 tickets.
What is the cost per raffle ticket?
Answer:
$0.25 per ticket
Step-by-step explanation:
$3 for 12 tickets so divided the number of tickets by amount of money spent to find price per ticket.
3/12 = $0.25 per ticket
Answer:
0.25
Step-by-step explanation:
beacuse it is 0.25 because 0.25 times 12 = $3.00
Gloria bought each of her three younger siblings a movie ticket. Find the total cost of the movie ticket if each cost $9.75. Justify your answer by using the Distributive Property.
Sry if i keep asking questions.
Answer: 29.25
Step-by-step explanation:
3(9.75)
Which of the following systems of linear equations has an infinite number of solutions?
Answer:
Here we do not have the options, but ill try to give an answer.
A system of equations is something of the shape:
A1*x + B1*y = C1
A2*x + B2*y = C2
Where this is a linear relationship, you could have a more complex system, but this will work for the example.
If you want to have a unique solution for a system of equations, you need to have the same number of linearly independent equations (this means that the equations are not repeated, like for example in x + y = 2, and 2x + 2y = 4, where the second equation is equal to two times the first one) than the number of variables, so if we have two variables X and Y, we need to have two linearly independent equations.
If we have less, suppose that you have two variables and only one equation, you will have:
A1*x + B1*y = C1
y = (C1 - A1*x)/B1
Here, for each value of x you have a different value of y, so you have infinite solutions.
So for an answer this you need to find the system where the number of linearly independent equations is smaller than the number of variables.
Can u please help me I dont understand it
Answer:
11.43 kilometers
Step-by-step explanation:
Answer:
11.43 kilometers.
Step-by-step explanation:
All you have to do is add the two distances (AKA numbers, to make it even simpler). It doesn't matter what distance was traveled by train or bus! The point is that the distances traveled were both in kilometers! With that being said, all we have to do is add 7.22 + 4.21, and voila! We get 11.43!
Hope this answer helps! Please rate it and give me Brainliest! :D
Have a great day!
What is the cube root of 216x18?
Answer:
The correct answer is 15.72 or 6 ∛18
Step-by-step explanation:
Let's calculate the cube root of 216 * 18
∛(216 * 18)
216 = 8 * 27
8 = 2³; 27 = 3³
18 = 9 * 2 or 3² * 2
∛(8 * 27 * 18)
Simplifying:
∛(2³ * 3³ * 3² * 2)
∛(2³ * 3³ * 3² * 2)
2 * 3 ∛(3² * 2
6 * 2.62 = 15.72 or 6 ∛18
Solve the equation
8.3v = -5.1
Answer:
v= -0.61445783132
Step-by-step explanation:
Divide both sides by 8.3
-5.1 ÷ 8.3= -0.61445783132
8.3v ÷ 8.3= v
So, v=-0.61445783132
8.3v ÷ 8.3= v
Which inequality is represented by this graph?
A. -34.5 >х
B. -34.5< x
C. -35.5 > x
D. –35.5 < x
Answer:
the answer would be A
Step-by-step explanation:
What is the difference between the yearly wages of the highest paying job and lowest paying job, assuming Araceli will be paid for working 40 hours a week, 52 weeks a year?
$1,160
$11,280
$2,600
$8,680
-> 40 hours per week, 52 weeks a year
shop and save grocers
monthly wages: $3,800
hourly wages: $3800 / 160 = $23.75 per hour
yearly wages: $23.75 per hour x 40 hours per week x 52 weeks a year
= $49,400
unbelievable toys
yearly wages: $43,000
convenience store
$16.50 per hour x 40 hours per week x 52 weeks a year
= $34,320
49,400 - 34,320 = 15,080
..? that's not even an answer choice what-
PLEASE ITS SUPER SUPER URGENT
3/5 divided by 1/3
Answer: 3/5 * 3/1 is 9/5 I think
Step-by-step explanation: Go to a calculator and type it but I think it’s KCF so yeah
Answer:
9/5 or 1.8
Step-by-step explanation:
3/5 * 3/1 = 9/5 or 9 divided by 5 gets 1.8
if sin square theta = 0.75, then cos =
Answer:
[tex]\cos\theta=\pm0.5[/tex]
Step-by-step explanation:
Given:
[tex]\sin^2\theta=0.75[/tex]
To find [tex]\cos\theta[/tex]
Using trigonometric relations for sums and differences of squares of the ratios.
We know:
[tex]\sin^2\theta+\cos^2\theta =1[/tex]
Plugging in [tex]\sin^2\theta=0.75[/tex] in the above relation.
[tex]0.75+\cos^2\theta =1[/tex]
Subtracting both sides by 0.75.
[tex]0.75+\cos^2\theta-0.75 =1-0.75[/tex]
[tex]\cos^2\theta =0.25[/tex]
Taking square root both sides.
[tex]\sqrt{\cos^2\theta} =\sqrt{0.25}[/tex]
∴ [tex]\cos\theta=\pm0.5[/tex] (Answer)
Find domain and range for f(x)=x^2-2x+2
Answer:
Domain: (-∞,∞) or -∞ <[tex]x[/tex]<∞
Range: [1,∞) or [tex]y\geq 1[/tex]
Step-by-step explanation:
Given function:
[tex]f(x)=x^2-2x+2[/tex]
To find range and domain of the function.
Solution:
The given function is a second degree function as the highest exponent of the variable is 2. Thus, it is a quadratic function.
For all quadratic functions the domain is a set of all real numbers. So, the domain can be given as: (-∞,∞) or -∞ <[tex]x[/tex]<∞
In order to find the range of the quadratic function, we will first determine if the function has a minimum point or the maximum point.
For a quadratic equation : [tex]ax^2+bx+c[/tex]
1) If [tex]a>0[/tex] the function will have a minimum point.
2) If [tex]a<0[/tex] the function will have a maximum point.
For the given function: [tex]f(x)=x^2-2x+2[/tex]
[tex]a=1[/tex] which is greater than 0, and hence it will have a minimum point.
To find the range we will find the coordinates of the minimum point or the vertex of the function.
The x-coordinate [tex]h[/tex] of the vertex of a quadratic function is given by :
[tex]h=\frac{-b}{2a}[/tex]
Thus, for the function:
[tex]h=\frac{-(-2)}{2(1)}[/tex]
[tex]h=\frac{2}{2}[/tex] [Two negatives multiply to get a positive]
[tex]h=1[/tex]
To find y-coordinate of the vertex can be found out by evaluating [tex]f(h)[/tex].
[tex]k=f(h)[/tex]
Thus, for the function:
[tex]k=f(1)=(1)^2-2(1)+2[/tex]
[tex]k=f(1)=1-2+2[/tex]
[tex]k=f(1)=1[/tex]
Thus, the minimum point of the function is at (1,1).
thus, range of the function is:
[1,∞) or [tex]y\geq 1[/tex]