We can express the area of a triangle as half the product of its base and height:
[tex]A=\frac{b\cdot h}{2}[/tex]Then, we can express the base in function of the known variables (area and height) as:
[tex]\begin{gathered} A=\frac{b\cdot h}{2} \\ 2A=b\cdot h \\ b=\frac{2A}{h} \end{gathered}[/tex]We replace with the known values (A=432 sq in, h=48 in) and calculate the base b:
[tex]b=\frac{2\cdot432\text{ in}^2}{48\text{ in}}=18\text{ in}[/tex]Answer: the base is 18 inches.
Granny Smith is making strawberry jelly. She places 6.3 ounces in each jar to give as gifts.granny was able to fill 9.5 jars. How many ounces of strawberry jelly did granny make
Working 5 hours a day, A can Complete a work in 8 days and working 6 hours a day, B can complete the same work in 10 days. Working 8 hours a day, they can jointly complete the work in how many days?
After solving the equation, If both A and B of them worked together, then Working 8 hours a day, they can jointly complete the work in 6 days.
What is an equation?Two mathematical expressions' values are said to be equal in an equation, which is a statement of this fact. A mathematical formula declares that two things are equal.
The equals sign ('=') is used to indicate it.
Let the work completed be W
For A
W = 5hours = 1/8 days
1 hour = 1/8 days ÷ 5
1 hour = 1/40 days
For B
W = 6 hours = 1/10 days
1 hour = 1/60 days
Add both the equation
1 hours + 1 hours = 1/40 days + 1/60 days
2 hours = 5/120 days
2 hours = 1/24days
If both of them worked for 1 hour a day
1 hour = 1/48 days
If both of them worked for 8hour a day
8 hours = 1/48 × 8
= 1/6 days
Thus, if both of them worked together, then Working 8 hours a day, they can jointly complete the work in 6 days.
Learn more about equations
https://brainly.com/question/2972832
#SPJ9
If sin 0= -3/5 in quadrant 3, what is cos 0?
Given
[tex]sin\theta=-\frac{3}{4}[/tex]Solution
Recall : SOHCAHTOA
The final answer
Option A
[tex]Cos\text{ }\theta=-\frac{4}{5}[/tex]I need help with this practice,I will send you an additional pic that goes along with this problem Freya went to her local park to find 5 organisms/species She found 5 and wrote down the name of these organisms and the quantity of each she seen:Eastern gray squirrels/14 individualsWolf spiders/2 individualsPaper wasps/9 individualsBlack vulture/1 individualNorthern cardinals/7 individuals
ANSWER :
The answer is 5/33 or 0.15
EXPLANATION :
From the problem, we have a total of 5 number of species.
Using the given Biodiversity Index formula :
[tex]\frac{\text{ total number of species}}{\text{ total number of individuals}}=\frac{5}{14+2+9+1+7}=\frac{5}{33}\quad or\quad0.1515[/tex]3 1/4 - 3 1/6 uhmmm yeahh
Given the Subtraction:
[tex]3\frac{1}{4}-3\frac{1}{6}[/tex]You can identify that the denominators are different, then, you need to follow these steps in order to find the Difference (the result of the Subtraction):
1. Find the Least Common Denominator (LCD):
- Decompose the denominators into their Prime Factors:
[tex]\begin{gathered} 4=2\cdot2=2^2 \\ 6=2\cdot3 \end{gathered}[/tex]- Multiply the common and non-common factors with the largest exponents:
[tex]LCD=2^2\cdot3=12[/tex]2. Divide the LCD by each original denominator and multiply the Quotient by the corresponding numerator:
[tex]\begin{gathered} =3\frac{1\cdot3}{12}-3\frac{1\cdot2}{12} \\ \\ =3\frac{3}{12}-3\frac{2}{12} \end{gathered}[/tex]3. Subtract the whole number parts and then subtract the fractions. You get:
[tex]\begin{gathered} =0\frac{3-2}{12} \\ \\ =\frac{1}{12} \end{gathered}[/tex]Hence, the answer is:
[tex]=\frac{1}{12}[/tex]Travelers arriving at Cape Town International Airport 70% of the travelers fly on major airlines, 20% by on privately owned planes and the remainder by on commercially owned planes not belonging to a major airline. Of those traveling on major airlines, 40 degrees are traveling for business reasons, whereas 70% of those arriving on private planes and 80% of those arriving on other commercially owned planes are traveling for business reasons Suppose that we randomly select one person arriving at this airport. What is the probability that the traveler is flying privately for business reasons?
Step 1
Given;
[tex]\begin{gathered} 20\text{\% fly privately owned jets} \\ 70\text{\% of those arriving on the plane are travelling for business reason} \end{gathered}[/tex]i need help with my homework PLEASE CHECK WORKnumber 4
ANSWER:
Option c
[tex]h=-\frac{\operatorname{\ln}(0.62)}{0.079}[/tex]STEP-BY-STEP EXPLANATION:
The function given in the statement is the following:
[tex]D(h)=615\cdot\:e^{-0.079h}[/tex]If D(h) = 383, we substitute and solve for h, just like this:
[tex]\begin{gathered} 383=615\cdot \:e^{-0.079h} \\ \\ e^{-0.079h}=\frac{383}{615} \\ \\ \ln(e^{-0.079h})=\ln\left(\frac{383}{615}\right) \\ \\ -0.079h=\ln(0.62) \\ \\ h=-\frac{\ln(0.62)}{0.079} \end{gathered}[/tex]Therefore, the correct answer is option c.
Jamar finds some nickels and quarters in his change purse. How much money (in cents) does he have if he has 4 nickels and 11 quarters? How much money (in cents) does he have if he has n nickels and q quarters?
1 nickel is worth 5 cents and 1 quarter is worth 25 cents.
So, if he has 4 nickels, this is worth 4 times 5 cents and if he has 11 quarters, this is worth 11 times 25 cents.
Both are worth the sum of these, so:
[tex]4\cdot5+11\cdot25=20+275=295[/tex]So, he has 295 cents.
If he has n nickels and q quarters, he has 5 times n plus 25 times q worth, so he has:
[tex]5n+25q[/tex]How many solutions does the system of equations have? Explain1. Y = 5x - 4Y = -4 + 5xHow many solutions does the system of equations have? Explain2.Y=2x+3Y=-3x+6How many solutions does the system of equations have? Explain3. Y=-4x+5Y=-4x+5How many solutions does the system of equations have? Explain
1. it has infinite solutions because since the equations are equal it is a line equation and a line has infinite points
2. It will have only one solutions, because the lines aren't parallel or the same line (we know that because there won't be a number that you can multiply by one of the equations and obtain the other one)
3.it has infinite solutions because since the equations are equal it is a line equation and a line has infinite points
Find the exact values of the remaining trigonometric functions of if terminates in Quadrant IV and tan() = −3/4.
We know that the angle terminates in the fourth quadrant and that the tangent of it is -3/4.
Angles that are on the fourth quadrant have a negative sine and a positive cosine.
We can start with the cot():
[tex]\cot\theta=\frac{1}{\tan\theta}=\frac{1}{-\frac{3}{4}}=-\frac{4}{3}[/tex]We can relate the cosine with the tangent as:
[tex]\begin{gathered} \tan\theta=\frac{\sin\theta}{\cos\theta}=\frac{\sqrt{1-\cos^2\theta}}{\cos\theta} \\ -\frac{3}{4}=\frac{\sqrt{1-\cos^2\theta}}{\cos\theta} \\ -\frac{3}{4}\cos\theta=\sqrt{1-\cos^2\theta} \\ (-\frac{3}{4}\cos\theta)^2=1-\cos^2\theta \\ \frac{9}{16}\cos^2\theta=1-\cos^2\theta \\ (\frac{9}{16}+1)\cos^2\theta=1 \\ \frac{9+16}{16}\cos^2\theta=1 \\ \frac{25}{16}\cos^2\theta=1 \\ \cos^2\theta=\frac{16}{25} \\ \cos\theta=\sqrt{\frac{16}{25}} \\ \cos\theta=\frac{4}{5} \end{gathered}[/tex]We can now calculate the sine of the angle as:
[tex]\begin{gathered} \sin\theta=\tan\theta\cdot\cos\theta \\ \sin\theta=-\frac{3}{4}\cdot\frac{4}{5}=-\frac{3}{5} \end{gathered}[/tex]We can now calculate the sec() and csc() as:
[tex]\begin{gathered} \sec\theta=\frac{1}{\cos\theta}=\frac{5}{4} \\ \\ \csc\theta=\frac{1}{\sin\theta}=-\frac{5}{3} \end{gathered}[/tex]Answer:
sin() = -3/5
cos() = 4/5
cot() = -4/3
sec() = 5/4
csc() = -5/3
Fine the end behavior and x-value of holeEquation is to the right
Given the function:
[tex]\: f\mleft(x\mright)=\frac{x+1}{\left(x-3\right)\left(x^2-1\right)}[/tex]The end behaviour of the function f(x) describes the behaviour of the function as x approaches +∞ and -∞.
When x approaches +∞,
[tex]\lim _{x\rightarrow\infty}f(x)=\text{ }\lim _{x\rightarrow\infty}\frac{x+1}{(x-3)(x^2-1)}=0[/tex]Thus, as x approaches +∞, the function f(x) approaches zero.
When x approaches -∞,
[tex]\lim _{x\rightarrow-\infty}f(x)=\text{ }\lim _{x\rightarrow-\infty}\frac{x+1}{(x-3)(x^2-1)}=0[/tex]Thus, as x approaches -∞, the function f(x) approaches zero.
x-value of the hole:
For a rational function f(x) given as
[tex]f(x)=\frac{p(x)}{q(x)}[/tex]Provided that p(x) and q(x) have a common factor (x-a), the function f(x) will have a hole at x=a.
Thus, from the function f(x)
[tex]f(x)=\frac{x+1}{(x-3)(x^2-1)}[/tex]by expansion, we have
[tex]f(x)=\frac{x+1}{(x-3)(x^{}-1)(x+1)}[/tex]The expression (x-1) is a common factor of the numerator and the denominator.
Thus,
[tex]\begin{gathered} x-1=0 \\ \Rightarrow x=1 \end{gathered}[/tex]Hence, the x-value of the hole is 1.
Use the ALEKS calculator to write as a percentage.
31
32
Round your answer to the nearest tenth of a percent.
0%
X 5
?
Divide 31 into 32 and then multiply the result by 100 to get the percent:
[tex]\begin{gathered} \frac{31}{32}=0.96875 \\ \\ 0.96875*100=96.875 \end{gathered}[/tex]Then, to the nearest tenth of a percent the given fraction is 96.9%Save-A-Lot Bank is advertising a rate of 2.5% interest compounded annually.If $2000 is invested, how much money, to the nearest cent, will be inthe account after 10 years.
Question on Compound Interest.
The formula below can be used to calculate the compound interest;
[tex]\begin{gathered} A\text{ = p(1+}\frac{r}{100})^n \\ \text{Where A = amount,(\$) (that is, the money that will be in the account)} \\ r=\text{interest rate per annum, (\%)} \\ P=Pr\text{incipal, (\$), ( that is, the money invested)} \\ n=\text{ number of periods, years, } \end{gathered}[/tex]Where A= ? , P =$2000, r =2.5% and n = 10 years
Substituting these values into the formula above, we get
Note that: Amount = Principal + Interest, though not needed in this question.
[tex]\begin{gathered} A=P(1+\frac{r}{100})^n_{} \\ \\ A=2000(1+\frac{2.5}{100})^{10} \\ \\ A=2000(1+0.025)^{10} \\ A=2000(1.025)^{10}\text{ }=\text{ 2560.169 }\approx\text{ \$2560.17} \end{gathered}[/tex]Thus, the correct answer is $2560.17
Consider the following system of equations 4x + 6=24 and 2x + 3y=8 How many solutions does this system have? Justify your answer. Part B If we triple each side of the first equation 4x+6y=24, we have 12x+18y=72. Explain why the new system 12x+18y=72 and 2x+3y=8 has the same number of solutions as the original system.
The solution of the given system of equation will have infinite many solutions.
In the above question, the following equations are given
4x + 6y = 24
2x + 3y = 8
Now, we need to find the number of solutions that this system of equation will have
We know that,
a1 x + b1 y = c1
a2 x + b2 y = c2
is the general system of equation, and
[tex]\frac{a1}{a2} \neq \frac{b1}{b2}[/tex] then unique solution, or
[tex]\frac{a1}{a2} = \frac{b1}{b2} = \frac{c1}{c2}[/tex] then there will be infinite solutions or,
[tex]\frac{a1}{a2} = \frac{b1}{b2} \neq \frac{c1}{c2}[/tex] then there will be no solution
Now, we'll check for the given system of equations
a1 = 4, b1 = 6 , c1 = 24
a2 = 2, b2 = 3 , c2 = 8
[tex]\frac{a1}{a2} = \frac{b1}{b2} \neq \frac{c1}{c2}[/tex] = 2 = 2 [tex]\neq[/tex] 3
As this condition satisfies the third condition, the solution of the given system of equation will have infinite many solutions.
Now as we multiply the first equation 4x + 6=24 by 3 we get we have 12x+18y=72, the system will still have same solutions as only the equations are multiplied by a constant k = 3 which does not affect the solution.
To learn more about, system of equations, here
https://brainly.com/question/24065247
#SPJ1
Given the formula FV = P + Prt, what is the future value of a savings account that had an initial deposit of $7,900 earning 6.5% simple interest for 4 years?$10,074.23$9,954.00$9,376.85$10.756.43None of these choices are correct.
Step 1: Use the formula below to find the future value:
Fv = P + Prt
P = present value or initial deposit
r = rate in %
t = time in years
Step 2: List the given data
P = $7900
r = 6.5% = 0.065
t = 4 years
Step 3: Substitute the values of P, r and t to find the future value.
FV = P + Prt
= 7900 + 7900 x 0.065 x 4
= 7900 + 2054
= $9954.00
Stop 4: Final answer
Future value = $9954.00
HELP PLEASEEEEE!!!!!!
One rational number between -0.45 and -0.46 is -0.451, such that:
-0.45 > -0.451 > -0.46
How to find a rational number in the given interval?
So we want to find a rational number between -0.45 and -0.46. Remember that any decimal number with a finite number of digits after the decimal point (like the above numbers) is a rational number.
So:
3.16436
2.21412
1.4
All of these are rational numbers.
Then a rational number on the interval -0.45 and -0.46 could be -0.451, which is smaller than -0.45 and larger than -0.46
Learn more about rational numbers:
https://brainly.com/question/12088221
#SPJ1
I need help identifying the coordinates
The z-score values for the given quantile are found.
What is defined as the z-score?A Z-Score is a measurable statistic of a score's connection to the mean among a set of scores.A Z-score can tell a trader whether a value is usual for a given data set or atypical.In contrast, the Z-score is the amount of standard deviations a provided data point is from the mean. The Z-score is negative for data points that fall below the mean. 99% of values in most large data sets have a Z-score among -3 and 3, indicating that they are three deviations above and below mean.For the given question;
The given normal quantile plot are-
-1.28, -0.52, 0.00, 0.52, 1.28
The corresponding z-score taken from the positive and negative z table are-
-1.28 = 0.101-0.52 = 0.3050.00 = 0.500.52 = 0.6981.28 = 0.899The z-score values for the given quantile are found.
To know more about the z-score, here
https://brainly.com/question/15333077
#SPJ13
Identifying the Type of Series
3+6+12+ 24 + ...
5+7+10+14+
1+2+3+4+
2+4+2+4+
Answer:
geometric, neither, arithmetic, and neither
Step-by-step explanation:
right on edg 2023
Jose hopes to earn $1400 in interest in 3.4 years times from $56,000
To solve this problem, we will use the formula for compound interest:
[tex]r=k\cdot((\frac{P_N}{P_0})^{1/(NK)}-1).[/tex]Where:
• Pₙ = principal amount after N years,
,• P₀ = initial principal amount,
,• r = interest ratio in decimals,
,• k = compound periods per year.
From the statement, we know that:
• N = 3.4 years,
• P₀ = $56,000,
• Pₙ = P₀ + interest = $56,000 + $1,400 = $57,400,
,• r = ?,
,• k = 4 (the interest is compounded quarterly.
Replacing these values in the formula above, we get:
[tex]r=4\cdot((\frac{57400}{56000})^{1/(3.4\cdot4)}-1)\cong0.00727=0.73\%.[/tex]AnswerThe annual interest must be 0.73%.
Find the equation for the circle with a diameter whose endpoints are (8,17) and (4, - 15).
Answer:
Given that,
Circle with a diameter whose endpoints are (8,17) and (4, - 15).
To find the equation for the circle
we know that,
Equation of the circle is of the form,
[tex](x-h)^2+(y-k)^2=r^2[/tex]where r is the radius and (h,k) is the center of the circle.
If the end points of the diameter is given, then the equation of the circle is,
[tex](x-x1)(x-x2)+(y-y1)(y-y2)=0[/tex]Substitute the points we get,
[tex](x-8)(x-4)+(y-17)(y+15)=0[/tex]On simplifying this we get,
[tex]x^2-8x-4x+32+y^2-17y+15y-255=0[/tex][tex]x^2+y^2-12x-2y-223=0[/tex]A submarine sandwich shop surveyed a group of 20 prospective customers surveyed would be willing to pay a maximum of $4.01 to $5
A. 20 %
B.30%
C.5%
D.10%
Answer: 10%
Step-by-step explanation:
2 out of 20 people are willing to pay a maximum of 4.01 to 5 which is 0.10 which equals 10%
10. The product of 6 and a number when added to 5 is equal to 1 less than 9 times the number.
Answer:
x = 2
Step-by-step explanation:
Hello!
Let the unknown number be x. The product of 6 and that number can be represented by 6x. And since we are adding 5, we can use 6x + 5 to represent that expression.
This equation is equal to the difference of 9x and 1, or 9x - 1.
Solve for x6x + 5 = 9x - 15 = 3x - 16 = 2x2 = xThe value of x is 2.
I'll send a picture! please answer fast!
Given data:
The given expression for the points is,
[tex]10w-3t+5[/tex]Thus, the expression or
Solve the following. List all possible possible solutions for the ambiguous case. #7
The sum of the interior angles of any triangle is always 180º:
[tex]A+B+C=180[/tex]Use the equation above and the given data to find C:
[tex]\begin{gathered} C=180º-A-B \\ C=180º-38º-72º \\ C=70º \end{gathered}[/tex]Law of sines:
[tex]\frac{a}{sinA}=\frac{b}{sinB}=\frac{c}{sinC}[/tex]Use the pair of ratios for a and b to solve a:
[tex]\begin{gathered} \frac{a}{sinA}=\frac{b}{sinB} \\ \\ a=sinA*\frac{b}{sinB} \\ \\ a=sin38º*\frac{12}{sin72º} \\ \\ a=7.8 \end{gathered}[/tex]Use the pair of ratios for b and c to solve c:
[tex]\begin{gathered} \frac{c}{sinC}=\frac{b}{sinB} \\ \\ c=sinC*\frac{b}{sinB} \\ \\ c=sin70º*\frac{12}{sin72º} \\ \\ c=11.9 \end{gathered}[/tex]Thenm, the solution for the given triangle is:A=38ºB=72ºC=70ºa=7.8b=12c=11.9After a 35% reduction, you purchase a new bike for $282.75. What was the price of the bike before the reduction?
A) First write an equation you can use to answer this question. Use x as your variable and express any percents in decimal form in the equation.
B) Solve your equation in part [A] to find the original price of the bike.
The equation to represent this situation is given by 0.65x = 282.75 .
In the various mathematical formulas that are used, the equals sign is used to show that two expressions on either side of the equal sign are equal. The meaning of the word equation and its cognates might vary slightly depending on the language.
Finding the exact values of the unknown variables that result in the given equality is the very first step in the solving of a variable equation. The values of the unknown variables that fulfil the equality are the equation's solutions, also known as the variables for which the equation must be solved. There are two sorts of equations.
Le t the original cost of the bike be x dollars.
After 35% reduction the new cost is x - (35% of x) = 0.65 x
Therefore 0.65 x = 282.75
or, x = 435
Therefore the cost of the bike is $435.
To learn more about equation visit:
https://brainly.com/question/10413253
#SPJ1
factorise 10y²+21y-10
Answer:
(2y+5)x(5y-2)
Step-by-step explanation:
For a polynomial of the form ax² - bx + c rewrite the middle term as a sum of two terms whose product is a·c=10·-10 = -100 and whose sum is b= 21.
We factor 21 out of 21y.
[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{10y^{2}+21(y)-10 } \end{gathered}$}}[/tex]
Rewrite 21 as −4 plus 25.
[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{10y^{2}+(-4+25)y-10 } \end{gathered}$}}[/tex]
Apply the distributive property.
[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{10y^{2}-4y+25y-10 } \end{gathered}$}}[/tex]
Factor the highest common denominator of each group. Group the first two terms and the last two.
[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{(10y^{2}-4y)+25y-10 } \end{gathered}$}}[/tex]
Factor the highest common denominator (GCF) of each group.
[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{2y(5y-2)+5(5y-2) } \end{gathered}$}}[/tex]
Factor the polynomial by factoring the greatest common denominator, 5y-2.
[tex]\boxed{\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{(5y-2)(2y+5) } \end{gathered}$}}}[/tex]
The answer is: (5y - 2)(2y + 5)Kali just started a new sales floor job to save for college. She earns 15.75 plus a flat fee of 50 . She wants to earn between 200 and 400 . The following inequality represents her earning potential
200 ≤ 15.75x + 50 ≤ 400 Solve the inequality PLEASE HELP ASAP
!!
Kali needs to work between 10 to 22 hours to earn an income between 200 and 400
Flat fee earned by Kali = 50
Earning per hour of Kali = 15.75
Required income is between 200 and 400
Inequality: Mathematical expressions with inequalities are those in which the two sides are not equal. Contrary to equations, we compare two values in inequality. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign.
Inequality represents the equation:
200<=15.75x + 50<=400
200<= 15.75x + 50
150<= 15.75x
x = 9.52
So, she needs to work a minimum of 10 hours
15.75x+50<=400
15.75x <=350
x <= 22.22
So, she can work a maximum of 22 hours
Learn more about inequality:
https://brainly.com/question/20383699
#SPJ1
In how many ways can a committee of 5 be chosen from 9 people given that Jones must be one of them?
There are 126 ways to choose a committee of five from a group of nine people using combinations; one of them must include JONES.
What do we mean by COMBINATIONS?Combinations are a mathematical method for calculating the number of alternative arrangements. In a collection of objects where the order of the selection is irrelevant. You are free to choose any combination of the available things.Mathematically it can be expressed as : nCr = n! / r!(n-r)!So, we have a comiitte of 5 be chosen from 9 people and JONES must be one of them -
Using the rule of combinantion - nCr = n! / r!(n-r)!We have n = 9 and r= 59C5 = 9! / 5!(9-5)!C(9,5) = 3024/24C(9,5) = 126Therefore, there are a total of 126 ways in which we can decide that JONES must be on it.
Know more about combinations here:
https://brainly.com/question/28065038
#SPJ9
URGENT!! ILL GIVE
BRAINLIEST!!!!! AND 100
POINTS!!!!!
The correct option b: 49° because the angles are supplementary to angle d.
What is defined as supplementary angles?The definition of supplementary is linked to angles that form a straight angle when joined together. When two angles add up to 180 degrees, they are referred to as supplementary angles. If two angles are supplementary. One of its angles is just an acute angle, while another is an obtuse angle.For the given question.
∠d = 131 degrees.
∠d + ∠f = 180 (supplementary angle)
∠f = 180 - 131
∠f = 49 degrees
Now,
∠f = ∠g = 49 degrees (vertically opposite angles)
∠f = ∠c = 49 degrees (alternate interior angles)
Thus, the angle d is supplementary to angle f, c and g.
To know more about the supplementary angles, here
https://brainly.com/question/12919120
#SPJ13
Given the general form: F( x )= a(x^2)+bx+cConvert it to vertex form (also known as standard form) by putting the values for a,h and k into the correct boxes.F(x)=a(x-h)^2+kIdentify the vertex(x,y)General form: F( x )=1 x^2+6 x +-1 Vertex form: F( x )= Answer for part 1 and coordinate 1 (x- Answer for part 1 and coordinate 2 )^2 +Answer for part 1 and coordinate 3Vertex: (Answer for part 2 and coordinate 1,Answer for part 2 and coordinate 2)
1) In order to convert from the standard version to the vertex form we'll need to find the vertex of that parabola:
[tex]f(x)=x^2+6x-1[/tex]We can find the vertex, using these formulas:
[tex]\begin{gathered} x=h=-\frac{b}{2a}=\frac{-6}{2}=-3 \\ k=(-3)^2+6(-3)-1=9-18-1=9-19=-10 \\ V(-3,-10) \end{gathered}[/tex]So this is the vertex of that parabola at point (-3,-10)
2) Now, note that the coefficient a = 1, and with the vertex, we can now rewrite that equation into the vertex form:
[tex]\begin{gathered} y=a(x-h)^2+k \\ y=(x-(-3))^2+(-10) \\ y=(x+3)^2-10 \end{gathered}[/tex]