To throw a seashell into the ocean, Mason needs to throw it above the line y = 1.5x + 13, which represents the shoreline.
This means that the seashell's height, y, must be greater than 1.5 times its horizontal distance, x, plus 13. We can use the Pythagorean theorem to find the distance, d, that Mason needs to throw the seashell, given by d = sqrt(x^2 + y^2).
We want to find the minimum value of d that satisfies y > 1.5x + 13. This occurs when y is equal to 1.5x + 13, since any larger value of y would require a larger value of d.
So we can substitute y = 1.5x + 13 into the equation for d and get:
d = sqrt(x^2 + (1.5x + 13)^2)
To find the minimum value of d, we can use calculus and find the derivative of d with respect to x, and set it equal to zero. Alternatively, we can use a graphing calculator or an online tool to plot the function d and find its minimum point. Either way, we get that the minimum value of d occurs when x is approximately -5.2 meters and y is approximately 5.2 meters. The corresponding value of d is approximately 14.7 meters.
Therefore, Mason needs to be able to throw the seashell at least 14.7 meters, or 1470 centimeters, to throw it into the ocean.
Question 2 Find the missing number that makes the expression a perfect square. a. r2 x +16 b. x2 + X – 25
(a)
Given data:
The given expression is x^2 -.......x +16.
The first expression can be written as,
[tex]\begin{gathered} x^2-.\ldots..x+16=x^2-2(x)(4)+(4)^2 \\ =x^2-8x+16 \\ =(x-4)^2 \end{gathered}[/tex]Thus, the unknown value is 8.
Solve the expression for x = -2.2x + 4[x - 2(3 + x)]
ANSWER
[tex]-20[/tex]EXPLANATION
To solve the expression for x = -2, substitute -2 for x in the expression and simplify:
[tex]2x+4\mleft\lbrace x-2(3+x)_{}\mright\rbrace[/tex]That is:
[tex]\begin{gathered} 2(-2)+4\mleft\lbrace-2-2(3+(-2))\mright\rbrace \\ -4+4\mleft\lbrace-2-2(3-2)\mright\rbrace \\ -4+4\mleft\lbrace-2-2(1)\mright\rbrace \\ -4+4\mleft\lbrace-2-2\mright\rbrace \\ -4+4\mleft\lbrace-4\mright\rbrace \\ -4-16 \\ -20 \end{gathered}[/tex]That is the solution of the expression for x = -2.
2 Which function represents a translation of the graph of 1 = x by 8 units to the right? O A. V=(x-8) O B. v = (x+8) O c. v=872 =x2+8
Given function is,
[tex]y=x^2[/tex]For the function
[tex]y=f(x)[/tex]If we shift the graph b units to the right, the new function is
[tex]y=f(x-b)[/tex]Now, if we shift the graph of the given function 8 units to the right, the equation is
[tex]y=(x-8)^2[/tex]Hence, the correct option is (A)
A teacher showed this animal to students on a field trip. Which tool will allow the students to best see the animal up close? O A Tape measure O B Graduated cylinder O c. Notebook O D. Hand lens Submit
ANSWER is hands lens.
This is the best tool to see the animal up close.
An observer in a lighthouse 350 feet above sea level observes two ships directly offshore. The angles of depression to the ships are B = 8°and 8 = 12.5 (see figure). How far apart are the ships? (Round your answer to one decimal place.)
ANSWER:
911.6 ft
EXPLANATION:
Given:
[tex]\begin{gathered} \theta=12.5^{\circ} \\ \beta=8^{\circ} \end{gathered}[/tex]To find:
The distance between the two ships
Let's go ahead and draw a sketch as seen below;
Let's go ahead and solve for the value of AC by taking the tangent of angle 12.5 degrees as seen below;
[tex]\begin{gathered} \tan12.5=\frac{350}{AC} \\ \\ AC=\frac{350}{\tan12.5} \\ \\ AC=1578.7\text{ }ft \end{gathered}[/tex]Let's now solve for the value of AD by taking the tangent of angle 8 degrees as seen below;
[tex]\begin{gathered} \tan8=\frac{350}{AD} \\ \\ AD=\frac{350}{\tan8} \\ \\ AD=2490.4\text{ }ft \end{gathered}[/tex]Therefore the distance between the two ships will be;
[tex]\begin{gathered} CD=AD-AC \\ CD=2490.4-1578.7 \\ CD=911.6\text{ }ft \end{gathered}[/tex]So the two ships are 911.6 ft
The table shows the number of apples and the total weight of the apples,number of applesweight of apples (grams)2120052016Estimate the weight of 6 apples.Type the answer in the box below.6 apples would weigh aboutgrams
2 apples 511 gr
5 apples 1200 gr
8 apples 2016 gr
weight / apples
511 / 2 = x / 6
x = weight of 6 apples
Cross multiply:
6 * 511 = 2 x
3066 = 2x
Divide both sides by 2
3066 / 2 = 2x/ 2
1533 = x
x= 1533
Same with the other rows:
1200/5 = x/6
6*1200 = 5x
7200 = 5x
7200/5= x
x= 1440
2016/8 = x/ 6
6*2016 = 8x
12,096 = 8x
12096/8= x
x = 1512
Average of three results: ( 1533 + 1440 + 1512 )/ 3 = 1495
6 apples would weigh about 1495 grams
____years will be spent on working and ___years will be spent on eating food
In the graph, we can see the following:
We know that a person will devote 28 years working and eating from the word problem. Also, the number of years working will exceed the number of years eating by 20. Then, we have:
[tex]\begin{gathered} \text{Number of years working }+\text{Number of years eating }=28 \\ 24+4=28 \end{gathered}[/tex]Therefore, a person will be spent 24 years working and 4 years eating food.
14. The measure of one side of an equilateral triangle is (s+6) inches long. Write 2 different, equivalent
expressions to represent the perimeter of the triangle.
Perimeter of the equilateral triangle = 3(s + 6) inches
Perimeter of the equilateral triangle = 3s + 18 inches
Explanation:Given:
One of the sides of an equilateral triangle = (s + 6)
To find:
2 different equivalent expressions that represent the perimeter of the triangle
To determine the expression, we need to apply the formula for the perimeter of an equilateral triangle
[tex]\begin{gathered} Perimeter\text{ of equilateral triangle = sum of all 3 sides} \\ since\text{ all sides of an equilateral triangle are equal,} \\ Perimeter\text{ = 3}\times\text{ one of the side} \end{gathered}[/tex][tex]\begin{gathered} one\text{ of the side = s + 6} \\ \\ Perimter\text{ = 3 }\times(s\text{ + 6\rparen} \\ Perimeter\text{ of the equilateral triangle = 3\lparen s + 6\rparen inches} \end{gathered}[/tex]Another expression for the perimeter:
[tex]\begin{gathered} Perimeter\text{ = 3\lparen s + 6\rparen} \\ Expanding\text{ the parenthesis using distributive property:} \\ Perimeter\text{ = 3\lparen s\rparen + 3\lparen6\rparen} \\ Perimeter\text{ of the equilateral triangle = 3s + 18 inches} \end{gathered}[/tex]How to complete a square for an expression then factor the trinomial
SOLUTION
We want to complete the square for the expression
[tex]x^2+20x[/tex]So we need to find what must be added to the expression to make it a perfect square.
We can use the formula
[tex]undefined[/tex]What's the inverse operation of a cubing number?Also, can you please solve and explain this examples?
The inverse of cubing a number is applying cubic root
[tex]a^3\leftrightarrow\sqrt[3]{a}[/tex]Now, let's go through the examples:
When you want to find the square root of a number x you have to ask yourself:
Which number, when multiplied by itself, will give me x ?
For example,
[tex]\sqrt[]{225}=15[/tex]Because
[tex]\begin{gathered} 15\times15=225 \\ 15^2=225 \end{gathered}[/tex]This way,
[tex]\begin{gathered} \sqrt[]{49}=7\Leftrightarrow7^2=49 \\ \sqrt[]{121}=11\Leftrightarrow11^2=121 \\ \sqrt[]{1600}=40\Leftrightarrow40^2=1600 \end{gathered}[/tex]Now for the cubic root:
When you want to find the cubic root of a number y you have to ask yourself:
Which number, when multiplied by itself two times, will give me y ?
For instance,
[tex]\sqrt[3]{64}=8[/tex]Because
[tex]\begin{gathered} 8\times8\times8=64 \\ 8^3=64 \end{gathered}[/tex]Therefore,
[tex]\begin{gathered} \sqrt[3]{8}=2\Leftrightarrow2^3=8 \\ \sqrt[3]{1}=1\Leftrightarrow1^3=1 \\ \sqrt[3]{2744}=14\Leftrightarrow14^3=2744 \end{gathered}[/tex]A house was valued at $302,000. over several years, the value increased by 9% given the house in new value.
It is given that a house was valued at $302,000.
Let old value =$302,000.
Over several years, the value increased by 9%.
New value=9 % of old value+old value
[tex]\text{New value=}\frac{9}{100}\times302000+302000[/tex][tex]\text{New value=}\frac{9}{100}\times302000+(1)\times302000[/tex]Taking out 302000 as common, we get
[tex]\text{New value=(}\frac{9}{100}+1)\times302000[/tex][tex]\text{Use }\frac{\text{9}}{100}=0.09,\text{ we get}[/tex][tex]\text{New value=(0.09+1)}\times302000[/tex][tex]A\text{dding 1 and 0.09 , we get 1+0.09=1.09}[/tex][tex]\text{New value=1.09}\times302000[/tex][tex]\text{New value=\$}329180[/tex]Hence the new value of the house is $329180.
What is the value of y in this simplified expression?11-4= 119118
A regular pentagon is shown below. Supposethat the pentagon is rotatedcounterclockwise about its center so that thevertex at E is moved to C, how many degreesdoes that pentagon rotate?
Solution:
Given:
A regular pentagon rotated counterclockwise about its center.
To get the angle by which it rotated, we draw lines from each of the vertexes to the center to divide the pentagon into 5 equal triangles as shown;
The angle by which the pentagon is rotated through its center so that the vertex at E is moved to C is;
[tex]\angle EOC[/tex]To get angle EOC, we use the property of the sum of angles at a point.
The sum of angles at a point is 360 degrees.
[tex]\angle AOB+\angle BOC+\angle COD+\angle DOE+\angle EOA=360^0[/tex]
Since it is a regular polygon, each of these angles is equal.
Hence,
[tex]\begin{gathered} \angle AOB=\angle BOC=\angle COD=\angle DOE=\angle EOA=x \\ \angle AOB+\angle BOC+\angle COD+\angle DOE+\angle EOA=360^0 \\ x+x+x+x+x=360^0 \\ 5x=360^0 \\ \text{Dividing both sides by 5;} \\ x=\frac{360}{5} \\ x=72^0 \end{gathered}[/tex]
Thus, the measure of angle EOC is;
[tex]\begin{gathered} \angle EOC=\angle COD+\angle DOE^{} \\ \angle EOC=x+x \\ \angle EOC=72+72 \\ \angle EOC=144^0 \end{gathered}[/tex]Therefore, the angle by which the pentagon is rotated through its center so that the vertex at E is moved to C is;
[tex]\angle EOC=144^0[/tex]
Tom and his three friends went out to eat Their total was $65.45. The tax rate is 8% and they tipped the waitress 20% What was the total price of their how much should each person pay? Show your work.
Total: $65.45
----------------------
Tax rate: 8%
[tex]65.45\cdot\frac{8}{1000}=5.236[/tex]The tax is: $5.236
------------------------
Tip: 20%
[tex]65.45\cdot\frac{20}{100}=13.09[/tex]Tip: $13.09
---------------------------
Total price(Tp)= Total + The tax +Tip
[tex]Tp=65.45+5.236+13.09=83.776[/tex]The total price is: $83.776
---------------------------
There were four people so the total price is divided into those 4:
[tex]\frac{83.776}{4}=20.944[/tex]Each person should pay: $20.944
If a seed is planted, it has a 85% chance of growing into a healthy plant 9 seeds are planted, what is the probability that exactly 3 don't grow?
ANSWER
0.1069
EXPLANATION
We have two possible outcomes for each experiment: the seed grows or the seed does not grow. So, this follows a binomial distribution, where, in this case, the probability of success is the probability that a seed does not grow - note that we want to find what is the probability that a number of seeds do not grow.
We know that the probability that a seed grows is 85%, so there is a 15% chance the seed does not grow. This experiment is repeated 9 times (9 seeds) and we want to find what is the probability that the number of successes is 3 - remember that "success" is that the seed doesn't grow.
To find this, we have to use the binomial probability formula,
[tex]P(X=x)=\binom{n}{x}\cdot p^x\cdot q^{n-x}[/tex]For this problem:
• n = 9
,• x = 3
,• p = 0.15
,• q = 0.85
So we have,
[tex]P(X=3)=\binom{9}{3}\cdot0.15^3\cdot0.85^6\approx0.1069[/tex]Hence, the probability that exactly 3 seeds don't grow is 0.1069, rounded to four decimal places.
-5+(-7) I have done this a d can't figure it out
Explanation:
The expression: -5+(-7)
Answer:
Step-by-step explanation:
1. Since we know that an addition sign and a negative sign will make a negative sign, we simply have to do -5-7.
2. The answer is -12.
Find the sum: 73 + 751 + 1,239 + 13,907 =
Answer:15,970
Step-by-step explanation:
base: 5 ft 5 area: 5-ft?
area of the triangle is
[tex]A=\frac{1}{2}bh[/tex]then solve for h:
[tex]\begin{gathered} 5\frac{5}{6}=\frac{1}{2}(5)h \\ \frac{35}{6}=\frac{5}{2}h \\ \frac{35}{6}\times\frac{2}{5}=\frac{5}{2}\times\frac{2}{5}h \\ h=\frac{70}{30}=\frac{7}{3} \\ h=2\frac{1}{3} \end{gathered}[/tex]answer: h = 2 1/3
A game uses a single 6-sided die. To play the game, the die is rolled one time, with the following results: Even number = lose $51 or 3 = win $15 = win $8What is the expected value of the game?State your answer in terms of dollars rounded to the nearest cent (hundredth).
To answer this question, we need to find, first of all, the corresponding probability for the events. Then, we have:
1. The probability of an even number is:
We have that in a single 6-sided die, we have that the only even numbers are 2, 4, and 6. If we roll the die one time, then the probability of this event is:
[tex]P(\text{even)}=\frac{3}{6}[/tex]2. The probability of resulting 1 or 3 is - if the die is rolled one time:
[tex]P(1,3)=\frac{2}{6}[/tex]3. The probability of resulting in a 5 is - if the die is rolled one time:
[tex]P(5)=\frac{1}{6}[/tex]Then, if we add all the corresponding probabilities we have:
[tex]P(\text{total)}=\frac{3}{6}+\frac{2}{6}+\frac{1}{6}=\frac{6}{6}=1[/tex]The expected value of the gameTo find the expected value of the game, we have to find the product of the probability by the corresponding amount of money of the event as follows:
[tex]E(v)=\frac{3}{6}\cdot-\$5+\frac{2}{6}\cdot\$1+\frac{1}{6}\cdot\$8[/tex][tex]E(v)=-\$2.5+\$(\frac{1}{3})+\$(\frac{4}{3})=-\$2.5+\$(\frac{5}{3})=-\$(\frac{5}{6})=-\$0.833333333333[/tex]Or
[tex]E(v)=-\$0.833333333333[/tex]If we round the answer in terms of dollars rounded to the nearest cent (hundredth), we have that the expected value is:
[tex]E(v)=-\$0.83[/tex]In other words, if we play the game, we will expect to lose 83 cents of a dollar (per game) or 0.83 dollars.
In summary, we have that the expected value of the game is -$0.83.
all (5) on ONE Coordinate Plane & LABEL EACH LINE WITH THE EQUATION: 1.) x = 2 2.) y = 2 3.) y = -1/3 x + 3 (Use Slope Int. Method Make apparent your Int. Point AND the point from your slope = RISE/RUN) 4.) y = 1/2 x-5 (Use Slope Int. Method Make apparent your Int. Point AND the point from your slope = RISE/RUN) 5.) y = -5/4 x + 10 (Use Slope Int. Method Make apparent your Int. Point AND the point from your slope = RISE/RUN)
The graph of y = - 1/3x + 3 is shown in the photo below
The graph of 1/2x - 5 is shown in the photo below
The graph of y = - 5/x + 10 is shown in the attached photo below
A high school teacher grades a math test. She wants to see the numericalgrade of each student. Which item should she use so she can quickly seehow many students got each score? A. Line plot B. None of these C. Frequency table D. Pie chart
Given: A high school teacher grades a math test. She wants to see the numerical grade of each student.
Required: To identify which item the teacher should use so she can quickly see
how many students got each score.
Explanation: A line plot is a plot that shows the frequency of data along a number line as shown in the figure below-
Frankie is saving for a new game system that costs $499. His savings account currently holds $150. He plans to deposit $10 a week into the savings account until he has enough to buy the game system.
In how many weeks will Frankie be able to purchase the game system?
Answer:
35 weeks
Step-by-step explanation:
If Frankie already has $150 in his bank account, we can subtract it from the cost of the game.
$499 - $150 = $349
Now we can begin to solve for the number of weeks it will take for Frankie to purchase the game system.
If he needs $349, and he adds $10 every week,
10 weeks would give him $100
5 weeks would give him $50
$100 + $100 + $100 + $50 = $350
10 + 10 + 10 + 5 = 35
It would take Frankie 35 weeks to be able to buy the game system.
Write the equation of the trigonometric graph. Try fractional values or __ for the box next to x.
Given:
Here a graph of cos function is given in the question.
Required:
We need to find the blank boxes.
Explanation:
First of all start with amplitude of graph
so here the height of graph is 1 so amplitude is 1
now to find the last box we need middle line of graph which is 0
now to find the coefficient x in terms of pi
for this the period of graph is 2
here the period of cosx is 2*pi and here also period is 2 so in the box of coefficient we put pi
now out final equation is
Final answer:
[tex]\begin{gathered} y=1\cos\pi x+0 \\ y=\cos\pi x \end{gathered}[/tex]Solve the following Equation:-5k=12
k = -2.4
Explanation:[tex]-5k\text{ = 12}[/tex]Divide both sides by -5:
[tex]\begin{gathered} \frac{-5k}{-5}=\frac{12}{-5} \\ \end{gathered}[/tex]Division of same sign gives positive number. Division of opposite signs give negative number.
[tex]\begin{gathered} k\text{ = -12/5} \\ k\text{ = -2.4} \end{gathered}[/tex]which statement is true about the cost of a frozen dessert?
The cost function is,
[tex]c=0.35y+1.25[/tex]The cost of 15 ounce container is,
[tex]\begin{gathered} c=0.35\times15+1.25 \\ c=6.5 \end{gathered}[/tex]Thus, option (A) is the correct solution.
an octagon has side lengths 10.9 in the perimeter of the Octagon is 87.2 in centimeter and the area is 573.67 inches squared a second octagon has corresponding side lengths equal to 18.03 in find the area of the second octagon round to the nearest tenth
The are of the octsagon is given by:
[tex]A=2a^2(1+\sqrt[]{2})[/tex]where a is the lenght of its side.
Since the second octagon has sile lengths equal to 18.03, its area is:
[tex]A=2(18.03)^2(1+\sqrt[]{2})=1563.6[/tex]Therefore the area is 1563.6 squared centimeters
Given a family with four children, find the probability of the event. The youngest is a boy, given that the birth order alternates between girls and boys is
Given that the birth alternates between a boy and a girl, there are 2 options which are as follows.
Let
G = Girls
B = boys
Therefore,
[tex]\begin{gathered} \text{GBGB} \\ BGBG \end{gathered}[/tex]The probability that the youngest will be a boy in this scenario will be
[tex]\frac{1}{2}[/tex]If you place these marbles in a bag,close your eyes, and choose a marble,what is the probability that it will beblue?Simplify the fraction.Enter the number that belongs in the green box.
The following information below can be obtained from the image;
Blue Marbles: 6
Red Marbles: 5
Yellow Marbles: 3
Total marbles = 14
The probability of an event, E, is given as:
[tex]\begin{gathered} Pr(E)\text{ = }\frac{number\text{ of favourable outomes}}{number\text{ of sample space}} \\ \text{Thus, the probability of of choosing a blue marble is;} \\ Pr(\text{choosing a blue marble)=}\frac{number\text{ of blue marbles}}{number\text{ of total marbles}} \\ Pr(choo\sin g\text{ a blue marble) = }\frac{6}{14} \\ \text{In simplified form;} \\ Pr(\text{choosing a blue marble)=}\frac{3}{7} \end{gathered}[/tex]Hence, the number that belongs in the green box is 3
What is the distance from A to B given
Using the triangle sum theorem, we can conclude:
[tex]\begin{gathered} m\angle A+m\angle B+m\angle C=180 \\ 40+m\angle B+50=180 \\ so\colon \\ m\angle B=180-50-40 \\ m\angle B=180-90 \\ m\angle B=90 \end{gathered}[/tex]Now, we can use the law of sines in order to find AB:
[tex]\begin{gathered} \frac{AB}{\sin(C)}=\frac{AC}{\sin (B)} \\ solve_{\text{ }}for_{\text{ }}AB\colon_{} \\ AB=\frac{\sin (C)\cdot AC}{\sin (B)} \\ AB=\frac{\sin (50)\cdot100}{\sin (90)} \\ AB=76.60444431ft \end{gathered}[/tex]what is the average rate of change f (t) t=0 t=236 seconds per second -36 feet per second -18 seconds per second 18 feet per second