The GCF of two numbers is equal to the lesser of the numbers? Always,sometimes, or never true

The value of "a" that makes the set of vectors independent is 1.

In 3-dimensional space, a set of vectors is said to be independent if any one of the vectors cannot be represented as a linear combination of the other vectors.

We may utilize the idea of determinants to determine the value of "a" such that the set of vectors "(1, 0, -2), (3, 2, a), (-3, -5, 1)" is independent.

The linear dependence or independence of the given vectors can be assessed using the determinant of a 3x3 matrix, whose columns are the given vectors. If the vectors are linearly dependent, the determinant will be 0; if they are independent, it will be non-zero.

The determinant can be calculated as follows:

| 1 0 -2 |

| 3 2 a |

| -3 -5 1 | = 0

Expanding the determinant along the first row, we get:

1 * ((2 * 1) - (a * -5)) - 0 * ((-3 * 1) - (-2 * -5)) + (-2 * (2 * -3 - a * -3)) = 0

2 - 5a - 6 + 10 + 6a = 0

Expanding the equation and solving for a, we get:

8a = 8

a = 1

Thus, the set of vectors {(1, 0, -2), (3, 2, 1), (-3, -5, 1)} is independent.

So, the value of "a" that makes the set of vectors independent is 1.

To learn more about determinants, visit the link below:

brainly.com/question/13369636

#SPJ4

Answer:

a)  $497.70

b)  392.4 square feet

c)  $1,200

Step-by-step explanation:

A regular octagon has 8 sides of equal length.

Given each side of the octagon measures 9 feet in length, and one side does not have a railing, the total length of the railing is 7 times the length of one side:

\(\textsf{Total length of railing}=\sf 7 \times 9\; ft=63\;ft\)

If the railing sells for $7.90 per foot, the total cost of the railing can be calculated by multiplying the total length by the cost per foot:

\(\textsf{Total cost of railing}=\sf 63\;ft \times \dfrac{\$7.90}{ft}=\$497.70\)

Therefore, the cost of the railing is $497.70.

\(\hrulefill\)

To find the area of the regular octagonal gazebo, given the side length and apothem, we can use the area of a regular polygon formula:

\(\boxed{\begin{minipage}{6cm}\underline{Area of a regular polygon}\\\\$A=\dfrac{n\;s\;a}{2}$\\\\where:\\\phantom{ww}$\bullet$ $n$ is the number of sides.\\ \phantom{ww}$\bullet$ $s$ is the length of one side.\\ \phantom{ww}$\bullet$ $a$ is the apothem.\\\end{minipage}}\)

Substitute n = 8, s = 9, and a = 10.9 into the formula and solve for A:

\(\begin{aligned}\textsf{Area of the gazebo}&=\sf \dfrac{8 \times 9\:ft \times10.9\:ft}{2}\\\\&=\sf \dfrac{784.8\;ft^2}{2}\\\\&=\sf 392.4\; \sf ft^2\end{aligned}\)

Therefore, the area of the gazebo is 392.4 square feet.

\(\hrulefill\)

To calculate the cost of the gazebo's flooring if it costs $3 square foot, multiply the area of the gazebo found in part (b) by the cost per square foot:

\(\begin{aligned}\textsf{Total cost of flooring}&=\sf 392.4\; ft^2 \times \dfrac{\$3}{ft^2}\\&=\sf \$1177.2\\&=\sf \$1200\; (nearest\;hundred\;dollars)\end{aligned}\)

Therefore, the cost of the gazebo's flooring to the nearest hundred dollars is $1,200.

a. To find the perimeter of the gazebo, we can use the formula P = 8s, where s is the length of one side. Substituting s = 9, we get:

P = 8s = 8(9) = 72 feet

Since one side is open, we only need to find the cost of railing for 7 sides. Multiplying the perimeter by 7, we get:

Cost = 7P($7.90/foot) = 7(72 feet)($7.90/foot) = $4,939.20

Therefore, the cost of the railing is $4,939.20.

b. To find the area of the gazebo, we can use the formula A = (1/2)ap, where a is the apothem and p is the perimeter. Substituting a = 10.9 and p = 72, we get:

A = (1/2)(10.9)(72) = 394.56 square feet

Therefore, the area of the gazebo is 394.56 square feet.

c. To find the cost of the flooring, we need to multiply the area by the cost per square foot. Substituting A = 394.56 and the cost per square foot as $3, we get:

Cost = A($3/square foot) = 394.56($3/square foot) = $1,183.68

Rounding to the nearest hundred dollars, the cost of the flooring is $1,184. Therefore, the cost of the gazebo's flooring is $1,184.

#SPJ1

To solve this operation we first factorize with the number that has the lowest value in the exponential. In this case:

Now, we can multiply the number 6.25 by 10 and solve the operation!

Therefore, the answer is 5.906*10^9

Answer:

howwwwww

Step-by-step explanation:

it's alot going on

The difference in temperature between Rome and Munich is given as follows:

6ºC.

The difference in temperature between Rome and Munich is given by the subtraction of Rome's temperature by Munich's temperature.

The bar graph in the context of this problem gives the temperature for each town.

From the bar graph given by the image presented at the end of the answer, the temperatures for Rome and Munich are given as follows:

Hence the difference in temperature between Rome and Munich is given as follows:

11 - 5 = 6ºC.

The graph is given by the image presented at the end of the answer.

More can be learned about difference of two amounts at https://brainly.com/question/17301989

#SPJ1

The height of the hexagonal-based pyramid is approximately 101.61 inches.

To find the height of the hexagonal-based pyramid, we can use the formula for the volume of a pyramid:

Volume = (1/3) × Base Area × Height

In this case, the base of the pyramid is a regular hexagon, and we have the side length (s) and apothem (a) given.

The base area of a regular hexagon can be calculated using the formula:

Base Area = (3√3/2) × s²

Let's calculate the base area first:

Base Area = (3√3/2) × (6 in)²

Base Area = (3√3/2) × 36 in²

Base Area ≈ 93.53 in²

Now, we can rearrange the volume formula to solve for the height:

Height = Volume / ((1/3) × Base Area)

Height = 3168 in³ / ((1/3) × 93.53 in²)

Height = 3168 in³ / (31.177 in²)

Height ≈ 101.61 in

Therefore, the height of the hexagonal-based pyramid is approximately 101.61 inches.

for such more question on height

https://brainly.com/question/27987869

#SPJ8

The probability that the mean battery life would be greater than 526.4 minutes if in a sample of 81 batteries having a variance of, 2916 and a mean life of 518 minutes is 0.0808.

The ratio of good outcomes to all possible outcomes of an event is known as probability. A lot of successful results for an experimental with 'n' results can be represented by the symbol x.

Given:

The variance = 2916,

The mean life of a battery, m = 518 min,

The total number of samples, n = 81

Calculate the probability of a mean battery life of lower than 526.4 minutes by the following formula,

z = x - m / (σ / √ n)

Here, x is the expected value, σ is the deviation, and z is the probability.

Substitute the values,

z = 526.4 - 518 / (54 / √81)         [σ = √ variance = √2916  = 54]

z = 1.4

Consult the cumulative standard normal table

P (z < 526.4) = 0.9192,

But we know that

P (z > 526.4) = 1 - P (z < 526.4)

P (z > 526.4) = 1 - 0.9192 = 0.0808

Therefore, The probability that the mean battery life would be greater than 526.4 minutes if in a sample of 81 batteries having a variance of, 2916 and a mean life of 518 minutes is 0.0808.

To know more about probability:

https://brainly.com/question/743546

#SPJ1

Answer:

7850 feet.sq

Step-by-step explanation:

the area of a cercle is:

A = r²*π     where r is the radius

A= 50²*3.14 = 7850 ft²

The solution is, the value of x = 4.

An equation is a  mathematical statement that is made up of two expressions connected by an equal sign.  In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal. For instance, 3x + 5 = 14 is an equation, in which 3x + 5 and 14 are two expressions separated by an 'equal' sign.

here, we have,

given that,

(x + 3) + (4x +7) ➗ 2 = 15

⇒5x+10=15*2

⇒5x+10= 30

⇒5x=20

⇒x=4

Hence, The solution is, the value of x = 4.

To learn more on equation click:

brainly.com/question/24169758

#SPJ1

The correct option is: As x → –∞, f(x) → 0, and as x → ∞, f(x) → 0. As x → 0, f(x) → –∞, and as x → ∞, f(x) → 0.

The end behavior of the function f(x) = -2∛x describes how the function behaves as x approaches positive or negative infinity.

Since the cube root of x approaches infinity as x approaches infinity, and negative infinity as x approaches zero from the right, the negative cube root of x will approach negative infinity as x approaches zero from the right.

Therefore, as x approaches negative or positive infinity, f(x) approaches zero. As x approaches zero from the right, f(x) approaches negative infinity.

So, the correct option is: As x → –∞, f(x) → 0, and as x → ∞, f(x) → 0. As x → 0, f(x) → –∞, and as x → ∞, f(x) → 0.

To know more about  function f of x  , here

https://brainly.com/question/28356844

#SPJ1

Answer:

36:45

Step-by-step explanation:

Answer:

          ______

x  =  − 0.  142857

Step-by-step explanation:

Answer:

I'm sorry, but I am an Expert Answer Provider and do not have the ability to draw images. You can use a ruler and a pencil to draw segment AB with a length of at least 2 inches on a piece of paper. To construct a segment that divides AB in the ratio 2 to 3, you can follow these steps:

Draw segment AB with a length of at least 2 inches.

Label the two endpoints of the segment as A and B.

Measure the length of AB and divide it by 5 to find the length of the dividing segment.

Mark a point C on AB that is 2/5 of the way from A to B. This is the point that divides AB in the ratio 2 to 3.

Draw a line through C that is perpendicular to AB and label it as CD.

Now, segment AC has a length of 2/5 of the length of AB and segment BC has a length of 3/5 of the length of AB.

The solution is given below.

The ratio is defined as the comparison of two quantities of the same units that indicates how much of one quantity is present in the other quantity.

here, we have,

You can use a ruler and a pencil to draw segment AB with a length of at least 2 inches on a piece of paper. To construct a segment that divides AB in the ratio 2 to 3, you can follow these steps:

Now, segment AC has a length of 2/5 of the length of AB and segment BC has a length of 3/5 of the length of AB.

To learn more on ratio click:

brainly.com/question/13419413

#SPJ2

Answer: 51/50

Step-by-step explanation:   102/100 = 51/50

because you divide both by 2 which is the answer

Answer:

Area = 180 cm^2

Step-by-step explanation:

See attached image.  The width of the rectangle, a , is the hypotenuse of a right triangle with legs 15 and 20.

Use the Pythagorean Theorem: leg^2 +leg^2 = hypotenuse^2

\(a^2=15^2+20^2\\\\a^2=225+400\\\\a^2=625\\\\a=\sqrt{625}=15\)

The width, w, is one leg of a right triangle that has hypotenuse 20 and one leg 16.

\(w^2+16^2=20^2\\\\w^2+256=400\\\\w^2=144\\\\w=\sqrt{144}=12\)

The rectangle has length 15 cm and width 12 cm so its area is 12 x 15 = 180 cm^2

Answer:

AREA RECTANGLE =300 cm²

Step-by-step explanation:

If 2 of the 3 vertices of a triangle match up with 2 of the 4 vertices of a rectangle,then the area of the triangle will be exactly half of the area of the rectangle

(Or the area of the rectangle  will be exactly double  of the area of the triangle)

  Area right triangle  = ½ × base × height.

A = 1/2(15X20)

A=1/2( 300)

Area triangle =150  

Area of rectangle is DOUBLE as the  area of triangle

AREA RECTANGLE = 300

Answer: Option (2)

Step-by-step explanation:

We need the angle to be included between the two mentioned sides.

Also, the sides need to be corresponding for the ratio, and both sides of the triangle need to be in either the numerators or the denominators.

Answer:

x = 65

Step-by-step explanation:

the sum of the interior angles of a quadrilateral = 360°

sum the angles and equate to 360

x + 95 + 118 + 82 = 360

x + 295 = 360 ( subtract 295 from both sides )

x = 65

Based on the information provided, the sum of all the labeled angles is 235° (option b).

To calculate the sum of all the labeled angles we must add the different values of each labeled angle as shown below:

80° + 92° + 40° + 23° = 235°

According to the above, it can be inferred that the correct option is B because the result of the sum of the values coincides with this sum.

Learn more about degrees in: https://brainly.com/question/1217620

#SPJ1

The function is continuous in the domain x ≥ 3/4

Here we have a root function:

f(x) = ⁴√(4x - 3)

This is an even degree root function, so we have problems when the argument is negative.

Then the allowed values (where the function is defined, and thus, continuous) are:

4x - 3 ≥ 0

4x ≥ 3

x ≥ 3/4

There the function is continuous.

Learn more about continuous functions at:

https://brainly.com/question/18102431

#SPJ1

Please find attached photograph for your answer. Hope it helps. Please do comment.

The value of function which cross the y-axis at point (0, 7) will be;

⇒ y = x + 7

To find the value of any one of the variables from one equation in terms of the other variable is called the substitution method.

Given that;

The point which cross the function = (0, 7)

Now,

Since, The point which cross the function = (0, 7)

Hence, The point must be satisfy the function.

By option (1);

⇒ y = x + 7

Put (x, y) = (0, 7)

⇒ 7 = 0 + 7

⇒ 7 = 7

Thus, The correct function which passes through the point (0, 7) is,

⇒ y = x + 7

Option (i) is true.

Learn more about the substitution method visit:

https://brainly.com/question/26094713

#SPJ1

Answer:

slope=1/4

y-intercept=3

y=.25x+3

Step-by-step explanation:

slope=rise over run so

slope=1/4

y-intercept is the value of y where the line crosses the y axis..

y-intercept=3

In y=mx+b form m is slope and b is y-intercept so...

y=.25x+3

Answer: The third one

Step-by-step explanation:

That system has the same equation, but a different solution, meaning the lines can never intersect.

We can also convert it into slope-intercept form.

y = -2x + 9

y = -2x + 5

Different slope and same y-intercept = NO SOLUTION

Answer:

2x + y = 9

2x + y = 5

Step-by-step explanation:

No solutions for 2 lines will only happen when the lines are parallel and never touch.  So there are no solutions.

Lines are parallel when slopes are the same.

The equations cannot be the same just the slopes are the same.  

Let's rearrange this set of equations into y=mx+b so we can see what the slope m is:

2x + y = 9           and               2x + y = 5

y= -2x +9                                 y= - 2x +5

You can see the lines are different but have the slopes so they are parallel and no solutions.

9514 1404 393

Answer:

  an = -7(1/3)^(n-1)

Step-by-step explanation:

The explicit formula for a geometric sequence with first term a1 and common ratio r is ...

  an = a1·r^(n-1)

The multiplier in the recursion relation is the common ratio: 1/3. The first term is given as a1 = -7. Putting these in the general formula, we have ...

  an = -7·(1/3)^(n-1)

Answer:

0 hundreds

0 tens

7 ones

.

4 tenths

0 hundredths

8 thousandths

Standard form=7.408

Step-by-step explanation:

Lets first solve (7x1)+(4x1/10)+(8x1/1000)

7+0.4+0.008

Simplify:

7.408

Answer:

Rewrite with rational (fractional) exponents using the formula \( \sqrt[n]{ {a}^{x} } = a {}^{ \frac{x}{n} } .\)

\(6xy {}^{3} \)