2. Find the equation of a line
a) With a slope of 4, passing through the origiin​

W be the set of all vectors \(\left[\begin{matrix}b-2d\\ 5b+d\\ b+3d\\ d\end{matrix}\right]\) where b and d are real. If W is a vector space because it can be expressed as W = span {v1,. . . .,vn}. So the option A is correct.

Let W be the set of all vectors

\(\left[\begin{matrix}b-2d\\ 5b+d\\ b+3d\\ d\end{matrix}\right]\)

where b and d are real.

We can write the matrix as;

\(\left[\begin{matrix}b-2d\\ 5b+d\\ b+3d\\ d\end{matrix}\right]=b\left[\begin{matrix}1\\ 5\\ 1\\ 0\end{matrix}\right]+d\left[\begin{matrix}-2\\ 1\\3\\ 1\end{matrix}\right]\)

Remember that if aα + bβ ∈ W, ∀ α, β ∈ W and a, b are scalers, then W is a vector space. Let,

\(\alpha=\left[\begin{matrix}1\\ 5\\ 1\\ 0\end{matrix}\right],\beta=\left[\begin{matrix}-2\\ 1\\3\\ 1\end{matrix}\right]\)

These are independent vectors.

bα + dβ ∈ W. where α, β are independent vectors.

That is WE is a span of {α, β}.

Hence, W is a vector space.

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The complete question is:

Let W be the set of all vectors \(\left[\begin{matrix}b-2d\\ 5b+d\\ b+3d\\ d\end{matrix}\right]\) where b and d are real. Determine if W is a vector space and check the correct answer below.

A. W is a vector space because it can be expressed as W = span {v1,. . . .,vn}.

B. W is a vector space because it contains the zero element.

C. W is not a vector space because it does not have additive closure

D. W is not a vector space because it does not have a zero element.

Moving 5 one digit to the left, one number in which the value of digit 5 is 10 times as great as in 253,829 is in 538,290.

It means that the value of the digit is multiplied by 10.

Hence, moving the digit 5 one position to the left, and appending a zero at the end, generating the number 538,290, the value of digit 5 is 10 times as great as in 253,829.

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Answer: both of them made ok estimates but i think issacs was better. hope this helps! ^-^

Step-by-step explanation:

Answer:

1515

Step-by-step explanation:

If m = -5 or m = 3, the system of linear equations has no solution.

To determine the values of m for which the system of linear equations has no solution, we need to check the determinant of the coefficient matrix, which is:

| 3 m |

| m+2 5 |

The determinant is

=  (3 x 5) - (m x (m+2))

= 15 - m^2 - 2m

= -(m^2 + 2m - 15)

= -(m+5)(m-3)

So, for the system to have no solution, the determinant must be zero, so we have:

-(m+5)(m-3) = 0

This gives us two values of m: m = -5 and m = 3.

Thus, if m = -5 or m = 3, the system of linear equations has no solution.

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The Boolean expression A >= B is equivalent to  !(A < B) (option A)

To simplify a Boolean expression, use De Morgan's Law.

De Morgan's Law is used to simplify or find the equivalent of a negation of compound expressions.

The principle is:

NOT (A AND B) is equivalent to (NOT A) OR (NOT B)

NOT (A OR B) is equivalent to (NOT A) AND (NOT B)

When the expression involves >, <, = signs, then to simplify the expression, move the not and flip the sign.

! is the symbol of negation or NOT.

Hence,

! (>) becomes <=

! (<) becomes >=

Here are some examples:

!(A > B) is equivalent to (A <= B)

!(A <= B) is equivalent to (A > B)

!(A >= B) is equivalent to (A < B)

!(A == B) is equivalent to (A != B)

!(A != B) is equivalent to (A == B)

!(A < B) is equivalent to (A >= B)

From the above list we can conclude that A >= B is equivalent to !(A < B) (option A)

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Answer:

  84°

Step-by-step explanation:

Adjacent angles in a parallelogram are supplementary:

  ∠A = 180° -96°

  ∠A = 84°

Answer:

c

Step-by-step explanation:

i got it right

Answer:

the first one

8x+5

Step-by-step explanation:

10x-2-2x+7= 8x+5

The equation to calculate the yearly interest earned on your investment of $750 at a 16% interest rate is: Interest = $750 * 0.16.

To write the equation for calculating the yearly interest earned on an investment, we can use the formula:

Interest = Principal * Rate

Where:

- Principal is the initial investment amount.

- Rate is the interest rate expressed as a decimal.

In this case, you invested $750, and the annual interest rate is 16%. To use the decimal form of the interest rate, we divide it by 100:

Rate = 16% = 16/100 = 0.16

Substituting the values into the equation:

Interest = $750 * 0.16

To calculate the interest, we multiply the principal by the interest rate:

Interest = $750 * 0.16 = $120

Therefore, the equation to calculate the yearly interest earned on your investment of $750 at a 16% interest rate is:

Interest = $750 * 0.16

Now, let's complete a table to show the growth of your investment over multiple years. We'll assume the interest is compounded annually.

Year | Initial Investment | Interest Earned | Total Value

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

 1        $750                 $120              $870

 2        $870                 $139.20          $1009.20

 3        $1009.20            $161.47          $1170.67

 4        $1170.67            $187.31          $1357.98

 5        $1357.98            $217.28          $1575.26

In each year, we calculate the interest earned by multiplying the initial investment by the interest rate (16% or 0.16). The total value is obtained by adding the initial investment and the interest earned. This process is repeated for each subsequent year.

The table shows the growth of your investment over five years, demonstrating how the interest compounds and increases the total value each year.

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The first step is to find a common denominator. I'm going to use 80.

So...

7/8 x 10/10=70/80 (Mark)

And...

3/10 x 8/8=24/80 (Claudia)

70/80 - 24/80 = 56/80

Please mark brainliest/5 stars if this was helpful!

Answer:

not

Step-by-step explanation:

Answer:

non-equivalent

Step-by-step explanation:

the equivalend fraction of \(\frac{2}{3}\) is \(\frac{6}{9}\) not \(\frac{6}{10}\)

Step-by-step explanation:

bring the common ones together

al +bl +am +bm

l(a+b) +m(a+b)

(l+m) (a+b)

Given:

The distance to the fishing spot, S=5 miles.

The time taken to reach the fishing spot travelling against the current, t=5/12 h.

The time taken to reach the fishing spot travelling with the current , T=1/4 h.

Now, the speed of the boat when it is travelling in the direction of the current or the downstream speed is,

The speed of the boat when it is travelling in the against the direction of the current or the upstream speed is,

Let b be the speed of the boat in still water and w be the speed of the current.

Hence, the speed of the boat in still water can be calculated as,

The speed of the current can be calculated as,

Therefore, the speed of the boat in still water is 16 mph .

The speed of the current is 4 miles mph.

The factored form of the polynomial x^3 - 12x^2 - 2x + 24 by grouping is (x - 12)(x^2 - 2).

To determine the factors of the polynomial x^3 - 12x^2 - 2x + 24 by grouping, we can follow these steps:

Step 1: Group the terms in pairs. In this case, we can pair the first two terms and the last two terms:

(x^3 - 12x^2) + (-2x + 24)

Step 2: Factor out the greatest common factor from each pair. From the first pair, we can factor out x^2, and from the second pair, we can factor out -2:

x^2(x - 12) - 2(x - 12)

Step 3: Notice that we now have a common binomial factor of (x - 12) in both terms. Factor out this common binomial factor:

(x - 12)(x^2 - 2)

Therefore, the factored form of the polynomial x^3 - 12x^2 - 2x + 24 by grouping is (x - 12)(x^2 - 2).

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Answer:

Option A : y = 40x - 85 is the correct answer.

Step-by-step explanation:

Given that:

Cost of purchasing supplies = $85

Cost charged for cleaning a pool = $40

Let,

x be the number of pools cleaned.

y be the profit

Profit = Cost of pools cleaned - purchase price of supplies

y = 40x - 85

Hence,

Option A : y = 40x - 85 is the correct answer.

Answer:

cos 30 + sin60 + sin30 - cos60

we know that sin ( 90 -a ) = cos a { and vice versa }

therefore by using this property,

sin ( 90 - 30 ) + sin 60 + sin 30 - sin ( 90-60)

sin 60 + sin 60 + sin 30 - sin 30 =

2 sin 60

That's the answer I got. Tell me if it's correct

Answer:

  (c)  The x-intercept of f⁻¹(x) is the same as the y-intercept of f(x).

Step-by-step explanation:

You want to know the relationship between the graphs of function f(x) and its inverse f⁻¹(x).

The inverse of a function maps every y-value of the original function to its corresponding x-value. That is if you have ...

  f(a) = b

then the graph of f(x) contains the ordered pair (a, b).

The inverse function will have the ordered pair (b, a). That is,

  f⁻¹(b) = a

If an ordered pair (x-intercept) of the inverse function is ...

  (P, 0)

Then there will be an ordered pair (0, P) on the graph of the original function. That point is the y-intercept, and its y-coordinate is the same as the x-coordinate of the x-intercept of the inverse function.

The x-intercept of f⁻¹(x) is the same as the y-intercept of f(x).

__

Additional comment

The graphs of the two functions are mirror images of each other across the line y=x.

<95141404393>

Answer:

87

Step-by-step explanation:

Hope this helps! Pls give brainliest!

Answer:

well the answer should be -1.8

but I'm guessing A

Answer:

\(-\frac{9}{10}\) \(or\) \(-0.9\) \(or\) \(C\)

Step-by-step explanation:

\(\frac{2}{4}\div\frac{-5}{9}\) = \(?\)

\(\frac{2}{4}\) = \(0.5\)

\(\frac{-5}{9}\) = \(-0.555555555556\)

\(0.5\div-0.555555555556\) = \(-0.899999999999\) = \(-0.9\)

\(So\), \(the\) \(answer\) \(is\) \(C\).

\(This\) \(is\) \(because\) \(A\) \(is\) \(\frac{-9}{10}\) \(instead\) \(of\) \(-\frac{9}{10}\).

Hope this helps! <3

The graph of y = x^2 should be translated by 1 unit to the right and 3 units up.

In Mathematics, the translation of a geometric figure to the right simply means adding a digit to the value on the x-coordinate (x-axis) of the pre-image of a function while a geometric figure that is translated upward simply means adding a digit to the value on the y-coordinate (y-axis) of the pre-image.

In Mathematics, a vertical translation to the positive y-direction (upward) is modeled by this mathematical expression g(x) = f(x) + N.

Where:

Therefore, we have the following:

f(x) = x^2

g(x) = f(x - 1) + N

g(x) = (x - 1)^2 + 3

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Did you use the formula

gradient =

\( \frac{y2 - y1}{x2 - x1} \)

??

I'm not shear but i think that run to -6 then 3 is the correct sorry am learning it

Answer:

its b4 + 7b3 + 4b2 + b5 + 7b4+ 4b3= b5+8b4+11b3+4b2

Answer:

When multiplying, add the exponents, (example) remember if there is "7b" the exponent is one.

Multiply b^2 * b^3 = b^5  (add the exponent 2 + 3 = 5)

Multiply 7b * b^3 = 7b^4 (the exponent of 7b is one, add 1 + 3 for the exponent to become 4)

Multiply 4 * b^3 = 4b^3 (4 doesn't have a variable, the exponent will be 3)

b^2 * b*2 = b^4 (add exponents)

7b * b^2 = 7b^3 (add the exponents 1 + 2)

4 * b^2 = 4b^2

              b^2             +               7b             +        4

b^3           b^5              +           7b^4            +   4b^3

+                                                                                      

b^2           b^4             +           7b^3            + 4b^2

b^5 + 7b^4 + 4b^3 + b^4 + 7b^3 + 4b^2

\(b^5 + 7b^4 + 4b^3 + b^4 + 7b^3 + 4b^2\)

Answer:

what is a square root...?

Step-by-step explanation:

Answer:add $750.00 + $1000.00 + $375.00 = $2125.00

Step-by-step explanation:

add all together. Your monthly expense of fixed amount, living, annual monthly,

3. The volume of the Pringle Chips container is approximately 2034.72 cubic inches.

4. The cake takes up approximately 7317 cubic inches of space.

5. The volume of foam in the model of the volcano is approximately 7234.08 cubic centimeters.

1. The units for Volume are always cubed.

2. Volume is the amount of space an object takes up. True.

3. To calculate the volume of the Pringle Chips container, we need to find the volume of a cylinder. The formula for the volume of a cylinder is V = πr^2h, where π is a constant (approximately 3.14), r is the radius, and h is the height. Given that the diameter is 9 inches, the radius would be half of that, which is 4.5 inches. Substituting the values into the formula, we have:

V = 3.14 * (4.5)^2 * 32

V = 3.14 * 20.25 * 32

V ≈ 2034.72 cubic inches

4. To find the volume of the 3-tier cake, we need to find the volume of each tier separately and then add them together. Since all the tiers are cylinders, we can use the formula V = πr^2h.

Tier 1:

V1 = 3.14 * (12)^2 * 10 = 4521.6 cubic inches

Tier 2:

V2 = 3.14 * (8)^2 * 10 = 2010.4 cubic inches

Tier 3:

V3 = 3.14 * (5)^2 * 10 = 785 cubic inches

Total volume:

Total V = V1 + V2 + V3

Total V = 4521.6 + 2010.4 + 785

Total V ≈ 7317 cubic inches

5. To find the volume of the Styrofoam model of the volcano, we can use the formula for the volume of a cone, V = (1/3)πr^2h. Given that the diameter is 48 centimeters, the radius would be half of that, which is 24 centimeters. Substituting the values into the formula, we have:

V = (1/3) * 3.14 * (24)^2 * 12

V = (1/3) * 3.14 * 576 * 12

V ≈ 7234.08 cubic centimeters

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The number of bricks of each 15cm x 10cm x 4cm are required to construct a wall of 20m x 10m x 30cm is 10 bricks.

Bricks:

Volume = 15cm x 10cm x 4cm

= 600 cm³

Wall:

Volume = 20m x 10m x 30cm?

= 6,000 cm³

Number of bricks required to construct the wall = Volume of the wall ÷ volume of bricks

= 6,000 cm³ ÷ 600 cm³

= 10 bricks

Therefore, the number of bricks of each 15cm x 10cm x 4cm are required to construct a wall of 20m x 10m x 30cm is 10 bricks

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