The graphs below have the same shape. f(x) = x2What is the equation of the graph of g(x)?10g(x)f(x)X10510-10O A. g(x) = (x+3)2B. g(x) = (x - 3)2C. g(x) = x2 - 3D. g(x) = x2 + 3
Answers
The equation of f(x) is
[tex]f(x)=x^2[/tex]The graph of g(x) is shifted 3 units to the left. This is a horizontal translation.
For horizontal translation, we follow the following rule >>>
Let parent function be f(x), then
• f(x+a) is the parent translated "a" units left
,• f(x-a) is the parent translated "a" units right
Thus, following the rule, we can clearly say that g(x) = f(x+3)
We can write >>
Related Questions
bvhftfgtfygygfygygftfghh vv g f f fyk jf khvy. ynnnnnnnnnnnnnn
Answers
what the??????????????
Graph the line y 3 on the axes shown below. Type of line: Choose one
Answers
We need to graph the line:
[tex]y=3[/tex]Notice that there is no restriction on the values of x. So, all the points with y-coordinate 3 belong to that line.
When we graph that line, we obtain:
Thus, this line is a horizontal line (parallel to the x-axis).
The students in Cassie's class got to choose between pizza and burgers for the celebration on the last day of school. 8 students picked the pizza. If there are 10 students in all in Cassie's class, what percentage of the students picked the pizza? Write your answer using a percent sign (%).
Answers
There is a total of 10 students in Cassie's class.
8 students choose Pizza
So, the percentage of the students who picked the pizza is 80%.
[tex]Percentage\%= \frac{Students who picked Pizza}{Total number of students in class} *100[/tex]
[tex]Percentage\%= \frac{8}{10}*100\%[/tex]
[tex]=\frac{800}{10}\%[/tex]
[tex]=80\%[/tex]
And 20% of students picked Burgers.
About Percentage
The Latin adverb "percent" means "by the hundred." The 16th century saw its invention. The abbreviation was later changed to %. Later, the period was eliminated, and the two words were merged to form the term "percent." Brief explanations employ the annotation sign %. Calculate your percentage of marks by comparing your final score to your overall score.
The percentage is a fraction or a ratio in which the value of the whole is always 100. For example, if Sam scored 30% marks in his math test, it means that he scored 30 marks out of 100. It is written as 30/100 in the fraction form and 30:100 in terms of ratio.
Percentage Definition:
The percentage is defined as a given part or amount in every hundred. It is a fraction with 100 as the denominator and is represented by the symbol "%".
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Solve e–5x = 7.4 for x correct to four decimal places. –0.40030.40030.8692–0.8692
Answers
Question:
[tex]e^{-5x}=7.4[/tex]Step 1: Apply the exponent rule but taking ln of both sides
[tex]\begin{gathered} e^{-5x}=7.4 \\ -5x=\ln 7.4 \end{gathered}[/tex]Step 2:Divide both sides by -5
[tex]\begin{gathered} -5x=\ln 7.4 \\ \frac{-5x}{-5}=\frac{\ln 7.4}{-5} \\ x=\frac{\ln7.4}{-5} \end{gathered}[/tex]Hence,
The value of x is
[tex]\begin{gathered} x=\frac{\ln7.4}{-5} \\ x=-4.003 \end{gathered}[/tex]Hence,
The final answer is = -0.4003
C lies at (1,5) and is the midpoint of AB. If A is at (3,2), find the coordinate for point B.(-1.8)(8.-1)(5.-1)(60)
Answers
Given:
The coordinates of C, the midpoint of AB, (X, Y)=(1, 5).
The coordinates of A, (x1, y1)=(3, 2).
Let the coordinates of B be (x2, y2).
The midpoint formula is given by,
[tex](X,\text{ Y)=(}\frac{x1+x2}{2},\text{ }\frac{y1+y2}{2})[/tex]Hence,
[tex]\begin{gathered} X\text{=}\frac{x1+x2}{2}\text{ ---(1)} \\ Y=\frac{y1+y2}{2}\text{ ---(2)} \end{gathered}[/tex]Substitute the known values in equation (1) and solve for x2.
[tex]\begin{gathered} 1=\frac{3+x2}{2} \\ 2=3+x2 \\ x2=2-3 \\ x2=-1 \end{gathered}[/tex]Hence, x2=-1.
Substitute the known values in equation (2) and solve for y2.
[tex]\begin{gathered} 5=\frac{2+y2}{2} \\ 5\times2=2+y2 \\ 10=2+y2 \\ y2=10-2 \\ y2=8 \end{gathered}[/tex]Therefore, the coordinates of point B is (x2,y2)=(-1, 8).
in July Leia sold 32 fruit bars what was her profit
Answers
Ai Mi was out at a restaurant for dinner when the bill came. Her dinner came to $9. After adding in a tip, before tax, she paid $11.79. Find the percent tip.
Answers
The percent tip which Ai mi added to the $9 dinner as required in the task content is; 31%.
What percent tip did Ai mi add to the dinner as described?It follows from the task content that the percent tip which Ai mi added to the dinner is to be determined by evaluation.
Since the dinner itself costs; $9 and she paid $11.79 after adding tip, it follows that the percent tip is the percentage change in price paid per unit original price as follows;
Percent tip = { ( 11.79 - 9 ) / 9} × 100%
Percent tip = 2.79/9 × 100%
Percent tip = 31%.
Therefore, the percent tip added by Ai mi to the original price of dinner is ; 31%.
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So far, Benny has run 3/2 miles, but that is only 2/5 of his total running distance. What is his total running
distance?
Answers
Step-by-step explanation:
this is 2/5 of his total.
that means we have to divide it by 2 (that delivers 1/5) and multiply by 5 (that delivers 5/5 or 1 = the whole).
in short : multiply by 5/2
3/2 × 5/2 = 15/4 miles = 3 3/4 miles
A bag contains 6 red marbles and 7 white marbles. Two marbles are drawn in succession without replacement. Find the probabilities of the following events:
1. The first marble drawn is red and the second is white.
2. Both marbles drawn are red.
Answers
Using it's concept, the probabilities are given as follows:
1. Red then white: 7/26.
2. Both red: 5/26.
What is a probability?The probability of an event in an experiment is calculated as the number of desired outcomes of the experiment divided by the number of total outcomes of the experiment.
For item 1, we have that:
For the first marble, the probability of it being red is of 6/13, as of the 13 marbles, 6 are red.Supposing that the first marble is red, the probability of the second being white is of 7/12, as of the 12 remaining marbles, 7 are white.Hence the probability is:
6/13 x 7/12 = 7/26.
For item 2, we have that:
For the first marble, the probability of it being red is of 6/13, as of the 13 marbles, 6 are red.Supposing that the first marble is red, the probability of the second being red is of 5/12, as of the 12 remaining marbles, 5 are red.Hence the probability is:
6/13 x 5/12 = 5/26.
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Three partners A, B, C start a business. B's Capital is four times C's capital
and twice A's capital is equal to thrice B's capital. If the total profit is Tk. 16500
at the end of a year, Find out B's share in it.
Answers
Suppose C's capital = x then
B's capital = 4x (Since B's Capital is four times C's capital)
A's capital = 6x ( Since twice A's capital is equal to thrice B's capital)
A : B : C =6x : 4x : x
= 6 : 4 : 1
B's share = 16500×411
= 1500 × 4 = 6000.
What is meant by Capital?
A factory and its equipment, intellectual property like patents, or the financial assets of a company or a person are all examples of things that provide value or benefit to their owners and fall within the wide definition of capital.
While money in and of itself might be considered capital, the term is most frequently used to refer to money that is being used for investments or productive purposes. In general, capital is an essential part of managing firm day-to-day and funding its expansion in the future.
Business capital may be generated via activities or obtained through debt or equity finance. Typical sources of funding are as follows:
individual savings
relatives and friends
Angel backers
financiers for startups (VC)
Corporations
State, municipal, or federal governments
Personal loans
Working or conducting business
getting an IPO to go public
Working capital, equity capital, and debt capital are the three types of capital that firms of all sizes commonly concentrate on when creating budgets. A company in the financial sector names trading capital as the fourth element.
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riya won a LCD TV in amall raffle draw , the tv screen measures 16 inches in height and 12 inches in width. find the hypotenuse of the TV
Answers
Step by step
Pythagorean theorem states
a^2 + b^2 = c^2
Solve for hypotenuse by substituting h & w for a and b and solve for c
16^2 + 12^2 = c^2
256 + 144 = c^2
400 = c^2
Take square root of both sides
20 = c
The tv screen diagonal = 20”
Jessica evaluates √2 on her calculator which
shows a value of 1.4142136.
She then writes √/2 =1.4142136.
Is she correct explain
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Generally, one should not write down values such as this directly from a calculator. √2 is an irrational number, which means that instead of writing it as a terminating decimal, it is best to write it in its exact form (√2) to ensure accuracy for further calculations.
The length of the base of an isosceles triangle is 49.96 meters. Each base angle is 31.43°. Find the length of each of the two equal sides of the triangle. Round to the hundredths place.
Answers
Given that:
- The triangle is isosceles.
- Its base is 49.96 meters.
- Each base angle is 31.43°.
You can draw the triangle. See the picture shown below (it is not drawn the scale):
Notice that the Isosceles Triangle can be divided into two equal Right Triangles. Then, you know that:
[tex]CD=BD=\frac{49.96m}{2}=24.98m[/tex]Since it is isosceles, the sides AB and AC have equal length.
Then, you can choose one of the equal Right Triangles and use the following Trigonometric Function in order to find the length of each equal side:
[tex]\cos \beta=\frac{adjacent}{hypotenuse}[/tex]In this case, you can set up that:
[tex]\begin{gathered} \beta=31.43\degree \\ adjacent=24.98 \\ hypotenuse=AC \end{gathered}[/tex]Therefore, substituting values and solving for AC, you get:
[tex]\begin{gathered} \cos (31.43\degree)=\frac{24.98}{AC} \\ \\ AC\cdot\cos (31.43\degree)=24.98 \end{gathered}[/tex][tex]\begin{gathered} AC=\frac{24.98}{\cos (31.43\degree)} \\ \\ AC\approx29.28 \end{gathered}[/tex]Hence, the answer is:
The length of the two equal sides of the triangle is:
[tex]length\approx29.28m[/tex]Jeff constructed a square inscribed in a circle:EFFDWhich provides enough justification to prove that CDEF is a square?All four angles of the quadrilateral are 90°.All four sides of the quadrilateral are congruent.O Opposite sides of the quadrilateral are parallel.The diagonals of the quadrilateral are perpendicular and congruent.
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A square is a quadrilateral with four equal straight sides and four right angles.
In this sense since the diagonals of a square bisect each other and meet at 90° and are congruent, we can conclude it is enough justification to prove that CDEF is a square
4. There are 6 red, 5 white, 3 blue, and 4 green marbles in a bag. What is the probability of selecting a red marble, given that a blue marble was already selected?5. While playing Blackjack, an Ace is dealt. To get Blackjack, or 21, a card worth 10 is needed. This could be a 10, Jack, Queen, or King. What is the probability of not getting Blackjack?
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Write the relation as a set of ordered pairs.
A relation. An arrow goes from negative 2 to 4, 0 to 6, 2 to 8.
a.
ordered pairs: {(4, –2), (0, 6), (2, 8)}
b.
ordered pairs: {(–2, 4), (0, 6), (2, 8)}
c.
ordered pairs: {(4, –2), (0, 6), (8, 2)}
d.
ordered pairs: {(–2, 4), (6, 0), (8, 2)}
Its not c.
Answers
The set of coordinate pairs that represents the relation is the one in option b.
{(–2, 4), (0, 6), (2, 8)}
How to write the relation as a set?
A relation maps elements "x" into elements "y", such that the notation used is:
An arrow that goes from x to y.A ordered pair fo the form (x, y)Here we know that:
An arrow goes from negative 2 to 4, 0 to 6, 2 to 8.
Then we have the coordinate pairs:
(-2, 4)
(0, 6)
(2, 8)
Then the correct option is B: {(–2, 4), (0, 6), (2, 8)}
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Answer:
b
Step-by-step explanation:
The scores of 12th-grade students on the National Assessment of Educational Progress year 2000 mathematics test have a distribution that is approximately Normal with mean μ = 300 and standard deviation σ = 35. (a) Choose one 12th-grader at random. What is the probability that his or her score is higher than 300? Higher than 335? Explain and show your work. (b) Now choose an SRS of four 12th-graders and calculate their mean score x. If you did this many times, what would be the mean and standard deviation of all the x-values? Explain and show your work. (c) What is the probability that the mean score for your SRS is higher than 300? Higher than 335? Explain and show your work.
Answers
a) To find the probability that the score is higher than 300 you have to find the Z-score for 300, by using the formula:
[tex]\begin{gathered} Z=\frac{x-\mu}{\sigma} \\ Z=\frac{300-300}{35}=\frac{0}{35}=0 \end{gathered}[/tex]The probability of x>300 P(z>0)=1-P(z<=0)
Using the Standard Normal Cumulative Probability Table, P(z<=0)=0.5
Then,
[tex]P(Z>0)=1-0.5=0.5[/tex]Now, you can do the same to find the probability that the score is higher than 335, let' see:
[tex]Z=\frac{335-300}{35}=\frac{35}{35}=1[/tex]The probability of x>335 is P(Z>1), then
[tex]P(Z>1)=1-P(Z\leq1)=1-0.8413=0.1587[/tex]These results mean that it is a 50% of probability that the score of the student chosen is greater than 300, and a 15.87% of probability that the score is greater than 335.
b) SRS=4, their mean score will be the same as the mean of the population = 300, the standard deviation of the sample is the standard deviation of the population divided by √n (n is the size of the sample=4).
[tex]\mu=300\text{ and }\sigma=\frac{35}{\sqrt[]{4}}=17.5[/tex]c) The probability that the mean score for the SRS is higher than 300 is:
[tex]\begin{gathered} Z=\frac{x-\mu}{\sigma} \\ Z=\frac{300-300}{17.5}=\frac{0}{17.5}=0 \end{gathered}[/tex][tex]P(Z>0)=1-P(Z\leq0)=1-0.5=0.5[/tex]The probability that the mean score for the SRS is higher than 335 is:
[tex]Z=\frac{335-300}{17.5}=2[/tex][tex]P(Z>2)=1-P(Z\leq2)=1-0.9772=0.0228[/tex]These results mean that it is a 50% of probability that the mean score of the SRS is greater than 300, and a 2.28% of probability that the mean score is greater than 335.
Donna and her husband are each starting a saving plan. Donna will initially set aside S50 and then add $20.55 every week to the savings. The amount A (in
dollars) saved this way is given by the function = 50+20.55N, where N is the number of weeks she has been saving.
Her husband will not set an initial amount aside but will add $80.55 to the savings every week. The amount B (in dollars) saved using this plan is given by the
function B=80.55 N.
Let T be total amount (in dollars) saved using both plans combined. Write an equation relating T to N. Simplify your answer as much as possible.
Answers
The total amount (in dollars) saved using both plans combined is T = 50 + 101.1N.
How to illustrate the equation?Based on the information, the function = 50+20.55N.
where N is the number of weeks she has been saving.
For the second function, this is illustrated as:
function B = 80.55 N.
Therefore, the total of the plans combined will be:
T = 50 + 20.55N + 80.55N
T = 50 + 101.1N
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Solve by graphing. If the population of a town is growing at a rate of 2.5% each year and the current population is 50,000. After how many years will the population reach 100,000 people. Round to the NEAREST whole number. Be sure to label your answer.
Answers
The situation describes an exponential growth, which can be expressed using the general formula:
[tex]y=a(1+r)^x[/tex]Where
a is the initial value
r is the growth rate, expressed as a decimal value
x is the number of times intervals
y is the final value after x time intervals
For the studied population, the growth rate is 2.5%, to express this number as a decimal value you have to divide it by 100:
[tex]\begin{gathered} r=\frac{2.5}{100} \\ r=0.025 \end{gathered}[/tex]The initial value is the current population of the town: a=50000
You can express the equation of exponential growth for this population as follows:
[tex]\begin{gathered} y=50000(1+0.025)^x \\ y=50000(1.025)^x \end{gathered}[/tex]We know that after x years the population will be y=100000, to determine how many years it will take to reach this value you have to equal the equation to 100000 and solve for x:
[tex]100000=50000(1.025)^x[/tex]-Divide both sides of the expression by 50000
[tex]\begin{gathered} \frac{100000}{50000}=\frac{50000(1.025)^x}{50000} \\ 2=(1.025)^x \end{gathered}[/tex]-Apply logarithm to both sides of the equal sign:
[tex]\begin{gathered} \log (2)=\log (1.025^x) \\ \log (2)=x\cdot\log (1.025) \end{gathered}[/tex]-Divide both sides by the logarithm of 1.025
[tex]\begin{gathered} \frac{\log(2)}{\log(1.025)}=\frac{x\cdot\log (1.025)}{\log (1.025)} \\ x\approx28.07\approx28 \end{gathered}[/tex]After approximately 28 years the population of the town will be 100,000.
Using the table, what is the average daily balance of the credit card for the May 1 - May 31 billing period? Round your answer to the nearest cent. Do not include a dollar sign or comma in your answer. For example, $5,678.00 should be entered as 5678.00.
Answers
The average daily balance for the credit card for the may 1 - may 2 billing period was 1566.13
From the table given, we have
The balance of the credit card from May 1 - May 5 was 2000 which is 5 days, from may 6- may 10 was 1600, which is again 5 days, from may 11 to may 20 was 1350, the interval is 10 days and 21 to may 31, 11 days the balance was 1550.
The avergae daily balance was
=[tex]\frac{(Balance (number of days))}{Total number of days}[/tex]
= [tex]\frac{2000(5)+1350(10)+1550(11)}{5+5+10+11}[/tex]
=[tex]\frac{48550}{31}[/tex]
=1566.13
So The average daily balance for the credit card for the may 1 - may 2 billing period was 1566.13
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write the ratio that represents the number of cars to total numbers of vehicles.A) 3/2B) 2/3C) 1/2D) 2/1
Answers
This is a simple question to be solved.
First we need to know the number of vehicles (there are 6 vehicles), and second we need to know the number of cars (there are 4 cars). So the relation between the number of cars and vehicles is ----> 4/6
But we can simplify this relation as follows and represent it in a simple way:
So the final answer is the letter B) 2/3
PLEASE HELP!!
A fair die is rolled 4 times. What is the probability of having no 1 and no 3 among the rolls? Round your answer to three decimal places.
Answers
Answer:
66.667%
Step-by-step explanation:
In a fair die, there are 6 possible rolls. Out of the 6, 1 number is chosen each time. Since orde does not matter in this problem, we will be applying combination, so this would be written as 6C1 x 4. In order to exclude 3 and 4, from 6, the choices must be narrowed down to 4. Written out as an equation, this would be 4C1 x 4. To get the percentage, simply divide the two equations.
(4C1 x 4)/(6C1 x 4) = 0.66667 = 66.667%
hope it will be helpful
2x+2y = 4 2x + 2y = 3 One Solution No Solutions Infinitely Many Solutions
Answers
The system has no solutions
Here, we want to solve the system of linear equations
As we can see, the exact expression is what we have on the left side of both equations
The only different thing is what we have on the right hand side
What this mean is that no values of x and y can satisfy both equations
With that in mind, we have it that the system of equations has no solutions
Sketch a graph representing f(x), indicating all intercepts and min or max points.
Answers
Given the function below;
[tex]f(x)=4-\frac{x^2}{8}[/tex]The x-intercept is the point where f(x) = 0 as shown:
[tex]\begin{gathered} 0=4-\frac{x^2}{8} \\ 0=32-x^2 \\ x^2=32 \\ x=\pm\sqrt{32} \\ x=\pm5.66 \end{gathered}[/tex]The x-intercept of the graph will be at (5.66, 0) and (-5.66, 0)
The y-intercept occurs at the. point where x = 0 to have:
[tex]\begin{gathered} f(0)=4-\frac{0^2}{8} \\ f(0)=4 \end{gathered}[/tex]The y-intercept is (0, 4)
The equivalent graphis as shown below
The graph shows that the function has a maxmum point at (0, 4) with no minimum point.
Blank 1 - 2850342043504625 Blank 2. - 20253035Blank 3 4350462550755225 Blank 4 20253035
Answers
The determinant of the matrix for the pineapple cake is 4350
The price of a pineapple cake is $30
The determinant of the matrix for the chocolate cake is 5075
The price of a chocolate cake is $35
Basically, what we want to do in this question is to form a set of linear equations then use matrix determinant method to solve for the unknowns in the linear equation.
Before we set up these equations,we need to use variables to represent the fruit prices;
Let p represent the price a of pineapple
Let c represent the price of a chocolate;
So let us proceed to form the linear equations;
The equation for the weekdays sales will be;
[tex]45p\text{ + 62c = 3520}[/tex]The equation for the weekend sales will be;
[tex]55p\text{ + 79c = }4415[/tex]Now, we have two equations that we need to use the matrix determinant method to solve;
[tex]\begin{bmatrix}{45} & {62} \\ {55} & {79} \\ {} & {}\end{bmatrix}\text{ }\begin{bmatrix}{p} & \\ {c} & {} \\ {} & \end{bmatrix}\text{ = }\begin{bmatrix}{3520} & {} & \\ {4415} & {} & \\ {} & {} & \end{bmatrix}[/tex]The above is the matrix set up we wil use;
Now, we start by calculating the determinant of 2 * 2 matrix; that would be;
[tex]\begin{gathered} \Delta\text{ = (45 }\times\text{ 79) - (62 }\times\text{ 55)} \\ \Delta\text{ = 3555-3410 = 145} \end{gathered}[/tex]Next is to find the determinant of the pineapple cake matrix;
To find this, what we will do is to substitute the coefficient of p with the total sales value to get a new matrix set;
The matrix for the pineapple cake will be;
[tex]\begin{gathered} \begin{bmatrix}{3520} & {62} \\ {4415} & {79} \\ {} & {}\end{bmatrix}\text{ } \\ \\ \text{The }\det er\min ant\text{ here will be ;} \\ \Delta_{p\text{ = }}(3520\text{ }\times\text{ 79) - (62 }\times\text{ 4415)} \\ =\text{ 4350} \end{gathered}[/tex]Next is to find the determinant of the chocolate cake matrix;
To find this, what we will do is to substitute the coefficient of c with the total sales value to get a new matrix set;
The matrix for the chocolate cake will be;
[tex]\begin{gathered} \begin{bmatrix}{45} & {3520} \\ {55} & {4415} \\ {} & {}\end{bmatrix} \\ \\ \Delta_c\text{ = (45 }\times\text{ 4415) - (55 }\times\text{ 3520)} \\ =\text{ 5075} \end{gathered}[/tex]Finally, we proceed to get the prices for the pineapple and the cake;
To get this, we simply divide the matrix of each by the initial matrix value;
[tex]\begin{gathered} p\text{ = }\frac{\Delta_p}{\Delta}=\frac{4350}{145}=30_{} \\ \\ c\text{ = }\frac{\Delta_c}{\Delta}\text{ = }\frac{5075}{145}\text{ = 35} \end{gathered}[/tex]Type the correct answer in each box. Use numerals instead of words.Consider this expression,-412 + 21 - 5(1 + r)What expression is equivalent to the given expression?12 + I +ResetNext
Answers
To answer this question, we need to expand the original equation, and then simplify to obtain the equivalent expression as follows:
[tex]-4x^2+2x-5(1+x)=-4x^2+2x-5(1)-5(x)[/tex]We used the distributive property for -5 (1 + 5).
Then, we have:
[tex]-4x^2+2x-5-5x=-4x^2+2x-5x-5[/tex]Adding like terms:
[tex]-4x^2-3x-5[/tex]In summary, therefore, the equivalent expression is:
[tex]-4x^2-3x-5[/tex]Complete the function for this graph.
Enter the correct
symbol,+ or -.
y = [?] |x|
Answers
Answer:
Step-by-step explanation:
y = -|x|
The graph is facing downwards, meaning it is negative.
Let sin 0 = 4/9. Find the exact value of cos 0.
Answers
we have the following
[tex]\sin \theta=\frac{4}{9}[/tex]sin of an angle is the same as:
[tex]\sin \theta=\frac{opposite}{hypotenuse}[/tex]therefore we can create the following right triangle:
we can calculate the adjacent side using the pythagorean theorem
[tex]h^2=a^2+b^2[/tex]where h is the hypotenuse, a is the adjacent side and b the opposite side to the angle.
thus, the adjacent side is:
[tex]a=\sqrt[]{h^2-b^2}=\sqrt[]{9^2-4^2}=\sqrt[]{81-16}=\sqrt[]{65}[/tex]Using that value, we can now calculate cos of the angle
[tex]\cos \theta=\frac{adjacent}{hypotenuse}[/tex][tex]\cos \theta=\frac{\sqrt[]{65}}{9}[/tex]which can't be simplify, thus that is the answer for the exact value
pls help l need to finish this
Answers
The equation of the linear function represented by the table below in slope-intercept form is y = -3x + 5
The linear function that will be obtained by using these values of x and y will be a Equation of line.
The slope-intercept form of line looks like this,
y = mx + c
where,
m is the slope.
c is the y intercept,
Firstly, to find the slope we can use any two points,
we will use (1,2) and (2,-1)
Hence, slope m,
m = (-1-2)/(2-1)
m = -3
Putting the value of slope in equation y = mx + c,
y = -3x + c
To fin the value of c,
Using the coordinate (1,2) and putting the values of x and y,
2 = -3 + c
c = 5.
Putting the values of c and m in the equation,
we get,
y = -3x + 5.
The required equation of the line in slope-intercept form is y = -3x + 5
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(2a² + 7a - 10) (a – 5)
Answers
2a³ - 3a² - 45a + 50 is the simplified form of the expression ( 2a² + 7a - 10 )( a - 5 ) using FOIL method.
What is the simplified form of the given expression?Given the expression in the question;
( 2a² + 7a - 10 )( a - 5 )
To expand ( 2a² + 7a - 10 )( a - 5 ), multiply each term in the first expression by each term in the second expression.
( 2a² + 7a - 10 )( a - 5 )
a( 2a² + 7a - 10 ) -5( 2a² + 7a - 10 )
a×2a² + a×7a + a×-10 -5×2a² -5×7a -5×-10
Multiply a and 2a²
2a³ + a×7a + a×-10 -5×2a² -5×7a -5×-10
Multiply a and 7a
2a³ + 7a² + a×-10 -5×2a² -5×7a -5×-10
Multiply a and -10
2a³ + 7a² - 10a -5×2a² -5×7a -5×-10
Multiply -5 and 2a²
2a³ + 7a² - 10a - 10a² -5×7a -5×-10
Multiply -5 and 7a
2a³ + 7a² - 10a - 10a² - 35a -5×-10
Multiply -5 and -10
2a³ + 7a² - 10a - 10a² - 35a + 50
Collect and add like terms
2a³ + 7a² - 10a² - 10a - 35a + 50
2a³ - 3a² - 45a + 50
Therefore, the simplified form of the expression is 2a³ - 3a² - 45a + 50.
Learn more about FOIL Method here: https://brainly.com/question/2092062
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