Pedro is going to use SAS to prove that △PQR ≅ △SQR. Which of these is a necessary step in Pedro’s proof? O A. Prove that ∠QPR ≅ ∠QSR by the Isosceles Triangle Theorem. O B. Prove that QR ≅ QR by the reflexive property. O C. Prove that PQ ≅ SQ by CPCTC. O D. Prove that ∠PQR ≅ ∠SQR by vertical angles.
Answer: B. Prove that \( \overline{QR} \cong \overline{QR} \) by the reflexive property. Explanation: To use the Side-Angle-Side (SAS) congruence theorem, we need to show that two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle. The reflexive property is used to show that […]
5712-3984= ?
Answer: 1728 Explanation: Subtracting 3984 from 5712 gives 1728. You can verify by adding 3984 back to 1728, which should result in 5712.
2) Mr Lim gave 3600 to his wife and two children altogether. His wife received 500 more than his son. His son received twice as much as his daughter. How much did Mr Lim’s wife received? (W.Bk 5A : pg 28 #6)
Answer: Mr. Lim’s wife received $1,700. Explanation: To solve this problem, we use algebraic equations to represent the relationships and total amount given. We define variables for the amounts received by the son and daughter, and express the wife’s amount in terms of these variables. Steps: Define Variables: Let \( x \) be the amount […]
P S 22° Q R If ∠PQR measures 75°, what is the measure of ∠SQR? ① 22° ② 45° ③ 53° ④ 97°
Answer: 53° Explanation: The problem involves the concept of the sum of angles around a point. Since \( \angle PQR \) and \( \angle SQR \) are adjacent angles forming a straight line with \( \angle PQS \), their sum is 180°. Given \( \angle PQR = 75^\circ \) and \( \angle PQS = 22^\circ […]
Which of the following is equivalent to the expression below? 7^8.27 A. 7^8 7^27/100 B. 7^8 7^2/10 7^7/100 C. 7^8 7^27/10 D. 7^8 * 7^2/10 + 7^7/100
Answer: C. \( 7^6 \cdot 7^{27/100} \) Explanation: The expression \( 7^{6.27} \) can be rewritten using the properties of exponents. Specifically, the expression can be split into two parts: the integer part and the fractional part. This uses the property \( a^{b+c} = a^b \cdot a^c \). Steps: Separate the Exponent: The given expression […]
4 A radio station is giving away tickets to a play. They plan to give away tickets to seats that cost 10 or 20. They plan to give away at least 20 tickets, and the total cost of all the tickets can be no more than $300. Make a graph showing how many tickets of each kind can be given away. x + y ≥ 20 10x + 20y ≤ 300
Answer: The solution involves graphing the system of inequalities: \( x + y \geq 20 \) and \( 10x + 20y \leq 300 \). Explanation: This problem involves linear inequalities and requires graphing the feasible region that satisfies both conditions. The variables \( x \) and \( y \) represent the number of $10 and […]
EXERCISE Change the following sentences into passive voice. 1. She likes chocolates. 2. The boy is climbing the wall. 3. We did not hear a sound. 4. They have bought a horse. 5. The Board has given me a gold medal. 6. He praised the boy for his courage. 7. The teacher was helping the students. 8. Why were they beating the boy? 9. They have not done their job. 10. A car ran over an old man. 11. He will give you a box of chocolates. 12. He had told me to do it. 13. They had not done their home task. 14. We shall have finished our work by March next. 15. He took away my books. 16. The sudden noise frightened the child. 17. We use milk for making cheese. 18. Why is he mending the chair? 19. The doctor asked her to stay in bed. 20. They caught the thief.
The image contains an English grammar exercise, not a mathematical problem. The task is to change sentences from active to passive voice. Here’s how you can approach it: Answer: Here are the passive voice conversions for some sentences: Chocolates are liked by her. The wall is being climbed by the boy. A sound was not […]
XVII _ 17 Tick the smallest Roman number. XXI XXV XIX 02 XXXIX XVII the larg es
Answer: XIX Explanation: The problem involves identifying the smallest Roman numeral from a given set. Roman numerals are a numeral system originating from ancient Rome, using combinations of letters from the Latin alphabet (I, V, X, L, C, D, M). The task is to convert each numeral to its Arabic equivalent and compare them. Steps: […]
x x x x x 4x=□ x 10
The answer is 20 Explanation
Three teachers share 2 packs of paper equally. How much paper does each teacher get? Select all that apply. A 2 halves of a pack B 3 fourths of a pack C 3 sixths of a pack D 1 third of a pack E 2 thirds of a pack
Answer: D and E Explanation: To find out how much paper each teacher gets, we divide the total number of packs by the number of teachers. The problem involves basic division of fractions. Steps: Total Packs: There are 2 packs of paper. Number of Teachers: 3 teachers. Division: Divide the total packs by the number […]