Please help me on #30

Please Help Me On #30

Answers

Answer 1

The equation of the tangent line to the graph of f(x) at the point where x = -1 is y = 7x + 5.

The point where the function f(x) = x² + 4x - 1 has a horizontal tangent line is (-2, -5).

We have,

To find the equation of a tangent line to the graph of f(x) = 4x³ - 5x + 3 at the point where x = -1, we need to find the derivative of the function and evaluate it at x = -1.

The derivative of f(x) = 4x³ - 5x + 3 can be found by applying the power rule for differentiation:

f'(x) = 12x² - 5

Now, let's evaluate the derivative at x = -1:

f'(-1) = 12(-1)² - 5

= 12 - 5

= 7

The derivative f'(-1) represents the slope of the tangent line at the point where x = -1.

Therefore, the slope of the tangent line is 7.

To find the equation of the tangent line, we can use the point-slope form of a linear equation.

We'll use the coordinates (-1, f(-1)) = (-1, f(-1)) = (-1, 4(-1)³ - 5(-1) + 3) = (-1, -2).

Using the point-slope form:

y - y₁ = m(x - x₁)

where (x₁, y₁) = (-1, -2) and m = 7:

So,

y - (-2) = 7(x - (-1))

y + 2 = 7(x + 1)

y + 2 = 7x + 7

y = 7x + 5

And,

To find the point where the function f(x) = x² + 4x - 1 has a horizontal tangent line, we need to find the derivative of the function and set it equal to zero.

The derivative of f(x) = x² + 4x - 1 can be found using the power rule:

f'(x) = 2x + 4

To find where the tangent line is horizontal, we set f'(x) = 0:

2x + 4 = 0

2x = -4

x = -2

So, the x-coordinate where the function f(x) has a horizontal tangent line is x = -2.

To find the corresponding y-coordinate, we can substitute x = -2 back into the function f(x):

f(-2) = (-2)² + 4(-2) - 1

= 4 - 8 - 1

= -5

Therefore,

The equation of the tangent line to the graph of f(x) at the point where x = -1 is y = 7x + 5.

The point where the function f(x) = x² + 4x - 1 has a horizontal tangent line is (-2, -5).

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Related Questions

A wooden plank is $5$ feet long and $1\frac{1}{2}$ inches thick. To make the plank $1\frac{1}{8}$ inches thick, a carpenter removes the same thickness of wood from the top and bottom of the plank. How many inches does the carpenter remove from the top of the plank

Answers

Carpenter remove [tex]3/16[/tex] inches from the top of the plank to the same thickness of wood from the top and bottom of the plank.

How many inches does the carpenter remove from the top of the plank ?

A wooden plank is [tex]5ft[/tex] long and [tex]1\frac{1}{2}[/tex] inches thick

to make the plank [tex]1\frac{1}{8}[/tex] inches thick

Carpenter needs  to cut off

[tex]=1\frac{1}{2} -1\frac{1}{8} \\=\frac{3}{2} -\frac{9}{8} \\=\frac{3}{8}[/tex]

Carpenter cuts each side

[tex]=\frac{3}{8} /2\\=\frac{3}{16} inches[/tex]

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The rug for the kitchen has an area of 80 square feet. the width is 40 feet. what is the length?

Answers

Area=length x width
80=length x 40
80/40=20
Length is 20 feet

HELPPPP‼️‼️

19. In a school election, 250 votes are tallied for 3
candidates: Eric, Kai, and Sarah. If Eric got 50
votes, and Kai gets 60% of the remaining votes,
how many votes did Sarah get?

Answers

Answer:

The answer is 75 and here's why.

Let's figure out the amount of remaining votes to prove this.

250 total votes   -    150 votes for candidate a = 100 votes.

               minus ↑ sign

Candidate B received 25% of the votes, so let's find 25% of 100

100 * 0.25 = 25 votes

Candidate B only got 25 votes (that's kinda sad, poor guy)

100 - 25 votes = the # of votes candidate C got

Candidate C got 75 votes!

4x−4<8 and 9x+5>23 find x

Answers

Answer:

Step-by-step explanation:

for the first one, it is x=2

for the second one, it is x=9

Students in a ninth grade class measured their heights, h, in centimeters. The height of the shortest student was 155 cm, and the height of the tallest student was 190 cm. Which inequality represents the range of heights?

A. h > 155 or h < 190
B. 155 ≤ h ≤ 190
C. 155 < h < 190
D. h ≥ 155 or h ≤ 190​

Answers

Answer:

a h>155 or h<190

Step-by-step explanation:

The height of the shortest student is 155 cm and the height of the tallest student is 190 cm, then the inequality shows the range is 155 ≤ h ≤ 190. Hence, option B is correct.

What is an inequality?

Inequalities are mathematical expressions where neither side is equal. In inequality, as opposed to equations, we compare the two values. Less than (or less than and equal to), larger than (or greater or equal to), or not similar to signs are used in place of the equal sign in between.

As per the provided data in the question,

The height of the shortest student is 155 cm and,

The height of the tallest student is 190 cm.

It means that the height rage is starting from 155 cm and ending at 190 cm.

The shortest height should be at least equal to 155 cm and the greater height is maximum 190 cm.

Therefore, the inequality according to this is 155 ≤ h ≤ 190.

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25 POINTS!!!!
The graph of f(x) = (0.5)x is replaced by the graph of g(x) = (0.5)x − k. If g(x) is obtained by shifting f(x) down by 7 units, the value of k is ________??

Answers

The answer is k = 7.

As the graph has been shifted down 7 units, the translation can be represented as :

g(x) = f(x) - 7

(0.5)x - k = (0.5)x - 7

k = 7

Determine if the solution set for the system of equations shown is the empty set, contains one point or is infinite.

2x - y = 7

2y = 4x - 14

Answers

Since there are same number of either side, hence the solution has infinite number of solution

System of equations

System of equations are equation that consist of two or more equations with unknown variables.

Given the equations

2x - y = 7

2y = 4x - 14

This can also be written as

2x - y = 7

y = 2x - 7

Substitute equation 2 into 1

2x - (2x - 7) = 7

2x-2x+7= 7

7 = 7

Since there are same number of either side, hence the solution has infinite number of solution

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Instructions: Find the missing side. Round your answer to the nearest tenth.
x=
Check
30
X
17

Answers

Sine rule:

30/sin(17) = x/sin(90)

x sin(90)

30 x sin(90) / sin(17) = x

x = 102.6091086

So, x = 102.6 to the nearest tenth.

Hope this helps!

I needed help solving this question please if u can

Answers

Answer:

1)  4x + 5y = 20         4x + 5y = 20  

  -2x + 3y = 12  -->  2(-2x + 3y) = 2(12)

2) 4x + 5y = 20  

  -4x + 6y = 24

3) 4x + 5y = 20  

   -4x + 6y = 24

   0x + 11y = 44

4) 11y = 44

5) y = 4

6) 4x + 5y = 20  

   4x + 5(4) = 20  

7) 4x + 20 = 20

8) 4x = 0

9) x = 0

10) The solution is the point (0, 4)

Find the product of:
(3x - 4)(2x^2 + 2x - 1).

A. 6x^3 + 2x^2 - 5x + 4
B. 6x^3 + 14x^2 - 11x + 4
C. 6x^3 - 14^2 - 5x + 4
D. 6x^3 - 2x^2 - 11x + 4

Answers

Answer:

6x^3 -2x^2-11x + 4

Step-by-step explanation:

(3x - 4)(2x^2 + 2x - 1)

(3x - 4)(2x^2 + 2x - 1)

[(3x)(2x^2 + 2x - 1)]  +  [-4(2x^2 + 2x - 1)]

6x^3 + 6x^2 - 3x           -8x^2 - 8x + 4

6x^3 + [6x^2-8x^2] [- 3x- 8x] + 4

6x^3 -2x^2-11x + 4

Answer:

[tex]6x^3-2x^2-11x+4[/tex]

Step-by-step explanation:

Given expression:

[tex](3x-4)(2x^2+2x-1)[/tex]

Distribute the parentheses:

[tex]\implies 3x(2x^2+2x-1)-4(2x^2+2x-1)[/tex]

[tex]\implies 3x \cdot 2x^2+3x \cdot 2x +3x \cdot -1 -4 \cdot 2x^2-4 \cdot 2x-4 \cdot -1[/tex]

[tex]\implies 6x^3+6x^2 -3x -8x^2-8x+4[/tex]

Collect like terms:

[tex]\implies 6x^3+6x^2-8x^2 -3x -8x+4[/tex]

Combine like terms:

[tex]\implies 6x^3-2x^2-11x+4[/tex]

Find the equation of the line that
is perpendicular to y = 6x-2 and
contains the point (6, -2).
y =
= [2²] x + [ ]

Answers

Answer:

y = - [tex]\frac{1}{6}[/tex] x - 1

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = 6x - 2 ← is in slope- intercept form

with slope m = 6

given a line with slope m then the slope of a line perpendicular to it is

[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{6}[/tex] , then

y = - [tex]\frac{1}{6}[/tex] x + c ← is the partial equation

to find c substitute (6, - 2 ) into the partial equation

- 2 = - 1 + c ⇒ c = - 2 + 1 = - 1

y = - [tex]\frac{1}{6}[/tex] x - 1 ← equation of perpendicular line

if we multiply or divide both sides of a linear equation with a non zero number, then the solution of the linear equation​

Answers

hi

"does not change "  or "remain the same "

She needs to know the length of each side so she can buy fencing. What is the length of line segment FJ

Answers

Using the Pythagorean theorem, the length of line segment FJ is: 42 ft.

How to Apply the Pythagorean Theorem?

To find the length of line segment FJ, we need to apply the Pythagorean theorem to find the length of the segment from F to the point, say point O, on FJ where a right triangle FOG will be gotten.

Thus, we have:

FO = √(GF² - GO²)

FO = √(30² - 24²)

FO = 18 ft.

FJ = FO + GH

Plug in the values

FJ = 18 + 24

FJ = 42 ft.

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Consider the function represented in this table. f(x) -1 -21 0 -9 1 3 2 15 Which of these tables could represent the inverse of function f? X X -1 0 1 2 q(x) 21 9 -3 -15​

Answers

If f(-1)=-21,f(0)=-9,f(1)=3,f(2)=15 then the inverse of function f(x) is p(-21)=-1,p(-9)=0,p(3)=1,p(15)=2 which is option d.

Given that f(-1)=-21,f(0)=-9,f(1)=3,f(2)=15 and we are required to find the inverse if the function.

Function is relationship between two or more variables expressed in equal to form. In a function each value of x must have corresponding value of y.

The given function is as under:

f(-1)=-21,

f(0)=-9,

f(1)=3

f(2)=15

In the inverse of the function the value of x becomes the value of y and the value of y becomes the value of x. So the inverse of the function is as under:

p(-21)=-1,

p(-9)=0,

p(3)=1,

p(15)=2

Hence if f(-1)=-21,f(0)=-9,f(1)=3,f(2)=15 then the inverse of function f(x) is p(-21)=-1,p(-9)=0,p(3)=1,p(15)=2 which is option d.

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Graph by hand or using a calculator to determine the solution to the given system. Put in slope-intercept form first if necessary.

Answers

The solution to the system of equations is (8, -4)

How to solve the system?

The system of equations is given as;

y = -1/4x - 2

y = 3/8x - 7

See attachment for the graph of the equations

From the attached graph, we have the point of intersection to be

(x, y) = (8, -4)

Hence, the solution to the system of equations is (8, -4)

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given that 4x-y=5 4y-z=7 and 4z-x=18 what is the value of x+y+z

Answers

Using simultaneous equations,
x=2, y=3, z=5.

Therefore x+y+z
=2+3+5
=10

Answer:

x + y +z= 10

Step-by-step explanation:

4x - y = 5  ---------(I)

 4y - z = 7 ---------(II)

4z - x = 18 ---------(III)

Add all the three equations,

  4x - y + 4y - z + 4z - x = 5 + 7 + 18

  4x - x  -y + 4y -z + 4z  = 30

              3x + 3y + 3z = 30

Divide the entire equation by 3

               [tex]\sf \dfrac{3x}{3}+\dfrac{3y}{3}+\dfrac{3z}{3} = \dfrac{30}{3}[/tex]

                 x + y + z = 10

Identify m∠EFH.

The figure shows triangle G F H. Angle G is equal to 76 degrees. A measure of angle H is given by the formula 3 times x minus 3 degrees. Side G F lies on ray G F with endpoint G. Angle H F E is an exterior angle and its measure is given by the formula 8 times x plus 8 degrees.

Answers

Based on the calculations, the magnitude of m∠EFH is equal to 112°.

How to find the magnitude of m∠EFH?

In Geometry, the sum of two (2) non-adjacent interior angles in a triangle is equal to its exterior angle. Thus, we have:

(3x - 3) + 76 = 8x + 8

3x + 73 = 8x + 8

73 - 8 = 8x - 3x

65 = 5x

x = 65/5

x = 13.

From triangle GFH, we have:

m∠EFH = ∠F = 8x + 8

m∠EFH = 8 (13) + 8

m∠EFH = 104 + 8

m∠EFH = 112°.

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How does the graph of g(x) = (x − 2)3 + 6 compare to the parent function of f(x) = x3?

Answers

The graph of g(x) is the graph of f(x) translated 2 units to the right and 6 units up.

How does the graph of g(x) compare to the one of f(x)?

Here we have:

[tex]f(x) = x^3\\\\g(x) = (x - 2)^3 + 6[/tex]

You can notice that if we take f(x), and we shift it 2 units to the right, we have:

g(x) = f(x - 2)

Then if we apply a shift upwards of 6 units, then we have:

g(x) = f(x - 2) + 3

Replacing f(x) by the cubic parent function, we have:

[tex]g(x) = (x - 2)^3 + 6[/tex]

So we conclude that the graph of g(x) is the graph of f(x) translated 2 units to the right and 6 units up.

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picture explains everything please help ASAP

Answers

Answer: Choice B is correct.

The answer is choice B

Laura is walking quickly and finds that she travels 54 feet in a span of 12 seconds witch of the following is the speed of Laura’s walking

Answers

Laura's walking speed is 4.50 feet per second.

What is Laura's walking speed?

Speed is the total distance travelled per time. Speed can be determined by dividing the distance walked by Laura by the time.

Average speed = total distance / total time

54 / 12 = 4.50 feet per second

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The sum of an integer and 7 more than the next consecutive integer is 66. find the integer

Answers

If the sum of an integer and 7 more than the next consecutive integer is 66 then the integers are 29 and 30.

Given that the sum of an integer and 7 more than the next consecutive integer is 66.

Integer is a number that is written without a fraction component. It can be positive as well as negative.

let the first integer be x.

Consecutive integer will be x+1.

Sum of integer and 7 more than the next consecutive integer is 66.

Sum according to the given information=x+x+1+7

=2x+8

2x+8=66

2x=66-8

2x=58

x=58/2

x=29

Next integer=29+1-30.

Hence if the sum of an integer and 7 more than the next consecutive integer is 66 then the integers are 29 and 30.

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The angle formed by the line of sight and the horizontal line can best be described as an

Answers

the angle formed by the line of sight and the horizontal line can best be described as an angle of elevation. Option B

What is angle of elevation?

Angle of elevation can be defined as the angle formed between a horizontal line and the line of sight up to an object with the image of the object located above the horizontal line.

It is the height greater than the height of the observer.

The opposite of the angle of elevation is the angle of depression which is formed with an observer

Words associated with the angle of elevation are;

angles horizontal linesline of sight

The angle of elevation is the angle between the line of sight and the horizontal line.

Hence, the angle formed by the line of sight and the horizontal line can best be described as an angle of elevation. Option B

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You roll two number cubes one red and one blue. the table shows the probability

Answers

Answer:

where is the table?

Step-by-step explanation:

i have no idea whats going on. PLEASE HELPPP

Answers

Answer:

  36 meters

Step-by-step explanation:

You are given an angle and the length of the side adjacent. You want to find the length of the side opposite, so the relevant trig relation is ...

  Tan = Opposite/Adjacent

Setup

The height of Yuri's balcony is the sum of the heights of Kim's balcony and the height of Yuri's balcony above that. Each of those height is the side opposite a given angle in a right triangle. These can be found by solving the tangent relation for the opposite side:

  Tan = Opposite/Adjacent

  (Adjacent)(Tan) = Opposite

  height of Kim's balcony = (30 m)tan(40°)

  height above Kim's balcony = (30 m)tan(20°)

__

  height of Yuri's balcony = height of Kim's + height above Kim's

  height of Yuri's balcony = (30 m)tan(40°) +(30 m)tan(20°)

  height of Yuri's balcony = (30 m)(tan(40°) +tan(20°))

Evaluation

  height of Yuri's balcony ≈ (30 m)(0.8391 +0.3640) ≈ 36.092 m

The height of Yuri's balcony is about 36 meters.

Can someone help me out on this please having trouble on both and show work please !!

Answers

The difference of the expression is as follows:

(6y⁴ + 3y² - 7) - (12y⁴ - y² + 5) = - 6y⁴ + 4y² - 12

3(x - 5) - (2x + 4) = x - 19

How to find the difference of the expression?

The difference of the expression can be found when we combine the like terms.

Therefore,

(6y⁴ + 3y² - 7) - (12y⁴ - y² + 5)

6y⁴ + 3y² - 7  - 12y⁴ + y² - 5

6y⁴ - 12y⁴ + 3y² + y² - 7 - 5

- 6y⁴ + 4y² - 12

3(x - 5) - (2x + 4)

3x - 15 - 2x - 4

3x - 2x - 15 - 4

x - 19

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Volume = length x width x height
1.
? ft
? ft
? ft
If the volume of the cube is 1 ft³,

Answers

The answer is 1 because 1*1*1 = 1 ft3

Can someone please explain how to do this? I don’t need the answer I just don’t know how to solve it.

Answers

Let [tex]P[/tex] be the number of plain cakes sold, and [tex]D[/tex] the number of decorated cakes sold.

Each plain cake sells for $7, so [tex]P[/tex] cakes sells for [tex]\$7P[/tex].

Similarly, each decorated cakes goes for $11, so [tex]D[/tex] cakes are worth [tex]\$11D[/tex].

The baker sells all but 3 cakes, so

[tex]P + D = 117[/tex]

After the sale, the baker earns a total of $991, so

[tex]7P + 11D = 991[/tex]

Now just solve the system of equations for [tex]P[/tex] and [tex]D[/tex]. This is easily done by substitution or elimination.

(The selected answer is actually the correct one.)

What is the angle at a

Answers

Answer and Step-by-step explanation:

We are given a triangle, a quadrilateral inside a triangle. and exterior angles of the triangle at linear bisectors.

We can figure out the interior angles of the shape to find a by using the linear bisector theorem, in which a line separated by another line will have two angles that will add to 180 degrees.

For the bisected line with the angle of 60 degrees, the other angle will have to equal 120. We know this by taking 60 from 180.

The perpendicularly bisected line will always have 90 degrees for the angles, so the interior angle will be 90 degrees.

For the bisected line with the angle of 80 degrees, the other angle will have to equal 100. We know this by taking 80 from 180.

Now, we have angles to determine a.

Quadrilaterals consist of 4 interior angles, which, when added together, equals 360 degrees.

360 - 90 - 100 - 120 = a

260 - 90 - 120 = a

140 - 90 = 50 = a

So, angle a is equal to 50 degrees.

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A graduate school entrance exam has scores that are normally distributed with a mean of 560 and a standard deviation of 90. What percentage of examinees will score between 600 and 700

Answers

26.8% of examinees will score between 600 and 700.

This question is based on z score concept.

A Z-score is a numerical measurement that describes a value's relationship to the mean of a group of values. Z-score is measured in terms of standard deviations from the mean. If a Z-score is 0, it indicates that the data point's score is identical to the mean score.

[tex]z={x-\mu \over \sigma }[/tex]

where:

μ is the mean

σ is the standard deviation of the population

Given:

μ = 560

σ = 90

For

600≤ X≤700

for x = 700

Z score =x - μ/σ

=(700 - 560)/90

      = 1.55556

P-value from Z-Table:

P(560<x<700) = P(x<700) - 0.5 = 0.44009

for x = 600

Z score =x - μ/σ

=(600 - 560)/90

      = 0.44444

P-value from Z-Table:

P(560<x<600) = P(x<600) - 0.5 = 0.17164

∴ P(600<x<700) = P(560<x<700) - P(560<x<600)

                           = 0.44009 - 0.17164

                          =0.26845

∴26.8% percentage of examinees will score between 600 and 700.

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does this inequality have a solution? 6(x+2)>x-3

Answers

Answer:

x > - 3

Step-by-step explanation:

6(x + 2) > x - 3 ← distribute parenthesis on left side

6x + 12 > x - 3 ( subtract x from both sides )

5x + 12 > - 3 ( subtract 12 from both sides )

5x > - 15 ( divide both sides by 5 )

x > - 3

[tex]\textbf{Heya !}[/tex]

✏[tex]\bigstar\textsf{Given:-}[/tex]✏

[tex]\sf{6(x+2) > x-3}[/tex]

✏[tex]\bigstar\textsf{To\quad find:-}[/tex] ✏

x -- ?

✏[tex]\bigstar\textsf{Solution \quad Steps:-}[/tex] ✏

use the distributive property

[tex]\sf{\longmapsto 6x+12 < x-3}[/tex]

subtract both sides by x and 12

[tex]\sf{\longmapsto{5x < -15}[/tex]

divide both sides by 5

[tex]\sf{\longmapsto x < -3}}[/tex]

`hope it's helpful to u ~

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A rubber stopper, which has a mass of m = 14.5 grams, is tied to the end of a string which is threaded through a glass tube. You then spin the rubber stopper about your head in a horizontal circle as shown to the right. The stopper sags = 18.0o below the horizontal as shown and the distance from the top of the tube to the stopper is L = 1.25 m.b. What will be the magnitude of the centripetal force acting on the stopper?c. What is the speed of the stopper?d. What is the tension in the string?e. How much Mass M is hanging on the end of the string? Write your answer as a decimal or whole number % of 80 =60 PLS HELP QUICK !!!!!what is the area of this figure? A wave hits an object as shown.Which kind of wave interaction is shown?absorptiondiffractionrefraction reflection Angela wants to know how many families in her neighborhood plan to attend the parade. She puts all 120 of the neighborhood addresses in a hat and draws a random sample of 30 addresses. She then asks those families if they plan to attend the parade. She finds that 40% of the families plan to attend the parade. She claims that 40% of the neighborhood families would be expected to attend the parade. Is this a valid inference? Yes, this is a valid inference because the 30 families speak for the whole neighborhood Yes, this is a valid inference because she took a random sample of the neighborhood No, this is not a valid inference because she did not take a random sample of the neighborhood No, this is not a valid inference because she asked only 30 families Which power was granted to the legislative branch by the Constitution? A car drives 40 km due east and then 50 km due west .what is the cars overall displacement? plzzzzzzz help quick i have 10 mins left!!!Isaac is making sandwiches for a group of friends. He needs 3 ounces of meat for each sandwich.Part A: Isaac is not sure how many sandwiches he will be able to make. Write an expression with a variable that represents the amount of meat Isaac needs for his sandwiches. Identify what the variable represents.Part B: If Isaac has 18 ounces of meat, how many sandwiches can he make? Create an equation and show all work to solve it. It is said that it is the male who determines the sex of the baby rather than it is the female. From your knowledge of the sex chromosome, is it true? PLEASE HELP !! GEOMETRY Find The Area of the parallelogram...Explain. Hellppp!! please help me find the answer Describe the patterns and atomic mass is an ion charges in the periodic table Which type of data is shown below? apple, 0.85 banana, 0.90 peach, 1.50multiple choice:structuredunstructured abstractinteger THANK PLZ HELP If f(x) = x + 1, and g(x) = 2x,thengf(x)) = ? The level of government responsible for conducting foreign policy, regulating commerce, and providing for the common defense is the 20 = x/4 - 13 help plz thank you Which sentence from the text best helps develop the idea that there are ways to shop safely online? Mi mam desayuna en la mesaA.) anaranjadaB.) amarillaC.) rojaD.) rosada What is the value of the 8th term of the sequence 4, 8, 16, 32, ...?1282,0485121,024