Consider the quadratic f(x)=x^2-x-30Determine the following ( enter all numerical answers as integers,fraction or decimals$The smallest (leftmost) x-intercepts is x=The largest (rightmost)x-intercepts is x=The y-intercept is y=The vertex is The line of symmetry has the equation
Answers
ANSWER
Smallest x-intercept: x = -5
Largest x-intercept: x = 6
y-intercept: y = -30
The vertex is (1/2, -121/4)
Line of symmetry x = 1/2
EXPLANATION
Given:
[tex]f(x)\text{ = x}^2\text{ - x - 30}[/tex]Desired Results:
1. Smallest x-intercept: x =
2. Largest x-intercept: x =
3. y-intercept: y =
4. The vertex is
5. Equation of Line of symmetry
1. Determine the x-intercepts by equating f(x) to zero (0).
[tex]\begin{gathered} 0\text{ = x}^2-x-30 \\ x^2-6x+5x-30\text{ = 0} \\ x(x-6)+5(x-6)=0 \\ (x-6)(x+5)=0 \\ x-6=0,\text{ x+5=0} \\ x\text{ = 6, x = -5} \end{gathered}[/tex]The smallest and largest x-intercepts are -5 and 6 respectively.
2. Determine the y-intercept by equating x to 0
[tex]\begin{gathered} y\text{ = \lparen0\rparen}^2-0-30 \\ y\text{ = -30} \end{gathered}[/tex]y-intercept is -30
3a. Determine the x-coordinate of the vertex using the formula
[tex]x\text{ = -}\frac{b}{2a}[/tex]where:
a = 1
b = -1
Substitute the values
[tex]\begin{gathered} x\text{ = -}\frac{(-1)}{2(1)} \\ x\text{ = }\frac{1}{2} \end{gathered}[/tex]3b. Determine the y-coordinate of the vertex by substituting x into the equation
[tex]\begin{gathered} y\text{ = \lparen}\frac{1}{2})^2-\frac{1}{2}-30 \\ y\text{ = }\frac{1}{4}-\frac{1}{2}-30 \\ Find\text{ LCM} \\ y\text{ = }\frac{1-2-120}{4} \\ y\text{ = -}\frac{121}{4} \end{gathered}[/tex]4. Determine the line of symmetry
In standard form the line of symmetry of a quadratic function can be identified using the formula
[tex]\begin{gathered} x\text{ = -}\frac{b}{2a} \\ x\text{ = }\frac{1}{2} \end{gathered}[/tex]Related Questions
In an experiment, the probability that event B occurs is , and the probability that event A occurs given that event B occurs is 3 7) What is the probability that events A and B both occur? Simplify any fractions.
Answers
We have to use the conditional probability formula:
[tex]P(A|B)=\frac{P(A\cap B)}{P(B)}[/tex]Where P(A|B) is the probability that A occurs given that B occurs, P(B) is the probability that B occurs, and P(A∩B) is the probability that both events A and B occur.
In this case, since we are asked for the probability that events A and B both occur, we need to solve the equation for P(A∩B):
[tex]P(A\cap B)=P(A|B)\cdot P(B)[/tex]And the information we have about the problem is:
[tex]\begin{gathered} P(A|B)=\frac{3}{7} \\ P(B)=\frac{2}{9} \end{gathered}[/tex]We substitute this into the formula for P(A∩B):
[tex]P\mleft(A\cap B\mright)=\frac{3}{7}\cdot\frac{2}{9}[/tex]Solving the multiplication of fractions:
[tex]\begin{gathered} P\mleft(A\cap B\mright)=\frac{3\cdot2}{7\cdot9} \\ P\mleft(A\cap B\mright)=\frac{6}{63} \end{gathered}[/tex]And finally, we simplify the fraction by dividing both numbers in the fraction by 3:
[tex]P\mleft(A\cap B\mright)=\frac{2}{21}[/tex]Answer: 2/21
pls help the hw is due today
Answers
Answer: the slope for the line is
y= -2x-4
Which of the following are equal to sec x? Choose all that apply. 3 answers
Answers
Verify each option
A ---> 1/sinx=cscx -----> is not the answer
B ---> 1/cosx=secx ----> is the answerC ---> cosx/tanx=cosx/(sinx/cosx)=cos^2x/sinx -----> is not the answer
D ---> tanx/sinx=(sinx/cosx)/sinx=1/cosx=secx -----> is the answerE ---> cotxsinx=(cos/sinx)sinx=cosx ----> is not the answer
F ----> tanxcscx=(sinx/cosx)(1/sinx)=1/cosx=secx ----> is the answertherefore
The answer is
options B, D and FAnswer:
B, D, E.
Step-by-step explanation:
B: [tex]\frac{1}{cos(x)}[/tex]
D: [tex]\frac{tan(x)}{sin(x)}[/tex]
E: [tex]tan(x) csc (x)[/tex]
21 - 7∆ = 4 - 8∆ 5∆ - 3 + 3∆ = ∆ + 7 + 6∆solve these.
Answers
We are given the following equation:
[tex]21-7\Delta=4-8\Delta[/tex]We need to solve for delta, to do that we will first add 8delta on both sides:
[tex]21-7\Delta+8\Delta=4-8\Delta+8\Delta[/tex]Now we add like terms:
[tex]21+\Delta=4[/tex]Now we subtract 21 on both sides:
[tex]21-21+\Delta=4-21[/tex]Adding like terms:
[tex]\Delta=17[/tex]Therefore delta is 17
2(4-2x)-5=-2(x+5)+8x
Answers
The equation 2(4-2x)-5=-2(x+5)+8x has a value of 1.3 for x
How to determine the solution to the equation?From the question, the equation to solve is given as
2(4-2x)-5=-2(x+5)+8x
Rewrite the equation properly
This is represented by the following representation
2(4 - 2x) - 5=-2(x + 5) + 8x
Start by opening the brackets in the equation
So, we have the following equation
8 - 4x - 5 =-2x - 10 + 8x
Collect the like terms in the equation
So, we have the following equation
8x - 2x + 4x = 10 +8 - 5
Evaluate the like terms in the equation
So, we have the following equation
10x = 13
Divide both sides of the equation by 10
So, we have the following equation
x = 1.3
Hence, the solution to the equation for x is 1.3
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Kevin went to the nursery and bought a 5 ft tall tree. After planting the tree, Kevin made a table to record theheight, h, of the tree, t years after it was planted. Verbally describe the relationship between h and t.t 0 1 2 3 4h 5 6 7 8 9
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As we can see inthe table foe every year that pass the thre grows 1 ft
As we can see inthe table foe every year that pass the thre grows 1 ft
The circle graph shows the results of a survey by a bakery on which of their new products 105 customerspreferred most. How many customers preferred cake? Round your answer to the nearest whole number.
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If 105 customers were the total, and 35% prefers cake, we must calculate 35% of 105, then we must do 105 multiplied by 35%, we can doit transforming the 35% in the fraction notation:
[tex]35\%=\frac{35}{100}[/tex]And the multiplication
[tex]105\cdot\frac{35}{100}=36.75[/tex]Therefore, if we round it to the nearest whole number, the number of customers that prefer cake is 37.
37 customers prefer cake.
please help me asap, Evaluate 9 exponent 2
Answers
81
Explanation
Remember
[tex]a^b=\text{ a multiplied by itself b times}[/tex]Step 1
apply
[tex]\begin{gathered} 9^2=9\cdot9 \\ 9\cdot9=81 \end{gathered}[/tex]
A math book is 2.5 cm thick.
How many of these books can
be stored on a shelf that is
one meter long?
Answers
The number of books that can be stored on one meter-long shelf is (forty) = 40.
Given
a book is 2.5 cm thick
number of books required are
Convert meters into centimeters first 1m = 100 cm now, divide them:
= 100 cm ÷ 2.5 cm to remove the decimal point divide 2.5 by 10 = 2.5/10
= [tex]100 * \frac{10}{25}[/tex]
= 40
thus the total number of books that can be stored on a one-meter bookshelf is 40 books.
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how many term has G.p whose 2nd term is 1/2 and common ratio and the last term are 1/4and1/128respestively
Answers
The geometric progression has the form:
[tex]\mleft\lbrace a,ar,ar^2,ar^3,\ldots,ar^n\mright\rbrace[/tex]We have the information about the second term, a*r:
[tex]ar=\frac{1}{2}[/tex]We know that the common ratio is
[tex]r=\frac{1}{4}[/tex]So from this information we can get the coefficient a:
[tex]\begin{gathered} ar=\frac{1}{2} \\ a\cdot\frac{1}{4}=\frac{1}{2} \\ a=\frac{4}{2}=2 \end{gathered}[/tex]And we also know that the last term is 1/128, that is
[tex]ar^n=\frac{1}{128}[/tex]From this one we can find n:
[tex]\begin{gathered} 2\cdot(\frac{1}{4})^n=\frac{1}{128} \\ (\frac{1}{4})^n=\frac{1}{128\cdot2} \end{gathered}[/tex]We can apply the property of the logarithm of power to get n:
[tex]\begin{gathered} \log ((\frac{1}{4})^n)=\log (\frac{1}{256}) \\ n\cdot\log (\frac{1}{4})^{}=\log (\frac{1}{256}) \\ n=\frac{\log (\frac{1}{256})}{\log (\frac{1}{4})} \\ n=4 \end{gathered}[/tex]Be careful, because n is not the number of terms. The number of terms is n+1, so the G.P. has 5 terms
use the distributive property to simplify the left side of the equation 2(x/8+3)=7+1/4x
Answers
Given data:
The given expression is 2(x/8+3)=7+1/4x.
The given expression can be written as,
2(x/8)+2(3)=7+1/4x
x/4+6=7+1/4x
x/4-1/4x=7-6
x/4-1/4x=1
x^(2)-1=4x
x^(2)-4x-1=0
Thus, the final expression is x^(2)-4x-1=0 after applying distributve property on left side.
Which expression is equivalent to 4 * 4 * 4 * 5 * 5?34 x 2543 x 5244 x 501224 x 102
Answers
Any of those expressions are equivalent to 4*4*4*5*5
Given right triangle ABC, with altitude CD intersecting AB at point D. If AD = 5 and DB = 8, find the length of CD, in simplest radical form. In your video include whether you would use SAAS or HYLLS to solve (and WHY), the proportion you would set up, how you would solve for the missing side, and how you know your answer is in simplest radical form.
Answers
First we dra a triangle:
To prove that the triangles are similar we have to do the following:
Considet triangles ABC and ACD, in this case we notice that angles ACB and ADC are equal to 90°, hence they are congruent. Furthermore angles CAD and CAB are also congruent, this means that the remaining angle in both triangles will also be congruent, therefore by the AA postulate for similarity we conclude that:
[tex]\Delta ABC\approx\Delta ACD[/tex]Now consider triangles ABC and BCD, in this case we notice that angles ACB and BDC are congruent since they are both equal to 90°. Furthermore angles ABC and DBC are also congruent, this means that the remaining angle in both triangles will, once again, be congruent. Hence by the AA postulate we conclude that:
[tex]\Delta ABC\approx\Delta BCD[/tex]With this we conclude that traingles BCD and ACD are both similar to triangle ABC, and by the transitivity property of similarity we conclude that:
[tex]\Delta ACD\approx BCD[/tex]Now that we know that both triangles are similar we can use the following proportion:
[tex]\frac{h}{x}=\frac{y}{h}[/tex]this comes from the fact that the ratios should be the same in similar triangles.
From this equation we can find h:
[tex]\begin{gathered} \frac{h}{x}=\frac{y}{h} \\ h^2=xy \\ h=\sqrt[]{xy} \end{gathered}[/tex]Plugging the values we have for x and y we have that h (that is the segment CD) has length:
[tex]\begin{gathered} h=\sqrt[]{8\cdot5} \\ =\sqrt[]{40} \\ =\sqrt[]{4\cdot10} \\ =2\sqrt[]{10} \end{gathered}[/tex]Therefore, the length of segment CD is:
[tex]CD=2\sqrt[]{10}[/tex]x-y=3x+y=5unit 7 systems of linear equations
Answers
then
[tex]\begin{gathered} x+y=5 \\ 3+y+y=5 \\ 3+2y=5 \\ 3+2y-3=5-3 \\ 2y=2 \\ \frac{2y}{2}=\frac{2}{2} \\ y=1 \end{gathered}[/tex]solve for x
[tex]\begin{gathered} x=3+y \\ x=3+1 \\ x=4 \end{gathered}[/tex]answer: C. (4,1)
Elijah is snorkeling above a shipwreck. The ship has an elevation of -105 feet. Elijah is snorkeling at 2/15 of the ship's elevation. What is Elijah's elevation?
Answers
Elijah's elevation when Elijah is snorkeling above a shipwreck is -14.
What is elevation?Elevation simply has to do with the height above sea level.
In this case, Elijah is snorkeling above a shipwreck and the ship has an elevation of -105 feet. Elijah is snorkeling at 2/15 of the ship's elevation.
Elijah's elevation will be:
= Fraction of his snorkeling × Ship's elevation
= 2/15 × (-105)
= -14
This shows the elevation of Elijah.
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Describe how the graph of the function g(x)=1/4|x|-2 can be obtained from the basic graph. Then graph the function.Start with the graph of h(x)=|x|. Then [__] it vertically by a factor of [__]. Finally, shift it [___] units.
Answers
Start the graph of h(x) = |x|, then stretch it vertically by a factor of 1/4 . Finally, shift it down by 2 units
The original graph can be seen above
what it becomes can be seen below
Hence the final answer is option B
f(x) = 3x² + 9x – 16
Find f(-8)
Answers
Answer: 104
Step-by-step explanation:
[tex]f(-8)[/tex] represents [tex]f(x)[/tex] evaluated at [tex]x=-8[/tex].
[tex]f(-8)=3(-8)^2 +9(-8)-16\\\\=192-72-16\\\\=120-16\\\\=104[/tex]
inding Total CostsStore AStore BWhat is the cost of the repair and sales tax combinedat Store B?ComputerRepair$1,200$1,350Sales Tax6%7%Gratuity15%15%ShippingFree2% of totalprice
Answers
Store B :
Computer repair : $1,350
Sale tax = 7%
To obtain the sale tax amount, multiply the price by the percentage in decimal form (divided by 100);
$1,350 x (7/100) = 1,350 x 0.07 = $94.5
Add both:
1,350+94.5=$1,444.5
What is the slope of this horizontal line from 10-13 minutes?
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We are asked to determien the slope of the line between 10 and 13 minutes. Since this is a horizontal line, it's slope is 0.
Find f.Write your answer in simplest radical form. ___ units
Answers
Answer:
The value of f is;
[tex]f=3\sqrt[]{2}\text{ units}[/tex]Explanation:
Given the triangle in the attached image.
Recall that;
[tex]\tan \theta=\frac{opposite}{adjacent}[/tex]from the given figure;
[tex]\begin{gathered} \theta=30^{\circ} \\ \text{opposite}=f \\ \text{adjacent}=3\sqrt[]{6} \end{gathered}[/tex]substituting the values;
[tex]\begin{gathered} \tan 30=\frac{f}{3\sqrt[]{6}} \\ f=3\sqrt[]{6}\tan 30 \\ f=3\sqrt[]{6}(\frac{\sqrt[]{3}}{3}) \\ f=3\sqrt[]{2} \end{gathered}[/tex]Therefore, the value of f is;
[tex]f=3\sqrt[]{2}\text{ units}[/tex]giving that -3+20=5x-4 write 3 more equations that you know are true
Answers
Answer:
Step-by-step explanation:
ft7654
i Which equation, when solved, results in a different value of x than the other three?' 7 3 4 37 X=-20 3 119-8-2014
Answers
You have the first equation:
[tex]-\frac{7}{8}x-\frac{3}{4}=20[/tex]Let's analize the others equation.
You can see that the second equation is just like the first one, but it was multiplied by -1:
[tex]\begin{gathered} (-1)(-\frac{7}{8}x-\frac{3}{4})=(20)(-1) \\ \frac{7}{8}x+\frac{3}{4}=-20 \\ \frac{3}{4}+\frac{7}{8}x=-20 \end{gathered}[/tex]So the value of "x" of the first one and the second one will be the same.
The third equation is:
[tex]-7(\frac{1}{8})x-\frac{3}{4}=20[/tex]If you simplify it, you get:
[tex]-\frac{7}{8}x-\frac{3}{4}=20[/tex]So you can notice that the three equations are the same, therefore the result of the third one will be the same too.
You can identify that even simplifying the last equation, it is not the same equation, then you will obtain a different value of "x" than the other three.
Therefore,the answer is the Last option.
Parking spaces in a parking lot are parallel to each other. Find the measure of the two
unknown angles and explain your reasoning.
measure of angle m:
measure of angle n:
Answers
Answer:
m = 70° , n = 110°
Step-by-step explanation:
m and 110° are same- side interior angles and sum to 180°
m + 110° = 180° ( subtract 110° from both sides )
m = 70°
n and 110° are corresponding angles and are congruent , then
n = 110°
what does frilling mean
Answers
Answer:
A ruffled, gathered, or pleated border or projection, such as a fabric edge used to trim clothing.
Step-by-step explanation:
Brainlest, Please!
The difference between two numbers is 28. The sum of the two numbers is 56. Let x be the larger number and y be the smaller number. Which system of equations represents this proble O y - x = 28 I + y = 56 O x=y= 28 x + y = 56 Oy - 2 = 56 x + y = 28 - y = 56
Answers
Since x is the larger number and y is the smaller number
Since their sum is 56
That means add x and y then equate them by 56
[tex]x+y=56(1)[/tex]Since the difference between them is 28
That means subtract y from x and equate the answer by 28
[tex]x-y=28(2)[/tex]Look at the answer to find the correct answer
It is B
x - y = 28 and x + y = 56
Assume that a particular professional baseball team has 12 pitchers, 5 infielders, and 8 other players. If 3 players' names are selected at random, determine the probability that 2 are pitchers and 1
is an infielder.
What is the probability of selecting 2 pitchers and 1 infielder?
(Type an integer or a simplified fraction.)
Answers
Step-by-step explanation:
Pitchers(p) = 12
Infielders(i) = 5
Others(o) = 8
Total players = 25
Probability(2p and 1i) =
[tex]( \frac{2}{25} ) \times ( \frac{1}{25} ) = ( \frac{2}{625} )[/tex]
The measure of angle c below is(Hint: Slide 2)95/640
Answers
we know that
The sum of the interior angles in any triangle must be equal to 180 degrees
In the right triangle of the figure
we have
c+d+64=180
we have that
d=90 degrees (right angle)
substitute
c+90+64=180
c+154=180
c=180-154
c=26 degrees
Find the length of the third side. If necessary, round to the nearest tenth. 12 5 x=what is the missing number x?
Answers
Step 1
Longest side is the hypotanuse = x
opposite = 5
Adjacent = 12
Apply pythagorus theorem
[tex]\begin{gathered} \text{Opposite}^2+Adjacent^2=Hypotanuse^2 \\ 5^2+12^2=x^2 \\ \\ 25+144=x^2 \\ x^2\text{ = 169} \\ x\text{ = }\sqrt[\square]{169} \\ x\text{ = 13} \end{gathered}[/tex][tex]undefined[/tex]Molly was on a long 136 mile road trip. The first part of the trip there was lots of traffic, she only averaged 16 mph. The second part of the trip there was no traffic so she could drive 44 mph. If the trip took her 5 hours, how long did she travel at each speed? In traffic she drove for _____ hours After the traffic cleared she drove for ____ hours.
Answers
Answer:
In traffic, she drove for 3 hours
and After the traffic cleared she drove for 2 hours.
Explanation:
Given that the road trip was 136 miles;
[tex]d=136[/tex]The first part of the trip there was lots of traffic, she only averaged 16 mph;
[tex]v_1=16[/tex]The second part of the trip there was no traffic so she could drive 44 mph;
[tex]v_2=44[/tex]She traveled for a total of 5 hours;
[tex]t=5[/tex]let x represent the time in traffic when she traveled at 16 mph
[tex]t_1=x[/tex]the time the traffic is clear would be;
[tex]t_2=t-t_1=5-x[/tex]Recall that distance equals speed multiply by time;
[tex]d=v_1t_1_{}_{}^{}+v_2t_2[/tex]substituting the values;
[tex]136=16x+44(5-x)[/tex]solving for x;
[tex]\begin{gathered} 136=16x+220-44x \\ 44x-16x=220-136 \\ 28x=84 \\ x=\frac{84}{28} \\ x=3 \end{gathered}[/tex]So;
[tex]\begin{gathered} t_1=3\text{ hours} \\ t_2=5-x=5-3=2 \\ t_2=2\text{ hours} \end{gathered}[/tex]Therefore, In traffic, she drove for 3 hours
and After the traffic cleared she drove for 2 hours.
The following table represents C, an appliance repairman’s charges based on t, the hours it takes to make a repair.Which of the following equations could be used to determine the repairman’s charges for a repair?A: C=27t +3B: C=27tC: C=35tD: C=35t + 2
Answers
Given the table below
To find the equation of the values of the table, we will first calculate the rate of change, then use a point and the rate of change calculated fo find the equation for the repairman's charges for the repair
To find the rate of change we have
[tex]\text{ Point 1}\Rightarrow(1,62)\Rightarrow t_1=1,c_1=62[/tex][tex]\text{ Point 2}\Rightarrow(3,116)\Rightarrow t_2=3,c_2=116[/tex]The rate of change formula is
[tex]m=\frac{c_2-c_1}{t_2-t_1}=\frac{116-62}{3-1}=\frac{54}{2}=27[/tex]Having calculated the rate, we can use slope and one point form equation of a line to get the desired equation. This is given below:
[tex]c-c_1=m(t-t_1)[/tex]Substitute the given values of t and c and the rate in the formula above
[tex]\begin{gathered} c-62=27(t-1) \\ c-62=27t-27 \\ c=27t-27+62 \\ c=27t+35 \end{gathered}[/tex]Hence, the repairman's charges for a repair is given as C = 27t + 35