The two triangles below are congruent. Which of the following are congruent by CPCTC?

Answer:

(i) 3.438159 kg

(ii) 5.336803297 cm

Step-by-step explanation:

the external diameter = 12 cm, => the radius = 6 cm.

the internal diameter = 12 - 2×2 = 8 cm, radius = 4 cm.

I assume the mass of 1 cm³ (not cm) is 5.4 g (very, very light metal).

the material is in the volume of external sphere minus internal (empty) sphere.

the volume of a sphere is

4/3 × pi×r³

V-e = 4/3 × pi×6³ = 4/3 × pi×216 = 4×pi×72 = 904.7786842 cm³

V-i = 4/3 × pi×4³ = 4/3 × pi×64 = 268.0825731 cm³

V-e - V-i = 4/3 × pi×(216-64) = 4/3 × pi×152 = 636.6961111 cm³

1cm³ = 5.4g

636.6961111 cm³ = 5.4×636.6961111 = 3438.159g = 3.438159 kg

for (ii) we need to work with the volume of the material and calculate backwards to find the radius of the sphere with the full volume of that size.

636.6961111 = 4/3 × pi×r³ = 4/3 × pi×152

152 = r³

r = 5.336803297

Answer:

f(x) > 0 over the interval  (–∞, –4)

Step-by-step explanation:

We know that:

Our curve has a minimum at (-2.5, -12)

Our curve has a maximum at (0, - 3)  (I assume that is a local maximum).

We know that the curve crosses the x-axes at (-4, 0)

We know that the curve crosses the y-axis at (0, -3)

Notice that when our curve crosses the x-axis at (-4, 0), it goes from above the axis to below the axis.

How we know this?

Remember that "crossing" the x-axis means that the sign of f(x) changes.

At the value x = -2.5  (which is larger than x = -4) the function is negative.

f(-2.5) = -12

and:

f(-4) = 0

So we can see that after f(x) crosses the x-axis at x = -4, the function is negative.

This means that before that point, the function must be positive.

So for values of x smaller than -4, the function should be larger than zero.

f(x) > 0 if x < -4

From this, we can conclude that in the range (-∞, –4), the function is above the x-axis.

Then we would write this as:

f(x) > 0 over the interval  (–∞, –4)

The correct option is the last option.

Answer:

Its D

Step-by-step explanation:

Step-by-step explanation:

Against the wind, the wind works against the speed. With the wind, the wind aids the speed.

4(p - w) = 2416

4(p + w) = 2896

p - w = 604

p + w = 724

2p = 1328

p = 664 mph

664 + w = 724

w = 60 mph

Answer: 27

Step-by-step explanation:

[tex]Mean=\frac{16 + 25 + 23 + 12 + 17 + x}{6}=20 \\16 + 25 + 23 + 12 + 17 + x=20(6)\\93+x=120\\x=120-93=27[/tex]

Answer:

27 years old

Step-by-step explanation:

There are originally 5 people in the room.

Their ages are: 16, 25, 23, 12, 17

The sum of their ages is: 93

One person enters the room. That person's age is unknown, so we call it x.

The sum of the ages of the 6 people is:

x + 93

There are 6 people in the room now, so the mean age is (total age divided by number of people):

(x + 93)/6

We are told the mean age is 20.

(x + 93)/6 = 20

x + 93 = 120

x = 27

Answer: 27 years old

Answer:

Each x-coordinate increased by 6 and each y-coordinate decreased by 3.

Step-by-step explanation:

Let us use the coordinates of a and a' as an example

a = (-3, 5) a' = (3, 2)

So -3 is for the x-axis in coordinate a and 3 is for the x axis in coordinate a'

Then -3 + 6 = 3 ( This is the x coordinate for a' )

So 5 is for the y -axis in coordinate a and 2 is for the y axis in coordinate a'

Then 5 - 3 = 2 ( This is the y coordinate for a' )

HOPE THIS HELPED

Answer:

It will be -6≤×≤4

Answer:

what is this question ??

This answer will also same 2.2.4.4.4=2.2.4.4.4

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Value of n:

[tex]5n - 17 = 2n + 1[/tex]

[tex]5n - 2n = 1 + 17[/tex]

[tex]3n = 18[/tex]

[tex]n = \frac{18}{3}[/tex]

[tex]n = 6[/tex]

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

Lengths:

The lengths are given as functions of n, since n = 6:

The length of the sides are: 13 cm, 13 cm and 6 cm.

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

Perimeter:

The perimeter is the sum of the lengths of all sides, so: 13 + 13 + 6 = 32 cm.

A similar question is given at https://brainly.com/question/6139098

Answer: 96 ft²

Step-by-step explanation:

This figure can be divided into two rectangles:

Find the area of both rectangles:

Add them together to find the total area of the figure:

84 + 12 = 96 ft²

Answer:

13 is answer

Step-by-step explanation:

hope it helps

[tex]\huge{\sf \left[{x-2y\atop 6x-2z}\:\:\:{4y-3\atop 2y-z}\right]=\left[{-3\atop 4}\:\:\:{5\atop 3}\right]}[/tex]

Creating equations

[tex]\\ \sf\longmapsto x-2y=-3\dots(1)[/tex]

[tex]\\ \sf\longmapsto 4y-3=5\dots(2)[/tex]

[tex]\\ \sf\longmapsto 6x-2z=4\dots(3)[/tex]

[tex]\\ \sf\longmapsto 2y-z=3\dots(3)[/tex]

[tex]\\ \sf\longmapsto 4y-3=5[/tex]

[tex]\\ \sf\longmapsto 4y=5+3[/tex]

[tex]\\ \sf\longmapsto 4y=8[/tex]

[tex]\\ \sf\longmapsto y=\dfrac{8}{4}[/tex]

[tex]\\ \bf\longmapsto y=2[/tex]

[tex]\\ \sf\longmapsto x-2y=-3[/tex]

[tex]\\ \sf\longmapsto x=-3+2y[/tex]

[tex]\\ \sf\longmapsto x=-3+2(2)[/tex]

[tex]\\ \sf\longmapsto x=-3+4[/tex]

[tex]\\ \bf\longmapsto x=1[/tex]

[tex]\\ \sf\longmapsto 2y-z=3[/tex]

[tex]\\ \sf\longmapsto z=2y-3[/tex]

[tex]\\ \sf\longmapsto z=2(2)-3[/tex]

[tex]\\ \sf\longmapsto z=4-3[/tex]

[tex]\\ \bf\longmapsto z=1[/tex]

Answer:

I think the answer is 2

Step-by-step explanation:

Between 30 and 60 is double b so just divide 4 by 2.

Answer:

I don't understand the equation, please state it differently

Function

It is a function

Answer:

Sunil = 3000 and raj = 2000

Step-by-step explanation:

there are total 5000 and if it will be divided into 5 parts( total of ratio ) then 3 will be equal to 3000 and 2 equal to 2000

Answer:

[tex]f^{-1}[/tex](x) = 0.5x + 2

Step-by-step explanation:

let y = f(x) and rearrange making x the subject , that is

y = 2x - 4 ( add 4 to both sides )

y + 4 = 2x ( divide both sides by 2 )

[tex]\frac{y+4}{2}[/tex] = x

Change y back into terms of x with x = [tex]f^{-1}[/tex] (x)

[tex]f^{-1}[/tex] (x) = [tex]\frac{x+4}{2}[/tex] = 0.5x + 2

Answer: F -1(x)  = 0.5 x + 2

Step-by-step explanation:

Just took the test on edmentum and got a 100

Answer:

4/63

Step-by-step explanation:

20/315 = (20÷5)/(315÷5)

Answer:

y=-4x

Step-by-step explanation:

Parallel to the line, slope is - 4. The equation of line is y=-4x

Answer:

0.5

Step-by-step explanation:

k = y/x

k = 0.5/1

k = 0.5

[tex]\huge\mathsf\green{ANSWER}:—[/tex]

[tex]option \: \: c \: \: \: \frac{3}{4} \: is \: the \: correct \: option[/tex]

Rational numbers are numbers which can be represent in the form of p/q where p and q are integers and q≠0 that's why 3/4 is the correct option

Answers:

===========================================================

Explanation:

I recommend drawing the two triangles as shown below. The diagram isn't to scale, but all that matters is that we get the general idea down.

Your teacher gave you this info:

These two pieces of info are enough to prove that triangle ABC is similar to triangle EDF. Use the angle angle (AA) similarity theorem to do this proof. The order of the lettering matters because it helps us see how the letters pair up.

Since the triangles are similar, the scale factor to go from ABC to EDF is EF/AC = 2/6 = 1/3

In other words, the side lengths of triangle EDF are exactly 1/3 that of the corresponding lengths of ABC. Or we can reverse things to say the sides of ABC are 3 times longer than the sides of EDF.

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

Use this scale factor to help determine the missing length ED.

(ED)/(AB) = scale factor

(ED)/(AB) = 1/3

(ED)/(3.3) = 1/3

ED = (1/3)*(3.3)

ED = 1.1

Note how ED/AB = (1.1)/(3.3) = 11/33 = 1/3

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

While we don't know how long sides BC or DF are, we are told that DF is 3.2 units shorter compared to BC.

This means

DF = BC - 3.2

DF = x - 3.2

Then we can say,

(DF)/(BC) = scale factor

(x-3.2)/(x) = 1/3

3(x - 3.2) = x*1

3x - 9.6 = x

3x - x = 9.6

2x = 9.6

x = (9.6)/2

x = 4.8

So BC is x = 4.8 units long and DF is x-3.2 = 4.8-3.2 = 1.6 units long

Answer:

(2,-7)

Step-by-step explanation:

The point moves down 3 units resulting in (2,-7)

Answer:

Pls give me the answers as soon as possible and make sure that the answers are correct.

Answer:

Step-by-step explanation:

Area of rectangle: l×b

Length = 72mm

= 7.2cm

Breadth = 65mm

= 6.5cm

(We know that 10mm = 1cm)

Area = 7.2×6.5

= 46.8cm²

The area of the rectangle is 46.8cm²

Must click thanks and mark brainliest

Answer:

area of a rectangle is (l×w)

Step-by-step explanation:

1cm=10mm

hb65mm

1cm×65mm

allover10mm

=6.5cm

do the same to 72mm to get 7.2cm

you then say 6.5cm×7.2cm

=46.8cm2

hope this helps

Answer:

I got that AE^2 = 8EC^2

Step-by-step explanation:

Here's what I did. I probably did this wrong, but this might give you an idea on how to solve it.

First, create equations:

AB = BC = AC = DE = 2EC

BD= BC = EC

Then, I used pythagorean theorem (since AD is perpendicular to BC): AD^2 + DE^2 = AE^2

Substitute: (2EC)^2 + (2EC)^2 = AE^2

Simplify: 4EC^2 + 4EC^2 = AE^2

AE^2 = 8CE^2

Answer:

Trinomial, 2

Step-by-step explanation:

Answer:

Trinomial, 2

Step-by-step explanation:

Answer:

[tex]50 N[/tex]

Step-by-step explanation:

To help us find our answer, we need to use Newton's Second law

[tex]F = m \times a[/tex]

Where F is the force (N), m is the mass (Kg) and a is the acceleration (m/s^2, on a planet this would just be the gravity)

So if we know that a person has a mass of 3Kg and weighs 30N, the acceleration (or the gravity on that planet is)

[tex]30 = 3 \times a\\a = 10 m/s^2[/tex]

Now that we know the acceleration we can easily find the weight of the person.

[tex]F = 5 * 10 = 50 N[/tex]