If x=2 calculate the value of x squared +2x

Answers

Answer 1

Firstly, I substituted the x for 2 in the equation [tex]2^2+2(2)[/tex].
Secondly, simplify 2(2) to 4 so [tex]2^2+4[/tex]
Thirdly, simplify 2^2 to 4 so 4+4.Fourth, 4+4 is 8.

Related Questions

At the corner store, Nico bought 5 pencils for $0.10 each and 3 pens for $0.50 each. He used t to represent the sales tax, in dollars, that he also paid. He paid a total of $2.12, including tax.

Nico wrote this equation to represent what he paid. What errors, if any, did he make?

5(0.10) + 3(0.50) - t = 2.12
He should have multiplied 0.10 by 3 instead of 5.
He should have multiplied 0.50 by 5 instead of 3.
He should have added t instead of subtracting t.
He should have multiplied by t instead of subtracting t.

Answers

Answer:

C. He should have added t instead of subtracting t.

Step-by-step explanation:

Answer:

Step-by-step explanation:

A recipe calls for 1 1/2 cups of flour, 3/4 cup of white sugar, and 1/3 cup of brown sugar. The recipe makes 6 servings.

How many cups of flour are there per serving? Show your work.
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How many total cups of sugar (white and brown) are there per serving? Show your work.
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Suppose you modify the recipe so that it makes 9 servings. How much more flour do you need for the modified recipe than you need for the original recipe? Show your work.
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Answer all 3 questions.

Answers

A recipe calls for 1 1/2 cups of flour, 3/4 cup of white sugar, and 1/3 cup of brown sugar. The recipe makes 6 servings.

How many cups of flour are there per serving? Show your work.

1 1/2 = 3/2

3/2 x 1/6 = 3/12 = 1/4
answer 1/4 cup of flour per serving

How many total cups of sugar (white and brown) are there per serving? Show your work.

sugar = 3/4 +1/3 = 9/12 + 4/12 = 13/12 (6 servings)

1 serving = 13/12 x 1/6 = 13/72

answer
13/72 sugar (white and brown) per serving

Suppose you modify the recipe so that it makes 9 servings.
1/4 cup of flour per serving
so
9 x 1/4 = 9/4 = 2 1/4

answer
2 1/4 cups of flour for 9 servings

Some luggage pieces have wheels and a handle so that the luggage can be pulled along the ground. Suppose the length from the bottom of the bag to the place on the floor perpendicular to the hand on the bag is 14 inches, and the length of the bag with its handle is 19 inches. At which angle made by the bag and the floor would it be comfortable to roll the bag?

Answers

Draw a right triangle with adjacent-leg equal to the length from the bottom to the place on the floor, whose meausre is 14 inches, and the hypotenuse is 19 inches.

The trigonometric ratio cosine, relates the angle with those lengths:

cos(angle) = adjacent-leg / hypotenuse = 14 / 19

=> angle = arc cosine (14/19) = 42.5°

Answer: 42.5°

Which of the following represents the zeros of the function
g(x) = x3 - 9x2 + 2x + 48 ?

A. x= -8, x= 2 , and x= -3
B. x = 8, x = -2 , and x = 3
C. x = 6, x = -4 , and x = 9
D. x = -6, x = 4 , and x = -9

Answers

g(x) = x^3 - 9x^2 + 2x + 48 ?

Probe some roots. When you use x = - 2

you will have: (-2)^3 - 9(-2)^2 + 2(-2) + 48 = -8 - 36 - 4 + 48 = 0

So, - 2 is a root

From that you can divide x^3 - 9x^2 + 2x + 48 by x + 2 and you will get

x^2 - 11x + 24

Then you can factor that: (x - 8)(x - 3)

So, the three roots are x = - 2, x = 3 and x = 8, which is the option B.

Answer: option B. x = 8, x = -2 , and x = 3

last week, several gas stations in a neighborhood all charged the same price for a gallon of gas.The table below shows how much gas prices have changed from last week to this week.

a. Order the numbers in the table from least to greatest.

b. Which gas station has the cheapest gas this week?

c. Critical Thinking. Which gas station changed their price the least this week?

Gas and Samson. Star
Go. Gas. Gas
-6.6. 5.8. -6 3/4

Corner store. tip top
27/5. shop
-5 5/8

Answers

To compare the numbers, we'd better convert the fractions into decimals.

–6 3/4 = –6.75
27/5 = 5.4
–5 5/8 = –5.625

Now that the numbers are –6.6, 5.8, –6.75, 5.4 and –5.625.
a) A negative number is always less than a positive number. In addition, a negative with a larger magnitude would be less. Like –4 < –3. So the order from least to greatest is –6.75 < –6.6 < –5.625 < 5.4 < 5.8. In other words, –6 3/4 < –6.6 < –5 5/8 < 27/5 < 5.8.

b) A negative change means that the gas price decreased. The gas station that decreased the gas price the most is the Star gas since the –6 3/4 is the least number in the list.

c) The changes in prices can be compared in relation to each other based on their magnitude, which is the value without the sign. For example, the magnitude of –4 is 4. The magnitudes of the changes in prices are 6.6, 5.8, 6.75, 5.4 and 5.625. So the least change is 5.4, that is, 27/5. So the Corner Store changed the price the least.

Final answer:

Without the correctly formatted data, we cannot give direct answers. However, the answers would come from ordering the data from least to greatest, identifying the least positive or most negative change as the cheapest gas, and the smallest change as the least change in price.

Explanation:

Unfortunately, the question you provided is a bit unclear because the table is not formatted correctly. However, it's clear that you're asked to analyze a set of data, which refers to changes in gas prices at several gas stations. Usually, to order the numbers from least to greatest, you would list them in ascending numerical order, taking into account whether they are positive or negative, with negative numbers being less than positive numbers. The gas station with the cheapest gas this week would be the one with the least positive change or the greatest negative change. The gas station that changed their price the least would be the gas station with the smallest change in price, whether positive or negative. However, without the correct formatting of data, I am unable to provide specific answers. It's always important to check your data for clarity in order to perform accurate mathematical analyses. These principles of data analysis and number order are crucial skills in your mathematical education.

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If 4f(x)+f(5-x)=x2

What is f(x)?

Answers

We are given that [tex]4f(x)+f(5-x)=x^2[/tex].

Substitute x with 5-x, then the above equation becomes:

[tex]4f(5-x)+f(5-(5-x))=(5-x)^2[/tex], that is

[tex]4f(5-x)+f(x)=(5-x)^2[/tex]

So, we have the following system of equations:

i) [tex]4f(x)+f(5-x)=x^2[/tex]
ii) [tex]4f(5-x)+f(x)=(5-x)^2[/tex]

multiply the first equation by -4, so that we eliminate f(5-x)'s

i) [tex]-16f(x)-4f(5-x)=-4x^2[/tex]
ii) [tex]4f(5-x)+f(x)=(5-x)^2[/tex]

adding the 2 equations side by side we have:

[tex]-15f(x)=-4x^2+(5-x)^2[/tex]

expanding the binomial, and collecting same terms we have:

[tex]-15f(x)=-4x^2+(25-10x+x^2)[/tex]

[tex]-15f(x)=-3x^2-10x+25[/tex]

dividing by -5:

[tex]3f(x)=\frac{3}{5}x^2+2x-5[/tex]

dividing by 3:

[tex]\displaystyle{f(x)= \frac{1}{5}x^2+ \frac{2}{3}x-\frac{5}{3} [/tex]

Answer: [tex]\displaystyle{f(x)= \frac{1}{5}x^2+ \frac{2}{3}x-\frac{5}{3} [/tex]

the volume of 10000 drops of liquid is 100 fluid ounces. what is the volume of 10 drops?

Answers

1000/10000=1/10=0.1 fluid ounces

Answer:

0.1 fluid ounces

Step-by-step explanation:

If 10000 drops lof liquid is 100 fluid ounces we can determine the drops of liquid per fluid ounces by dividing the two values:

[tex]100/10000=0.01[/tex]

Therefore 0.01 fluid ounces is equivalent to 1 drop. We have our conversion factor now we can determine the volume by multiplying the conversion factor by the number of drops:

[tex]0.01*10=0.1[/tex]

10 drops is 0.1 fluid ounces

Owl can clean piglets house in 25 minutes. eeyore can clean piglets house in 40 minutes. how long will it take owl and eeyore to do the job if they work together?

Answers

Let us say that the task of cleaning the house is equal to 1 job. Therefore the rates are:

rate of Owl = 1 job / 25 minutes

rate of eeyore = 1 job / 40 minutes

So working together, the time is:

(1 / 25) + (1 / 40) = 1 / t

0.065 = 1 / t

t = 15.38 minutes

So it takes about 15.38 minutes working together.

Benny wants to put a rectangular fence in his yard, and he wants the length of the fence to be 5 less feet than twice its width. He also found that every foot of fencing will cost $3.16. The total cost of the fence is C = 3.16(6w - 10), where w is the width of the fence. What does 6w - 10 represent?

Answers

6w-10 represents the total amount of fence will need to complete the rectangle of fence in his yard. The fence will need two lengths and 2 widths to complete the rectangle. If the width is w, and the length is 2w-5, then the total for the rectangle would be w+w+2w-5+2w-5 which simplifies to 6w-10.

brainleiest!!! What is the unit rate for 4543.08 km in 52.4 h? Enter your answer, as a decimal, in the box. km/h

Answers

(52.4) / (4543.08) = 0.0115 hour per kilometer

(4543.08) / (52.4) = 86.7 km per hour

Answer:

86.7

Step-by-step explanation:

you divide 4543.08 by 52.4

what is the equation of the line graph shown? (-2,-3), (3, -3)

Answers

the equation is y= -3 because it is a horizontal line that goes across 0,-3

If you put all the flowers together end to end, what would be the total length of all the flowers?

Answers

1/8 + 3(1/4) + 2(1/2) + 5/8 + 3/4 + 7/8 + 1 =
1/8 + 3/4 + 1 + 5/8 + 3/4 + 7/8 + 1 =
13/8 + 6/4 + 2 =
13/8 + 12/8 + 16/8 =
41/8 =
5 1/8 inches <==

Which of the following expressions is in simplified form?
1n + 2.9n
4w - 5
-2 + 1.4m + 0.5
9j - 3 - j

Answers

The only one that's in simplified form is 4w - 5 since it's the only one out of the four that doesn't have any more like terms.

Hello!

I believe the answer is B. 4w - 5, because B is the most short (or simplified) of all the rest..

Hope this helps! ☺♥

Toby, a toy store buyer, ordered 2 gross rubber spiders, 60 teddy bears, and 5 dozen video games. The spiders cost 7 cents each, the bears cost 59.76 dollars per dozen, and the video games were on sale for a special price—12 for 156 dollars. What was the total cost of Toby’s order, in dollars?

Answers

Rubber spider total cost:
7 × 2 gross (1 gross = 144 units)
7 cents x 288 = 2016 cents = $20.16

Total cost of teddy bear:
59.76 x (60÷12) (1 dozen = 12 units)
59.76 x 5 = $298.80

Total cost of video games:
156 x 5 = $780.00

Total spent:
780 + 298.80 + 20.16 = $1098.96

Suzan sees a bag of marbles, she grabs a handful at random. She has seen a bag containing four red marbles, two green ones, four white ones, and three purple ones. She grabs eight of them. Find the probability of the following event, expressing it as a fraction in lowest terms. HINT [See Example 1.] She does not have all the green ones.

Answers

Final answer:

Explanation of calculating the probability of choosing 3 green marbles out of 10 from a bag with 50 marbles.

Explanation:

The probability of choosing exactly 3 green marbles if a total of 10 marbles are selected from a bag filled with 50 marbles, 15 of which are green, can be calculated as follows:

Calculate the total number of ways to choose 3 green marbles out of 15: C(15, 3).Calculate the total number of ways to choose 7 non-green marbles out of 35: C(35, 7).Find the total number of ways to choose 10 marbles out of 50: C(50, 10).Calculate the probability by dividing the product of the above two calculations by the total ways to choose 10 marbles.

Find the minimum and maximum values of the function subject to the given constraint. (if an answer does not exist, enter dne.) f(x, y) = x2y + x + y, xy = 5

Answers

Via Lagrange multipliers:

[tex]L(x,y,\lambd)=x^2y+x+y+\lambda(xy-5)[/tex]
[tex]L_x=2xy+1+\lambda y=0[/tex]
[tex]L_y=x^2+1+\lambda x=0[/tex]
[tex]L_\lambda=xy-5=0[/tex]

[tex]\underbrace{10}_{2xy}+1+\lambda y=0\implies \lambda=-\dfrac{11}y[/tex]
[tex]xy=5\implies y=\dfrac5x\implies\lambda=-\dfrac{11}5x[/tex]

[tex]\impliesx^2+1+\left(-\dfrac{11}5x\right)x=0\implies x^2=\dfrac56\implies x=\pm\sqrt{\dfrac56}[/tex]
[tex]xy=5\implies y=\pm\sqrt{30}[/tex]

At these points, we get local minima of [tex]f\left(\pm\sqrt{\dfrac56},\pm\sqrt{30}\right)=\pm2\sqrt{30}[/tex].

- - -

Another way to do this is to make [tex]f(x,y)[/tex] a function independent of [tex]y[/tex], which is made possible by the constraint.

[tex]xy=5\implies y=\dfrac5x[/tex]
[tex]\implies f(x,y)=f\left(x,\dfrac5x\right)=F(x)=6x+\dfrac5x[/tex]
[tex]\implies F'(x)=6-\dfrac5{x^2}=0\implies x=\pm\sqrt{\dfrac56}[/tex]

and so on.

Over the last three evenings, Raina received a total of 83 phone calls at the call center . The first evening, she received 7 more calls than the third evening. The second evening, she received 2 times as many calls as the third evening. How many phone calls did she receive each evening ?

Answers

x = 1st evening, y = 2nd evening, z = 3rd evening

x + y + z = 83
x = z + 7
y = 2z

z + 7 + 2z + z = 83
4z + 7 = 83
4z = 83 - 7
4z = 76
z = 76/4
z = 19 <=== 3rd evening calls

x = z + 7
x = 19 + 7
x = 26 <=== 1st evening calls

y = 2z
y = 2(19)
y = 38 <=== 2nd evening calls

An indoor water park has two giant buckets that slowly fill with 1000 gallons of water before dumping it on the people below. One buckets dumps water every 18 min. The other buckets dumps water every 21min. It is currently 1:15 p.m. and both buckets dumped water 5 minutes ago. Find the next two times that both buckets dump water at the same time

Answers

5 minutes ago of 1:15 pm is 1:10 pm. This is the last time that both buckets dump water together. The least multiple of both 21 and 18 is 126. Therefore, every after 126 minutes they will dump water together.

126 minutes is equal to 2 hours and 6 minutes.

(1) Time 1:

1:10 pm + 2:06 = 3:16 pm

(2) Time 2:

3:16 pm + 2:06 = 5:22 pm

PLEASE HELP ASAP DUE IN A DAY What is the unit rate for 768.57 m 41.1 h? Enter your answer, as a decimal, in the box.

Answers

The unit rate for 768.57 meters in 41.1 hours is approximately 18.68 meters per hour. This calculation is derived by dividing the distance by the time to find the rate of movement.

To find the unit rate, divide the distance by the time:

[tex]\[ \text{Unit rate} = \frac{\text{Distance}}{\text{Time}} \][/tex]

[tex]\[ \text{Unit rate} = \frac{768.57 \, \text{m}}{41.1 \, \text{h}} \][/tex]

[tex]\[ \text{Unit rate} \approx \frac{768.57}{41.1} \, \text{m/h} \][/tex]

[tex]\[ \text{Unit rate} \approx 18.68 \, \text{m/h} \][/tex]

So, the unit rate is approximately 18.68 meters per hour.

Each class at briarwood elementary collected at least 54 cans of food lduring the food drive.If tbere are 29 clases in the school what was the least numbet of cans collected?

Answers

the answer is 54 cans of food

Let's turn the words into numbers:
For each class → x ≥ 54
Full School → x ≥ 54(29)

If we simplify the second inequality, we get this:
x ≥ 1566

The answer to your query is x ≥ 1566. Hope this helps and have a fantastic day!

If the equation were y=40x+70.What would the x-intercept be? Plz...Help!?!

Answers

[tex]( - \frac{7}{4} .0)[/tex]
the period is a comma

Evaluate 3 to the power of 3 + 6 (2 + 3/6)

Answers

if 3 + 6(2 + 3/6) is actually the power, then simplify 3 + 6(2 + 3/6) as a first step. Must follow Order of Operations rules (PEMDAS): mult and div BEFORE addition and subtraction.

Thus, 3 + 6(2 + 3/6) = 3 + 6 (15/6)
= 3 + 15 = 18.

Then: 3^18 is the answer. You could expand this if you wanted, but what would be the point of that?

At an interest rate of 8% compounded annually, how long will it take to double the following investments?
$50
$500
$1700

Answers

let's see, if the first one has a Principal of $50, when it doubles the accumulated amount will then be $100,

recall your logarithm rules for an exponential,

[tex]\bf \textit{Logarithm of exponentials}\\\\ log_{{ a}}\left( x^{{ b}} \right)\implies {{ b}}\cdot log_{{ a}}(x)\\\\ -------------------------------\\\\ \qquad \textit{Compound Interest Earned Amount} \\\\ [/tex]

[tex]\bf A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\to &\$100\\ P=\textit{original amount deposited}\to &\$50\\ r=rate\to 8\%\to \frac{8}{100}\to &0.08\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{annnually, thus once} \end{array}\to &1\\ t=years \end{cases} \\\\\\ 100=50\left(1+\frac{0.08}{1}\right)^{1\cdot t}\implies 100=50(1.08)^t \\\\\\ \cfrac{100}{50}=1.08^t\implies 2=1.08^t\implies log(2)=log(1.08^t) \\\\\\ [/tex]

[tex]\bf log(2)=t\cdot log(1.08)\implies \cfrac{log(2)}{log(1.08)}=t\implies 9.0065\approx t\\\\ -------------------------------\\\\ [/tex]

now, for the second amount, if the Principal is 500, the accumulated amount is 1000 when doubled,

[tex]\bf \qquad \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\to &\$1000\\ P=\textit{original amount deposited}\to &\$500\\ r=rate\to 8\%\to \frac{8}{100}\to &0.08\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{annnually, thus once} \end{array}\to &1\\ t=years \end{cases} \\\\\\ 1000=500\left(1+\frac{0.08}{1}\right)^{1\cdot t}\implies 1000=500(1.08)^t \\\\\\ [/tex]

[tex]\bf \cfrac{1000}{500}=1.08^t\implies 2=1.08^t\implies log(2)=log(1.08^t) \\\\\\ log(2)=t\cdot log(1.08)\implies \cfrac{log(2)}{log(1.08)}=t\implies 9.0065\approx t\\\\ -------------------------------[/tex]

now, for the last, Principal is 1700, amount is then 3400,

[tex]\bf \qquad \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\to &\$3400\\ P=\textit{original amount deposited}\to &\$1700\\ r=rate\to 8\%\to \frac{8}{100}\to &0.08\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{annnually, thus once} \end{array}\to &1\\ t=years \end{cases}[/tex]

[tex]\bf 3400=1700\left(1+\frac{0.08}{1}\right)^{1\cdot t}\implies 3400=1700(1.08)^t \\\\\\ \cfrac{3400}{1700}=1.08^t\implies 2=1.08^t\implies log(2)=log(1.08^t) \\\\\\ log(2)=t\cdot log(1.08)\implies \cfrac{log(2)}{log(1.08)}=t\implies 9.0065\approx t[/tex]

how do i calculate an estimated regression line with the information
n=12, ∑x=66, ∑y=588, ∑xy=2244, ∑x2=396

Answers

The regression line is
y = ax + b
where
a = [(Σy)(Σx²) - (Σx)(Σxy)]/D
b = [n(Σxy) - (Σx)(Σy)]/D
D = n(Σx²) - (Σx)²

Therefore,
D = 12(396) - 66² = 396
a = [588*396 - 66*2244]/396 = 214
b = [12*2244 - 66*588]/396 = -30

Answer:
The regression line is y = 214x - 30

f(x) = x2 + 5x – 1 is shifted 3 units left. The result is g(x). What is g(x)?

A. g(x) = (x – 3)2 + 5(x – 3) – 1
B. g(x) = x2 + 5x + 2
C. g(x) = (x + 3)2 + 5x – 1
D. g(x) = (x + 3)2 + 5(x + 3) – 1

Answers

D. When you shift left you add the units to all x because the x is what shifts. Even though you moved left, it is positive. If you move right , it is minus.

Answer:

g(x) = (x+3)² + 5(x+3) – 1.

Step-by-step explanation:

Given : f(x) = x² + 5x – 1 is shifted 3 units left.

To find : The result is g(x). What is g(x).

Solution : We have given that

f(x) = x² + 5x – 1 is shifted 3 units left.

By the transformation rule : If f(x) →→ f(x +h) shifted by h unit left .

f(x) = x² + 5x – 1 is shifted 3 units left.

Here , h = 3

Then g(x) = (x+3)² + 5(x+3) – 1.

Therefore, g(x) = (x+3)² + 5(x+3) – 1.

I need to solve and show work for 3x over4 divided by 5-1 over 8

Answers

3or4vxe
4

Is the answer

Sounds as tho' you want to evaluate

3x
---
4

over

5x-1
------
8

To accomplish this, invert the 2nd fraction and then multiply:

3x 5x-1
--- * ------ = 15x^2-3x divided by 32.
4 8

Since the ratios for sides of triangles are the same, when the angles are the same, ? have been developed which show these ratios for every angle encountered in a triangle. select one:
a. cos tables
b. sin tables
c. tan tables
d. trigonometric tables

Answers

Presuming that I am reading the question correctly, the answer is D. A trigonometric table would provide all of the ratios of the sides in relationship to the angles. Sin, cos, and tan are just one example of the ratio.

Answer: d. trigonometric tables

Step-by-step explanation:

A trigonometric table would provide all of the ratios of the sides in respect to the angles. Sin, cos, and tan are parts of trigonometric table.

Trigonometry table, tabulated values for some or all of the six trigonometric functions for various angular values.

Since the ratios for sides of triangles are the same, when the angles are the same, trigonometric tables have been developed which show these ratios for every angle encountered in a triangle.

A line has a slope of -2/3 and a y-intercept of (0, 3). What is the value of y when x = 4?

Answers

recall the slope-intercept form.

ahemmm so, we know the slope, and we also know the y-intercept, thus the equation of that line is

[tex]\bf y=\stackrel{slope}{-\cfrac{2}{3}}x\stackrel{y-intercept}{+3} \\\\\\ \textit{when x = 4, what is \underline{y}?}\qquad y=-\cfrac{2}{3}(4)+3\implies y=-\cfrac{8}{3}+3 \\\\\\ y=\cfrac{-8+9}{3}\implies y=\cfrac{1}{3}[/tex]

Find an equation of the normal line to the parabola y = x2 â 9x + 7 that is parallel to the line x â 7y = 2.

Answers

Please, could you proof read your input before posting a question? The character " â " does not belong here. "x2" should be written as x^2, where the "^" denotes exponentiation.

I'm taking the liberty of correcting your input: "Find an equation of the normal line to the parabola y = x2 â 9x + 7 that is parallel to the line x â 7y = 2." may be:

Find an equation of the normal line to the parabola y = x^2 - 9x + 7 that is parallel to the line x - 7y = 2.

How do you find the slope of a normal line to the graph of a given quadratic? Differentiate y = x^2 - 9x + 7: dy/dx = 2x - 9

You can see that this slope varies with x. You have not named an x-value here, so I will have to stop at dy/dx = 2x - 9.

The slope of a line perpendicular to the tangent line is the negative reciprocal of the slope of the tangent line, or

-1
------- which obviously depends upon the x value you choose or are given.
(2x)

Now focus on the given line x - 7y = 2. Solving for y, 7y =x-2. The slope of this line is (1/7). Thus,

-1 1
--------- = ---------- Cross-multiplying, -7 = 2x; x = -3.5
2x 7

So it appears we DO have the x-value at the point of tangency on the curve.

Find the associated y-value by subst. x = -3.5 into the eq'n of the parabola.

Call it Y.

Then the eq'n of the normal line to the parabola that is parallel to x - 7y = 2

is y-Y = (1/7)(x-[-3.5])

Final answer:

The normal line to the parabola y = x^2 - 9x + 7 that is parallel to the line x - 7y = 2 is y = -7x + 65, which was determined by finding the normal slope and point of tangency using the derivative.

Explanation:

In mathematics, the normal line to a curve at a particular point is the line that is perpendicular to the tangent of the curve at that point. First, it's important to establish that any line parallel to x - 7y = 2 would have the same slope, which in this case is 1/7. To find the normal line, we need a line that is perpendicular to this -- hence, it would have a slope of -7.

Now, to find the point of tangency, you must take the derivative of y = x^2 - 9x + 7, making it 2x - 9. Set this equal to -7 (the slope of the normal line) and solve for x, which comes out to be 8. Substituting x = 8 back into our parabola equation gives us y = -9. Therefore, our point of tangency is (8, -9).

Finally, using the point-slope form of a line formula, we can find our equation of the normal line, which is y - (-9) = -7*(x - 8), simplifying to y = -7x + 65.

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The salaries of the president and the Vice President of a certain country total $562,500 a year. If the president makes $237,400 more than the Vice President , find each of their salaries.

Answers

To do this question, you simply add what the Vice President makes to how much more the President makes. $562,500+ $237,400=799,900.

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