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3 years ago

Please help quick!! Given ΔΡHS & ΔCNF, find the values of x, y, and z.

Mathematics

1 answer:

valkas [14]3 years ago

3 0

Answer:

$x=24, y=10, z=17$

Step-by-step explanation:

We know that $\Delta PHS\cong\Delta CNF$ .

Then by CPCTC, ∠P≅∠C, ∠H≅∠N, and ∠S≅∠F.

Therefore, let’s solve for each of the angle relations.

∠P≅∠C:

We know that ∠P is 36°. ∠C is (4z-32)°. Therefore:

$36=4z-32$

Solve for z:

$\begin{aligned}36&=4z-32\;\;\; \text{Add 32 to both sides}\\68&=4z\;\;\;\;\;\;\;\;\;\;\;\text{Divide both sides by 4}\\17&=z\end{aligned}$

So, the value of z is 17.

∠H≅∠N

∠H is (6x-29) and ∠N is 115. So:

$6x-29=115$

Solve for x:

$\begin{aligned} 6x-29&=115\;\;\;\;\;\;\text{Add 29 to both sides}\\6x&=144\;\;\;\;\;\;\text{Divide both sides by 4}\\\ x&=24\end{aligned}$

Therefore, the value of x is 24.

∠S≅∠F

We will need to find ∠S.

We already know that ∠P is 36.

∠H will be (6x-29). Substitute 24 for x to acquire: (6(24)-29)=144-29=115.

A triangle always totals 180°. Therefore, 115+36+∠S=180 or 151+∠S=180.

Therefore, ∠S=29.

∠F is (3y-1). So:

$29=3y-1$

Solve for y:

$\begin{aligned} 29&=3y-1\;\;\;\;\;\text{Add 1 to both sides}\\ 30&=3y\;\;\;\;\;\;\;\;\;\;\text{Divide both sides by 3}\\ 10&=y\end{aligned}$

Therefore, the value of y is 10.

So, x=24, y=10, and z=17.

And we are done!

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Make and test a conjecture about the given quantity.

larisa [96]

Answer:

18. The conjecture is: The product of two negative even integers is an even integer.

Testing: Let integers be -4 and -6. [Two negative even integers]

Then (-4) × (-6) = 24 [Even integer]

19. The conjecture is: Sum of two negative odd integers is a negative even integer.

Testing: Let the two negative odd integers be -3 and -7.

Then -3 + (-7) = -10 is a negative even integer

20. The conjecture is: Sum of two even integers and two odd integers is an even integer.

Testing: Let integers be 4, 12, 13, 17 (Two even integers and two odd integers)

Then 4 + 12 + 13 + 17 = 46 (Even integer)

21. The statement is: p------->q [If you ran 1 mile, then you ran 5280 feet]

Decide whether statement is true: So if p is True then q is also True.

Hence p------->q is True. So the given statement is True.

Step-by-step explanation:

18. The product of two negative even integers.

Let the integers be -2m and -2n, m and n are positive integers

Product in (-2m) × (-2n) = 4mn = 2(2mn)

= 2p, p = 2mn

The conjecture is: The product of two negative even integers is an even integer.

Testing: Let integers be -4 and -6. [Two negative even integers]

Then (-4) × (-6) = 24 [Even integer]

19. The sum of two negative odd integers.

Let the integers be -(2m + 1) and -(2n + 1), m and n are positive integers

Then -(2m + 1) + [-(2n + 1)] = -2m - 1 - 2n - 1

= -2m - 2n - 2

= -2(+m + 2 + 1)

= -2p, p = m + n + 1

The conjecture is: Sum of two negative odd integers is a negative even integer.

Testing: Let the two negative odd integers be -3 and -7.

Then -3 + (-7) = -10 is a negative even integer

20. The sum of two even integers and two odd integers.

Let the integers be 2m, 2n, 2p + 1, 2q + 1 (m, n, p, q are positive integers)

Then, 2m + 2n + 2p + 1 + 2q + 1 = 2(m + n + p + q + 1)

= 2r, r = m + n + p + q + 1

The conjecture is: Sum of two even integers and two odd integers is an even integer.

Testing: Let integers be 4, 12, 13, 17 (Two even integers and two odd integers)

Then 4 + 12 + 13 + 17 = 46 (Even integer)

21. Let p: You ran 1 mile

Let q: You 5280 feet

The statement is: p------->q [If you ran 1 mile, then you ran 5280 feet]

Since 1 mile = 5280 feet

So if p is True then q is also True.

Hence p------->q is True. So the given statement is True.

6 0

3 years ago

Triangle HJK is transformed to similar triangle H’J’K’: A coordinate plane is shown. Triangle HJK has vertices H at 8 comma 8, J

Serggg [28]

We are given coordiates of vertices of triangle ΔHJK as H(8,8), J(8,4), K(4,4)

and coordinates of transformed triangle ΔH’J’K are H'(2,2), J'(2,1), k'(1,1).

We can clealry see that if we divide each value in coordinate by 4, we get the coordinates of the transformed triangle.

Let's see, what's dilation being applied there : H(8,8) ---> 1/4 (8,8) = H' (2,2) ,

J(8,4) ---> 1/4(8,4) = J'(2,1) and

K(4,1) ---> 1/4 (4,4) = K'(1,1).

So, we can clearly see that each coordinate is being multiplied by 1/4.

So, we can say the scale factor of dilation is 1 over 4, that is 1/4.

4 0

3 years ago

Read 2 more answers

For a trip, one high school rented and filled 5 vans and 6 buses with 187 students. Another high school instead fit its 176 stud

serious [3.7K]

Answer:

A bus can carry 22 students and a van can carry 11 students.

Step-by-step explanation:

Let the number of students bus can carry be 'b'.

Let the number of students van can carry be 'v'.

Given:

One High school:

Number of bus = 6

Number of vans = 5

Number of students = 187

So we can say that;

Number of bus multiplied by number of students bus can carry plus Number of vans multiplied by number of students van can carry is equal to Number of students.

framing in equation form we get;

$6b+5v=187$ ⇒ Equation 1

Also Given:

One High school:

Number of bus = 7

Number of vans = 2

Number of students = 176

So we can say that;

Number of bus multiplied by number of students bus can carry plus Number of vans multiplied by number of students van can carry is equal to Number of students.

framing in equation form we get;

$7b+2v=176$ ⇒ Equation 2