Answers
Answer: option a.
Step-by-step explanation:
The [tex]\lim_{x \to a} f(x)[/tex] give us information about the behavior of the function when the variable x gets closer to the value a. In other words, it tells us to what value y gets closer when x gets closer to the value a.
In this case we are evaluating the limits when:
[tex]{x \to -3}[/tex]
[tex]{x \to 0}[/tex]
[tex]{x \to 2}[/tex]
of the function shown in the graph.
As you can observe in the graph, when:
[tex]{x \to -3}[/tex] , [tex]y=3[/tex]
[tex]{x \to 0}[/tex] , [tex]y=0[/tex]
[tex]{x \to 2}[/tex] , [tex]y=-2[/tex]
Related Questions
Simply the expression (Picture provided)
Answers
Answer:
b. [tex]\csc(x)[/tex]
Step-by-step explanation:
The given expression is
[tex]\frac{\sec(x)}{\tan(x)}[/tex]
We express in terms of basic trigonometric ratios to obtain;
[tex]\frac{\frac{1}{\cos(x)} }{\frac{\sin(x)}{\cos(x)} }[/tex]
This is the same as
[tex]\frac{1}{\cos(x)}\div \frac{\sin(x)}{\cos(x)}[/tex]
[tex]\frac{1}{\cos(x)}\times \frac{\cos(x)}{\sin(x)}[/tex]
Cancel out the common factors;
[tex]\frac{1}{\sin(x)}=\csc(x)[/tex]
Answer:
[tex]\frac{secx}{tanx}[/tex] = cscx
Step-by-step explanation:
We have given a trigonometric expression.
[tex]\frac{secx}{tanx}[/tex]
We have to simplify the above expression.
Since, we know that
secx is reciprocal of cosx.
secx = 1/cosx
Tanx is the ratio of sinx and cosx.
Tanx = sinx / cosx
Given expression becomes
[tex]\frac{1/cosx}{sinx/cosx}[/tex]
[tex]\frac{1}{cosx}\frac{cosx}{sinx}[/tex]
[tex]\frac{1}{sinx}[/tex]
[tex]\frac{secx}{tanx}[/tex] = cscx which is the answer.
The time required for an automotive center to complete an oil change service on an automobile approximately follows a normal distribution, with a mean of 19 minutes and a standard deviation of 3.5 minutes. (a) The automotive center guarantees customers that the service will take no longer than 20 minutes. If it does take longer, the customer will receive the service for half-price. What percent of customers receive the service for half-price? (b) If the automotive center does not want to give the discount to more than 2% of its customers, how long should it make the guaranteed time limit?
Answers
Answer:
a. 61.41%
b. 27 minutes
Step-by-step explanation:
a: Find the z-score for the situation.
µ = 19
x-bar = 20
σ = 3.5
z = (20 - 19)/3.5 = 0.29
The p-value for z = 0.29 is 0.6141, so 61.41% of people will get this discount
b: They want no more than 2% to get the discount, so they want less than 98% getting the discount. The z-score for 98% (0.98 as a decimal) is 2.055
*You need to look at the chart and find where 0.98 would be. It's between a z-score of 2.05 and 2.06.
The z-score is 2.055 = (x - 19)/3.5 We are solving for the time for this one. So solve for x...
7.1925 = x - 19 (multiply both sides by 3.5)
26.1925 = x (add 19 to both sides)
So 26.1925 minutes, or about 26 minutes, 12 seconds, so round up to 27 minutes because they want less than 2%. I chose 27 minutes because no places give odd wait times like 26 minutes 12 seconds.
A) The percent of customers receive the service for half-price is; 61.41%
B) The time to make the guaranteed limit is; 26 minutes 12 seconds
What is the p-value of the distribution?
A) We are given;
Population mean; µ = 19
Sample mean; x' = 20
Standard deviation; σ = 3.5
Thus, z-score is;
z = (20 - 19)/3.5
z = 0.29
From online p-value from s-score calculator, the p-value for z = 0.29 is;
p = 0.6141 = 61.41%
B) We are told that they now want more than 2% to get the discount. This means that they want less than 98% or 0.98 getting the discount.
The z-score for 0.98 is; z = 2.055
Thus, using z-score formula, we have;
2.055 = (x' - 19)/3.5
x' - 19 = 3.5 * 2.055
x' - 19 = 7.1925
x' = 26.1925 = 26 minutes 12 seconds
Read more about P-value at; https://brainly.com/question/4621112
A rectangular pyramid is sliced such that the cross section is perpendicular to its base and the cross section does not intersect its vertex.
What is the shape of the cross section?
square
trapezoid
triangle
rectangle
Answers
The vertex, would be the tip of the pyramid. If it was sliced at the vertex, the shape would be a triangle. Since the slice doesn't intersect the vertex, the point of the pyramid would net be included, it would be as if the tip was cut off.
You would then have a trapezoid, because the top would be a straight horizontal line parallel with the bottom line.
Identify the graph of 2x^2+2y^=9 for theta=30º and write and equation of the translated or rotated graph in general form.
Answers
Answer:
The answer is circle; (x')² + (y')² - 4 = 0
Step-by-step explanation:
* At first lets talk about the general form of the conic equation
- Ax² + Bxy + Cy² + Dx + Ey + F = 0
∵ B² - 4AC < 0 , if a conic exists, it will be either a circle or an ellipse.
∵ B² - 4AC = 0 , if a conic exists, it will be a parabola.
∵ B² - 4AC > 0 , if a conic exists, it will be a hyperbola.
* Now we will study our equation:
* 2x² + 2y² = 8
∵ A = 2 , B = 0 , C = 2
∴ B² - 4AC = (0) - 4(2)(2) = -16 < 0
∵ B² - 4AC < 0
∴ it will be either a circle or an ellipse
* Lets use this note to chose the correct figure
- If A and C are equal and nonzero and have the same sign,
then the graph is a circle.
- If A and C are nonzero, have the same sign, and are not equal
to each other, then the graph is an ellipse.
∵ A = 2 and C = 2
∴ The graph is a circle.
∵ D and E = 0
∴ The center of the circle is the origin (0 , 0)
∵ Ф = 30°
∴ The point (x , y) will be (x' , y')
- Where x = x'cosФ - y' sinФ and y = x'sinФ + y'cosФ
∴ x = x'cos(30°) - y'sin(30°)
∴ y = x'sin(30°) + y'cos(30°)
∴ x = (√3/2)x' - (1/2)y' and y = (1/2)x' + (√3/2)y'
∴ [tex]x=\frac{\sqrt{3}x'-y'}{2}[/tex]
∴ [tex]y=\frac{x'+\sqrt{3}y'}{2}[/tex]
* Lets substitute x and y in the first equation
∴ [tex]2(\frac{\sqrt{3}x'-y'}{2})^{2}+2(\frac{x'+\sqrt{3}y'}{2})^{2}=8[/tex]
* Use the foil method
∴ [tex]2(\frac{3x'^{2}-2\sqrt{3}x'y'+y'^{2}}{4})+2(\frac{x'^{2}+2\sqrt{3}x'y'+3y'^{2}}{4})=8[/tex]
* Open the brackets
∴ [tex]\frac{3x'^{2}-2\sqrt{3}x'y'+y'^{2}+x'^{2}+2\sqrt{3}x'y'+3y'^{2}}{2}=8[/tex]
* Collect the like terms
∴ [tex]\frac{4x'^{2}+4y'^{2}}{2}=8[/tex]
* Simplify the fraction
∴ 2(x')² + 2(y')²= 8
* Divide each side by 2
∴ (x')² + (y')² = 4
∴ The equation of the circle is (x')² + (y')² = 4
* The general equation of the circle is (x')² + (y')² - 4 = 0
after rotation 30° about the origin
* Look to the graph
- The blue circle for the equation 2x² + 2y² = 8
- The blue circle for equation (x')² + (y')² - 4 = 0
* That is because the two circles have same centers and radii
- The green line is x' and the purple line is y'
Answer:
The answer is D
Good luck on the Ed-genuity test
Which of the following statements is true? a. sin 18° = cos 72° b. sin 55° = cos 55° c. sin 72° = cos 18° d. Both a and c. Please select the best answer from the choices provided A B C D
Answers
D
generally,
[tex] \sin( \alpha ) = \cos(90 - \alpha )[/tex]
you can visualize this by drawing a right triangle with acute angles a and 90-a
Answer:
D. Both a and c are true.
Step-by-step explanation:
a . sin 18 = cos (90 - 18) = cos 72 so a is True.
b. this is not true.
c. sin 72 = cos(90 - 72) = cos 18, so c is true.
Write these numbers in order from least to greatest. ( 3-3/10), (3.1) , (3-1/4)
Answers
Our three numbers are...
3 3/10 = 3.3
3.1
3 1/4 = 3.25
So, if we order those from least to greatest, we have...
3.1, 3.25, 3.3
which, in the forms given, is...
3.1, 3-1/4, 3-3/10
Please help me out........ :)
Answers
Answer:
x = 5
Step-by-step explanation:
For the parallelogram to be a square we use the property
The diagonals of a square are congruent, hence
12x - 23 = 4x + 17 ( subtract 4x from both sides )
8x - 23 = 17 ( add 23 to both sides )
8x = 40 ( divide both sides by 8 )
x = 5
The division algorithm states that if p(x) and d(x) are polynomial functions with d left parenthesis x right parenthesis not equals 0 comma and the degree of d(x) is less than or equal to the degree of p(x), then there exist unique polynomial functions q(x) and r(x) such that
Answers
Final answer:
The division algorithm for polynomials establishes that a polynomial p(x) can be divided by a non-zero polynomial d(x) (with degree less or equal to p(x)), to yield unique quotient q(x) and remainder r(x), with r(x) having a lower degree than d(x).
Explanation:
The division algorithm in the context of polynomials is a fundamental concept in algebra that stipulates for any two polynomials p(x) and d(x), with d(x) ≠ 0 and the degree of d(x) less than or equal to the degree of p(x), there exist unique polynomials q(x) and r(x) such that p(x) = d(x) × q(x) + r(x).
In this scenario, q(x) is referred to as the quotient and r(x) is the remainder. The degree of the remainder r(x) will always be less than the degree of d(x), following the division algorithm.
When applying this algorithm to special sets of polynomials like Legendre polynomials, additional properties can be observed, such as the roots of the polynomials or specific transformations like the Poisson bracket that could arise in mathematical physics. Moreover, the concept extends to rational functions, which are the quotients of polynomials.
Find the missing values for the exponential function represented by the table below.
x y
-2 7
-1 10.5
0 15.75
1
2
Answers
Answer:
x y
-2 7
-1 10.5
0 15.75
1 23.625
2 35.4375
Step-by-step explanation:
The general equation of the exponential function is [tex]y=ab^x[/tex].
We know from our table that when [tex]x=0[/tex], [tex]y=15.75[/tex]. Let's replace those values in our equation:
[tex]y=ab^x[/tex]
[tex]15.75=ab^0[/tex]
Remember that [tex]b^0=1[/tex], so:
[tex]15.75=a(1)[/tex]
[tex]15.75=a[/tex]
[tex]a=15.75[/tex]
We also know from our table that when [tex]x=-1[/tex], [tex]y=10.5[/tex]. Let's replace the values again:
[tex]y=ab^x[/tex]
[tex]10.5=ab^{-1}[/tex]
But we now know that [tex]a=15.75[/tex], so let's replace that value as well:
[tex]10.5=15.75b^{-1}[/tex]
Remember that [tex]b^{-1}=\frac{1}{b}[/tex], so:
[tex]10.5=\frac{15.75}{b}[/tex]
[tex]10.5b=15.75[/tex]
[tex]b=\frac{15.75}{10.5}[/tex]
[tex]b=1.5[/tex]
Now, we can put it all together to complete our exponential function:
[tex]y=ab^x[/tex]
[tex]y=15.75(1.5)^x[/tex]
To find the missing values, we just need to evaluate our function at [tex]x=1[/tex] and [tex]x=2[/tex]:
- For [tex]x=1[/tex]
[tex]y=15.75(1.5)^x[/tex]
[tex]y=15.75(1.5)^1[/tex]
[tex]y=23.625[/tex]
- For [tex]x=2[/tex]
[tex]y=15.75(1.5)^x[/tex]
[tex]y=15.75(1.5)^2[/tex]
[tex]y=35.4375[/tex]
Of 500 students going on a class trip 350 are student band members and 65 are athletes 25 band members and student athletes what is the probability that one of the students on the trip is an athlete or a band memeber?
Answers
Answer:
0.78
Step-by-step explanation:
There are 500 students in total. Thus,
350 students are band members;65 students are athlets;25 students are both band members and athlets;350-25=325 students are only band members. not athlets;65-25=40 students are only athlets, not band members.The probability that one of the students on the trip is an athlete or a band memeber is
[tex]Pr=\dfrac{325+40+25}{500}=\dfrac{390}{500}=0.78.[/tex]
How to find the final price of a 120$ pair of shoes discounted by 20% and the by 5%
Answers
Describe a realistic situation that could cause you or someone you know to have to use money from a financial reserve
Answers
Answer:
Step-by-step explanation:
Your car breaks down unexpectedly and you must have it repaired immediately. That's an example of a situation where you might use money from a financial reserve.
. A soccer team played 32 games. If they won 25% of them, how many games did the team win?V
Answers
Answer:
[tex]8\ games[/tex]
Step-by-step explanation:
Let
x----->number of games won by the football team
we know that
[tex]25\%=25/100=0.25[/tex]
so
[tex]x=0.25(32)=8\ games[/tex]
On Monday Paula has $20 is her bank account. She spends $25 and then spends another $10. How much money does she need to add into her account (deposit) to return to the original amount she started with on Monday?
Answers
Answer:
15
Step-by-step explanation:
10 + 25= 35 and 35-20 = 15
please give branlest
Answer:
Step-by-step explanation: She Needs To Deposit $35 Dollars To Return To The Orginal Ammount She Started With On Monday.
Remi invests ?600 for 5 years in a saving account. By the end of the 5 years he has received a total of ?75 simple interest. Work out the annual rate of simple interest
Answers
Answer:
2.5 %
Step-by-step explanation:
The simple interest formula is
I = Prt
Data:
I = $75
P = $600
t = 5 yr
Calculation:
75 = 600 × r × 5
75 = 3000 r
Divide each side by 3000
r = 75/3000 = 0.025 = 2.5 % APR
The annual percentage rate is 2.5 %.
Final answer:
The annual rate of simple interest that Remi received from his savings account is 2.5%. This was calculated using the simple interest formula I = PRT, rearranged to solve for R, the annual interest rate.
Explanation:
To work out the annual rate of simple interest that Remi received from his savings account, we can use the formula for simple interest:
I = PRT
where I is the total interest earned, P is the principal amount invested, R is the annual interest rate, and T is the time the money is invested in years.
From the question, we know that Remi invested £600 (P=600), received £75 in interest (I=75), and the investment was for 5 years (T=5). We need to find the annual rate (R).
Rearranging the formula to get value of R, we get:
R = I / (PT)
Substituting the given values:
R = 75 / (600 × 5) (× is the multiplication symbol)
R = 75 / 3000
R = 0.025
To Convert decimal to a percentage, we multiply by 100:
R = 0.025 × 100
R = 2.5%
So, the annual rate of simple interest that Remi received is 2.5%.
Find the value of x in the polygon.
Answers
Answer:
x = 25 mm
Step-by-step explanation:
The perimeter of a rectangle is given by
P = 2(l+w) where l is the length and w is the width
We know the perimeter is 60 mm and the width is 5 mm and the length is x
60 = 2(x +5)
Divide each side by 2
60/2 = 2/2(x+5)
30 = x+5
Subtract 5 from each side
30-5 = x+5-5
25 =x
x = 25 mm
[tex]\huge\bold\red{Answer}[/tex]
☑The diagram which is shown above is a rectangle.
✍ Perimeter= 60mm
✍ breadth = 5mm
➡ Perimeter of rectangle = 2(l+b)
✍ 60 = 2(l +5)
✍ 60/2 = l+5
✍ 30 - 5 = l
✍ 25 = l
☑ L = 25mm
❣..hope it helps you..❣
If a single six sided die is rolled once, what are the odds that you will roll a number less than 3?
Answers
Answer:
1/3
Step-by-step explanation:
1/3 since there are two numbers less than three, and there are 6 possible outcomes, so 2/6 = 1/3.
Which is the correct cofunction identity for cos theta
A. csc(90° - theta)
B. sec(90° - theta)
C. sin(90° - theta)
D. cos(90° - theta)
E. tan(90° - theta)
Answers
Answer:
C. sin(90° - θ)
Step-by-step explanation:
A trig function of an angle equals the cofunction of the angle's complement.
The cofunction of cosine is sine, and the complement of θ is 90° - θ.
∴ cosθ = sin(90° - θ)
Answer: Option 'C' is correct.
Step-by-step explanation:
Since we have given that
[tex]\cos \theta[/tex]
We need to find the correct cofunction identity for it.
Cofunction identities represent the relationship among the trigonometric functions.
The value of trigonometric function of an angle is equal to cofunction of its complement.
As we know that sine is a complement of cosine.
so, it becomes,
[tex]\cos \theta=\sin(90^\circ-\theta)[/tex]
Hence, Option 'C' is correct.
Solve for x for 0 ≤ x < 2 π .
cotxcosx - cotx = 0
0
Pi/2
Pi
3Pi/2
2Pi
Answers
[tex]\bf cot(x)cos(x)-cot(x)=0\implies cot(x)[cos(x)-1]=0 \\\\[-0.35em] ~\dotfill\\\\ cot(x)=0\implies \cfrac{cos(x)}{sin(x)}=0\implies cos(x)=0\\\\\\ x=cos^{-1}(0)\implies \boxed{x= \begin{cases} \frac{\pi }{2}\\\\ \frac{3\pi }{2} \end{cases}} \\\\[-0.35em] ~\dotfill\\\\ cos(x)-1=0\implies cos(x)=1\implies x=cos^{-1}(1)\implies \boxed{x=0}[/tex]
Answer:
x = π/2, 3π/2
Step-by-step explanation:
cot(x)cos(x) - cot(x) = 0
Factor out cot(x)
cot(x)[cos(x) -1] = 0
Solve each part separately
cot(x) = 0 cos(x) - 1 = 0
x = π/2, 3π/2 cos(x) = 1
x = 0
There are three possible solutions:
x = 0, π/2, 3π/2
However, the function is undefined for x = 0.
∴ x = π/2, 3π/2
Please answer this question, will give brainliest!
Answers
Answer:
9.9 cm
Step-by-step explanation:
We can use the Pythagorean theorem to find the length of CY
a^2 + b^2 = c^2
CY^2 + YZ^2 = CZ^2
YZ = XY since CZ is the perpendicular bisector
YZ = 5
CZ = 7
CY ^2 + 5^2 = 7^2
CY^2 +25 = 49
Subtract 25 from each side
CY^2 = 49-25
CY^2 = 24
Take the square root of each side
sqrt(CY^2) = sqrt(24)
CY = 4.898979
CY = 4.9 cm
We want the length of WY
WY = WC + CY
WC is a radius which is 5 cm
WY = 5cm + 4.9cm
WY = 9.9 cm
Answer:
We should work backwards we need to find YC+CW to get YW
angle bisector theorem means that ZC and XC are equal
then we can use the Pythagorean theorem to get YC
5^2 + x = 7^2
YC= √13
CW = 7 because they are both the radius of a circle
YW= 7+√13
YW=10.60 (rounded)
if f(x)=sqrt x+12 and g(x)= 2 sqrt x what is the value of (f – g)(144)?.
Answers
Answer:
the answer is 0
Step-by-step explanation:
HELP!! Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s).
A professor is examining a new strain of bacteria. The amount of bacteria can be modeled by function s(n) = 20 · bn, where n is the number of hours and b is an unknown positive base.
Based on the model, there were initially (answer space) bacteria.
If b = 1.85, the hourly percent growth rate of the bacteria would be
(answer space) %.
Answers
Answer:
20
85%
Step-by-step explanation:
You are given the function [tex]S(n)=20\cdot b^n.[/tex]
If n is the number of hours, then initially n=0 and
[tex]S(0)=20\cdot b^0=20\cdot 1=20.[/tex]
If S(n) is the function of exponential growth, then it can be represented as
[tex]S(n)=I\cdot (1+r)^n,[/tex]
where I is the initial amount, r -is the percent growth rate and n is the number of hours.
If b = 1.85, we can represent it as b = 1 + 0.85. Thus, the hourly percent growth rate of the bacteria would be 0.85=85%.
s(n) = 20b^n
n is the time in hours. At the beginning, the time is zero hours, so n = 0.
s(0) = 20 * b^0
s(0) = 20 * 1
s(0) = 20
The initial amount was 20.
For b = 1.85,
s(n) = 20(1.85)^n
s(n) = 20(1 + 0.85)^n
The hourly growth is 0.85.
0.85 * 100% = 85%
The hourly percent change is 85%.
Which is the best estimate for the mass of a desktop computer?
Answers
Answer:
I would say about 60 to 70 pounds. But I have no more information from you to better answer your question, so that's all I have right now.
Step-by-step explanation:
Evaluate the expression under the given conditions. sin(θ − ϕ); tan(θ) = 4/3 , θ in Quadrant III, sin(ϕ) = − 10/10 , ϕ in Quadrant IV
Answers
Answer: -0.6
Step-by-step explanation:
First thing to do is to solve for θ and ϕ from the given information
tan(θ) = 4/3,
θ = tan-¹4/3,
θ = 53.1°
Since tan is positive in quadrant III, θ = 53.1°
Also,
sin(ϕ) = − 10/10 ,
ϕ = sin-¹-1
ϕ = 270°
If ϕ is in the fourth quadrant, that gives 360 - ϕ i.e 360 - 270 = 90°
Substituting the values of θ and ϕ into sin(θ − ϕ), we have;
Sin(53.1 - 90)
= sin (-36.9°)
= -0.6
The given expression sin(θ - ϕ), with tan(θ) = 4/3, θ in Quadrant III, sin(ϕ) = -10/10, and ϕ in Quadrant IV, is evaluated by using trigonometric principles and identities. Upon calculations, sin(θ - ϕ) comes out to be -3/5.
Explanation:The question is asking us to evaluate the expression sin(θ − ϕ), given that tan(θ) = 4/3, θ is in Quadrant III, sin(ϕ) = -10/10, and ϕ is in Quadrant IV. In trigonometry, tan θ = sin θ/cos θ. We have tan θ = 4/3 and we know that in Quadrant III, tangent is positive but sine and cosine are negative. So, we can make a right triangle where the opposite side is 4 (basing this on the absolute value of the tan θ) and the adjacent side is 3. The hypotenuse then, by using Pythagoras theorem, comes out to be 5. Then sin θ = -4/5 and cos θ = -3/5.
For sin(ϕ), we are given that it equals -1. In Quadrant IV, sine is negative and cosine is positive, so cos ϕ = √(1 - (-1)^2) = 0.
Finally, utilizing the formula sin (a ± ß) = sin a cos ß ± cos a sin ß, we plug in our values to come to the solution sin(θ - ϕ) = (sin θ cos ϕ) - (cos θ sin ϕ) = ((-4/5)*0) - ((-3/5)*-1) = -3/5
Learn more about Trigonometry here:https://brainly.com/question/11016599
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Solve the equation. Round to the nearest hundredth. Show work.
[tex]6e^{2x} - 5e^{x} = 6[/tex]
Answers
Answer:
The value of x = 0.41
Step-by-step explanation:
∵ [tex]6e^{2x}-5e^{x}=6[/tex]
Let [tex]e^{x}=y[/tex]
∴ [tex]e^{2x}=y^{2}[/tex]
∴ 6y² - 5y = 6
∴ 6y² - 5y - 6 = 0 ⇒ factorize
∴ (3y + 2)(2y - 3) = 0
∴ 3y + 2 = 0 ⇒ 3y = -2 ⇒ y = -2/3
∴ 2y - 3 = 0 ⇒ 2y = 3 ⇒ y = 3/2
∵ [tex]y=e^{x}[/tex]
∴ [tex]e^{x}=\frac{-2}{3}[/tex] ⇒ refused
([tex]e^{ax}[/tex] never gives -ve values)
∵ [tex]e^{x}=3/2[/tex] ⇒ insert ln in both sides
∵ [tex]lne^{ax}=axlne=ax[/tex] ⇒ ln(e) = 1
∴ [tex]xlne=ln(3/2)[/tex]
∴ x = ln(3/2) = 0.41
Twenty is fourteen more than 3 times a number. What is the number?
Answers
Answer:
2
Step-by-step explanation:
Let's disect the problem. Three times a particular number plus fourteen equals 20. Let's make an equation, and replace the number with x.
3x + 14 = 20The "3x" represents the 3 times the number,the 14 represents the 14 added to make 20.Let's solve the equation!We'll first minus 14 from each side to balance the equation, but with the intention of isolating the variable, x.
3x = 6We have almost successfully isolated the variable. To isolate the variable, we can divide by three on each side.
x = 2The number is 2.The sum of the measures of angleUWV and angleUWZ is 90°, so angleUWV and angleUWZ are angles.
Answers
Answer:
Angles UWV and UWZ are complementary
Step-by-step explanation:
we know that
If the sum of the measures of two angles is equal to 90 degrees, then, the angles are complementary
so
In this problem
[tex]m<UWZ+m<UWV=90\°[/tex]
therefore
Angles UWV and UWZ are complementary
What is the volume of a rectangular prism with the dimensions: base 3 1 2 cm, height 1 1 2 cm, and length 5 1 2 cm?
Answers
Answer:
The volume of a rectangular prism is [tex]28\frac{7}{8}\ cm^{3}[/tex]
Step-by-step explanation:
we know that
The volume of the rectangular prism is equal to
[tex]V=BHL[/tex]
Convert the given dimensions to an improper fractions
[tex]B=3\frac{1}{2}\ cm=\frac{3*2+1}{2}=\frac{7}{2}\ cm[/tex]
[tex]H=1\frac{1}{2}\ cm=\frac{1*2+1}{2}=\frac{3}{2}\ cm[/tex]
[tex]L=5\frac{1}{2}\ cm=\frac{5*2+1}{2}=\frac{11}{2}\ cm[/tex]
substitute in the formula
[tex]V=(\frac{7}{2})(\frac{3}{2})(\frac{11}{2})=\frac{231}{8}\ cm^{3}[/tex]
Convert to mixed number
[tex]\frac{231}{8}=\frac{224}{8}+\frac{7}{8}=28\frac{7}{8}\ cm^{3}[/tex]
Simplify the expression.
sec x/tan x
Answers
Answer:
Option b
Step-by-step explanation:
We know that, by definition:
[tex]secx = \frac{1}{cosx}[/tex]
We also know that:
[tex]tanx = \frac{sinx}{cosx}[/tex]
Applying these identities we can simplify the given expression
[tex]\frac{secx}{tanx} = \frac{\frac{1}{cosx}}{\frac{sinx}{cosx}}\\\\\frac{secx}{tanx} = \frac{cosx}{sinxcosx}\\\\\frac{secx}{tanx} = \frac{1}{sinx}[/tex]
We know that, by definition:
[tex]\frac{1}{sinx} = cscx[/tex]
Final answer:
To simplify sec x/tan x, we use trigonometric identities to show that sec x/tan x equals csc x, which is the cosecant of x.
Explanation:
To simplify the expression sec x/tan x, we need to recall the trigonometric identities for secant (sec) and tangent (tan). We know that sec x is equal to 1/cos x and tan x is equal to sin x/cos x. When we divide sec x by tan x, we are essentially dividing 1/cos x by sin x/cos x. This simplifies to:
sec x/tan x = (1/cos x) / (sin x/cos x)Multiply the numerator by the reciprocal of the denominator: (1/cos x) * (cos x/sin x)The cos x terms cancel out, leaving us with: 1/sin xThe expression 1/sin x is the definition of cosecant (csc x), thus:sec x/tan x = csc xTo summarize, the simplified form of the expression sec x/tan x is csc x.
Suppose you are a casino owner, and your casino runs a very simple game of chance. The dealer flips a coin. The customer wins $9 from the casino if it comes up heads and loses $10 if it comes up tails. Question 1. Assuming no one is cheating and the coin is fair, if a customer plays twice, what is the chance they make money?
Answers
Answer:
Step-by-step explanation:
The outcome of the game is
Toss 1 Toss 2 Result
H H 18
H T -1
T H -1
T T -20
His only winning position is H ---- H
That means he has only a 1/4 chance in winning. He shouldn't play at all. It might be a fair coin, but it is not a fair game.