What is the image of (-9,12)(−9,12) after a dilation by a scale factor of \frac{1}{3} 3 1 ​ centered at the origin?

Answers

Answer 1

The image of (-9,12) after a dilation by a scale factor of 1/3 centered at the origin is (-3,4).

In the given question,

We have to find the image of (-9,12) after a dilation by a scale factor of 1/3 centered at the origin.

Since we have to find the image after a dilation.

So we learn about it now,

Any scale factor will dilate the image of any coordinate. A specific scale factor can be used to scale the coordinate up or down. To determine the answer, consider the scale factor in the equation and multiply or divide the coordinates of dilation by the appropriate scale factor.

So the given point is (-9,12).

Scale factor is 1/3.

So the image of (-9,12) after a dilation by a scale factor of 1/3 centered at the origin is define as

=(-9×1/3,12×1/3)

Simplifying

=(-3,4)

Hence, the image of (-9,12) after a dilation by a scale factor of 1/3 centered at the origin is (-3,4).

To learn more about image after dilation link is here

brainly.com/question/11799770

#SPJ1


Related Questions

Differentiate the function with respect to x.

Answers

Differentiation of the function [tex]f(x) = (-x^{2} - 4)x^{5}[/tex] with respect to [tex]x[/tex] is [tex]f'(x) = -7x^{6} - 20x^{4}[/tex].

What is the differentiation of the function?

A function differentiation is a method of displaying the rate of change of a function at a given moment. It is the slope of the tangent line at a point on a graph for real-valued functions.

We have,

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

By simplifying the given function, we get

                                      [tex]f(x) = -x^{7} - 4x^{5}[/tex]

Now, we will differentiate the given function with respect to [tex]x[/tex].

                                    [tex]\frac{d}{dx} f(x) = \frac{d}{dx} (-x^{7} - 4x^{5})[/tex]

                                    [tex]f'(x) = \frac{d}{dx} (-x^{7}) - \frac{d}{dx} (4x^{5}))[/tex]

                                     [tex]f'(x) = -7x^{6} - 20x^{4}[/tex]

Hence, differentiation of the given function with respect to [tex]x[/tex] is [tex]f'(x) = -7x^{6} - 20x^{4}[/tex].

To learn more about Differentiation of the function visit,

https://brainly.com/question/954654

#SPJ1

Name the image of R(1, 2) after a 270 rotation about (0, - 2)

Answers

The image after a 270 rotation is (4, -3)

How to determine the image after rotation about a point?

If the point of rotation is not the origin, the steps are as follows:

1. Subtract the point of rotation off each vertex point of

the shape

2. Rotate as you would around the origin

3. Add the point of rotation back to each vertex point of

the shape

Given: R(1, 2) after a 270 rotation about (0, - 2)

step1: (1-0, 2-(-2)) = (1, 4)

step 2: For rotation about the origin through 270°, the image is (y, -x). Thus, (1, 4) => (4, -1)

step 3: (4, -1) => (4+0, -1+(-2) ) = (4, -3)

Therefore, the image of R(1, 2) after a 270 rotation about (0, - 2) is (4, -3)

Learn more about rotation on:

brainly.com/question/29321467

#SPJ1


Ana runs 3/4 in 6 minutes. Fill in the missing values in the table. Using
the table, find the constant of proportionality. Then write an equation to
represent this relationship. Lessons 2-3 7.AR.4.2

Answers

Answer:

In the first one you should write: 6, because the test tells you that in 6 minutes she runs 3/4miles.

So in 12 minutes she runs (3/4miles)*2. (basically 3/4 miles in the first 6 minutes, and other 3/4 miles in the remaining 6munutes).

So in the second space you can write 12, and on the right 2*(3/4), which is... (3/2).

To find the equation:

3/4 = 6

(3/4)*2= 6*2

so we know that in 1 minute we do 1/8miles, and now we have our formula. (1/8)*6=1*6

the formula is: y(miles) =(1/8)*x

in fact is x=6 minutes, y= (1/8)*6, so y=3/4.

What are the slope and vertical intercept of 5x+7y=10

Answers

Answer:

-5/7, 10/7

Step-by-step explanation:

The slope of an equation in standard form is -a/b

so -5/7

Set x to 0 to find the vertical intercept

5(0)+7y=10

7y=10

y=10/7

Suppose a basketball player has made 215 out of 322 free throws. If the player makes the next 2 free throws, I will pay you $32. Otherwise you pay me $24. Step 1 of 2 : Find the expected value of the proposition. Round your answer to two decimal places. Losses must be expressed as negative values.

Answers

The expected value of the proposition is -$1007.41

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

P(X = x) = [tex]C_{n},x.p^x.(1-p)^n^-^x[/tex]

In which [tex]C_{x},x[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{x},x= \frac{n!}{x!(n-x)!}[/tex]

And p is the probability of X happening.

Suppose a basketball player has made 215 out of 322 free throws.

This means that p = 215/322 = 0.6677

2 free throws:

This means that

Probability of making two free throws.

This is P(X = 2).

P(X = x) = [tex]C_{n},x.p^x.(1-p)^n^-^x[/tex]

P(X = 2) = [tex]C_{2},2.(0.6677)^2.(0.3323)^0[/tex] = 0.29629

Expected value:

If he makes both free throws, you earn $24. So 0.29629 probability of you earning $24.

Otherwise, you have to pay $32. 1 - 0.29629 = 31.70371 probability of you losing $32.

E = 0.29629*24 - 31.70371*32 = -1007.41

Hence, The expected value of the proposition is -$1007.41

Learn more about Binomial Probability Distribution at:

https://brainly.com/question/7283210

#SPJ1

Select the correct answer A developer buys an empty lot to build a small house. What is the area of the lot?
A. 323 yd²
B. 183 yd²
C. 193 yd²
D. 171 yd²​

Answers

The area of the plot is 193 sq.yd.

What is Area?

Area is defined as the total space taken up by a flat (2-D) surface or shape of an object.

Given that, A developer buys an empty lot to build a small house.

To find the area, we need to be divided the figure into triangles and rectangles

Area of the first triangle = (1/2) * base * height

base = 17 unit and height = 10 unit

= (1/2) * 17 * 10

= 17*5=85 sq. unit

Area of the second triangle = (1/2)* 9* 8

=36 sq. unit

Area of the rectangle = base * height

base = 9 unit and height = 7 unit

Area = 9*7= 63 sq. unit

Area of the last triangle = (1/2) * 2*9

= 9 unit

Adding all the areas to get the area of the plot = 85+36+63+9

Hence, Area of the plot = 193 sq.yd.

For more references about the Area, click;

brainly.com/question/27683633

#SPJ1

A cable TV company has 3400 customers paying $130 each month. If each $1 reduction in price attracts 50 new customers, find the price that yields maximum revenue.

Answers

The price that yields maximum revenue is equal to $99. Also, the maximum revenue is equal to $490,050.

How to determine the unit price that yields a maximum revenue?

In order to determine the price that would yield the maximum revenue, we have to find the derivative of the revenue function R(p) by applying the Power Rule.

Mathematically, the revenue function, R(p) is given by this mathematical expression:

Revenue function, R(p) = NP

Where:

N represents the number of customersP represents the monthly price of the subscription

Let the variable n represent the number of reductions in the price. Therefore, we have:

N = 3,400 + 50n    ....equation 1.

P = 130 - n

n = 130 - P

From equation 1, we have:

N = 3,400 + 50(130 - P)

N = 3,400 + 6,500 - 50P

Next, we would re-write the revenue function R(p) as follows:

Revenue function, R(p) = (3,400 + 6,500 - 50P)P

Revenue function, R(p) = 3,400P + 6,500P - 50P²

Revenue function, R(p) = 9,900P - 50P²

Taking the derivative of R(p), we have:

R'(p) = 9,900 - 100P

100P = 9,900

Price, P = 9,900/100

Price, P = $99

For the the maximum revenue, we have:

Maximum revenue, R(p) = 9,900P - 50P²

Maximum revenue, R(p) = 9,900(99) - 50(99)²

Maximum revenue, R(p) = 980,100 - 490,050

Maximum revenue, R(p) = $490,050.

Read more on maximum revenue here: https://brainly.com/question/15463241

#SPJ1

Complete Question:

A cable TV company has 3400 customers paying $130 each month. If each $1 reduction in price attracts 50 new customers, find the price that yields maximum revenue. Find the maximum revenue.

if Julie average arts test score at 85 and what would you predict her average math test score would be ​

Answers

1. Her Average would be 80

2. Yes, there are more dots around points 80.

How long is 10:00am to 5:00 pm

Answers

Answer:

7 hours.

Step-by-step explanation:

Use a clock and count forward.

PLEASE HELP!!!! "CLEVERLY CONICS Portfolio"


Choose one of your conic examples to study in greater detail. Complete the table to create the graph and equation for your chosen example.
1. If possible, use a photo of the structure or item. Otherwise, draw a detailed sketch.
2. Measure and label the key dimensions of the shape in order to duplicate them in a to-scale graph. Be sure to label your units of measure to reflect the actual measurements.
3. Draw the underlying conic section on a coordinate grid.
4. Identify the coordinates of the appropriate key parts of the conic section.
5. Determine the closest approximation of the equation in standard form for the conic section.

Answers

Answer:

Hello there! While I didn't have this assignment, I found the assignment on Coursehero and took the liberty of downloading the pdf.

BE SURE TO USE QUILLBOT FOR PARAPHRASING AND PREPOSTSEO FOR PLAGIARISM CHECKING

Step-by-step explanation:

What is the value of (−13)4

Answers

Answer: -52

Step-by-step explanation: multiply by breaking apart a factor (-13) x 4

Answer:

28561

Step-by-step explanation:

Find the Exact Value:

Raise -13 to the power of 4.

28561 is the answer.

Please help! I will award top rating for the first to help! (the questions are on the image)
It needs to be fully simplified!

Answers

Answer:

Step-by-step explanation:

4x(power of 5) divided by x(power of 2)

5y(po7) div by y(po2)

not 100% sure as i havent learnt this before lol

A surveyor is determining the area of a triangle piece of land bordered by three stretts. In the coordinate plane,the vertices of the triangle are at 0,0 -100,-300,and 200 -200. One unit in the coordinate plane represents 1m.what is the area of piece of land

Answers

The area of the piece of land with coordinates (0, 0), (-100, 300) and (200, -200) is as measured by the surveyor is 4000 square meter

How to calculate the area of the piece of the land

The given coordinates being plotted as

A (0, 0)

B (-100, 300)

C (200, -200)

Area of triangle is solved by 0.5 * base * height

dimensions from attached plot, BC = 316.2, Aa = 253

= 0.5 * BC * Aa

= 0.5 * 253 * 316.2

= 39 999.3 approximately 40 000

The plot gave an area of 40 000 square units on paper converting using the given scale which is: One unit in the coordinate plane represents 1m

1 unit = 1 m

1 square unit = 1 square meter

4000 square units = ?

cross multiplying

? = 4000 square units

Learn more about scale factor here:

https://brainly.com/question/29395620

#SPJ1

what is the probability that a random sample of 20 second grade students from the city results in a mean reading rate of more than 97 words per minute

Answers

The probability that a random sample of 20 second grade students from the city results in a mean reading rate of more than 97 words per minute is; 0.012676.

How to find the probability from z-score?

This z-score is used to tell us the number of standard errors that exists between the sample mean and the population mean.

The formula for z-score here is;

z = (x' - μ)/(σ/√n)

where;

x' is sample mean

μ is population mean

σ is standard deviation

n is sample size

We are given;

Sample mean; x' = 97

Population mean; μ = 91

Standard deviation; σ = 10

Sample size; n = 20

Thus;

z = (x' - μ)/(σ/√n)

z = (97 - 91)/(10/√20)

z = 2.236

From online p-value from z-score calculator, we have;

p = 0.012676

Read more about p-value from z-score at; https://brainly.com/question/4621112

#SPJ1

Complete question is;

The reading speed of second grade students in a large city is approximately​ normal, with a mean of 91 words per minute​ (wpm) and a standard deviation of 10 wpm.

what is the probability that a random sample of 20 second grade students from the city results in a mean reading rate of more than 97 words per minute

Help pls I need a fraction answer

7 4/10 + 2/10 =

Answers

Answer:  7 4/10 + 2/10 = 38/5 = 7 3/5 = 7.6

Answer Overall : 38/5

Step-by-step explanation:  Conversion a mixed number 7 4/10 to a improper fraction: 7 4/10 = 7 4/10 = 7 · 10 + 4/10= 70 + 4/10= 74/10

To find a new numerator:

a) Multiply the whole number 7 by the denominator 10. Whole number 7 equally 7 * 10/10 = 70/10

b) Add the answer from previous step 70 to the numerator 4. New numerator is 70 + 4 = 74

c) Write a previous answer (new numerator 74) over the denominator 10.

Seven and four tenths is seventy-four tenths

Add: 74/10 + 2/10 = 74 + 2/10 = 76/10 = 2 · 38/2 · 5 = 38/5

The common denominator you can calculate as the least common multiple of both denominators - LCM(10, 10) = 10. In practice, it is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 10 × 10 = 100. In the following intermediate step, cancel by a common factor of 2 gives 38/5.

In other words - seventy-four tenths plus two tenths is thirty-eight fifths.

First convert the mixed number to a fraction by multiplying 7 by 10 and adding 4

74/10+2/10

add them together but DONT add the denominators

76/10

These numbers can be simplified by 2 so the final answer is:

38/5

A test consists of 10 true/false questions. To pass the test a student must answer at least 7 questions correctly. If a student guesses each question, what is the probability that the student will pass the test?

Answers

The probability that the student will pass the test, using the binomial distribution, is of:

0.172 = 17.2%.

What is the binomial distribution formula?

The formula that gives the probability of x successes is presented as follows:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

The parameters of the formula are listed as follows:

n is the number of trials of the experiment.p is the probability of a success on a single trial of the experiment.

In the context of this problem, the values of these parameters are given as follows:

n = 10, as there are 10 questions.p = 0.5, as each question has two outcomes, and the student will guess the answer at random.

The probability of passing is given by:

P(X ≥ 7) = P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10).

In which:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 7) = C_{10,7}.(0.5)^{7}.(0.5)^{3} = 0.1172[/tex]

[tex]P(X = 8) = C_{10,8}.(0.5)^{8}.(0.5)^{2} = 0.0440[/tex]

[tex]P(X = 9) = C_{10,9}.(0.5)^{9}.(0.5)^{1} = 0.0098[/tex]

[tex]P(X = 10) = C_{10,10}.(0.5)^{10}.(0.5)^{0} = 0.0010[/tex]

Then:

P(X ≥ 7) = P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10) = 0.1172 + 0.0440 + 0.0098 + 0.0010 = 0.172 = 17.2%.

More can be learned about the binomial distribution at https://brainly.com/question/24756209

#SPJ1

Let a=2 b=5 c= -3


8b-4b=4b Please help quick!!!!!

Answers

Answer:

40-20= 20

Step-by-step explanation:

8(5)- 4(5)= 4(5)

40-20=20

select shapes which have one line of symmetry

Answers

Answer:

A semicircle has 1 line of symmetry.

Step-by-step explanation:

The total cost of a plane ride, C, is given below as a function of the time flown, m, in minutes.

C = $33.00 + $1.20m

If a customer spends $267.00 on a plane ride, how many minutes does the ride last?
A. 250
B. 195
C. 223
D. 325

Answers

The number of minutes is 195 minutes when the customer spends $267.00. The correct option is B.

How to calculate the time?

From the information, the total cost of a plane ride, C, is given as a function

C = $33.00 + $1.20m

where n = number of minute

Since the customer spends $267.00 on a plane ride, this will be:

C = = 33.00 + $1.20m

33 + 1.2m = 267

Collect like terms

1.2m = 267 - 33

1.2m = 234

Divide

m = 234 / 1.2

m = 195

Minutes used is 195 minutes

Learn more about time on:

brainly.com/question/26046491

#SPJ1

GCF ( 160, 320, 480)​

Answers

The greatest common factor of 160, 320 and 480 will be 160.

What is the Greatest Common Factor?

The largest positive number that can be evenly divided into the supplied numbers is the most common factor. The largest number that evenly divides all the specified numbers is the greatest common factor.

In maths, the largest positive integer that divides each of the integers is known as the greatest common divisor of two or more integers that are not all equal to zero. The greatest common divisor of two numbers x and y is represented by the symbol GCD(x,y)

Assumed to be 160, 320 and 480. The numbers are factored to determine the largest common factor.

Factorize number 160

160 = 2×2×2×2×2×5

Factorize number 320

320 = 2×2×2×2×2×2×5

Factorize number 480

480 = 2×2×2×2×2×3×5

The common number between all three numbers is 2⁵×5. Therefore, the greatest common factor of 160, 320 and 480 will be 160.

To know more about 'greatest common factor' related questions

visit- https://brainly.com/question/19682313

#SPJ9

An online electronic store's sales are currently increasing at a rate of 2.7% monthly. If they had $65,000 in sales for this month, what will their sales be in 1 year?​

Answers

The Sales of the electronic store in 1 year is 66,776.88    

Applications of Compound interest:

Compound interest is an interest that is calculated on the principal and the interest accumulated over the previous period. The concept of compound interest can be used in different types of situations like an Increase in population or a decrease in population, Depreciation, or increasing the value of an item, etc.

The formula for compound interest is given by

Total amount, A = P(1 + r/n)^nt  

where  P = initial amount

r = rate of increase              

n = number of compounds in year

t = time period in years

Here we have,

The rate of increase in sales r = 2.7% (per monthly)  

=> r = 2.7/100 = 0.027

Here sales are increased monthly

then the number of compounds per year = 12

Sales in this month, P = 65000  

From above formula

Sales in 1 year, A = 65000(1 + 0.027/12)¹²

= 65,000(1 + 0.00225)¹²

= 66,776.88    

Therefore,

Sales of the electronic store in 1 year =  66,776.88      

Learn more about Compound interest at

https://brainly.com/question/13155407  

#SPJ1

2. Determine if the diagram is a function.
Why or why not?
Please

Answers

Answer:

IT IS A FUNCTION

It is specifically a Surjective/ onto Mapping/function

Step-by-step explanation:

surjective or onto function is when y has an image in x

Answer:

The graph is a function

Step-by-step explanation:

-For every input (x) there is only one output value (y)

Since the function does not have two of the same x values for several inputs, its considered a function. If the x values do not repeat values, or if you graph the function and it does not cross on more than one point, it is also considered a function.

Ex.

X: 2, 4, 7 , 2, 5         This is not a function. More than one input for each output.

Y: 1, 2, 4, -3, 7

Ex.

X: 5, 6, -5, 8  this is a function. Exactly one input for every output.

Y: 1, 4, 5, 9

 

The measure of the largest angle in a triangle is 110° larger than the sum of the measures of the other two angles. The measure of the smallest angle is three-
quarters the measure of the middle angle. Find the measure of each angle.

Answers

Measure of largest. smallest and middle angle of a triangle under given conditions is 145°, 15° and 20° respectively.

What is angle sum property of a triangle?

Angle sum property of triangle states that the sum of interior angles of a triangle is 180°.

According to the given question:

Let the measure of middle angle = x

The measure of the smallest angle is three-quarters the measure of the middle angle.

∴ Smallest angle = (3/4)x

The measure of the largest angle in a triangle is 110° larger than the sum of the measures of the other two angles.

∴ Largest angle = 110° + x + (3/4)x

Now, by Angle sum property of a triangle

x + (3/4)x + 110° + x + (3/4)x = 180°

On solving for the value of x we get

2x + (3/2)x = 70°

7x = 140°

x = 20°

Therefore,

measure of middle angle x = 20°

measure of smallest angle (3/4)x = 15°

measure of the largest angle 110° + x + (3/4)x = 145°

To know more about angle sum property of a triangle visit

https://brainly.com/question/8492819

#SPJ1

on a standardized exam the scores are normally distributed with a mean of 70 and a standard deviation of 20. find the z of a person who scored 128 on the exam

Answers

The z-score of a person who scored 128 on the exam is equal to 2.9

What is a z-score?

A z-score is also referred to as a z-value or standard score and it can be defined as a measure of the distance between a raw score and the mean, when standard deviation units are used.

Mathematically, the z-score of a given sample score in a normal distribution can be calculated by using this formula:

[tex]z=\frac{x\;-\;u}{\sigma}[/tex]

Where:

x represents the sample score.u represents the mean score.σ represents the standard deviation.

Substituting the given parameters into the formula, we have;

Z-score, z = (128 - 70)/(20)

Z-score, z = 58/20

Z-score, z = 2.9

Read more on z-scores here: https://brainly.com/question/26714379

#SPJ1

1/3 divide by 4 3/4 simplest form

Answers

Step-by-step explanation:

first put 4 3/4 into a improper fraction ---> 19/4

you get 19/4 because  4 is equal to 16/3 plus the 3/4

then you will do keep, flip change so it becomes multiplication

so instead of 1/3 divided by 19/4 it will be 1/3 x 4/19 then

multiply it out to get 19/12

Degree 5; zeros: 7, -i, 3+i; let a represent the leading coefficient

Answers

Therefore the required polynomial is [tex]f(x) = a(x^5+13x^4+53x^3+83x^2+52x+70)[/tex]

What is an leading coefficient?

The numbers placed in front of the variable with the biggest exponent are known as leading coefficients. They can be whole numbers, fractions, or decimals, as well as positive, negative, real, or imaginary, just like conventional coefficients.

According to fundamental theorem of algebra , if a + bi be a zero of a polynomial with real coefficients then a-bi is also a zero

Now given that f(x) be a polynomial with degree 5 and with zeros -7,-i,-3+i

and f(x) be a polynomial with real coefficients.

therefore by fundamental theorem of algebra

+i and -3-i are also zeros of f(x)

so zeros of f(x) are 7, -i, -3 + i, i, -3 -i

Degree is 5, so there is at most 5 zeros therefore the required polynomial will be

f(x) = a(x + 7)(x + i )(x - i)(x +3- i)(x +3 +i)

= a[(x +7)(x² + 1)(x² +6x + 10)]

[tex]= a\left[x^5+ 13x^4 + 53x^3 +83x^2 + 52x + 70]\right[/tex]

[tex]f(x) = a(x^5+13x^4+53x^3+83x^2+52x+70)[/tex]

Therefore the required polynomial is [tex]f(x) = a(x^5+13x^4+53x^3+83x^2+52x+70)[/tex]

To learn more about the leading coefficients visit,

https://brainly.com/question/24881460

#SPJ9

Complete sheet below

Answers

Answer:

1: D

2: B

3: A

D: C

Step-by-step explanation:

solve the absolute value inequality.
|-3x|-7≥ 11

Answers

Answer:

x ≥ 6

Step-by-step explanation:

|-3x| - 7 ≥ 11     The absolute value of -3x is 3x

3x - 7 ≥ 11        Cancel the 7 by adding it on both sides

3x ≥ 18            To get x by itself divide 3 on both sides

x ≥ 6

Suppose that f(x)= −4x^2+5.

(A) Find the slope of the line tangent to f(x) at x= 1.

(B) Find the instantaneous rate of change of f(x) at x= 1.

(C) Find the equation of the line tangent to f(x) at x= 1. y=

Answers

The slope of the line tangent to f(x) at x = 1 is -8

The instantaneous rate of change of f(x) at x = 1 is -8

The equation of line tangent to f(x) at x = 1 is y  = -8x + 9

What is a tangent to a curve?

The tangent line to a curve at a given point is the line which intersects the curve at the point and has the same instantaneous slope as the curve at the point.

so the slope of a line at that point is the slope of the curve at that point.

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

To find the slope, we differentiate f(x) with respect to x

dy/dx  = d/dx( -4[tex]x^{2}[/tex]) + d/dx(5)

           = -8x + 0

dy/dx = -8x

The slope = -8x

at x = 1,

the slope becomes, -8(1) = -8

The instantaneous rate of change of f(x) at x = 1 is the same as the slope of the line tangent to f(x) = -8

The slope of the line is -8

to find the equation of the tangent line, we need to find the coordinates of the point the line touches the curve.

one of the coordinates x = 1, to find y, we substitute x into f(x)

f(x) = -4[tex](1)^{2}[/tex] + 5

f(x) = 1

so the point is (1, 1)

so equation of straight line

[tex]\frac{y - y_{1} }{x - x_{1} }[/tex] = m

y - 1/x - 1 = -8

by cross multiplying

y - 1 = -8(x - 1)

y - 1 = -8x +8

y = -8x + 9

In conclusion,

The slope o the line tangent to f(x) at x = 1 is -8

The instantaneous rate off change of f(x) at x = 1 is -8

The equation of line tangent to f(x) at x = 1 is y  = -8x + 9

Learn more about tangent to a curve: https://brainly.com/question/28199103

#SPJ1

The equation for line t can be written as y+3= 1/2(x–7). Line u, which is perpendicular to line t, includes the point (3,3). What is the equation of line u?
Write the equation in slope-intercept form. Write the numbers in the equation as simplified proper fractions, improper fractions, or integers.

Answers

The equation of a line u perpendicular to line t and passes through (3, -3) is  y = -2x + 3

How to represent the slope of a line?

The equation of a line can be represented in slope intercept form as follows:

y = mx + b

where

m = slopeb = y-intercept

Line t has equation as y + 3 = 1 / 2 (x - 7).

Line u is perpendicular to line t and it passes through (3, -3).

The products of the slope of perpendicular lines is equals to negative 1.

Therefore,

m₁ m₂ = -1

1 / 2 m₂ = -1

m₂ = -2

Therefore,  the equation of the line have a slope of -2.

let's find the y-intercept using (3, -3)

-3 = -2(3) + b

b = -3 + 6

b = 3

Therefore, the equation in slope intercept form is y = -2x + 3.

learn more on equation of a line here: brainly.com/question/25974245

#SPJ1

Other Questions
Infer Authors often leave things unstated in a story, leaving the reader with questions about the outcome. What can you infer about what Gordimer leaves unstated at the end of her story? How does it relate to her statements about the family living happily ever after? modern computer systems enable users to work with more than one program at the same time. this technique is known as The plays closing passage mainly suggests that .Narrators Voice. The tools of conquest do not necessarily come with bombs and explosions and fallout. There are weapons that are simply thoughts, attitudes, prejudicesto be found only in the minds of men. For the record, prejudices can kill and suspicion can destroy and a thoughtless frightened search for a scapegoat has a fallout all its own for the children . . . and the children yet unborn. (A pause) And the pity of it is . . . that these things cannot be confined to . . . The Twilight Zone!Answer choices for the above questionA. The Monsters Are Due on Maple Street is only a fictional story and any similarity to real events is unintentionalB. monsters from outer space are a threat to people in the modern worldC. the narrator was once a made a scapegoat for something himselfD. the kind of paranoia and violence that befell Maple Street also occurs in real life Transformation of functions f(x)=-7(x-8)^2 +2 what are you weaknesses in life and how do you cope-Up with it? using five should and five must 7. Help question is in picture below! a man travels xkm at 60 km per hour and ykm at 40 km per hour and takes 11/4 hours for the Journey,if the time taken for 5x km at 40 km per hour and 3y km at 50 km per hour is 11 hours 42 minutes find X and Y The carbon cycle is one type of biogeochemical cycle that is necessary for the movement of matter.What would happen if plants were removed from the environment? If the random variable Zhas a standard normal distribution, then P(1.17 S ZS 2.26) is if you were able to find a drug that could inhibit the reactivation of telomerase activity in cancer cells, the cancer cells would it takes a hose 3 minutes to fill a rectangular aquarium 8 inches long, 11 inches wide, and 13 inches tall. how long will it take the same hose to fill an aquarium measuring 26 inches by 33 inches by 35 inches? The relationship between the number of crocodiles and the number of alligators is not proportional across all lakes. Only two of the lakes have crocodiles and alligators in the same proportion. Which two lakes are they? Who is the state senator in Georgia in a multiple regression problem involving two independent variables, if b1 is computed to be 2.0, it means that What would be a good title for the graph? Pls help due today Which statement is true? All decimals are rational. All rational numbers can be written as the quotient of Integers the phenomenon in which people tend to interact with people who are similar to themselves and avoid interacting with those who are dissimilar is known as multiple choice question. disjunctive diversity. punctuated equilibrium. the similarity-attraction approach. the diversity problem-solving approach. an example on why you should have a positive attitude during a difficult time a car weighing 13,000 n starts from rest and accelerates to 84.0 km/h in 5.00 s. the friction force is 1,500 n. find the applied force (in n) produced by the engine. 9. explain how nucleotide incorporation errors by dna polymerase can be repaired, and the role of methylation in the process.