let be an matrix and an matrix so that the product is defined. suppose we know that the rref of both a and b have pivots in every column. explain why it follows that every column of rref(a b) also has a pivot in each column.

The given lines L1 ⇒ x = 5-12t, y = 3+9t, z = 1-3t and L2 ⇒ x = 3+8s, y = -6s, z = 7+2s  are parallel lines .

In the question ,

it is given that ,

the two lines are :

L1 ⇒ x = 5-12t, y = 3+9t, z = 1-3t

L2 ⇒ x = 3+8s, y = -6s, z = 7+2s

If the lines are intersecting then :

5 - 12t = 3 + 8s

8s + 12t = 2

4s + 6t = 1 ;   .....equation(1)

and 3 + 9t = -6s

3t + 2s + 1 = 0

multiplying both sides by 2 ,

we get ,

6t + 4s + 2 = 0  ....equation(2)

Solving equation(1) and equation(2) , we get

3 ≠ 0 .

So , the lines are not intersecting .

For lines to be parallel , the cross product of their directions must be 0 .

So , [tex]\left|\begin{array}{ccc}i&j&k\\-12&9&-3\\8&-6&2\end{array}\right|[/tex]

On simplifying further ,

we get ,

⇒ 0i - 0j + 0k

= 0

So , the cross product is 0 ,  lines will be parallel .

Therefore , the lines L1 and L2 are parallel .

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y = -1.893x + 31.901

Detailed explanation:

We are given the following values in a table:

x  y

2  30

5  19

7  20

12  9

16  2

It is now abundantly evident from the set of values that when x increases, the y-value decreases, indicating a negative connection.

Therefore, the line of best fit will have a negative slope.

Consequently, a scatter plot is used to display the data values.

As can be seen, the line of best fit equation

y = -1.893x + 31.901T

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Answer:

Hypotenuse = 7.3 cm

Step-by-step explanation:

We can find the hypotenuse using the Pythagorean Theorem, which is:

[tex]a^2+b^2=c^2[/tex], where a and b are the legs of the right triangle and c is the hypotenuse.

By plugging in 2 and 7 for a and b, we have:

[tex]2^2+7^2=c^2\\4+49=c^2\\53=c^2\\7.2801=7.3=c[/tex]

Answer:

256 feet.

Step-by-step explanation:

The equation for the surface area of a rectangular prism is lw x lh x hw. That means it would be 12x4, 12x5, and 4x5. In total that is 256.

The coordinates of the intersection with the x-axis are (-2,0), and (4, 0) and the maximum point is (1,9).

What are the coordinates of the axis?

A Cartesian coordinate system in a plane is a system of coordinates that uniquely identifies each point by a pair of numerical coordinates. These numerical coordinates are the signed distances from two fixed perpendicular oriented lines to the point, measured in the same unit of length.

We have,

The graph shows the sketch of y=f(x).

The graph passes through the points (-2,0), (0,8), (4, 0), and (1,9).

The coordinates of the intersection with the x-axis are

(-2,0), and (4, 0).

The maximum point is (1,9).

Hence, the coordinates of the intersection with the x-axis are

(-2,0), and (4, 0) and the maximum point is (1,9).

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Answer:

i think the answer will be 6%

Answer:

below

Step-by-step explanation:

46 / 780  * 100% = 5.9 %

the anwser is 14 degrees for angle 1

Answer:

answer :J LOOK THE DIAGRAM CAREFULLY AND UNDERSTAND

Answer:

A <c - <b = 10

Step-by-step explanation:

The area of the given figure is 48 [tex]ft^{2}[/tex].

Area is a measurement of the space inside a two-dimensional shape. It is determined by multiplying the length and width of the shape together. Area is most commonly measured in square units, such as square feet, square meters, or square kilometers. When measuring curved shapes, the area is determined by measuring the space inside the shape and applying a mathematical formula to calculate the total area. Area is an important concept in mathematics and is used to measure surface area, volume, length, and other measurements. It can also be used to compare the sizes of different shapes.

Firstly, to calculate the area assume the figure as two separate rectangles. Think that you a drawing an imaginary line in the gap between the two 4-ft segments to make a line of 12ft in length.

To solve, multiply to find individual areas then add together to get the total area.

Given: The first rectangle is 5ft by 4ft.

We know, the area of a rectangle = Base × Height

[tex]4ft[/tex] × [tex]3ft[/tex] = [tex]12ft^{2}[/tex] .....(1)

The next rectangle is 12 by 3ft, as you have to add the missing length in the middle to accurately calculate the length of the line.

[tex]12ft[/tex] × [tex]3ft[/tex] = [tex]36ft^{2}[/tex] .....(2)

Adding (1) and (2) we get,

[tex]12ft^{2} +36ft^{2}[/tex] = [tex]48ft^{2}[/tex]

Hence, the area is [tex]48ft^{2}[/tex].

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Answer:

y = 5x - 2

Step-by-step explanation:

y-8 = 5(x-2)

y-8 = 5x - 10

y = 5x - 10 + 8

y = 5x -2

A) The probability that the tyre wears out before 60000 miles is 0.4221

B) The probability that the tyre lasts more than 83000 miles is 0.49534

The distance the tyres can run until wear-out is a normally distributed, the formula for normal distribution is expressed as

z = (x - u)/s

Where

x = the distance the tyres can run until wear-out

u = mean distance

s = standard deviation

From the information given,

u = 70000 miles

s = 7000 miles

A) We want to find the Probability that the tyre wears out before 60000 miles. It is expressed as

P(x lesser than 60000)

For x = 60000,

z = (60000 - 70000)/7000 = - 1.42

Looking at the normal distribution table, the corresponding z score is 0.4221

B)We want to find the probability that the tyre lasts more than 83000 miles. It is expressed as

P(x greater than 83000) = 1 - P(x lesser than or equal to 83000)

For x = 83000,

z = (83000 - 70000)/5000 = 2.6

Looking at the normal distribution table, the corresponding z score is 0.49534

P(x greater than 83000)

= 1 - 0.49534  = 0.50466

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The total years taken to double the money according to Compounding will be  12.5 years.

What is compound interest?

Compound interest is that the interest on savings calculated on each the initial principal and therefore the accumulated interest from previous periods.

Main body:

Given :

rate = 6%

amount = $2500

Total amount = $5000

Compounded semi -anually,so formula becomes,

Total amount = amount (1+r/200)^2t

T = A[tex](1+r/200)^{2t[/tex]

5000 = 2500 (1+3/100)^2t

2 =(1+ 0.03)^2t

2 =(1.003)^2t

taking log on both sides

log 2 = 2t *log 1.03

0.3/0.012 = 2t

t = 12.5 years

Hence the time taken to double the money is 12.5 years.

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The ball may rise up to a height of 20 feet. and it will strike the ground in 1 second.

Height is the vertical measurement from an object's top to its base. On sometimes, it has the designation "altitude."

The vertex at point (h,k) of a parabola, y = ax2 + bx + c, is first determined using the equation h = -b / 2a, and then that point is entered into the equation to determine k.

Let's now solve for h in this issue. We know that a = -16, b = 32, and c = 4 in the equation y = -16t2 + 32t + 4.

h = -b/2a

h = -(32) / 2(-16) (-16)

1 second is equal to h = -32/-32.

This means the the ball will reach it's maximum height after 1 seconds. But the problem is asking is for what that height is. So for our final step, let's plug in t=1 to our equation:

y = -16t^2 + 32t + 4

y = -16*(1)^2 + 32*(1)+ 4

y = -16 + 36

y = 20 feet

which means that the final answer is that the maximum height of the ball is 20  feet. and it will take 1sec to hit the ground.

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(p-124) / 9 min many liters of water are in the tank after 109 seconds.

for 4 min =  65 + (6.5x4) = 91 lit

for  109 sec = 65 + (9x 109/60) = 81.35 lit

for m min = 65 + (9m) lit

how long time

for 151 lit = (151 - 124)/9 = 3 min

for 191.5 lit = (191.5-124) /9 = 67.5/9 = 7.5 min means 7 min 30 sec

for 270.25 lit = (270.25 - 124)/9 = 146.25/9 = 16.25 means 16 min 15 sec

for p lit = (p-124) / 9 min

What is liters ?

The water must be measured and expressed in the same unit for all of the containers. The litre is the name of that common unit for measuring liquid. Liquids are measured in litres, millilitres, centilitres, kiloliters, etc., including water, milk, gasoline, and oil.

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The given statement can be written in terms of inequality as b + 10.7 ≤ 3.2. The correct option is (d).

Linear inequality refers to the relation between a linear algebraic expression to some known value that contains inequality sign.

Unlike a linear equation it can have a range of values inside an interval.

The given statement can be written in terms of inequality as follows,

The statement is, "the sum of a number and 10.7 is at most −3.2".

Suppose the number be b.

The following expression can be written,

b + 10.7 ≤ 3.2

Hence, the required inequality expression for the given problem is b + 10.7 ≤ 3.2.

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The expression that is an equivalent expression of 12x+10+4y is D 2(6x + 5 + 2y).

In Mathematics, expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both.

Addition, subtraction, multiplication, and division are all possible mathematical operations. As an illustration, the expression x + y has the terms x and y with an addition operator between them.

In this case, the expression that is an equivalent expression of 12x+10+4y is 2(6x + 5 + 2y). The correct option is D.

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Which expression is an equivalent expression of 12x + 10 + 4y?

A.) 2(6x + 2y + 6)

B.) 3(4x + y + 10)

C.) 2(6x + 4y + 8)

D.) 2(6x + 5 + 2y)

The expression for the given variable is -276

What is variable?

A variable is anything that can take on any one of a number of values. A variable is a symbol. A variable is something that can change in an experiment.An amount that can fluctuate depending on the mathematical issue is referred to as a variable. The generic letters x, y, and z are often employed in mathematical expressions and equations. A variable, then, is a symbol denoting a number whose value is unknown. In this case, x + 5 Equals 10. "X" in this case is a variable.

[tex]\sqrt[3]{6 \times 288}-288[/tex]

[tex]\sqrt[3]{6 \times 288}=12[/tex]

[tex]=12-288[/tex]

[tex]Subtract the numbers: $12-288=-276$$$=-276$$[/tex]

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Answer: Based on the information you provided, it seems that the correct answer is "left 6 units, down 1 unit." This translation will map the graph of the function f(x) = x² onto the graph of the function g(x) = x² - 6x + 6.

To understand why this is the case, it helps to understand what the different parts of the function g(x) represent. The term x² represents the original function f(x) = x², the term -6x represents a horizontal translation of the graph of f(x) by 6 units to the left, and the constant term 6 represents a vertical translation of the graph of f(x) by 1 unit downward. Together, these transformations map the graph of f(x) onto the graph of g(x).

Note that if we were to apply the other translations you listed, they would not produce the correct graph. For example, if we were to apply a translation of "right 3 units, down 3 units," this would produce a graph that is shifted 3 units to the right and 3 units down, which is not the same as the graph of g(x). Similarly, if we were to apply a translation of "right 6 units, down 1 unit," this would produce a graph that is shifted 6 units to the right and 1 unit down, which is also not the same as the graph of g(x).

Hence, we get the curve, [tex]$$\mathrm{y}(\mathrm{x})=\left[-\frac{3}{4 \mathrm{x}^4}+7 \ln (\mathrm{x})-\mathrm{x}\right]+\frac{23}{4}$$[/tex].

What is  slope of function ?

Algebra. Finding the rate at which the value of y (the dependent variable) changes in relation to x is what this process entails. The slope itself identifies the line's slope and direction.

Given the slope of function is,

[tex]$$\begin{aligned}\frac{\mathrm{dy}}{\mathrm{dx}} & =\frac{3}{\mathrm{x}^5}+\frac{7}{\mathrm{x}}-1 \\\Rightarrow \mathrm{dy} & =\left(\frac{3}{\mathrm{x}^5}+\frac{7}{\mathrm{x}}-1\right) \mathrm{dx}\end{aligned}$$[/tex]

Taking integration both side, we get

[tex]$$\begin{aligned}\int \mathrm{dy} & =\int\left(\frac{3}{\mathrm{x}^5}+\frac{7}{\mathrm{x}}-1\right) \mathrm{dx} \\\Rightarrow \mathrm{y} & =3 \int \mathrm{x}^{-5} \mathrm{dx}+7 \int \frac{1}{\mathrm{x}} \mathrm{dx}-\int \mathrm{dx} \\& =\left[3 \cdot \frac{\mathrm{x}^{-5+1}}{-5+1}+7 \ln (\mathrm{x})-\mathrm{x}\right]+\mathrm{c} \\& =\left[-\frac{3}{4 \mathrm{x}^4}+7 \ln (\mathrm{x})-\mathrm{x}\right]+\mathrm{c}\end{aligned}$$[/tex]

( where, [tex]$\mathrm{c}=$[/tex] constant)

Now. given that the curve is passing through point (1,4). So, putting $x=1$ and, y=4 into the curve,

[tex]$$\begin{aligned}\mathrm{y} & =\left[-\frac{3}{4 \mathrm{x}^4}+7 \ln (\mathrm{x})-\mathrm{x}\right]+\mathrm{c} \\\Rightarrow 4 & =\left[-\frac{3}{4}+7 \ln 1-1\right]+\mathrm{c} \\\Rightarrow 4 & =-\frac{7}{4}+\mathrm{c} \\\Rightarrow \mathrm{c} & =\frac{23}{4}\end{aligned}$$[/tex]

Therefore,

[tex]$$\mathrm{y}(\mathrm{x})=\left[-\frac{3}{4 \mathrm{x}^4}+7 \ln (\mathrm{x})-\mathrm{x}\right]+\frac{23}{4}$$[/tex]

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Answer:

a=10

m=28

Step-by-step explanation:

2/3= 0.666666666666666

a/15=??????

try all numbers divided by 15 untill you found 0.666666666666666 which is =10/15

4/7=0.571428571428571

44/m=???????

do the same as the first one

it will be 44/28=0.571428571428571

Answer:

The ball reaches 14 ft in 0.75 seconds

Step-by-step explanation:

[tex]h(t) = -16t^2+24t+5\\h'(t) = -32t+24\\[/tex]

The highest point occurs when the derivative is equal to 0, because the tangent line is horizontal at that point

[tex]-32t + 24 = 0\\24 = 32t\\t = \frac{24}{32}=\frac{3}{4}=0.75s\\[/tex]

plug t back into h(t) to get height

[tex]h(0.75) = -16(0.75)^2+24(0.75)+5\\=(-16)(9/16)+23\\=-9 + 23\\= 14 ft[/tex]

Note: If you are not familiar with the concept of derivatives yet, you can find the time of the highest point using the equation [tex]t =-\frac{b}{2a}[/tex] where [tex]h(t) = at^2 + bt + c[/tex]

The no. of cars that must drive by until a white one drives by is 40.

In an experiment with two possible outcomes, the likelihood of exactly x successes on n repeated trials is known as the binomial probability (commonly called a binomial experiment). The binomial probability is

[tex]^nC_xp^Xq^{n-x}[/tex].

We know the expected value of a binomial distribution E(x) = np.

Given, Suppose that 40% of the cars in a certain town are white.

Therefore 50% of cars in the town are not which.

Let, The no. of cards in the town be 'n'.

So, p = 40/n and q = 60/n

Therefore from the formula E(x) = np we get,

E(x) = n×40/n

E(x) = 40.

So, The expected value of X is 40.

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Answer: We expect 2.5 cars to

The expected value of X is 2.5.

Step-by-step explanation:

In this case, it is a geometric distribution because we do not have a fixed number of trials.

We use the formula of a geometric distribution to find the mean (the expected value) such that mu_x = 1/p.

In this case:

mu_x=1/0.4 = 2.5

In this case, we do not round up or down even if we cannot have half a car because we want the expected value (mean).

Answer: (x-5)²=8

Step-by-step explanation:

x²-10x+17=0

x²-2(x)(5)+5²-5²+17=0

(x²-2(x)(5)+5²)-25+17=0

(x-5)²-8=0

(x-5)²-8+8=0+8

(x-5)²=8

Answer:

(x - 5)² = 8

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

Given

Expression  x² - 10x +17.

Convert this to vertex form by completing the square.

Recall identity (a ± b)² = a² ± 2ab + b² and apply as given below:

x² - 10x + 17  =

x² - 2*5*x + 5² - 5² + 17  =

(x - 5)² - 25 + 17 = (x - 5)² - 8

(x - 5)² = 8

The equation for the line of best fit from the given data, will be y = 2.12 x + 4.42.

The line of best fit would be the line that has an equal number of points above it, as the number of points beneath it.

Going by this definition, two points that would be on the line are (6, 17) and ( 7, 19 ).

The slope of this line would be:

= ( Y2 - Y1 ) / ( X 2 - X1)

= ( 19 - 17 ) / (7 - 6 )

= 2.12

The y intercept would be:

y = mx + c

19 = 2.12 (7 ) + c

c = 4.42

The equation of the  line of best fit is then :
y = 2.12 x + 4.42

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The answers to all the parts are given below.

We have a function h = -16t² + 1800, that gives the height of the person at time [t] seconds.

[A] -

For [x] = 1000ft, we can write -

1000 = -16t² + 1800

16t² = 800

t² = (800/16)

t² = 50

t = 7.07 seconds

[B] -

For [x] = 950ft, we can write -

950 = -16t² + 1800

16t² = 850

t² = 53.125

t² = √(53.125)

t = 7.29 seconds

[C] -

The domain of the function will be -

0 ≤ x ≤ 10

[D] -

The range of the function will be -

0 ≤ h ≤ 1800

Therefore, the answers to all the parts are given above.

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Answer:

- 7 < x < 6

Step-by-step explanation:

- 8 < x - 1 < 5 ( add 1 to each interval )

- 7 < x < 6

Answer:

7330.36

Step-by-step explanation:

A = P (1+i)^n

n  = 4×5 = 20

i = 0.03075

12.3% / 4 = 3.075  × 1/100

= 0.03075

A = 4000 ( 1+ 0.03075 ) ^20

= 7330.36

Yosef's average weekly fuel cost is $24.35.

Yosef drove 11,190 miles last year.  His truck's fuel efficiency averages 19 mpg, and the average cost of gas last year was $2.15 per gallon.

Yosef average weekly fuel cost can be computed as follows:

Yosef used 11190 / 19 = 588.95 gallons to drive 11190 miles.

Therefore, the average cost of gas last year was 2.15 dollars per gallon.

Therefore, Yosef's average weekly fuel cost would be as follows:

Yosef's average weekly fuel cost = 2.15 x 588.95 ÷ 52 = $1266.23684211 ÷ 52

Yosef's average weekly fuel cost = 24.350708502

Yosef's average weekly fuel cost = $24.35

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Answer:

The 3rd statement is a lie and other two are truth.

Step-by-step explanation:

when two same numbers with power are divided their respective powers are subtracted.

1.

[tex] {b}^{a } \div {b}^{c} = {b}^{a - c} [/tex]

Using this formula for

[tex] {b}^{9} \div {b}^{y} = {b}^{4} [/tex]

[tex] {b}^{9 - 5} = {b}^{4} [/tex]

Here RHS =LHS

so the equation is true

2.

[tex] {b}^{z} \div {b}^{x} = {b}^{5} [/tex]

[tex] {b}^{7 - 2} = {b}^{2} [/tex]

Here RHS=LHS,

so the equation is true

[tex] {b}^{8} \div {b}^{x} = {b}^{8} [/tex]

[tex] {b}^{8 - 2} = {b}^{8}[/tex]

Here RHS is not equal to LHS

so the equation is false

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