which of the following must be true

Answer:

∠ACB≅∠CAD, Alternate Interior Angles Theorem

∠BAC≅∠DCA, Alternate Interior Angles Theorem

AC≅AC, Reflexive Property of Congruence

By A-S-A congruence, the △ABC≅△CDA.

Step-by-step explanation:

Given the figure:

We are given that:

Side BC || AD

Side AB || DC

Let us have a look at a few properties first.

Alternate Interior Angle Theorem: It states that when two parallel lines are cut by a line then the alternate angles which are on the interior side are equal to each other.

Reflexive Property of Congruence: It states that a side or angle is always congruent to itself.

Now, let us consider the triangles:

△ABC and △CDA.

Side BC || AD

Therefore,

∠ACB≅∠CAD, Alternate Interior Angles Theorem

Side AB || DC

Therefore,

∠BAC≅∠DCA, Alternate Interior Angles Theorem

Also, Side AC is common.

AC≅AC, Reflexive Property of Congruence

Therefore, by A-S-A congruence, the △ABC≅△CDA.

Answer:

15000  ( I THINK)

Step-by-step explanation:

you have to mutiply 100000 times 5 times 3% and you get 100000.

Answer:

:)

Step-by-step explanation:

Examples: 1+2, 1/3+1/4, 2^3 * 2^2

(x+1)(x+2) (Simplify Example), 2x^2+2y a x=5, y=3 (Evaluate Example)

y=x^2+1 (Graph Example), 4x+2=2(x+6) (Solve Example)

Answer:

x=1 half,3

Step-by-step explanation:

Answer:

look at the pic below

Step-by-step explanation:

Answer:

b=24

Step-by-step explanation:

40^2 - 32^2 = 576

√576 = 24

Answer:

.875

Step-by-step explanation:

Answer:

C

3 in per wk

Step-by-step explanation:

12

12×3=15

15+3=18

The constant of proportionality is 3 inches/week

The general equation of a straight line is -

[y] = [m]x + [c]

where -

[m] is slope of line which tells the unit rate of change of [y] with respect to [x].

[c] is the y - intercept i.e. the point where the graph cuts the [y] axis.

The equation y = Kx also represents direct proportionality. Here, K is called constant of proportionality. It is same as slope.

We have a plant grows at a constant rate.

The data recorded by Daniel is as follows -

Week 4       12 inches

Week 5       15 inches

Week 6       18 inches

The equation y = Kx also represents direct proportionality. Here, K is called constant of proportionality. We have to find the slope of the line represented by the data as -

K = slope

K = (15 - 12)/(5 - 4)

K = 3/1

K = 3

Therefore, the constant of proportionality is 3 inches/week.

To solve more questions on straight lines, visit the link below-

brainly.com/question/29030795

#SPJ2

Answer:

3x+85= 21

or, 3x= 85- 21

or, 3x= 64

or,x= 64/3

;. x= 21.3

Step-by-step explanation:

the value of x is 21.3

Answer:

8 and 24

Step-by-step explanation:

let width be X

then length will be 3x

2(3x+X)=64

3x+X=32

4x=32

X=8

then 3x=24

Answer:

[tex]x= 3i, -3i[/tex]

Step-by-step explanation:

please mark me brainliest :)

Answer:

B

Step-by-step explanation:

Answer:

12.3

Step-by-step explanation:

6*205=1230

1230/100=12.3

Answer:

3300ft

Step-by-step explanation:

5280 x 0.625=3,300

Answer:

4(49a²+7ab+9)

Step-by-step explanation:

Answer: Y=mx+b

m=-4/5

Step-by-step explanation:

Answer:-2/3

Step-by-step explanation:

Slope formula is (y2-y1)/(x2-x1)

(4--4)/(8-20)

8/-12

Simplify

-2/3

Answer:

x=-1

Step-by-step explanation:

7x-5=2x

-7x -7x

-5=-5x

-5/-5=-5x/-5

-1=x

hopefully this helps :)

Answer:

A reflection of the line segment across the y-axis

Step-by-step explanation:

hope you are having a great day ଘ(੭ˊᵕˋ)੭* ੈ✩‧₊˚

Answer:

B. a reflection of the line segment across the y-axis

Answer:

39.00%

Step-by-step explanation:

Given

Dimension: 36⅞ by 19 by 24⅝

Volume of Water = 6039in³

Required

What percent of the volume of the aquarium is filled with water?

First, we need to calculate the volume of the aquarium.

This is calculated by multiplying the dimensions of the aquarium

Volume = 36⅞ * 19 * 24⅝

Volume = 295/8 * 19 * 197/8

Volume = 1104185/64

Volume = 17252.89

The percent filled with water is calculated using the following formula:

%Percent = (Volume of water * 100%)/(Volume of aquarium)

%Percent = (6039 * 100%)/(17252.89)

%Percent = (603900%)/(17252.89)

%Percent = 39.00% (approximated)

Hence, the water occupies 39.00% of the aquarium

Answer:

-1.20

Step-by-step explanation:

You are correct because you just had to subtract 2.50 - 3.75 and you get -1.20.

Answer:

-1.25 feet below surface level.

Answer:

The probability is 2/9

Step-by-step explanation:

Here , we want to find the probability of getting a violet ball first and a pink ball secondly if the violet ball is replaced

probability = number of balls of same color/total number of balls

The total number of balls = (2 + 4) = 6 balls

Probability of selecting a violet = 2/6 = 1/3

Probability of selecting a pink afterwards with replacement = 4/6 = 2/3

So the probability of selecting the balls in that order will be;

1/3 * 2/3 = 2/9

Answer:

1000 miles

Step-by-step explanation:

Answer:

16786

Step-by-step explanation:

16786

12143

9643

Answer:

yeah yeah i think the answer is rectangle jp

Step-by-step explanation:

Answer:

no

Step-by-step explanation:

it is not strait

Hope this works!

Answer:

x=28.75

Step-by-step explanation:

Answer:

Mrs. Neduz has 3.75 gallons of soda.

Answer:

These numbers are not the same as 4/9 is bigger than 2/5.

Step-by-step explanation:

As we have to compare the decimal forms of 2/5 and 4/9.

We determine that the numbers in decimal forms are:

[tex]\frac{2}{5}=0.4[/tex]

[tex]\frac{4}{9}=0.44444...\:[/tex]

so

[tex]\frac{4}{9}=0.44444[/tex] is clearly bigger than [tex]\frac{2}{5}=0.4[/tex].

Therefore, these numbers are not the same as 4/9  is bigger than 2/5.

Answer:

[tex] \frac{15}{13} = 1.1538461538[/tex]

Step-by-step explanation:

[tex] \frac{3 \times 5}{13} = \frac{15}{13} = 1.1538461538[/tex]

Step-by-step explanation:

=6÷2(1+2)

=6÷2(3)

=3×3

=9 ans