Solve the system of equations
-2x - 6y + 8z = 14
3x + 2y - z = 4
2x - y + 2z = 10

The explicit formula of the given geometric sequence is a(n) = 8(1/2)ⁿ⁻¹.

Every term in a geometric series is obtained by multiplying the term before it by the same number aₙ= aₙ₋₁ + d is the general phrase for it. The common ratio is denoted by the number r. Any term in the sequence can be used to find it by dividing it by the word before it.

Any number series in which the ratio of succeeding terms is constant is referred to as a geometric sequence. where r is the proportion shared by all following terms. For instance, "2,6,18,54,162,486,1458,...

We have a sequence: 8, 4, 2, 1

The above sequence represents the geometric sequence with common ratio:

r = 4/8 = 1/2

First term a = 8

nth term:

a(n) = 8(1/2)ⁿ⁻¹

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The component form of vector is (-6,8)

Geometrical objects with magnitude and direction are called vectors. A line with an arrow pointing in its direction can be used to represent a vector, and the length of the line corresponds to the vector's magnitude. As a result, vectors are depicted as arrows and have starting and ending points. It took 200 years for the idea of vectors to develop. Physical quantities like displacement, velocity, acceleration, etc. are represented by vectors.Additionally, the development of the field of electromagnetic induction in the late 19th century marked the beginning of the usage of vectors. Here, we'll examine the definition of vectors as well as their characteristics, mathematical formulas, and uses.

The component form of vector is (-6,8)

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The X- intercept of the graph of the function at x =>-4 and x = 2.

The provided function is g(x)=-1(x-4)(x+2).

The x intercept of the function means, that point at which the graph of function will have the y coordinate as zero.

So, the x intercept of the function will be at the point where the function g(x) will be equal to zero.

g(x) = 0

-1(x-4)(x+2) = 0

(4-x)(x+2) = 0

Here,

We will get two values of x at which g(x) will be zero,

X = 4 and -2.

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Answer:

Step-by-step explanation:

Drawing two marbles at once is the same as drawing one and then drawing the second  without replacing the first.

Starting with 8 red balls and 14 blue balls, the probability of drawing a red ball  is 8/22 = 4/11.

Assuming red was drawn in the first draw, the probability of getting a red ball in the second  draw means that you are  drawing from a collection containing 7 red balls and 14 blue balls, so the probability is: 7/21 = 1/3.

So when calculating the odds of the second draw, we took into account the change in the number of hits and the number of chances, so these two events are  independent and the total probability is the product of the two individual probabilities.

P(2 reds) = (4/11) (1/3) = 4/33

The probability that both marbles are red is 4/33.

It should be noted that from the information given, the jar contains 8 red marbles and 14 blue marbles.

The total marbles will be:

= 8 + 14 = 22

The probability of selecting the first red marble will be:

= 8/22 = 4/11

The probability of selecting the second red marble will be:

= 7/21 = 1/3

Therefore, the probability that both marbles are red will be:

= 4/11 × 1/3

= 4/33

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The given equation written in standard format is 3x - 2y = -6

From the question, we are to write the given equation in standard format.

The given equation is

2y = 3x + 6

The standard form of a linear equation with two variables is

Ax + By = C

Where x and y are the variables

A is the coefficient of x

B is the coefficient of y

and C is the constant

Now, we will write the given equation in the format

2y = 3x + 6

Subtract 3x from both sides of the equation

2y - 3x = 3x - 3x + 6

-3x + 2y = 6

Multiply through by -1

3x - 2y = -6

The standard format of the equation is 3x - 2y = -6

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Answer: x+6 and x+7

Step-by-step explanation:

[tex]x^{2} +13x + 42 = 0\\D = b^{2} - 4ac = 169 - 4*42 = 169 - 168 = 1\\x_{1} = (-13 + 1)/2 = -6\\x_{2} = (-13 -1)/2 = -7\\\\So, x^{2} + 13x + 42 = (x+6)(x+7) \\\\\\[/tex]

Hence, the possible dimensions are x+6 and x+7.

Answer: (x + 6) and (x + 7)

Step-by-step explanation: Determine if the polynomial terms contain a common factor. In this case, there's no common factor. Next, find two numbers whose product is 42 and whose sum is 13. The only pair of numbers that satisfies these conditions is 6 and 7. Finally, write the polynomial in factored form as (x + 6)(x + 7). Therefore, the possible dimensions of the rectangle are (x + 6) by (x + 7).

Answer:

The correct answer is 1/6 for the question, "In 3 billion repetitions of an experiment, a random event occurred in 500 million cases..."

The correct answer is 1/10 for the question, "A shelf has 20 bags of potatoes. Two of the bags have potatoes starting to go bad."

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The percentage that equivalent to 15/50 is 30%

The given term is 15/50

The percentage is defines as a relative value indicating hundredth parts of any number. It is denoted using the percentage symbol "%". We can also say that percentage is a number or ratio expressed as a fraction of 100.

The given term is 15/50

Here the denominator is 50 and numerator is 15

To find the equivalent percentage, first we have to divide 15 by 50, then multiply the result by 100

15/50 = 0.3

Multiply the result by 100

0.3×100 = 30%

Hence, the percent that equivalent to 15/50 is 30%

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The given coordinate's line of reflection is the x-axis, Option D.

After intersecting the co-ordinates A(-3,5), B(2,8) and C(-4,-5) of line 1 and co-ordinates A'(-3,-5), B'(2,-8) and C'(-4,5) of line 2. It is deduced that both lines are similar.

The point of intersection of lines 1 and 2 is on the X-axis as the reflection of the coordinate,

A(-3,5) on the negative x-axis and positive y-axis is A'(-3,-5) on the negative y-axis and the negative x-axis.

B(2,8) on the positive x-axis and positive y-axis is B'(2,-8) on the negative y-axis and the positive x-axis.

C(-4,-5) on the negative x-axis and negative y-axis is C'(-4,5) on the positive y-axis and the negative x-axis.

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0.166 meters is the minimum distance between the contours on the map that allow Antonio to go uphill. For downhill, it is 0.1 meters.

Given,

The maximum gradient uphill is 0.3 meters.

The maximum gradient downhill is 0.5 meters.

distance according to the scale,

1000m ÷ 2m = 500 meters

a) distance for uphill,

= 25 ÷ (500 × 0.3)

= (25 × 10) ÷ (500 × 3)

= 250 ÷ 1500

= 1 ÷ 6

= 0.166 meters

b) distance for downhill,

= 25 ÷ (500 × 0.5)

= 250 ÷ (500 × 5)

= 250 ÷ 2500

= 1 ÷ 10

= 0.1 meters

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Part A) The tank's water level is changing at a rate of -[tex]\frac{2}{3}[/tex] gallons per minute.

Part B) The tank will finish draining in 7.5 minutes.

Part C) Jada arrived 4.5 minutes before the water tank was empty.

The rate of change (ROC) measures how quickly a variable alters over a predetermined amount of time.

Given Data

Up to 10 gallons can be stored in a water tank.

A drain continuously drains water from the tank when it is operational.

When Jade first noticed the tank, there were 7 liters of water inside.

3 minutes later, there were 5 gallons of water remaining.

Part A: How quickly is the tank's water level changing?

In three minutes, the gallons were reduced from seven to five. It indicates that 2 gallons were lost in three minutes.

Thus, gallons Change in gallons per minute would be -[tex]\frac{2}{3}[/tex]. As a result, the tank's water level is changing at a rate of -[tex]\frac{2}{3}[/tex] gallons per minute.

Note that a negative sign means there are less gallons of water available.

Part B) How long will it take for the tank to entirely drain?

The amount of time it will take the tank to entirely empty is denoted by the letter "m."

As,

2.3 gallons per second (5 gallons) in (m minutes).

So,

m = 5 ([tex]\frac{3}{2}[/tex])

= [tex]\frac{15}{2}[/tex]

= 7.5 min.

As a result, the tank will finish draining in 7.5 minutes.

Part C: How long did it take the water tank to fill up entirely before Jada arrived?

When there are 10 gallons of water, r is complete. This means that there are now 7 gallons more of water than there were when Jada arrived, an increase of 3 gallons.

Let 'm' be the time in minutes when the water tank was full and before Jada arrived.

So,

([tex]\frac{2}{3}[/tex]) (m) = 3

m = 3([tex]\frac{3}{2}[/tex]) = [tex]\frac{9}{2}[/tex]

= 4.5 min.

The water tank was thus full before to Jada's arrival by 4.5 minutes.

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When a figure is dilated by a factor of 3, the statement about the image of the figure that is true is C Both the area and the perimeter decrease.

Resizing an item uses a transition called dilation. Dilation is used to enlarge or contract the items. The result of this transformation is an image with the same shape as the original.

The x and y coordinates of the original figure are multiplied by the scale factor to discover spots on the dilated image when a dilation in the coordinate plane has the origin as the center of dilation. The algebraic representation of the dilation is (x, y) for scale factor k. (kx, ky).

In this situation, since the figure is dilated by a factor of 3, there will be a reduction. In conclusion, the correct option is C.

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A figure is dilated by a factor of 3. Which of the following statements about the image of the figure is true?

A The perimeter decreases.

B The area decreases.

C Both the area and the perimeter

decrease.

D Both the area and the perimeter

increase.

Answer:

see explanation

Step-by-step explanation:

assuming the dilatation is centred at the origin

then multiply each of the original coordinates by the scale factor 2

A (1, 1 ) → A' (2(1), 2(1) ) → A' (2, 2 )

B (5, 2 ) → B' (2(5), 2(2) ) → B' (10, 4 )

C (3, 5 ) → C' (2(3), 2(5) ) → C' (6, 10 )

Answer:

a. Using a graphing calculator: 4.486089611

b. To 2 decimal places: 4.49

Answer:

B, D, E

Step-by-step explanation:

We can find the area of B since the height and lengths is known, so the area is just 2*4 = 8 cm^2
D also has the height and length given, it is 4*3 = 12 cm^2
E gives 3 values, but only focus on the height and length, which are 2 and 5 respectively. 3 is also a side length, but there is no height to match that length. The area of E is 2*5 = 10 cm^2

The reasons A, C, and F don't work:
A seems like it would work, until you realize that 5 is a height, not a length, and so is 2. They are both heights, and multiplying heights together won't usually get you an accurate area unless the shape is a rectangle.
C has a length, but no height. the 3 cm is pretty much an arbitrary measurement.
F has two lengths, which would only give the area if the shape was a rectangle, which it is not.

Given -

2m² + m +3 = 0​

To Find -

2m² + m +3 = 0

Step-by-Step Explanation -

2m² + m +3 = 0​

We will first calculate the roots of the equation:

So, Both the roots are imaginary.

having d = -23

Final Answer:

Graph :

[tex]x^{2} +5x-3=-4x-3\\x^{2} +5x+4x-3+3=0\\x^{2} +9x=0\\\\x(x+9)=0\\x=0 or x+9=0\\x= -9[/tex]

I hope this helps.

Answer:

x = 0

or

x = (-9)

Step-by-step explanation:

[tex] {x}^{2} + 5x - 3 = - 4x - 3[/tex]

transfer like terms to the same side of the equation

[tex] {x}^{2} + 5x + 4x = - 3 + 3[/tex]

Add/subtract like terms

[tex] {x}^{2} + 9x = 0[/tex]

Now we can factor terms

[tex] {x}^{2} = x \times x \: and \: 9x = 9 \times x[/tex]

we can write them with their common divisor

x*(9+x) = 0 for this equation to be correct either x = 0 or (9+x) = 0

if x = 0 well then that's the first value of x

if (9+x) = 0 then x = -9 and this is the second value of x

If 1/4 of the box is green apples, then 3/4 of the box is red apples. Thus, 3 times the number of green apples is equal to the number of red apples, which would give 3 * 5 = 15 red apples.

Explanation

iven the points (-1,-4) and t(3,2). The points slope form of the equation can be found using the formula

We would then substitute the value into the formula;

Answer: Option 3

Using either method, we can conclude that x - 5 is a factor of the polynomial

This is further explained below.

Explain, based on the fact that, using either approach, whether or not we can consider x-5 to be a factor in the polynomial.

Generally, the equation for the problem is mathematically given as

f(x)=x^3-x^2-17 x-15

Therefore,  If (x-5) is factor of f(x) then at x=5 ,f(x)=0 then apply this

[tex]\begin{aligned}f(x) &=5^3-5^2-17 \times 5-15 \\&=125-25-85-15 \\&=0\end{aligned}[/tex]

In conclusion,Since f(x) is equal to 0 when x = 5, the factor of f is (x-5) (x).

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The probability of winning the minimum award of $100 in the lottery is [tex]\frac{113}{140448}[/tex]

The probability of picking first winning number (out of 57 white balls) is [tex]\frac{1}{57}[/tex]

Now, out of the remaining 56 white balls, the probability of picking second winning number is [tex]\frac{1}{56}[/tex]

So total probability of the correctly matching two numbers drawn from the white balls is  [tex]\frac{1}{57} + \frac{1}{56}[/tex]

Next, to match the winning number on the gold ball, probability of this event is [tex]\frac{1}{44}[/tex]

Thus overall probability of winning the minimum award is calculated by multiplying the individual probabilities of aforesaid two independent events as follows:

[tex](\frac{1}{44}) (\frac{1}{57}+\frac{1}{56})[/tex]

= [tex]\frac{113}{140448}[/tex]

Above value is the probability of winning the minimum award of $100.

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A linear equation has no solutions if both sides of the equation have distinct constant values but the same variable term.

An equation will have no solutions if the variables are the same on either side.

A mathematical statement known as an equation is made up of two expressions joined together by the equal sign. An equation is a formula that uses the equals sign to connect two expressions to show that they are equal.

For example, an equation can be illustrated as:

x + 5 = x - 5

Collect like terms

x - x = 5 - 5

0

This illustrates that the equation gas no solution.

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The x-intercept of the function is found to be x = (y + 80)/5 and the values of x calculated are 17,18,19 and so on.

Given, the x-axis and y-axis are intersected by two intercepts, P(2,0) and Q(0,3). => 3x + 2y – 6 = 0, Consequently, the line's equation is 3x + 2y - 6 = 0. Figure.

A line's x-intercept and y-intercept are the points at which the x- and y-axes, respectively, are crossed.

The given function is:

f(x) = 5x¹ - 80

Let,

y = f(x)

∴ y = 5x – 80

  y + 80 = 5x

  (y + 80)/5 = x

∴ x = (y + 80)/5

If y = 5,

x = (5 + 80)/5 = 17

If y = 10,

x = (10 + 80)/5 = 18

If y = 15,

x = (15 + 80)/5 = 19

Thus, by substituting y values in multiples of 5, we can get x values as 17, 18, 19 and so on.

Thus, the x-intercept of the function is found to be x = (y + 80)/5 and the x values calculated are 17,18,19 and so on.

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oluition

or this case we have the folllowing:

Part a

e select (0,0) and (3,24)

the slope would be:

then the equation for this case would be:

y= 8x +b

Using (0,0) we can find b:

0 ) 8*0 +b

b= 0

Then the equation is:

y= 8x

Part b

or this case we can conclude that for each n8 passengers is required a new car for the rooller coaster

The answer to the expression [2-|-2/3-2(-1/5)|] divided by 13 is 2/15 .

In the question ,

the expression is given as

=[2-|-2/3-2(-1/5)|] divided by 13

which means

= [2-|-2/3-2(-1/5)|] ÷ 13

Solving the terms inside [ ] first , we have

-2*(-1/5) = 2/5

Substituting the value of -2*(-1/5) in the expression , we get

= [2-|-2/3+2/5|] ÷ 13

Solving the norm(modulus) first

|-2/3+2/5| = |-10/15+6/15|  = |-4/15| = 4/15

Substituting the value of |-2/3+2/5| in the expression , we get

= [2-4/15] ÷ 13

Simplifying further we get ,

= [30/15-4/15] ÷ 13

= [26/15] ÷ 13

= [tex]\frac{\frac{26}{15} }{13}[/tex]

= [tex]\frac{26}{15} \times \frac{1}{13}[/tex]

= 2/15

Therefore , the answer to the expression [2-|-2/3-2(-1/5)|] divided by 13 is  2/15 .

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The least water depth and greatest depth will be 0.97d and 1.03d.

An expression is used to show the relationship between the variables.

In this case, the depth of water d in a swimming pool increases and decreases by 3% over a one-month period.

The least water depth will be:

= d - (3% × d)

= d - 0.03d

= 0.97d

The greatest water depth will be:

= d + (3% × d)

= d + 0.03d

= 1.03d

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Answer:

61

Step-by-step explanation:

Answer:

72 m

Step-by-step explanation:

We observe that 7y+6=18, and thus y=12/7.

So, the perimeter is:

[tex]2(18+7y+6) \\ \\ =14y+48 \\ \\ =14(12/7)+48 \\ \\ =72[/tex]