6c –2c =4 into a real life word problem

The result of the matrix 4|D| -3|B|

[tex]\left[\begin{array}{ccccc}31&6&36&-14&-57\\-19&-27&-18&18&27\\47&14&-1&-40&9\\10&12&-19&-15&-58\\-14&-23&10&-8&19\end{array}\right][/tex]

To solve the 5 x 5 matrix, we have to multiply and subtract the matrix this way;

4 x 7 - 3 x -1 = 31

4 x -6 - 3 x-10 = 6

4 x 3 - 3 x-8 = 36

4 x -8 - 3 x-6 = -14

4 x -9 - 3 x 7 = -57

Therefore 31, 6, 36, -14, and -57 makes the first role of the matrix 4|D| - 3|B|

4 x 2 - 3 x 9 = -19

4 x -9 - 3 x -3 = -27

4 x -6 - 3 x -2 = -18

4 x 6 - 3 x 2 = 18

4 x 9 - 3 x 3 = 27

Therefore -19, -27, -18, 18, and 27 make the second role of the matrix 4|D| - 3|B|

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The reduced row echelon form of the matrix is given as follows:

[tex]\left[\begin{array}{cccc}1&0&0&8\\0&1&0&-2\\0&0&1&-6\end{array}\right][/tex]

The row echelon form of a matrix contains the entire matrix except the last column in the format of an identity matrix, with the last column containing the solution to the system of equations represented by the matrix.

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

[tex]\left[\begin{array}{cccc}-1&5&-3&6\\0&3&6&-42\\0&-6&-1&18\end{array}\right][/tex]

First we want a value of 1 at line 1, column 1, hence we multiply the first line by -1, that is:

R1 -> -R1.

Hence:

[tex]\left[\begin{array}{cccc}1&-5&3&-6\\0&3&6&-42\\0&-6&-1&18\end{array}\right][/tex]

Then we want a value of 1 at line 2 column 2, thus:

R2 -> R2/3.

Hence:

[tex]\left[\begin{array}{cccc}1&-5&3&-6\\0&1&2&-14\\0&-6&-1&18\end{array}\right][/tex]

Then we want a value of 0 at line 3, column 2, hence:

L3 -> L3 + 6L2

[tex]\left[\begin{array}{cccc}1&-5&3&-6\\0&1&2&-14\\0&0&11&-66\end{array}\right][/tex]

Then the solution to the system of equations is given as follows:

Hence the row echelon form of the matrix is given as follows:

[tex]\left[\begin{array}{cccc}1&0&0&8\\0&1&0&-2\\0&0&1&-6\end{array}\right][/tex]

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Answer:

C

Step-by-step explanation:

x=base angle

2x+130=180

2x=50

x=25

base angle = 25

The final coordinates of the transformed figure are A"(-12,-8), B"(0,-16) and C"(-16,-16)

To translate the figure by <6,4>:

Add 6 to the x-coordinate of each point to get the new x-coordinate

Add 4 to the y-coordinate of each point to get the new y-coordinate

New coordinates:

A'(-3+6,-2+4) = (3,2)

C'(-4+6,-4+4) = (2,0)

B'(0+6,-4+4) = (6,0)

To dilate the figure K=4:

The coordinates x and y are multiplied by 4.

New coordinates:

A"(-34,-24) = (-12,-8)

C"(-44,-44) = (-16,-16)

B"(04,-44) = (0,-16)

Hence, the final coordinates of the transformed figure are A"(-12,-8), B"(0,-16) and C"(-16,-16)

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The operating charges, including parcel  expenditure and payroll costs( including sales commissions, amounted to$ 7,242. thus, the net profit before  levies for the month of February was$ 11,758.          

Donation  periphery income statement for Naomi's Quilt Shoppe for the month of February  Deals  profit  95 bedspreads  vended

x$ 490 per spread = $ 46,550  Cost of goods  vended  95 bedspreads  vended x$ 290 cost per spread = $ 27,550  

Gross profit  Deals  profit- cost of goods  

vended = $ 46,550-$ 27,550 = $ 19,000  

Operating charges  Lease  expenditure = $ 1,300  

Payroll charges( including deals commissions)$ 1,800 8 of$ 46,550 = $ 5,942

Total operating charges$ 1,300$ 5,942 = $ 7,242.

Net profit before  levies  Gross profit- operating charges = $ 19,000-$ 7,242 = $ 11,758  .

Naomi's Quilt Shoppe's  donation  periphery income statement shows that the shop earned$ 19,000 in gross profit from dealing  95 Amish bedspreads, after paying the cost of goods  vended.

The operating charges, including parcel  expenditure and payroll costs( including deals commissions), amounted to$ 7,242. thus, the net profit before  levies for the month of February was$ 11,758.

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Answer:

x = -1, -7

Step-by-step explanation:

(2x + 14) (x + 1) = 0

2x + 14 = 0, 2x = -14, x = -7.

x + 1 = 0, x = -1.

The vertex and the range of the quadratic function in this problem are given as follows:

The quadratic function in the context of this problem is defined as follows:

y = x² + 4x  + 5.

The coefficients are given as follows:

a = 1, b = 4, c = 5.

Hence the x-coordinate of the vertex is given as follows:

x = -b/2a

x = -4/2

x = -2.

Then the y-coordinate of the vertex is given as follows:

y = (-2)² + 4(-2) + 5

y = 1.

As a > 0, the vertex (-2, 1) is the minimum value of the function, hence the range is given as follows:

1 ≤ y < ∞.

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Spinning a spinner with four equal sized sections and assigning a novel to each section.

Spinning a spinner with four equal-sized sections and assigning a novel to each section is the correct option to stimulate randomly choosing a novel. The spinner can be designed with each section representing one of the four novels

The spinner is spun to randomly select one of the novels. Since each section is equal-sized, each novel has an equal probability of being selected.

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The complete question Members of a book club have 4 different novels to choose from each time they meet. Which of the following could be used to stimulate randomly choosing a novel?

(a) Placing 6 marbles in a bag (3 red and 3 blue) and drawing one ball from the bag

(b) spinning a spinner with four equal sized sections and assigning a novel to each section

(c)Tossing a fair coin, where each of the outcomes represents a novel

(d) Rolling a number cube labeled 1-6, where each book is represented by 2 numbers

this photo is not clear.Am sorry

The Chillan earthquake had an intensity about 5 times greater than the Taiwan earthquake.

The Richter scale is logarithmic, meaning that a difference of 1 on the scale corresponds to a tenfold difference in the amplitude of the seismic waves. Therefore, we can calculate the difference in intensity between the two earthquakes using the formula:

difference in intensity

= 1[tex]0^{((magnitude of earthquake 1) - (magnitude of earthquake 2))[/tex]

For the Chillan earthquake:

magnitude = 8.3

difference in magnitude = 8.3 - 7.6 = 0.7

For the Taiwan earthquake:

magnitude = 7.6

Plugging these values into the formula, we get:

difference in intensity = 10^(0.7) = 5.01187

This means that the Chillan earthquake had an intensity about 5 times greater than the Taiwan earthquake.

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The median is the measurement that is the same for Charles and Jermod.

In a dot plot, the median represents the middle value when the data points are arranged in ascending or descending order.

From the given dot plots, we can see that both Charles and Jermod have their median values at 35 minutes per day.

Therefore, the median is the measurement that is the same for Charles and Jermod.

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The linear function giving the volume of the balloon after t seconds is given as follows:

V(t) = 4 + 0.5t.

The time that it takes to fill the balloon is given as follows:

24 seconds.

The slope-intercept representation of a linear function is given by the equation shown as follows:

y = mx + b

The coefficients m and b have the meaning presented as follows:

The slope and the intercept for this problem are given as follows:

Hence the linear function giving the volume of the balloon after t seconds is given as follows:

V(t) = 4 + 0.5t.

The total capacity is of 16 ft³, hence the time needed to fill the balloon is obtained as follows:

16 = 4 + 0.5t

0.5t = 12

t = 12/0.5

t = 24 seconds.

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Answer:

$839.20

Step-by-step explanation:

To find the finance charge, we need to first calculate the total amount financed, which is the price of the snow thrower minus the down payment.

The down payment is 20% of $1,501, which is:

0.20 x $1,501 = $300.20

So the total amount financed is:

$1,501 - $300.20 = $1,200.80

The total amount of the 12 monthly payments is:

12 x $170 = $2,040

The finance charge is the difference between the total amount of the payments and the amount financed:

$2,040 - $1,200.80 = $839.20

Therefore, the finance charge is $839.20.

Find the sum of the first six terms of the geometric sequence for which a2 = 0.7 and a3 = 0.49.

Let the common ratio of the geometric sequence be r. Then we have:

a2 = ar = 0.7

a3 = ar^2 = 0.49

Dividing the second equation by the first, we get:

r = a3/a2 = 0.49/0.7 = 7/10

So the first six terms of the sequence are:

a1 = a2/r = 0.7/(7/10) = 1

a2 = 0.7

a3 = 0.49

a4 = ar^2 = 0.343

a5 = ar^3 = 0.2401

a6 = ar^4 = 0.16807

The sum of the first six terms is:

S6 = a1 + a2 + a3 + a4 + a5 + a6

S6 = 1 + 0.7 + 0.49 + 0.343 + 0.2401 + 0.16807

S6 = 2.94017

Therefore, the sum of the first six terms of the geometric sequence is approximately 2.94017.

Rewrite using radicals.

The expression (x^3/4)^2 can be rewritten as:

(x^3/4)^2 = x^3/4 * x^3/4

(x^3/4)^2 = (x^3)^2 / 4^2

(x^3/4)^2 = x^6 / 16

So (x^3/4)^2 is equivalent to (x^6/16) using radicals.

Rewrite using rational exponents.

The expression √(a^3b^2) can be rewritten using rational exponents as:

√(a^3b^2) = (a^3b^2)^(1/2)

√(a^3b^2) = a^(3/2)b^(1)

So √(a^3b^2) is equivalent to a^(3/2)b^(1) using rational exponents.

Hello !

Answer:

[tex] \boxed{h = 6}[/tex]

Step-by-step explanation:

He has grown :

We also know that in total, he has grown 11 vegetables.

We will have to solve an equation !

[tex]h + 2h + 5 = 11[/tex]

[tex] \iff3h + 5 = 11[/tex]

We want to isolate h.

[tex]3h + 5 - 5= 11 - 5 \\ \iff3h = 6 \\ \iff \frac{3h}{3} = \frac{6}{3} = 2[/tex]

The value of h is 2.

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The exponential function for the data in the table is given as follows:

[tex]y = 0.0625(2)^x[/tex]

An exponential function has the definition presented as follows:

[tex]y = ab^x[/tex]

In which the parameters are given as follows:

When the input x increases by one, the output y is doubled, hence the parameter b has the value given as follows:

b = 2.

The parameter a is the value of y when x = 0. When x = 1, the output is double when x = 0, as b = 2, hence:

2a = 0.125

a = 0.0625.

Thus the function is:

[tex]y = 0.0625(2)^x[/tex]

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Step-by-step explanation:

Starting with the equation E = mgh, we can solve for h in terms of E, m, and g as follows:

E = mgh

Divide both sides by mg:

E/mg = h

Therefore, h = E/mg.

So the solution for h in terms of E, m, and g is h = E/mg.

Answer: 62.8

Step-by-step explanation:

20x3.14=62.8

Answer:

#4. 62.83

#5. 314.16

Step-by-step explanation: READ THIS IS IF YOU ARE HAVING TROUBLE LIKE I DID!! Anytime you are trying to find the circumference of a circle, you multiply the radius (the 20 ft part) by 3.14, 3.14 is a number known as Pi. Number five should be 314.16, you take the radius and put it to the power of Pi. Use this formula for the area: 3.14 X half of the length of the circle (radius) then put it to the power of 2. I hope this helped.

Step-by-step explanation:

Continuous compounding formula   e^(rt)

  2 = e^(.13 * t)                   '2' is 'double    r = .13 which is 13% in decimal

LN   both sides

   ln(2) = .13 t

   ln (2) / .13 = t = 5.33 yrs

The net force on the knot is 42.7 N. Therefore, option D is the correct answer.

The force of 301 N to the North can be broken into components of 301 N in the x-direction and 0 N in the y-direction.

The force of 280 N at 10.0° South of East can be broken into components of 250.5 N in the x-direction and -247.8 N in the y-direction.

The force of 313 N to the Southwest can be broken into components of -208.1 N in the x-direction and -278.9 N in the y-direction.

The net force is then the sum of the components in both the x- and y-directions.

The net force in the x-direction is 301 N + 250.5 N - 208.1 N = 343.4 N and the net force in the y-direction is 0 N - 247.8 N - 278.9 N = -526.7 N.

The net force is then the hypotenuse of a right triangle with the x- and y-components as the legs.

The net force is thus equal to √(343.4 N² + (-526.7 N)²) = 42.7 N.

Therefore, option D is the correct answer.

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The second number line has a point that is equivalent to point P = 32.

Given information:

There are four choices of number lines given.

The first line has an open dot at 32, the second line has a closed dot at 32, the third line has a closed dot, and moving towards greater than 32, the third line has a closed dot at 31.

And we have to find at P = 32.

The first line has an open dot at 32, indicating that 32 is not included in the set of numbers on the line. The second line has a closed dot at 32, indicating that 32 is included in the set of numbers on the line. Therefore, the second line has a point that is equivalent to point P = 32.

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The complete question:

Which number line has a point that is equivalent to point P = 32?

The first line has an open dot at 32, the second line has a closed dot at 32, the third line has a closed dot, and moving towards greater than 32, the third line has a closed dot at 31.

Step-by-step explanation:

5.8 %  means 94.2 % remains after 24 hours    .5 is 1/2 :

.5 = (.942)^n     where n = the number of 24 hour periods (days)

LOG (.5) / LOG(.942) = n = 11.60 days    <==== this is the half life

The figure shows a graph of the function fx in the coordinate plane. f2 is greater than g2.

As the graph of function f(x) is a parabola, so that the equation of function f(x) is:

f(x) = [tex]ax^2+bx+c[/tex]

As it can be seen in thee figure, the graph of function f(x) cross points (0;8) ;(-2; 0) and (4;0)

=> f(0) = 8; f(-2) = 0; f(4) = 0

We have:

f(x=0) = a x 0 + b x 0 + c = 8  => c = 8

We have:

+) 4a -2b + 8 = 0 => 2 x (4a -2b + 8) = 8a - 4b + 16 = 0 (1)

+) 16a + 4b + 8 = 0 (2)

We take (2) minus (1)

=> (16a + 4b + 8) - (8a - 4b + 16) = 0

=> 8a - 8 = 0 => a = 1

Replace a = 1 into (1)

=> 8 x 1 - 4b + 16 = 0 => b = 6

f (2) = 2^2 + 6 x 2 + 8 = 24

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

Thus, f(2) is greater than g(2).

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The solution to the inequality |x − 2| ≥ 5 is x ≤ -3 or x ≥ 7.

We have,

To solve the inequality |x − 2| ≥ 5, we need to consider two cases:

Case 1:

x - 2 is non-negative (i.e., x - 2 ≥ 0)

In this case, the absolute value simplifies to x - 2, so we have:

x - 2 ≥ 5

Adding 2 to both sides, we get:

x ≥ 7

So any value of x that is greater than or equal to 7 satisfies the inequality.

Case 2:

x - 2 is negative (i.e., x - 2 < 0)

In this case, the absolute value simplifies to -(x - 2), so we have:

-(x - 2) ≥ 5

Multiplying both sides by -1, we get:

x - 2 ≤ -5

Adding 2 to both sides, we get:

x ≤ -3

So any value of x that is less than or equal to -3 satisfies the inequality.

Therefore,

The solution to the inequality |x − 2| ≥ 5 is x ≤ -3 or x ≥ 7.

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Answer:

2x

Step-by-step explanation:

hope this helps

Rule for the first transformation : (x, y) → (2.5x, 2.5y)

Rule for the second transformation : (x, y) → [(x - 4), (y + 1)]

Transformations of a figure:

If a figure is dilated by a scale factor 'k', rule defining the dilation will be,       If a point (x, y) is shifted 'a' units left and 'b' units upwards,

         Rule defining the translation will be,

         (x, y) → (x - a, y + b)

we have,

Radius of image circle = 2.5 units

Radius of pre image circle = 1 unit

Scale factor 'k' = 2.5/1

                        = 2.5

Since, image circle (blue) is shifted to the left and upwards, rule for the translation will be,

(x, y) → [(x - a), (y + b)]

Following the rule, coordinates of the image circle will be,

(0, 0) → [(0 - a), (0 + b)]

        → (-a, b)  

Coordinates of the image circle from the picture → (-4, 1)

Therefore, -a = -4 ⇒ a = 4

                  b = 1

         First transformation: (x, y) → (2.5x, 2.5y)

         Second transformation : (x, y) → [(x - 4), (y + 1)]

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complete question:

Write an algebraic description for the sequence of transformations that will map the preimage onto the image, to show that the two circles are similar.

Answer:

35

Step-by-step explanation:

The Absolute value function takes the same value for positive and negative values of its argument.

The graph of the absolute value function y = -|x + 6|, we first need to understand the properties of an absolute value function.

The absolute value of a number is its distance from 0 on the number line. Thus, the absolute value function |x| will always return a non-negative value, regardless of the sign of x. When the absolute value function is multiplied by -1, as in -|x|, the function reflects the graph over the x-axis and makes it negative.

Applying these principles to the given function y = -|x + 6|, we can start by identifying the vertex, which is the point where the absolute value term inside the function equals 0. In this case, the vertex is at x = -6.

Next, we can plot some points to get a sense of the shape of the graph. We can choose values of x that are greater than or less than -6, and use the fact that the function is negative to find the corresponding y-values. For example:

- When x = -7, y = -|(-7) + 6| = -1

- When x = -5, y = -|(-5) + 6| = -1

We can see that the graph has a "V" shape, with the vertex at (-6,0). The line of symmetry is the vertical line passing through the vertex, which is the equation x = -6. The graph approaches the x-axis on either side of the vertex, but never touches it. The negative sign in front of the absolute value term causes the graph to be reflected over the x-axis.

since the absolute value function takes the same value for positive and negative values of its argument.

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Answer:

Step-by-step explanation:

4 | x - 6 | ≤ 16

| x - 6 | ≤ 4

-4 ≤ x - 6 ≤ 4

-4 + 6 ≤ x ≤ 4 + 6

2 ≤ x ≤ 10

Answer:

Subtract the same degrees only.

Step-by-step explanation:

When subtracting polynomials, you can only subtract variables from those with the same degree (like term).

For example:

[tex]x^{2} -x^ = 0[/tex]

You can't subtract as the first x has a degree (exponent) of 2 and the second x has a degree of 1.

However, for example:

[tex]3x^{4} -1x^{4}=0[/tex]

You can subtract this to be [tex]2x^{4}[/tex] as both variables have a degree of 4.