find the length asap

Answer:

The correct option is;

[tex]\overline{AB}\cong \overline{DB}[/tex]  and  [tex]\overline{AC}\cong \overline{DC}[/tex]

Step-by-step explanation:

The steps to prove that ΔABC ≅ ΔDBC with the SSS Congruence postulate

We have;

Statement,                     Reason

BC ≅ BC,                       Reflexive property

[tex]\overline{AB}\cong \overline{DB}[/tex],                      Option selected

[tex]\overline{AC}\cong \overline{DC}[/tex],                      Option selected

ΔABC ≅ ΔDBC,              SSS Congruency Postulate

Therefore, whereby all three sides of the triangles ABC and DBC are congruent, then ΔABC is congruent to ΔDBC.                      

Answer:

AC≅DF

AB≅DE

Step-by-step explanation:

took the test :)

Answer:

y = x-4

Step-by-step explanation:

The first thing we need here is to find the slope m of the line passing through the two points.

Mathematically;

m = y2-y1/(x2-x1)

Where (x1,y1) = (0,-4) and (x2,y2) = (5,1)

Thus; m = (1-(-4))/(5-0) = 5/5 =0

The standard form of the equation is;

y = mx + c

where m is the slope and c is the intercept. We already calculated m to be 1, so the equation of the line would be;

y = x + c

To get c, what we need to do is to use any of the points and substitute the values of x and y to get c

Let’s use (5,1)

1 = 5 + c

c = 1-5

c = -4

So the line would be

y = x -4

Answer:

110

Step-by-step explanation:

There are 200 people in a cinema- This is our total amount.

25 % of the people are men.

.25 times 200= 50

There are 50 men.

1/5 (20%) of the people are women.

.2 times 200 = 40

There are 40 women.

50+40 = 90

There are 90 adults in the cinema.

If there are 200 total people in the cinema, and 90 of them are adult, then 110 of them are children.

The percentage is 55%.

The simplified fraction is 11/20.

The decimal is .55  

Answer:

V = 3534 cm^3

Step-by-step explanation:

The volume of a cylinder is given by

V = pi r^2 h

the radius is 7.5 and the height is 20

V = pi ( 7.5)^2 * 20

V =1125 pi cm^3

Using the pi button for pi

V =3534.291735 cm^3

Rounding to the nearest whole number

V = 3534 cm^3

Answer:

b)3534 cm^3

Step-by-step explanation:

To find the area of a cylinder, you first have to find the area of the base which is in the shape of a circle. The area of a circle is given by the equation πr^2. In this case r, the radius, is 7.5 cm. So plugging in 7.5 for r you get 7.5^2 × π. Plugging in 3.1415 for π you get ~176.671. Now all you do is multiply this by the height, 20cm, and get the answer of ~3534 cm^3.

Answer:

The car's average speed for the entire journey = 84.315 km/h

Step-by-step explanation:

Correct Question

A car travels the first 50km of its journey at an average speed of 25m/s and the next 120 km at an average speed of 80km/h. the car completes the last part of its journey at an average speed of 90km/h in 35 minutes. Find the average speed for its entire journey, giving your answer in km/h.

Solution

Average speed is given as total distance travelled divided by total time taken.

So, we will compute the distance covered for each part of the journey and the corresponding time it takes to cover each of these distances.

- The car travels the 50 km first part of the journey at a speed of 25 m/s.

25 m/s = 90 km/h

We have the distance covered in the first part of the journey, now, we need the time taken to cover the distance.

Speed = (Distance/Time)

Time = (Distance/Speed)

Distance = 50 km, Speed = 90 km/h

Time = (50/90) = 0.5556 hr

- The next part, the car covers 120 km at a speed of 80 km/h

Time = (Distance/Speed) = (120/80) = 1.5 hr

- For the last part of the journey, the car travels with an average speed of 90 km/h for 35 minutes.

35 minutes = (35/60) hr = 0.5833 hr

Here, we need to calculate the distance covered for the last part.

Speed = (Distance/Time)

Distance = (Speed) × (Time) = 90 × 0.5833 = 52.5 km

Total distance covered = 50 + 120 + 52.5 = 222.5 km

Total time taken = 0.5556 + 1.5 + 0.5833 = 2.6389 hr

Average Speed = (222.5/2.6389) = 84.315 km/h

Hope this Helps!!!

Answer:

Step-by-step explanation: so you calculate how many people ate chicken, beef, fish or are vegetarian then you will add it all together

chicken=128

beef= 80

fish=32

vegetarian=112

128+80+32+112= 352 people ate at the restaurant

Answer:

Altogether, 88 people went to the restaurant.

Step-by-step explanation:

Answer:

The volume of the composite figure is 162.7 in^3

Step-by-step explanation:

Here, we have a cylinder placed over a cube

The volume of the cube is L^3

With L being the length of its side = 5

The volume of the cube is 5^3 = 125 in^3

The volume of the cylinder is pi * r^2 * h

with r = 2 in and h = 3 in

The volume of the cylinder = 22/7 * 2^2 * 3 = 37.699 = 37.7 in*3

Total volume is thus;

37.7 + 125 = 162.7 in^3

Answer:

C: 38 units

hope this helps!!

Answer:

not d

Step-by-step explanation:

i tried it hehhe

Answer: 60 square units

Step-by-step explanation:

Answer:

When two vectors are parallel, it's because the angles of inclination are equivalent. They are defined by

[tex]\theta = tan^{-1}(\frac{y}{x} )[/tex]

So, we just need to find the angle for each vector and see if they are equivalent.

We have vectors [tex](3,1)[/tex] and [tex](-13,-1)[/tex]. You already can deduce that these vectors are not parallel, because, their divisions are not equivalent.

[tex]\frac{1}{3} \neq \frac{-1}{-13}[/tex]

Which will give different angles in the end.

Let's try the other pair of vectors [tex](2,3)[/tex] and [tex](-3.-2)[/tex]. Their division would be

[tex]\frac{3}{2} \neq \frac{-2}{-3}\\ 1.5 \neq 0.67[/tex]

As you can observe, their divisions are not equivalent, which means their tangents are not equivalent.

Therefore, those vectors are not parallel, because they don't have equivalent angles of inclination, not matter if they are pointing to the same or different direction.

Answer:

126 people

Step-by-step explanation:

9/5 is the ratio tea/coffee

let x be the one who preferred coffee and x+36 preferred tea

9/5=x+36/x

9x=5x+5(36)

9x-5x=180

4x=180

x=180/4=45

x=45 coffee

x+36=45+36=81

45+81=126

check : 81/45= 9/5

Answer:

(2)They are perpendicular.

Step-by-step explanation:

Answer:

Colin got £126

Step-by-step explanation:

Here we want to know how much Colin got from the sharing.

We can collapse the ratio to mean;

Colin : Caroline + Sarah

= 9:1 + 1 = 9:2

So total ratio is 9 + 2 = 11

If Caroline and Sarah got £28 we need to find the total money shared

Let the total money shared be £x

Thus;

2/11 * x = 28

2x = 11 * 28

x = (11 * 28)/2

x = 11 * 14 = £154

So the amount of money Colin got would be;

£154 - £28 = £126

Answer:

9

Step-by-step explanation:

Answer:

9m

Step-by-step explanation:

Let x be the length of the rectangle and P the perimeter

P= 4*2+ 2x

26= 8+2x

18= 2x

x= 9 m

Answer:

The given relation R is equivalence relation.

Step-by-step explanation:

Given that:

[tex]((a, b), (c, d))\in R[/tex]

Where [tex]R[/tex] is the relation on the set of ordered pairs of positive integers.

To prove, a relation R to be equivalence relation we need to prove that the relation is reflexive, symmetric and transitive.

1. First of all, let us check reflexive property:

Reflexive property means:

[tex]\forall a \in A \Rightarrow (a,a) \in R[/tex]

Here we need to prove:

[tex]\forall (a, b) \in A \Rightarrow ((a,b), (a,b)) \in R[/tex]

As per the given relation:

[tex]((a,b), (a,b) ) \Rightarrow ab =ab[/tex] which is true.

[tex]\therefore[/tex] R is reflexive.

2. Now, let us check symmetric property:

Symmetric property means:

[tex]\forall \{a,b\} \in A\ if\ (a,b) \in R \Rightarrow (b,a) \in R[/tex]

Here we need to prove:

[tex]\forall {(a, b),(c,d)} \in A \ if\ ((a,b),(c,d)) \in R \Rightarrow ((c,d),(a,b)) \in R[/tex]

As per the given relation:

[tex]((a,b),(c,d)) \in R[/tex] means [tex]ad = bc[/tex]

[tex]((c,d),(a,b)) \in R[/tex] means [tex]cb = da\ or\ ad =bc[/tex]

Hence true.

[tex]\therefore[/tex] R is symmetric.

3. R to be transitive, we need to prove:

[tex]if ((a,b),(c,d)),((c,d),(e,f)) \in R \Rightarrow ((a,b),(e,f)) \in R[/tex]

[tex]((a,b),(c,d)) \in R[/tex] means [tex]ad = cb[/tex].... (1)

[tex]((c,d), (e,f)) \in R[/tex] means [tex]fc = ed[/tex] ...... (2)

To prove:

To be [tex]((a,b), (e,f)) \in R[/tex] we need to prove: [tex]fa = be[/tex]

Multiply (1) with (2):

[tex]adcf = bcde\\\Rightarrow fa = be[/tex]

So, R is transitive as well.

Hence proved that R is an equivalence relation.

The relation R is an equivalence if it is reflexive, symmetric and transitive.

The order to options required to show that R is an equivalence relation are;

Reasons:

Prove that the relation R is reflexive

Reflexive property is a property is the property that a number has a value that it posses (it is equal to itself)

The given relation is ((a, b), (c, d)) ∈ R if and only if a·d = b·c

By multiplication property of equality; a·b = b·a

Therefore;

((a, b), (a, b)) ∈ R

Prove that the relation, R, is symmetric

Given that if ((a, b), (c, d)) ∈ R then we have, a·d = b·c

Therefore, c·b = d·a implies ((c, d), (a, b)) ∈ R

((a, b), (c, d)) and ((c, d), (a, b)) are symmetric.

Prove that R is transitive

Symbolically, transitive property is as follows; If x = y, and y = z, then x = z

From the given relation, ((a, b), (c, d)) ∈ R, then a·d = b·c

Therefore, ((c, d), (e, f)) ∈ R, then c·f = d·e

By multiplication, a·d × c·f = b·c × d·e

a·d·c·f = b·c·d·e

Therefore;

a·f·c·d = b·e·c·d

a·f = b·e

Which gives;

Therefore;

R is an equivalence relation, since R is reflexive, symmetric, and transitive.

Based on a similar question posted online, it is required to rank the given options in the order to show that R is an equivalence relation.

Learn more about equivalent relations here:

https://brainly.com/question/1503196

Answer:

0.075

Step-by-step explanation:

To represent 7 1/2 as a decimal, it would be 0.075 since there are 7 hundredths and half a hundredth.

Answer:

she wills substitute r with 7%.

Step-by-step explanation:

Just did it.

Answer:

R = 7%

Principal (P)

Rate (R)

Time (t)

Step-by-step explanation:

The full intrest rate formula is i=prt

You are looking for r

R is the interest rate 7%

So i = 12,876*7%*3years will be the full equation.

Answer:

(x + 2)

Step-by-step explanation:

When we factor the expression x² - 8x - 20, we should get (x + 2)(x - 10).

Alternatively, we can use synthetic division or long division to get our answer.

Answer:

x + 2

Step-by-step explanation:

got it right edg '22

Answer:a

Step-by-step explanation:

Answer:

Hello!

`~~~~~~~~~~~~~~~~~~~~~

Your answer would be (C)  10x2 + 18x+ 30

~~~~~~~~~~~~~~~~~~~~~~

Hope this helped you!

P . S I would've put the explaintion but it's to long.

Answer:

I hope it's correct

Answer:

30 people

Step-by-step explanation:

If you start off with 1/2 a lemon for 6 people, then 1 whole would be 12. 1 1/2 would be 18 people and 2 whole lemons would be 24. so 2 1/2 is 30 people.

Answer:

$43.64

Step-by-step explanation:

Answer:

1.64

Step-by-step explanation:

To find the tax, multiply the cost by the tax rate

42 * 3.9%

Change to decimal form

42 *.039

1.638

Round to the nearest cent

1.64

Answer:

k≥12

Step-by-step explanation:

If k must be equal to or greater than 12, it can be expressed as k≥12. This is because the sign ≥ shows that k can both be 12 and could be higher than 12.

I hoped that helped!

:)

Answer:

c

Step-by-step explanation:

it says above

Answer: 343 cm³

Step-by-step explanation:

The surface area of a cube is 6s^2, where s is the side length of a square.  Thus, first do 294/6 to get 49.  Then take the square root of 49 to get that each side of the cube is 7.  The volume of a cube is s^2, so simply do 7*7*7 to get that the volume of the cube is 343cm^3

Hope it helps <3

Answer:

V =343 cm^3

Step-by-step explanation:

The surface area of a cube is given by

SA = 6s^2 where s is the side length

294 = 6s^2

Divide by 6

294 / 6 = s^2

49 = s^2

Take the square root of each side

sqrt(49) = sqrt(s^2)

7 =s

The volume of a cube is

V = s^3

V = 7^3

V =343 cm^3

Answer:

a) 12 (Simply divide 4800/5 to get 960.  Then divide 960/80 to get 12)

b) 2100 (Simply multiply 12 by 25 by 7)

Hope it helps <3

Answer:

About $3.28

Step-by-step explanation:

Divide 24.33 by 7.4

Answer:

3.28783783784...

Step-by-step explanation:

You're description could turn into 24.33 : 7.4.

You turn 7.4 into 1, and divide 7.4 / 1.

(It is 7.4)

Then, you divide 24.33 / 7.4.

It is 3.28783783784.......

or, If you want you're answer close to an natural number, It is 3.