All categories

2 years ago

In the figure, CD = EF and AB = CE. Complete the statements to prove that AB = DF.

Mathematics

2 answers:

myrzilka [38]2 years ago

5 0

Answer:

answers is c

Step-by-step explanation:

CD=EF -----> given

CD+ DE= EF+ DE -----> add DE to both side

CE = CD+DE

DF= EF+ DE

CE=DF -----> transitive property of equality, since CD+DE = EF+ DE

Since CE=DF and AB=CE (given), then AB=DF

viva [34]2 years ago

3 0

Answer:

1. Addition Property of Equality

2. Segment addition

3. Substitution Property of Equality.

4. Transitive Property of Equality.

Step-by-step explanation:

Here, given : CD = EF and AB = CE

To Show: AB = DF

Now, as given in the steps:

1. CD + DE = EF + DE by the (addition) Property of Equality.

As we have added the EQUAL QUANTITY on both sides of the equality.

2.CE = CD + DE and DF = EF + DE by (segment addition).

As here CE and DF are line segments. And the length of a

Line Segment = Sum of all its parts in which it is divided.

3.CE = DF by the (Addition, subtraction, substitution, transitive)Property of Equality.

Here, as we know CE = CD + DE

but CD = EF , so SUBSTITUTE EF in place of CD

⇒ CE = EF + ED = FD (by substitution) Property of Equality.

4.Given, AB = CE and CE = DF implies AB = DF by the (transitive)Property of Equality.

As, x = y , y = z ⇒ x = z is the TRANSITIVE PROPERTY

You might be interested in

Logan can read at a rate of 2/3 page per minute. At that rate, how many pages can he read in 2 hours?

Anon25 [30]

Answer:

240- 360

Step-by-step explanation:

You have to find out how many minutes in an hour which is 60. Then multiply it by 2 for 2 hours to get 120. Then you multiply 2x120 to get 240. Then you multiply 3x120 to get 360.

I'm not sure if this is correct but this is how I would go about it. :)

7 0

2 years ago

The starting salary for a particular job is 1.2 million per annum. The salary increases each year by 75000 to a maximum of 1.5mi

Vlada [557]

<h2>Answer:</h2>

In the 5th year

<h2>Step-by-step explanation:</h2>

For the first year, the salary is 1.2million = 1,200,000

For the second year, the salary is 1.2million + 75000 = 1,200,000 + 75,000 = 1,275,000

For the last year, the salary is 1.5million = 1,500,000

This gives the following sequence...

1,200,000 1,275,000 . . . 1,500,000

This follows an arithmetic progression with an increment of 75,000.

<em>Remember that,</em>

The last term, L, of an arithmetic progression is given by;

L = a + (n - 1)d ---------------(i)

<em>Where;</em>

a = first term of the sequence

n = number of terms in the sequence (which is the number of years)

d = the common difference or increment of the sequence

<em>From the given sequence,</em>

a = 1,200,000 [which is the first salary]

d = 75,000 [which is the increment in salary]

L = 1,500,000 [which is the maximum salary]

<em>Substitute these values into equation (i) as follows;</em>

1,500,000 = 1,200,00 + (n - 1) 75,000

1,500,000 - 1,200,000 = 75,000(n-1)

300,000 = 75,000(n - 1)

$\frac{300,000}{75,000} = n - 1$

4 = n - 1

n = 5

Therefore, in the 5th year the maximum salary will be reached.

3 0

2 years ago

tom and barb have only nickels and dimes. barb has 75 cents and Tom has 90 cents. both have the same number of coins and Tom has

Galina-37 [17]

They both he 9 coin barb has 3 nickels and 6 dimes

4 0

2 years ago

Read 2 more answers

Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function. g(x) = 7x u2 − 1 u2 + 1 du 6x Hint: 7x

VikaD [51]

It looks like you're given

$g(x)=\displaystyle\int_{6x}^{7x}\frac{u^2-1}{u^2+1}\,\mathrm du$

Then by the additivity of definite integrals this is the same as

$g(x)=\displaystyle\int_0^{7x}\frac{u^2-1}{u^2+1}\,\mathrm du-\int_0^{6x}\frac{u^2-1}{u^2+1}\,\mathrm du$

(presumably this is what the hint suggests to use)

Then by the fundamental theorem of calculus, we have

$\dfrac{\mathrm dg}{\mathrm dx}=7\dfrac{(7x)^2-1}{(7x)^2+1}-6\dfrac{(6x)^2-1}{(6x)^2+1}=\dfrac{1764x^4+169x^2-1}{1764x^4+85x^2+1}$

8 0

2 years ago

The sum of the measures of the angles of a triangle is 180. The sum of the measures of the second and third angles is five times

rusak2 [61]

Answer:

$x=30\\y=68\\z=82$

Step-by-step explanation:

x = measure of the first angle

y = measure of the second angle

z = measure of the third angle

The sum of the measures of the second and third (y+z) is five times the measure of the first angle (=5x)

$y+z=5x$

The third angle is 14 more than the second

$z=y+14$

And remember that the sum of these three angles must be equal to 180.

$x+y+z=180$

Let's take these equations

$y+z=5x\\z=y+14\\x+y+z=180$

If you take a look at the first equation, we have y+z = 5x and we have y+z in the third equation as well, we can replace that....

$x+y+z=180\\x+(y+z)=180\\x+(5x)=180$

Distribute the + sign

$x+5x=180$

Combine like terms;

$6x=180$

Divide by 6.

$x=\frac{180}{6}\\ x=30$

We have now defined that the measure of the first angle is 30º.

Let's take another equation... for example $z=y+14$

I'm going to take this one because if I replace x and z in the third equation, all I'll have left will be y.

$x+y+z=180\\30+y+(y+14)=180$

Distribute the + sign and Combine like terms;

$30+y+y+14=180\\44+2y=180\\$

Subtract 44 to isolate 2y.

$2y=180-44\\2y=136$

Now divide by 2.

$y=\frac{136}{2}\\ y=68$

We already have the value of x and y. Once again, replacing this in the third equation will leave us with z to solve for.

$x+y+z=180\\30+68+z=180\\98+z=180\\z=180-98\\z=82$

5 0

2 years ago