If an image of a triangle is congruent to the pre image what is the scale factor of the dilation

Answer: 240 seconds OR 4 minutes

Step-by-step explanation:

Length of the train = 1 km

Length of the tunnel = 1 km

Therefore, length of the train + length of the tunnel = (1 + 1) km = 2 km

= 2000 m

Speed of the train = 30 km/hr = 8.333 metres per second

Therefore, time taken by the train to cross the tunnel = 2000 m/ 8.333 m/sec.

= 240 seconds = 4 minutes

Answer:

E = (28 + 66i) Volts

Step-by-step explanation:

Note that: i = √-1 ; i² = -1

Ohm's law: E = IR

E = (16+ i) (2 + 4i)

Expand the equation.

E = 16x2 + 16x4i + ix2 + ix4i

E = 32 + 64i + 2i + 4i²

E = 32 + 64i + 2i + 4(-1)

E = 32 + 64i + 2i - 4

Collect like terms:

E = 32 -4 + 64i + 2i

E = (28 + 66i) Volts

Answer:

f(4) = 24

Step-by-step explanation:

Plug in 4 for x in the equation:

f(x) = x² + 3x - 4

f(4) = (4)² + 3(4) - 4

Remember to follow PEMDAS. PEMDAS =

Parenthesis

Exponents (&  Roots)

Multiplication

Division

Addition

Subtraction

and is the order of operation.

First, solve the power:

(4)² = 4 * 4 = 16

Next, multiply 3 with 4:

3 * 4 = 12

Next, combine the terms:

f(4) = 16 + 12 - 4

f(4) = (16 + 12) - 4

f(4) = 28 - 4

f(4) = 24

f(4) = 24 is your answer.

~

Answer:

24

Step-by-step explanation:

Plug x as 4.

(4)² + 3(4) - 4

16 + 12 - 4

= 24

Answer:

9

Step-by-step explanation:

x2 + 3

(3)2 + 3

6 + 3

9

Answer:

12.

Step-by-step explanation:

x = 3; x^2 + 3.

(3)^2 + 3 = 3 * 3 + 3 = 9 + 3 = 12

Hope this helps!

Answer:

22

Step-by-step explanation:

x-1 is a midsegment.

According to the Triangle midsegment theorem, x-1 is half of the third side (42)

x-1 = 42/2

x-1 = 21

x= 22

or

2x-2=42

2x=44

x=22

Hope this helps!

If you look at the top sides and bottom sides of both figures, this means that they are the same or similar.

In this figure, they are similar because one side is half of the other.

So... divide the longer length in half and solve for x.

42 / 2 = 21

x - 1 = 21

x - 1 + 1 = 21 + 1

x = 22

Therefore, the answer is C.

Best of Luck!

Answer:

the value of x_y is 1.

hope u get it.....

Answer:

The answer is 1/3.

Step-by-step explanation:

This is because when dividing you switch the sign to multiplication and flip the second fraction so that the denominator is the numerator and the numerator is the denominator. You would then just multiply as normal to get 1/3.

Answer:

About 2.72

Step-by-step explanation:

From reading the comments, I suppose you meant v actually means x so:

14 × 14 = 196

196 ÷ 72 ≈ 2.72

Hope this helped! :)

Answer:

Hello!

I'm not sure what the " v " means but I think you meant to put x instead of v

____________________

14 x 14 = 196

196 ÷ 72 = [tex]\frac{49}{18}[/tex]

Step-by-step explanation: Reduce the expression, if possible, by cancelling the common factors.

Hope I got this right.

Answer:

Oregon:

Median: 467.5

Mean: 451.33

Standard Deviation: 113.6

Washington:

median: 380

Mean: 396.6

Standard deviation: 56.3

Step-by-step explanation:

To calculate the median, we need to organize the price and select the value that is in the middle position.

To calculate the mean, we need to sum all the values and divide them by the number of values

To calculate the standard deviation, we need to square the distances between every price and the mean, sum it all and divide them by the number of values less 1 and finally calculate the square root.

So, for Oregon, the organized values are:

$295, $345, $460, $475, $538, $595

The median is a value between $460 and $475. it is calculated as:

[tex]\frac{460+475}{2}=467.5[/tex]

The mean is:

[tex]\frac{295+475+345+595+538+460}{6}=451.33[/tex]

The standard deviation is:

[tex]\sqrt{\frac{(295-451.3)^2+(475-451.3)^2+(345-451.3)^2+(595-451.3)^2+(538-451.3)^2+(460-451.3)^2}{6-1}}=113.6[/tex]

At the same way, we can calculate the median, mean, and standard deviation for Washington and get:

median: 380

Mean: 396.6

Standard deviation: 56.3

Answer:

V= -2000t + 20000

Step-by-step explanation:

Let m be the slope of our function :

Let's check :

Answer:

I think this is the distributive property.

Step-by-step explanation:

Answer:

A, C, E, G

Step-by-step explanation:

Answer:

x + 2x + 1/2x = 224

Step-by-step explanation:

x + 2x + 1/2x = 224

3.5x = 224

x= 64

64×2=128

Hen baked 128 cookies on the second day

Answer:

  y = (1/3)x +4

Step-by-step explanation:

The line intercepts the y-axis at y=4. It has a "rise" of 1 unit for each "run" of 3 units, so its slope is rise/run = 1/3.

The slope-intercept form of the equation of a line is ...

  y = mx + b . . . . . where m is the slope and b is the y-intercept.

When we put the proper numbers in the equation, we have ...

  y = (1/3)x + 4

Answer:

[tex]\boxed{\sf \ \ \ x=-9 \ \ or \ \ x=2 \ \ \ }[/tex]

Step-by-step explanation:

hello,

[tex]2x^2+7x-14=x^2+4\\<=> 2x^2+7x-14-x^2-4=0\\<=> x^2+7x-18=0\\<=>x^2-2x+9x-18=0\\<=> x(x-2)+9(x-2)=0\\<=> (x+9)(x-2)=0\\<=> x+9 = 0 \ \text{or} \ x-2=0\\<=> x = -9 \ \text{or} \ x=2[/tex]

hope this helps

Answer:

4 sqrt(7)

Step-by-step explanation:

We can use the leg rule

hyp            leg

------- = -------------------

leg          part

9+7          z

------- = -------------------

z          7

Using cross products

(9+7) *7 = z^2

16*7 = z^2

112 = z^2

Taking the square root of each side

sqrt( 16*7) = sqrt(z^2)

4 sqrt(7) = z

Answer:

Length of each side of the square = 8 cm

Step-by-step explanation:

In the figure attached, diagrams of a right triangle and a square have been given.

"Area of the square is twice the area of the triangle."

Let one side of the square = x cm

Therefore, area of the square = x²

Area of the given triangle = [tex]\frac{1}{2}(\text{Base})(\text{Height})[/tex]

                                           = [tex]\frac{1}{2}(16)(4)[/tex]

                                           = 32 cm²

Therefore, x² = 2 × 32

x² = 64

x = 8 cm

Therefore, length of each side of the square will be 8 cm.

I hope this helps you

Answer:  B) sin θ = 5/13    and    D) tan θ = 5/12

Step-by-step explanation:

[tex]\csc\theta=\dfrac{r}{y}=\dfrac{13}{5}[/tex]

Use Pythagorean Theorem: x² + y² = r² to calculate x = 12

[tex]\sin \theta=\dfrac{y}{r}=\dfrac{5}{13}\qquad \qquad \qquad \csc \theta=\dfrac{r}{y}=\dfrac{13}{5}\\\\\\\\\cos \theta=\dfrac{x}{r}=\dfrac{12}{13}\qquad \qquad \qquad \sec \theta=\dfrac{r}{x}=\dfrac{13}{12}\\\\\\\\\tan \theta=\dfrac{y}{x}=\dfrac{5}{12}\qquad \qquad \qquad \cot \theta=\dfrac{x}{y}=\dfrac{12}{5}[/tex]

Answer:

The answer is option C.

Step-by-step explanation:

h(x) = 2(3x – 5) = 6x - 10

k(x) = –2x + 1

h • k (x) = (6x - 10) ( - 2x + 1)

= - 12x² + 6x + 20x - 10

The final answer is

= - 12x² + 26x - 10

Hope this helps you

Answer:

C)  h · k(x) = –12x2 + 26x – 10

Step-by-step explanation:

Extract the normal vectors from the given planes:

[tex]-2x+y+z+2=0\implies\vec n_1=(-2,1,1)[/tex]

[tex]x+y-3z+1=0\implies\vec n_2=(1,1,-3)[/tex]

(which are unique up to their signs, meaning either [tex]\vec n_1[/tex] or [tex]-\vec n_1[/tex] are valid choices for the normal vector)

The third plane must be perpendicular to both these given planes, which means it would be parallel to both [tex]\vec n_1[/tex] and [tex]\vec n_2[/tex], which in turn means its own normal vector [tex]\vec n_3[/tex] should be perpendicular to both [tex]\vec n_1[/tex] and [tex]\vec n_2[/tex].

Enter the cross product:

[tex]\vec n_3=\vec n_1\times\vec n_2=(-4,-5,-3)[/tex]

or (4, 5, 3), which also works.

The given plane passes through (-1, 1, 4), so its equation is

[tex](x+1,y-1,z-4)\cdot\vec n_3=0[/tex]

Simplify:

[tex](x+1,y-1,z-4)\cdot(4,5,3)=0[/tex]

[tex]4(x+1)+5(y-1)+3(z-4)=0[/tex]

[tex]\boxed{4x+5y+3z=13}[/tex]

Answer:

52

Step-by-step explanation:

the total is 180

so u add 61 and 67 which gives u 128

so u subtract 180 and 128 which gives u 52

hope this helps

Answer:the answer is 52

Step-by-step explanation:

First a triangle equals 180 degrees. Knowing that Q is 67 degrees and R is 61 degrees 67 plus 61 is 128. 180 subtract 128 is 52 therefore S is 52 degrees.

Answer:

Step-by-step explanation:

Given figure : Trapezium

Upper base of trapezium ( b1 ) = 7

Lower base ( b2 ) = 3

Height ( h ) = 3

Now, finding the area of trapezium:

[tex] \frac{1}{2} (b1 + b2)h[/tex]

Plugging the values

[tex] \frac{1}{2} \times (7 + 3) \times 3[/tex]

Calculate the sum

[tex] \frac{1}{2} \times 10 \times 3[/tex]

Reduce the numbers with G.C.F 2

[tex]5 \times 3[/tex]

Calculate the product

[tex] = 15 \: {units}^{2} [/tex]

Hope this helps..

Best regards!

Answer:

Lateral surface area of cuboid = 448 ft²

Step-by-step explanation:

Given:

Height of cuboid(h) = 14 ft

Length of cuboid(l) = 9 ft

width of cuboid(b) = 7 ft

Find:

Lateral surface area of cuboid

Computation:

Lateral surface area of cuboid = 2 h(l + b)

Lateral surface area of cuboid = 2(14)(9 + 7)

Lateral surface area of cuboid = 28(16)

Lateral surface area of cuboid = 448 ft²

Answer:

No I don't agree with Clare.

You will get more than 11 yards

Step-by-step explanation:

Answer:

you need 36cups of flour

Step-by-step explanation:

3 cups of flour = 8 ounces of water

x cups of flour = 96 ounces of water

96*3 =8x

288 =8x

288/8=36

x=36

Answer:

  Eva used a side dimension instead of the height.

Step-by-step explanation:

The base needs to be multiplied by the height, then the result needs to be divided by 2. Eva's mistake is using a side dimension instead of the height. Her approach only works for a right triangle.

Eva multiplied the base by the side height, not the actual height.

Step-by-step explanation:

The area of a triangle is b×h×½, or b×h÷2. Eva multiplied the length times one side, as it says in the problem. The actual height of the triangle we don't know, but we know that Eva multiplied the base, 7.8 cm, by the wrong height.

Hope this helps! (Plz give me brainliest, it will help me achieve my next rank.)

Answer:

3x3 +5x2

Step-by-step explanation:

f(x).g(x)

(3x+5)(x2)

(3x×x2)(5×x2)

3x3+5x2