.Let = ( 1 2 3 4 2 4 5 7 5 10 13 18 ) and rref () =( 1 2 0 1 0 0 1 1 0 0 0 0 ) a) Determine whether the vectors (1, 2, 5) T ,(2, 4, 10) T , (3, 5, 13) T , (4, 7, 18) T linearly independent? b) Do they span ? Explain

Answer:

a. F(x)=10x-1  , the value of F(-2) is

F(-2)=10(-2)-1

f(-2)= -20-1

f(-2)= -21

b. g(x)= -5x+13 , the value of g(1)

g(1)= -5(1)+13

g(1)= -5+13

g(1)= 8 or +8

c. h(x)=\(x^{2}\)-x-12 , the value of h(3) is

h(3)=\(3^{2}\)-3-12

h(3)=9-3-12

h(3)= -6

Step-by-step explanation:

Answer:

No

Step-by-step explanation:

x=(b-5)/c≠(5-b)/c

supposedly

b=6

c=1

x=6-5/1=1

x=5-6/1= -1

1≠ -1

Answer:

No

Step-by-step explanation:

x = b - 5 / L equal to - (5 - b) / L

Answer:

d. The APR helps compare loans with the same payback period, but with different monthly rates and different fees.

Step-by-step explanation:

A loan can be defined as an amount of money that is being borrowed from a lender and it is expected to be paid back at an agreed date with interest.

Generally, the financial institution such as a bank lending out the sum of money usually requires that borrower provides a collateral which would be taken over in the event that the borrower defaults (fails) in the repayment of the loan.

An annual percentage rate (APR) is an amount of money paid as interest by borrowers or earned on loans by lenders such as banks, expressed as a percentage of the amount borrowed or invested over a 12-month period i.e on an annual basis.

Generally, the annual percentage rate (APR) helps compare loans with the same payback period, but with different monthly rates and different fees.

Answer:

A- If you have good credit, you will get a higher APR

Step-by-step explanation:

Answer: For three hours of work, she'll get paid $54. For 2.1 hours of work she'll get paid $37.8

Hope this helps you.

Answer:

$54, $37.8

Step-by-step explanation:

3 hrs=$54, 2.1 hrs=$37.8

can i have brainlyest please

The inequality that represents all the solutions of -2(3x + 6) ≥ 4(x + 7) is x ≤ -4

From the question, we have the following parameters that can be used in our computation:

-2(3x + 6) ≥ 4(x + 7)

Divide both sides of the inequality by -2

So, we have the following representation

3x + 6 ≤ -2(x + 7)

Open the brackets

This gives

3x + 6 ≤ -2x - 14

Add 2x to both sides of the inequality

So, we have the following representations

5x + 6 ≤ -14

Subtract 6 from both sides of the inequality

So, we have the following representations

5x ≤ -20

Divide both side of the inequality

x ≤ -4

Hence, the solution is x ≤ -4

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Dilation involves changing the size of a quadrilateral or any shape

The coordinates of the image of the dilation are: \(W^{\prime}=(1 / 4,-3), X^{\prime}=(10,0)$, $Y^{\prime}=(7,-9)$\) and \($Z^{\prime}=(4,-9)$\)

This is further explained below

The vertices of the pre-image are given as:

W=(0,-4)

X=(13,0)

Y=(9,-12)

Z=(5,-12)

The scale factor is given as:

k=3 / 4

The center of dilation is given as:

(a, b)=(1,0)

To calculate the vertices of the image, we make use of the following formula \($\left(x^{\prime} y^{\prime}\right)=(k(x-a)+a, k(y-b)+b)$\)

So, we have:

W'=(3 / 4(0-1)+1,3 / 4(-4-0)+0)

W'=(1 / 4,-3)

X'=(3 / 4(13-1)+1,3 / 4(0-0)+0)

X'=(10,0)

Y'=(3 / 4(9-1)+1,3 / 4(-12-0)+0)

Y'=(7,-9)

Z'=(3 / 4(5-1)+1,3 / 4(-12-0)+0)

Z'=(4,-9)

Hence, the coordinates of the image of the dilation are:

W'=(1 / 4,-3),

X'=(10,0),

Y'=(7,-9)

Z'=(4,-9)

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Answer:

C: (12,4)

Step-by-step explanation:

We can find the slope of the line with "rise over run"

The pattern is 1 unit up, 3 units to the right

By following this pattern from point (9,3),

we go 1 unit up on the y axis, moving (9,3) to (9,4)

Next we move 3 units right on the x-axis,

moving (9,4) to (12,4)

Answer is (12,4)

Step-by-step explanation:

\(49 - 28 = 21 \\ 51 - 32 = 19 \\ 23 \times 7 = 161 \\ 14 \times 5 = 70\)

The answer is 0.75 because I took the test and that's what the answer was :)

Answer:

see explanation

Step-by-step explanation:

(a)

The sum of the 3 angles in a triangle = 180°

Subtract the sum of the given angles from 180° for B

∠ B = 180° - (90 + 63)° = 180° - 153° = 27°

(b)

Using the sine ratio in the right triangle

sin63° = \(\frac{opposite}{hypotenuse}\) = \(\frac{BC}{AB}\) = \(\frac{15}{x}\) ( multiply both sides by x )

x × sin63° = 15 ( divide both sides by sin63° )

x = \(\frac{15}{sin63}\) ≈ 16.8 ( to 1 dec. place )

(c)

Using the tangent ratio in the right triangle

tan63° = \(\frac{opposite}{adjacent}\) = \(\frac{BC}{AC}\) = \(\frac{15}{y}\) ( multiply both sides by y )

y × tan63° = 15 ( divide both sides by tan63° )

y = \(\frac{15}{tan63}\) ≈ 7.6 ( to 1 dec. place )

The board weighs approximately 8.05 pounds. Hence, its density is 46.80  lb/ ft³

The density of something is a measure of how heavy it is in relation to its size. When a thing is more dense than water, it sinks; when an object is less dense than water, it floats. Density is a feature of a substance that is independent of the amount of substance.

The formula for density is given by:

ρ = m/V

Where:

ρ = density

m = mass

V = volume

In this case, the dimension of the oak board is:

wide = 5.5 inches = 0.458 feet

thick = 1.5 inches = 0.125 feet

length = 3 feet

Hence, the volume of the board is:

V = 0.458 x 0.125 x 3 = 0.172 ft³

The weight is 8.05 pounds, therefore, the density:

ρ = 8.05/0.172  lb/ ft³

ρ = 46.80  lb/ ft³

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Answer:

B because it's a fraction I just divided them and got b

Answer:

Y-3=2(x-0)

Step-by-step explanation:

To find our answer, we have to use point slope form

Point slope form looks like this:

Y-y1=m(x-x1)

When we fill these things in we get,

Y-3=2(x-0)

Hope this helps and please award brainliest

Answer:

y-3 = 2(x-0)

Step-by-step explanation:

The solution to the given initial value problem is \(y(t) = -(t * e^(-1) - e) * U(t - 1) - t + e(t) - 1.\)

To solve the given initial value problem using Laplace transform, let's denote the Laplace transform of a function f(t) as F(s), where s is the complex variable. Applying the Laplace transform to the given differential equation and using the linearity property, we get:

sY(s) + 2Y(s) + Y(s) = F(s)

Combining the terms, we have:

(s + 3)Y(s) = F(s)

Now, let's find the Laplace transform of the given input function f(t). We can split the function into two parts based on the given conditions. For t < 1, f(t) = 1, and for t > 1, f(t) = 0. Using the Laplace transform properties, we have:

L{1} = 1/s (Laplace transform of the constant function 1) L{0} = 0 (Laplace transform of the zero function)

Therefore, the Laplace transform of f(t) can be expressed as:

F(s) = 1/s - 0 = 1/s

Substituting this into the equation (s + 3)Y(s) = F(s), we get:

(s + 3)Y(s) = 1/s

Simplifying further, we obtain:

Y(s) = 1/[s(s + 3)]

Now, we need to find the inverse Laplace transform of Y(s) to obtain the solution y(t) in the time domain. Using partial fraction decomposition, we can write:

Y(s) = A/s + B/(s + 3)

To find the constants A and B, we can multiply both sides by the denominators and solve for A and B. This yields:

1 = A(s + 3) + Bs

Substituting s = 0, we get A = 1/3. Substituting s = -3, we get B = -1/3.

Therefore, we have:

Y(s) = 1/(3s) - 1/(3(s + 3))

Taking the inverse Laplace transform of Y(s), we get:

\(y(t) = (1/3)(1 - e ^ (-3t)\)

Finally, we can simplify the expression further:

\(y(t) = -(t * e^(-1) - e) * U(t - 1) - t + e(t) - 1\)

Thus, the solution to the given initial value problem is \(y(t) = -(t * e^(-1) - e) * U(t - 1) - t + e(t) - 1.\)

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To calculate the cash balance at the end of the period, we need to consider the cash inflows and outflows.

Starting cash balance: $4,520

Cash inflows: $1,654 (receivables collected)

Cash outflows: $1,961 (payments to suppliers) + $500 (cash expenses)

Total cash inflows: $1,654

Total cash outflows: $1,961 + $500 = $2,461

To calculate the cash balance at the end of the period, we subtract the total cash outflows from the starting cash balance and add the total cash inflows:

Cash balance at the end of the period = Starting cash balance + Total cash inflows - Total cash outflows

Cash balance at the end of the period = $4,520 + $1,654 - $2,461

Cash balance at the end of the period = $4,520 - $807

Cash balance at the end of the period = $3,713

Therefore, the cash balance at the end of the period is $3,713.

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Answer:

C

Step-by-step explanation:

Clustered data emerge when the data from the entire sample can be grouped into a variety of different categories, refers to as clusters. Each cluster involves numerous observations, giving the data a “clustered” or “hierarchical” structure, with each observations encapsulated within the cluster.

Also, if we plot a series of numbers on a graph and we will see several of our dots gathered together, we have a cluster

From the above definition of clustered data the only option that is fitting into it is option C .

25,50,50,25,75,75

M<1 =  52*

M<2 = 38*

Step-by-step explanation:

The angle is a 90 degree angle (we know because of the little square.)

(X+33) + 2x = 90

3x+33=90

3x= 57

X=19

( Then solve the original problems with X -=19)

The vertex form of the new function is \(\rm (x+7)^2 -47\).

The function \(\rm f(x) = x^2 + 22x + 58\)  is translated 4 units to the right and 16 units up.

The vertex of a parabola is the point at which the parabola passes through its axis of symmetry.

The standard equation which represents the vertex form of the function is;

\(\rm f(x) = (x - h)^2 + k\)

Where h and k are vertexes of the given parabola.

The new function after translating 4 units to the right and 16 units up is;

\(\rm f(x) = x^2+22x+58\\\\f(x) = x^2 + 22x + 58 +(11)^2 -(11)^2\\\\\f(x) = x^2+22x+(11)^2 +58-(11)^2\\\\ f(x) = (x+11)^2+58-121\\\\f(x)=(x+11)^2-63\)

On comparing with the standard equation of vertex of parabola;

h = -11 and k = -63

Then,

The vertex form of the new function is after translated 4 units to the right and 16 units up.

h = -11 + 4 and k = -63+16 = -47

Therefore,

The vertex form of the new function is;

\(\rm =(x+7)^2 -47\)

Hence, the vertex form of the new function is \(\rm (x+7)^2 -47\).

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Answer:

C

Step-by-step explanation:

The point is [-13,-7] when the actual numbers are all at least two units away from 4.

Given that,

To specify the interval (or pair of intervals) on the real number line, use absolute value notation. (Utilize the x variable.) actual numbers are all at least two units away from 4.

We know that,

We get,

|-4-x| = 3

-3 = -4-x = 3

7 = -x = 13

-13 = x = -7

Therefore, The point is [-13,-7] when the actual numbers are all at least two units away from 4.

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Answer:

-103

Step-by-step explanation:

a(1) = 12

a(n) = a(n-1) - 23

a(2) = a(1) - 23

       = 12 - 23

      = -11

Common difference (d) = a(2) -a(1) = -11 - 12  = -23

a(n) =  a1 + (n-1)d

a(6) = 12 + 5 * (-23)

       = 12 - 115

       = -103

Answer:

The ones selected are correct

Answer: l=50 m, w=20 m

Step-by-step explanation:

Given

A rectangular city has an area of \(1000\ m^2\)

Also, length is 10 m more than twice its width

suppose width is w

So, length is given by

\(\Rightarrow l=10+2w\)

The area is given by

\(\Rightarrow A=l\times w\\\Rightarrow 1000=(10+2w)\times w\\\Rightarrow 2w^2+10w-1000=0\\\Rightarrow w^2+5w-500=0\\\Rightarrow w^2+25w-20w-500=0\\\Rightarrow (w+25)(w-20)=0\\\therefore w=20\ m\\l=10+2w=10+2\times 20=50\ m\)

Below is the picture attached for the five vectors in span {bold v1 v1, bold v2 v2}.

Given a subspace S, every basis of S contains the same number of vectors; this number is the dimension of the subspace. To find a basis for the span of a set of vectors, write the vectors as rows of a matrix and then row reduce the matrix. The span of the rows of a matrix is called the row space of the matrix.

Then any linear combination of all three vectors is also a linear combination of the first two, so the span of all three is the same as the span of the first two, i.e. it is the set of all vectors in the plane. Case 3: no plane contains all three vectors. (So the vectors are all 3-space vectors.)

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First, we want to note two things:

We can describe this with an inequality:  x ≥ -10
Be sure you use ≥ and not >, since -10 is included.

We can describe this with interval notation: [ -10, infty )
Be sure you use [ and not ( on -10, since -10 is included.

You can also use set-builder notation: { x | x ≥ -10 }

At the 95% confidence level, the margin of error for the mean is 26.4.

To estimate the margin of error for the mean SAT scores at the 95% confidence level using the normal distribution/empirical rule, we can use the formula:

Margin of Error = Critical Value * (Standard Deviation / Square Root of Sample Size)

First, let's determine the critical value corresponding to a 95% confidence level. Since the sample size is small (n < 30), we'll use a t-distribution instead of the normal distribution. With a sample size of 56 and a confidence level of 95%, the critical value can be found using a t-table or a statistical calculator. For a 95% confidence level with 55 degrees of freedom (n-1), the critical value is approximately 2.009.

Next, we substitute the given values into the formula:

Margin of Error = 2.009 * (98 / √56)

To calculate the square root of 56, we get approximately 7.483.

Margin of Error ≈ 2.009 * (98 / 7.483)

Evaluating the expression inside the parentheses, we have:

Margin of Error ≈ 2.009 * 13.106

Finally, multiplying 2.009 by 13.106 gives us approximately 26.35.

Therefore, at the 95% confidence level, the margin of error for the mean SAT scores is approximately 26.4 (rounded to the nearest tenth). This means that the estimated mean score of 453 could be off by about 26.4 points in either direction.

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Answer:

M a t h W a y

Step-by-step explanation:

you can put graphs and  calculate cool stuff

hope it helps

Answer:

D

Step-by-step explanation:

\( \sin(30) = \frac{y}{12} \\ y = 6 \\ \cos(30) = \frac{x}{12 } \\ x = \sqrt{108} = 6 \sqrt{3} \)

Answer:

75 cu in

Step-by-step explanation:

the formula for volume is V = l w h (volume equals length times width times height) and can also be written V = B h (volume equals the area of the base times the height). Notice that the version, V = l w h is only true for rectangular prisms and cubes.

V = L x W x H

V = 5 x 5 x 3

V = 75

Answer: 75 in³

Step-by-step explanation:

    We will use the given formula to solve for volume by substituting and multiplying.

V = LWH

V = (5 in)(5 in)(3 in)

V = 75 in³

Answer:

60%

Step-by-step explanation:

Divide 250 by 50, to get 5. The person paid 150, which is three 50s. So they paid 3/5. Double both sides to get 6/10. 6/10 is equal to 60%

The price of a cell phone is usually $250. Elena’s mom buys one of these cell phones for $150. She did pay 60% percent of the usual price.

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.

The price of a cell phone is usually $250.

Elena’s mom buys one of these cell phones for $150.

= 250 / 50

= 5.

The person paid 150, which is three 50s.

So they paid 3/5.

Double both sides to get 6/10.

Therefore, 6/10 is equal to 60%.

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Answer:

negative

hope it helps;)