The function is solved below
What is a function?
The function is instantly given a name, such as a, in functional notation, and its description is supplied by what it does to the input x, using a formula in terms of x. Instead of sine, put sine x. (x). Leonhard Euler invented functional notation in 1734. Some commonly used functions are represented with a symbol made up of many letters (usually two or three, generally an abbreviation of their name). In this scenario, a roman font is typically used, such as "sine" for the sine function, rather than an italic font for single-letter symbols. A function is also known as a map or a mapping, however some writers distinguish between "map" and "function."
The function can be written as
3x+4y-7 = 0
or, y = (-3/4)x + 7/4
so, slope = -3/4
and other function is
kx+12y+3 = 0
or, y = (-k/12)x - 1/4
so, slope = -x/12
Given the lines are parallel, so slopes are equal
i.e., -3/4 = -k/12
or, k = (3/4)12 = 9
Hence, the value of k is 9.
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How to tell if a sequence is linear, exponential, quadratic or absolute value as simply as possible without graphing (8th grade algebra) examples will be greatly appreciated
We will have the following:
We will be able to tel apart sequences as follows:
Linear sequence: We have that linear sequences follow the form:
[tex]y=mx+b[/tex]Here "x" represents the iteration value for the sequence, "m" the ratio (slope) and "b" a value that modifies the "position" of the sequence. This sequences grows in a linear manner.
Example:
[tex]\begin{cases}y_{}=2x+2 \\ \\ y_1=4 \\ y_2=6 \\ y_3=8 \\ \ldots\end{cases}[/tex]Exponential sequence: We have that exponential sequences follow the form:
[tex]y=a_1(r)^{x-1}[/tex]Here "a1" is the first term of the sequence, "r" is the ratio and "x" the iteration of the sequence.
We obtain the ratio as follows:
[tex]r=\frac{y_n}{y_{n-1}}[/tex]Example:
[tex]\begin{cases}y=1(5)^{x-1}_{} \\ \\ y_1=1 \\ y_2=5 \\ y_3=25 \\ \\ \ldots\end{cases}[/tex]The ratio for this case:
[tex]r=\frac{y_3}{y_2}\Rightarrow r=\frac{25}{5}\Rightarrow r=5[/tex]Quadratic sequence: A quadratic sequence follows the general form
Point P is in the interior of
∵ m< OZQ = m[tex]\because m\angle OZP=62[/tex]Substitute the measures of the given angles in the equation above
[tex]\therefore125=62+m\angle PZQ[/tex]Subtract 62 from both sides
[tex]\begin{gathered} \therefore125-62=62-62+m\angle PZQ \\ \therefore63=m\angle PZQ \end{gathered}[/tex]The measure of angle PZQ is 63 degrees
Note:enter your answer and show all steps that you use to solve this problem3.jaoquin buys 3 dozen lightbulbs.after changing the lightbulbs in his house, he has 15 lightbulbs left how many lightbulbs did he use?*btw the not is the same thing to my question I have for number 6*6. the empire state building in new York City is 1,250 feet tall. it has 103 floors. rounded to the nearest whole, what is the height of each floor?
Answer: Number of lightbulbs that he used = 21 lightbulbs
1 dozen of light bulbs = 12 light bulbs
Jaoquin buys 3 dozens
3 dozens of lightbulbs = 3 * 12 lightbulbs
3 dozens of lightbulbs = 36 lightbulbs
This means that :
The number of light bulbs Jaoquin bought = 36
The number of lightbulbs that remain = 15
The number of lightbulbs that he used = (Number of lightbulbs that he buys) - (Number of lightbulbs that remains)
Number of lightbulbs that he used = 36 - 15
Number of lightbulbs that he used = 21 lightbulbs
the points (-4,-2) and (8,r) lie on a line with slope 1/4 . Find the missing coordinate r.
The points (-4, -2) and (8, r) are located on a line of slope 1/4, We are asked to find the value of "r" that would make suche possible.
So we recall the definition of the slope of the segment that joins two points on the plane as:
slope = (y2 - y1) / (x2 - x1)
in our case:
1/4 = ( r - -2) / (8 - -4)
1/4 = (r + 2) / (8 + 4)
1/4 = (r + 2) / 12
multiply by 12 both sides to cancel all denominators:
12 / 4 = r + 2
operate the division on the left:
3 = r + 2
subtract 2 from both sides to isolate "r":
3 - 2 = r
Then r = 1
Carolina wants to find out how many different ways can she arrange the apps on her Iphone on the first row. The first row has space for 4 apps, and she has 12 apps to choose from
ANSWER
495 ways
EXPLANATION
Carolina has 12 apps to choose from and she only has space for 4 apps.
To find out how many ways she can do it, we will need to use combination.
That is:
[tex]^{12}C_4[/tex]Note: we use combination because the order of the apps is not a factor
So, we have that:
[tex]\begin{gathered} ^{12}C_4\text{ = }\frac{12!}{(12\text{ - 4)! 4!}}\text{ = }\frac{12!}{8!\text{ 4!}} \\ =\text{ 495 ways} \end{gathered}[/tex]She can arrange them in 495 ways.
the digits 1through 6 are used for a set of locker codes. suppose the digits cannot repeat. find the number of possible two digit codes and three digit codes. describe any pattern and use it to predict the number of possible five digit codes
SOLUTION
This is a permutation problem.
a) To find the number of possible two digits codes
[tex]^6P_2[/tex][tex]^6P_2=\frac{6!}{(6-2)!}[/tex][tex]\begin{gathered} =\frac{6!}{4!} \\ =\frac{720}{24} \\ =30\text{ ways} \end{gathered}[/tex]There are 30 possible two-digit codes pattern.
b) To find the number of three digits codes
[tex]\begin{gathered} ^6P_3=\text{ }\frac{6!}{(6-3)!} \\ \text{ =}\frac{6!}{3!} \\ \text{ =}\frac{720}{6} \\ \text{ = 120 ways} \end{gathered}[/tex]There are 120 possible three-digit codes pattern.
Any other pattern can be calculated using
[tex]\begin{gathered} ^6P_r \\ \text{where r is the number of digits code (1,2,3,4,5,6)} \end{gathered}[/tex]So to predict the number of possible five-digit codes will be:
[tex]^6P_5[/tex][tex]\begin{gathered} =\frac{6!}{(6-5)!} \\ =\frac{6!}{1!} \\ =720\text{ways} \end{gathered}[/tex]There are 720 different possible five-digit codes
the answer of this question is 720 ways
Eddie brought his DVD set to the secondhand store to sell he was paid for all three DVDs in the set before he left Eddie used $15.70 of his earnings to purchase a pair of headphones had $2.30 remaining which equation can you use to find the amount of money Eddie received for each DVD
15.70(d-3)=2.30
3d-15.70=2.30
15.70d-3=2.30
3(d-15.70)=2.30
Eddie brought his DVD set to the secondhand store to sell he was paid for all three DVDs in the set before he left Eddie used $15.70 of his earnings to purchase a pair of headphones had $2.30 remaining which equation can you use to find the amount of money Eddie received for each DVD:
15.70(d-3)=2.30
3d - 15.70 = 2.30
15.70d-3=2.30
3(d-15.70)=2.30
Find all the solutions and if there is an extraneous solution, identify them and explain why they are extraneous.
ANSWER
Solution: b = 3
It is extraneous
EXPLANATION
We want to solve the equation given and to see if there are any extraneous solutions.
We have:
[tex]\begin{gathered} \frac{7}{b\text{ + 3}}\text{ + }\frac{5}{b\text{ - 3}}\text{ = }\frac{10b}{b^2\text{ - 9}} \\ \Rightarrow\text{ }\frac{7}{b\text{ + 3}}\text{ + }\frac{5}{b\text{ - 3}}\text{ = }\frac{10b}{(b\text{ + 3)(b - 3)}} \\ \text{Multiply both sides by (b + 3)(b - 3):} \\ \Rightarrow\text{ }\frac{7(b+3)(b\text{ - 3)}}{b\text{ + 3}}\text{ + }\frac{5(b\text{ + 3)(b - 3)}}{b\text{ - 3}}\text{ = }\frac{10b(b\text{ + 3)(b - 3)}}{(b\text{ + 3)(b - 3)}} \\ 7(b\text{ - 3) + 5(b + 3) = 10b} \\ 7b\text{ - 21 + 5b + 15 = 10b} \\ \text{Collect like terms:} \\ 7b\text{ + 5b - 10b = 21 - 15} \\ 2b\text{ = 6} \\ Divide\text{ both sides by 2:} \\ b\text{ = }\frac{6}{2} \\ b\text{ = 3} \end{gathered}[/tex]That is the solution to the equation.
To find if the solution is extraneous, we will insert the value of b = 3 into the original equation.
That is:
[tex]\begin{gathered} \Rightarrow\text{ }\frac{7}{3\text{ + 3}}\text{ + }\frac{5}{3\text{ - 3}}\text{ = }\frac{10(3)}{(3\text{ + 3)(3 - 3)}} \\ \frac{7}{6}\text{ + }\frac{5}{0}\text{ = }\frac{30}{(6)(0)} \\ \frac{7}{6}\text{ + }\frac{5}{0}\text{ = }\frac{30}{0} \end{gathered}[/tex]An extraneous solution is a solution that derives from solving a rational equation but does not exactly satisfy the original equation, that is, it is invalid for the equation.
By inserting b = 3 into the equation, we see that the equation is undefined.
Therefore, since b = 3 is a solution, but it does not satisfy the equation, it is an extraneous solution.
For triangle ABC, AB = 3 cm and BC = 5 cm.Which could be the measure of AC?A 2 cmB 4 cmC 8 cmD 15 cm
ANSWER
2, 4 and 8
EXPLANATION
We have that in a triangle ABC, AB = 3 cm and BC = 5 cm.
To find the possible length of AC, we can apply the triangle inequality theorem.
It states that in any triangle, the sum of the lengths of any two sides must be greater than or equal to the length of the remaining side.
This means that:
[tex]\begin{gathered} AB\text{ + AC }\ge\text{ BC} \\ \text{and } \\ AB\text{ + BC }\ge\text{ AC} \\ \text{and} \\ AC\text{ + BC }\ge\text{ AB} \end{gathered}[/tex]So, we have that:
[tex]\begin{gathered} 3\text{ + AC }\ge\text{ 5 }\Rightarrow\text{ AC }\ge\text{ 2} \\ 3\text{ + 5 }\ge\text{ AC }\Rightarrow\text{ AC }\leq\text{ 8} \\ AC\text{ + 5 }\ge3\Rightarrow\text{ AC }\ge\text{ -2} \end{gathered}[/tex]We have to disregard the third line, since the length of a triangle side can only be positive.
So, using the first 2 lines, we see that:
[tex]2\text{ }\leq\text{ AC }\leq\text{ 8}[/tex]This means that from the options, the measure of AC can either be 2, 4 or 8.
The graph models the heights, in feet, of two objectsdropped from different heights after x seconds.Which equation represents g(x) as a transformation off(x)?y45+O g(x) = f(x) -5O g(x) = f(x-5)O g(x) = f(x) + 5O g(x) = f(x + 5)40+35y = f(x)30-25+20-15+10+5+ly = g(x)0.5 1.0 1.5 20
For this problem we know that y=f(x) at x=0 is 5 units above y=g(x). So then the best solution for this case it seems to be:
[tex]f(x)=g(x)+5[/tex]And solving for g(x) we got:
[tex]g(x)=f(x)-5[/tex]Y=-x^2+x+12 write in intercept form and show work
Given that y= x^2+x+12, to write the expression in an intercept form we need to factorize the expression.
[tex]y=-x^2+x+12[/tex]The intercept form is of the format
[tex]y=a(x\pm p)(x\pm q)_{}[/tex]This is obtained by factoring the quadratic equation above
[tex]\begin{gathered} y=-x^2+4x-3x+12 \\ y=-x(x-4)-3(x-4) \\ y=(x-4)(-x-3) \\ y=-1(x+3)(x-4) \end{gathered}[/tex]Hence, the intercept form of the equation is y= -1 (x + 3) ( x - 4 )
960 watts hour per how many watts hour does it consume in 4 days and 6 hours
Answer:
Explanation:
[tex]undefined[/tex]Fill in the table using this function rule. y = -10x +3 y X 6 ? 1 0 a 1
the function is
[tex]y=-10x+3[/tex]we must replace the value of x and obtain y
x=-5
[tex]\begin{gathered} y=-10(-5)+3 \\ y=50+3 \\ y=53 \end{gathered}[/tex]x=-1
[tex]\begin{gathered} y=-10(-1)+3 \\ y=13 \end{gathered}[/tex]x=0
[tex]\begin{gathered} y=-10(0)+3 \\ y=3 \end{gathered}[/tex]x=1
[tex]\begin{gathered} y=-10(1)+3 \\ y=-7 \end{gathered}[/tex]How many different three-digit numbers can be written using digits from the set 5, 6, 7, 8, 9 without any repeating digits?A. 625B. 20C. 120D. 60
Given:
The given numbers are 5,6,7,8,9.
Required:
Find the way so three-digit numbers can be written using digits from the sets 5, 6, 7, 8, 9 without any repeating digits.
Explanation:
Let n is the total number then the way to write m digits number is given by the formula:
[tex]A(n,m)=\frac{n!}{(n-m)!}[/tex]So the way to write 3 digits numbers are:
[tex]\begin{gathered} A(5,3)=\frac{5!}{(5-3)!} \\ =\frac{5!}{2!} \\ =5\times4\times3 \\ =60 \end{gathered}[/tex]Final Answer:
Option D is the correct answer.
Yesterday, Alan had k baseball cards. Today, he gave 19 away. Using k, write an expression for the number of cards Alan has left.
Answer:
k-19
Step-by-step explanation:
If Alan had k baseball card and gave 19 away then he would have 19 less then k
Answer:
K - 19= X
Step-by-step explanation:
I hope this helps!
The Environmental Protection Agency (EPA) fuel economy estimates for automobile models tested recently predicted a mean of 30.8 miles per gallon, with a standard deviation of 4.1 miles per gallon. Assume that a Normal model applies. Find the probability that a randomly selected automobile will average: 1. Less than 28 miles per gallon. Chapter 6 Assignment 2. More than 26 miles per gallon.
I need much help with this normal distribution question.
The normal distribution, often known as the Gaussian distribution, is a symmetric probability distribution about the mean.
What is meant by normal distribution?The probability density function for a continuous random variable in a system defines the Normal Distribution.
A data collection with a normal distribution is put up so that the majority of the values cluster in the middle of the range and the remaining values taper off symmetrically in either direction.
The normal distribution, often known as the Gaussian distribution, is a symmetric probability distribution about the mean. This shows that data close to the mean occur more frequently than data far from the mean. On a graph, the normal distribution is represented by a "bell curve."
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UsetheprimefactorsmethodtofindtheGCFof76,190,and931.
There are several ways to calculate the GCF
Let's use the Prime Factorization.
1) List the numbers in a row. As we can see, 76, 190 are both divisible by 2
So le's start dividing by the prime number 2, up to next divisible prime number as it follows:
As we can see the Greatest Common Divisor to both 76,190 and 931 is the prime number 19
Therefore, we can state the GCD of 76,190, 931 as 19
Nick skates 2 1/8 miles in 1/2 of an hour. What is Nick's average speed, in miles per hour ?
Average speed = distance / time
From the question;
distance = 2 1/8 miles = 17/8 miles
time = 1/2
substitute the values into the formula;
[tex]\text{Average sp}eed\text{ =}\frac{\frac{17}{8}}{\frac{1}{2}}[/tex][tex]=\frac{17}{8}\times\frac{2}{1}[/tex][tex]=\frac{17}{4}[/tex][tex]=4\frac{1}{4}\text{ miles per hour}[/tex]Determine if the two triangles shown are similar. If so, write the similarity statement.Question options:A) Impossible to determine.B) ΔBCG ∼ ΔEFGC) ΔGCB ∼ ΔGFED) The triangles are not similar.
ANSWER
Option D: The triangles are not similar
STEP BY STEP EXPLANATION
Now, two (2) triangles are said to be similar if the three (3) angles of triangle A are congruent or equal to the corresponding three (3) angles of triangle B.
If you take a close look at the two (2) triangles, you will notice that the only angle in ∆BCG that is equal to the corresponding angles in ∆EFG is ∆BGC; the two (2) remaining angles in ∆BCG are not congruent with the two (2) corresponding angles in ∆EFG
Hence, it can be concluded that both triangles are not similar.
solve for x. then find the missing piece(s) of the parallelogram for #7
Let us find the angles of the parallelogram below
[tex]\begin{gathered} 2x+30 \\ x=40 \\ 2(40)+30 \\ 80+30 \\ 110^0 \end{gathered}[/tex][tex]\begin{gathered} 2x-10 \\ 2(40)-10 \\ 80-10 \\ 70^0 \end{gathered}[/tex]Theorem+: opposite angles of a parallelogram are the same
Hence the angles of the parallelogram are 110, 70, 110, and 70
hi I'm 9 years old my name is Emma can
Given:
Perimeter = 40 feet,
The measure of the four sides is 11 feet, g, 11 feet, and g.
We know that the perimeter = the sum of the four sides.
[tex]\text{perimeter =11+g+11+g}[/tex]Replace perimeter =40, we get
[tex]\text{40=11+g+11+g}[/tex]Adding 11 and 11, we get
[tex]\text{40=11+11+g+g}[/tex][tex]\text{40=22+g+g}[/tex]a digital music player is marked down from its list price of $249.99 to a sale price of $194.99. What is the discount rate?
The discount rate of the digital player is 22%
How to determine the digital player's discount rate?From the question, we have the given parameters:
List price = $249.99
Sales price = $194.99
Start by calculating the change in the price.
This is calculated as follows
Change = List price - Sales price
So, we have
Change = $249.99 - $194.99
Evaluate the difference
Change = $55
The discount rate of the digital player is then calculated as
Discount = Change/List price x 100%
This gives
Discount = 55/249.99 x 100%
Evaluate
Discount = 22%
Hence, the discount rate is 22%
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In a group of 80 animals, 32 are dogs. Dogs make upwhat percent of the animals in the group?A. 32.00B. 28.6C. 35.5D. 38.00E 40.00
Let's calculate the percentage of dogs in the animal group
[tex]\begin{gathered} P=\frac{32}{80} \\ P=0.40 \\ P=40\text{ \%} \end{gathered}[/tex]The answer would be 40%.
2 x— =-------7 x+ 10x = ???
Answer:
x = 4
Explanation:
Given the expression;
2/7 = x/x+10
Cross multiply
2(x+10) = 7x
Expand the bracket
2x + 20 = 7x
Subtract 7x from btoh sides
2x+20-7x = 7x - 7x
2x-7x+20 = 0
-5x + 20 = 0
-5x = -20
Divide both sides by -5;
-5x/-5 = -20/-5
x = 4
hence the value of x is 4
The ratio of 1.2 to 32 is equal to the ratio of 3.6 to____.
Answer:
96
Step-by-step explanation:
let the number be x then
1.2x=32
x=80/3
again
3.6x
3.6×80/3
96
The denominator of a fraction is five more than twice the numerator if both the numerator and the denominator are decreased by three the simplified result is 1/4 find the original fraction
Answer:
7/19
Step-by-step explanation: we could get two equations from the question if we set the denominator as x and the numerator as y:
1: x=2y+5
2:(y-3)/(x-3)=1/4
cross multiply
4(y-3)=1(x-3)
4y-12=x-3
x=4y-9
3: Then we can choose one of them and minus by another one
x-x=4y-2y-(9+5)
0=2y-14
2y=14
y=7
Then we only have to plug in
x=2*7+5
x=14+5
x=19
Jane invested her savings in two investment funds. The $2000 that she invested in Fund A returned a 3% profit. The amount that she invested in Fund B returned a 10% profit. How much did she invest in fund B, if both funds together returned a 8% profit?
Fund A, Jane invested $2000 and has a profit of 3%
Profit at Fund A is :
[tex]\$2000\times0.03=\$60[/tex]at Fund B, let $x be the amount she invested that gives her a profit of 10%
The profit at Fund B is :
[tex]\$x\times0.10=\$0.10x[/tex]It is said that the total amount she invested returned a 8% profit
The total amount she invested is :
[tex]\$2000+\$x[/tex]and the 8% profit of her total investment is :
[tex](2000+x)\times0.08=160+0.08x[/tex]Now we need to equate the sum of her profits from Fund A and Fund B, and this must be equal to the 8% profit.
3% Profit at Fund A = $60
10% Profit at Fund B = $0.10x
8% Profit at both funds together = 160 + 0.08x
[tex]\begin{gathered} 60+0.10x=160+0.08x \\ 0.10x-0.08x=160-60 \\ 0.02x=100 \\ x=\frac{100}{0.02}=5000 \end{gathered}[/tex]Therefore, the amount she invested in Fund B is $5000
If the formula x=1/n, is used to find the mean of the following sample, what is the value of n? 2, 63, 88, 10, 72, 99, 38, 19
Given:
The formula is:
[tex]x=\frac{1}{n}\sum_{i=1}^nx_i[/tex]Series is:
[tex]2,63,88,10,72,99,38,19[/tex]Find-:
The value of "n"
Explanation-:
In the given formula "n" represent the number of member in a series.
Given series is:
[tex]2,63,88,10,72,99,38,19[/tex]The number of members is:
The members are 8.
So the value of "n" is:
[tex]n=8[/tex]The value of "n" is 8.
Answer: The answer to this problem is 6
Step-by-step explanation: i took the quiz, this is the correct answer.
Which value of x proves that the two triangles above are similar? 42.7 ft 26.7 ft 10 ft 25.6 ft
Explanation
Step 1
we have two triangles
ACE and BCD
if the triangles are similar, then the ratio of the sides must be the same:
[tex]\begin{gathered} \frac{\text{red line}}{purple\text{ line}}=\frac{blue\text{ line}}{\text{green line}} \\ \text{replacing} \\ \frac{16+x}{32}=\frac{x}{20} \end{gathered}[/tex]Step 2
solve for x
[tex]\begin{gathered} \frac{16+x}{32}=\frac{x}{20} \\ \text{cross multiply} \\ 20(16+x)=32\cdot x \\ 320+20x=32x \\ \text{subtrac 20x in both sides} \\ 320+20x-20x=32x-20x \\ 320=12x \\ \text{divide both sides y 12} \\ \frac{320}{12}=\frac{12x}{12} \\ \text{ x=26.66} \end{gathered}[/tex]rounded
[tex]x=26.7\text{ }[/tex]I hope this helps you
What is the solution to the following system of equations. Enter your answer as an ordered pair.3x+2y=17and4x+6y=26As an ordered pairHelp me pls
The system of equation are:
[tex]\begin{gathered} 3x+2y=17 \\ 4x+6y=26 \end{gathered}[/tex]to solve this problem we can solve the second equation for x so:
[tex]\begin{gathered} 4x=26-6y \\ x=6.5-1.5y \end{gathered}[/tex]Now we can replace x in the firt equation so:
[tex]3(6.5-1.5y)+2y=17[/tex]and we can solve for y so:
[tex]\begin{gathered} 19.5-4.5y+2y=17 \\ 19.5-17=2.5y \\ 2.5=2.5y \\ \frac{2.5}{2.5}=1=y \end{gathered}[/tex]Now we replace the value of y in the secon equation so:
[tex]\begin{gathered} x=6.5-1.5(1) \\ x=5 \end{gathered}[/tex]So the solution as a ordered pair is:
[tex](x,y)\to(5,1)[/tex]