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Bad White [126]
3 years ago
10

Look at the figure. Name the postulate or theorem you can use to prove the triangles congruent.

Mathematics
1 answer:
valentinak56 [21]3 years ago
4 0

Answer:

AAS Theorem

Step-by-step explanation:

we can see that

angle ZVY ≅ angle WVY

angle VZY ≅ angle VWY

side VY shared by both triangles.

by Angle- Angle- SIde (AAS), the triangles are congruent.

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Factor: 81y^2-49<br> Your answer
oksian1 [2.3K]

Answer:(9y-7)(9y+7)

Step-by-step explanation:

81y^2-49

=(9y)^2-(7)^2

=(9y-7)(9y+7)

4 0
2 years ago
Find two positive integers such that the sum of the first number and four times the second number is 1000, and the product of th
vladimir2022 [97]

Answer:

The two numbers are:

x = 500

y = 125

Step-by-step explanation:

We want to find two numbers x and y, such that:

x + 4*y = 1000

f(x, y) = x*y is maximum.

From the first equation, we can isolate one of the variables to get

x = 1000 - 4y

now we can replace it in f(x, y):

x*y = (1000 - 4*y)*y  = 1000*y - 4*y^2

So now we want to maximize the function:

f(y) =- 4*y^2 + 1000*y

where y must be an integer.

Notice that this is a quadratic equation with a negative leading coefficient (so the arms of the graph will open downwards), thus, the maximum will be at the vertex.

Remember that for a general quadratic equation:

y = a*x^2 + bx + c

the x-value of the vertex is:

x = -b/(2*a)

so, in the case of:

f(y) =- 4*y^2 + 1000*y

the y-value of the vertex will be:

y = -1000/(2*-4) = 1000/8 = 125

So we found the value of y.

now we can use the equation:

x = 1000 - 4*y

x = 1000 - 4*125 = 1000 - 500 = 500

x = 500

Then the two numbers are:

x =500

y = 125

6 0
2 years ago
Ms Wallwill Roll a single number cube. What is the What is the probability she will roll an even number ?
sveta [45]

Answer:

50/50

Step-by-step explanation:

half the numbers are odd, half even, on a die, so its a 50/50 chance

7 0
3 years ago
James determined that these two expressions were equivalent expressions using the values of x = 4 and x = 6. Which statements ar
GarryVolchara [31]

Answer:

When x=2, both expressions have a value of 18.

The expressions have equivalent values for any value of x.

The expressions have equivalent values if x=8

Step-by-step explanation:

James determined that these two expressions were equivalent expressions using the values of x = 4 and x = 6. Which statements are true? Check all that apply. 7 x + 4 and 3 x + 5 + 4 x minus 1

When x = 2, both expressions have a value of 18.

7x + 4

= 7(2) + 4

= 14 + 4

= 18

3x + 5 + 4x - 1

3(2) + 5 + 4(2) - 1

6 + 5 + 8 - 1

= 18

The expressions are only equivalent for x = 4 and x = 6.

• This is not true because the expression is also equivalent for x = 2

The expressions are only equivalent when evaluated with even values.

When x = 1

7x + 4

7(1) + 4

= 7 + 4

= 11

3x + 5 + 4x - 1

3(1) + 5 + 4(1) - 1

3 + 5 + 4 - 1

= 11

The expressions have equivalent values for any value of x.

Yes, it has an equivalent value at any value of x

The expressions should have been evaluated with one odd value and one even value.

When x = 0, the first expression has a value of 4 and the second expression has a value of 5.

7x + 4

7(0) + 4

= 0 + 4

= 4

3x + 5 + 4x - 1

3(0) + 5 + 4(0) - 1

0 + 5 + 0 -1

= 4

The expressions have equivalent values if x = 8.

7x + 4

7(8) + 4

56 + 4

= 60

3x + 5 + 4x - 1

3(8) + 5 + 4(8) - 1

24 + 5 + 32 - 1

= 60

6 0
3 years ago
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You bought a car for $20,000. You have owned it for one year, and it is now worth $16,000. What is the percent decrease in your
Ganezh [65]
I think it'd be 20%.. I could be wrong. 
7 0
3 years ago
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