Answer:
12 friends
Step-by-step explanation:
Fill in the given number and solve for x.
855 = 5x +795 . . . . . the total fee was 855
60 = 5x . . . . . . . . . . . subtract 795
12 = x . . . . . . . . . . . . . divide by 5
The number of friends you brought was 12.
The sum of first three terms of a finite geometric series is -7/10 and their product is -1/125. [Hint: Use a/r , a, and ar to represent the first three terms, respectively.] The three numbers are _____, _____, and _____.
Answer:
-1/10, -1/5 , -2/5 or -2/5, -1/5 , -1/10
Step-by-step explanation:
let a/r, a, ar be the first 3 terms of the geometric series
their product would be equal to a^3
a^3=-1/125
a=-1/5
Substitute a=-1/5 into the first 3 terms
-1/5r + -1/5+-r/5=-7/10
Multiply the terms such that they have a common denominator:
-1/5r +-r/5r + -r^2/5r = -3.5r/5r
Multiply both sides by 5r
-r^2-r-1=-3.5r
Add 3.5r to both sides and multiply the equation by 2
-2r^2 + 5r -2=0
Factorize the equation
(2r-1)(r-2)=0
r=0.5 or r-2
For the first three terms where r=0.5
-2/5, -1/5 , -1/10
For the first three terms where r=2
-1/10, -1/5 , -2/5
A car dealer wants to draw a Pie Graph representing the different types of cars he sold in a given month. He sold a total of 90 this month with 15 of those cars being convertables. How many degrees should be used to represent convertables in the Pie Graph? (You do not have to use the degree symbol in your answer.)
Answer:
60°
Step-by-step explanation:
Here we are given that the number of convertibles cars. Total number of cars owned by the dealers is 90. We have to draw the pie graph for above ratio. The pie chart is a circular statistical graph , where the different portion in form of sectors on the circle showing the amount of different entities.
The angle covered by an entity is in the same proportion as its number is in ration to the total number of all the entities.
Hence
[tex]\frac{15}{90}=\frac{\theta}{360}\\\\\theta=\frac{15*360}{90}\\\theta=\frac{15*4}{1}\\\theta=60\\[/tex]
Hence we will represent 60 degrees in order to represent 15 cars in our chart.
To represent convertibles on the pie graph, calculate the proportion of convertibles sold to the total number of cars sold (15/90) and multiply by the total degrees in a circle (360). Convertibles should be represented by a 60-degree slice on the pie graph.
The question is asking how to calculate the degree measure for the convertibles slice in a pie chart based on the total sales in a month. We know that a pie chart represents 100% of a data set, with the entire chart being a 360-degree circle. To find the degree measure for the convertibles, we would perform a proportion calculation based on the number of convertibles sold (15) out of the total number of cars sold (90). The calculation is as follows:
Proportion of convertibles to total sales = (Number of convertibles sold / Total cars sold) = 15 / 90
Now, multiply this proportion by the total degrees in a circle to get the degree measure for convertibles:
Degree measure for convertibles = Proportion of convertibles imes Total degrees in a circle = (15 / 90) * 360 = 1/6 * 360 = 60 degrees
Therefore, the convertibles should be represented by a 60-degree slice on the Pie Graph.
$20000 is invested in an account that earned 6% p.A. Compounding yearly for 3 years. The interest rate then went up to 8% p.A. For the next 4 years. After this period the amount of money in the account would be?
[tex]\bf ~~~~~~ \textit{Compound Interest Earned Amount \underline{for the first 3 years}} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$20000\\ r=rate\to 6\%\to \frac{6}{100}\dotfill &0.06\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{per annum, thus once} \end{array}\dotfill &1\\ t=years\dotfill &3 \end{cases}[/tex]
[tex]\bf A=20000\left(1+\frac{0.06}{1}\right)^{1\cdot 3}\implies A=20000(1.06)^3\implies \boxed{A=2382.032} \\\\[-0.35em] ~\dotfill\\\\ ~~~~~~ \textit{Compound Interest Earned Amount \underline{for the next 4 years}}[/tex]
[tex]\bf A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$2382.032\\ r=rate\to 8\%\to \frac{8}{100}\dotfill &0.08\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{per annum, thus once} \end{array}\dotfill &1\\ t=years\dotfill &4 \end{cases}[/tex]
[tex]\bf A=2382.032\left(1+\frac{0.08}{1}\right)^{1\cdot 4}\implies A=2382.032(1.08)^4\implies \boxed{A\approx 3240.73} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{amount for this period}}{2382.032+3240.73}\implies 5622.762[/tex]
The difference between two numbers is 10. The greater number is b. Write an expression that represents the lesser number.
Answer:
B-10=N
Step-by-step explanation:
N is the lesser number. So if B is the greater number & there is a difference of 10 this would be your expression
Which ordered pair makes both inequalities true? y < –x + 1 y > x Which ordered pair makes both inequalities true? y < –x + 1 y > x (–3, 5) (–2, 2) (–1, –3) (0, –1) (–3, 5) (–2, 2) (–1, –3) (0, –1) Mark this and return
Answer:
(-2, 2)
Step-by-step explanation:
You can graph the equations and points and see which points fall into the doubly-shaded area. The only one that does is (-2, 2).
___
You can also evaluate the inequalities at the given points to see which might work. The inequality y > x is the simplest to evaluate, and it immediately eliminates the last two choices:
-3 > -1 . . . not true
-1 > 0 . . . not true
So, we can check the first two choices in the first inequality:
-(-3) +1 > 5 . . . not true
-(-2) +1 > 2 . . . TRUE
The ordered pair (-2, 2) makes both inequalities true.
Answer:
2nd Option is correct.
Step-by-step explanation:
Given Inequalities are,
y < x + 1 .....................(1)
y > x .....................(2)
To find: Ordered pair which makes he inequalities true.
Pair 1:
x = -3 , y = 5
Inequality (1),
LHS = 5
RHS = -(-3) + 1 = 4
⇒ LHS > RHS
Thus, this pair does not satisfy the pair of inequalities.
Pair 2:
x = -2 , y = 2
Inequality (1),
LHS = 2
RHS = -(-2) + 1 = 3
⇒ LHS < RHS
Inequality (2),
LHS = 2
RHS = -2
⇒ LHS > RHS
Thus, this pair satisfies the pair of inequalities.
Pair 3:
x = -1 , y = -3
Inequality (1),
LHS = -3
RHS = -(-1) + 1 = 0
⇒ LHS < RHS
Inequality (2),
LHS = -3
RHS = -1
⇒ LHS < RHS
Thus, this pair does not satisfy the pair of inequalities.
Pair 4:
x = 0 , y = -1
Inequality (1),
LHS = -1
RHS = -(0) + 1 = 1
⇒ LHS < RHS
Inequality (2),
LHS = -1
RHS = 0
⇒ LHS < RHS
Thus, this pair does not satisfy the pair of inequalities.
Therefore, 2nd Option is correct.
Enter the values for a and b that complete
the sum:
3/x + 5/x^{2} =ax+b/x^{2}
ANSWER
a=3, b=5
EXPLANATION
The given equation is
[tex] \frac{3}{x} + \frac{5}{ {x}^{2} } = \frac{ax + b}{ {x}^{2} } [/tex]
We simplify the left hand side.
We collect LCD to obtain:
[tex] \frac{3x + 5}{ {x}^{2} } = \frac{ax + b}{ {x}^{2} } [/tex]
Both sides of the equation are now the same.
By comparing the coefficients of x, we have
[tex]a = 3[/tex]
By comparing the constant terms
[tex]b = 5[/tex]
Answer:
For the first part
A=3
B=5
For the second part
M=3
N=14
P=2
Step-by-step explanation:
Right on edge 2020
I can't tell the difference!! :(
Answer:
the first one is 350 inches (350 in) and the second on is 350 square inches (350 in2)
Step-by-step explanation:
A boat is 122 meters from the base of a lighthouse that is 34 meters above sea level. What is the angle of elevation from the boat to the top of the lighthouse? Round to the nearest degree.
Answer: [tex]15.57\°[/tex]
In order to understand better this problem, we can use the figure attached, in which we have a right triangle (with a 90 degree angle), where [tex]c[/tex] is its hypotenuse, [tex]a[/tex] is the adjacent side to the angle of elevation [tex]\theta[/tex] from the boat to the top of the lighthouse and [tex]b[/tex] is the opposite side to [tex]\theta[/tex].
Knowing this, we will use the tangent trigonometric function to find [tex]\theta[/tex]:
[tex]tan\theta=\frac{oppositeside}{adjacentside}=\frac{b}{a}[/tex] (1)
[tex]tan\theta=\frac{34m}{122m}[/tex] (2)
[tex]tan\theta=0.278[/tex] (3)
[tex]\theta={tan}^{-1} (0.278)[/tex] (4)
Finally:
[tex]\theta=15.572\°[/tex]
Answer:
16
Step-by-step explanation:
A boat is 122 meters from the base of a lighthouse that is 34 meters above sea level. What is the angle of elevation from the boat to the top of the lighthouse? Round to the nearest degree.
Find the area 6m, 3m
Check the picture below.
Factor this expression:
mn - 4m - 5n + 20
Answer:
(m-5) (n-4)
Step-by-step explanation:
mn - 4m - 5n + 20
We will factor by grouping
mn -5n -4m +20
Factor an n out of the first 2 terms and a -4 out of the last 2 terms
n (m-5) -4(m-5)
Now factor out a m-5
(m-5) (n-4)
Which is TRUE about ALL expressions?
contain variables
contain only numbers
are the same as equations
do not include an equal sign
Expressions do not have an equal sign (although they can have operators such as plus or minus).
[tex]2x+1[/tex] is an expression.
[tex]2x+1=1[/tex] is an equation since it has an equal sign.
What intervals would you use to determine where
the function is positive and negative?
Answer:
B.
Step-by-step explanation:
The function is positive when it is above the x-axis
The following x values are where the function has positive y coordinates:
(-2,0)
(4,inf)
The function is negative when it is below the x-axis
The following x values are where the function has negative y coordinates:
(-inf,-2)
(0,4)
So you should see all of these intervals listed in choice B
Answer:
B
Step-by-step explanation:
URGENT! thanks!
Bonnie makes the frame of a cube out of 12 pieces of wire that are each six inches long. Meanwhile Roark uses 1-inch-long pieces of wire to make a collection of unit cube frames that are not connected to each other. The total volume of Roark's cubes is the same as the volume of Bonnie's cube. What is the ratio of the total length of Bonnie's wire to the total length of Roark's wire? Express your answer as a common fraction.
Answer:
1/36
Step-by-step explanation:
Bonnie uses 12×6" = 72" of wire to make her cube.
Roark uses 12×1" = 12" of wire to make each of his cubes. He must make 6³ = 216 cubes to match the volume of Bonnie's cube.
The ratio of wire lengths is then ...
72/(12×216) = 6/6³ = 1/6² = 1/36
Ryan is riding his bike. He biked a distance of 12 miles at a rate of 4 miles per hour. Rearrange the distance formula, d = rt, to solve for Ryan's time in minutes.
480 minutes
180 minutes
8 minutes
3 minutes
Answer:
180 minutes
Step-by-step explanation:
Starting with the distance formula ...
d = rt
dividing by the coefficient of t will give an equation for t:
t = d/r
Ryan's rate of 4 miles per hour can be expressed in minutes as 4 miles per 60 minutes. The Ryan's time is ...
t = (12 mi)/(4 mi/60 min) = 12·60/4 min = 180 min
Ryan's time is 180 minutes.
Answer:
180 MINUTES
Step-by-step explanation:
I TOOKTHE TEST ON FLVS
Please help!!
If θ is an angle in standard position whose terminal side passes through (3, 4), evaluate tan1/2θ
1/4
3/10
1/2
4/5
Answer:
1/2 is the answer (actually, it's ±1/2)
Step-by-step explanation:
The identity you need here is for a half angle of tangent. That identity is as follows:
[tex]tan(\frac{\theta }{2})=[/tex]±[tex]\sqrt{\frac{1-cos\theta }{1+cos\theta } }[/tex]
If we need the cos of that angle, we need to find the missing hypotenuse. Applying Pythagorean's Theorem to that right triangle, we get that the hypotenuse is 5. The cos of the angle is 3/5. Filling in the formula, using only the principle root since you have not allowed for the negative in the choices you gave:
[tex]tan(\frac{\theta }{2})=\sqrt{\frac{1-\frac{3}{5} }{1+\frac{3}{5} } }[/tex]
Turning each one of those 1's into 5/5 we combine the fractions to simplify to:
[tex]tan(\frac{\theta }{2})=\sqrt{\frac{\frac{2}{5} }{\frac{8}{5} } }[/tex]
Bringing up the lower fraction and flipping to multiply gives us:
[tex]tan(\frac{\theta }{2})=\sqrt{\frac{2}{5}*\frac{5}{8} }[/tex]
Canceling out the 5's and reducing the remaining fraction gives us
[tex]tan(\frac{\theta }{2})=\sqrt{\frac{1}{4} }[/tex]
and since the square root of 4 is 2, we end with a solution of 1/2
Find the area of the shaded sector. Round your answer to the nearest tenth. Use 3.14 for π.
A. 141.3 m2
B. 22.5 m2
C. 3.8 m2
D. 70.7 m2
Answer:
B
Step-by-step explanation:
The area of the shaded sector Rounded to the nearest tenth, is 22.5
How to find the area of a sector of a circle?Sector of a circle is like slice of a circular pizza. Its two straight edge's having an angle, and edge's length(the radius of the circle) are two needed factors for finding the area of that sector.
If the entire circle was shaded the radius sweeping out the circle would go through 360 degrees.
Too solve this problem is to multiply the entire area of the circle by (81/360)
Area of the sector = (81/360) x π x r^2
π = 3.14
r = cm
Area of the sector = (81/360) x 3.14 x 8.91^2
Area of the sector = 22.5
The area is 22.5 m2
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Miles rode his mountain bike over some trails in a state park. He biked a total of 5 1/2 miles. How many yards did miles bike? There are 1,760 yards in a mile.
9680 yards. Miles biked a total of 9680 yards.
The key to solve this problem is coverting the Mixed Fraction to Improper Fraction, and make the conversion from miles to yards.
Convert the Mixed Fraction 5 1/2 to an Improper Fraction:
- Multiply the whole number 5 by the denominator
5 x 2 = 10
- Add the result to the numerator
1 + 10 = 11
- Write the Improper Fraction with the same denominator of the Mixed Fraction, and the numerator with the result above
5 1/2 miles ----------> 11/2 miles
To convert miles to yard with mile = 1760 yards:
11/2 * 1760 yards = 19360 yards/2 = 9680 yards
Final answer:
Miles biked for a total of 5 1/2 miles. By converting miles to yards using the fact that there are 1,760 yards in one mile, Miles biked a total of 9,680 yards.
Explanation:
The student has asked how many yards Miles biked if he rode a total of 5 1/2 miles. To find the answer, we need to convert miles to yards. Since there are 1,760 yards in a mile, we can multiply the number of miles by this conversion factor.
First, let's represent 5 1/2 miles as an improper fraction: 5 1/2 = 11/2 miles. Next, we multiply 11/2 by 1,760:
11/2 miles
= 11/2
* 1760 yards/mile
= 11*880 yards
= 9,680 yards.
Therefore, Miles biked a total of 9,680 yards.
The factorization of x2 + 3x – 4 is modeled with algebra tiles. What are the factors of x2 + 3x – 4? A) (x + 4) and (x – 4) B) (x + 3) and (x – 4) C) ( x + 4) and (x – 1) D) (x + 3) and (x – 1)
Answer:
C: (x + 4)(x - 1)
Step-by-step explanation:
Please use " ^ " to indicate exponentiation. Thanks.
x2 + 3x – 4 → x^2 + 3x - 4 = (x + 4)(x - 1) This matches Answer C.
The length of a rectangle is units greater than its width. If the width is w, which expression gives the perimeter of the rectangle in terms of its width?
Answer: 2l+2w
Step-by-step explanation:
Answer:21 plus 2w
Step-by-step explanation:
Susan Williams purchased $80,000 of whole life. What will the cash value of her policy be at the following anniversary dates?
Anniversary date Cash Value
5 year _________
20 year _________
Answer:
5 year = $2,400
20 year = $18,560
Step-by-step explanation:
Firstly,
You have to identify the cash value per unit. so It 'll be 5 years = 30 dollars per unit.
Secondly,
Now, take the face value of the policy divided by 1000, to find how many units the person has. 80,000 divided by 1000 is 80. Now take the # of units time the cash value it has. so It'll be 80 times 30 is $2,400
Answer: $2,400
Now,
Just like the previous one identify the cash value per unit. so It'll be 20 years= 232 dollars per unit.
Next,
take the face value of the policy divided by 1000, to find how many units the person has. 80,000 divided by 1000 is 80. Now take the # of units time the cash value it has. 80 times 232 is $18,560
Answer: $18,560
What are the next three numbers in this pattern
Hello There!
Divide by 3 each time
so
#1 is 9, because 27/3 = 9
#2 is 3, because 9/3 = 3
#3 is 1, because 3/3 = 1
So your answer is 9, 3, 1
HELP ASAP PLEASE!!!!
Describe the transformations required to obtain the graph of the function f(x) from the graph of the function g(x). F(x)=-5.8sin x. G(x)=sin x. A: Vertical stretch by a factor of 5.8, reflection across y-axis. B: Vertical stretch by a factor of 5.8,reflection across x-axis. C: Horizontal stretch by a factor of 5.8, reflection across x-axis. D:Horizontal stretch by a factor of 5.8 reflection across y-axis.
Answer:
Vertical stretch by a factor of 5.8 , reflection across x-axis ⇒ answer B
Step-by-step explanation:
* Lets revise the vertical and horizontal stretch with reflection
- A vertical stretching is the stretching of the graph away from the
x-axis
- If k > 1, the graph of y = k•f(x) is the graph of f(x) vertically stretched
by multiplying each of its y-coordinates by k.
- If k should be negative, the vertical stretch is followed by a reflection
across the x-axis
- A horizontal stretching is the stretching of the graph away from
the y-axis
- If 0 < k < 1 (a fraction), the graph of y = f(k•x) is f(x) horizontally
stretched by dividing each of its x-coordinates by k.
- If k should be negative, the horizontal stretch or shrink is followed
by a reflection in the y-axis
* Lets solve the problem
∵ G(x) = sin x
∵ F(x) = -5.8 sin x
∴ F(x) = -5.8 G(x)
- From the rule above
∴ G(x) is stretched vertically by scale factor -5.8
∵ The scale factor is negative
∴ The vertical stretch is followed by a reflection across the x-axis
* The transformation is:
Vertical stretch by a factor of 5.8 , reflection across x-axis
To obtain the graph of f(x) = -5.8sin x from g(x) = sin x, a vertical stretch by a factor of 5.8 and a reflection across the x-axis are required.
Explanation:To transform the graph of the function g(x) = sin x into the graph of f(x) = -5.8sin x, two main transformations are required:
A vertical stretch by a factor of 5.8. This is due to the coefficient of the trigonometric function being 5.8, thereby stretching the graph vertically by 5.8 times its original height.A reflection across the x-axis. This is a result of the negative sign in front of the 5.8 which means that every point on the graph of g(x) is reflected over the x-axis, changing the sign of the corresponding y-coordinates on the graph of f(x).Option B (vertical stretch by a factor of 5.8 and reflection across the x-axis) correctly describes the required transformations to obtain the graph of f(x) from the graph of g(x).
What is the probability of drawing three black cards, one at a time with replacement, from a standard deck of 52 cards?
A.'3/52
Its not b
C.1/8
d.75/676
Answer: I think it is A.
Step-by-step explanation:
Which of the following transformations appears to be a dilation? HELP ASAP!
Answer:
The answer is the 2nd one
Step-by-step explanation:
A dilation is a transformation in which the lines connecting every point P with its image P' all intersect at a point C.
C is called the center of dilation, and CP'/CP is the same for every point P.
The only picture where the objects are similar and the image has not been rotated or reflected is
It is also seen from the picture that all the faces of the first figure appears to be parallel to all the faces of the second figure. Thus, CP'/CP is the same for every point P.
Therefore, the transformation in the picture above appears to be a dilation.
The transformation in the picture above appears to be a dilation is option 2nd.
How does dilation works?Dilation of a figure will leave its sides get scaled (multiplied) by same number. That number is called the scale factor of that dilation.
Its also called scaling of a figure, but due the involvement of coordinates, it involves a center of a dilation, which is like a pinned point which stays at same place after dilation.
Its like we enlarge or shorten the size of the figure (or keep it same, when scale factor = 1).
C is called the center of dilation, and CP'/CP is the same for every point P.
It is also seen from the picture that all the faces of the first figure appear to be parallel to all the faces of the second figure.
Thus, CP'/CP is the same for every point P.
Therefore, the transformation in the picture above appears to be a dilation is option 2nd.
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Use the Binomial Theorem and Pascal’s Triangle to write each binomial expansion.
(X +4)2
HELP IN NEED ASAP ):
Answer:
x² + 8x + 16
Step-by-step explanation:
You can draft the Pascal's Triangle as below;
Exponent
1-----------------------0
1 1 -------------------1
1 2 1 ------------------2
1 3 3 1 -----------------3
According to the question, we use values for exponent 2 because (a+b)²
Given (x+4)²...................................expand
x² × 4⁰ + x¹ × 4¹+ x⁰ × 4²
x² × 1 + x × 4 + 1 × 16
x² + 4x + 16---------------------------------introduce values in exponential 2 of the table which are 1 2 1
x² × 1 + 2 × 4x + 16 × 1
⇒ x² + 8x + 16
25 Points!!! This should be quick and easy for anyone who knows math well!
Answer:
Output = 8- input
Step-by-step explanation:
The first point is (1,7)
The input is 1 and the output is 7
The lines goes down, so we know that this is subtraction
Output = 8- input
7 = 8-1
Lets check another point
(5,3)
3 = 8-5
This checks
Use a calculator to find the values of the inverse trigonometric functions. Round to the nearest degree.
sin–1 (2/3) = °
tan–1(4) = °
cos–1(0.1) = °
Answer:
A. [tex]\text{sin}^{-1}(\frac{2}{3})\approx 42^{\circ}[/tex]
B. [tex]\text{tan}^{-1}(4)\approx 76^{\circ}[/tex]
C. [tex]\text{cos}^{-1}(0.1)\approx 84^{\circ}[/tex]
Step-by-step explanation:
We have been given inverse trigonometric functions. We are asked to find the value of each function.
A. [tex]\text{sin}^{-1}(\frac{2}{3})[/tex]
We will use inverse sin to solve our given equation as:
[tex]\text{sin}^{-1}(\frac{2}{3})=41.81^{\circ}[/tex]
Round to nearest degree:
[tex]\text{sin}^{-1}(\frac{2}{3})\approx 42^{\circ}[/tex]
B. [tex]\text{tan}^{-1}(4)[/tex]
We will use inverse tann to solve our given equation as:
[tex]\text{tan}^{-1}(4)=75.963756^{\circ}[/tex]
Round to nearest degree:
[tex]\text{tan}^{-1}(4)\approx 76^{\circ}[/tex]
C. [tex]\text{cos}^{-1}(0.1)[/tex]
We will use inverse cosine to solve our given equation as:
[tex]\text{cos}^{-1}(0.1)=84.2608295^{\circ}[/tex]
Round to nearest degree:
[tex]\text{cos}^{-1}(0.1)\approx 84^{\circ}[/tex]
To solve the problem we must know about the concept of trigonometry.
The value of [tex]\rm sin^{-1} (2/3), tan^{-1}(4), and\ cos^{-1}(0.1)[/tex] is 42, 76, and 85 degrees respectively.
What is trigonometry?Trigonometry deals with the relationship between the sides and angles of a right-angle triangle.
Given
[tex]\rm sin^{-1} (2/3), tan^{-1}(4), and\ cos^{-1}(0.1)[/tex] are the trigonometric function.
To find
The value of the [tex]\rm sin^{-1} (2/3), tan^{-1}(4), and\ cos^{-1}(0.1)[/tex].
How to get the value of the trigonometric function?[tex]\rm 1. \ \ sin^{-1} (2/3) = 41.81^o = 42^o\\\\ 2. \ \ \ \ \ tan^{-1}(4) = 75.96^o = 76^o \\\\3. \ \ cos{-1}(0.1)= 84.26^o = 85^o[/tex]
The value of [tex]\rm sin^{-1} (2/3), tan^{-1}(4), and\ cos^{-1}(0.1)[/tex] is 42, 76, and 85 degrees respectively.
More about the trigonometry link is given below.
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New help with this question
Answer:
8
Step-by-step explanation:
Answer:
8
Step-by-step explanation:
What are the possible numbers of positive, negative, and complex zeros of f(x) = −3x4 −
5x3 − x2 − 8x + 4?
Select one:
a. Positive: 2 or 0; negative: 2 or 0; complex: 4 or 2 or 0
b. Positive: 1; negative: 3 or 1; complex: 2 or 0
c. Positive: 3 or 1; negative: 1; complex: 2 or 0
d. Positive: 4 or 2 or 0; negative: 2 or 0; complex: 4 or 2 or 0
Answer:
b.
Step-by-step explanation:
We have to look at sign changes in f(x) to determine the possible positive real roots.
[tex]f(x)=-3x^4-5x^3-x^2-8x+4[/tex]
There is only one sign change here, between the -8x and the +4. So that means there is only 1 possible real positive root.
Now we have to look at sign changes in f(-x) to determine the possible negative real roots.
[tex]f(-x)=-3x^4+5x^3-x^2+8x+4[/tex]
There are 3 sign changes here. That means there are either 3 negative roots or 3-2 = 1 negative root. So we have:
1 positive
3 or 1 negative
We need to pair them up now with all the possible combinations.
If we have 1 positive and 1 negative, we have to have 2 imaginary
If we have 1 positive and 3 negative, we have to have 0 imaginary
Keep in mind that the total number or roots--positive, negative, imaginary--have to add up to equal the degree of the polynomial. This is a 4th degree polynomial, so we will have 4 roots.
If (x, y) is a solution to the system of equations above, then what is the value of x - y?
A. 1/4
B. 1
C. 3
D. 18
1. The first step to solving this problem is to find the values of x and y. This can be done in a multitude of different ways, however I will go with the method of substitution.
Thus, the first thing we must do is write out both equations and rearrange one of them so that either x or y is the subject of the equation. Looking at the two equations, I can see that in the second equation this would be easier, and that we could also simplify the first equation a little further. Thus:
a) Collecting like terms to simplify equation 1:
4x + 3y = 14 - y
4x + 4y = 14 (Add y to both sides)
b) Rearranging equation 2 to make x the subject:
x - 5y = 2
x = 2 + 5y (Add 5y to both sides)
Now, we can substitute x = 2 + 5y into the first equation:
4x + 4y = 14
if x = 2 + 5y:
4(2 + 5y) + 4y = 14
8 + 20y + 4y = 14 (Expand 4(2 + 5y))
8 + 24y = 14 (Add 20y and 4y)
24y = 6 (Subtract 8 from both sides)
y = 1/4 (Divide both sides by 24)
Now that we know that y = 1/4, we can substitute this back into x = 2 + 5y:
x = 2 + 5y
if y = 1/4: x = 2 + 5(1/4)
x = 2 + 5/4
x = 13/4
2. So now we know that x = 13/4 and y = 1/4. Given these values, we can now solve x - y as such:
x - y = 13/4 - 1/4
= 12/4
= 3
Thus, the value of x - y is 3 (answer C).