Answers
a. Graph -f(x):
By the transformations rules for functions, the graph of -f(x) is equal to a reflection over the x-axis, and a change of the y-coordinates:
[tex](x,y)\rightarrow(x,-y)[/tex]Then, given the function:
[tex]f(x)=\sqrt[]{x}[/tex]The graph of -f(x) is:is
The domain of the function is the set of all possible x-values, then it is:
[tex]\lbrack0,+\infty)[/tex]The range is the set of all possible values of the function, then it is:
[tex]\lbrack0,-\infty)[/tex]b. Graph f(x+2)-4:
The transformation f(x+2) is an horizontal translation left 2 units.
And the transformation f(x+2)-4 is a vertical translation down 4 units.
Then, the coordinates of this graph in comparison to the given graph are:
[tex](x,y)\rightarrow(x-2,y-4)[/tex]Then for the point (1,1) the new coordinates are (1-2,1-4)=(-1,-3).
For (4,2): the new coordinates (4-2,2-4)=(2,-2)
For (9,3): the new coordinates (9-2,3-4)=(7,-1)
The graph is:
The domain of this function is:
[tex]\lbrack-2,+\infty)[/tex]And the range is:
[tex]\lbrack-4,+\infty)[/tex]
Related Questions
(Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression.) And determine the quadrants of A+B and A-B.
Answers
Given that:
[tex]\cos A=\frac{5}{13}[/tex]Where:
[tex]0And:[tex]\cos B=\frac{3}{5}[/tex]Where:
[tex]0You need to remember that, by definition:[tex]\theta=\cos ^{-1}(\frac{adjacent}{hypotenuse})[/tex]Therefore, applying this formula, you can find the measure of angles A and B:
[tex]A=\cos ^{-1}(\frac{5}{13})\approx67.38\text{\degree}[/tex][tex]B=\cos ^{-1}(\frac{3}{5})\approx53.13\text{\degree}[/tex](a) By definition:
[tex]\sin \mleft(A+B\mright)=sinAcosB+cosAsinB[/tex]Knowing that:
[tex]\sin \theta=\frac{opposite}{hypotenuse}[/tex]You can substitute the known values into the equation in order to find the opposite side for angle A:
[tex]\begin{gathered} \sin (67.38\text{\degree)}=\frac{opposite}{13} \\ \\ 13\cdot\sin (67.38\text{\degree)}=opposite \\ \\ opposite\approx12 \end{gathered}[/tex]Now you know that:
[tex]\sin A=\frac{12}{13}[/tex]Using the same reasoning for angle B, you get:
[tex]\begin{gathered} \sin (53.13\text{\degree)}=\frac{opposite}{5} \\ \\ 5\cdot\sin (53.13\text{\degree)}=opposite \\ \\ opposite\approx4 \end{gathered}[/tex]Now you know that:
[tex]\sin B=\frac{4}{5}[/tex]Substitute values into the Trigonometric Identity:
[tex]\begin{gathered} \sin (A+B)=sinAcosB+cosAsinB \\ \\ \sin (A+B)=(\frac{12}{13})(\frac{3}{5})+(\frac{5}{13})(\frac{4}{5}) \end{gathered}[/tex]Simplifying, you get:
[tex]\begin{gathered} \sin (A+B)=\frac{36}{65}+\frac{20}{65} \\ \\ \sin (A+B)=\frac{36+20}{65} \end{gathered}[/tex][tex]\sin (A+B)=\frac{56}{65}[/tex](b) By definition:
[tex]\sin \mleft(A-B\mright)=sinAcosB-cosAsinB[/tex]Knowing all the values, you get:
[tex]\begin{gathered} \sin (A-B)=(\frac{12}{13})(\frac{3}{5})-(\frac{5}{13})(\frac{4}{5}) \\ \\ \sin (A-B)=\frac{36-20}{65} \\ \\ \sin (A-B)=\frac{16}{65} \end{gathered}[/tex](c) By definition:
[tex]\tan (A+B)=\frac{\tan A+\tan B}{1-\tan A\cdot\tan B}[/tex]By definition:
[tex]\tan \theta=\frac{opposite}{adjacent}[/tex]Therefore, in this case:
- For angle A:
[tex]\tan A=\frac{12}{5}[/tex]- And for angle B:
[tex]\tan B=\frac{4}{3}[/tex]Therefore, you can substitute values into the formula and simplify:
[tex]\tan (A+B)=\frac{\frac{12}{5}+\frac{4}{3}}{1-(\frac{12}{5}\cdot\frac{4}{3})}[/tex][tex]\tan (A+B)=\frac{\frac{56}{15}}{1-\frac{48}{15}}[/tex][tex]\tan (A+B)=\frac{\frac{56}{15}}{-\frac{11}{5}}[/tex][tex]\tan (A+B)=-\frac{56}{33}[/tex](d) By definition:
[tex]\tan (A-B)=\frac{\tan A-\tan B}{1+\tan A\cdot\tan B}[/tex]Knowing all the values, you can substitute and simplify:
[tex]\tan (A-B)=\frac{\frac{12}{5}-\frac{4}{3}}{1+(\frac{12}{5}\cdot\frac{4}{3})}[/tex][tex]\tan (A-B)=\frac{\frac{16}{15}}{\frac{21}{5}}[/tex][tex]\tan (A-B)=\frac{16}{63}[/tex](e) Knowing that:
[tex]\sin (A+B)=\frac{56}{65}[/tex][tex]\tan (A+B)=-\frac{56}{33}[/tex]Remember the Quadrants:
By definition, in Quadrant II the Sine is positive and the Tangent is negative.
Since in this case, you found that the Sine is positive and the Tangent negative, you can determine that this angle is in the Quadrant II:
[tex]A+B[/tex]While munching on some skittles, Bobby the Vampire lost a tooth that just so happened to be one of his fangs. He measured it to be 27 centimeters long. How long was his tooth in inches?
Answers
Answer: 10.6299
Step-by-step explanation:
There are 0.3937 inches in a cm., So, the length of the tooth in inches is [tex]27(0.3937)=10.6299 \text{ in }[/tex]
Rami practices his saxophone for 5/6 hour on 4 days each week.
How many hours does Rami practice his saxophone each week?
[] 2/[] Hr
Answers
Answer:
you take 5/6 and multiply it by 4/1.
which gives you 20/6
then reduce it by dividing the top number by the bottom number
which gives you 3 with a remainder of 2
you then place the remainder over the
This tells you he practicedfor 3 2/6
Step-by-step explanation:
I need help on 3 it says find the value of x round each answer to the nearest tenth
Answers
In problem 3, we have a right triangle with:
• cathetus ,a = 7,,
,• cathetus ,b = x,,
,• and hypotenuse ,h = 9,.
Pigatoras Theorem states that:
[tex]h^2=a^2+b^2.[/tex]Where a and b are cathetus and h the hypotenuse.
Replacing the data of the problem in the equation above, we have:
[tex]9^2=7^2+x^2.[/tex]Solving for x the last equation, we get:
[tex]\begin{gathered} 81=49+x^2, \\ x^2=81-49, \\ x^2=32, \\ x=\sqrt[]{32}\cong5.7. \end{gathered}[/tex]Answer
The value of x to the nearest tenth is 5.7.
17. A moving company charges a flat rate of $85 plus and additional $0.17 per mile driven. How far must the company drive to earn at least $100? Round to thenearest mile.x2 84x2 78x2 80x2 88
Answers
ANSWER
88
EXPLANATION
Let x be the miles driven and y be the earnings of the company when they drive for x miles.
If the company charges $0.17 per mile driven plus a flat rate of $85, then the total cost for moving x miles away is,
[tex]y=85+0.17x[/tex]Now, we have to find for how many miles, x, the company must drive to earn $100 or more,
[tex]85+0.17x\ge100[/tex]Subtract 85 from both sides,
[tex]\begin{gathered} 85-85+0.17x\geq100-85 \\ \\ 0.17x\ge15 \end{gathered}[/tex]And divide both sides by 0.17,
[tex]\begin{gathered} \frac{0.17x}{0.17}\ge\frac{15}{0.17} \\ \\ x\ge88.24 \end{gathered}[/tex]Hence, the company must drive for at least 88 miles to earn at least $100, rounded to the nearest mile.
Solve the right triangle. Write your answers in simplified, rationalized form. DO NOT ROUND!
Answers
base = FG = root 30
perpendicular HG = x
angle = 45 degrees,
we know that
[tex]\text{tan}\theta=\frac{perpendicualr}{base}[/tex][tex]\tan 45=\frac{HG}{\sqrt[]{3}}[/tex][tex]\begin{gathered} 1=\frac{HG}{\sqrt[]{3}} \\ HG=\sqrt[]{3} \end{gathered}[/tex]so, the value of HG = root 3
I need help with my statistics homework " -compute the range ,sample variance,and sample standard deviation cost."
Answers
We need to find the range, sample variance, and sample standard deviation cost.
The range is already given: $247. It can be found by subtracting the least from the greatest value:
[tex]466-219=247[/tex]Now, in order to find the sample variance and the sample standard deviation, we first need to find the mean of the sample:
[tex]\text{ mean }=\text{ }\frac{415+466+400+219}{4}=\frac{1500}{4}=375[/tex]Now, we can find the sample variance s² using the formula:
[tex]s²=\frac{\sum_{i\mathop{=}1}^n(x_i-\text{ mean})²}{n-1}[/tex]where n is the number of values (n = 4) and the xi are the values of the sample.
We obtain:
[tex]\begin{gathered} s²=\frac{(415-375)²+(466-375)²+(400-375)²+(219-375)²}{4-1} \\ \\ s²=\frac{40²+91²+25²+(-156)²}{3} \\ \\ s²=\frac{1600+8281+625+24336}{3} \\ \\ s²=\frac{34842}{3} \\ \\ s²=11614 \end{gathered}[/tex]Now, the sample standard deviation s is the square root of the sample variance:
[tex]\begin{gathered} s=\sqrt{11614} \\ \\ s\cong107.8 \\ \\ s\cong108 \end{gathered}[/tex]Therefore, rounding to the nearest whole numbers, the answers are:
Answer
range: $247
s² = 11614 dollars²
s ≅ $108
Find the exact value of sin A and cos A where a = 9 and b = 10 and
Answers
Given data:
a=9 , b = 10
use the phythagoras theorem,
[tex]c=\sqrt[]{a^2+b}^2[/tex][tex]\begin{gathered} c=\sqrt[]{9^2+10^2} \\ c=\sqrt[]{81+100} \\ =\sqrt[]{181} \end{gathered}[/tex]thus,
[tex]\sin A=\frac{opp}{\text{hypo}}[/tex][tex]\text{sinA}=\frac{9}{\sqrt[]{181}}[/tex]and,
[tex]undefined[/tex](A) The lines have different slopes and intersect at one point?(B) The lines have the same slope and y intercept.?(C) The lines are parallel and do not intersect.?(D) The lines have the same slope and y-intercept.?(E) Infinitely many solutions.?(F) They are the same line.? (G) No Solution ? (H) One solution.?
Answers
Recall that if two lines have the same slop then these two lines are parallel to each other.
the y-intercept is an x-coordinate of the point where the line intersects at the y-axis.
Consider graph 1.
The line intersects at one point and has different slopes, hence this has one solution.
(A) and (H) is true for graph 1.
Consider graph 2.
The lines have the same slope, therefore parallel but there is no y-intercept point.
This have infinitely many solutions.
They are also the same line.
(E) and (F) is true for this graph 2.
Consider graph 3.
The lines have the same slope and they are parallel.
It gives B) is correct
They do not intersect since parallel does not intersect each other.
It gives C) is correct
There is no solution since they do not intersect.
It gives G) is correct.
These lines have intercepted at -1 and -4.
It gives D) is correct
B), D), C), G), D) are correct for graph 3.
Results:
Options Graph
A) 1
B) 3
C) 3
D) 3
E) 2
F) 2
G) 3
H) 1
The scale factor on a floor plan is 1 in8 ft. What is the actual distance represented by a 2.5 inches on the floor plan
Answers
Given:
Scale factor = 1 inch 8ft
Floor Plan measurement = 2.5 inches
Solution
We should re-write the scale factor in units of inches only.
Recall that:
[tex]1\text{ f}eet\text{ = 12 inches}[/tex]Then, the scale-factor in inch:
[tex]\begin{gathered} \text{Scale factor = 1 + 8 }\times\text{ 12} \\ =\text{ 1 + 96 } \\ =\text{ 97 inches} \end{gathered}[/tex]We can then find the actual distance by multiplying the represented distance (2.5 inches) by the scale factor.
So, we have:
[tex]\begin{gathered} \text{Actual distance = Represented distance }\times\text{ scale factor} \\ =2.5\text{ }\times\text{ 97} \\ =\text{ }242.5\text{ inches} \end{gathered}[/tex]Answer: Actual distance = 242.5 inches
Use a calculator to find the values of X. Round sides to the nearest 10th and angles to the nearest whole number. Use sin or COS as appropriate.
Answers
Given the information about the triangle, we can use the cosine function on angle x to get the following:
[tex]\begin{gathered} \cos x=\frac{\text{adjacent side}}{hypotenuse}=\frac{7}{16} \\ \Rightarrow\cos x=\frac{7}{16} \end{gathered}[/tex]solving for x, we get:
[tex]\begin{gathered} \cos x=\frac{7}{16} \\ \Rightarrow x=\cos ^{-1}(\frac{7}{16})=64.1 \\ x=61.1\degree \end{gathered}[/tex]therefore, the value of x is 61.1
A country's population in 1994 was 182 million.In 2002 it was 186 million. Estimatethe population in 2004 using the exponentialgrowth formula. Round your answer to thenearest million.
Answers
we have the exponential formula
[tex]P=Ae^{(kt)}[/tex]so
we have
A=182 million ------> initial value (value of P when the value of t=0)
The year 1994 is when the value ot t=0
so
year 2002 -----> t=2002-1994=8 years
For t=8 years, P=186 million
substitute the value of A in the formula
[tex]P=182e^{(kt)}[/tex]Now
substitute the values of t=8 years, P=186 million
[tex]\begin{gathered} 186=182e^{(8k)} \\ e^{(8k)}=\frac{186}{182} \\ \text{apply ln both sides} \\ 8k=\ln (\frac{186}{182}) \\ k=0.0027 \end{gathered}[/tex]the formula is equal to
[tex]P=182e^{(0.0027t)}[/tex]Estimate the population in 2004
t=2004-1994=10 years
substitute the value of t in the formula
[tex]\begin{gathered} P=182e^{(0.0027\cdot10)} \\ P=187 \end{gathered}[/tex]therefore
the answer is 187 millionZaria is making pipe cleaner flowers for
her friends. She has 215 pipe cleaners.
How many flowers can she make with 3
pipe cleaners in each?
[?] flowers and pipe cleaners leftover
I
Answer
Enter
Answers
We can get the answer by dividing 215 by 3
What is dividing?
One of the four fundamental arithmetic operations, or ways to combine numbers to create new ones, is division. The other operations are multiplication, addition, and subtraction. The process of counting the instances in which one integer is included into the others is the most fundamental definition of the division of two natural numbers. This amount need not be an integer. For instance, if twenty apples are divided equally among four people, everyone will get five of them.
We can get the answer by dividing 215 by 3
215/3 = 71.67
Hence, 71 flowers are made
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Camera has Alyssa price of $768.95 before tax the sales tax rate is 8.25% final total find the total cost of the camera with sales tax included round your answer to the nearest cent as necessary
Answers
We know that the listed price of the camera is $768.95 and the tax rate is 8.25%.
To find the total cost we must use the next formula
[tex]\text{Total cost }=\text{listed price before tax+(listed price before tax }\cdot\text{rate tax)}[/tex]Now, we must replace the values in the formula using that 8.25% = 0.0825
[tex]\text{Total cost}=768.95+(768.95\cdot0.0825)[/tex]Simplifying,
[tex]\text{Total cost}=832.39[/tex]ANSWER:
$O32
what is the constant of proportionality in this proportional relationship? x 2 2-1/2 3 3-1/2 y 5/2 25/8 15/4 35/8. answer choices 4/5, 5/4, 4, 5
Answers
a proportional relationship has the following form:
yyy=
Which operation results in a binomial?+(3y6 + 4)(9y12 - 12y6 + 16)ResetNextntum. All rights reserved.
Answers
Answer:
Explanations:
According to the question, we need to determine which of the signs will fit in that will make the expression a binomial.
In simple terms, a binomial is a two-term algebraic expression that contains variable, coefficient, exponents, and constant.
We need to determine the required sign by using the trial and error method.
Using the positive sign (+) first, we will have:
[tex]\begin{gathered} =\mleft(3y^6+4\mright)+(9y^{12}-12y^6+16) \\ =3y^6+4+9y^{12}-12y^6+16 \\ =3y^6-12y^6+4+9y^{12}+16 \\ =-9y^6+9y^{12}+20 \end{gathered}[/tex]Using the product sign, this will be expressed as:
[tex]\begin{gathered} (3y^6+4)\cdot(9y^{12}-12y^6+16) \\ (3y^6+4)\cdot\lbrack(3y^6)^2-(3y^6)(4)^{}+4^2)\rbrack \end{gathered}[/tex]According to the sum of two cubes;
[tex]a^3+b^3=\mleft(a+b\mright)•(a^2-ab+b^2)[/tex]Comparing this with the expression above, we will see that a = 3y^6 and
b = 4. This means that the resulting expression above can be written as a sum of two cubes to have;
[tex]\begin{gathered} (3y^6+4)\cdot\lbrack(3y^6)^2-(3y^6)(4)^{}+4^2)\rbrack^{} \\ =(3y^6)^3-4(3y^6)^2+4(3y^6)^2+16(3y^6)+4(3y^6)^2-16(3y^6)+4^3 \\ \end{gathered}[/tex]Collect the like terms:
[tex]undefined[/tex]A batting cage charges a flat fee of $5 to practice and th Write an equation that models the charges (C) in terms of the number of bucket balls (b) that you use: O C = 1.50 b + 5 O C = 5 b + 1.50 6 Ob = 1.60 C + 5 Ob = 5 C + 1.50
Answers
we have
C -----> total charge
b -----> number of buckets of balls
Remmeber that
the equation of the line in slope intercept form is equal to
y=mx+b
where
m is the slope and b is the initial value or y-intercept
In this problem
m=$1.50 per buckey
b=$5
therefore
y=1.50x+5
or
C=1.50b+5
answer is first option(2i) - (11+2i) complex numbers
Answers
Hope this helps :)
What is the value of f(3) on the following graph?
Answers
Answer
f(3) = -2
Explanation
We are asked to find the value of f(3) from the graph.
This means we are looking for the value of f(x) or y on the graph, at a point where x = 3.
From the graph, we can see that at the point where x = 3, y = -2
Hence, f(3) = -2
Hope this Helps!!!
At a point on the ground 35 ft from base of a tree, the distance to the top of the tree is 1 ft more than 3 times the height of the tree. Find the height of the tree. The height of the tree is ___. (ft^3, ft^2, or ft)(Simply your answer. Round to the nearest foot as needed)
Answers
At a point on the ground 35 ft from the base of a tree, the distance to the top of the tree is 1 ft more than 3 times the height of the tree. Find the height of the tree
see the attached figure to better understand the problem
Applying the Pythagorean Theorem
(3h+1)^2=h^2+35^2
9h^2+6h+1=h^2+1,225
solve for h
9h^2-h^2+6h+1-1,225=0
8h^2+6h-1,224=0
Solve the quadratic equation
Using a graphing tool
the solution is
h=12 ftBill Jensen deposits $8500 with Bank of America in an investment paying 5% compounded semiannually. Find the interest in 6 years
Answers
Amount deposited = $8500
Rate = 5%
time for interest = 6years
Compounded semiannually
The formula for semiannually is
[tex]A=P(1+\frac{r}{100n})^{nt}[/tex]From the given information
P = $8500
r = 5
t = 6
Since the investment was compounded semiannually then
n = 2
Substitute the values into the formula
This gives
[tex]A=8500(1+\frac{5}{100\times2})^{6\times2}[/tex]Solve for A
[tex]\begin{gathered} A=8500(1+0.025)^{12} \\ A=8500(1.025)^{12} \\ A=11431.56 \end{gathered}[/tex]To find the interest
Recall
[tex]I=A-P[/tex]Where I, is the interest
Hence
[tex]\begin{gathered} I=\text{\$}11431.56-\text{\$}8500 \\ I=\text{\$}2931.56 \end{gathered}[/tex]The following probability table shows probabilities concerning Favorite Subject and Gender. What is the probability of selecting an individual who is a female or prefers science?
Gender Favorite Subject Total
Math English Science
Male 0.200 0.050 0.175 0.425
Female 0.100 0.325 0.150 0.575
Total 0.300 0.375 0.325 1.000
Answers
Answer: 2
Step-by-step explanation: 0.300 0.375 0.325 1.000 = 2
help meeeeeeeeeeeeeeeee
Answers
For the given function f(x) = x³ +x +1,g(x) =-x, composition of the given function is given by ( fog)(x) = -x³ -x +1 , ( g of)(x) = -(x³ +x +1).
As given in the question,
Given function :
f(x) = x³ +x +1
g(x) =-x
Composition of the given function is equal to :
(fog)(x) = f(g(x))
= f(-x)
= (-x)³ +(-x) +1
= -x³ -x +1
(g of)(x) = g(f(x))
=g(x³ +x+1)
= -(x³ +x+1)
Therefore, for the given function f(x) = x³ +x +1,g(x) =-x, composition of the given function is given by ( fog)(x) = -x³ -x +1 , ( g of)(x) = -(x³ +x +1).
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what is the final cost of the purchase at discount heaven?
Answers
First, let's sum the single costs of each item.
[tex]32+32+20=84[/tex]Because they are buying 1 jacket, 2 pairs of jeans, and 1 vest. So, the subtotal of these items is $84. (At Discount Heaven)
Then, we apply a 7% sales tax.
[tex]84+0.07\cdot84=84+5.88=89.88[/tex]As you can observe, the sales tax is $5.88 for all the items purchased, and the total cost they have to pay is $89.88.
Katie opened a savings account and deposited 1,000.00 as principal the account earns 4% interest compounded quarterly what is the balance after 6 years
Answers
P = $1000
r = 4% = 4/100 = 0.04
t = 6 years
Therefore,
[tex]\begin{gathered} A=P(1+\frac{r}{n})^{nt} \\ A=1000(1+\frac{0.04}{4})^{4\times6} \\ A=1000\times1.26973464853 \\ A=1269.73464853 \\ A=\text{ \$1269.73} \end{gathered}[/tex]AMNP ~ AQRP N x + 8 28 M 24 P 3x - 9 R Create a proportion and find the length of side PR*
Answers
Using thales theorem:
[tex]\begin{gathered} \frac{24}{28}=\frac{x+8}{3x-9} \\ 24(3x-9)=28(x+8) \\ 72x-216=28x+224 \\ 44x=440 \\ x=\frac{440}{44} \\ x=10 \\ PR=3(10)-9=21 \end{gathered}[/tex]Given the zeros of the following polynomial 2 +2i, 3, - 4 select the corresponding factors AND the polynomia O (x + 2i) (2 - 2i) (2 - 3)(x+4) o f(c) = 24 - 23 822 - 42 - 48 0 (2 – 2i) (x + 2i) (2+3)(– 4) 24 – 13 + 82 40 - 48 0 (0 - 2) (+2)(x - 3)(x +4) 24 - 23 - 822 + 4x + 48 1 3 N
Answers
a)
d)
1) Since the zeros of that polynomial were given, then we can write it into the factored form. Note that there are 4 zeros, so we can write:
[tex]\begin{gathered} (x-x_1)(x-x_2)(x-x_3)(x-x_4)=0 \\ (x-(-2i))(x-2i)(x-3)(x-(-4))=0 \\ (x+2i))(x-2i)(x-3)(x+4))=0 \end{gathered}[/tex]2) To find out the corresponding polynomial then we can expand it by rewriting "i" as -1
[tex]\begin{gathered} (x+2i))(x-2i)(x-3)(x+4) \\ (x+2i)(x-2i)=x^2+4 \\ (x-3)(x+4)=x^2+4x-3x-12 \\ (x^2+4)(x^2+x-12) \\ x^4+x^3-8x^2+4x-48 \end{gathered}[/tex]3) Hence, the answers are
a)
d)
[tex]x^4+x^3-8x^2+4x-48[/tex]Determine if the ordered pair provided is a solution to the linear system:3x+7y=1 and 2x+4y=0; (2,3) The system has no solution as the lines are parallel. The ordered pair (2, 3) is not a solution to the system. Yes, (2, 3) is a solution to the system. The system has no solution as the lines are perpendicular.
Answers
Answer:
The correct answer is:
The ordered pair (2, 3) is not a solution to the system.
Explanation:
The system given is:
[tex]\begin{cases}3x+7y={1} \\ 2x+4y={0}\end{cases}[/tex]If (2, 3) is a solution of the system, then replacing x = 2 and y = 3 on both equations should give a correct result and the same on both equatiions.
In the first equation;
[tex]\begin{gathered} 3\cdot2+7\cdot3=1 \\ 6+21=1 \\ 27=1 \end{gathered}[/tex]We can see that this result is not true, as 27 is not equal to 1.
In the second equation:
[tex]\begin{gathered} 2\cdot2+4\cdot3=0 \\ 4+12=0 \\ 16=0 \end{gathered}[/tex]Once again, a false result.
To see in the system has equations, let's solve for x in the second equation:
[tex]\begin{gathered} 2x+4y=0 \\ 2x=-4y \\ x=-2y \end{gathered}[/tex]Now, we can use substitution in the first equation:
[tex]3(-2y)+7y=1[/tex]And solve for y:
[tex]\begin{gathered} -6y+7y=1 \\ y=1 \end{gathered}[/tex]Now, we can find the value of x:
[tex]x=-2\cdot1=-2[/tex]The solution to the system is (-2, 1)
Thus, the correct option is "The ordered pair (2, 3) is not a solution to the system"
I need help with this practice problem solving This is the subject trigonometry
Answers
Given the fucntion:
f(x) = tanx
Let's graph the function and input the correct values in the box.
• To find the y-intercept of the function, input 0 for x and solve:
[tex]\begin{gathered} f(0)=\tan 0 \\ \\ f(0)=0 \end{gathered}[/tex]Therefore, the y-intercept is:
(0, 0)
• The period of the function:
The fundamental period of a tangent function is π.
Now, let's find points on the graph:
Therefore, the points are:
[tex]\mleft(-\frac{\pi}{3},-\sqrt{3}\mright),\mleft(-\frac{\pi}{4},-1\mright),\mleft(0,0\mright),\mleft(\frac{\pi}{4},1\mright),\mleft(\frac{\pi}{3},\sqrt{3}\mright)[/tex]ANSWER:
The tangent function's period is π . The y-intercept of the function is (0, 0).
The points are:
[tex](-\frac{\pi}{3},-\sqrt[]{3}),(-\frac{\pi}{4},-1),(0,0),(\frac{\pi}{4},1),(\frac{\pi}{3},\sqrt[]{3})[/tex]I think of a number.
I add 5 to it and then double the result.
I then subtract 10 from this answer.
I then subtract the original number I thought of.
Using algebra and a pronumeral to represent the number I think of, explain
why I get back to the number I started with.
Answers
Answer: [2(x + 5)] - 10 - x = 2x+10-10-x = 2x-x = x
Step-by-step explanation:
I think of a number, represented by the variable/pronumeral x.
I add 5 to it: x + 5
then double the result: 2(x + 5)
I then subtract 10 from this answer: [2(x + 5)] - 10
I then subtract the original number I thought of: [2(x + 5)] - 10 - x
Simplifying the expression will explain why you get the original number.
[2(x + 5)] - 10 - x = 2x+10-10-x = 2x-x = x.
