Find dx/dy when y =(3x−1)(2x+5)

The axis of symmetry of the given quadratic function f(x) = -(x - 2)(x + 4) is x = -1.

Given the function in the question:

f(x) = -(x - 2)(x + 4)

To find the axis of symmetry, first expand  quadratic function f(x) = -(x - 2)(x + 4).

f(x) = -(x - 2)(x + 4)

f(x) = (-x + 2)(x + 4)

f(x) = -x(x + 4) + 2( x + 4 )

f(x) = -x² - 4x + 2x + 8

Collect and add like terms

f(x) = -x² - 2x + 8

To find the axis of symmetry, we can use the formula:

x = -b/2a

Where a = -1 and b = -2.

Substituting these values, we get:

x = -(-2) / 2(-1)

Simplify

x = 2 / -2

x = -1

Therefore, the the axis of symmetry is x = -1.

Option D) x = -1 is the correct answer.

Learn more about axis of symmetry here: https://brainly.com/question/22495480

#SPJ1

The given matrix has no solution. Therefore, option A is the correct answer.

From the given matrix,

[tex]\left[\begin{array}{ccc}1&1&-4\\-2&-1&6\\-5&-3&16\end{array}\right]\left[\begin{array}{ccc}x\\y\\x\end{array}\right] = \left[\begin{array}{ccc}6\\-10\\-26\end{array}\right][/tex]

[tex]\left[\begin{array}{ccc}x+y-4z\\-2x-y+6z\\-5x-3y+16z\end{array}\right] =\left[\begin{array}{ccc}6\\-10\\-26\end{array}\right][/tex]

x+y-4z=6  -------(i)

-2x-y+6z=-10 ---------(ii)

-5x-3y+16z=-26 ---------(iii)

Multiply equation (i) by 2, we get 2x+2y-8z=12 ---------(iv)

Add equation (ii) and (iv), we get

-2x-y+6z+2x+2y-8z=-10+12

y-2z=2 ---------(v)

Multiply equation (i) by 5, we get

5x+5y-20z=30 ---------(vi)

Add equation (vi) from (iii), we get

5x+5y-20z+(-5x-3y+16z)=30-26

5x+5y-20z-5x-3y+16z=4

2y-4z=4

y-2z=2 ---------(vii)

From equation (vi) and (vii), we understood the matrix has no solution

Therefore, option A is the correct answer.

To learn more about the product of matrices visit:

brainly.com/question/24810141.

#SPJ1

The algebraic expression is:

4x + 12

We have,

Algebraic expressions are mathematical statements that involve variables, numbers, and mathematical operations like addition, subtraction, multiplication, and division.

In this case,

We have been given the phrase "Four times a number(x) more than twelve" and we need to translate it into an algebraic expression.

The first step is to identify the key information in the phrase.

Here, the phrase tells us to take a number (which we represent by x) and multiply it by four.

It then says we should add 12 to this.

Now,

Four times a number more than twelve can be translated to four times a number increased by twelve.

And,

Since the number is represented by x, we can write it as 4x + 12.

Thus,

The algebraic expression is:

4x + 12

Learn more about expressions here:

https://brainly.com/question/3118662

#SPJ1

The algebraic expression that represents the phrase "Four times a number (x) more than twelve" is 4(x + 12).

We have the statement

"Four times a number(x) more than twelve"​

let the number be x.

So, four times of a number = 4x

Then, the algebraic expression that represents the phrase "Four times a number (x) more than twelve" is 4(x + 12).

Learn more about expression here:

https://brainly.com/question/14083225

#SPJ1

Answer: 149

Step-by-step explanation: 15 17 19 21

23 25 27 29 31 33 35 37 39 41

43 45 47 49 51 53 55 57 59 61

63 65 67 69 71 73 75 77 79 81

83 85 87 89 91 93 95 97 99 101

103 105 107 109 111 113 115 117 119 121

123 125 127 129 131 133 135 137 139 141

143 145 147 149 151 153 155 157 159 161

163 165 167 169 171 173 175 177 179 181

183 185 187 189 191 193 195 197 199 201

203 205 207 209 211 213 215 217 219 221

223 225 227 229 231 233 235 237 239 241

243 245 247 249 251 253 255 257 259 261

263 265 267 269 271 273 275 277 279 281

283 285 287 289 291 293 295 297 299 301

303 305 307 309 311 313 315 317 319 321

323 325 327 329 331 333

The Experimental probability and the theoretical probabilities are 0.2 and 0.3 respectively.

If the spinner is fair, then each color must have the same probability,

this means that the probability for each color is the number of times that the color (in this case blue) is in the spinner divided by the total amount of colors in the spinner, then the theoretical probability for each color is:

Pt = 1/5 = 0.20

The experimental probability can be found by dividing the number of times that the spinner landed on a given color (in this case for blue we have 15 times) divided by the total number of spins ( 50)

Pe = 15/50 = 0.30

Therefore, the Experimental probability and the theoretical probabilities are 0.2 and 0.3 respectively

Learn more about probability here:

https://brainly.com/question/30034780

#SPJ1

Complete question:

A spinner has 5 equal-sized sections with different colors. You spin the spinner 50 times. The results are shown in the table. Find the theoretical and experimental probabilities of spinning blue.

Red Green Blue Yellow Orange

8           11      15       9          7

The theoretical probability is

The experimental probability is

The measure of angle A and angle C from the given cyclic quadrilateral are 81° and 99° respectively.

From the given figure, m∠D=86°.

Here, m∠D+m∠B=180°  (Opposite angles of cyclic quadrilateral adds to 180° )

86°+m∠B=180°

m∠B=180°-86°

m∠B=94°

Let O be the center of circle.

Since, the legs of the radii are equal, the triangles AOD, DOC and COB are isosceles. Hence, their base angles are congruent. Thus,

77°+2∠ADO=180°

2∠ADO=180°-77°

2∠ADO=103°

∠ADO=103/2

∠ADO=51.5°

∠ADO=∠DAO=51.5°

2∠BAO=180°-121°

2∠BAO=59°

∠BAO=59°/2

∠BAO=29.5°

∠BAD=∠DAO+∠BAO

∠BAD=51.5°+29.5°

∠BAD=81°

So, m∠A=81°

m∠A+m∠C=180°

m∠C=180°-81°

m∠C=99°

Therefore, the measure of angle A and angle C from the given cyclic quadrilateral are 81° and 99° respectively.

To learn more about the circle theorems visit:

https://brainly.com/question/19906313.

#SPJ1

After the mathematical calculations, we can see that the value of z = 5 - 15i.

To simplify, let's square the complex number (2 - i):

[tex](2 - i)^2 = 2^2 - 2i + 2i - i^2 = 4 - 4i - 1 = 3 - 4i.[/tex]

Divide the complex number (7 - 4i) by (2 + i):

The approach we will take involves multiplying the top and bottom of the equation by the complex conjugate of the denominator.

[tex](7 - 4i) * (2 - i) / (2 + i) * (2 - i) = (14 - 7i - 8i + 4i^2) / (4 + 1) = (14 - 15i + 4(-1)) / 5[/tex]

= (10 - 15i) / 5

= 2 - 3i.

We have to minus 8i:

[tex](3 - 4i) + (2 - 3i) - 8i = 5 - 7i - 8i = 5 - 15i.[/tex]

Therefore, z = 5 - 15i.

Read more about complex numbers here:

https://brainly.com/question/10662770

#SPJ1

The inverse of matrix of A, that is A⁻¹ is [tex]\begin{bmatrix}-3 & 2 \\ 2& -1\end{bmatrix}[/tex].

To find the inverse of the matrix A, we can use the formula.  

A⁻¹ = (1 / det(A)) x adj (A)

Where det(A) represents the determinant of matrix A and adj(A) represents the adjugate of matrix A.

First, let's calculate the  determinant of matrix  A

det (A) = (1 x 3)  - (2 x2)

= 3 - 4

= -1

Next, let's calculate the adjugate of matrix A

adj(A) =

[tex]\begin{bmatrix}3 & -2 \\ -2& 1\end{bmatrix}[/tex]

Now, we can calculate the inverse of matrix A using the formula:

A⁻¹  = (1 / det(A)) x  adj(A)

= (1 / -1) *

[tex]\begin{bmatrix}3 & -2 \\ -2& 1\end{bmatrix}[/tex]

Multiplying each element of the adjugate matrix by -1  

A⁻¹ =

[tex]\begin{bmatrix}-3 & 2 \\ 2& -1\end{bmatrix}[/tex]

So , the inverse of the matrix A is:

A⁻¹  =

[tex]\begin{bmatrix}-3 & 2 \\ 2& -1\end{bmatrix}[/tex]

Learn more about matrix:
https://brainly.com/question/29132693
#SPJ1

the next two terms in the sequence would be 12 and 17.

Step-by-step explanation:

The student's chances of answering all five questions correctly are 7/64.

This is an example of a binomial distribution, where each question has a probability of 1/2 of being answered correctly and there are 8 independent trials.

The probability mass function for a binomial distribution is:

P(X = k) = (n choose k) * p^k * (1-p)^(n-k)

where n is the number of trials, p is the probability of success, and k is the number of successes.

In this case, n = 8, p = 1/2, and we want to find P(X = 5).

P(X = 5) = (8 choose 5) * (1/2)^5 * (1/2)^(8-5)

P(X = 5) = (8 choose 5) * (1/2)^8

Using the formula for combinations, (n choose k) = n! / (k! * (n-k)!) we get:

P(X = 5) = (8! / (5! * 3!)) * (1/2)^8

P(X = 5) = 56 * 1/256

P(X = 5) = 7/64

Therefore, the probability of the student getting 5 questions correct is 7/64.

Learn more about probability here:

https://brainly.com/question/30034780

#SPJ1

[tex]6 + 3 = 9 \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ [/tex]

The value of x is given as follows:

x = 76º.

To obtain the value of x, we must consider that the sum of the internal angle measures of a triangle is of 180º.

The internal angles of the triangle in this problem are given as follows:

Considering that the sum of the measures is of 180º, the value of x is obtained as follows:

48 + 56 + x = 180

x = 180 - (48 + 56)

x = 76º.

More can be learned about the sum of the interior angle measures of a polygon brainly.com/question/224658

#SPJ1

The value of angle a is 80 degrees.

The two chords intersect angle theorem, also known as the intersecting chords theorem, states that when two chords intersect inside a circle, the product of the segments of one chord is equal to the product of the segments of the other chord.

From two chords intersect angle theorem

∠a=(∠b+∠c)/2

in a given case,

∠b=36°

∠c =124°

So, ∠a=(36+124)/2

∠a= 80°

Therefore, the value of angle a will be 80 degrees.

Learn more about chords here:

https://brainly.com/question/8944240

#SPJ1

Complete question:

the total number of posts needed is, 56

Since, we know that the area of the horse corral is 10,000 square feet.

So, it is a square corral, we can find the length of each side by taking the square root of the area, which is 100 feet.

Now, For the total number of posts needed, we need to calculate the perimeter of the corral.

Since there are four sides of equal length, the perimeter of the corral is 4 times the length of one side.

Therefore, the total perimeter is 400 feet.

Now, we need to find the number of posts needed.

We know that each post is placed 10 feet apart along the sides of the corral.

Since there are 4 sides, we need 3 intervals of 10 ft between each post, which gives us a total of 4 posts for every 30 feet of fencing.

Therefore, the total number of posts needed is,

= (400 / 30) x 4 + 4

= 56 posts.

Learn more about the multiplication visit:

https://brainly.com/question/10873737

#SPJ1

The area of the trapezoid is 104 square yards

As given a table was made by Veronica which is in the shape of a trapezoid.

twice as long as the table's width

Let us find the area of the trapezoid by the given data and formula of trapezoid

The length of the bottom base is x= 16 yd.

Area A=(a+b)h/2

a=10 yd

b=16 yd

h =8 yd

Substitute the values of a, b and h in the area of trapezoid

Area =1/2(10+16)8

=208/2

=104 square yards

Hence, the area of the trapezoid is 104 square yards

To learn more on Area click:

https://brainly.com/question/20693059

#SPJ1

Answer:

quadratic formula, completing the square, factorisation

Step-by-step explanation:

Quadratic formula:

x = (-b ± √(b² - 4ac) ÷ 2a)

where a is the value of the first coefficient, b is value of the second and c is value of the constant.

x = ((-b ± √(b² - 4ac)) ÷ 2a)

 = (( -16± √((-16)² - 4(8)(3)) ÷ 2(8))

 = ((-16 ± √(256 - 96)) ÷  16)

= (-16 ± √(160)) ÷  16

= -1 ±  (√10)/4

Completing the square:

divide through by 8

x² + 2x + 3/8 = 0

1) put the x, not ^2, in parenthesis.

(x +  )      = 0

2) half the coefficient (2) of x. that is 1. Put that into same parenthesis.

(x + 1)       = 0

3) we have (x + 1)

4) square this and multiply out. (x + 1)² = x² + x + x +4 = x² +2x + 1

5) this looks just like the original equation (x² + 2x + 3/8) except for +1. What do we have to do to get back to original? 1 – (3/8) = 5/8. We have to subtract 5/8

6) now we have (x + 1)² – 5/8 =0

7) (x + 1)² = 5/8

8) (x + 1) = ± √(5/8)

9) x = ± √(5/8)  - 1

     =  -1 ± (√10)/4

Factorisation:

(8x (- (2√10)) + 8) = 0,

8x = -8 +  (2√10)),

x = -1 + (√10)/4

(x ( + (√10)/4 + 1) = 0

x = -1 -  (√10)/4

An exponential equation that best fit the data above is [tex]y = 535.02(1.15)^x[/tex]

a = 535.02

b = 1.15.

In this scenario, the x-values (x) would be plotted on the x-axis of the scatter plot while the y-values (y) would be plotted on the x-axis of the scatter plot.

By critically observing the scatter plot (see attachment) which models the relationship between the x-values (x) and y-values (y), the exponential equation and the correlation coefficient are given by:

[tex]y = 535.02(1.15)^x[/tex]

Correlation coefficient, r = 0.9973006 ≈ 1.0

In conclusion, we can logically deduce that there is a strong correlation between the data because the correlation coefficient (r) is is greater than 0.7;

0.7＜|r| ≤ 1.0   (strong correlation)

Read more on exponential equation here: brainly.com/question/28939171

#SPJ1

Answer:

21cm

Step-by-step explanation:

Pythagoras Theorem for right angled triangle a² = b² + c²

hypotenuse² = opposite ² + adjacent ²

Call vertical height of wall (where ladder meets it) H

call ladder L and call ground distance G

50cm = 0.5m

3² = 0.5² + H², H² = 3² - 0.5² = 9 - 0.25 = 8.75. H = √8.75.

length of ladder is always 3m.

After ladder has slipped, G is now 0.5 + 0.7 = 1.2m.

H² = 3² - 1.2²

    = 9 - 1.44

    = 7.56

H = √7.56

H has changed from √8.75 to √7.56

It has slipped (√8.75 - √7.56)m

= 0.208m

= 20.8 cm

=21cm to nearest cm.

There will be no sugar left after the transfer.

Given are two containers in the shape of a rectangular prism and the second one is a composite solid of rectangular prism and a triangular prism,

We need to compare the volume of both prisms,

For the volume of the composite solid we will add the volume of both solids = 1/2 × base area × height + length × width × height

= 1/2 × 300 × 8 + 12 × 12 × 25

= 1200 + 3600

= 4800 cm³

Now the volume of the old container (rectangular prism - the blue one) = length × width × height = 30 × 20 × 8 = 4800 cm³

Since the volume of both old and new container is same, so there will be no sugar left after the transfer.

Hence there will be no sugar left after the transfer.

Learn more about volumes click;

https://brainly.com/question/13338592

#SPJ1

Bonjour,

v1 = 60/(5/6) = 60 x 6/5 = 360/5 = 72km/h

v2 = 54/(2/3) = 54 x 3/2 = 162/2 = 81km/h

it's Bernie

The mapping of the function f(x) given as 3x⁴ - 4x³ + 3x² - 5x - 3 is define at; -3, f(-3) = 390 and at 4, f(4) = 537

A function is a rule that defines a relationship between one variable. It is the mapping whose codomain is the set of real numbers

For x = -3;

f(-3) = 3(-3)⁴ - 4(-3)³ + 3(-3)² - 5(-3) - 3

f(-3) = 3(81) + 4(27) + 3(9) + 15 - 3

f(-3) = 243 + 108 + 27 + 15 - 3

f(-3) = 390

For x = 4;

f(4) = 3(4)⁴ - 4(4)³ + 3(4)² - 5(4) - 3

f(4) = 3(256) - 4(64) + 3(16) - 20 - 3

f(4) = 768 - 256 + 48 - 20 - 3

f(4) = 537

Therefore, for the mapping of the function f(x) = 3x⁴ - 4x³ + 3x² - 5x - 3 for the values of x: -3 and 4 we have the results 390 and 537.

A statement that is true about the mapping shown include the following: A. It represents a function because each x-value corresponds to exactly one y-value.

In Mathematics and Geometry, a function can be defined as a mathematical equation which is typically used for defining and representing the relationship that exists between two or more variables such as an ordered pair.

Based on the mapping diagram below, we can reasonably infer and logically deduce that it represent a function because the input values (domain, x-value, or independent values) are uniquely mapped to the output values (range, y-value or dependent values).

In this context, we can reasonably infer and logically deduce that the mapping diagram represent a function.

Read more on function here: brainly.com/question/27862183

#SPJ1

Complete Question:

Which is true about the mapping shown?

A. It represents a function because each x-value corresponds to exactly one y-value.

B. It represents a function because each y-value corresponds to exactly one x-value.

&. It does not represent a function because each x-value corresponds to exactly one -value.

D, It does not represent a function because each y-value does not correspond to exactly one x-value.

Answer:

So 98 adult tickets were sold.

Step-by-step explanation:

Let's use a system of equations to solve the problem.

Let x be the number of child tickets sold and y be the number of adult tickets sold. Then we have:

x + y = 176 (equation 1)

5.10x + 8.20y = 1201.40 (equation 2)

We can solve for x by isolating y in equation 1 and substituting into equation 2:

y = 176 - x (from equation 1)

5.10x + 8.20(176 - x) = 1201.40 (substitute into equation 2)

5.10x + 1443.20 - 8.20x = 1201.40

-3.10x = -241.80

x = 78

Therefore, 78 child tickets were sold that day. We can find the number of adult tickets by substituting x into equation 1:

78 + y = 176

y = 98

So 98 adult tickets were sold.

The step function evaluated in x = 1.4 gives the outcome y = 1, thus, the correct option is the first one.

The step function, written as:

f(x) = [x]

Is a function that rounds down the value of x to the nearest whole number.

So, for any input that we give to that function, the output will be equal to the number before the decimal point.

If we evaluate this function in x = 1.4, then we will round to the number before the decimal point, thus the outcome is y = 1.

Then we will get:

f(1.4) = [1.4] = 1

The correct option will be the first one.

Learn more about the step function at:

https://brainly.com/question/12000188

#SPJ1

The drama club must sell at least 74 adult tickets to meet the cost requirement, in addition to the 45 student tickets that have already been sold.

Let's use "a" to represent the number of adult tickets sold, and "s" to represent the number of student tickets sold.

Since s = 45, and we want to find the minimum number of adult tickets required to satisfy the $890 cost requirement.

The total revenue from ticket sales can be expressed as:

Revenue = 5s + 9a

We want to find the values of s and a that satisfy the following conditions:

- s + a <= 122 (the maximum capacity of the auditorium)

- Revenue >= 890

Substituting s = 45, we get:

5(45) + 9a >= 890

225 + 9a >= 890

9a >= 665

a >= 73.89

Since we cannot sell a fraction of a ticket, the minimum number of adult tickets we need to sell to meet the cost requirement is 74.

Therefore, the drama club must sell at least 74 adult tickets to meet the cost requirement, in addition to the 45 student tickets that have already been sold.

Learn more about word problems at https://brainly.com/question/21405634

#SPJ1

Answer: d.8

the answer is d 8ndndinwidnwidnwidnwidnwiud

It will take Adrian 16 full months to save enough money for the electric keyboard.

- Price of the keyboard (with tax) at Macelli's: $2,400
- Adrian's monthly savings: $150
We need to find how long it will take Adrian to save for the keyboard. To do this, we'll divide the total cost of the keyboard by his monthly savings and round up to the nearest full month.
Step 1: Divide the total cost by monthly savings.
Time (in months) = (Total Cost) / (Monthly Savings) = ($2,400) / ($150)
Step 2: Calculate the result.
Time (in months) = 16
So, it will take Adrian 16 full months to save enough money for the electric keyboard.

For more such questions on save , Visit:

https://brainly.com/question/18917547

#SPJ11