Jim began a 156 mile bike trip to build up stamina . Unfortunately his bike chain broke so he finished walking. Th whole trip took 6 hours. If Jim walks at a rate of 5 miles per hour and rides at 33 miles per hour find the amount he spent on the bike.
Answers
This diagram represents the problem
We know that distance = speed*time; D=S*t
Total distance: 156 miles
time: 6 h
Speed1: 33 miles/h
Speed2: 5 miles/h
for interval 1:
[tex]\begin{gathered} D_1=S_1\cdot t_1 \\ D_1=33\cdot t_1 \end{gathered}[/tex]for interval 2:
[tex]\begin{gathered} D_2=S_2\cdot t_2 \\ D_2_{}=5\cdot t_2 \end{gathered}[/tex]for the whole trip: -Eq 1. Distance
[tex]\begin{gathered} D=D_1+D_2 \\ D=33\cdot t_1+5\cdot t_2 \\ 156=33\cdot t_1+5\cdot t_2 \end{gathered}[/tex]and also: -Eq 2. Time
[tex]\begin{gathered} t=t_1+t_2 \\ 6=t_1+t_2 \end{gathered}[/tex]Now we have a system of 2 equations with 2 unknowns.
Let's solve it!
[tex]\begin{gathered} 156=33t_1+5t_2 \\ t_1=\frac{156-53t_2}{33} \\ \frac{156-5t_2}{33}+t_2=6 \\ t_2=\frac{3}{2} \\ t_1=\frac{156-5\cdot\frac{3}{2}}{33} \\ t_1=\frac{9}{2} \end{gathered}[/tex]We can see that he spent 4.5 hours riding the bike and 1.5 h walking
Related Questions
O GRAPHS AND FUNCTIONSFinding inputs and outputs of a two-step function that models a...
Answers
Given the function:
[tex]A(t)=256-16t[/tex]Where A is the amount of money (in dollars) Diane has left in her account after t trips on the toll roads.
(a)
After 8 trips on the toll roads (t = 8):
[tex]\begin{gathered} A(8)=256-16(8)=256-128 \\ \\ \therefore A(8)=\$128 \end{gathered}[/tex](b)
If her account is empty:
[tex]\begin{gathered} A(t)=0 \\ \\ \Rightarrow256-16t=0 \end{gathered}[/tex]Solving the equation for t:
[tex]\begin{gathered} 256=16t \\ \\ \therefore t=16\text{ trips} \end{gathered}[/tex]7. Flora has a square fountain. It is a square fountain and she wants to place a walkway around it. The square fountain measures 4 meters on each side. The walkway will be one meter wide around the fountain.. a. Find the area of the walkway. b. One bag of colored stones covers 1 square meter, how many bags of stones will be needed to cover the entire walkway around the fountain? C. A bag of colored stones cost $24.99. How much will it cost to fill in he walkway with colored stones?
Answers
Answer:
[tex]\begin{gathered} a)20m^2 \\ b)\text{ 20 bags of colored stones} \\ c)\text{ \$499.8} \end{gathered}[/tex]Step-by-step explanation:
Since the square fountain measures 4 meters on each side and the walkway will be one meter wide, let's make a diagram to see the situation:
Then, to calculate the area of the walkway (green shaded region)
[tex]\begin{gathered} A_{total}=b\cdot h \\ A_{total}=6\cdot6=36m^2 \\ A_{founta\in}=4\cdot4=16m^2 \end{gathered}[/tex][tex]\begin{gathered} A_{walkway}=A_{total}-A_{fountain} \\ A_{walkway}=36-16=20m^2 \end{gathered}[/tex]Now, how many colored stones will be needed if one bag covers 1 square meter:
There are 20 square meters on the walkway, then will be needed 20 bags of colored stones.
A bag of colored stones costs $24.99, then multiply 20 by $24.99:
[tex]20\cdot24.99=\text{ \$499.8}[/tex]Find the value of 4v-8 given that 11v-8 = 3.Simplify your answer as much as possible.
Answers
Given that 11v - 8 = 3
add 8 to both sides
11v = 3 + 8
11v = 11
Divide both sides by 11
v = 1
to simplify 4v - 8
= 4 (1) - 8
= 4 - 8
= -4
-4
Explanation
Suppose that the balance of a person’s bank account in US is normally distributed with mean $580 and standard deviation $125. Find the amount of money which would guarantee a person has more money in their account than 80% of US residents.I want an answer and explanation.
Answers
Answer:
[tex]\text{ \$685.25}[/tex]Explanation:
Here, we want to get the amount of money that would guarantee that a person has more money than 80%
That means the probability is greater than 80% or 0.8
Thus, we need to get the z-score that corresponds to this probability
Using a z-score table, we can get this as follows:
[tex]P(x\text{ }>\text{z\rparen= 0.842}[/tex]We will now get the value from the obtained z-score
Mathematically:
[tex]\begin{gathered} z\text{ = }\frac{x-\mu}{\sigma} \\ \\ \text{ x is the value we want to calculate} \\ \mu\text{ is the mean} \\ \sigma\text{ is the standard deviation} \end{gathered}[/tex]Substituting the values, we have it that:
[tex]\begin{gathered} 0.842\text{ = }\frac{x-580}{125} \\ \\ \text{ x = 580 + 125\lparen0.842\rparen} \\ x\text{ = \$685.25} \end{gathered}[/tex]Hello,May I please request for help on the word problem number 37, please?
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As the last stand-up comic of the evening is granted. The combination of schedules is made with the other 5 performers.
To find how many ways you can order 5 performers you multiply 5x4x3x2x1 (or factorial 5: 5!)
[tex]5!=5\times4\times3\times2\times1=120[/tex]Then, there are 120 different ways to schedule the appearancesOn a recent survey, students were asked if they ice skate, snowboard, or ski. The Venn diagram below shows the results of the survey
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The number of students who took the survey was 47 (option B).
How to identify the number of students who took the survey?To identify the number of students who took the survey, we must look at the number of students in each of the Venn diagram spaces. In this case, the number of students who practice each sport are:
Ice Skate: 7 students.Snowboarding: 10 students.Ski: 13 students.Ice Skate and Snowboard: 4 students.Ski and Snowboard: 8 students.Ice Skate and Ski: 2 students.Ice Skate, Snowboard and Ski: 3 students.To know the number of students who took the survey, we must add the number of students in each space as shown below:
7 + 10 + 13 + 4 + 8 + 2 + 3 = 47According to the above, the correct answer is option B, since 47 students took the survey.
Note: This question is incomplete because there is some information missing. Here is the complete information:
Question:
How many students took the survey?
Options
A.32
b.47
c.53
D.56
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Problem solving.When two expressions are not equivalent, you can use an inequality symbol to show their relationship. Do you ever use an inequality symbol when two expressions are equivalent? Use an example in your explanation.
Answers
Explanation
When two expressions are not equivalent, you can use an inequality symbol
[tex]\begin{gathered} \leq\Rightarrow less\text{ or equal } \\ \ge\Rightarrow greater\text{ or equal } \\ >\Rightarrow greater\text{ than } \\ <\Rightarrow smaller\text{ than} \end{gathered}[/tex]
now, when comparing two expressions that are equivalent , WE CAN NOT USE an inequality simbol, instead of we need to use The equals sign or equal sign formerly known as the equality sign
[tex]=[/tex]for example
[tex]3x+19x=30x-8x[/tex]the = symbold indicates that both sides have the same value ( rigth and left)
I hope this helps you
Help I need a example for graphing two variable inequalities
Answers
Solution:
To graph, a linear inequality in two variables (say, x and y ), first get y alone on one side. Then consider the related equation obtained by changing the inequality sign to an equals sign. The graph of this equation is a line.
If the inequality is strict ( < or > ), graph a dashed line. If the inequality is not strict ( ≤ and ≥ ), graph a solid line.
For example,
Consider the linear inequality in two variables below
[tex]y\leq4x-8[/tex]Step 1:
Put x=0 and find y
[tex]\begin{gathered} y=4x-8 \\ y=4(0)-8 \\ y=0-8 \\ y=-8 \\ (0,-8) \end{gathered}[/tex]Step 2:
Put y=0 and find x
[tex]\begin{gathered} y=4x-8 \\ 0=4x-8 \\ 4x=8 \\ \frac{4x}{4}=\frac{8}{4} \\ x=2 \\ (2,0) \end{gathered}[/tex]Hence,
We are going to use the coordinates below to graph the inequality using a solid line because
The inequality sign used is greater than or equal to
[tex](0,-8),(2,0)[/tex]Hence,
The graph of the inequality will be
need help asap look in file attached
Answers
Answer:
length: 21 cm
width: 16 cm
Step-by-step explanation:
. A rectangle has two lengths and two widths, or two sides that are vertical (up and down) and two sides that are horizontal (left and right)
. In order to find the perimeter we must add up all four side lengths.
. You can find the perimeter of a rectangle by adding the length and the width then multiplying by 2, because there are two of each side length.
P = 2(l+w)
In the question the perimeter is given, which is 74.
We can divide 74 by 2 so that we can find the sum of the length and width.
74/2 = 37
l + w = 37
In the question is states that the length is 5 inches longer than the width.
l = (5 + w)
There are two widths and two lengths in a rectangle, the measurement of the two lengths is 5 inches longer than the two widths.
5 + w + w = 37
5 + 2w = 37
Now that we have our equation we can solve for w, or the width.
1. Move the term containing the variable to the left
5 + 2w = 37
2w + 5 = 37
2. Subtract 5 from both sides of the equation, the opposite of adding 5
2w + 5 = 37
2w + 5 - 5 = 37 - 5
2w = 32
3. Divide by 2 in both sides of the equation, the opposite of multiplying 2
2w = 32
2w/2 = 32/2
4. Cancel out the 2s on the left, but leave the x
2w/2 = 32/2
w = 16
So, now that w, or the width = 16, we can find the length:
l = 5 + w
l = 5 + 16
l = 21
You can check your answer by plugging in our values into the original perimeter formula:
P = 2(l+w)
P = 2(21 + 16)
P = 2(37)
P = 74, so my answer is correct, because 74 is the perimeter given in the question.
O GRAPHS AND FUNCTIONSIdentifying solutions to a linear equation in two variables
Answers
Given:
Function is:
[tex]9x+2y=13[/tex]Find-:
Check for solution
Explanation-:
The value of "y" is:
[tex]\begin{gathered} 9x+2y=13 \\ \\ 2y=13-9x \\ \\ y=\frac{13-9x}{2} \end{gathered}[/tex]For (0,8)
Check value of "y" at x = 0 then,
[tex]\begin{gathered} x=0 \\ \\ y=\frac{13-9x}{2} \\ \\ y=\frac{13-9(0)}{2} \\ \\ y=\frac{13-0}{2} \\ \\ y=\frac{13}{2} \\ \\ y=6.5 \end{gathered}[/tex]So (0,8) it is not a solution.
Check (3,-7) the value of "x" is 3
[tex]\begin{gathered} x=3 \\ \\ y=\frac{13-9x}{2} \\ \\ y=\frac{13-9(3)}{2} \\ \\ y=\frac{13-27}{2} \\ \\ y=-\frac{14}{2} \\ \\ y=-7 \end{gathered}[/tex]So (3,-7) is the solution of function.
Check for (1 , 2) value of "x" is 1.
[tex]\begin{gathered} x=1 \\ \\ y=\frac{13-9x}{2} \\ \\ y=\frac{13-9}{2} \\ \\ y=\frac{4}{2} \\ \\ y=2 \end{gathered}[/tex]So, (1,2) is the solution.
Check for (4,-5) the value of "x" is 4.
[tex]\begin{gathered} x=4 \\ \\ y=\frac{13-9x}{2} \\ \\ y=\frac{13-9(4)}{2} \\ \\ y=\frac{13-36}{2} \\ \\ y=-\frac{23}{2} \\ \\ y=-11.5 \end{gathered}[/tex]So, (4,-5) is not a solution
Evaluating functions I don’t understand this one and I can’t find it no where else
Answers
The function given is
[tex]f(x)=4x[/tex]We are to find the inverse of the function
let f(x) =y
[tex]y=4x[/tex]Then, we make x the subject of the formula from here
[tex]\begin{gathered} y=4x \\ x=\frac{y}{4} \\ x=\frac{1}{4}y \end{gathered}[/tex]Then The inverse of the function becomes
[tex]f(x)=\frac{1}{4}x[/tex]Therefore the fourth option is correct
Find the surface area of a right cone with diameter 30 in. and slant height 8 in.Your answerEXTRA CREDIT: Find the surface area of the figure below. Round to the nearesttenth, if necessary.10 in?
Answers
Answer:
Surface area = 1084 in²
Step-by-step explanation:
To find the surface area of a right cone, we can use the following formula:
[tex]\boxed{{Area = \pi r^2 + \pi rl}}[/tex],
where:
• r = radius
• l = slant height.
In the question, we are told that the diameter of the cone is 30 in. Therefore its radius is (30 ÷ 2 = ) 15 in. We are also told that its height is 8 in.
Using this information and the formula above, we can calculate the surface area of the cone:
Surface area = [tex]\pi \times (15)^2 + \pi \times 15 \times 8[/tex]
= [tex]345 \pi[/tex]
[tex]\approx[/tex] 1084 in²
What is the slope of the line in the graph?A. 1 B. 2C. 0 D. -2
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Always remember that the slope is the number of units on the Y-axis in relation to the X movement.
A horizontal line always has a slope of 0. (it is not increasing in the Y-axis)
Question 11 > Alvin can go upstream at a rate of 25 miles per hour and downstream at a rate of 35 miles per hour. One day while Alvin was on the river, he received a call telling him he needs to turn around and come home. So he turned around and went back to his starting point. If his entire trip took 12 hours, how far did he travel on the river? Alvin traveled miles. (Roundtrip) Question Help: Message instructor Submit Question
Answers
Given Data:
The upstream speed is, 25 miles/hr.
The downstream speed is, 35 miles/hr.
The total time is, 12 hr.
Let d be the distance traveled. He can travel 25 miles/ hr in upstream, so the time taken will be,
[tex]t=\frac{d}{25}[/tex]He can travel 35 miles/ hr in upstream, so the time taken will be,
[tex]t^{\prime}=\frac{d}{35}[/tex]Total time is, 12 hr. So we have,
[tex]\begin{gathered} 12=\frac{d}{25}+\frac{d}{35} \\ 12=\frac{d}{5\times5}+\frac{d}{7\times5} \\ 12=\frac{1}{5}(\frac{d}{7}+\frac{d}{5}) \\ 12\times5=\frac{d}{7}+\frac{d}{5} \\ 60\times35=5d+7d \\ 2100=12d \\ d=\frac{2100}{12}=175 \end{gathered}[/tex]Therefore the total distance is, 350 mile
Tori is writing an essay for her English class. She already has 235 words, andon average writes 175 words every hour. The essay needs to be at least 1,600words. How many more hours should she plan to work on it? Write and solvean inequality for the situation.
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Let be "h" the number of hours Tori should plan to work on it.
You know that she writes an average of 175 per hour. This can be represented with this expresion:
[tex]175h[/tex]You also know that there must be at least 1,600 words in the essay for her English class. Since she has 235 words written, you can set up the following inequality:
[tex]235+175h\ge1,600[/tex]The symbol used in the inequality means "Greater than or equal to".
In order to solve it, you can follow these steps:
1. Subtract 235 from both sides of the inequality:
[tex]\begin{gathered} 235+175h-(235)\ge1,600-(235) \\ 175h\ge1,365 \end{gathered}[/tex]2. Divide both sides of the inequality by 175:
[tex]\begin{gathered} \frac{175h}{175}\ge\frac{1,365}{175} \\ \\ h\ge7.8 \end{gathered}[/tex]The answer is:
[tex]7.8\text{ }hours[/tex]URGENT!! ILL GIVE
BRAINLIEST! AND 100 POINTS
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Answer:
Option is the the. correct answer A
I don't understand how to do this (this is a practice assessment)
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Math | English | Art | Total
Boys 13 25 11 49
Girls 7 20 6 33
Total 20 45 17 82
1) Let's set a table, based on the given information:
• Since there are 20 students enrolled in Math let's place it into the Total, 20 -13 = 7
,• 82 students altogether.
,• 11 boys are in Art , 17 altogethe then 17 -11 = 6 girls
,• 20+6+7 = 20+13 = 33 girls altogether.
,• 82 -33 =49 13 +x +11 = 49 x = 49 -24=25
,• And lastly English: 20 +25 = 45
2) That's our table:
Math | English | Art | Total
Boys 13 25 11 49
Girls 7 20 6 33
Total 20 45 17 82
Simplify -(x+ 5) + 3x completely.A. -4x+ 5OOB. 2x + 5C. 2x - 5D. -4x - 5
Answers
-(x+ 5) + 3x
Distributing the -1:
(-1)*x + (-1)*5 + 3x
-x - 5 + 3x
Combining similar terms:
(-x + 3x) - 5
2x - 5
Pat bought a washer/dryer for $900 and made 24 payments of $46.23. Howmuch did she pay in interest?a. $1,109.52b. $900c. $92.40d. $209.52
Answers
Given that:
Cost of the washer/dryer = $900
Number of payments made = 24
Amount paid in each payment = $46.23
Total amount she paid
[tex]\begin{gathered} =\text{Amount paid in each payment}\cdot Number\text{ of payments} \\ =46.23\cdot24 \\ =1109.52 \end{gathered}[/tex]Interest paid = Total amount paid - Cost of the washer/dryer
[tex]\begin{gathered} =1109.52-900 \\ =209.52 \end{gathered}[/tex]Option d is correct.
[tex]4(3w-2)=8(2w+3)[/tex]
Answers
The most appropriate choice for linear equation will be given by -
w = -8 is the required answer
What is linear equation?
At first it is important to know about equation
Equation shows the equality between two algebraic expressions by connecting the two algerbraic expressions by an equal to sign.
A one degree equation is known as linear equation.
Here
[tex]4(3w - 2) = 8(2w+3)\\12w - 8 = 16w+24\\16w - 12w = -8-24\\4w = -32\\w = -\frac{32}{4}\\w = -8[/tex]
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i invest $250 in a simple account that earns 10% annually. After 6 years, how much money have i earned? Hint round to the nearest cent.
Answers
We have to use the simple interest formula
[tex]A=P(1+rt)[/tex]Where P = 250; r = 0.10 (10%); t = 6. Replacing these values, we have
[tex]A=250(1+0.10\cdot6)=250(1+0.6)=250(1.6)=400[/tex]Hence, after 6 years, you have $400.
If we subtract this amount from the investment, we get the profits.
[tex]400-250=150[/tex]Hence, the earnings are $150.martin earns $23.89 per hour proofreading ads at a local newspaper.His weekly wage w can be describe by the equation w= 23.89h, where h is the number of hours worked (a). write the equation in function notation (b). find f(23) f(35) and f(41)
Answers
SOLUTION
(a) The equation in function notation is
[tex]\begin{gathered} w=23.89h=f(h) \\ w=f(h)=23.89h \end{gathered}[/tex]Hence the answer is
[tex]w=f(h)=23.89h[/tex](b). f(23) becomes
[tex]\begin{gathered} f(h)=23.89h \\ f(23)=23.89\times23 \\ f(23)=549.47 \end{gathered}[/tex]f(35) becomes
[tex]\begin{gathered} f(h)=23.89h \\ f(35)=23.89\times35 \\ f(35)=836.15 \end{gathered}[/tex]f(41) becomes
[tex]\begin{gathered} f(h)=23.89h \\ f(41)=23.89\times41 \\ f(h)=979.49 \end{gathered}[/tex]simplify the following expression using the distributive property and combining like terms:3(y-4) -5(y+8)
Answers
3(y-4) - 5(y+8)
3y - 12 - 5y - 40
-2y - 52
Question 10 of 12, Step 1 of 29/14CorrectConsider the following quadratic equation:3.x2 - 13x + 2 = -2Step 1 of 2: Using the standard form ax2 + bx + c = 0 of the given quadratic equation, factor theleft hand side of the equation into two linear factors.AnswerKeypadKeyboard Shortcuts= 0
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Solution
- The question would like us to solve the quadratic equation:
[tex]3x^2-13x+2=-2[/tex]- The solution to this equation is given below:
[tex]\begin{gathered} 3x^2-13x+2=-2 \\ \text{Add 2 to both sides} \\ 3x^2-13x+4=0 \\ \\ \text{ We can rewrite the x-term as follows:} \\ -13x=-12x-x \\ \\ 3x^2-12x-x+4=0 \\ Let\text{ us factorize} \\ \\ 3x(x-4)-1(x-4)=0 \\ (x-4)\text{ is common } \\ \\ (x-4)(3x-1)=0 \end{gathered}[/tex]- Thus, the linear factors are
[tex]undefined[/tex]Translate each English phrase in the following problem into an algebraic expression and set up the related equation. Let z be the unknown number. The sum of a number and -41 is equal to the quotient of the number and 11. Step 2 of 3: Translate "the quotient of the number and 11". Answer
Answers
An algebraic expression which represents the translation of "The sum of a number and -41 is equal to the quotient of the number and 11" is z - 1 = z/11.
How to translate an English phrase into an algebraic expression?In order to translate a word problem into an algebraic expression, we would have to assign a variable to the unknown number:
Let z represent the unknown number.
The sum of a number and -41 is given by:
z + (-1) = z - 1 ....equation 1.
The quotient of the number and 11 is given by:
z/11 .....equation 2.
Next, we would equate equation 1 and equation 2 as follows:
Translation; z - 1 = z/11
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5.Given the sample triangle below and the conditions a=3, c = _51, find:cot(A).
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Depending on the angle we are analyzing on the right triangle, each side of it takes a different name. In this case, we are going to name them depending on the angle A. Then,
a: opposite side (to A)
b: adjacent side
c: hypotenuse
STEP 2: formula for cot(A)We know that the formula for cot(A) is:
[tex]\cot (A)=\frac{\text{adjacent}}{\text{opposite}}[/tex]Replacing it with a and b:
[tex]\begin{gathered} \cot (A)=\frac{\text{adjacent}}{\text{opposite}} \\ \downarrow \\ \cot (A)=\frac{b}{a} \end{gathered}[/tex]Since a = 3:
[tex]\cot (A)=\frac{b}{3}[/tex]STEP 3: finding bWe have an expression for cot(A) but we do not know its exact value yet. First we have to find the value of b to find it out.
We do this using the Pythagorean Theorem. Its formula is given by the equation:
[tex]c^2=a^2+b^2[/tex]Since
a = 3
and
c = √51
Then,
[tex]\begin{gathered} c^2=a^2+b^2 \\ \downarrow \\ \sqrt[]{51}^2=3^2+b^2 \\ 51=9+b^2 \end{gathered}[/tex]solving the equation for b:
[tex]\begin{gathered} 51=9+b^2 \\ \downarrow\text{ taking 9 to the left} \\ 51-9=b^2 \\ 42=b^2 \\ \downarrow square\text{ root of both sides} \\ \sqrt{42}=\sqrt{b^2}=b \\ \sqrt[]{42}=b \end{gathered}[/tex]Then,
b= √42
Therefore, the equation for cot(A) is:
[tex]\begin{gathered} \cot (A)=\frac{b}{3} \\ \downarrow \\ \cot (A)=\frac{\sqrt[]{42}}{3} \end{gathered}[/tex]Answer: DPoint M is the midpoint of AB. If AM = b² + 5b and
MB = 3b + 35, what is the length of AM?
Answers
Step-by-step explanation:
since M is the midpoint, it means that AM = MB.
so,
b² + 5b = 3b + 35
b² + 2b - 35 = 0
the general solution to such a quadratic equation
ax² + bx + c = 0
is
x = (-b ± sqrt(b² - 4ac))/(2a)
in our case (x is called b, don't get confused, as this is not the factor of x) this gives us
b = (-2 ± sqrt(2² - 4×1×-35))/(2×1) =
= (-2 ± sqrt(4 + 140))/2 = (-2 ± sqrt(144))/2 =
= (-2 ± 12)/2 = -1 ± 6
b1 = -1 + 6 = 5
b2 = -1 - 6 = -7
therefore, we have 2 solutions
b = 5
AM = 5² + 5×5 = 25 + 25 = 50
b = -7
AM = (-7)² + 5×-7 = 49 - 35 = 14
control, as AM = MB
MB = 3×5 + 35 = 15 + 35 = 50
or
MB = 3×-7 + 35 = -21 + 35 = 14
AM = MB in both cases, so, all is correct.
is it a function? X (-2, -1, 0, 1, 2 ) Y (-7, -2, 1, -2, -7 )
Answers
To be a function, it is nesessary that the values of x correspond to a unique value of y (a value of x cannot correspond to 2 different values of y). The same value of y can correspond to two or more values of x
As in the given data each value of x has just one value of y. Then, it is a function.
HeyI need help with this, having trouble solvingIt is from my ACT prep guide
Answers
We will determine the height of the building as follows:
First, we determine the height above her window, that is:
[tex]\tan (56)=\frac{h_u}{150ft}\Rightarrow h_u=(150ft)\tan (56)[/tex][tex]\Rightarrow h_u=222.3841453\ldots ft[/tex]Now, we calculate the height below her window:
[tex]\tan (32)=\frac{h_l}{150ft}\Rightarrow h_l=(150ft)\tan (32)[/tex][tex]\Rightarrow h_l=93.73040279\ldots ft[/tex]Then, we will have that:
[tex]h_T=h_l+h_l\Rightarrow h_T=150(\tan (56)+\tan (32))[/tex][tex]\Rightarrow h_T=316.1145581\ldots ft\Rightarrow h_T\approx316.1ft[/tex]So, the height of the building is approximately 316.1 ft tall.
Tyrone randomly interviewed 55 8th graders at the Westwood Mall Saturday afternoon to determine their reason for going to the mall. Based on the results of his survey, he made the following claim:Two out of four middle school students visit the mall to go shopping.Explain why this claim is misleading.a. Tyrone only interviewed students in the food court.b. Tyrone did not survey enough 8th graders to draw a valid conclusion.c. Tyrone did not use a random sample of 8th graders.d. Since Tyrone surveyed only 8th graders, his sample is not representative of all middle school students.
Answers
Tyrone randomly interviewed 55 8th graders at the Westwood Mall Saturday afternoon to determine their reason for going to the mall.
Based on the results he made the following claim.
"Two out of four middle school students visit the mall to go shopping".
Let us analyze each of the given options.
a. Tyrone only interviewed students in the food court.
There is no evidence that suggests the interview was conducted at the food court so this is not the correct answer.
b. Tyrone did not survey enough 8th graders to draw a valid conclusion
He interviewed 55 8th graders which are more than enough students so this is not misleading.
c. Tyrone did not use a random sample of 8th graders
It is given in the question that he used a random sample so this is not misleading.
d. Since Tyrone surveyed only 8th graders, his sample is not representative of all middle school students.
If you notice closely, Tyrone interviewed only 8th graders whereas the claim was about all middle school students.
So this is clearly misleading, 8th graders do not represent all middle school students.
Therefore, option d is correct.