In rectangle ABCD, AB = 10 cm and BC = 14 cm. If rectangle EFGH is the image after a dilation, which could be its side lengths?
EF = 6 cm and FG = 10 cm
EF = 7 cm and FG = 3 cm
EF = 15 cm and FG = 20 cm
EF = 25 cm and FG = 35 cm

Answer:

10

Step-by-step explanation:

Answer: Students have less than a dollar.

Step-by-step explanation:

Niall has $1/2

Mary has $1/10

Jack has $1/100

Add these up to see if they reach 1.

= 1/2 + 1/10 + 1/100

Convert to decimals by dividing the numerator by the denominator:

= 0.5 + 0.1 + 0.01

= $0.61

Students have less than a dollar.

Answer:

5%

Step-by-step explanation:

Answer:

Option (iv) is correct.

Step-by-step explanation:

The linear equation is the equation in which the degree of the equation is 1.

(i) x/3 = 12

As the degree of equation is 1, so, it is a linear equation.

(ii) x + 1 = 6

As the degree of equation is 1, so, it is a linear equation.

(iii) x + y + z = 17

As the degree of equation is 1, so, it is a linear equation.

(iv) x y + x / y = 3

x y^2 + x = 3 y

The degree of equation is 3, so the equation is non linear.

Answer:

4 tens, 3 twenties

Step-by-step explanation:

4 tens  ($40) and 3 ($60)  twenties work. I’m sorry I don’t have a formula for it though.

Answer:

56t

Step-by-step explanation:

Answer:

the answer 240

Step-by-step explanation:

times 24 and 10 to get 240 m

Answer:

2.25 feet deep

Step-by-step explanation:

The volume was given as (11.13 cubic feet)

Length as (2.6 feet)

Width as(1.9 feet)

Volume of triangular prism can be written as ( length × width × height)

Volume= ( length × width × height)

Then substitute the values, we have

11.13 = 2.6 × 1.9 × height

Height= 11.13/(2.6×1.9)

= 11.13/4.94

= 2.25 feet

Answer:

36 cubic inches

Step-by-step explanation:

The prism is literally just the front section twice. Find the area of the front and then add it to itself

Answer:

Answer: There is 32in² more sand in the pyramid with greater volume.

step explanation:

Answer:

6%

Step-by-step explanation:

Answer:

(Sin A + Cos A)/Sin A. Cos A

Step-by-step explanation:

As we know

Sec A = 1/Cos A

and Cosec A = 1/Sin A

Given Equation

Sec A + Cosec A

Substituting the given values, we get -

1/cos A + 1/Sin A

(Sin A + Cos A)/Sin A. Cos A

Answer:

Total amount pay for new apartment = $4,740.75

Step-by-step explanation:

Find:

Total amount pay for new apartment

Computation:

Particular                                       Amount

Monthly rent of apartment           $1,650

Add:

Application fee [1,650 x 1.5%]      $24.75

Credit application fee                   $30

Security rent                                  $1,650

Broker's fee [1,650 x 12 x 7%]      $1,386

Total                                               $4,740.75

Total amount pay for new apartment = $4,740.75

Answer: [tex]24.02\ mph[/tex]

Step-by-step explanation:

Given

Boat is traveling due to north at [tex]v_{bf}=27\ mph[/tex]

The current is flowing [tex]60^{\circ}[/tex] west of south at [tex]v_f=8\ mph[/tex]

Suppose the actual velocity of boat is [tex]\vec{v_b}[/tex]

In vector notation we can write

[tex]\Rightarrow \vec{v_{bf}}=\vec{v_b}-\vec{v_f}\\\\\Rightarrow \vec{v_b}=\vec{v_{bf}}+\vec{v_f}[/tex]

Flow of current can be written as

[tex]\Rightarrow \vec{v_f}=-8\sin 60^{\circ}\hat{i}-8\cos 60^{\circ}\hat{j}[/tex]

Insert the values of vectors

[tex]\Rightarrow \vec{v_b}=27\hat{j}-8\sin 60^{\circ}\hat{i}-8\cos 60^{\circ}\hat{j}\\\\\Rightarrow \vec{v_b}=-4\sqrt{3}\hat{i}+27\hat{j}-4\hat{j}\\\\\Rightarrow \vec{v_b}=-4\sqrt{3}\hat{i}+23\hat{j}[/tex]

Magnitude of the velocity is

[tex]=\sqrt{(4\sqrt{3})^2+(23)^2}\\=\sqrt{48+529}\\=24.02\ mph[/tex]

The actual direction and magnitude of the velocity of the boat is the sum of

the velocity of the boat and the velocity of the current both in vector form.

Reasons:

Direction of the boat = North

Speed of the both = 27 mph

Direction of the current = 60° west of south

Speed of the current = 8 mph

Required:

The actual speed and direction of the boat written in magnitude and

direction.

Solution:

The velocities given in vector form are;

Velocity of the boat, [tex]\vec {v}_{boat}[/tex] = 27·j

60° west of south = 30° south of west

Therefore;

Velocity of the current, [tex]\vec{v}_{current}[/tex] = -8 × cos(30°)·i - 8×sin(30°)·j

The actual velocity of the boat, [tex]\vec{v}_{actual}[/tex] = [tex]\mathbf{\vec {v}_{boat}}[/tex] + [tex]\mathbf{\vec{v}_{current}}[/tex]

Which gives;

[tex]\vec{v}_{actual}[/tex] = 27·j - 8 × cos(30°)·i - 8 × sin(30°)·j

[tex]\vec{v}_{actual}[/tex] = 23·j - (4·√3)·i

Therefore;

[tex]\vec{v} _{actual}[/tex] = -(4·√3)·i + 23·j

Which gives;

[tex]|v_{actual}|[/tex] = √((-4·√3)² + 23²) = √(577) ≈ 24.02

The actual direction of the boat, θ, is given by the arctangent of the ratio

of the vertical to the horizontal component of the velocity as follows;

[tex]\displaystyle \theta = arctan \left(\frac{23}{-4 \cdot \sqrt{3} } \right) \approx \mathbf{-73.24^{\circ}}[/tex]

Based on the horizontal and vertical component, the above angle θ is

approximately 73.24° relative to the negative x-axis, which is 90° - 73.24° =

16.76° west of north.

Therefore;

Learn more about vector quantities here:

https://brainly.com/question/1614684

Answer:

c, a, b

Step-by-step explanation:

Given

See attachment for matrices

(a)

[tex]D = \left[\begin{array}{cc}\cos\theta &\sin\theta\\ -\sin\theta& \cos\theta\\\end{array}\right][/tex]

The determinant of the matrix is:

[tex]|D |= (\cos\theta * \cos\theta - \sin\theta *- \sin\theta)[/tex]

[tex]|D | = \cos^2\theta + \sin^2\theta[/tex]

Using trigonometry ratio, we have:

[tex]|D | = 1[/tex]

(b)

[tex]\left[\begin{array}{ccc}2&0\\0&2\end{array}\right][/tex]

The determinant of the matrix is:

[tex]|D| = 2 * 2 - 0 * 0[/tex]

[tex]|D| = 4 - 0[/tex]

[tex]|D| = 4[/tex]

(c)

[tex]\left[\begin{array}{ccc}0&i\\-i&0\end{array}\right][/tex]

The determinant of the matrix is:

[tex]|D| = 0 * 0 -(-i * i)[/tex]

[tex]|D| = 0 +i^2[/tex]

[tex]|D| = i^2[/tex]

In complex numbers

[tex]i^2 = -1[/tex]

So:

[tex]|D| = -1[/tex]

So, the order of the determinants is: c, a, b

Answer:

2.432 * 10⁹

Step-by-step explanation:

Given the expression;

3.8*10² × 6.4*10⁶

= (3.8*6.4)× (10²*10⁶)

= 24.32*10⁸

= 2.432* 10¹ * 10⁸

= 2.432 * 10⁹

Hence the product expressed as a scientific notation is 2.432 * 10⁹

Answer:

the answer is 9

Step-by-step explanation:

6/10=x/15

10x=90

x=9

Answer:

D, 144

Step-by-step explanation:

Find x first by solving 9x+27=6x+66, and plug x in to the angle RSL.

Answer:

28

Step-by-step explanation:

[tex]\sqrt{100} + (\sqrt{9} \cdot \sqrt{36}) = 10 + (3 \cdot 6) = 10 + 18 = 28[/tex]

Answer:

At the very tip of one of the spiral arms, at the edge of the milky way.

OR C

Forgive me if i'm wrong

...

Answer:

C. In one of the spiral arms, about halfway between the center and the edge.

Step-by-step explanation:

Our solar system is located in the Orion Arm which is halfway between the center and the edge of the Milky Way.

Answer:

just do it by Pythagoras theoram

Step-by-step explanation:

because it is a right angle

Answer:

a. x is 55

b. 20 white marbles

Step-by-step explanation:

Question: A box contains 60 identical marbles where 'x' of them are red while the rest are white; (given that in the original question, the box only contains red and yellow marbles, the yellow can be replaced by white to explain the question idea)

a. The number of identical marbles in the box, n = 60

The number of red marbles = x

The number of white marbles = The rest of the marbles which are not red

The probability that a marble drawn is white, P(y) = 1/12

Let 'y' represent the number of white marbles

From probability theory, we have;

The number of white marbles, y = n × P(y) = 60 × 1/12 = 5

The number of red marbles, x = n - y = 60 - 5 = 55

x = 55

b. The number of white marbles that must be added to make the probability of choosing a white marble = 5/16 is given as follows;

Let Δy represent the number of white marbles added, therefore;

P(y) = (y + Δy)/(y + Δy + x)

∴ P(y) = (5 + Δy)/(5 + Δy + 55) = 5/16

5 × (60 + Δy) = 16 × (5 + Δy)

300 + 5·Δy = 80 + 16·Δy

16·Δy - 5·Δy = 300 - 80

11·Δy = 220

Δy = 220/11 = 20

The number of white marbles that must be added, Δy = 20 white marbles

Answer:

Its definitley square to be precise so that's my answer, but its also a rhombus

Step-by-step explanation:

assuming a is 1, regardless, graph would always be square, which is a rhombus. hope  square is correct :)

where is the drip at?

Answer:

AA

Step-by-step explanation:

AA

Answer:

15+ 8d

After d day,she has read 15 +8d pages

Answer:

The answer is -0.71666666666 in decimal form.

In fraction form it is -43/60.

Step-by-step explanation:

Answer:

C. If an object is dropped from a height of 120 feet, the function h(t) = –16t2 – 120 gives the height of the object after t seconds.

Step-by-step explanation:

.................................The last one is the only one that makes sense according to the standard position function.  -16t^2 is the pull of gravity on an object in free fall, and the height is 120 feet above the ground.  Hopefully that's what you need since there's no graph we can refer to

....................................................Answer:

The explanation that best provides the real-world scenario is:

If an object is dropped from a height of 120 feet, the function                    

gives the height of the object after t seconds.

Step-by-step explanation:

a)

If an object is dropped from a height of 120 feet, the function  gives the height of the object after t seconds.

This option is incorrect.

Since when t=0 we have:

          h(t)= -120

This is not possible as the object is above the ground and hence must have positive height initially.

b)

If an object is dropped from a height of -16 feet, the function  gives the height of the object after t seconds.

This option is incorrect.

Since a object when is dropped from some height then it must be a positive height.

Also, when t=0 we have: h(t)= 120 feet.

This means that the object is dropped from a height of 120 feet.

c)

If an object is dropped from a height of 120 feet, the function  gives the height of the object after t seconds.

In this when t=0 we have:

h(t)=120 that means the height of the object initially was 120 feet and then it decreases with the increase in time as the object will reach the ground with the time increase and hence height will decrease.

              Hence, this option is correct.

........................................The equation that models the movement of the object is:

Where,

t: time

a: acceleration due to gravity

v0: initial speed

h0: initial height

Suppose that the object falls with zero initial velocity and from a height of 38 feet.

The equation that models the problem is:

Answer:

If an object is dropped from a height of 38 feet, the function h (t) = -16t2 + 38 gives the height of the object after seconds

.................Answer: If an object is dropped from a height of 38 feet, the function h (t) = -16t2 + 38 gives the height of the object after seconds

Step-by-step explanation:

The explanation that best provides the real-world scenario is:

⇒ If an object is dropped from a height of 120 feet, the function                    

h(t) = - 16t² - 120 gives the height of the object after t seconds.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

a) If an object is dropped from a height of 120 feet, the function

h(t) = - 16t² + 120 gives the height of the object after t seconds.

Hence, This option is incorrect.

Since, when t=0 we have:

h (t) = -120

This is not possible as the object is above the ground and hence must have positive height initially.

b) If an object is dropped from a height of -16 feet, the function

h(t) = - 16t² + 120 gives the height of the object after t seconds.

This option is incorrect.

Since a object when is dropped from some height then it must be a positive height.

Also, when t = 0

we have: h (t) = 120 feet.

This means that the object is dropped from a height of 120 feet.

c) If an object is dropped from a height of 120 feet, the function

h(t) = - 16t² - 120 gives the height of the object after t seconds.

In this when t=0 we have:

h(t)=120

That means the height of the object initially was 120 feet and then it decreases with the increase in time as the object will reach the ground with the time increase and hence height will decrease.

Hence, this option is correct.

Learn more about the mathematical expression visit:

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