Hello please, I did not understand this exercise. In the plane referred to an orthonormal reference (o, i, j) place the points A, B, C and D defined by: A(6; 4); B(3; 7); C(12; -2); D(9; 7).
Show that C is the image of A by dilation with center B and ratio 3.

The apothem and the lateral surface area are 5/2√3 and 210 square units while the surface areas are 210 + 75√3 square units and 339.90 square units

Given that

Side length, s = 5

The apothem is calculated as

a = 1/2√3 * s

Where

Side length, s = 5

So, we have

a = 1/2√3 * 5

Evaluate

a = 5/2√3

The lateral area of the prism is calculated as

LA = 6sh

So, we have

LA = 6 * 5 * 7

LA = 210

This is calculated as

SA = LA + 3√3 s²

So, we have

SA = 210 + 3√3 * 5²

Evaluate

SA = 210 + 75√3

In decimal form, we have

SA = 339.90

Hence, the decimal form of the surface area is 339.90 square units

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After considering all the given data we conclude that the probability of randomly choosing a specified point within the circle that comes in the red-shaded square is 0.06.

Now we can clearly evaluate the possible probability of selecting a point randomly inside the circle under the section of red shaded square and derive a formula
[tex]P = (d - 4r)^2 / d^2[/tex]
Here,
d = diameter of the circle
r = square side length
For the given case,
d = 4 and r = 3.
Then,
P = (4 - 4×3)² / 4²
P = (4 - 12)²/ 4²
P = 0.06
Rounding to the nearest hundredth, P = 0.06.

Hence, the evaluated probability of selecting a point randomly inside a circle which falls in the red-shaded square is approximately 0.06.
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Answer:

Part a)

[tex]MG = \begin{pmatrix}1&k_1+9&4k_2+36\\ 2t_1+4&t_1k_1-17&-19t_1+3k_2-11\\ t_2+1&k_1-4t_2+5&t_2k_2-8\end{pmatrix}[/tex]

Part b)

[tex]t_1 = -2\\\\t_2 = -1\\\\k_1 = -9\\\\k_2 = -9\\[/tex]

Step-by-step explanation:

a) Computing MG

We have
[tex]M = \begin{pmatrix}1&4&5\\ \:t_1&3&-1\\ \:1&t_2&1\end{pmatrix}[/tex]

[tex]G = \begin{pmatrix}2&k_1&-19\\ \:1&-4&k_2\\ \:-1&5&11\end{pmatrix}[/tex]

[tex]MG = \begin{pmatrix}1&4&5\\ \:t_1&3&-1\\ \:1&t_2&1\end{pmatrix}\times \begin{pmatrix}2&k_1&-19\\ \:1&-4&k_2\\ \:-1&5&11\end{pmatrix}[/tex]

[tex]= \begin{pmatrix}1&k_1+9&4k_2+36\\ 2t_1+4&t_1k_1-17&-19t_1+3k_2-11\\ t_2+1&k_1-4t_2+5&t_2k_2-8\end{pmatrix}[/tex]

I am using a matrix calculator to compute the product rather than going through the rather cumbersome multiplication exercise by hand

b) One property of matrices is that if M is a matrix and M⁻¹ is its inverse
M x M⁻¹ is the identity matrix which has a 1 along the primary diagonal (top left - bottom right) and zeros everywhere

Here we are given G = M⁻¹ so M x G is an identity matrix

[tex]MG(1, 2) \\= k_1 + 9 = 0\\= > k_1 = -9\\\\MG(1, 3)\; is\\ 4k_2 + 36 = 0\\k_2 = -36/4 = -9\\\\MG(2, 1) = 2t_1 + 4 = 0\\\implies t_1 = -4/2 = -2\\\\MG(3, 1) = t_2 + 1\\t_2 + 1 = 0\\t_2 = -1\\[/tex]

So the values of the variables are

[tex]t_1 = -2\\\\t_2 = -1\\\\k_1 = -9\\\\k_2 = -9\\[/tex]

To check if these are correct, you can plug in these values into the product matrix MG. You will see that all elements except the diagonal elements are 0; diagonal elements are 1

The figure is not a rectangular pyramid but it is a triangular prism.

The base is a triangle not a rectangle.

The given figure is a triangular prism not a rectangular pyramid

A triangular prism is a prism composed of two triangular bases and three rectangular sides.

Rectangular pyramid is a solid with a rectangle-shaped base and triangular lateral faces

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Answer:

Step-by-step explanation:

the answer is 22

hoped this helped !

g is greater than -218,020.041.

We have,

To solve this inequality, we need to simplify the left side first:

9999899(-989789) = -9,899,782,581,211

Next, we can solve for g by dividing both sides by 45,426,663:

-9,899,782,581,211 / 45,426,663 < g

Simplifying the left side:

-218,020.041 < g

Therefore,

g is greater than -218,020.041.

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Answer: x = 15

Step-by-step explanation:

Answer:

the answer for 2/3(x-6) = 6. what's x? is 15

The simplified polynomials are:

10. -3(y+1) = -3y - 3

To simplify the expression, we distribute the -3 to both terms inside the parentheses.

11. 5x(3x²-4) = 15x³ - 20x

To simplify the expression, we distribute the 5x to both terms inside the parentheses.

12. 7(-2m²+5m+6) = -14m² + 35m + 42

To simplify the expression, we distribute the 7 to all the terms inside the parentheses.

13. (x+1)(3x-4) = 3x² - x - 4

To simplify the expression, we use the distributive property and multiply x with 3x and 1 with 3x, and then multiply x with -4 and 1 with -4.

14. (-2z²+5z)(-4x-8) = 8z³ + 16z² - 20xz - 40z

To simplify the expression, we use the distributive property and multiply -2z² with -4x and -8, and then multiply 5z with -4x and -8.

15. (9x+5)(-4x-8+10x²) = -40x³ + 45x² - 40x - 72x - 40

To simplify the expression, we use the distributive property and multiply 9x with -4x, -8, and 10x². Then we multiply 5 with -4x, -8, and 10x². Finally, we combine like terms.

Solving for the sum of all coefficients

-3 + (-3) + 15 + (-20) + (-14) + 35 + 42 + 3 + (-1) + (-4) + 8 + 16 + (-20) + (-40) - 40 + 5 + 45 + (-40) + (-40) + (-72) + (-40)

Simplifying, we get:

-148

Therefore, the code to unlock section 3 is -148.

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The value of secβ = (-21√10)/60.

Given that

Cosecβ = 7/3

Cotβ = -(2[tex]\sqrt{10}[/tex])/3

Since,

Cosecβ  =  1/sinβ = 7/3

⇒ sinβ = 3/7

And Cotβ = -(2[tex]\sqrt{10}[/tex])/3

⇒ cosβ/sinβ =  -(2[tex]\sqrt{10}[/tex])/3

⇒ 1/cosβ = -3/[(2[tex]\sqrt{10}[/tex])sinβ]

⇒ secβ = -21/(6√10)

Hence,

⇒ secβ = (-21√10)/60

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The surface area of the box increases by 67.26 cm² when the height is increased by 0.7 cm.

Recall the formula, Surface Area (SA) of the rectangular prism is given as:

SA = 2lw + 2lh + 2wh

where

l = length,

w = width,

h =  height

From the diagram, we know that:

l = 18cm

w = 6.3cm

h = 30cm

Substituting these values into the surface area formula, we get:

SA₁ = 2(18)(6.3) + 2(18)(30) + 2(6.3)(30) = 2376 cm²

When the height is increased by 0.7cm, the new height becomes:

h' = h + 0.7cm = 30.7cm

The new surface area can be calculated using the same formula:

SA₂ = 2(18)(6.3) + 2(18)(30.7) + 2(6.3)(30.7) = 2443.26 cm²

The increase in surface area is the difference between the new surface area and the original surface area:

SA₂ - SA₁ = 2443.26 cm² - 2376 cm²

= 67.26 cm²

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By using the synthetic division we have find that the quotient of x³-4x²+7 divided by x-3 is x² - x - 3, with a remainder of 4.

To use synthetic division, we first need to set up the equation in the correct format. We write the coefficients of the polynomial equation in descending order, and then we include any missing coefficients as 0. In this case, the equation x^3-4x²+7 can be written as:

1x^3 - 4x² + 0x + 7

Next, we write the linear equation in the format (x-a), where "a" is the value being divided out of the polynomial equation. In this case, a = 3, so we write the linear equation as:

(x-3)

We start by copying the first coefficient (1) from the top row to the bottom row.

We then multiply this coefficient by the value of "a" (3) and write the result (3) under the next coefficient (which is -4).

We add these two values together to get -1, which we write under the 0 coefficient.

We then repeat this process by multiplying -1 by 3 to get -3, which we write under the last coefficient (which is 7). We add these two values together to get 4.

Our synthetic division table should look like this:

3 | 1 -4 0 7 | 3 -1 -3

-----------------------------

   | 1 -1 -3 4

The bottom row of the table shows the coefficients of the quotient, which are 1, -1, and -3. These coefficients form the quotient of the division, which can be written as:

x² - x - 3

The last number in the bottom row of the table (4) is the remainder of the division. This means that our original equation x³-4x²+7, when divided by x-3, has a remainder of 4.

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The m<3 is approximately equal to 85.39 degrees.

The sum of the measures of the angles of a triangle is 180 degrees. So, we have:

m<1 + m<2 + m<3 = 180

So, (3x + 12) + (3x + 18) + (7x + 10) = 180

Simplifying and solving for x, we get:

13x + 40 = 180

13x = 140

x = 10.77

Now, we can find m<3 by substituting x in the expression for m<3:

m<3 = 7x + 10

m<3 = 7(10.77) + 10

m<3 = 85.39

Therefore, m<3 is approximately equal to 85.39 degrees.

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The  greater rate of change is 12.5, which is the rate of change of the first function.

The rate of change of a linear function is the slope of the line, which is represented by the coefficient of x in the equation y = mx + b. Therefore, the rate of change of the first function y = 12.5x + 2 is 12.5.

To find the rate of change of the second function, we can use any two points on the table and use the formula:

rate of change = (change in y) / (change in x)

Let's use the points (-3, -28.5) and (3, 37.5):

rate of change = (37.5 - (-28.5)) / (3 - (-3))

rate of change = 66 / 6

rate of change = 11

Therefore, the greater rate of change is 12.5, which is the rate of change of the first function.

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Answer:

Step-by-step explanation:

The problem specifies that you may use a calculator. The formula, as reference, is:

You can use a regular calculator or an online spreadsheet to solve. In sheets, arrange your data and use the =PERCENTILE( ) function. In the parentheses, write the range of your data and the requested percentile as a decimal. So if I type the data (the ages of the signers for this example) in cells A:4 through A:23, I'd write =percentile(A7:A23,0.25).

So the answers:

25th percentile is 34.

80th percentile is 48.4.

7 groups of 2/7 is equivalent to the whole, which is represented by the number 2.

When we have 7 groups of 2/7, we are essentially multiplying the fraction 2/7 by the whole number 7. To perform this operation, we can use the following formula:

a/b × c/d = ac/bd

where a, b, c, and d are any numbers, and a/b and c/d are two fractions.

In our case, a is 2, b is 7, c is 7, and d is 1. This is because we want to multiply 2/7 by 7 to get 7 groups of 2/7. Therefore, we can substitute these values into the formula:

2/7 × 7/1 = (2 × 7) / (7 × 1) = 14/7

The result is a fraction 14/7, which can be simplified to 2. This means that 7 groups of 2/7 is equal to 2. To simplify this further, we can say that if we divide a whole into 7 equal parts, each part is 2/7. If we have 7 of these parts, we have the whole.

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Answer: it's 300cm, hope this helps

The probability that that arrow will land on the part labelled C after the first spin would be = 1/5.

To calculate the probability of the chosen event, the formula for probability should be used which is given as follows:

Probability = possible outcome/ sample space

Where possible outcome = 2

sample space = A,B,B,B,C,C,D,D,D,E = 10

Therefore the probability that the arrow will land on the part labelled C after the first spin = 2/10 = 1/5.

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Solution:

1. t/5 + 3/4

+4      

___   + 5-3= 20

20

2. Combine fractions w/ common denominator.

3. multiply the #'s.

4. last but not least is: Solution:

4t+15

_____

20

Answer:

(4,0) & (9,5)

Step-by-step explanation:

Where the equations cross are the solutions!

Hope this Helps! :)
Happy Studies

The surface area of the prism is A = 227.953 cm²

Given data ,

Let the prism be represented as T

Now , the surface area of the prism is A

where the side lengths of the prism are

a = 6 cm

b = 7 cm

c = 4 cm

And , the height of the prism is h = 12 cm

Now , total surface area of prism is A = A ( top ) + A ( bot ) + A ( lat )

where A ( top ) = ( 1/4 ) √ ( a + b + c ) ( b + c - a ) ( c + a - b ) ( a + b - c )

And , A ( top ) = 11.9765 cm²

where A ( bot ) = A ( top ) = 11.9765 cm²

And , A ( lat ) = h ( a + b + c )

A ( lat ) = 12 ( 6 + 7 + 4 )

A ( lat ) = 204 cm²

So , the total surface area A = 227.953 cm²

Hence , the surface area of prism is A = 227.953 cm²

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Answer:

The zeroes of this function are 2 and -1.

A and C are the correct choices.

Answer:

The x-intercepts are -3,1

Step-by-step explanation:

The x-intercepts are where it crosses the x-axis.

It crosses the x-axis at -3 and 1

The x-intercepts are -3,1

Answer:

D. 1,0 & -3,0

Step-by-step explanation:

have a nice day.

The quadratic function f(x) = 2x² - 5x + 3, it is found :

a. The factored function is, f(x) = 2(x - 1)(x - 1.5).

b. The x-intercepts of the function are: x = 1, x = 1.5.

c. The end behavior of the graph is:

As x -> -∞, f(x) -> -∞.

As x -> ∞, f(x) -> ∞.

The quadratic function is :

f(x) = 2x² - 5x + 3.

Hence the coefficients are:

a = 2, b = -5, c = 3.

Using a calculator with these coefficients, the x-intercepts are:

x = 1.

x = 1.5.

Then the factored form of the function;

f(x) = 2(x - 1)(x - 1.5).

Let the leading coefficient of 2 and the x-intercepts.

This is a concave-up parabola, it goes to positive infinity to the left and to the right of the graph.

Hence the end behavior is;

As x -> -∞, f(x) -> -∞.

As x -> ∞, f(x) -> ∞.

To determine the graph, the axis of symmetry is:

x = -b/2a = 5/(2(2)) = 1.25.

The y-coordinate at this point, that is the turning point of the function, is:

f(1.25) = 2(1.25)² - 5(1.25) + 3 = -0.125.

The y-intercept of the function

f(0) = 2(0)² - 5(0) + 3 = 3.

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Answer:

51

Step-by-step explanation:

To find the speed, we must divide the distance traveled by the time it took to travel that distance:

[tex]v = \frac{D}{t} = \frac{153\ miles}{3\ hours} = 51\ mph[/tex]

Now that we've found the speed, we must see how fast the car travels in an hour

[tex]D = vt = 51 \ mph * 1 \ h = 51 \ miles[/tex]

A) rectangle

C) parallelogram

D) rhombus

E) rectangle

Answer:

Step-by-step explanation:

The area of the square is given as 1134 m². Let's assume that the side length of the square is "s". Then, we can write the area of the square as s² = 1134. Solving for "s", we get s = √1134. The perimeter of the square is given by P = 4s. Substituting the value of "s", we get P = 4√1134. To simplify this expression, we can factor out the perfect square factor of 36 from 1134, which gives us 1134 = 36 x 31. Therefore, P = 4√(36 x 31) = 4 x 6√31 = 24√31. Hence, the perimeter of the square is 24√31 m.

Answer:

Option 2 and Option 3 are equivalent to 5-3 × [10x (6-2)]

Step-by-step explanation:

Option 2:

5-3 × [10x (6-2)] = 5-3 × [10x4] = 5-3 × 40 = 5-120 = -115

Option 3:

5-3 × [10x (6-2)] = 5-3 × 40 = 5-120 = -115

The required graph has been attached below that represents the inverse equation f(x) = 4x-1.

To graph the inverse equation f(x) = 4x - 1, we can follow these steps:

Replace f(x) with y:

y = 4x - 1

Switch the x and y variables: x = 4y - 1

Solve for y:

y = (x + 1) / 4

The graph of the original function f(x) = 4x - 1 is a line with a slope of 4 and a y-intercept of -1.

The graph of the inverse function is the reflection of this line over the line y = x, which means that the x and y coordinates of each point are swapped.

To plot points for the inverse function, we can choose some values of x and find the corresponding values of y using the equation y = (x + 1) / 4. For example:

x y

-3 -1/4

-2 0

-1 1/4

0 1/4

1 1/2

2 3/4

3 1

Therefore, the graph of the inverse equation f(x) = 4x - 1 is a line that passes through the points (-3, -1/4), (-2, 0), (-1, 1/4), (0, 1/4), (1, 1/2), (2, 3/4), and (3, 1).

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The results of each iteration are given as follows:

The iterative formula in the context of this problem is defined as follows:

[tex]x_{n + 1} = \sqrt{8x_n - 5}[/tex]

The first value is given as follows:

[tex]x_1 = 3[/tex]

Hence each value is obtained applying the previous value to the iterative formula.

The second value is given as follows:

[tex]x_2 = \sqrt{8 \times 3 - 5}[/tex]

[tex]x_2 = \sqrt{19}[/tex]

[tex]x_2 = 4.359[/tex]

The third value is then given as follows:

[tex]x_3 = \sqrt{8 \times 4.359 - 5}[/tex]

[tex]x_3 = \sqrt{29.872}[/tex]

[tex]x_3 = 5.466[/tex]

The fourth value is then given as follows:

[tex]x_4 = \sqrt{8 \times 5.466 - 5}[/tex]

[tex]x_4 = \sqrt{38.728}[/tex]

[tex]x_4 = 6.233[/tex]

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Answer: C

Step-by-step explanation: Polygons are defined as two-dimensional.

Answer:

C

Step-by-step explanation:

A polygon lies entirely in one plane, so it cannot be three dimensional. The rest of the statements are true, so the answer is C