The given function is:
[tex]f(x)=3x^2+6x-2[/tex]Complete the square and factor as follows:
[tex]\begin{gathered} f(x)=3(x^2+2x+1)-2-3 \\ f(x)=3(x+1)^2-5_{} \end{gathered}[/tex]Compare with:
[tex]f(x)=a(x-h)^2+k[/tex]To get:
[tex](h,k)=(-1,-5)[/tex]Since the parabola is vertical the axis of symmtery is vertical which is x=-1.
which is the scatter plot for the data set{(1960,3), (1970,3.5), (1990,6)}?
Given the data set:
(x, y)==> {(1960,3), (1970,3.5), (1980, 5), (1990,6)}
To plot the data above, the x-corrdinates: (1960; 1970; 1980; 1990) which are the first values will be on the horizontal axis, while the y-coordinates (3, 3.5, 5, 6), will be on the vertical axis.
Thus, the correct scatter plot for the data set above will be Scatter Plot A.
The graphical representation is below
ANSWER:
A
consider the following.find formula simplify answer .Find the domain for the formula and round answer to two decimal places if necessary.
The sum of functions is given as:
[tex](f+g)(x)=f(x)+g(x)[/tex]In this case we have:
[tex](f+g)(x)=5x+\sqrt[]{x-1}[/tex]The domain of the functions is any number that makes the squared root a real number, then:
[tex]\begin{gathered} x-1\ge0 \\ x\ge1 \end{gathered}[/tex]Hence the domain of the functions is:
[tex]\lbrack1,\infty)[/tex]Select the correct answer.What is the area of STR?A. 30 square feetB. 34.5 square feetC. 57.5 square feetD. 60 square feet
Hello!
To calculate the area of a triangle, we must use the formula below:
[tex]\mathrm{Area=\dfrac{base\times height}{2}}[/tex]In this triangle, we have:
• base,: 6 feet
,• height,: 10 feet
Knowing it, let's replace the formula with the values:
[tex]\mathrm{Area=\dfrac{6\times10}{2}}=\frac{60}{2}=30\text{ }\mathrm{feet^2}[/tex]Answer:A. 30 square feet
Aniya can dribble a basketball 50 times inminute with her right handand 30 times inminute with her left hand. What is the ratio of herright-hand to her left-hand dribbling rate?
To find the ratio of her right-hand to her left-hand dribbling rate
We will simply divide 50 by 30 and then reduce to its lowest term
50/30 = 5/3
The ratio is 5:3
a stairway consists of 4 in rises and treads of 18 in if the height of the stairs is 4 feet what is the distance taken up by the stairway on the lower floor
If we have x flights of stairs.
The height of the stairs would be 4x.
The height of the stairs is given as 4 feet = 4 x 12 = 48 inches.
Therefore there are 48/4 = 12 flights of stairs.
The distance taken by the stairs on the lower floor would be
18 x 12 = 216in or 18 feet.
Find the average rate of change of the functionf (x) = 3x2 + 4x – 5over the interval [0,h], where h is a positive real number.
The average rate of change of the function over the interval (0, h) is
[tex]\frac{f(h)-f(0)}{h-0}=\frac{f(h)-f(0)}{h}[/tex]Now,
[tex]f(h)=3h^2+4h-5[/tex]and
[tex]f(0)=-5[/tex]Therefore, the average rate of change is
[tex]\frac{3h^2+4h-5-5}{h}=\textcolor{#FF7968}{\frac{3h^2+4h-10}{h}.}[/tex]If f(x) = 5x - 2 and g(x) = 1 - 2x, find (fg)(x).I am not sure if my answer is right please help me
Given:
f(x) = 5x - 2
g(x) = 1 - 2x
Let's find (fg)(x).
To solve the function operation, we have:
(fg)(x) = f(x) * g(x)
Thus, we have:
[tex](fg)(x)=(5x-2)(1-2x)[/tex]Solving further:
Expand using FOIL method, then apply distributive property
[tex]\begin{gathered} (fg)(x)=5x(1-2x)-2(1-2x) \\ \\ (fg)(x)=5x(1)+5x(-2x)-2(1)-2(-2x)_{} \\ \\ (fg)(x)=5x-10x^2-2+4x \\ \\ (fg)(x)=+5x+4x-10x^2-2 \\ \\ (fg)(x)=9x-10x^2-2^{} \end{gathered}[/tex]ANSWER:
[tex]9x-10x^2-2^{}[/tex]11. A fair die is rolled 8 times. What is the probability of getting a. I on each of the 8 rolls? b. 6 exactly twice in the 8 rolls? c. 6 at least once in the 8 rolls?
To asnwer this questions we can use the binomial distribution. The probability of having a number k of successes in a binomial experiment is given by:
[tex]P(X=k)=\frac{n!}{k!(n-k)!}p^k(1-p)^{n-k}[/tex]where n is the number of trials and p is the probability of succes.
a.
Since we like to have a one in each roll this means that in this case the probability of succes will be 1/6 (1 possibility out of 6). Also we have 8 rolls then n=8, and we like that the one is the result in each of them, then k=8. Plugging this values in the distribution we have:
[tex]\begin{gathered} P(X=8)=\frac{8!}{8!(8-8)!}(\frac{1}{6})^8(1-\frac{1}{6})^{8-8} \\ =\frac{1}{1679616} \\ =0.595\times10^{-6} \end{gathered}[/tex]Therefore the probability of getting a one in each roll is 0.00000595.
b.
Since we like a 6 exactly twice this means that k=2. The probability of succes is 1/6. Plugging the values in the distribution we have:
[tex]\begin{gathered} P(X=2)=\frac{8!}{2!(8-2)!}(\frac{1}{6})^2(1-\frac{1}{6})^{8-2} \\ =0.26 \end{gathered}[/tex]Therefore the probability of obtaining 6 exactly twice is 0.26.
c.
The probability of obtaining at least once a six is the sum of obtaining 1 and obtaining 2 and obtaining 3 and so on.
That means that the probability is:
[tex]\begin{gathered} P=P(X=1)+P(X=2)+P(X=3)+P(X=4) \\ +P(X=5)+P(X=6)+P(X=7)+P(X=8) \end{gathered}[/tex]but this is more easily obtain if we notice that this is the same as:
[tex]P=1-P(X=0)[/tex]This comes from the fact that the sum of all the successes possibilities (in this case obtaining a 6) have to be 1.
Then the probability of obtaniing at least once a six is:
[tex]\begin{gathered} P=1-P(X=0) \\ =1-\frac{8!}{0!(8-0)!}(\frac{1}{6})^0(1-\frac{1}{6})^{8-0} \\ =0.767 \end{gathered}[/tex]Therefore the probability of obtaining at least once a six is 0.767.
What is the value of this matrix at az?Matrix A
ANSWER:
27
STEP-BY-STEP EXPLANATION:
A matrix is represented by an uppercase letter (A,B, …) and its elements with the same lowercase letter (a,b, …), with a double subscript where the first indicates the row and the second the column a the one that belongs.
Just like that:
Therefore, if we look at the matrix of the statement, we can determine that a2,1 is equal to 27
Find the formula for the geometric sequence 1, 5, 25, 125,...OA4, = 5-1OB. 0,= 5.50-1OC. a, = (-2)"-1D. 0,= -2"-1Reset Selection
Given: geometric series 1 , 5, 25 , 125,.................
Find: formula for the geometric series
Explanation: the general formula for the series is
[tex]\begin{gathered} ar^{n-1} \\ 1.5^{n-1} \\ 5^{n-1} \end{gathered}[/tex]Final answer:
[tex]a_n=5^{n-1}[/tex]brainliest if you can answer this math question
a cylinder has a height of 9 feet and a radius of 5 feet. find the a volume and b surface area ( Use 3.14 for pi ) round your answer to the nearest tenth0 if necessary.
The volume of the cylinder is computed as follows:
[tex]V=\pi\cdot r^2\cdot h[/tex]where r is the radius and h is the height.
Substituting with r = 5 ft, and h = 9 ft, we get:
[tex]\begin{gathered} V=3.14\cdot5^2\cdot9 \\ V=706.5ft^3 \end{gathered}[/tex]The surface area of the cylinder is computed as follows:
[tex]A=2\cdot\pi\cdot r^2+2\cdot\pi\cdot r\cdot h[/tex]Substituting:
[tex]\begin{gathered} A=2\cdot3.14\cdot5^2+2\cdot3.14\cdot5\cdot9 \\ A=157+282.6 \\ A=439.6ft^2 \end{gathered}[/tex]A school sells adult tickets and student tickets for a play. It collects $1,400 in total The graph shows the possible combinations of the number of adult tickets sold and the number of student tickets sold. What does the vertical intercept (0.200) tell us in this situation? O (1 Point) It tells us the decrease in the sale of adult tickets for each student ticket sold It tells us that if no adult tickets were sold, then 200 student tickets were sold It tells us that is no students tickets were sold, then 200 adult tickets were sold It tells us the decrease in the sale of student tickets for each adult ticket sold.
In the graph, the horizontal axis represents the number of adult tickets sold
And the vertical axis represents the corresponding number of student tickets sold.
The vertical intercept, as we are indicated is at (0,200)
That point is at 0 in the horizontal axis and at 200 on the vertical axis, comparing with what each axis represents:
(0,200) represents that when 0 adult tickets are sold, 200 student tickets are sold.
Answer:
it tells us that if no adult tickets were sold, 200 student tickets were sold
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let the number be represented by x
so, if 1 is added to the number
the result would be 5 more than (5 plus) 4 times the number
let's write out an equation for this
[tex]1+x=4x+5[/tex]the equation above is a mathematical translation of the statement
step one
collect like terms
[tex]\begin{gathered} 1+x=4x+5 \\ 1-5=4x-x \\ -4=3x \end{gathered}[/tex]step two
divide both sides by the coeffiecient of x
[tex]\begin{gathered} 3x=-4 \\ \frac{3x}{3}=-\frac{4}{3} \\ x=-\frac{4}{3} \end{gathered}[/tex]from the calculation above, the unknown number is -4/3
Can you pls help me with this question thank you
1) In this problem, we need to make use of the order of operations.
2) Notice that we have divisions, so let's prioritize the division inside the parentheses, we can also rewrite another one, like this:
[tex]\begin{gathered} 10\div(-6--6\div6) \\ 10\div(-6-(-6)\div6) \\ 10\div(-6-(-1)) \\ 10\div(-6+1) \\ 10\div(-5) \\ -2 \end{gathered}[/tex]Notice that minus outside the parentheses work like a product (-1) x
2) Thus the answer is -2
write the following equations in function format.must include all the steps
We need to write the equation in function format:
So,
[tex]y=f(x)[/tex]So, we need to solve the given equation for y
a)
[tex]-8x+y-3=0[/tex]solve for y:
[tex]y=8x+3[/tex]So, the equation in function format is y = 8x + 3
Match definition to the terms below Circle Sector Ranger Radians Arc Chord Circumcenter Circumscribed polygon Circumscribed circle Inscribed angle
Given
Circle, Sector, Tangent, Radians, Arc, Chord, Circumcenter, Circumscribed polygon, Circumscribed circle, Inscribed angle.
To match with the definition of the terms.
Explanation:
Circle: A set of points in a plane that are equidistant from a given point.
Sector: Region of a circle bounded by an arc and two radii.
Tangent: A line that intersects a circle in exactly 1 point.
Radians: Another way to measure the angles using the ratio of
arc length /radius.
Arc: The part of circle lying between two points on the circle.
Chord: A line segment whose endpoints are on the circle.
Circumcenter: The intersection of all three perpendicular bisectors of a triangle's sides and the center of the triangle.
Circumscribed Polygon: Circle about a polygon in which all vertices intersect the circle.
Circumscribed circle: Polygon in which all the sides are tangent to the inscribed circle.
Inscribed angle: An angle formed by two chords in a circle that share an end point.
I need help with this practice problem It’s from my trig bookI attempted this problem earlier, later, if you can, check if I am correct. I will send a pic of my work.
Given the right triangle:
Taking the cosine of the angle θ:
[tex]\cos \theta=\frac{2\sqrt[]{6}}{2\sqrt[]{15}}=\frac{\sqrt[]{2}}{\sqrt[]{5}}[/tex]Now, taking the arc cosine to find θ:
[tex]\begin{gathered} \theta=\arccos (\sqrt[]{\frac{2}{5}}) \\ \therefore\theta\approx50.8\degree^{} \end{gathered}[/tex]Rigid Transformations:Question 1Circle P has center (-9, 3) and radius 3. Circle P' is formedby shifting circle P to the right 4 units and reflecting aboutthe line y = x. What is the coordinate of the center of circleP'?Select one:O(-13, 3)O(-5,3)O(3.-13)(3-5)
To shift the coordinates in a cartesian plane we have to remember that a translation can be described as:
[tex](x,y)\rightarrow(x+a,y+b)[/tex]where a and b is the amount we would like to translate in the horizontal and vertical direction, respectively.
In this case we would like to translate the center to the right four units, then a=4. Since we don't wish to translate it in the vertical direction then b=0. Then, the center, after the tanslation is
[tex]P^{}=(-9+4,3)=(-5,3)[/tex]Now, if we want to reflect about the line y=x we have to remember that the rule describing it is
[tex](x,y)\rightarrow(y,x)[/tex]Then the point P' is
[tex]P^{\prime}=(3,-5)[/tex]Therefore the center of the circle after the transformations given is (3,-5)
How do you write 37.5% as a mixed number?
FIrst, write the given percentage as a fraction:
37.5% = 37.5/100 = 375/1000 = 75/200 = 15/40 = 3/8
3/8 is the same as 0 3/8 as a mixed number
g(n)= -2n-4f(n)= 2n+1find (g-f) (2)
Now
[tex](g-f)(2)=g(2)-f(2)=-8-5\Rightarrow(g-f)(2)=-13[/tex]Solve the system of equations. If the system has no solution, say that it is inconsistent.
Answer:
D. The system is inconsistent
Step-by-step Explanation:
Given the below system of equations;
[tex]\begin{gathered} 2x-2y+5z=11\ldots\ldots\ldots\text{Equation 1} \\ 6x-5y+13z=30\ldots\ldots\ldots\text{.}\mathrm{}\text{Equation 2} \\ -2x+3y-7z=-13\ldots\ldots\ldots\text{Equation 3} \end{gathered}[/tex]We'll follow the below steps to solve the above system of equations;
Step 1: Add Equation 1 and Equation 3;
[tex]\begin{gathered} (2x-2x)+(-2y+3y)+(5z-7z)=(11-13) \\ y-2z=-2 \\ y=2z-2\ldots\ldots\text{.}\mathrm{}\text{Equation 4} \end{gathered}[/tex]Step 2: Multiply Equation 3 by 3, we'll have;
[tex]-6x+9y-21z=-39\ldots\ldots\text{.Equation 5}[/tex]Step 3: Add Equation 2 and Equation 5, we'll have;
[tex]4y-8z=-9\ldots\ldots\ldots\text{Equation 6}[/tex]Step 4: Put Equation 4 into Equation 6 and solve for z;
[tex]\begin{gathered} 4(2z-2)-8z=-9 \\ 8z-8-8z=-9 \\ 8z-8z=-9+8 \\ 0=-1 \end{gathered}[/tex]From the above, we can see that we do not have a solution for z, therefore, we can say that the system of equations has no solution, hence, it is inconsistent.
Which of the following phrases represents n ÷ 5?the sum of five and a numbera number decreased by fivethe quotient of a number and fivefive divided by a number
Answer:
The quotient of a number and five
Explanation:
Given:
[tex]n\div5[/tex]To find:
The phrase that represents the above expression
The below phrase represents the given expression;
The quotient of a number and five
emeline can type at a constant rate of 1/4 pages/minute.c emeline has to type a 7 page article. How much time will it take her?
Step 1. Since Emeline can type at a constant rate of 1/4 pages per minute, she will write 1 page in
[tex]\frac{1}{4}\text{pages in 1minute }\longrightarrow\frac{1}{4}\cdot4=1page\text{ in }1\cdot4=4\text{ minutes}[/tex]She writes 1 page in 4 minutes.
Step 2. Now that we know how much it takes Emeline to write one page, we multiply that by the number of pages that she has to write for the article:
[tex]4\text{ minutes }\cdot7=28\text{ minutes}[/tex]It will take her 28 minutes.
Answer: 28 minutes
please help me I truly dont understand this question also this is not college work this is for middle school
To answer this question we need to remember the definition of the trigonometric functions:
[tex]\sin \theta=\frac{\text{opp}}{\text{hyp}}[/tex][tex]\cos \theta=\frac{\text{adj}}{\text{hyp}}[/tex][tex]\tan \theta=\frac{\text{opp}}{\text{adj}}[/tex]where opp denotes the opposite leg of the angle, adj the adjacent leg of the angle and hyp the hypotenuse.
Now, in this triangle we notice that for angle B the opposite leg is 15, the adjacent leg is 8 and the hypotenuse is 17. Plugging this values into the definitions above we have that:
[tex]\tan B=\frac{15}{8}[/tex][tex]\sin B=\frac{15}{17}[/tex][tex]\cos B=\frac{8}{17}[/tex]50 points!
What is the value of x?
Enter your answer in the box.
x =
Answer: x = 1
Step-by-step explanation:
Solve 3 x − 5 = 2 − 6 x for x
Answer:
[tex]\boxed{\sf \boxed{\sf x=\frac{1}{3}}\; or\;\boxed{\sf x=0.333...}}[/tex]
Step-by-step explanation:
[tex]\sf 3x-5=2-6[/tex]
Subtract numbers:-
[tex]\sf 2-6=\bf -4[/tex]
[tex]\sf 3x-5=-4[/tex]
Add 5 to both sides:-
[tex]\sf 3x-5+5=-4+5[/tex]
Simplify:-
[tex]\sf 3x=1[/tex]
Divide both sides by 3:-
[tex]\sf \cfrac{3x}{3}=\cfrac{1}{3}[/tex]
Simplify:-
[tex]\sf x=\cfrac{1}{3}[/tex]
__________________
Hope this helps!
Have a great day! :)
Answer:
x = 7/9
Step-by-step explanation:
Given equation,
→ 3x - 5 = 2 - 6x
Now the value of x will be,
→ 3x - 5 = 2 - 6x
→ 3x + 6x = 2 + 5
→ 9x = 7
→ [ x = 7/9 ]
Hence, value of x is 7/9.
for the arithmetic sequence 42, 32, 22, 12... find the 18th term.
Answer:
The18th term of the given sequence is -128
Explanation:
To find the 18th term of the sequence:
42, 32, 22, 12, ..., we need to find the nth term of the sequence first.
The nth term of a sequence is given be the formula:
[tex]T_n=a+(n-1)d[/tex]Where a is the first term, and d is the common difference.
Here, a = 42, d = 32 - 42 = -10
[tex]\begin{gathered} T_n=42+(n-1)(-10) \\ =42-10n+10 \\ T_n=52-10n \end{gathered}[/tex]To find the 18th terem, substitute n = 18 into the nth term
[tex]\begin{gathered} T_{18}=52-10(18) \\ =52-180 \\ =-128 \end{gathered}[/tex]Hello! I'm feeling unsure on this answer. Can we please review?
From the given graph, let's identify the solution.
The solution will be the point(s) where both lines meet.
In this given graph, the lines meet at one point.
So we have just one solution.
From the graph, the point of intersection(point where both line meet) is:
(x, y) ==> (-1, -2)
Therefore, the solution of the graphed system is:
(-1, -2)
ANSWER:
(-1, -2)
what is the greatest possible integer solution of the inequality 2.877x <27.174 ?
We have to isolate the x in the inequality:
[tex]\begin{gathered} 2.877x<27.174 \\ x<\frac{27.174}{2.877} \\ x<9.45 \end{gathered}[/tex]So, the greatest possible integer is 9.