Given that :
[tex]f(x)\text{ = 5x + 2}[/tex]We can prove that :
[tex]g(x)\text{ = }\frac{x\text{ -2}}{5}[/tex]is it's inverse doing the following:
Step 1. Set y = f(x):
[tex]y\text{ = 5x + 2}[/tex]Step 2. Switch the variables:
[tex]x\text{ = 5y + 2}[/tex]Then we solve for y:
[tex]\begin{gathered} 5y\text{ = x - 2} \\ \text{Divide both sides by 5} \\ y\text{ = }\frac{x\text{ -2}}{5} \end{gathered}[/tex]Step 3. The inverse of :
[tex]g(x)\text{ = }\frac{x-2}{5}[/tex]can be found in a similar way.
[tex]\begin{gathered} y\text{ = }\frac{x-2}{5} \\ x\text{ = }\frac{y-2}{5} \\ \text{Cross}-\text{Multiply} \\ 5x\text{ = y -2} \\ y\text{ = 5x + 2} \end{gathered}[/tex]This tells us that f(x) and g(x) are one to one functions are f(x) is the mirror image of g(x)
write an equation in point slope form that passes through (-4,-6) and is parallel to y= -7/2x +6. I added the pic for better information
as the line is parallel to the other line. They have the same slope. So the equation is:
[tex]y+6=-\frac{7}{2}(x+4)[/tex]If x = 8 units and y = 24 units, then what is the volume of the square pyramid shown above?
In this problem, we want to find the volume of a pyramid. In general, the formula for the volume of a pyramid is
[tex]V=\frac{1}{3}Bh[/tex]where B represents the base shape's area, and h represents the height.
From the image, we can see the base shape is a square, and we can use the formula:
[tex]V=\frac{1}{3}x^2y[/tex]Note: the area of a square is the side-length squared, and since we know the side length is labeled x, we can update the formula as we did above.
We are given x = 8 and y = 24, so we can substitute and simplify to find the volume:
[tex]\begin{gathered} V=\frac{1}{3}(8)^2(24) \\ \\ V=\frac{1}{3}(64)(24) \\ \\ V=512 \end{gathered}[/tex]The final volume is 512 cubic units.
The formula used to calculate the value of a savings accounty =(1+)120What does theafter t years is A(t)=0.04= 1500 1+120.04fraction represent?12y=a(1)aeAthe daily interest rateB how long the money has been in the accountCthe monthly interest rateD the starting balance in the account
We have here the formula for Compound Interest:
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]Where:
• A is the accrued amount.
,• P is the Principal (the original amount of money, the starting amount of money).
,• r is the interest rate.
,• n is the number of times per year compounded.
,• t is the time in years.
When we have that n is equal to 12, we are talking here about that the amount of money is being compounded monthly (we have 12 months in a year, 12 periods, n = 12). Therefore, we are dividing the rate, r, by the number of compoundings per year, n, and this is the rate per each new compounding period of time, r/n, and, in this case, n = 12 (monthly interest rate).
Therefore, in few words, the fraction (0.04/12) is the monthly interest rate (option C).
[If we see the other options, we have:
• The daily interest rate would be given by 0.04/365.
,• How long the money has been in the account is time, t.
,• The starting balance in the account is the Principal, P. ]
Mason was practicing free throws at basketball practice he made 5 throws every 2 he missed
Mason made 3 correct throws as every second he missed
x^2 - 9x - 36 = 0Use zero product property. Solve for x
Given the Quadratic Equation:
[tex]x^2-9x-36=0[/tex]You need to remember that the Zero Product Property states that if:
[tex]ab=0[/tex]Then:
[tex]a=0\text{ }or\text{ }b=0[/tex]In this case, you can factor the given equation by finding two numbers whose sum is -9 and whose product is -36. These numbers are 3 and -12. Then:
[tex](x+3)(x-12)=0[/tex]Based on the Zero Product Property, you know that:
[tex](x+3)=0\text{ }or\text{ }(x-12)=0[/tex]Then, by solving each part by "x", you get:
[tex]x=-3\text{ }or\text{ }x=12[/tex]Hence, the answer is:
[tex]x=-3\text{ }or\text{ }x=12[/tex](1,-4) (-2,5) in slope intercept form
We want the equation of the line through the points (1, -4) and (-2, 5)
So we start by finding the slope of the segment that joins those two points using the formula for slope:
slope = (y2 - y1) / (x2 - x1)
slope = (5 - -4) / (-2 - 1) = 9 / (-3) = -3
Then the slope is -3
Now we use the general slope-intercept form of a line:
y = m x + b
with m = -3
y = -3 x + b
and request one of the points to be on the line in order to determine "b"
-4 = -3 (1) + b
- 4 = -3 + b
add 3 to both sides to isolate b on the right
- 4 + 3 = b
then b = -1
Then the equation of the line is:
y = -3 x - 1
Find the y-intercept of a line that passes through (-2,6) and has a slope of -5
First find the equation of the line whose slope is -5 and passes through (-2, 6).
[tex]\begin{gathered} y-6=-5(x-(-2)) \\ y-6=-5(x+2) \\ y-6=-5x-10 \\ y=-5x-4 \end{gathered}[/tex]For y-intercept, substitute x = 0.
[tex]\begin{gathered} y=-5(0)-4 \\ y=-4 \end{gathered}[/tex]Thus, the y-intercept is -4.
Use the information in the table to complete the remaining information. Note: The section to the right of the table states "Rewrite the information from the table as a list of ordered pairs in the form of (height, shoe size).
Given:
A table represents the height and the shoe size of seven students
We will rewrite the information from the table as a list of ordered pairs in the form of (height, shoes size).
So, the order pairs will be as follows:
[tex]\lbrace(5^{\prime}6^{\prime}^{\prime},8),(5^{\prime}7^{\prime}^{\prime},9),(5^{\prime}8^{\prime}^{\prime},9),(5^{\prime}10^{\prime}^{\prime},10),(6^{\prime}6^{\prime}^{\prime},13),(5^{\prime}10^{\prime}^{\prime},12),(5^{\prime}8^{\prime}^{\prime},11)\rbrace[/tex]A mapping diagram:
The table could be represented by the relationship as shown in the following figure:
solve using the an=a1+(n-1)d formulaa1= -20, d=-4
Answer:
[tex]a_n=-20-4(n-1)[/tex]
Explanation:
We have the formula:
[tex]a_n=a_1+(n-1)d[/tex]And we are given:
a_1 = -20
d = -4
Thus:
[tex]a_n=-20+(n-1)(-4)=-20-4(n-1)[/tex]Use trigonometric ratios to determine the length of x in the right triangle below.71°5 cmRound your answer to the nearest tenth, and do not include "x ="or the units in your answer. Just enter the numericalvalue
For the given right triangle, one angle is 71 degree, and perpendicular side for angle 71 degree is x and base side is 5 cm.
Determine the measure of side x by using trigonometric ratio.
[tex]\begin{gathered} \tan 71=\frac{x}{5} \\ x=5\cdot\tan 71 \\ =14.5210 \\ \approx14.5 \end{gathered}[/tex]So value of x is 14.5 cm
Answer: 14.5
find the order pairs by following the tablegiven:y=x^2 -12x+36table of x : ?,5,9,4y : 0,?,1,?,?
x = ? , 5 , 9 , 4
y= 0, ? , 1 , ?
To find the missing x value, replace the matching value of y (0) in the equation and solve for x:
0 = x^2-12x +36
Apply the quadratic formula
[tex]\frac{-b\pm\sqrt[]{b^2-4\cdot A\cdot c}}{2\cdot a}=\frac{12\pm\sqrt[]{(-12)^2-4\cdot1\cdot36}}{2\cdot1}[/tex][tex]\frac{12\pm\sqrt[]{144-144}}{2}=\frac{12}{2}=6[/tex]For x = 5:
y= (5)^2-12 (5) +36 = 25-60+36 = 1
For y=1
1 =x^2-12x+36
0 = x^2-12x+36-1
0= x^2-12x+35
[tex]\frac{12\pm\sqrt[]{(12)^2-4\cdot1\cdot35}}{2\cdot1}=\frac{12\pm\sqrt[]{144-140}}{2}=\frac{12\pm2}{2}=\frac{14}{2}=7\text{ }[/tex]x =7
For x=9
y= (9)^2-12 (9)+36 = 81-108+36=9
For x=4
y= (4)^2-12(4)+35 = 16-48+36=4
My test is tomorrow and I need help with my review please!
It is important to know that the sample would be the starters and the population is all members.
So, let's use the mean formula to find the mean sample
[tex]\bar{x}=\frac{\Sigma(x)}{n}[/tex]Where n = 21.
Now, we have to add all the heights of the starter players.
[tex]\begin{gathered} \Sigma(x)=75+81+72+84+79+68+77+84+79+78+83+76+83+71+80+75+77+84+77+80+75 \\ \Sigma(x)=1638 \end{gathered}[/tex]Then, we divide
[tex]\bar{x}=\frac{1638}{21}=78[/tex]Therefore, the mean sample is 78 inches.Now, let's find the population mean using all team data instead
[tex]\mu=\frac{\Sigma(x)}{N}[/tex]Where N = 35. Let's do the same process.
[tex]\begin{gathered} \mu=\frac{75+80+69+77+70+77+68+81+80+77+80+84+72+69+79+84+75+78+84+76+79+83+72+77+75+76+79+84+78+76+71+83+75+69+77}{75} \\ \mu=\frac{2689}{35}=76.83 \end{gathered}[/tex]Therefore, the mean population is 76.83 inches.can someone help me with this question explain
Given expression [tex]\frac{2x^3+11x^2-21x}{x^2+3x}[/tex] is equivalent to [tex]2x+5 -\frac{36}{x+3}[/tex].
What do you mean by algebraic expression?
The concept of algebraic expressions is the use of letters or alphabets to represent numbers without providing their precise values. We learned how to express an unknown value using letters like x, y, and z in the fundamentals of algebra. Here, we refer to these letters as variables.
Variables and constants can both be used in an algebraic expression.
There are 3 main types of algebraic expressions which include:
Monomial Expression
Binomial Expression
Polynomial Expression
Given expression:
[tex]\frac{2x^3+11x^2-21x}{x^2+3x}[/tex] for [tex]x[/tex] ≠ -3 or 0.
Using long division method and euclid lemma
On dividing [tex]2x^3+11x^2-21x[/tex] by [tex]x^2+3x[/tex] we get, (given in the snip)
As we know division can be written as
dividend = divisor × quotient + remainder
[tex]2x^3+11x^2-21x = (2x+5)(x^2+3x)-36x[/tex]
⇒ [tex]2x^3+11x^2-21x = 2x+5 -\frac{36x}{x^2+3x}[/tex]
⇒ [tex]2x^3+11x^2-21x = 2x+5 -\frac{36}{x+3}[/tex]
Therefore, given expression [tex]\frac{2x^3+11x^2-21x}{x^2+3x}[/tex] is equivalent to [tex]2x+5 -\frac{36}{x+3}[/tex].
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a diver stands on a platform 15ft above a lake. he doesn't dive off the platform and lands in the water below. his height (H) above the lake after X seconds is shown on the graph below. what is the reasonable domain for the scenario?
The reasonable domain is when the time starts at 0 seconds and when the height is equal to 0 meters. Then, the domain is
[tex]0\le x\le3[/tex]which corresponds to the first option
List all zeros for the function f(x) = x^4 - 81. Be sure to include real and complex zeros.
The roots can be found as,
[tex]\begin{gathered} x^4-81=0 \\ (x^2+9)(x^2-9)=0 \\ (x^2+9)(x+3)(x-3)=0 \\ x=\pm3i,3\&-3 \end{gathered}[/tex]Thus, the roots of the equations are 3i,-3i,3 and -3.
hi Mr or Ms i need help with this problem please guide me step by step because I don't understand this. the part with the Hj=7x-27 do i bring that down and make an equation? or do i leave that there and make an equation with 3x-5 and x-1?
Let's begin by listing out the information given to us:
HJ = 7x - 27
HI = 3x - 5
IJ = x - 1
The key to solving this is to bear in mind that HJJ = HI + IJ
7x - 27 = 3x - 5 + x - 1
7x - 27 = 3x + x - 5 - 1
7x - 27 = 4x - 6
Subtract 4x from each side, we have:
7x - 4x - 27 = 4x - 4x - 6
3x - 27 = - 6
Add 27 to each side, we have:
3x - 27 + 27 = 27 - 6
3x = 21
Divide each side by 3, we have:
x = 7
represents holly records
The holly records a temperature at 15 below zero
This implies that the temperature i
Does the following equation have a unique solution, no solution or infinitely manysolutions:3x + 9 = 3x - 9A. Unique SolutionB. No SolutionC. Infinitely Many Solutions
The given equation is:
[tex]3x+9=3x-9[/tex]Solve the equation:
[tex]\begin{gathered} \text{ Subtract }3x\text{ from both sides:} \\ 3x+9-3x=3x-9-3x \\ \Rightarrow9=-9 \end{gathered}[/tex]Notice that the equation results in a contradiction. Hence, the equation has no solution.
The answer is B.
(Worth 50 points) Jell E. Bean owns the local frozen yogurt shop. At her store, customers serve themselves a bowl of frozen yogurt and top it with chocolate chips, frozen raspberries, and any of the different treats available. Customers must then weigh their creations and are charged by the weight of their bowls.
Jell E. Bean charges for five pounds of dessert, but not many people buy that much frozen yogurt. She needs you to help her figure out how much to charge her customers. She has customers that are young children who buy only a small amount of yogurt as well as large groups that come in and pay for everyone’s yogurt together.
A. Is it reasonable to assume that the weight of the yogurt is proportional to its cost? How can you tell?
B. Assuming it is proportional, make a table that lists the price for at least ten different weights of yogurt. Be sure to include at least three weights that are not whole numbers.
C. What is the unit rate of the yogurt? (Stores often call this the unit price.) Use the unit rate to write an equation that Jell E. Bean can use to calculate the amount any customer will pay.
D. If Jell E. Bean decided to start charging for each cup before her customers started filling it with yogurt and toppings, could you use the same equation to find the new prices? Why or why not?
Answer:
D.
Step-by-step explanation:
Which type of association does the scatter plot show? ту 00:00 Weak positive 00:00 Strong negative Strong positive Nonlinear
SOLUTION
From the diagram, we can see that Scatter Plot is NON- LINEAR.
It takes Anastasia 50 minutes to walk 3 1/2 miles to the park. At this rate, about how many minutes should it take her to walk 5 miles?
Answer:
about 71minutes
Explanation:
If it takes Anastasia 50 minutes to walk 3 1/2 miles to the park, then;
50 minutes = 3.5 miles
To get the time taken for her to walk 5miles;
x = 5miles
Divide both expressions
50/x = 3.5/5
Cross multiply
3.5x = 50*5
3.5x = 250
x = 250/3.5
x = 71.42miles
Hence it will take her about 71minutes to walk 5miles
caluculate the length of AC to 1 decimal place in the trapezium below.
Check the picture below.
usign the pythagorean theorem let's find the side CD, then let's get the side AC using the same pythagorean threorem.
[tex]\textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies \sqrt{c^2 - b^2}=a \qquad \begin{cases} c=\stackrel{hypotenuse}{16}\\ a=\stackrel{adjacent}{CD}\\ b=\stackrel{opposite}{7}\\ \end{cases} \\\\\\ \sqrt{16^2 - 7^2}=CD\implies \sqrt{207}=CD \\\\[-0.35em] ~\dotfill[/tex]
[tex]c^2=a^2+b^2\implies c=\sqrt{a^2 + b^2} \qquad \begin{cases} c=\stackrel{hypotenuse}{AC}\\ a=\stackrel{adjacent}{CD}\\ b=\stackrel{opposite}{11}\\ \end{cases} \\\\\\ AC=\sqrt{(\sqrt{207})^2~~ + ~~11^2}\implies AC=\sqrt{207 + 121}\implies \boxed{AC\approx 18.1}[/tex]
The equation and graph of a polynomial are shown below. The graph reaches its maximum when the value of x is 3. What is the y-value of this maximum? y=-x+6x-8
The maximum value of y is
[tex]Y=x^2+6x-8[/tex][tex]y=(3)^2+6(3)-8[/tex][tex]\begin{gathered} y=\text{ 9+18-8} \\ y=19 \end{gathered}[/tex]So, the maximum value of y when x=3 is 19
write the following in scientific notation:(5 • 10^13) (3 • 10^15)
Solution
Step 1
Obey the multiplication law of indices where
[tex]a^b\times a^{d\text{ }}=a^{b+d}[/tex]So that we will have
[tex]5\times3\times10^{13}\times10^{15}[/tex][tex]\begin{gathered} 15\times10^{13+15} \\ =15\times10^{28} \end{gathered}[/tex]Instructions: Determine the word or words that appropriately complete the sentence.
Okay, here we have this:
Considering the provided statement, we are going to identify wich is the correct word, so we obtain the following:
Remember that if two lines intersect, it means that there is a unique point (x, y) that satisfies both equations. According to this we have:
A system of linear equation will have one solution when the equation intersect.
For the function f(x)= 8/9+4xfind f-1(x)
The inverse of the function is f⁻¹(x) = x/4 - 2/9
The given function is :
f(x)= 8/9+4x
This can be written in the form of an equation such as
y = 8/9+4x
Now we have to find the value of x in terms of y
4x = y - 8 / 9
or, x = y/4 - 2/9
When a code is formed, the domain and its codomain are sometimes not clearly given, and without doing a calculation, one may just be aware that such a domain is a part of a bigger set.
A function from X to Y" often refers to an action that may accept a sufficient subset of X as its domain in mathematical analysis. A "function as from reals here to reals" might be used to explain the function of a valid real variable, for example.
Instead of the entire set of real numbers, a "function out from reals to the reals" refers to a group of real numbers with a non-empty open interval. This kind of job is
Hence the inverse of the function is given by f⁻¹(x) = x/4 - 2/9
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Directions - Graph the following slope intercept equation:y=-1/3x+4
Answer:
See below for graph
Explanation:
Given the slope-intercept equation:
[tex]y=-\frac{1}{3}x+4[/tex]To graph it, first, we find the x and y-intercepts.
When x=0
[tex]\begin{gathered} y=-\frac{1}{3}(0)+4 \\ y=4 \end{gathered}[/tex]We have the point (0,4).
When y=0
[tex]\begin{gathered} 0=-\frac{1}{3}x+4 \\ \frac{1}{3}x=4 \\ x=12 \end{gathered}[/tex]We have the point (12,0).
We then draw a line joining points (0,4) and (12,0).
describe the formations between f(x) = x-5 to g(x)=-6x+2
The given function is,
f(x) = x- 5
The transferred equation is,
g(x) = -6x + 2
So the transformation is,
[tex]g(x)=-6(f(x))-28[/tex]if the area of a rectangle is 6 m, then the dimension would be 2 meters by 3 meters?True or False
To be able to verify the statement, let's first recall the formula in getting the area of a rectangle:
B. When are the y-values the same? When are theydifferent?
B. When are the y-values the same? When are they
different?
Since there are absolute values, and the y =|x| and y =x will be the same when the values of x are positive and they're going to be different when the values for x are negative ones.
Like this:
y =x | y = |x|
3 y =3
-3 3