Alonso has $460 to spend at a bicyclestore for some new gear and bikingoutfits. Assume all prices listed includetax.• He buys a new bicycle for $270.71.•He buys 4 bicycle reflectors for $3.09each and a pair of bike gloves for$33.71.• He plans to spend some or all of themoney he has left to buy new bikingoutfits for $68.20 each.Write and solve an inequality which canbe used to determine x, the number ofoutfits Alonso can purchase while stayingwithin his budget.>Inequality:XîVIAI>
Answers
Solution:
[tex]\begin{gathered} 68.20x+307.51\leq460 \\ x\leq2.236 \end{gathered}[/tex]
Analysis:
We have a budget of $ 460. In the first step, we need to calculate the total amount of money spent on a bicycle, reflectors, and bike gloves.
[tex]Total\text{ }amount\text{ }spent=270.71+(4\ast3.09)+33.71=316.78[/tex]When we calculate the amount spent, we can write the inequation:
[tex]68.20x+316.78\leq460[/tex]X would be the number of outfits and adding to 316.78, it has to be less or equal to 460.
Now, let's
Related Questions
Write the trigonometric form of the complex number. (Round your angles to two decimal places. Let 0 ≤ < 2.)
Answers
Given a complex number z:
[tex]z=a+bi[/tex]We can write this number in trigonometric form, using:
[tex]\begin{gathered} z=r(\cos\theta+i\sin\theta) \\ . \\ a=r\cos\theta \\ . \\ b=r\sin\theta \\ . \\ r=\sqrt{a^2+b^2} \end{gathered}[/tex]In this case, we are given:
[tex]z=-8+2i[/tex]We need to find r and θ. We know:
· a = -8
· b = 2
Thus:
[tex]r=\sqrt{(-8)^2+2^2}=\sqrt{64+4}=\sqrt{68}=2\sqrt{17}[/tex]And now, we can find θ:
[tex]-8=2\sqrt{17}\cos\theta[/tex]And solve:
[tex]\begin{gathered} \cos\theta=-\frac{8}{2\sqrt{17}} \\ . \\ \theta=\cos^{-1}(-\frac{4\sqrt{17}}{17})\approx2.89661 \end{gathered}[/tex]Now we can write the number in trigonometric form:
[tex]z=2\sqrt{17}(\cos(2.9)+i\sin(2.9))[/tex]You are a game manufacturer. You and your team are trying to find the best pair of dice for a new board game you have made. You are examining the possible results of using one 12-sided die and one 12-sided die and rolling them together. If the random variable is defined as the sum of the two dice when rolled, what are the random variables?
Answers
As per given by the question,
There are given that, two 12-sided die and rolling together.
Now,
If there are two 12-sided die, and rolling together,
Then the total oucomes of the both die is,
[tex]12\times12=144[/tex]Now,
15 POINTS PLEASE ANWSER ASAP
Answers
Answer:
Congruent
Step-by-step explanation:
Angle 3 and angle 7 are congruent because of congruent angles. But more specifically they are both corresponding.
Question 10 of 10It's possible to build a triangle with side lengths of 5, 5, and 10.A. TrueB.False
Answers
Triangle iequality: The sum of any two sides of a triangle is greater than or equal to the third side.
Use the theorem above to find if the given lengths can form a triangle:
[tex]\begin{gathered} 5+5\ge10 \\ 10\ge10 \\ \\ 5+10\ge5 \\ 15\ge5 \\ \\ 10+5\ge5 \\ 15\ge5 \end{gathered}[/tex]As you get true inequalities above, the sum of any two sides of the given triangle are greater than or equal to the third side. Given lengths form a triangle
Answer: TrueDebbie has already taken 2 pages of notes on her own, and she will take 1 page during each hour of class. In all, how many hours will Debbie have to spend in class before she will have a total of 16 pages of notes in her notebook?
Answers
Based on the given information, we can define the following expression
[tex]y=2+1x[/tex]Where x represents hours and y represents pages.
For 16 pages, we have
[tex]\begin{gathered} 16=2+x \\ 16-2=x \\ x=14 \end{gathered}[/tex]Debbie will have to spend 14 hours to have 16 pages of notes.A rectangle is 1.2 in wide and 6.1 in tall.If it is enlarged to a width of 7.2 in, thenhow tall will it be?
Answers
Answer:
The rectangle is 36.6 in tall;
[tex]l_2=36.6\text{ in}[/tex]Explanation:
Given that a rectangle is 1.2 in wide and 6.1 in tall.
[tex]\begin{gathered} w_1=1.2\text{ in} \\ l_1=6.1\text{ in} \end{gathered}[/tex]If it was then enlarged to a width of 7.2 in, then the length l would be;
[tex]w_2=7.2[/tex]Since they would be similar shapes, then we can write;
[tex]\begin{gathered} \frac{w_2}{w_1}=\frac{l_2}{l_1} \\ l_2=\frac{l_1\times w_2}{w_1} \\ \text{substituting the given values;} \\ l_2=\frac{6.1\times7.2}{1.2} \\ l_2=36.6\text{ in} \end{gathered}[/tex]Therefore, the rectangle is 36.6 in tall;
[tex]l_2=36.6\text{ in}[/tex]
HURRY!! select ALL the correct answers
Which operations involving complex numbers have solutions represented by point A on the graph?
Answers
We have to find the solutions represented by point A on graph.
point A is represented (1 , 5i)
1. (1 - 4i) - (2 + i)
= 1 - 4i - 2 - i
= -1 - 5i
This option is not correct because it does not as same point as A.
2. -1(1 - 4i) + (2 + i)
= -1 + 4i + 2 + i
= 1 + 5i
This solution is same as point A so this option is correct.
3. (-1 + 4i) - (2 + i)
= -1 + 4i - 2 - i
= -3 + 3i
This option is not correct because it does not as same point as A.
4. (-1 + 4i) + (2 + i)
= -1 + 4i + 2 + i
= 1 + 5i
This solution is same as point A so this option is correct.
Therefore options 2 and 4 are correct.
Learn more about the solutions and graph here:
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one of the triangles you cut out is shown below. List the angles of ABC in order from smallest to largest
Answers
The angles of ABC from smallest to largest: 52.83°, 57.53°, 69.64°
Explanation:Given:
AC = 18in, AB = 20 in, BC = 17 in
To find:
the angles of ABC from smallest to largest
To determine the angles, we will apply cosine rules:
[tex]a^2\text{ = b}^2\text{ + c}^2\text{ - 2bcCosA}[/tex][tex]\begin{gathered} c\text{ = side opposite angle C}=\text{ AB} \\ c\text{ = 20} \\ b\text{ = side opposite angle B = AC} \\ b\text{ = 18} \\ a\text{ = side oppsite angle A = BC} \\ a\text{ = 17} \end{gathered}[/tex][tex]\begin{gathered} 17^2\text{ = 18}^2\text{ + 20}^2-\text{ 2\lparen18\rparen\lparen20\rparen cos A} \\ \\ 289\text{ = 724 -720cosA} \\ \\ -435\text{ = -720cosA} \\ \\ cosA\text{ = }\frac{-435}{-720}\text{ = 0.6042} \\ \\ A\text{ = cos}^{-1}(0.6042) \\ \\ A=\text{ 52.83\degree} \end{gathered}[/tex][tex]\begin{gathered} To\text{ get B, we will use the formula:} \\ b^2\text{ = a}^2\text{ + c}^2\text{ - 2acCosB} \\ \\ 18^2\text{ = 17}^2\text{ + 20}^2\text{ - 2\lparen17\rparen\lparen20\rparen cosB} \\ \\ 324\text{ = 689 -680cosB} \\ \\ -365\text{ = -680cosB} \\ \\ cosB\text{ = }\frac{-365}{-680}=\text{ 0.5368} \\ \\ B\text{ = cos}^{-1}(0.5368) \\ \\ B=\text{ 57.53\degree} \end{gathered}[/tex][tex]\begin{gathered} To\text{ get C, wewill apply sum of angles in a triangle:} \\ A+\text{ B}+\text{ C}=\text{ 180\degree} \\ \\ 52.83°\text{ + 57.53\degree +}C=\text{ 180} \\ \\ 110.36\text{ + C = 180} \\ \\ C\text{ = 180 - 110.36} \\ \\ C=\text{ 69.64\degree} \end{gathered}[/tex]The angles of ABC from smallest to largest: 52.83°, 57.53°, 69.64°
Question 3 of 10 * - 3 is a factor of P(x) =*? – 73? + 158-9 O A. True O B. False
Answers
Given,
The expression is,
[tex]P(x)=x^3-7x^2+15x-9[/tex]If x- 3 is the factor of the given polynomial function, then on substituting the value of x = 3 in the polynomial function, it become zero.
Thus subsituting the value of x in the polynomial,
[tex]\begin{gathered} P(3)=3^3-7\times3^2+15\times3-9 \\ =27-7\times9+45-9 \\ =27+45-63-9 \\ =72-72 \\ =0 \end{gathered}[/tex]Here, the obtained value of polynomial is 0.
Hence, x-3 is a factor of the given polynomial.
Thus, option A(true) is correct.
If the frequency of a sine function is 2, what is the period?
Answers
A sine function in the form:
[tex]y=A\sin(B(x+C))+D[/tex]has its period equal to 2/B, and its frequency equal to the reciprocal of that.
Simply put, the period and the frequency are reciprocals of each other.
So, it the frequency is equal to 2, then the period is equal to 1/2.
Write 3 and 2 fifths as an improper fraction and as a mixed number. b. 16 : a. C. 13 d. 17.2 Please select the best answer from the choices provided|| A B С D
Answers
Given the fraction 3 and 2 fifths,
[tex]2\text{fifths}=\frac{2}{5}[/tex]Converting 3 and 2/5 to mixed fraction,
Mixed fraction is the combination of a whole number and a proper fractiion.
A proper fraction is the fraction with the numerator smaller than the denominator.
Therefore,
[tex]\begin{gathered} 3\text{ and}\frac{\text{ 2}}{5}\text{ to mixed fraction will be,} \\ 3+\frac{2}{5}=3\frac{2}{5} \end{gathered}[/tex]Hence, 3 and 2/5 to mixed fraction is,
[tex]=3\frac{2}{5}[/tex]Let us now convert 3 2/5 to improper fraction,
[tex]\begin{gathered} 3\frac{2}{5}=\frac{(3\times5)+2}{5} \\ =\frac{15+2}{5}=\frac{17}{5} \end{gathered}[/tex]Hence, 3 2/5 to improper fraction is 17/5.
Option D is correct answer.
Suppose f(x) = x2. What is the graph of g(x) = f(2x)?10ухO A. *10n.B.1010уXO c.
Answers
The given information is:
f(x)=x^2
We need to find the graph of g(x)=f(2x).
We can make a table of values to find the graph of g(x).
As g(x)=f(2x) it means we need to replace the argument x in f(x) by 2x, so:
[tex]\begin{gathered} g(x)=f(2x) \\ g(x)=(2x)^2 \\ g(x)=4x^2 \end{gathered}[/tex]If x=0, so:
[tex]g(0)=4*0^2=4*0=0[/tex]If x=1:
[tex]g(1)=4*1^2=4*1=4[/tex]If x=-1:
[tex]g(-1)=4*(-1)^2=4*1=4[/tex]It means the function opens upward, and has its vertex at (0,0).
In the given graph, we can observe the x-axis and y-axis are divided every 2 units, then the first division at the right of the origin is equal to x=2. And the second division over the origin is equal to y=4.
Thus, we can observe in the second graph, that at x=1, the function takes the value y=4, and at x=-1, y=4 too, and the vertex of the graph is located at (0,0).
The answer is then option B.
A cylinder popcorn tin had lid with a circumference of approximately 25.12 inches which expression can be used to describe the relationship between circumference and the diameter of the popcorn tin lid.
Answers
Answer:
The last choice: 25. 12 / pi
Explanation:
The relationship b
how do you analyze functionsf(x)=7e to exponent .5xg(x) 3x squared +7x-4if you can explain ysing different numbers that works also
Answers
The general formula for an exponential function is f(x) = ae^rt while the general form of a quadratic equation is f(x) = ax^2 + bx + c
Thus,
f(x) = 7e^0.5x is an exponential function and
g(x) = 3x^2 + 7x - 4 is a quadratic function
Let us substitute values of x into each function and compare the growth rates
For x = 1,
f(1) = 7e^0.5 = 11.4
g(1) = 3(1)^2 + 7(1) - 4 = 3 + 7 - 4 = 6
For x = 2,
f(1) = 7e^2(0.5) = 19
g(1) = 3(2)^2 + 7(2) - 4 = 12 + 14 - 4 = 22
For x = 3,
f(3) = 7e^3(0.5) = 31
g(1) = 3(3)^2 + 7(3) - 4 = 27 + 21 - 4 = 44
We can see that g(x) is increasing at a faster rate than f(x).
4(1.8h-2) I need help please.
Answers
To simplify the expression, you need to apply the distributive property as shown above
the points (-9,-9)and (-6,a)fall on a line with a slope of 6.what is the value of a
Answers
Answer:
a=9
Explanation:
Given that the slope of the points below is 6:
• (x1,y1) = (-9,-9)
,• (x2,y2) = (-6,a)
Substitute the points into the slope formula below:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]This gives:
[tex]\begin{gathered} 6=\frac{a-(-9)}{-6-(-9)} \\ 6=\frac{a+9}{-6+9} \\ 6=\frac{a+9}{3} \\ \text{Cross multiply} \\ a+9=6\times3 \\ a+9=18 \\ a=18-9 \\ a=9 \end{gathered}[/tex]The value of a is 9.
Aubrey has 25 bracelets. She wants to divide among her 4 friends. What is the rounded number of bracelets Aubrey should give them?
Answers
ANSWER
6
EXPLANATION
Aubrey has 25 bracelets.
To divide it among her 4 friends, she has to divide the number of bracelets she has by 4.
That is:
[tex]\frac{25}{4}\text{ = 6.25}[/tex]Because number of bracelets can only be a whole number, we have to look for the whole number that is closest to 6.25 and lower than it.
To do that, we round down:
[tex]6.25\text{ }\cong6[/tex]So, the rounded number of bracelets that Aubrey should give them is 6.
consider the following system of equations mad up of line 1 and 2. which of the following statements are ture
Answers
the options that apply are:
option #1. because 0+5*2=10
option #2. Because -2*-5-2*3=4 and -5+5*3=10
Option#4 because -2*-10-2*8=4
Find the inverse function of g(x) = 1 /x − 2
Answers
we have teh function
[tex]g(x)=\frac{1}{x}-2[/tex]step 1
Let
y=g(x)
[tex]y=\frac{1}{x}-2[/tex]step 2
Exchange the variables
x for y and y for x
[tex]x=\frac{1}{y}-2[/tex]step 3
Isolate the variable y
[tex]\begin{gathered} \frac{1}{y}=x+2 \\ y=\frac{1}{(x+2)} \end{gathered}[/tex]step 4
[tex]g^{(-1)}(x)=\frac{1}{x+2}[/tex]Find the mean, median, mode, and range of this data: 47, 56, 57, 63, 89, 44, 56. If the answer is not a whole number, round to the nearest tenth.
Answers
The data given are 47, 56, 57, 63, 89, 44, 56
To calculate the mean:
The mean of the data can be defined as
[tex]undefined[/tex]Find the equation of the line that has a y-intercept of 1 and is perpendicular to the graph of the line 2x + y = 4.y = -2x + 1y = 2 + 1y = -x + 1y=x+1
Answers
We have the equation
2x+y = 4
We need to find the slope so we rewrite the equation in slope intercept form y = mx+b where m is the slope and b is the y intercept
2x+y-2x = -2x+4
y = -2x +4
The slope is -2
Perpendicular lines have slopes that multiply to -1
-2 * m = -1
m = 1/2
The slope of a line that is perpendicular is 1/2
Using slope intercept form
y = mx+b and a slope of 1/2 and the y intercept of 1
y = 1/2x + 1
Find the area a of the sector of a circle radius 50 centimeters formed by central angle1/10 radian
Answers
Given:
Radius of the circle = 50 cm
Central angle = 1/10 rad
Let's find the area of the sector.
To find the area of the sector, apply the formula:
[tex]Area=\frac{1}{2}\times r^2\theta[/tex]Where:
r is the radius = 50 cm
θ is the central angle in radians = 1/10 radian
Hence, we have:
[tex]\begin{gathered} \text{Area}=\frac{1}{2}\times50^2\times\frac{1}{10} \\ \\ \text{Area}=\frac{1}{2}\times2500\times\frac{1}{10} \\ \end{gathered}[/tex]Solving further:
[tex]Area=\frac{1\times2500\times1}{2\times10}=\frac{2500}{20}=125\operatorname{cm}^2[/tex]Therefore, the area of the sector of the circle is 125 square centimeters.
ANSWER:
125 cm²
A map of a park is shown below. What is the distance between the cave entrance and the canoe rentals on the map? у 5 Cave Entrance 3 Canoe Rentals 2 1 -5 -4 -3 2 1 2 3 4 5 -2 Campsite -3 4 -5
Answers
1 If (a +3,5 - 1) = (-2 , 4) , then a + b
Answers
Given the following information:
[tex](a+3,b-1)=(-2,4)[/tex]We can find a and b as follows:
[tex]\begin{gathered} a+3=-2 \\ _{\text{ }}solve_{\text{ }}for_{\text{ }}a\colon \\ a+3-3=-2-3 \\ a=-5 \\ ------- \\ b-1=4 \\ _{\text{ }}solve_{\text{ }}for_{\text{ }}b\colon \\ b-1+1=4+1 \\ b=5 \end{gathered}[/tex]Now we know the values of a and b, we can find a+b:
[tex]a+b=-5+5=0[/tex]Answer:
(a) 0
A single die is rolled. Find the probability of rolling an oddnumber or a number less than 6.
Answers
Given
A single die is rolled.
To find the probability of rolling an odd number or a number less than 6.
Explanation:
It is given that,
A single die is rolled.
Then, the sample space is,
[tex]\begin{gathered} S=\lbrace1,2,3,4,5,6\rbrace \\ n(S)=6 \end{gathered}[/tex]Let A be the event of getting an odd number.
Then,
[tex]\begin{gathered} A=\lbrace1,3,5\rbrace \\ n(A)=3 \end{gathered}[/tex]Let B be the event of getting a number less than 6.
Then,
[tex]\begin{gathered} B=\lbrace1,2,3,4,5\rbrace \\ n(B)=5 \end{gathered}[/tex]Also,
[tex]\begin{gathered} A\cap B=\lbrace1,3,5\rbrace \\ n(A\cap B)=3 \end{gathered}[/tex]Therefore,
[tex]\begin{gathered} P(A\cup B)=P(A)+P(B)-P(A\cap B) \\ =\frac{n(A)}{n(S)}+\frac{n(B)}{n(S)}-\frac{n(A\cap B)}{n(S)} \\ =\frac{3}{6}+\frac{5}{6}-\frac{3}{6} \\ =\frac{3+5-3}{6} \\ =\frac{5}{6} \end{gathered}[/tex]Hence, the answer is 5/6.
The probability of rolling an odd number or a number that is less than 6 is 5/12
Probability is the likelihood of the occurrence of an event and is the ratio of the number of favorable outcomes to the total number of outcomes of an event.
The sample space or possible outcomes when rolling a die is S = {1, 2, 3, 4, 5, 6}
We can say, n(S) = 6
Consider X as an event of getting an odd number
X = {1, 3, 5}
n (X) = 3
So P (X) = n(X)/ n(S)
By substituting the values,
P(X) = 3/6 = 1/2
Consider Y as an event of getting a number less than 6
Y = {1, 2, 3, 4, 5}
n (Y) = 5
So P (Y) = n(Y)/ n(S)
Substituting the values
P(Y) = 5/6
The probability of rolling an odd number or a number less than 6 = 1/2 × 5/6 = 5/12
Hence, the probability of rolling an odd number or a number less than 6 is 5/12.
Learn more about the probability of dice:
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Segment the resultat reflecting acrostine Select all of the correct statements about the unchanged properties of segment AB and segment A'B! Band 8 have the same coordinates Segment AB and Segment AB' have the same lengths
Answers
Take into account that when a line or a segment is reflected across a reference axis or line, the length of the line or segment remains the same.
Furthermore, only points on the reference axis or life of reflection have the same coordinates after the reflection (then, the image of point B, which is B' has different coordinates).
Hence, the only valid statement about the segment A'B' is:
Segment AB and segment A'B' have the same length
16.) A. Given a parallelogram with angles a, B, C, and D, as in figure 10.90, describe how angle A is related to the other three angles. Your answer should be general and that it would hold for every parallelogram not just the particular parallelogram shown in the figure. B. use the definition of parallelogram and the parallel postulate to explain why the relationships you found in part a hold.
Answers
We need to write the Parallel Postulate and the definition for parallelogram:
• A parallelogram is a quadrilateral with two pairs of parallel sides.
• If two lines are cut by a transversal and the corresponding angles are equal, then the lines are parallel.
How are the angles related to each other?
We have corresponding angles with the same color (and also vertical angles). From the definition for parallelogram both sides are parallel. And from it, we can say, using the postulate, we have that the corresponding angles are equals (because lines are parallel).
Then angle blue and red are supplementary (they sum 180), and the angles yellow and green are supplementary too (they also sum 180).
We can also say that:
[tex]\measuredangle a\cong\measuredangle c\text{ }[/tex][tex]\measuredangle b\cong\measuredangle d[/tex][tex]m\measuredangle a+m\measuredangle b=180,m\measuredangle c+m\measuredangle d=180[/tex]Additionally, in this way, we can say that the inner angles in a parallelogram sum 360.
Which side lengths represent the side of a right triangle
Answers
ANSWER
B) 7, 24, 25
EXPLANATION
The sides of a right triangle always satisfy the Pythagorean Theorem,
[tex]c^2=a^2+b^2[/tex]Where a and b are the legs, and c is the hypotenuse - which is the longest side.
Thus, to answer this question, we have to see for what set of lengths the sum of the squares of the shortest ones is equal to the square of the longest one.
• For 2, 3, 5,
[tex]\begin{gathered} 5^2=2^2+3^2 \\ 25=4+9 \\ 25=13\rightarrow FALSE \end{gathered}[/tex]So, this set does not represent a right triangle.
• For 7, 24, 25,
[tex]\begin{gathered} 25^2=7^2+24^2 \\ 625=49+576 \\ 625=625\rightarrow TRUE \end{gathered}[/tex]So, this set does represent a right triangle.
• For 7, 23, 25,
[tex]\begin{gathered} 25^2=7^2+23^2 \\ 625=578\rightarrow FALSE \end{gathered}[/tex]This set does not represent a right triangle.
• For 12, 16, 21,
[tex]\begin{gathered} 21^2=12^2+16^2 \\ 441=400\rightarrow FALSE \end{gathered}[/tex]This set does not represent a right triangle.
Hence, the side lengths that represent the lengths of the sides of a right triangle are 7, 24, 25.
Plot the points and determine the slope of the line containing them. Graph the line.
Answers
We were given the following details:
[tex]\begin{gathered} (x_1,y_1)=(-2,-4) \\ (x_2,y_2)=(7,-4) \end{gathered}[/tex]We will proceed to graph these points, we have:
The slope is given by:
[tex]\begin{gathered} slope(m)=\frac{\Delta y}{\Delta x}=\frac{y_2-y_1}{x_2-x_1} \\ slope(m)=\frac{-4-(-4)}{7-(-2)} \\ slope(m)=\frac{0}{9}=0 \\ slope(m)=0 \\ \\ \therefore slope(m)=0 \end{gathered}[/tex]Hence, the slope (m) = 0
The diagram shows two parallel lines A & B cut by a transversal line .what is the value of x
Answers
Vontae, this is the solution:
Angle that measures 52 degrees is congruent to the third angle adjacent to angle X.
Therefore,
X = 180 - 52 -48
X = 180 - 100
X = 80
The correct answer is 80 degrees