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Mathematics

1 answer:

amid [387]3 years ago

6 0

It is given that QS bisects ∠PQR. So, ∠PQS ≈ ∠SQR by the definition of the term bisect. Therefore, m∠PQS = m∠SQR by the angle congruence postulate. It is given that m∠PQS is 45°, so 45° = m∠SQR by the Linear Pair Postulate property of equality. m∠PQS + m∠SQR = m∠PQR by the Angle Additional Postulate, so 45° + 45° = m∠PQR by the substitution property of equality, and simplifying gives 90° = m∠PQR. Therefore, ∠PQR is a right angle angle by the definition of the term right angle.

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3 years ago

The roosevelt middle school band is having a fundraiser. They sold a total of 300 hotdogs and hamburgers. Hot dogs were sold for

STALIN [3.7K]

Answer:

180 hamburgers

120 hotdogs

Step-by-step explanation:

In this question, we are asked to calculate the number of hamburgers and hotdogs sold by a company given the amount made by them and the total number of these snacks sold

We proceed as follows;

Let the amount of hotdogs sold be x and the amount of hamburgers sold be y.

We have a total of 300 snacks sold, mathematically;

x + y = 300 ..........(I)

Now let’s look at the prices.

x number of hotdogs sold at $2, this give a total of $2x hotdogs

y number of hamburgers sold at $3, this give a total of $3y.

Adding both to give total, we have ;

2x + 3y = 780.......(ii)

This means we have two equations to solve simultaneously. From equation 1, we can say x = 300 -y

Now let’s insert this in the second equation;

2(300-y) + 3y = 780