What is the slope of the line represented by the equation y = -2/3- 5

The Amy has 42 books, Betty has 36 books, and Carol has 18 books.

Let's set up equations to represent the given information:

Let A represent the number of books Amy has.

Let B represent the number of books Betty has.

Let C represent the number of books Carol has.

Let's say Amy has x books.

Betty has 6 books less than Amy, so Betty has (x - 6) books.

Carol has half as many books as Betty, so Carol has (x - 6)/2 books.

According to the problem, the total number of books they have is 96.

So, we can write the equation:

x + (x - 6) + (x - 6)/2 = 96

To solve the equation, we can simplify it by multiplying through by 2 to remove the fraction:

2x + 2(x - 6) + (x - 6) = 192

2x + 2x - 12 + x - 6 = 192

5x - 18 = 192

5x = 210

x = 42

Amy has 42 books.

Betty has (42 - 6) = 36 books.

Carol has (36)/2 = 18 books.

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Based on the information we can infer that the equation shown in the image is 1.23 - 0.35 = 0.88 (option B).

To identify the correct equation we must look at the graph and identify the information it provides. In this case we have two squares divided into 100 squares each. Additionally, the square on the left has 88 squares painted in red and 12 squares with an X inside. In the case of the square on the right, it has 23 squares colored in red with an X inside.

In total we have 123 squares painted in red, which in decimal number is equivalent to 1.23. On the other hand, the number of squares painted red and with an X inside is 35, this value would be 0.35.

On the other hand, the squares painted only in red are 88, so the equivalent in decimal numbers would be 0.88. Therefore, the correct way to express this relationship through an equation would be:

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Answer:

the last digit is 5

Step-by-step explanation:

The equation of the normal line to the curve x^2y^2 = 4 at the point (-1,-2) is y = x - 1.

To find the tangent line and normal line to the curve x^2y^2 = 4 at the point (-1,-2), we need to determine the derivative of the curve equation with respect to x and evaluate it at the given point.

First, let's differentiate the equation x^2y^2 = 4 implicitly with respect to x using the chain rule:

2x * (y^2) + 2y * (2xy * dy/dx) = 0

Simplifying the equation, we have:

2xy^2 + 4xy(dy/dx) = 0

Now, let's find the value of dy/dx at the point (-1,-2). Substitute x = -1 and y = -2 into the equation:

2*(-1)(-2)^2 + 4(-1)*(-2)(dy/dx) = 0

Simplifying further:

8 + 8(dy/dx) = 0

8(dy/dx) = -8

dy/dx = -1

We have found the derivative dy/dx at the point (-1,-2), which is -1. This represents the slope of the tangent line to the curve at that point.

Using the point-slope form of a line, we can write the equation of the tangent line as:

y - y₁ = m(x - x₁)

Substituting the values of (-1,-2) and dy/dx = -1 into the equation, we have:

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

y + 2 = -1(x + 1)

y + 2 = -x - 1

y = -x - 3

Therefore, the equation of the tangent line to the curve x^2y^2 = 4 at the point (-1,-2) is y = -x - 3.

To find the normal line, we know that the slope of the normal line is the negative reciprocal of the slope of the tangent line. Therefore, the slope of the normal line is 1.

Using the point-slope form of a line again, we can write the equation of the normal line as:

y - y₁ = m'(x - x₁)

Substituting the values of (-1,-2) and m' = 1 into the equation, we have:

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

y + 2 = x + 1

y = x - 1

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Answer:

A

Step-by-step explanation:

when you look, you see the y value is always bigger by 2 than the x value.

so, the function is clearly to take the x value, add 2 to it and deliver this as the functional result (y value).

only A fits.

Answer:

mark me as brainliest

Step-by-step explanation:

common stocks

Answer:

f(x) = x³ - 4x + 6

f'(x) = 3x² - 4

a) f'(2) = 3(2²) - 4 = 12 - 4 = 8

6 = 8(2) + b

6 = 16 + b

b = -10

y = 8x - 10

b) 3x² - 4 = 0

3x² = 4, so x = ±2/√3 = ±(2/3)√3

= ±1.1547

f(-(2/3)√3) = 9.0792

f((2/3)√3) = 2.9208

c) 3x² - 4 = 8

3x² = 12

x² = 4, so x = ±2

f(-2) = (-2)³ - 4(-2) + 6 = -8 + 8 + 6 = 6

6 = -2(8) + b

6 = -16 + b

b = 22

y = 8x + 22

f(2) = 6

y = 8x - 10

The equation perpendicular to the tangent is y = -1/8x + 25/4

-The smallest slope on the curve is 2.92

The curve has the smallest slope at the point (1.15, 2.92)

The equations at tangent points are y = 8x + 16 and  y = 8x - 16

From the question, we have the following parameters that can be used in our computation:

y = x³ - 4x + 6

Differentiate

So, we have

f'(x) = 3x² - 4

The point is (2, 6)

So, we have

f'(2) = 3(2)² - 4

f'(2) = 8

The slope of the perpendicular line is

Slope = -1/8

So, we have

y = -1/8(x - 2) + 6

y = -1/8x + 25/4

We have

f'(x) = 3x² - 4

Set to 0

3x² - 4 = 0

Solve for x

x = √[4/3]

x = 1.15

So, we have

Smallest slope = (√[4/3])³ - 4(√[4/3]) + 6

Smallest slope = 2.92

So, the smallest slope is 2.92 at (1.15, 2.92)

Here, we set f'(x) to 8

3x² - 4 = 8

Solve for x

x = ±2

Calculate y at x = ±2

y = (-2)³ - 4(-2) + 6 = 6: (-2, 0)

y = (2)³ - 4(2) + 6 = 6: (2, 0)

The equations at these points are

y = 8x + 16

y = 8x - 16

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Answer:

The answer is 275 students.

Step-by-step explanation:

In 75 students, 33 students attend.

So the ratio is 33/75.

so multiply with 625.

625 x 33/75 = 275

when running a line, in a right-triangle, from the 90° angle perpendicular to its opposite side, we will end up with three similar triangles, one Small, one Medium and a containing Large one.  Check the picture below.

\(\cfrac{a}{18}=\cfrac{32}{a}\implies a^2=(32)(18)\implies a=\sqrt{(32)(18)}\implies a=24 \\\\[-0.35em] ~\dotfill\\\\ \cfrac{b}{50}=\cfrac{32}{b}\implies b^2=(32)(50)\implies b=\sqrt{(32)(50)}\implies b=40\)

By variatiοn methοd the acceleratiοn οf the οbject will be 5 m/s².

In mathematics Variatiοn can be clear frοm the idea οf variables. Any change in οne quantity due tο a change in anοther quantity that is dependence between twο variable is referred tο as variatiοn. There are twο types οf variatiοn. Direct and Inverse variatiοn.

Fοr a mοving οbject, the fοrce acting οn the οbject varies directly with the οbject's acceleratiοn.

Let the fοrce οf the οbject be F and the οbject's acceleratiοn is a

Since bοth varies directly, sο by variatiοn methοd we have,

                             F∝ a

                            F= ka------------(1)   where k is the variational constant

When a fοrce οf 36 N acts οn a certain οbject, the acceleratiοn οf the οbject is 6 m/s²

Sο putting F= 36 and a= 6 in equatiοn (1) we get,

36= 6k

k= 6

The fοrce is changed tο 30 N

Nοw putting F= 30 and k = 6 in equatiοn (1) we get,

30= 6a

a= 5

Hence, the acceleratiοn οf the οbject will be 5 m/s².

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Answer:

x=11

Explanation:

If triangles QRS and TUV are similar, then the ratio of the corresponding sides are:

Substituting the given lengths:

We solve the equation above for x:

The value of x is 11.

Answer: 1540

Explanation: Just multiply or use a calculator. The prime factorization is all the prime factors, meaning you can multiply all of them to get the original number.

Answer:

a) 6ab

b) c⁶

c) 10y⁷

d) 12g⁴h⁵

Answer:

Remainder is -53/8

Step-by-step explanation:

the divisor is (2x - 3):

make x the subject:

\(2x - 3 = 0 \\ 2x = 3 \\ x = \frac{3}{2} \)

substitute for x in the function:

\(f(x) = {x}^{3} - 6 {x}^{2} + 3x - 1 \\ f( \frac{3}{2} ) = {( \frac{3}{2}) }^{3} - 6 {( \frac{3}{2}) }^{2} + 3( \frac{3}{2} ) - 1 \\ \\ f( \frac{3}{2} ) = \frac{ - 53}{8} \)

Answer: -8

Step-by-step explanation:

All of the values are equal to 8 except for the last one

The absolute value of -8 is 8

8 is 8... lol

The absolute value of 8 is 8

2^3 =8

-8 does not equal 8

Answer:

535 is the cirrext answer

Mean value for the given data is 8.129, median = 7.7, Standard deviation is 1.699, Probability for MPa value greater than 10 is 0.148 and Coefficient of variation = 20.9

a) To estimate the mean value, we have to calculate all the observations and divide it by number of observations.

  x = ∑ xi / n = 219.5/27 = 8.129

So here the estimator used is x

b) To estimate the strength value or to separate weakest 50% from strongest 50%, we have to calculate the median. For that we have to arrange in ascending order and find the middle most term.

Since  n is odd, middle term is (n+1)/2 th term = (27+1)/2 = 28/2 = 14th term. Ascending order is given as image. the 14th term is 7.7.

c) Next we have to calculate standard deviation

 σ =  √(∑xi² - (∑x)²/n)/(n-1) = [1859.53 - (219.5²/27)] /(27-1)

                                          = (1859.53- 1784.454) / 26

                                         = 1.699

d) We have to calculate the probability flexural strength greater than 10. Here there are 4 values above 10.

So, p = 4/27 = 0.148

e) Coefficient of variation = (σ/x) ×100

                                           = \(\frac{1.699}{8.129} * 100\)

                                            = 20.9

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1. The height of the cone is, 22.18 mm.

2. The slant height is, 28.14 mm.

3. The ant crawl to get from the base of the cone to the top of the hill is, 28.14 mm.

In mathematics, Space occupied by three dimensional objects is called Volume. Basically it is a space within a closed region of every three dimensional object.

The volume of cone V = (1/3)πr²h

Given that,

The volume  = 8792 mm³

1. by using the formula to solve for h,

we get h = (3V)/(πr²).

Plugging in the values given,

we have h = (3(8792 mm³))/(π(20 mm)²) ≈ 22.18 mm.

Therefore, the height of the cone is approximately 22.18 mm.

2. it is known that, from the Pythagoras theorem

s² = h² + r²,

where s is the slant height, h is the height, and r is the radius.

Plugging in the values we found in part 1,

we have s² = (22.18 mm)² + (20 mm)² ≈ 791.88 mm².

Taking the square root of both sides, we get s ≈ 28.14 mm.

Therefore, the slant height is approximately 28.14 mm.

3. To find the distance the ant crawls to get from the base of the cone to the top of the hill, we need to find the length of the slant height.

Using the value we found in part 2,

the length of the slant height is approximately 28.14 mm.

Therefore, that is the distance the ant would crawl to get from the base of the cone to the top of the hill.

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Answer:

5

Step-by-step explanation:

All you would have to do is read the question. Because if it is like a block than it couldn't be any closer to the bottom than five inches.

Answer:

En este problema se trata de una función exponencial, donde la cantidad de microbios en el recipiente se duplica cada minuto.

Si x representa el número de minutos transcurridos y y la cantidad de microbios en el recipiente, entonces se puede expresar la función exponencial como:

y = a * (2)^x

Donde "a" es la cantidad inicial de microbios en el recipiente, en este caso a = 1.

Después de 30 minutos, la cantidad de microbios en el recipiente es:

2^30 = 1,073,741,824

Esto significa que si se coloca un solo microbio en el recipiente, se tardará 30 minutos en llenarlo.

Si se colocan 2 microbios en el recipiente, entonces la cantidad inicial de la función exponencial es a = 2, y se busca el valor de x tal que:

2 * (2)^x = 1,073,741,824

Dividiendo ambos lados por 2, se tiene:

(2)^x = 536,870,912

Tomando logaritmos base 2 en ambos lados, se tiene:

x = log2(536,870,912) = 29

Por lo tanto, si se colocan 2 microbios en el recipiente, se tardará 29 minutos en llenarlo.

Step-by-step explanation:

Answer:

1/2

Step-by-step explanation:

20 times 1/2 = 10

10-2 = 8

Answer:

option B Is correct

in the above angle F is the vertex and EG are the arm of angles

The name of the angle below is ∠EFG.

Option B is the correct answer.

The angles between two lines are the angles formed by two intersecting lines, measured in degrees or radians.

Several different types of angles can be formed between two lines, including acute angles, right angles, and obtuse angles.

We have,

From the figure,

There is only one angle.

i.e

∠EFG = ∠GFE

Thus,

The name of the angle below is ∠EFG.

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Answer:

  (c)  y = 3^x

Step-by-step explanation:

A function is described as exponential if the independent variable is found in the exponent.

  y = x^(1/2) . . . a square root function, not exponential

  y = 2x^3 . . . . a cubic (polynomial) function, not exponential

  y = 3^x . . . . . an exponential function

Answer:

Step-by-step explanation:

9. sin 18 = x/21

 x = 21* sin 18

  x = 6.5

10. tan 55 = 29/x

  x* tan 55 = 29

x = 29/tan 55

x = 20.3

11. sin 23 = x/25

  x = 25 * sin 23

  x = 9.8

12. sin 47 = 33/x

  x * sin 47 = 33

 x = 33/sin 47

  x = 45.1

Answer:

6

Step-by-step explanation:

Divide the amount of eggs by the amount of people this gives you the amount of eggs needed for one person then times by 9

(4÷6) x9

Answer:

Therefore, the measure of angles x is 70°.

Step-by-step explanation:

From the given figure ,

115° is the exterior angle

x° and 45° are the two interior opposite angles to 115°

We know that

An exterior angle formed by extending the side of a triangle is equal to the sum of the two interior opposite angles

⇛ x° + 45° = 115°

⇛ x° = 115°-45°

⇛ x° = 70°

Therefore , x = 70°

The length to cut-off is 2.57 inches

The given parameters are:

Available length = 10 inches

Length needed = 7.43 inches

The length to cut off is calculated as:

Length = Available length - Length needed

So, we have:

Length = 10 inches - 7.43 inches

Evaluate the difference

Length = 2.57 inches

Hence, the length to cut-off is 2.57 inches

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Answer:

452.16

Step-by-step explanation:

di is twice the radius and to get area you need radius so 24/2=12

now insert 12 into the formula 12^2*3.14 now use pemdas

12^2=144

144*3.14

452.16

Answer:

Area of circle = 452.16

Step-by-step explanation:

Conversion of diameter into radius,

→ r = 24/2

→ [ r = 12 ]

Formula we use,

→ Area = π × r²

Now the area of circle will be,

→ π × r²

→ 3.14 × (12)²

→ 3.14 × 144

→ 452.16

Hence, area of circle is 452.16.