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3 years ago

5. It is known that AABC = ADEF. If AB = 5, BC = 10, AC = 8, and DF = 2x-6, then solve for the value of

Mathematics

1 answer:

lorasvet [3.4K]3 years ago

3 0

Answer:

The value of x is 7

Step-by-step explanation:

we know that

If two figures are congruent, then the corresponding angles and the corresponding sides are equal

In this problem

Triangles ABC and DEF are congruent

ABC≅DEF

therefore

AB=DE ----> equation A

AC=DF ----> equation B

BC=EF ----> equation C

Substitute the given values in the equation B

$8=2x-6$

Solve for x

$2x=8+6$

$2x=14$

$x=7$

therefore

The value of x is 7

The draw in the attached figure

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For a school play, Rico bought 3 adult tickets and 5 child tickets for $40. Sasha bought 1 adult ticket and 5 child tickets for

Serhud [2]

The cost of one adult ticket is $7.5 and one child ticket is $3.5

Julia will pay $48 for 5 adult tickets and 3 child tickets.

Step-by-step explanation:

Let,

Cost of one adult ticket = x

Cost of one child ticket = y

According to given statement;

3x+5y=40 Eqn 1

x+5y=25 Eqn 2

Subtracting Eqn 2 from Eqn 1

$(3x+5y)-(x+5y)=40-25\\3x+5y-x-5y=15\\2x=15$

Dividing both sides by 2

$\frac{2x}{2}=\frac{15}{2}\\x=7.5$

Putting x=2.5 in Eqn 1

$3(7.5)+5y=40\\22.5+5y=40\\5y=40-22.5\\5y=17.5$

Dividing both sides by 5

$\frac{5y}{5}=\frac{17.5}{5}\\y=3.5$

The cost of one adult ticket is $7.5 and one child ticket is $3.5

5 adult tickets = 5*7.5 = $37.5

3 child tickets = 3*3.5 = $10.5

Total = 37.5+10.5 =$48

Julia will pay $48 for 5 adult tickets and 3 child tickets.

Keywords: linear equation, subtraction

Learn more about subtraction at:

#LearnwithBrainly

8 0

3 years ago

The function f(x)=50⋅0.8x models the number of ants in Jonathan's ant farm after it is stricken by a deadly ant disease, where x

alina1380 [7]

Answer:

Step-by-step explanation:

In the exponential growth/decay function

$y=a(b)^x$ , in our situation,

y is the number of ants remaining in the colony after the growth or decay,

a is the initial number of ants in the colony, and

b is the growth/decay rate. Rule: if b is greater than 1, the function is growth; if b is greater than 0 but less than 1, the function is decay.

Our equation looks like this (it's given):

$y=50(.8)^x$

a = 50, which is the initial number of ants in the colony.

b = .8 (which actually means that then number of ants is declining by 20% each week). Since .8 is a fraction of 1, this is decay.

So far, we know that 1 and 4 are true. Let's look at 5. We have to do some solving to find out if it's true or not. If the number of ants after x = 2 weeks is 32, then we plug in 2 for x and see if the y we get as the answer is 32:

$y=50(.8)^2$ and

y = 50(.64) so

y = 32

5 is true as well. Let's test 6 by replacing x with 8 and seeing if y = 10:

$y=50(.8)^8$ and

y = 50(.16777216) so

y = 8.388

6 is not true.

1, 4, 5 are true

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