The family is hiking in the mountains at a rate of 6 miles every 3 hours
How long would it take the family to hike 7.5 miles?
(Hint: You will have a decimal or fraction in your final answer!)

T satisfies the homogeneity property.

To prove that T is a linear transformation, we need to show that it satisfies two properties: additivity and homogeneity.

Additivity:

Let's consider two arbitrary vectors z₁ = [x₁, y₁] and z₂ = [x₂, y₂] in R².

T(z₁ + z₂) = T([x₁ + x₂, y₁ + y₂])

= [-2(x₁ + x₂) - 1, -2(x₁ + x₂) + 2(y₁ + y₂)]

= [-2x₁ - 2x₂ - 1, -2x₁ - 2x₂ + 2y₁ + 2y₂]

= (-2x₁ - 1, -2x₁ + 2y₁) + (-2x₂ - 1, -2x₂ + 2y₂)

= T(z₁) + T(z₂)

Therefore, T satisfies the additivity property.

Homogeneity:

Let's consider an arbitrary vector z = [x, y] in R² and a scalar k.

T(kz) = T([kx, ky])

= [-2(kx) - 1, -2(kx) + 2(ky)]

= (-2kx - 1, -2kx + 2ky)

= k(-2x - 1, -2x + 2y)

= kT(z)

Since T satisfies both additivity and homogeneity, we can conclude that T is a linear transformation.

For more questions on homogeneity property

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Answer/Step-by-step explanation:

As the input increases by 1, the output decreases by 4. The missing number for the Input is 6, and the missing number for output is -17.

Answer:he can buy at least 7 pairs of socks

Step-by-step explanation:

Answer:

  (c)  x

Step-by-step explanation:

You want to know the value of h(f(x)) if h(x) is the inverse of f(x).

The point of an inverse function is that it gives the input value that results in the output value of the function it is the inverse of.

If f(x) has output value y, then its inverse function h(x) will give you ...

  h(y) = x

That is, h(f(x)) = x.

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Answer:

If h(x) is the inverse of f(x), then by definition, h(f(x)) would yield the value of x. In other words, h(f(x)) = x.

Step-by-step explanation:

The equation of the circle graphed below is (x + 2)² + (y - 3)² = 16.

To determine the equation of the circle graphed below, we need to use the standard form equation of a circle.

The standard form of a circle equation is (x - h)² + (y - k)² = r², where (h, k) is the center of the circle and r is the radius.

Given the graph, we can see that the center is located at (-2, 3), and the radius is 4 units. Therefore, we can substitute these values into the standard form equation as follows:(x - (-2))² + (y - 3)² = 4²(x + 2)² + (y - 3)² = 16

To lear more about : circle graphed

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Answer:

[tex](x +3)^2+(y-2)^2=4[/tex]

Step-by-step explanation:

The equation of a circle in standard form is:

[tex]\boxed{\begin{minipage}{4 cm}\underline{Equation of a circle}\\\\$(x-h)^2+(y-k)^2=r^2$\\\\where:\\ \phantom{ww}$\bullet$ $(h, k)$ is the center. \\ \phantom{ww}$\bullet$ $r$ is the radius.\\\end{minipage}}[/tex]

To determine the equation of the graphed circle, we need to find its center and radius.

The center of the circle is a single point that lies at an equal distance from all points on the circumference of the circle.

From inspection of the graphed circle, we can see that its domain is [-5, -1] and its range is [0, 4].  The x-coordinate of the center is the midpoint of the domain, and the y-coordinate of the center is the midpoint of the range.

[tex]x_{\sf center}=\dfrac{-5+(-1)}{2}=-3[/tex]

[tex]y_{\sf center}=\dfrac{0+4}{2}=2[/tex]

Therefore, the center of the circle is (-3, 2).

The radius of the circle is the distance from the center to all points on the circumference of the circle.  From observation, we can see that the radius of the circle is r = 2.

To determine the equation of the circle, substitute the center and radius into the standard formula.

[tex](x - (-3)^2+(y-2)^2=2^2[/tex]

[tex](x +3)^2+(y-2)^2=4[/tex]

Therefore, the equation of the graphed circle is:

[tex]\boxed{(x +3)^2+(y-2)^2=4}[/tex]

Answer:

1.5 feet

Step-by-step explanation:

12/8 = 1.5 feet

ddhrsjfhffhhrry7tt5566

Answer:

Corresponding side of AB is FE

Corresponding side of CB is DE

Corresponding side of AC is FD

[tex]k =2[/tex]

[tex]DE = 6[/tex]

[tex]FD=10[/tex]

Step-by-step explanation:

Given

[tex]\triangle ABC[/tex] and [tex]\triangle FED[/tex]

See attachment for triangles

Solving (a): Corresponding side of AB

Going by the names of the triangle, the corresponding sides are:

AB and FE; CB and DE; AC and FD

Hence, the corresponding side of AB is FE

Solving (b): Corresponding side of CB

This has been solved in (a) above.

The corresponding side of CB is DE

Solving (c): Corresponding side of AC

This has been solved in (a) above.

The corresponding side of AC is FD

Solving (d): Scale factor from ABC to FED

To do this, we simply divide the lengths of corresponding sides.

The scale factor k is:

[tex]k = \frac{FE}{AB}[/tex]

[tex]k = \frac{8}{4}[/tex]

[tex]k =2[/tex]

Solving (e): Length of DE

We make use of the scale factor calculated in (d) above

[tex]k = \frac{DE}{CB}[/tex]

[tex]2 = \frac{DE}{3}[/tex]

[tex]DE = 2 * 3\\[/tex]

[tex]DE = 6[/tex]

Solving (f): Length of FD

Using Pythagoras:

[tex]FD^2 = DE^2 + EF^2[/tex]

[tex]FD^2 = 6^2 + 8^2[/tex]

[tex]FD^2 = 100[/tex]

[tex]FD = \sqrt{100[/tex]

[tex]FD=10[/tex]

Answer:

sorry but the picture if you put one on here isn't showing up maybe Repost and I could answer

Answer:

31

Step-by-step explanation:

Answer:

Cannot be determined with the information given in and of itself.

Step-by-step explanation:

You would have 1 apple left. However, there is absolutely no information given about the original amount of peanuts, how many peanuts are given to you, how many peanuts are taken from you, how many apples to a peanut, etc. etc. No answer in peanuts can be given.

I would appreciate Brainliest, but no worries.

Answer:

0

Step-by-step explanation:

if you have 2 and you take one away you have 1,

you'll have 0 peanuts since apples can't become peanuts, unless you have them already or buy them; apples won't help you get peanuts.

Answer:

Zack has 8 stamps with pictures of animals

Step-by-step explanation:

Number of Stamps that Zack has = 10

Number of Zack's Stamps that have the pictures of animals = ⅘ of 10

= ⅘ × 10

= 40/5

= 8

Zack has 8 stamps with pictures of animals

Answer:

2./10

Step-by-step explanation:

It's simply by finding the square root of its area which is √40 giving 6.325 for an answer

If simplified by dividing each side with 3 then the answer would be 2./10

Answer:

75%

Step-by-step explanation:

18 divided by 24 equals .75 and that equals 75 as a percent.

Answer:

C. 150

Step-by-step explanation:

It's right on Plato.

Answer:

201 2.1

Step-by-step explanation:

adad yes

Step-by-step explanation:

[tex] {x}^{2} - 8x + 15 = 0 \\ (x - 3)(x - 5) = 0 \\ x = 3 \: or \: x = 5[/tex]

Answer:

Greater Than [The second choice]

Step-by-step explanation:

Answer:

864

Step-by-step explanation:

144x6

Answer:

b

Step-by-step explanation:

Answer:1-5

Step-by-step explanation:Assuming the spinner is numbered 1–5 and has an equal chance of landing on any number, you have two independent probabilities, each 1 in 5.

Just multiply those: 1/5 * 1/5 = 1/25. You have a 4% chance of getting 2 twice.

Of course, if there’s anything special about spinning “2”, you’ll be keyed to watch for it after getting 2 the first time. Now there’s a 20% chance (1 in 5) you’ll spin it again, and you’ll be very excited that you got 2 twice in a row. Another way of saying that is that the probability of something that has already happened is 100%.

Answer:

75/6 = 12.5

Step-by-step explanation:

Mean = The sum divided by the number of numbers.

Answer:

I think it is either C or D

Step-by-step explanation:

I'm so sorry id didn't find the answer, i tried

Answer:

the answer is 228 so b

Step-by-step explanation:

i foot has 12 inches so you multiply 12 and 19 and then you get 228

hope this helped

can i get brainliest

Answer:2/3

Step-by-step explanation:

Answer:

Step-by-step explanation:

hello :

the perimeter of the rectangle is P=2(w+l)

l : The length  and w the width    ..... continu   calculate

Answer:1 + 1

Step-by-step explanation:because 1+1 is 1+1

SAS, I guess (side angle side)

Step-by-step explanation:

Since AM=BC then AM+MB=MB+BN.

Therefore, AB=MN. So, the two triangle have one congruent angle, and the sides adjacent to it are congruent as well. Those triangle are thus congruent

Answer:

B. SAS (Side Angle Side)

Step-by-step explanation:

its right on E2020

Answer:

Its C

Step-by-step explanation: