Can someone me step up and solve this problem

Problem 5

The sum of two numbers is 175

Let the two numbers be x and y

Therefore x + y = 175

Their difference is = x - y and is equal to 19

x + y = 175

x - y = 19 Add

2x = 194 Divide by 2

x = 194/2

x = 97

x + y = 175

97 + y = 175

y = 175 - 97

y = 78

Problem 4

Let the nickels = N

Let the Pennies = P

N + P = 199 (1)

0.05*N +0.01 P = 7.67 Multiply the entire equation by 100

5N + P = 767 (2) Multiply equation (1) by 5 and subtract.

5N +5P =995

- 4P = - 228 Divide by -4

P = 57

N + P = 199

N + 57 = 199

N = 199 - 57

N = 142

Answer

Pennies = 57

Nickels = 142

Check

142*5 + 57*1 = ? 767

710 + 57 = ? 767

767 = 767

*see attachment for the diagram

Answer/Step-by-step explanation:

1. Antonio's statement is correct because the sum of measure of the minor intercepted arc DE and the angle formed by tangents CE and CD outside the circle equal 180°.

According to the theorem. Therefore, the statement is correct.

2. To find the measure of <A, which is a central angle of the circle, find the value of x. Then find the measure of the intercepted arc.

According to the central angle theorem, the measure of a central angle equal the intercepted minor arc.

Therefore, the measure of the intercepted minor arc DE = m<A.

Step 1: find the value of x using the equation gotten in question 1.

Combine like terms

Step 2: find the measure of the minor intercepted arc DE, by substituting x = 25 into 5x - 2.

measure of arc DE = 5x - 2

= 5(25) - 2 = 125 - 2

measure of arc DE = 123°

Step 3: find the measure of centra angle A.

m<A = intercepted arc DE (central angle theorem)

m<A = 123°