Two lines are parallel if they have the same slope. Two lines are said to be perpendicular if the product of their slopes is -1.
Note that none of the slopes are equal, so the either are perpendicular or neither.
Note that the product of the slope of line 1 and line 3 is
[tex]3\cdot\frac{-1}{3}=-1[/tex]So, line 1 and line 3 are perpendicular.
For the other cases, it can easily be seen that their are not perpendicular, neither parallel.
All changes saved1. (02.02 MC)Describe how to transform (827)into an expression with a rational exponent. Make sure you respond with complete sentences. (10 points)
SOLUTION
We want write this as a rational exponent
[tex](\sqrt[5]{x^7})^3[/tex]This simply means the 5th root of x to power 7 all raised to power 5.
First step is to write the root form to exponent form we have
[tex]\begin{gathered} \sqrt[5]{x^7}=(x^7)^{\frac{1}{5}^{}} \\ =(x^7)^{\times\frac{1}{5}^{}} \\ x^{\frac{7}{5}} \end{gathered}[/tex]Next is the exponent 3, we have
[tex]\begin{gathered} (x^{\frac{7}{5}})^3 \\ (x^{\frac{7}{5}})^{\times3} \\ x^{\frac{21}{5}} \end{gathered}[/tex]Hence the answer is
[tex]x^{\frac{21}{5}}[/tex]Find the volume of the sphere Formula: V= 4/3 * 3.14 * r^3
First, to solve this problem, we need to use the formula for the circumference of the middle section of the sphere to find its radius:
C = 2pi * R
Given that C = 20pi, we get:
20pi = 2pi * R
Divide both sides by a factor of 2pi
R = 10 cm
Now, using the
set up a table of values and then graph the line form its parametric form
The given parametric equation:
x = -3t + 4
y = 2t - 5
The coordinates x & y at t = 0,
t=0,
x = -3(0) +4
x = 4
y = 2(0) - 5
y = (-5)
at t = 1
x = -3(1) + 4
x = 1
y = 2(1) - 5
y = (-3)
at t = 2
x = -3(2) + 4
x =-2
y = 2(2) - 5
y = (-1)
So, the coordinates are : (x,y) = (4,-5), (1,-3), (-2, -1)
table :
1) What is the slope (grade) of a road that rises 6 feet for every horizontal change of 600 feet?a) 1100b) 16d) seChoose
Let's conside the change in values in y axis with the increasing order of 600,1200,1800......
And the change in values in x axis with increasing order of 6,12,18,24.......
To find the slope, let'ss take
[tex]\begin{gathered} x_1=6 \\ x_2=12 \\ y_1=600 \\ y_2=1200 \end{gathered}[/tex]The formula to find the slope is,
[tex]m=\frac{y_2-y_1}{x_2-x_1_{}}[/tex]By substituting the values in the formula,
[tex]\begin{gathered} m=\frac{1200-600}{12-6} \\ m=\frac{600}{6} \\ m=100 \end{gathered}[/tex]Hence the value of slope, m is 100
12. Dave gave Charlotte half of his hockey cards. Charlotte gave Johnnie half of the cards she received from Dave. Johnnie kept 8 of those cards and gave the remaining 10 to Dana. How many hockey cards did Dave have to start?
To determine how many hockey cards Dave has to start, let's start from the bottom.
a.) Charlotte gave Johnnie half of the cards she received from Dave.
Johnnie kept 8 of those cards.
He gave the remaining 10 to Dana.
Total number of cards Johnnie received = 8 + 10 = 18 hockey cards
Johnnie received 18 hockey cards from Charlotte.
Thus, for Charlotte:
No. of cards Charlotte received ÷ 2 = No. of cards Johnnie received
No. of cards Charlotte received = No. of cards Johnnie received x 2
No. of cards Charlotte received = 18 x 2 = 36 hockey cards
Therefore, Charlotte received 36 hockey cards from Dave.
b.) Dave gave Charlotte half of his hockey cards.
No. of cards Dave has ÷ 2 = No. of cards Charlotte received
No. of cards Dave has = No. of cards Charlotte received x 2
No. of cards Dave has = 36 x 2 = 72 hockey cards
Therefore, originally, Dave has 72 hockey cards from the start.
The answer is 72 hockey cards
Which equation represents a line parallel to the line whose equation is2x - Зу =9(1) y = 2/3x - 4 (3) y = 3/2x - 4(2) y = -2/3x + 4 (4) y = -3/2x + 4
Explanation
when two ines are parallel , the slope is the same in both equations, so
Step 1
get the from y=mx+b in the given equation, to do this, isolate y
[tex]undefined[/tex]Which of the following is the product of the rational expressions shown below? 3x x + 2 X-4 X + 4 3x2 + 6x O A. X – 16 O B. 3x + 2x x - 16 O c. *** 3x + 6 x2 - 16 O D. 4x + 2 x2
EXPLANATION
Given the rational expression:
[tex]\frac{x+2}{x-4}\cdot\frac{3x}{x+4}[/tex]Expanding (x+4)(x-4) and multiplying terms:
[tex]\frac{x+2}{x-4}\cdot\frac{3x}{x+4}=\frac{3x(x+2)}{x^2-4x+4x-16}[/tex]Applying the distributive property:
[tex]\frac{3x(x+2)}{x^2-4x+4x-16}=\frac{3x^2+6x}{x^2-16}[/tex]Hence, the appropiate expression is as follows:
[tex]\frac{x+2}{x-4}\cdot\frac{3x}{x+4}=\frac{3x^2+6x}{x^2-16}[/tex]The answer is the option A
a model rocket is fired straight up from the ground. The heigth of the rocket (in feet) at any time T (in seconds) can be modeled by the equation h= -16t^2+ 128 when will the height of the rocket be 240feets from the ground.
The height is modeled by,
[tex]h(t)=-16t^2+128[/tex]Where
t is time in seconds
We want to find the time, t, rocket will be 240 feet above the ground.
So we will substitute 240 into h(t) and find the corresponding value of "t".
The steps are shown below:
[tex]\begin{gathered} h(t)=-16t^2+128 \\ 240=-16t^2+128 \\ 16t^2=112 \\ t^2=7 \\ t=\sqrt[]{7} \end{gathered}[/tex]Square root of 7 is approximately 2.65 seconds.
So,
Answer2.65 secondsUse the following information to answer questions #2 and 3 The track team has 20 members and will be sending 5 members to the next competition. How many 5-person teams are possible?
the method is Combination
we have that
The formula for combinations is
C=n!/[(n-r)!*r!]
where
n is the total number of objects you choose from
r is the number that you choose to arrange
in this problem
n=20
r=5
substitute in the formula
C=20!/[(20-5)!*5!]
C=20!/[(15)!*5!]
C=(20*19*18*17*16*15!)/[15!*5!]
simplify
C=(20*19*18*17*16)/(5*4*3*2*1)
C=1,860,480/120
C=15,504Everything about stats
Given the following:
Speed (km/hr) Number of players
10 -13.9 3
14 - 17.9 7
18 - 21.9 19
22 - 25.9 72
26 - 29.9 290
30 - 33.9 171
(a) to find the number of classes
To find the number of class, we use the formuar
K = 1 + 3.3logN
Where = Number of Classes
N = total number of classes
K = 1 + 3.3 log 6
K = 1 + 3.3 (0.7781)
K = 1 + 2.3344
K = 3.3344
(b) We are to find the class limit for the first class.
The class limit is the is the smallest value of the said class. therefore, the The lower class limit for the first class is 10
The upper class limit of the first class is 13.9
c) class width
The class width is the difference between the upper class and the lower class.
Therefore, the class width is:
13.9 - 10 = 3.9
17.9 - 14 = 3.9
So, the class width is 3.9 = 4 (approximately).
A coffee growing company sells coffeebeans for $2.00 per pound. The coffee bean pickerscan pick 1 ton of beans per day. How many days ofpicking are necessary for the company to make$100,000?
Start by using the conversion factor to know what is the sales price for the coffee beans per ton.
[tex]\frac{\text{\$}2.00}{pound}\times\frac{2000pound}{1ton}=\frac{\text{\$}4000}{ton}[/tex]then, the earnings can be found as:
[tex]earnings=(price)(amount\text{ }picked)(days)[/tex]then,
[tex]\begin{gathered} \text{\$}100,000=(\frac{\text{\$}4,000}{ton})(\frac{1ton}{day})(x\text{ }days) \\ solve\text{ }for\text{ }x: \\ x\text{ }days=\frac{\text{\$}100,000}{(\frac{\text{\$}4000}{ton})(\frac{1ton}{day})} \\ x=25\text{ }days \end{gathered}[/tex]Answer:
There is 25 days needed of picking for the company to make $100,000
Jillian, a pro golfer, is practicing chip shots (shorter andslower swings). Jillian hits a golf ball off the ground with aninitial velocity of 50 ft/sec at an angle of elevation of 35°above the horizon. If the ball took approximately 1.792seconds to fall back to the ground, and it reached itsmaximum height halfway through its flight, what was itsmaximum height?
We'll assume the shot has a parabolic arc since we are told it reaches its maximum height midway through its flight.
The equation that describes its movement through the y axis is
[tex]y=v_0\cdot\sin (\theta_0)\cdot t-\frac{1}{2}g\cdot t^2[/tex]Where v₀ is the initial velocity, θ₀ is the initial angle and g is the force of gravity.
The equation that descibes its speed at any point in the y axis is
[tex]v_y=v_0\cdot\sin (\theta_0)-g\cdot t[/tex]In order to find its maximum height, we need to find a point at which
[tex]v_y=0[/tex]as that would mean the ball is no longer moving up or down. Let's keep in mind that the end of the trajectory would satisfy this condition, so let's dicard it right away.
In order to proeed we must consider the equation
[tex]0=v_{0y}\cdot\sin (\theta_0)-g\cdot t[/tex]We already have all the data we need in order to solve it, so let's plug in the given values
whatis 30, 000 + 50,19130
We put above the term with more decimals, and below the term with less decimals
Now we sum the terms in a vertical way
Angle X is an inscribed angle in the given circle. Determine the measure of AB. Explain the relationshipbetween an inscribed angle and its intercepted arc.
Using the inscribed angle theorem, we have
[tex]x=\frac{1}{2}(AB)[/tex]Where x = 34. Let's solve
[tex]\begin{gathered} 34=\frac{1}{2}(AB) \\ AB=34\cdot2=68 \end{gathered}[/tex]Therefore, the arc AB measures 68°.Find the exact acute angle 0 for the given function value
we have that
[tex]\begin{gathered} tan\theta=\sqrt{3} \\ using\text{ a calculator} \\ \theta=60^o \end{gathered}[/tex]The answer is 60 degreesThe estimated number of dogs is 6.99 x 107 The estimated number of cats is 3.61 x 107 The estimated number of birds is 8.3 x 10 The power of 10 in 8.3 x 10 is 6, which is less than the power of 10 in the other two numbers. To make the calculation simpler, convert this number so the exponents are all the same. Multiply and divide 8.3 x 10 by 10 to increase its exponent by 1: 8.3 x 10% = 1.8.3 x 100 13.106.10 = 0.83 x 107 Part B Now that the three numbers have the same power of 10, find the sum using the Distributive Property.Please help me
You have the following information:
- estimated number of dogs = 6.99 x 10⁷
- estimated number of cats = 3.61 x 10⁷
- estimated number of birds = 0.83 x 10⁷
In order to find the sum of the previos quantities, by using the distribution property, you take into account that 10⁷ is a factor present in all given numbers. Thus, you can sum all the coefficients before the factor 10⁷, just as follow:
6.99 x 10⁷ + 3.61 x 10⁷ + 0.83 x 10⁷ use distribution property
= (6.99 + 3.61 + 0.83) x 10⁷ simplify terms inside the parenthesis
= 11.43 x 10⁷
Hence, the answer is 11.43 x 10⁷
Given the linear functions f(x) = x − 2 and g(x) = −3x + 4, determine (f ⋅ g)(x).
A: (f ⋅ g)(x) = −3x − 8
B: (f ⋅ g)(x) = −3x2 − 8
C: (f ⋅ g)(x) = −3x2 + 10x − 8
D: (f ⋅ g)(x) = −3x2 − 2x − 8
The linear function are f(x)=x-2 and g(x)=-3x+4. The function (f.g)(x) =-3x+2.
Given that,
The linear function are f(x)=x-2 and g(x)=-3x+4
We have to find (f.g)(x)
Each element of a non-empty set A is connected to at least one element of a second non-empty set B by a procedure or connection known as a function. The domain and co-domain of a function f between two sets, A and B, are terms used in mathematics.
= (f.g)(x)
= f(g(x))
= f(-3x+4)
= (-3x+4)-2
= -3x+4-2
= -3x+2
Therefore, The function we get (f.g)(x) =-3x+2
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which expression is equal to b + 4.A. 48. B. 4b. C. b+b+b+b. D. 4 + b
which expression is equal to b + 4.
A. 48.
B. 4b.
C. b+b+b+b.
D. 4 + b
Answer:
Option D: 4 + b
Hi I’m having trouble I need help with this It’s from my ACT prep guide 21’ textbook
Hello there. To solve this question, we'll have to remember some properties about convergence of series.
Starting by the fact that for a given series:
[tex]\sum ^{\infty}_{n=0}a_n[/tex]We always take the limit to see whether or not:
[tex]\lim _{n\to\infty}a_n=0[/tex]But in this case, we have to use the ratio test. Given two elements of the sequence we're adding the terms:
[tex]\mleft\lbrace a_1,_{}a_2,\ldots,a_n,a_{n+1},\ldots,a_k\mright\rbrace_{}[/tex]We say that for the following limit:
[tex]\lim _{n\to\infty}\left|\frac{a_{n+1}}{a_n}\right|=L[/tex]If L > 1, the series diverges by the ratio test.
If L = 1, the test is inconclusive.
If L < 1, the series converges by the ratio test.
In this case, the series is:
[tex]\frac{1}{3^1}^{}+\frac{2}{3^2}+\frac{3}{3^3}+\ldots[/tex]In which we can suppose that the general term is:
[tex]a_n=\frac{n}{3^{n^{}}},n\ge1[/tex]Hence we know that
[tex]a_{n+1}=\frac{n+1}{3^{n+1}},n\ge1[/tex]Now plugging in these terms in the ratio test, we have:
[tex]\lim _{n\to\infty}\left|\frac{\frac{n+1}{3^{n+1}}}{\frac{n}{3^n}}\right|[/tex]Knowing that:
[tex]\frac{\frac{a}{b}}{\frac{c}{d}}=\frac{a\cdot d}{b\cdot c}[/tex]We have:
[tex]\lim _{n\to\infty}\mleft|\frac{(n+1)\cdot3^n}{3^{n+1}\cdot n}\right|\mright.[/tex]In which we can simplify the fraction by a factor 3^n
[tex]undefined[/tex]A ladder leans against the side of a house. The angle of elevation of the ladder is 68°, and the top of the ladder is 13 ft above the ground. Find the distancefrom the bottom of the ladder to the side of the house. Round your answer to the nearest tenth.
Answer:
5.3ft
Explanation
Given the following
Angle of elevation = 68degrees
height of the house (opposite) = 13ft
Required
Distance from the bottom of the ladder to the side of the house (adjacent) D
Using the SOH CAH TOA identity
tan theta = opposite/adjacent
tan 68 = 13/D
D = 13/tan68
D = 13/2.4751
D = 5.25
D = 5.3ft (to the nearest tenth)
Hence the distance from the bottom of the ladder to the side of the house is 5.3ft
which of these tables represent a function? x 2 4 6 7
A function is a rule which uniquely associates elements of one set A to another set B. An element can either be one to one or many to one.
For a one to one function, it is one input to one output
For a many to one function, more than one input can have the same output
The inputs are the values of x while the outputs are the values of y
If one input has more than one output, then it is not a function
Looking at the given options, table W is a function because no input has more than one output. For the others, a particular input has more than one output
The correct option is table W
Put the following in ascending order. (starting at the top), -5, 0, 5, 7, -9?
The answer of the ascending order is -9, -5, 0, 5, 7
What is Ascending order?
Ascending order is a method of arranging numbers in ascending order from lowest to largest value. The sequence is from left to right. Ascending order is also known as ascending order. A set of natural numbers, for example, is in ascending order, such as 1 2 3 4 5 6 7 8... and so on. The less than symbol () is used to represent the ascending order. Descending order is the inverse method of rising order, in which the numbers are organised in decreasing order of value.
for example,
-10, -8, -7, -6, -5, -4, -3, -2, -1
⇒⇒⇒⇒⇒⇒⇒⇒⇒⇒⇒⇒⇒⇒⇒
So, -1 is biggest and -10 is smallest.
Hence, the ascending order is -9, -5, 0, 5, 7
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The ray GJ is the angle bisector of ZFGH and m_FGH = 30°. Enter m ZFGJ.The measure of ZFGJ is
Let's recall that an angle bisector divides into two equal parts or angles any angle.
Example: We have an angle of 88 degrees.
The angle bisector divides this angle into two equal parts of 44 degrees.
Now, if the measure of the angle FGH is 30 degrees, what would be the measure of one of the equal parts (angle FGJ) divided by ray GJ?
Ready, Jazmin?
The answer is:
• 60?
,• 90?
,• 30?
,• 15?
,• None of them?
Correct answer, Jazmin: 15 degrees
In this triangle, which of the following is true?A. The measure of x is 55° and a = 5.74.B. The measure of x is 35º and a = 5.74.WC. The measure of xis 35º and a = 8.19.D. The measure of xis 55° and a = 11.47.
The given figure is a right triangle, and the sum of two acute angles other than the 90 degree is always 90.
So the equation will be :
[tex]x+55=90[/tex]Solve for the value of x :
x = 90 - 55
x = 35
Use sine function in finding the value of a :
Note that :
[tex]\sin \alpha=\frac{\text{ opposite}}{\text{ hypotenuse}}[/tex]Where alpha is the angle equal to 55,
"a" is the opposite side
and
10 is the hypotenuse
[tex]\begin{gathered} \sin 55=\frac{a}{10} \\ a=10\sin 55 \\ a=8.19 \end{gathered}[/tex]Therefore, the correct answer is Option C.
A swimming pool is draining at a constant rate of -3.5 inches every two hours what is the change in the level after 9 hours
Answer:-15.75 inches
Step-by-step explanation:
First, since the pool is drained at a constant rate we can use the rate given (every two hours) to help us figure out how often the value (-3.5) is subtracted from the pool's total volume.
For this, we divide 9 by 2: 9/2=4.5
Where 4.5 is how many times the value changed by 3.5inches.
then we multiply how many(4.5) by how much(-3.5) to get the total value subtracted from the pool being:-15.75 inches.
Answer:
15.75
Step-by-step explanation:
First multiply -3.5 by 4 to get 14 which is the number of inches it drained in 8 hours. Then divide 3.5 by 2 to get the unit rate (the number of inches it drains in one hour) and add that to 14 to get 15.75!
(P.S. Nice to find someone who is doing the same thing as me in school )
2(1-3y) - 13x evaluate if x= 4 and y = -9 Evaluate each expression given the variable replacement
The given expression is
[tex]2(1-3y)-13x[/tex]The value of x is 4
The value of y is -9
Substitute x by 4 and y by -9 in the expression above
[tex]2(1-3\lbrack-9\rbrack)-13(4)[/tex]We will multiply -3 by -9 first
[tex]2(1+29)-13(4)[/tex]Multiply -13 by 4
[tex]2(1+29)-52[/tex]Add 1 and 29, then multiply the answer by 2
[tex]\begin{gathered} 2(30)-52= \\ 60-52 \end{gathered}[/tex]Subtract 52 from 60
[tex]60-52=8[/tex]The value of the expression is 8
The starting salary for a particular job is 1,200,000 per annum.The salary increases each year by 75,000 to a maximum of 1,500,000.How much money would a person earn in that time?
The number of years when you would earn the maximum salary is 4 years.
In how many years will he earn the maximum salary?The equation that represents the total salary earned is a linear equation. A linear equation is an equation that is made up of a single number that is raised to the power of one.
Salary earned = starting salary + (increase per year x number of years)
$1,500,000 = $1,200,000 + (75,000 x y)
$1,500,000 = $1,200,000 + 75,000y
$75,000y = $1,500,000 - $1,200,000
$75,000y = $300,000
y = 300,000 / 75,000
y = 4 years
Here is the complete question:
The starting salary for a particular job is 1.2 million per annum. The salary increases each year by 75000 to a maximum of 1.5million. In which year is the maximum salary reached
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this is a practice homework that I dont really understand I need help finding the answers and a quick explanation. :)
Answer:
12. g(2) = 0
13. g(0) = 2
14. g(-4) = 6
15. x = -4
16. x = 3
17. x = 2
Explanation:
To find g(2) we need to look at the point of the graph where x is equal to 2 and identify the value for y. So, In the graph when x is equal to 2, y is equal to 0. So,
g(2) = 0
In the same way, when x is equal to 0, the graph is at y equal to 2, so:
g(0) = 2
Finally, when x is -4, y is 6, so:
g(-4) = 6
Now, we know that g(x) = 6 and we need to find x, so in the graph when y is equal to 6, x is equal to -4, then:
x = -4 when g(x) = 6
When y is equal to -2, x is equal to 3, so:
x = 3 when g(x) = -2
Finally, when y is equal to 0, x is equal to 2, so:
x = 2, when g(x) = 0
the problem 1.75 ÷ 0.25 is modeled what is the solution
The operation we have to solve is:
[tex]1.75\div0.25[/tex]Step 1. The operation is not affected if we multiply both numbers by the same amount. In this case, is convenient to multiply both numbers by 100 in order to get rid of the decimal point:
[tex]\begin{gathered} 1.75\times100=175 \\ \text{and} \\ 0.25\times100=25 \end{gathered}[/tex]Thus, the division we have to make is equivalent to a new division without the decimal points:
[tex]1.75\div0.25=175\div25[/tex]Step 2. Arrange the numbers to make the division:
And then check how many times does 25 can fit into the number 175.
The answer is 7 because
[tex]25\times7=175[/tex]We put 7 in the place of the quotient and subtract 175 to the dividend:
The remainder is 0, and thus we have finished the operation.
Answer: 7
hello my child needs help with this problem can someone please provide me through this question Max's carton has a height of 6 inches with a base area of 12 inches squared. Tucker's carton has a height of 7 inches with a base area of 10 inches squared. How much more volume does Max's carton have than Tucker's? Explain how you know.
Answer:
Max's carton has 2 inches squared more volume than Tucker's carton.
Explanation:
First, calculate the volume of each of the cartons.
Max's Carton
• Height = 6 inches
,• Base Area = 12 inches squared.
[tex]\begin{gathered} Volume=Base\;Area\times Height \\ =12\times6 \\ =72\text{ cubic inches} \end{gathered}[/tex]Max's carton has a volume of 72 cubic inches.
Tucker's Carton
• Height = 7 inches
,• Base Area = 10 inches squared.
[tex]\begin{gathered} Volume=Base\;Area\times Height \\ =10\times7 \\ =70\text{ cubic inches} \end{gathered}[/tex]Tucker's carton has a volume of 70 cubic inches.
Next, we find the difference in volume.
[tex]\begin{gathered} \text{ Difference}=\text{ Max's Carton's Volume-Tucker's Carton's Volume} \\ =72-70 \\ =2\text{ cubic inches} \end{gathered}[/tex]Max's carton has 2 inches squared more volume than Tucker's carton.
