The graph represents a quadratic function. Write an equation of the function in standard form. PLEASE HELP ME
Answers
Explanation:
Standard form is Ax + By = C
Known points are (-3, 6) and (-1.5, 6.75)
Find the slope:
6.75-6/-1.5+3 = 0.75/1.5 = 0.5
Put in point slope form first: y - y1 = m (x-x1)
y - 6 = 0.5 (x + 3)
Then rewrite to standard form:
y - 6 = 0.5x + 1.5
-0.5x + y = 1.5 +6
-0.5x +y = 7.5
Related Questions
I need to graph thid inequality, while showing work. I get some right and others wrong.
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Y < 2x^2 - 1
Then first graph equation parabolic
2x^2 -1,
Then draw green lines , below 2x^2 -1
At which angle is secant of theta equals negative radical 2 question mark
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The equation is given to be:
[tex]\sec\theta=-\sqrt{2}[/tex]Recall that sec is the inverse of cos. Thus, we have:
[tex]\frac{1}{\cos\theta}=-\sqrt{2}[/tex]Rewriting the equation, we have:
[tex]\cos\theta=-\frac{1}{\sqrt{2}}[/tex]We can find the arccos of both sides:
[tex]\theta=\arccos(-\frac{1}{\sqrt{2}})[/tex]Since we know that:
[tex]\cos(-x)=\cos(x)[/tex]Then, we have:
[tex]\theta=\arccos(\frac{1}{\sqrt{2}})[/tex]Recall the identity:
[tex]\arccos(\frac{1}{\sqrt{2}})=\frac{3\pi}{4}+2\pi n,\:θ=\frac{5\pi}{4}+2\pi n[/tex]Therefore, the answer is the SECOND OPTION.
A store has 6 TV Graphic magazines and 8 News time magazines on the counter. If two customers purchased a magazine,find the probability that one each magazine was purchased
Answers
SOLUTION:
Case: Probability
Given:
Number of TV Graphic magazines = 6
Number of News time magazines = 8
Total number of magazines on the stand = 14.
*two customers purchased a magazine*
Required: find the probability that one each magazine was purchased
Method:
[tex]\begin{gathered} Pr\left(one\text{ magazine each}\right? \\ =\text{ }\frac{^{n1}C_{x1}\times^{n2}C_{x2}}{^nC_x} \\ n1=\text{ number of TV graphic magazines} \\ x1=\text{ number of TV graphic magazines selected} \\ n2=\text{ number of News time magazines} \\ x2=\text{ number of News time magazines selected} \\ n=\text{ total number of magazines selected} \\ x=\text{ total number sslected} \end{gathered}[/tex][tex]\begin{gathered} \frac{^{n1}C_{x1}\times^{n2}C_{x2}}{^nC_x} \\ \frac{^6C_1\times^8C_1}{^{^14}C_2} \\ \frac{6\times8}{91} \\ \frac{48}{91} \end{gathered}[/tex]Final answer:
The probability that one each magazine was purchased is 48/91
how manh 1- miligram doses are there in one 2- decagram container?
Answers
1 decagram = 10 grams
Also 1000 milligrams = 1 gram
From the information provided, 2 decagrams = 20 grams
If 1000 milligrams = 1 gram, then
1000 x 20 = 20 x 20 grams
20,000 milligrams = 400 grams
Similarly, If 1 decagram = 10 grams, then
0.1 decagram = 1 gram
(that is, divide 1 decagram by 10 and also divide 10 grams by 10)
However, a 2-decagram container can hold 20 grams.
(Remember that 1000 milligrams = 1 gram).
If a 2-decagram container can hold 20 grams, which is equal to 20,000 milligrams, then;
2 decagrams = 20,000 milligrams
Therefore, a 2-decagram container can hold 20,000 1-milligram doses.
Write the ratio as a fraction in lowest terms.35 minutes to 5 hours
Answers
7 : 60
Explanation:Note that:
1 hour = 60 minutes
5 hours = 5 x 60 minutes
5 hours = 300 minutes
35 minutes : 5 hours = 35 minutes : 300 minutes
35 minutes : 5 hours = 35 : 300
Divide both the numerator and denominator by 5
35 minutes : 5 hours = (35 ÷ 5) : (300 ÷ 5)
35 minutes : 5 hours = 7 : 60
The ratio of girls to boys on Mr.Miller's team is 4 to 5. If thereare 60 boys on his team, thenhow many students are there onhis team?
Answers
We have a ratio is 4 girls to 5 boys. There are 60 boys, then, we have:
[tex]\frac{4}{5}=\frac{x}{60}\Rightarrow x=\frac{60\cdot4}{5}\Rightarrow x=\frac{240}{5}\Rightarrow x=48[/tex]Then, we have 48 girls in the class.
Therefore, there are 60 boys + 48 girls = 108 students on Mr. Miller's team.
Debra started washing at 8:33 AM and finished at 9:22 AM.How long did it take her? Give your answer in minutes.
Answers
According to the given data we have the following:
Debra started washing at 8:33 AM
finished at 9:22 AM
One easy way to find out the amount of time it took to her washing her clothes would be the following:
Debra started washing at 8:33 AM, so from 8:33 am to 9 o clock 27 minutes passed.
So, if she finished at 9:22 AM, that means that we would have to add to the 27 minutes another 22 minutes, so 27+22=49 minutes.
Therefore, it took to her 49 minutes to wash her clothes.
1. The number of people attending a school meeting was 80. There were four times as many parents as supervisors atthe meeting. How many supervisors attended the meeting? How many parents?Let x = number of supervisors at the meeting.4x = number of parents at the meeting
Answers
Step 1: Write out the information provided in the question.
Number of people attending the meeting is 80.
Let the number of supervisors be x
Since there were four times as many parents as supervisors, then the number of parents will be 4x
Step 2: convert the above information to mathematical equation, the number of people attending the meeting equals to the sum of the parents and the supervisors, thus,
[tex]x+4x=80[/tex]Step 3: Solve the above equation to get the value of x
[tex]\begin{gathered} x+4x=80 \\ 5x=80 \\ \frac{5x}{5}=\frac{80}{5}(\text{divide both side by 5)} \\ x=16 \end{gathered}[/tex]Step 4: Since the number of supervisors equals x which is 16, the number of parents attending the meeting will be 4x which is
[tex]4x\Rightarrow4\times16=64[/tex]Hence, 16 supervisors and 64 parents attended the meeting
Solve for x. 9x + 7 - 3 - 4x = -26
Answers
Starting with the equation:
[tex]9x+7-3-4x=-26[/tex]Rewrite using the commutative property of addition to bring together similar terms:
[tex]9x-4x+7-3=-26[/tex]Add like terms on the left hand side of the equation:
[tex]5x+4=-26[/tex]Substract 4 fom both sides of the equation:
[tex]\begin{gathered} 5x=-26-4 \\ =-30 \end{gathered}[/tex]Divide both sides by 5:
[tex]\begin{gathered} x=-\frac{30}{5} \\ =-6 \end{gathered}[/tex]Plug in the value of x=-6 into the original equation to check your answer:
[tex]\begin{gathered} 9x+7-3-4x=-26 \\ \Rightarrow9(-6)+7-3-4(-6)=-26 \\ \Rightarrow-54+7-3+24=-26 \\ \Rightarrow-26=-26 \end{gathered}[/tex]Therefore:
[tex]x=-6[/tex]The figure represents the side view of a rectangular frame for metal shelves. Two diagonal bracessupport the frame.8 ft2 ftWhich is closest to the measure of x?7°14°28°76
Answers
AD=BC=8 ft
AB=CD=2 ft
Then,
[tex]\begin{gathered} AC=BD=\sqrt[]{2^2+8^2} \\ =\sqrt[]{68} \\ OA=OB=OC=OD=\frac{\sqrt[]{68}}{2}\text{ ft} \end{gathered}[/tex]In triangle BDC,
[tex]\begin{gathered} \tan \angle BDC=\frac{8}{2} \\ =4 \\ \angle BDC=75.963 \\ \angle DBC=14.04 \end{gathered}[/tex][tex]\begin{gathered} OE=\frac{8}{2} \\ =4\text{ ft} \\ \angle BDC=\angle OCD=75.96 \end{gathered}[/tex]In triangle ODC,
[tex]\begin{gathered} \angle ODC+\angle OCD+\angle OCD=180 \\ \\ \angle\text{DOC}=180-(2\cdot75.96) \\ \angle DOC=28 \\ \angle X=\angle DOC=28 \end{gathered}[/tex]So, the correct option is option C.
watch your P's and Q's texas instruments incorporated
Answers
Start by graphing your function in the calculator or systme you are using to graph.
we can get closer to the zeros of the functions.
The zeros of a function are the points the function cross over the x-axis, menaing that y is always 0.
According to the graph the functions has 2 zeros.
The approximate zeros will be (-9,0) and (0,0) since they are the closer to the actual point crossing th x.-axis.
Marvin is hoping to buy a used car for S4025. His parents give him $275 towards the car. To earn the rest of the money he plans to mowlawns for $50 per yard. How many yards will he need to mow to earn enough money to buy the car?O 86 yardsO 50 yardsO 80 yardsO 75 yards
Answers
Let's call the amount of yards he needs to mown as 'y'. The total value of the car is $4025, since he already have $275 from his father, the rest of the money will be the difference between those values. The rest of the money, he plans to gain by working at a rate of $50 per yard. Writing all of those informations as an equation, we get:
[tex]4025-275=50y[/tex]To find the amount of yards he needs to mow, we just have to solve this equation for 'y':
[tex]\begin{gathered} 4025-275=50y \\ 3750=50y \\ y=\frac{3750}{50}=75 \end{gathered}[/tex]He needs to mow 75 yards to buy the car.
to the nearest hundreds it says in red it got cropped out
Answers
The Circumference of the circle = 2 π r
Given the radius = r = 13 cm
So,
C = 2 * π r = 2 * 3.14 * 13 = 81.64 cm
So, to the nearest hundredth = 81.64 cm
Let angle C be congruent to angle C' and POC be congruent to P'O'C'.Let O" be a point on line CO so that CO" is equal to C'O'. Let P" be the point on line CP so that the dilation of P is represented by P".Which statement is true?A. triangle COP is equal to triangle C'O'P'B. line CP is congruent to line CP"C. triangle C'O'P is a glide reflection of triangle COP, whereas triangle CO"P" is congruent to triangle C'O'P'D. triangle CO"P" is a dilation of triangle COP with center C and a scale factor of r = C'O'/CO equals CO/CO
Answers
ANSWER
D. Triangle CO''P'' is a dilation of triangle COP with center C and a scale factor of r = C'O'/CO = CO''/CO
EXPLANATION
Given:
• ∠C ≅ ∠C'
,• ∠POC ≅ ∠P'O'C'
,• C'O' = CO''
Triangles COP and C'O'P' are similar triangles, by AA postulate.
Since CO'' and C'O' have the same length - they are congruent, then angle CO''P'' is congruent to angle C'O'P', and we can conclude that segments O''P'' and OP are parallel:
Hence, triangle CO''P'' is a dilation of triangle COP with center C and a scale factor of r = C'O'/CO = CO''/CO
4. The perimeter of a rectangular garden is 36 feet. The length of the garden is 6 less than twicethe width. Find the length and width of the garden.Variable:Equation:Variable:Equation:LengthWidth
Answers
From the question, we've been given the perimeter of the rectangular garden to be 36ft and we're told that the length is 6 less than twice the width of the garden
Given the function f(x) =x2-3x-10, determine the function of its reflection over the x axis.....x squared minus 3x minus 10.
Answers
1) Examining the function f(x)= x²-3x -10 to get this function reflected over the x axis,
We'll need to multiply the "a" parameter by -1, so that we can get:
f(x) = -x²-3x -10
15 m 9 m 9 m 9 m Find the area of this figure. I m2
Answers
we divide the figure to calculate each area and add them at the end
Parallelogram Area
[tex]\begin{gathered} A_P=b\times h \\ A_P=15\times9 \\ A_P=135 \end{gathered}[/tex]
Triangle Area
[tex]\begin{gathered} A_T=\frac{b\times h}{2} \\ \\ A_T=\frac{6\times9}{2} \\ \\ A_T=27 \end{gathered}[/tex]Total Area
[tex]\begin{gathered} A=A_T+A_P \\ A=27+135 \\ A=162 \end{gathered}[/tex]the are of this figure is 162 square meters
a woman earns $3000 per month and budgets $420 per month for food. what percent of her monthly income is spent on food
Answers
In order to calculate the required percentage, first calculate the quotient between the money spent for food and the total money of the incomes:
420/3000 = 0.14
next, multiply the previous result by 100:
0.14 x 100 = 14%
Hence, the percentage spent in food is 14%
You rent an apartment that costs $1,400 per month during the first year, but the rent is set to go up 10.5% per year. What would be the rent of the apartment during the 6th year of living in the apartment?
Answers
We will determine the rent cost after 6 years as follows:
[tex]S=1400(1+0.105)^6\Rightarrow S=2548.600147[/tex][tex]\Rightarrow S\approx2548.6[/tex]So, the rent cost after 6 years would be approximately $2548.6.
quadratic function with x intercepts -1 and 1
Answers
quadratic function with x intercepts -1 and 1:
[tex]f(x)=(x+1)(x-1)=x^2-x+x+1=x^2+1[/tex]Bх1-7-6-5.-303141516-4Find the distance between A and B.OA. V6 unitsB. 2/3 unitsC. 2V5 unitsD.4 units
Answers
With the information in the graph we have to:
[tex]\begin{gathered} AB=\sqrt{4^2+2^2} \\ AB=\sqrt{16+4} \\ AB=\sqrt{20}=\sqrt{2^2\cdot5} \\ AB=2\sqrt{5} \end{gathered}[/tex]therefore the answer is C.
I need help on solving this Did I get the right answer ? And do the table right ?
Answers
graphing on the coordinate plane how does absolute value help you write a number sentence to help you find the distance
Answers
Given:
The points 7 and -7.
Required:
We need to find the distance between 7 and -7 by using absolute values.
Explanation:
1)
We need to subtract the given numbers to find the distance.
Subtract 7 from -7 and take absolutely to find the distance.
[tex]Distance=|-7-7|[/tex]Just add the absolute value of each number together, put a negative sign in front,
[tex]Distance=|-(|-7|+|-7|)|[/tex][tex]Distance=|-(7+7)|[/tex][tex]Distance=|-14|[/tex][tex]Distance=14[/tex][tex]We\text{ know that abosulute values of negative number is postive.}[/tex]The absolute value of a number is never negative.
Answer:
The distance is non-negative. so absolute values help to avoid the negative values for distance since the absolute value of a number is never negative.
2)
Subtract 5 from -5 and take absolutely to find the distance.
[tex]Distance=|-5-5|[/tex]Just add the absolute value of each number together, put a negative sign in front,
[tex]Distance=|-(|-5|+|-5|)|[/tex][tex]Distance=|-(5+5)|[/tex][tex]Distance=|-10|[/tex][tex]Distance=10[/tex]Answer:
The distance is non-negative. so absolute values help to avoid the negative values for distance since the absolute value of a number is never negative
3)
Subtract 2 from -2 and take absolutely to find the distance.
[tex]Distance=|-2-2|[/tex][tex]Distance=|-4|[/tex][tex]Distance=4[/tex]Answer:
The distance is non-negative. so absolute values help to avoid the negative values for distance since the absolute value of a number is never negative
Final answer:
1)
The absolute value of the difference between 7 and -7 is 14.
The distance is non-negative. so absolute values help to avoid the negative values for distance since the absolute value of a number is never negative.
2)
The absolute value of the difference between 5 and -5 is 10.
The distance is non-negative. so absolute values help to avoid the negative values for distance since the absolute value of a number is never negative.
3)
The absolute value of the difference between 2 and -2 is 4.
The distance is non-negative. so absolute values help to avoid the negative values for distance since the absolute value of a number is never negative.
12. Given.4(9.2), B(-1,y), C(-5, 16),and D(-8. 11), find the value ofy so that ABCD
Answers
ok, we need to draw both segment of lines... that are parallel.
We need to re draw, because we need more space for point C (-5,16)
The steps to solve this problem are:
1) We draw segment line CD... later,
2) we express the segment line AB,
3) We find the slopes of both segments
4) finally, we found the value of y.
Do you understand? or have questions of the process?
We have done the segment line CD, after that from the graphic we can make a prediction of the value of y, because we need to find a line perpendicular to cd.. like this one (green in the graphic)... line green will be perpendicular to line yellow...
Now, we find the general equation of the yellow line.. that's it:
[tex]\begin{gathered} \text{slope = m = }\frac{\text{(y}_2-y_1\text{)}}{(x_2-x_1)};\text{ C(x}_1,y_1)=C(-5,16);\text{ D(x}_2,y_2\text{)}=D(-8,11) \\ \text{ m = }\frac{\text{(y}_2-y_1\text{)}}{(x_2-x_1)}=\frac{\text{(11}-16\text{)}}{(-8-(-5))}=\frac{\text{(11}-16\text{)}}{(-8+5)}=\frac{-5}{-3}=\frac{5}{3} \\ m=\frac{5}{3} \end{gathered}[/tex]After that, we should remember that two lines are paralell when a multiplication of its slopes it's equal to -1, like this:
[tex]\begin{gathered} \text{slope 1 }\cdot\text{ slope 2 = -1} \\ m_1\cdot m_2=-1 \\ \frac{5}{3}.m_2=-1 \\ m_2=\frac{-3}{5} \end{gathered}[/tex]Finally, we find the generall equation of the line green with the point A(9,2) and the value of its slope m2, we apply:
[tex]\begin{gathered} (y-y_1)=m(x-x_1);\text{ A(x}_1,y_1)=A(9,2);\text{ m=}\frac{-3}{5};\text{ We replace and get} \\ y-2=\frac{-3}{5}(x-9) \\ y=\frac{-3}{5}x+\frac{3}{5}\cdot\frac{9}{1}+2 \\ y=\frac{-3}{5}x+\frac{27}{5}+2 \\ y=\frac{-3}{5}x+\frac{37}{5} \end{gathered}[/tex]Now, to find the value of y in the poin B, we replace the value of x = -1 in the equation of the green line, like this:
[tex]\begin{gathered} y=\frac{-3}{5}x+\frac{37}{5};\text{ x=-1} \\ y=\frac{-3}{5}(-1)+\frac{37}{5} \\ y=\frac{3}{5}+\frac{37}{5}=\frac{40}{5}=8 \end{gathered}[/tex]The answer has the value of 8. In graphic is similar.. green line... It's not equal because I do the graphic at inexact way.
Angles C and D are acute angles of a right triangle. Given sin D=2/7, which statement is true?
Answers
Answer
Option D is correct.
Cos C = (2/7)
Explanation
In a right-angle triangle, the side opposite the right angle is the Hypotenuse, the side opposite the given angle that is non-right angle is the Opposite and the remaining side is the Adjacent.
A sketch of this right triangle will be
This sketch allows Sin D = (2/7)
To know the right answer, we need to find the last side of the triangle
The Pythagoras Theorem is used for right angled triangle, that is, triangles that have one of their angles equal to 90 degrees.
The side of the triangle that is directly opposite the right angle or 90 degrees is called the hypotenuse. It is normally the longest side of the right angle triangle.
The Pythagoras theorem thus states that the sum of the squares of each of the respective other sides of a right angled triangle is equal to the square of the hypotenuse. In mathematical terms, if the two other sides are a and b respectively,
a² + b² = (hyp)²
For this question,
a = 2
b = ?
hyp = 7
a² + b² = (hyp)²
2² + b² = 7²
4 + b² = 49
b² = 49 - 4
b² = 45
b = √45
So, we can evaluate each of these
Cos D = (√45)/7
Cos C = (2/7)
Hope this Helps!!!
Answer: cos C = 2/7
Step-by-step explanation: I took the test.
Evaluate the function when x= -2,0, and 59) v(x)=12-2x-5
Answers
we have the function
[tex]V(x)=12-2x-5[/tex]Combine like terms and rewrite the given function
[tex]V(x)=7-2x[/tex]Evaluate for x=-2
[tex]\begin{gathered} V(-2)=7-2(-2) \\ V(-2)=7+4 \\ V(-2)=11 \end{gathered}[/tex]Evaluate for x=0
[tex]\begin{gathered} V(0)=7-2(0) \\ V(0)=7 \end{gathered}[/tex]Evaluate for x=5
[tex]\begin{gathered} V(5)=7-2(5) \\ V(5)=7-10 \\ V(5)=-3 \end{gathered}[/tex]The junior class is selling fruit bars to raise money. They purchased 1250 fruit bars and paid a delivery fee of $25. The total cost, including the delivery fee, was $800. What was the cost of each bar?
Answers
Number of fruit bars purchased = 1250.
Delivery fee = $25
Total cost including the delivery fee = $800.
Therefore, the cost without delivery fee = 800-25 = $775.
Therefore, the cost of fruit bars purchased = $ 775.
So, the cost of 1 fruit bar, is,
[tex]\frac{775}{1250}=0.62[/tex]Therefore, the cost of 1 fruit bar is $ 0.62.
Can someone calculate this using the correct number of significant figures? 7166.0-2.4*10^23
Answers
Writing both terms in scientific notation, we have:
7166.0 = 7.1660*10³
So, this term has 4 significant figures (.1660)
2.4*10^23 is already written in scientific notation. So it has 1 significant figure (.4)
Now, when summing or subtracting two quantities, the number of significant figures of the result equals the smaller number of significant figures. So, in this case, the result has 1 significant figure.
Then, proceeding with the calculation, we have:
7166.0 - 2.4*10^23 = 7.1660*10³ - 2.4*10^23 = (7.1660 - 2.4*10^20) * 10³
= (7.1660 - 240,000,000,000,000,000,000.0) * 10³
= -239,999,999,999,999,999,992.8340
Finally, we need to round the first significant figure, so there will be only one significant figure in the result:
-239,999,999,999,999,999,992.8
An applicant receives a job offer from two different companies. Offer A is a starting salary of $58,000 and a 3% increase for 5 years. Offer B is a starting salary of $56,000 and an increase of $3,000 per year. Determine whether offer B can be represented by an arithmetic or geometric series and write the equation for Bn that represents the total salary received after n years. Justify your reasoning mathematically.
Answers
Offer B canbe represented by an arithmetic sequence because there is a constant difference between the salary of two consecutive years.
The sequence can be written as follow:
Bn = 56,000 + 3,000n
where n is the number of years in the job.
By subtracting B(n+1) - Bn, you obtain:
[tex]\begin{gathered} B_{n+1}-B_n=56,000+3,000(n+1)-56,000-3,000n \\ B_{n+1}-B_n=3,000 \end{gathered}[/tex]As you can notice, the difference of the salaries between two consecutive years is constant, which means that Bn is an arithmetic sequence.
6x = 3/2 what does the x equal to
Answers
The equation to be solved is given to be:
[tex]6x=\frac{3}{2}[/tex]To get the value of x in the equation, we just multiply both sides of the equation by 1/6. This is shown below:
[tex]6x\times\frac{1}{6}=\frac{3}{2}\times\frac{1}{6}[/tex]Hence, we have:
[tex]x=\frac{3}{12}[/tex]We can further simplify by dividing the numerator and denominator of the right-hand side by 3. Hence, the answer is:
[tex]x=\frac{1}{4}[/tex]