Since a golden rectangle is what the artist tend to achieve, we have to know the golden ratio in order to answer this.
A golden rectangle has a length = 1.62 its width.
Hence, its length = 1.62 (24) = 38.88
So, the length of the golden rectangle is 39 rounded to the nearest inches.
a. Write an equation in slope-intercept form for the line of best fit that is drawn.b. Then interpret the slope and y-intercept.
(a)The line of best-fit drawn intercepts the y-axis at 60.
To determine the slope, we use the points (3,65) and (8,70).
[tex]\text{Slope}=\frac{Change\text{ in y}}{\text{Change in x}}=\frac{70-65}{8-3}=\frac{5}{5}=1[/tex]Therefore, an equation for the line in slope-intercept form is: y=x+60
(b)Since the y-intercept = 60, we have that the initial graduation rate is 60% and it increases at a rate of 1% per year.
(c)To determine the graduation rate in 2020
2020 - 1998 = 22
x=22
Therefore, the graduation rate in 2020 will be:
y=22+60
y=80%
1. Write a linear equation of the form y1 = mx + b for your first set of data.2. Write a linear equation of the form y2 = mx + b for the other equation in your system. 3. How many round trips in a 12-hour day can each mode of transportation produce?
Given the distance of 382 miles, and a velocity of 760 miles/hour and a time of 0.583 hour, we can writte the following equation:
[tex]382\text{ miles}=760\frac{miles}{hour}*0.583hour+b[/tex]Then the intercept b is:
[tex]\begin{gathered} b=382-760*0.583 \\ b=-61.08\text{ miles} \end{gathered}[/tex]Hence the equation for the first data set is:
[tex]distance=0.583*speed-61.08[/tex]Now the next dataset:
[tex]\begin{gathered} 382miles=\frac{535miles}{hour}*1.25hour+b \\ b=-286.5\text{ miles} \end{gathered}[/tex]Hence the equation for the second point is:
[tex]distance=1.25*speed-286.5[/tex]Next, for the third point. By hyperloop, a round trip takes 0.583*2=1.166 hour (go and back), hence in a 12-hour day:
[tex]\frac{12}{1.166}=10.29\text{ trips}[/tex]Hence by hyperloop we got 10 trips.
On the other way, by airplane it takes 1.25*2=2.5hour:
[tex]\frac{12}{2.5}=4.8\text{ trips}[/tex]Then by airplane we got 4 round trips.
is the graph of this equation a horizontal or a vertical line y=10
Let's begin by identifying key information given to us:
[tex]y=10[/tex]This equation is a horizontal line (as shown below)
A 42Inch suggests that the main diagonal of the is 42 inches Determine the dimensions of the screen a 42 inch TV with a 4 3 aspect ratio
Answer:
The dimensions are 33.6 and 25.2 inches.
Step-by-step explanation:
Let's say the screen is a rectangle with sides "x" and "y".
We know that x/y = 4/3. So, x = (4/3)y
Since the diagonal is known, we can represent the tv as:
The measures of x and y can be found using the green part of the figure. As we can see, we have a triangle rectangle.
The hypothesis of the triangle is 42 and the sides y and (4/3)y.
Using the Pythagorean Theorem, we know that:
[tex]\text{hyp}^2=a^2+b^2[/tex]where "hyp" is the hypotenuse and a and b the sides.
So,
[tex]\begin{gathered} 42^2=(\frac{4}{3}y)^2+y^2 \\ 1764=\frac{16}{9}y^2+y^2 \\ 1764=\frac{16y^2+9y^2}{9} \\ 1764=\frac{25y^2}{9} \\ 1764\cdot9=25y^2 \\ \frac{15876}{25}=y^2 \\ y^2=635 \\ y=\pm25.2\text{ } \\ \text{ Since y is a positive a measurement, } \\ y=25.2\text{ inches} \end{gathered}[/tex]Also, since x = (4/3)y:
[tex]\begin{gathered} x=\frac{4}{3}y \\ x=\frac{4}{3}\cdot25.2 \\ x=33.6\text{ inches} \end{gathered}[/tex]Thus, the dimensions of the screen are 25.2 and 33.6 inches.
6. Y= x + 3 Y= 2x + 4
Given y=x+3 and y=2x+4.
Substitute y=2x+4 in y=x+3.
[tex]\begin{gathered} y=x+3 \\ 2x+4=x+3 \\ 2x-x=3-4 \\ x=-1 \end{gathered}[/tex]Put -1 for x in y=2x+4.Hence,
[tex]\begin{gathered} y=2x+4 \\ y=2\times(-1)+4 \\ y=-2+4 \\ y=2 \end{gathered}[/tex]Therefore, the value of x is -1 and the value of y is 2.
Is the leading term of this function x^2 or just 2.
Answer:
[tex]x^2[/tex]Step-by-step explanation:
In a polynomial function, the leading term is the term containing the highest power of x.
Therefore, the leading term would be:
[tex]x^2[/tex]Parallel lines j and k are cut by transversal t. Which statement is true about 22 and 26?They are alternate interior angles, so m/2+m/6 = 180°.They are alternate exterior angles, so m/2+m/6 = 180°.They are corresponding angles, so /2 26.They are vertical angles, so 2 26.
The two angles are corresponding because they are in matching corners, which means they occupy the same relative position where the transversal line crosses the two parallel lines l and k from the given figure.
Also, corresponding angles are congruent.
Therefore, <2 ≅ <6
Option C is correct.
Consider the pyramid. 10 mm 8 mm 8 mm (a) Draw and label a net for the pyramid, (b) Determine the surface area of the pyramid. Show your work.
Given:
A pyramid. 10 mm, 8 mm, and 8 mm
(a) Draw and label a net for the pyramid
The figure will be as shown:
(b) Determine the surface area of the pyramid
We will use the following formula to find the total surface area:
[tex]Surface\text{ }Area=A+\frac{1}{2}ps[/tex]where: A is the base area, (p) is the perimeter of the base, (s) slant height
The base has a square shape with a side length = 8 mm
The slant height = 10 mm
substitute into the formula of the surface area:
[tex]SA=8*8+\frac{1}{2}*(4*8)*10=224\text{ }mm^2[/tex]So, the answer will be:
The surface area = 224 mm²
All of the following are equivalent except: 4% .04 .4 1/25
Answer:
Explanation:
Let's go ahead and determine the equivalent values as shown below;
An airplane is flying at a steady elevation of 1 1,500 feet. The pilots of the airplane are informed they are approaching a storm, and they will need to ascend to an elevation of 33.000 feet to avoid flying through the storm. As soon as the pilots received the information about the storm, they immediately began to ascend at a constant rate. After 2 minutes, the airplane reached an elevation of 17,000 feet Part A Write an equation that could represent the amount of time it takes the airplane to ascend to the elevation necessary to avoid flying through the storm. Use t to represent the amount of time, in minutes, spent ascending
Consider that the motion of the airplane is uniform, that is, the speed of the airplane is constant. Use the following formula:
[tex]t=\frac{y-y_0}{v}[/tex]where v is the speed of the airplane, y0 is the initial height of the airplane respect to the ground and y is the height of the airplane after t minutes.
Consider that the airplane travels from 11,500 feet to 17,000 feet in 2 min. Then, the airplane travels 17,000 - 11,500 = 5,500 in 120 s.
The speed of the airplane on this interval is:
v = 5,500 ft/2 min = 2,750 ft/min
The equation for the time t is:
[tex]t=\frac{y-11,500ft}{2,750ft/\min }[/tex]Damon was measuring to make a rectangular play area in the backyard forhis dog.He knows the width is 4 feei. His length is twice his width. What is the amount of playspace Damon's dog will have? Explain.What is the area?
Given the width is 4 feet
The length is twice the width so, the length = 2 * 4 = 8 feet
Space = area = length * width = 4 * 8 = 32 square feet
3. If all three friends worked 20 hours during the week, how much would each person earn?if all three fans for 20 hours during the week how much would each person end
To find out how much each of them earns for 20 hours we need to find how much they earn per hour. To do that we need to find the constant of proportionality for each of them:
In Savannah's case we have:
[tex]k_S=\frac{38-19}{4-2}=\frac{19}{2}=9.5[/tex]In Greg's case we have:
[tex]k_G=\frac{54-27}{6-3}=\frac{27}{3}=9[/tex]In Kevin's case we have:
[tex]k_K=\frac{41.25-16.50}{5-2}=\frac{24.75}{3}=8.25[/tex]Now that we have each of the constant of proportionality we multiply them by 20 to find out how much each of them earn for 20 hours.
[tex]\begin{gathered} 20\cdot9.5=190 \\ 20\cdot9=180 \\ 20\cdot8.25=165 \end{gathered}[/tex]Therefore Savannah earns $190, Greg earns $180 and Kevin earns $165 for 20 horus of work.
At a fabric store, fabrics are sold by the yard. A dressmakerspent $36.35 on 4.25 yards of silk and cotton fabrics for adress. Silk is $16.90 per yard and cotton is $4 per yard.Here is a system of equations that represent the constraintsin the situation.x + y = 4.2516.90x + 4y = 36.35What does the solution to the system represent?
Vestuary prices are represented by two equations
Silk have higher price than cotton, obviously
Since x is related to higher price 16.90 , then it represents
number of Silk yards buyed.
And since y is related to lower price $4 , then it represents number of cotton yards acquired.
Solve the following inequality algebraically. 3∣x−3∣+8<20
The inequality to solve is:
[tex]3\vert x-3\vert+8<20[/tex]Let's get the absolute value isolated:
[tex]\begin{gathered} 3|x-3|<20-8 \\ 3|x-3|<12 \\ |x-3|<\frac{12}{3} \\ |x-3|<4 \end{gathered}[/tex]Now we have an absolute value equation. One thing to note here is:
If
|x - a| < b
We can write:
x - a < b
and
x - a > - b
From our equation, we can thus say:
x - 3 < 4
and
x - 3 > -4
Solving 1st:
[tex]\begin{gathered} x-3<4 \\ x<4+3 \\ x<7 \end{gathered}[/tex]and solving 2nd one:
[tex]\begin{gathered} x-3>-4 \\ x>-4+3 \\ x>-1 \end{gathered}[/tex]Together, we can write the solution set as:
[tex]-1The turtle tank is a curcular cylinder.The diameter of the tank is 50 feet and the height is 2.5 feet. In order to clean the tank the cleaners need to purify the water with chlorine. If one gallon of liquid chlorine treats 3000 gallons of water, how many full gallons will the cleaners need to buy.(hint 1 cubic foot = 7.48 gallons)
Find the volume of the tank:
[tex]V=\pi\cdot r^2\cdot h[/tex]The radius of a circle is equal to the half of its diameter:
[tex]\begin{gathered} d=50ft \\ \\ r=\frac{50ft}{2}=25ft \end{gathered}[/tex]Then, the volume of the tank is:
[tex]\begin{gathered} V=\pi\cdot(25ft)^2\cdot2.5ft \\ \\ V=4908.73ft^3 \end{gathered}[/tex]1 cubic foot = 7.48 gallons
1 gallon of chlorine = 3000 galons of water
[tex]4908.73ft^2water\cdot\frac{7.48\text{gal water}}{1ft^2\text{ water}}\cdot\frac{1\text{ gal chlorine}}{3000\text{ gal water}}=12.24gal\text{ chlorine}[/tex]It is necesary to buy 13 gallons of chlorine as it is necesary to use 12.24 gallons to clean the tank
Your expected value calculations for your Friday night activities proved to be very accurate, so you wish to do the same thing for Saturday night. Your friends havedecided to go to dinner together. You decide that there are 5 possible outcomes. After each is the probability and relative pleasure rating of that outcome that youcalculated.Outcome 1: All of your good friends show up. Probability: 0.33. Relative pleasure rating: 7.Outcome 2: Your good friends, but also your one annoying friend shows up. Probability: 0.25. Relative pleasure rating: 4.Outcome 3: Only your one annoying friend shows up. Probability: 0.18. Relative pleasure rating: -5.Outcome 4: Your good friends, plus that one person you have a crush on show up. Probability of 0.19. Relative pleasure rating: 10Outcome 5: Only that one person that you have a crush on show up. Probability: 0.05. Relative pleasure rating: 20.Compute the expected value of your relative pleasure rating for going out to dinner with your friends. Select the correct value from the options below.5.3112.966.194.487.443.41
5.31
Explanation:The expected value of a probability distribution is:
[tex]\mu=\sum_^xp(x)[/tex]where x is the number of trials (or rating in this case)
p(x) is the probability of success
For outcome 1:
x = 7, p(x) = 0.33
For outcome 2:
x = 4, p(x) = 0.25
For outcome 3:
x = -5, p(x) = 0.18
For outcome 4:
x = 10, p(x) = 0.19
For outcome 5:
x = 0.05, p(x) = 20
Substituting these values in the expected value formula for probability distribution
[tex]\begin{gathered} \mu=x_1p(x_1)+x_2p(x_2)+x_3p(x_3)+x_4p(x_4)+x_5p(x_5) \\ \\ \mu=7(0.33)+4(0.25)+(-5)(0.18)+10(0.19)+0.05(20) \\ \\ \mu=2.31+1-0.9+1.9+1 \\ \\ \mu=5.31 \end{gathered}[/tex]George is saving money to buy a new video game. He has $43 and earns an additional $5 every week forcompleting his chores. Drag and drop the values to create an equation to represent the total amount ofmoney, t, he has after w weeks.
Answer:
Explanation:
George initially has $43 and each week he add $5, so after w weeks he will have $5 times w plus the initial $43. Therefore, the equation that represent the total amount of money is
t = 43 + 5w
Where w is the number of weeks.
Need this soon please - Select the correct answer.What is the inverse of functionf(x)=√x + 7
GIVEN:
We are given the following function;
[tex]f(x)=\sqrt{x}+7[/tex]Required;
To find the inverse of the function.
Step-by-step solution;
To solve for the inverse of a function f, we begin by re-writing the function as an equation in terms of y. We now have;
[tex]\begin{gathered} f(x)=\sqrt{x}+7 \\ \\ Becomes: \\ \\ y=\sqrt{x}+7 \end{gathered}[/tex]Next step we switch sides for x and y variables and then solve for the y variable as shown below;
[tex]\begin{gathered} y=\sqrt{x}+7 \\ \\ Becomes: \\ \\ x=\sqrt{y}+7 \\ \\ Solve\text{ }for\text{ }y; \\ \\ Subtract\text{ }7\text{ }from\text{ }both\text{ }sides: \\ \\ x-7=\sqrt{y} \\ \\ Square\text{ }both\text{ }sides: \\ \\ (x-7)^2=(\sqrt{y})^2 \\ \\ (x-7)^2=y \end{gathered}[/tex]We now re-write in function notation. Take note however that this is the inverse;
[tex]\begin{gathered} Where\text{ }y=(x-7)^2 \\ \\ f^{-1}(x)=(x-7)^2 \end{gathered}[/tex]Therefore,
ANSWER
[tex]f^{-1}(x)=(x-7)^2\text{ };for\text{ }x\ge7[/tex]The correct answer is option A.
I need to find x and under neath the problem are the answer choices
Given:
There are given two right-angle triangles.
Explanation:
According to the question:
We need to find the value of x:
So,
First, we will find the value for the second triangle by using 60 degrees.
So,
[tex]\begin{gathered} sin60=\frac{y}{12\sqrt{6}} \\ \frac{\sqrt{3}}{2}=\frac{y}{12\sqrt{6}} \\ 2y=12\sqrt{18} \\ y=6\sqrt{18} \end{gathered}[/tex]Now,
For the x:
[tex][/tex]Help me urgently.It takes the earth 24 h to complete a full rotation, it take mercury approximately 58 days and 15 h to complete a full rotation. How manny hours does it take mercury to complete a full rotation? Show all work and use correct conversion factors.Part A. Identify what are you trying to find in the problem. Hint look for the question.Part B. Strategize what units do you need to convert ( convert from 58 and 24Part C. Set up your fractions using the conversion factors, (for credit) multiply to convert the units don’t forget to include units,Part D . Solve show your work convert the units and solve the problem Part E. Answer the question step by step include correct units.
SOLUTION:
Case: Time Conversion
Method:
Part A. Identifying the problem
How many hours does it take mercury to complete a full rotation?
Part B. Unit
Converting from Days and Hours to Hours
Part C. Set up your fractions using the conversion factors
1 day is equivalent to 24 hours
Part D. Workings
[tex]\begin{gathered} 1day\equiv24hours \\ 58days\text{ }15hours=\frac{58}{1}\times24+15 \\ =1392hours+15hours \\ =1407hours \end{gathered}[/tex]Part E. Final answer with correct units
It takes mercury 1407 hours to complete a full rotation
how many number of buttons of each jar
• The number of textured is 18, all the other buttons combined are 21
Therefore, it is false that the button is more likely to be textured than all the other buttons combined.
• Plaid, polka dot, chevron and textured are of different numbers, therefore, it is false that they are equally likely.
• Polka dot is 9, textured is 18, therefore, it is true that it twice as likely to be textured as polka dot.
• Chevron is 8, plaid is 4, therefore, it is true that the button is half as likely to be plaid as it is to be chevron.
Angles 1 ans 2 are complimentary. If m<1 = 56° , what is the measure of <2?
Two angles are complementary if the sum of their degrees is equal to 90º. therefore:
[tex]\begin{gathered} m\angle1+m\angle2=90 \\ 56+m\angle2=90 \\ 56+m\angle2-56=90-56 \\ m\angle2=34 \end{gathered}[/tex]answer m<2= 34°
4) -16 - 10x = 4(1 - 5x)
To solve this question first open the brackets on the right-hand side
[tex]4(1-5x)=4-20x[/tex]Then re-write the equation as
[tex]-16-10x=4-20x[/tex]Collect the like terms,the terms with x's and those with no x's
[tex]-16-4=-20x+10x\text{ }[/tex]Apply addition
[tex]-20=-10x[/tex]Apply division by dividing both sides of the equation by -10 to get the value of x
[tex]\frac{-20}{-10}=\frac{-10x}{-10}[/tex][tex]2=x[/tex]The answer is x=2
Solve the first inequality and express your answer in interval notation. Use decimal form for numerical values.
EXPLANATION
Given the system of inequalities:
-5(y-4) ≤ 30 or 18 + y < 20
Applying the distributive property:
-5y + 20 ≤ 30 or 18 + y < 20
Subtracting -2 to both sides of the first inequality and -18 to the second one:
-5y ≤ 30 - 20 or y < 20 - 18
Subtracting numbers:
-5y ≤ 10 or y < 2
Dividing both sides by 5 in the first inequality:
-y ≤ 10/5 or y < 2
Simplifying the first inequality:
-y ≤ 2 or y < 2
Dividing by -1 the first inequality and reversing:
y ≥ 2 or y < 2
In conclusion, the solution in interval notation is as follows:
(-∞,∞)
Which ordered pair is a solution to the equation y=-3x-4A: Only (-2,4)B: Only (-3,5)C: Both (-2,4) and (-3,5)D: Neither
Answer:
B: Only (-3,5)
Explanation:
We test whether the ordered pairs given are the solution to the equation. We do this by putting their values into the equation and seeing whether they satisfy it.
Now, (-2, 4) says that when x = -2, y = 4, meaning it must be that
[tex]\begin{gathered} y=-3(-2)-4 \\ y=6-4 \\ y=2 \end{gathered}[/tex]we see that when x = -2 y is not 4; therefore, the ordered pair given is not a solution.
Now for (-3, 5) we put in x = -3 into the equation and get
[tex]\begin{gathered} y=-3(-3)-4 \\ y=9-4 \\ y=5 \end{gathered}[/tex]we see that when x = -3, y = 5, meaning that the ordered pair (-3, 5) satisfies the equation.
Therefore, the ordered pair is a solution and choice B is correct.
Colette is 4 times as old as Jack. Colette is 52. Write a one-step equation and solve to determine Jack's age.
Let's define:
x: Colette's age
y: Jack's age
If Colette is 4 times as old as Jack, then:
x = 4y
Given that Colette is 52, then x = 52, which means that
52 = 4y
4 is multiplying on the right, then it will divide on the left
52/4 = y
13 = y
Jack's age is 13
The sound wave of two music notes can be represented by the function y = 2sin2x and y = −sin x, where x represents the time since the note is played. At what times will the frequencies of the sound waves be the same in the interval [0°, 360°)?
ANSWER
x = 0°, 180°, 210°, 330°
EXPLANATION
We have to find x when both functions have the same value,
[tex]2\sin ^2x=-\sin x[/tex]Add sin(x) to both sides,
[tex]2\sin ^2x+\sin x=0[/tex]And we have a quadratic equation, where the variable is sin(x). Factor out 2 sin(x),
[tex]2\sin x(\sin x+\frac{1}{2})=0[/tex]The solutions are,
[tex]\begin{cases}\sin x=0 \\ \\ \sin x=-\frac{1}{2}\end{cases}[/tex]Now we have to find the values of x whose sine is 0 and the ones whose sine is -1/2,
[tex]\begin{gathered} \sin x=0\Rightarrow x=0\degree;x=180\degree \\ \\ \sin x=-\frac{1}{2}\Rightarrow x=210\degree;x=330\degree \end{gathered}[/tex]Hence, the values where they are the same are 0°, 180°, 210° and 330°
the formula C equals 5/9 (f - 32 (is used to convert the temperature in degrees Fahrenheit () to the temperature in degrees celsius. CC (enter the temperature in degrees celsius prophecies seed) equal to 113 degrees Fahrenheit (F)
Find the value of C if the value of F is 113 degrees, given the formula below:
[tex]\begin{gathered} C=\frac{5}{9}(F-32) \\ \text{Where F=113} \end{gathered}[/tex]Substituting 113 for F, we get,
[tex]\begin{gathered} C=\frac{5}{9}(113-32) \\ \\ C=\frac{5}{9}(81)=\frac{5}{9}\times81=5\times9=45\text{ degrees Celsius} \end{gathered}[/tex]Is it no horizontal or is it One horizontal or is it Two horizontal
Looking at the function, it is an exponential function.
When x tends to positive infinity, the function tends to negative infinity.
When x tends to negative infinity, the function tends to zero, because the expression 2^x will be close to 0. That means the function has a horizontal asymptote at y = 0.
Therefore the answer is one horizontal asymptote (y = 0).
During its first week in business, a new coffee shop served 153 customers. During the second week, 468 customers were served. What was the percent increase in customers served, from the first week to the second week?
Determine the change in number of customer served in a week.
[tex]\begin{gathered} \text{Change}=468-153 \\ =315 \end{gathered}[/tex]Determine the percent change in number of customer.
[tex]\begin{gathered} \text{Percent change=}\frac{315}{153}\times100 \\ =2.0588\times100 \\ =205.88 \end{gathered}[/tex]Thus, increase in number of customer is 205.88%.
