Answers
Answer:
A
Step-by-step explanation:
We can write this as Sinx by "flipping" the [tex]-\sqrt{2}[/tex].
So we will have: [tex]Sin(x)=-\frac{1}{\sqrt{2} }[/tex]
From basic trigonometry, we know the value of [tex]\frac{1}{\sqrt{2}}[/tex] of sine is of the angle [tex]\frac{\pi}{4}[/tex]
But when is sine negative? Either in 3rd or 4th quadrant. But the answer has to be between 0 and [tex]\frac{3\pi}{2}[/tex], so we disregard 4th quadrant.
To get the angle in 3rd quadrant, we add π to the acute angle of the first quadrant (which is π/4 in our case). Thus we have:
[tex]\frac{\pi}{4}+\pi\\=\frac{\pi +4\pi}{4}\\=\frac{5\pi}{4}[/tex]
A is the right answer.
Related Questions
NEED HELP ASAP! PLEASE HElp!!
Answers
the answer should be C
Solve the equation. Round to the nearest hundredth. Show work.
[tex]8^{-x+7} = 3^{7x+2}[/tex]
Answers
Answer:
Final answer is approx x=1.27.
Step-by-step explanation:
Given equation is [tex]8^{-x+7}=3^{7x+2}[/tex].
Now we need to solve equation [tex]8^{-x+7}=3^{7x+2}[/tex] and round to the nearest hundredth.
[tex]8^{-x+7}=3^{7x+2}[/tex]
[tex]\log(8^{-x+7})=\log(3^{7x+2})[/tex]
[tex]\left(-x+7\right)\cdot\log\left(8\right)=\left(7x+2\right)\cdot\log\left(3\right)[/tex]
[tex]-x\cdot\log\left(8\right)+7\cdot\log\left(8\right)=7x\cdot\log\left(3\right)+2\cdot\log\left(3\right)[/tex]
[tex]-x\cdot\log\left(8\right)-7x\cdot\log\left(3\right)=2\cdot\log\left(3\right)-7\cdot\log\left(8\right)[/tex]
[tex]x\left(-\log\left(8\right)-7\cdot\log\left(3\right)\right)=\left(2\cdot\log\left(3\right)-7\cdot\log\left(8\right)\right)[/tex]
[tex]x=\frac{\left(2\cdot\log\left(3\right)-7\cdot\log\left(8\right)\right)}{\left(-\log\left(8\right)-7\cdot\log\left(3\right)\right)}[/tex]
Now use calculator to calculate log values, we get:
[tex]x=1.26501646392[/tex]
Round to the nearest hundredth.
Hence final answer is approx x=1.27.
Please help me with this...
Answers
3x+4=5x-50
54=2x
27=x
Answer:
x = 27
Step-by-step explanation:
The diagonals of a rectangle are congruent, hence
BD = AC ← substitute values
5x - 50 = 3x + 4 (subtract 3x from both sides )
2x - 50 = 4 ( add 50 to both sides )
2x = 54 ( divide both sides by 2 )
x = 27
In your own words, summarize how the Jacksonian Era was characterized?
Answers
Answer: Actually The Jacksonian Era was characterized by the thought that each individual also equally have right and he or she is important and that all should be able to have a say or participate in any government activities.
All in all i think its actually giving greater right to the common man.
60 POINTS!!! Please Help ASAP
Question:
Find the distance between the points (1, 4) and (-5, -4) on the coordinate plane. Show your work to justify your answer and earn full credit.
Answers
ANSWER
The distance is 10 units.
EXPLANATION
Let us use the distance formula to find the distance between,
[tex](x_1,y_1)=(1,4)[/tex]
and
[tex](x_2,y_2)=( - 5, - 4)[/tex]
The distance formula is given by,
[tex]d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2} [/tex]
We plug in the values to get,
[tex]d = \sqrt{( - 5-1)^2 + ( - 4-4)^2} [/tex]
[tex]d = \sqrt{( -6)^2 + ( - 8)^2} [/tex]
[tex]d = \sqrt{36+ 64} [/tex]
[tex]d = \sqrt{100} [/tex]
[tex]d = 10[/tex]
Find the limit, picture provided
Answers
Answer:
C
Step-by-step explanation:
You are given that
[tex]\lim_{x \to 4} f(x)=5;[/tex][tex]\lim_{x \to 4} g(x)=0;[/tex][tex]\lim_{x \to 4} h(x)=-2.[/tex]Use the rule
[tex]\lim_{x\to x_0}(f(x)+g(x))=\lim_{x\to x_0} f(x)+\lim_{x \to x_0} g(x).[/tex]
In your case,
[tex]\lim_{x\to4}(f+g)(x)=\lim_{x\to4} (f(x)+g(x))= \lim_{x\to4} f(x)+ \lim_{x\to 4} g(x)=5+0=5.[/tex]
a scientist is growing bacteria in a lab for study one particular type of bacteria grows at a rate of y=2t^2+3t+500 a different bacteria grows at a rate of y=3t^2+t+300 in both of these eqiations y is the number of bacteria after t minutes when is there an equal number of both types of bacteria
Answers
t=15 minutes.
EXPLANATION
The equation that models the growth rate of the first type of bacteria is,
[tex]y = 2 {t}^{2} + 3t + 500[/tex]
The growth rate of a second type of bacteria is modeled by:
[tex]y = 3 {t}^{2} + t + 300[/tex]
Since y is the number of bacteria after t minutes in both equations, we equate both equations to find the time when there is an equal number of both types of bacteria.
[tex]3 {t}^{2} + t + 300 = 2 {t}^{2} + 3t + 500[/tex]
We rewrite as standard quadratic equation,
[tex]3 {t}^{2} - 2 {t}^{2} + t - 3t + 300 - 500 = 0[/tex]
[tex] {t}^{2} - 2t - 200 = 0[/tex]
We use the quadratic formula to obtain,
[tex]t = \frac{ - - 2 \pm \sqrt{ {( - 2)}^{2} - 4(1)( - 200) } }{2(1)} [/tex]
[tex]t = \frac{ -2 \pm \sqrt{ 804} }{2} [/tex]
[tex]t = \frac{ -2 \pm 2\sqrt{ 201} }{2} [/tex]
[tex]t = 1 - \sqrt{201} \: or \: t = 1 + \sqrt{201} [/tex]
t=-13.177 or t=15.177
We discard the negative value. Hence there is an equal number of both types of bacteria after approximately 15 minutes.
Mateo wants to make a toy sailboat. He has two pieces of wood to choose from.
His first piece of wood is a block that measures 18'' x 10" x 8". It weighs 46.65 lbs.
His second piece of wood is a log of wood measuring 21" long, with an average circumference of 25.12". It weights 39.25 lbs.
The sailboat needs to float, but both blocks of wood are denser than wood usually is, and he's not sure either piece of wood will float. He doesn't want to get the water wet before he's applied a sealant, so he isn't willing to just drop them in the water to find out.
2a. Which common solid can he use to represent the block? Which common solid can he use to represent the log? (2 points)
2b. What is the density of the block in pounds per cubic inch? Give the formula for density and show your work. (3 points)
2c. What is the density of the log in pounds per cubic inch? Give the formula for density and show your work. Use 3.14 for π. (Hint: you can determine the radius from the circumference.) (3 points)
2d. Water has a density of about 0.0361 pounds/cubic inch. Anything rarer will float, and anything denser will sink. Which of the pieces of wood are suitable for making a toy boat that will float? (2 points)
Answers
Answer:
wut is it
Step-by-step explanation:
An artist wants to paint a mural. She mixes blue paint and red paint to make paint that is a certain shade of purple. The ratio of blue paint to red paint should be 3 to 2. She needs 20 gallons of the purple paint. How much more blue paint than red paint does she need?
Answers
Answer:
She needs 4 more gallons of blue paint than red paint
Step-by-step explanation:
Since the ratio is 3 to 2, 3 + 2 = 5.
The artist needs 20 gallons of purple paint, so 20/5 = 4
The amount of blue and red paint needed is 4x3 to 4x2, or 12 to 8.
She needs 12 gallons of blue paint and 8 gallons of red paint.
12 - 8 = 4
She needs 4 more gallons of blue paint than red paint.
Answer:
ok!
Step-by-step explanation:
blue = 8 gallons
red = 12 gallons
Question part points submissions used use newton's method with the specified initial approximation x1 to find x3, the third approximation to the root of the given equation. (round your answer to four decimal places.) 2x3 − 3x2 + 2 = 0, x1 = −1
Answers
Set [tex]f(x)=2x^3-3x^2+2[/tex]. Find the tangent line [tex]\ell_1(x)[/tex] to [tex]f(x)[/tex] at the point when [tex]x=x_1[/tex]:
[tex]f'(x)=6x^2-6x\implies f'(x_1)=12[/tex] (slope of [tex]\ell_1[/tex])
[tex]\implies\ell_1(x)=12(x-x_1)+f(x_1)=12(x+1)-3=12x+9[/tex]
Set [tex]x_2=-\dfrac9{12}[/tex], the root of [tex]\ell_1(x)[/tex]. The tangent line [tex]\ell_2(x)[/tex] to [tex]f(x)[/tex] at [tex]x=x_2[/tex] has slope and thus equation
[tex]f'(x_2)=\dfrac{63}8\implies\ell_2(x)=\dfrac{63}8\left(x+\dfrac9{12}\right)-\dfrac{17}{32}=7x+\dfrac{151}{32}[/tex]
which has its root at [tex]x_3=-\dfrac{151}{224}\approx-0.6741[/tex].
(The actual value of this root is about -0.6777)
If a procedure meets all the conditions of a binomial distribution except that the number of trials is not fixed, then the geometric distribution can be used. The probability of getting the first success on the xth trial is given byP(x) = p(1-p)^(x-1)where p is the probability of success on any one trial.Assume that the probability of a defective computer component is 0.34. Find the probability that the first defect is found in the second component tested.(Round answer to four decimal places.)P(2) =
Answers
Answer:
0.2312
Step-by-step explanation:
Using the formula given,
[tex]P(x) = p(1-p)^{x-1}[/tex],
we use 0.34 for p and 2 for x:
[tex]P(2) = 0.34(1-0.34)^{2-1}\\\\P(2) = 0.34(0.68)^1\\\\P(2) = 0.34(0.68) = 0.2312[/tex]
It takes Ebru 13 minutes to bike to school. If she walks, it takes her twice as long. Ebru leaves for school at 7;15 What time will Ebru get to school if she walks?
Answers
Answer:
[tex]7;41[/tex]
Step-by-step explanation:
Let
x----> the time it take Ebru to walk to the school
we know that
[tex]x=2(13)=26\ min[/tex]
so
[tex]7;15 +26\ min=7;41[/tex]
Ebru takes 26 minutes to walk to school, twice as long as biking. Leaving at 7:15 AM means she would arrive at school by walking at 7:41 AM.
If Ebru bikes to school, it takes her 13 minutes. Walking takes her twice as long, which would be 26 minutes. If Ebru leaves her house at 7:15 AM, we can calculate the time she will get to school by walking by adding 26 minutes to the departure time.
7:15 AM + 20 minutes = 7:35 AM7:35 AM + 6 minutes = 7:41 AMTherefore, if Ebru walks to school, she will arrive at 7:41 AM.
a bag contains 'p' white balls 'Q' red balls and 'R'
Blue Balls A ball is drawn at the random find the probability of getting blue ball
Answers
Answer:
probability is r/p+q+r
Step-by-step explanation:
to find the probability, you take the number of desired balls (blue in this case )
and divide it by the total number of balls in the problem (add them all up) to get your answer
I hope that answered your question!!
Theres 5 boxes of candle. One box has 16 candles Four boxes has 24 candles each How many candles do the five boxes have altogether?
Answers
Answer:
112 candles
Step-by-step explanation:
We can simply add up the 5 numbers of candles, or we can take advantage of the invention of multiplication to replace repeated addition. The number of candles altogether is the sum of the numbers of candles in each of the 5 boxes.
16 + 4×24 = 16 +96 = 112
The total number of candles is 112.
the question and answers are below on the picture
Answers
Answer:
[tex]\large\boxed{B)\ 16x^2-25}[/tex]
Step-by-step explanation:
[tex]\text{Use}\ (a-b)(a+b)=a^2-b^2[/tex]
[tex](4x-5)(4x+5)=(4x)^2-5^2=16x^2-25[/tex]
Use the x-intercept method to find all real solutions of the equation.
x^3-6x2+3x+10=0
Answers
Answer:
Three solutions were found :
x = 5
x = 2
x = -1
Step-by-step explanation:
Answer:
d. [tex]x=-1,2,\:or\:5[/tex]
Step-by-step explanation:
The given equation is;
[tex]x^3-6x^2+3x+10=0[/tex]
To solve by the x-intercept method we need to graph the corresponding function using a graphing calculator.
The corresponding function is
[tex]f(x)=x^3-6x^2+3x+10[/tex]
The solution to [tex]x^3-6x^2+3x+10=0[/tex] is where the graph touches the x-axis.
We can see from the graph that; the x-intercepts are;
(-1,0),(2,0) and (5,0).
Therefore the real solutions are:
[tex]x=-1,2,\:or\:5[/tex]
At a football game, the ratio of filled seats to empty seats was 7 to 3. The maximum capacity of the stadium is 70,580 seats. How many seats were filled for the game?
Answers
Add the two numbers in the ratio: 7 +3 = 10
Divide total capacity by 10:
70,580 / 10 = 7,058
Multiply that by the ratio of filled seats:
7,058 x 7 = 49,406
49,406 seats were filled.
Landon is building new bookshelves for his bookstore's new mystery section. Each shelf can hold 36 books. There are 1,260 mystery books. How many shelves will he need to build?
Answers
Answer:
35 shelves
Step-by-step explanation:
If each shelf holds 36 books and there are a total of 1,260 books, divide 1,260 by 36 to get the number of shelves needed. 1,260/36 = 35 shelves. Think of it like 36 books per shelf and 35 shelves, 36*35 = 1,260.
A counterexample for the expression sin y tan y= cos y is 0.
Answers
Answer:
True
Step-by-step explanation:
To answer this question we must evaluate
y = 0° on both sides of the equation.
For the left side we have:
[tex]sin(0\°) tan(0\°)[/tex]
We know that [tex]tan(0\°) =\frac{sin(0\°)}{cos(0\°)}[/tex]
We know that [tex]cos(0\°) = 1[/tex] and [tex]sin(0\°) = 0[/tex].
Therefore [tex]tan(0\°) = 0[/tex].
Then the left-hand side of the equals is equal to zero.
On the right side we have:
[tex]cos(y)[/tex]
When evaluating [tex]cos(y)[/tex] at [tex]y = 0[/tex]
We have to [tex]cos(0\°) = 1[/tex].
0 ≠ 1
The equation is not satisfied. Therefore y = 0 ° is a counterexample to the equation
Answer:true
Step-by-step explanation:
edge
A credit card company charges a customer 1.8% per month on the unpaid balance of charges on a credit card. What is the finance charge in a month in which the customer has an unpaid balance of $1,205.62?
$217.01
$21.70
$1.81
$13.72
Answers
Answer:
217.01
Step-by-step explanation:
Answer:
Roughly $21.70
Step-by-step explanation:
1,205.62 times 0.018 (1.8% converted into decimal, to do so, move the decimal over to the right two places) equals 21.7
Store A sells 12 juice bottles for $4 and store B sells 18 juice bottles for $6 are the rates equivalent
Answers
Answer:
Yes
Step-by-step explanation:
If e^-3 ≈ 0.0498, which equation is also true?
A: ln(-3) ≈ 0.0498
B: ln(0.0498) ≈ -3
C: ln(e) ≈ 0.0498
D: ln (-3) ≈ e
Answers
the answer is B ln(0.0498)=-3
If 3(r+300)=6, then what would be the value of r+300-2?
Answers
Solve for r in the first equation:
3(r+300) = 6
Use the distributive property:
3r + 900 = 6
Subtract 900 from both sides:
3r = -894
Divide both sides by 3:
r = -894 / 3
r = -298
Now you have r, replace r in the second equation and solve:
r +300 -2 =
-298 + 300 - 2 = 0
The answer is 0.
Answer:
0 is the value of r+300-2
Solve for r in the first equation:
3(r+300) = 6
Use the distributive property:
3r + 900 = 6
Subtract 900 from both sides:
3r = -894
Divide both sides by 3:
r = -894 / 3
r = -298
Now you have r, replace r in the second equation and solve:
r +300 -2 =
-298 + 300 - 2 = 0
The answer is 0.
The dimensions of Square A are three times The dimensions of Square B. The area of Square A is 1,296 cm2. What is the area of Square b?
Answers
Square B Area = 144cm²
Square B = X
The dimensions of Square A are three times The dimensions of Square B
Square A = 3 * Square B
Square A = 3X
The area of Square A is 1,296 cm2.
Square A Area = (3X)² = 1296
Square B Area = X²
Solve to find X.
(3X)² = 1296
3X = 36
X = 36/3 = 12
Square B Area = 12² = 144
Square B Area = 144cm²
Final answer:
The area of Square B is 144 cm², calculated by dividing the area of Square A (1,296 cm²) by 9, because the area of a square scales with the square of its linear dimensions.
Explanation:
The area of Square A is given as 1,296 cm². Since the dimensions of Square A are three times the dimensions of Square B, we can find the area of Square B by understanding that area scales in proportion to the square of the linear dimensions. This means that if one dimension is three times another, the area will be nine times (3² = 9) larger.
To find the area of Square B, we simply divide the area of Square A by 9:
Area of Square B = Area of Square A / 9
Area of Square B = 1,296 cm² / 9
Area of Square B = 144 cm².
Therefore, the area of Square B is 144 cm².
Find all real solutions of the equation, approximating when necessary.
x^3+4x^2=10x+15=0
Answers
Answer:
b. [tex]x\approx -2.426[/tex]
Step-by-step explanation:
The given equation is;
[tex]x^3+x^2+10x+15=0[/tex]
We solve by the x-intercept method. We need to graph the corresponding function using a graphing tool.
The corresponding function is
[tex]f(x)=x^3+x^2+10x+15[/tex]
The solution to [tex]x^3+x^2+10x+15=0[/tex] is where the graph touches the x-axis.
We can see from the graph that; the x-intercept is;
(-2.426,0)
Therefore the real solution is:
[tex]x\approx -2.426[/tex]
Answer:
b. x ≈ -2.426
Step-by-step explanation:
Given that we have possible roots we can replace these values into the equation and check if it is satisfied.
option a: 2.426^3+4*2.426^2+10*2.426+15 = 77.08 ≠ 0
option b: (-2.426)^3+4*(-2.426)^2+10*(-2.426)+15 ≈ 0
option c: 5.128^3+4*5.128^2+10*5.128+15 = 306.31 ≠ 0
option d: (-5.128)^3+4*(-5.128)^2+10*(-5.128)+15 = -65.94 ≠ 0
the graph of F(x), shown below, has the same shape as the graph of G(x)=x^2. but it is shifted up 4 units and to the right 3 units. What is its equation
Answers
Answer:
C
Step-by-step explanation:
The equation is y = a(b(x-c))+d
So for it to move right three units, it would be x - 3.
For it to move up 4 unites, it would be x+4.
So the equation would be y = (x - 3)^2 + 4
The correct answer is C
First you would substitute the expression moving it to the left then you change the signs the power function with an even exponent is always a positive or 0 but there is no x intercept.
How many times greater is the value of the 4 in 64781 than the value of the 2 in 25409
Answers
64,781 --- 4,000
25,409 --- 400
4,000÷400=10
Which expression is equivalent to 8(a-6)
a. w>36
b w<36
c.w>5
d.w<5
Answers
Answer:
8a - 48
Step-by-step explanation:
An equivalent expression is an expression which is equal to 8(a-6). You can expand or simplify an expression to make an equivalent expression. Apply the distributive property to form a new equivalent expression by multiplying 8 into each term. 8(a-6) = 8*a - 8*6 = 8a - 48. The options listed below do not connect to this problem since they do not use the same variable as the expression.
Find a number less than 100 that is increased by one-fifth of its value when its digits are reversed.
Answers
Lets say the number is ab. Its value is 10a + b
When it is reversed it is 10b + a = 12a+1.2b (from the condition its value should increase 0.2 times).
11 a = 8.8b
a/b = 8.8/11 = 0.8/1 = 8/10 = 4/5 ( we do this because a and b should be natural numbers less than 10).
answer is 45.
A two-digit number less than 100 that increases by one-fifth of its original value, when its digits are reversed, can be found by setting up an equation. By defining the tens digit as 'a' and the unit digit as 'b', the equation 6a = 9b is derived. Solving for the digits within their possible values, the number 12 is found.
Explanation:To find a number less than 100 that increases by one-fifth of its value when its digits are reversed, we need to set up an equation. Let's call the tens digit a and the units digit b. The number can be written as 10a + b. When the digits are reversed, the number becomes 10b + a. The problem states that reversing the digits increases the number by one-fifth of its original value, which gives us the equation:
(10a + b) + \frac{1}{5}(10a + b) = 10b + a
Now solving the equation:
6a = 9b
As a and b are digits, their possible values range between 0 and 9. We find that a = 1 and b = 2 satisfy the equation. Hence, the number is:12
When we reverse the digits, we get 21, which is greater than 12 by \frac{1}{5} of 12, as required.
Learn more about Reversing Digits Problem here:https://brainly.com/question/34687674
#SPJ2
Which function has the graph shown?
Answers
Answer:
y = csc(x) -1
Step-by-step explanation:
The vertical offset of -1 is your first clue. Your second clue is that the range does not include (-2, 0), typical of cosecant and secant functions (offset by -1).
_____
Comment on answer choices
Apparently the cosine choices are intended to be confused with the cosecant choice. The cosine function has a range of [-1, 1], so will not show any vertical asymptotes anywhere, regardless of scaling or translation.