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Answer:definition of midpoint, angle BCA is congruent to angle DCA

The triangles ΔABC and ΔADC are congruent triangles by

a) definition of mid-point

b) measure of ∠ACB = measure of ∠ACD = 90°

Transformations change the size or position of shapes. Congruent shapes are identical, but may be reflected, rotated or translated. Scale factors can increase or decrease the size of a shape. Congruent Triangles simply mean the triangles that possess the same size and shape

The three sides are equal (SSS: side, side, side)

Two angles are the same and a corresponding side is the same (ASA: angle, side, angle)

Two sides are equal and the angle between the two sides is equal (SAS: side, angle, side)

A right angle, the hypotenuse and a corresponding side are equal (RHS, right angle, hypotenuse, side)

Given data ,

Let the first triangle be represented as ΔABC

Let the second triangle be represented as ΔADC

Now , the side AC is the common bisector of both the triangles such that

C is the midpoint of BD

So , the measure of side BC = measure of side CD

And , the perpendicular bisector is right angle

So , the measure of ∠ACB = measure of ∠ACD = 90°

And , the measure of AC = measure of AC ( reflexive property )

Therefore , the triangles are congruent by SAS theorem

Hence , the triangles are congruent

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Answer: 5^5.

Step-by-step explanation: Using the equation x^a*x^b = x^(a+b), we find that 5^2*5^3 is equal to 5^5.

Answer:

Interest would be $15 every 3 years

Step-by-step explanation:

Interest = Principal x Rate x Time

Interest = 100 x 5% x 3

Interest = 5 x 3

Interest = 15

Answer:

The answer is 8

Step-by-step explanation:

Since there's already a negative sign right beside h and one outside of it, the answer has to be positive, and since 12-4=8, the answer is 8

Answer:

A

Step-by-step explanation:

Answer:

the answer is C hope this helps

The given function is

[tex]h(x) = \{ (0,1), (2,3), (-4, 1) \}[/tex]

The inverse function is

[tex]h^{-1}(x) = \{ (1,0), (3,2), (1,-4)\}[/tex]

To get the inverse, we swap each x and y coordinate.

The rule is [tex](x,y) \to (y,x)[/tex]

So that's why the point (0,1) becomes (1,0) for instance.

Answer:

Complementary, x=78

Step-by-step explanation:

90= (x-8)+20

complementary angles add up to 90 degrees.

Answer:

Complementary, x is 78

Step-by-step explanation:

Let's first define what complementary and supplementary angles are. Complementary angles add up to 90 degrees, and supplementary add up to 180. From this image, we can see that this is a right angle. Right angles add up to 90 degrees, therefore, this is a complementary angle.

Now, because we know that it is 90 degrees and that (x-8)+(20) = 90, then we can solve for x. However, if the angle is unknown, then we would do x-8=20. In this case, sense we know for sure this angle is complementary, we do

(x-8)+(20) = 90

X+12=90 We combined like terms

X=78 Inverse operations

You can plug 78 into x and check to see if it is correct if they are 90 degrees total.

Answer:

he would get 10$

Step-by-step explanation:

if you divide 500 by 1 you get 5 times that by 2

Answer:

10:18   10 gal of blue paint and 18 gal of yellow paint.

Step-by-step explanation:

Answer:

i'm going to guess either 5:9 or 9:5...

Step-by-step explanation:

Step-by-step explanation:

r-5r-6s+8s-15

-4r+2s-15

= 2s-4r-15

The simplified form of the given expression is -4r+2s-15.

The given expression is r-5r-6s+8s-15.

An expression is a combination of terms that are combined by using mathematical operations such as subtraction, addition, multiplication, and division.

The given expression can be solved as follows:

r-5r-6s+8s-15

= -4r+2s-15

Therefore, the simplified form of the given expression is -4r+2s-15.

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Answer:

-316

Step-by-step explanation:

...................

Answer:

we conclude that the intervals in which the function P(t) is decreasing are:

Step-by-step explanation:

At x< 1, the function P(t) is decreasing

From the figure, it is clear that the function seems to be increasing

from (1, 3) and then 4 to onwards.

But it is clear that the function seems to be decreasing from the x < 1 and from the interval (3, 4).

Therefore, we conclude that the intervals in which the function P(t) is decreasing are:

Answer : 12z - 32

Explaination:

Uhhh yeah math?

Answer:

6 boys

Step-by-step explanation:

Subtract to find the total number of girls.

9 - 2 = 7 girls

Write a ratio from boys to girls.

2:7

Divide to find the scale factor.

21 / 7 = 3

Multiply to find the total number of boys.

3 * 2 = 6

Best of Luck!

Answer:

182.353745455

Answer:180

Step-by-step explanation:

Answer:

d

Step-by-step explanation:Angle 12 & 10 are effectively corresponding angles, but angle 10 & 7 are alternate interior angles. Anyways, Angle 12 & 10 are congruent and 10 & 7 are congruent. At the end, the three angles 12, 10, and 7 have the same measure. If we put it otherwise, the line B is intersecting line D which form right angles equals to 90 degrees, so angle 12 = 90, and the same happens with angle 10 and 7, so the three angles are congruent, but at the same time, angle 7 is supplementary with angle 12 because their sum is equal to 180, (90 + 90 = 180). If you think from different angles is hard to choose the right answer, so what I guess is that we don't need to take into account the angle 10, just the fact that line A intersect line C, and Line B intersect line D forming right angles, and that angle 7 and 12 are right angles which sum equals 180, therefore, we could say that they are supplementary angles, but also congruent because they measure the same, so at the end,

Answer:

4.44 infinet

Step-by-step explanation:

If you are asking and need to round it up it will come up to

4.444

You need to round it up because the 4.444 goes on and on infinitely.

If you needed another answer comment what it is you need and I will answer you on there.

YW

Answer:

500 (or 5) is in the hundreds place, 30 (or 3) is in the tens place, and 8 is in the ones place.

Step-by-step explanation:

500 is five-hundred, 30 is a ten (10, 20, 30, 40...), and 8 is a one because it is a single digit number and no other numbers come before it, unless it is a decimal.

Answer:

pretty sure it's B, its just really hard to see

Step-by-step explanation:

Answer: (0.1118, 0.3454)

Step-by-step explanation:

Confidence interval for population proportion is given by :-

[tex]\hat{p}\pm z^c\sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}[/tex] , where [tex]\hat{p}[/tex]= sample proportion , n= sample size, [tex]z^c[/tex] = critical z-value for c confidence level.

Let p = the proportion of all households in Cherry Creek that pretend not to be home on Halloween.

Given : n= 35

[tex]\hat{p}=\dfrac{8}{35}\approx0.2286[/tex]

Critical z-value for 90% confidence level =1.645

A 90% confidence interval for p, the proportion of all households in Cherry Creek that pretend not to be home on Halloween:

[tex]0.2286\pm (1.645)\sqrt{\dfrac{0.2286(1-0.2286)}{35}}\\\\=0.2286\pm 0.1168\\\\=(0.2286-0.1168,\ 0.2286+0.1168)\\\\=(0.1118,\ 0.3454)[/tex]

∴ Required confidence interval : (0.1118, 0.3454)

Answer:

D. 1000 gallons per hour

Step-by-step explanation:

5000 / 5 = 1000

Answer: If it drained 5000 gallons and there were 5 hours, then 5000 divided by 5 is 1 so that would be answer D.

Hoped this helped!

Answer:

Step-by-step explanation:

5 x ( 9 + 4 ) = ( 5 x __ ) + ( 5 x __ )

using distributive property,

the answer is

( 5 x 9 ) + ( 5 x 4 )

if u want the final answer

it becomes

45 + 20

= 65

Hope this helps

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Answer:

16.66

Step-by-step explanation:

Answer:

16.6666666667

Step-by-step explanation:

you take 100 and divide it by 6 and you will get 16.6666666667 or if you round it you will get 17 dollars

Answer:

im not sour if this is what you want but i got 1.3 repeating

Step-by-step explanation:

u simplify in ur head