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4 years ago

Find the value of x in each case. Give reasons to justify your solutions!

Mathematics

1 answer:

Leno4ka [110]4 years ago

6 0

Answer:

The value of x in this case is 34°.

Step-by-step explanation:

Here, Lines TR and UP is intersecting lines at the point S.

⇒∠ TSU = ∠ PSR (VERTICALLY OPPOSITE ANGLES)

⇒ 4x = ∠ PSQ + ∠ QSR

= ∠ PSQ + 3x

⇒ ∠ PSQ = 4x - 3x = x

⇒ ∠ PSQ = x

Now, by The INTERIOR EXTERIOR ANGLES THEOREM In a TRIANGLE:

Sum of Two Interior angle of a triangle is equal to opposite exterior angle.

So, here in Δ PSR

∠ PSQ + ∠ SPQ = ∠ SQR

or, x + x = 68°

or, 2 x = 68°

⇒ x = 68/2 = 34°

Hence, the value of x in this case is 34°.

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15% of 9 dollars is how many dollars

Ket [755]

9 .............. 100%
x................ 15%

100x = 15 . 9
100x = 135
x = <u>135</u>
100
x = 1,35

6 0

3 years ago

Ellie buys a baseball for $13 plus an 8% tax. Jason buys a phone case for $16 plus an 8% tax. Enter the difference in the amount

Over [174]

Ellie baseball will be $14.04 because it’s a 8% tax the difference is cheaper than Jason.

3 0

3 years ago

On Thursday afternoon at camp Alice played basketball and went swimming before dinner she spent 45 minutes playing basketball an

ivann1987 [24]

Answer:

3:45 PM.

Step-by-step explanation:

We have been given that on Thursday afternoon at camp Alice played basketball and went swimming before dinner she spent 45 minutes playing basketball and one hour swimming dinner lasted for an hour. The dinner ended at 5:30 PM.

Since she spent 1 hour for swimming, so 1 hour before 5:30 PM would be 4:30 PM.

To find the time, when Alice started playing basketball, we need to find 45 minutes before 4:30 PM.

30 minutes before 4:30 PM would be 4:00 PM and 15 minutes before 4:00 PM would be 3:45 PM.

Therefore, Alice started playing basket ball at 3:45 PM.

7 0

3 years ago

Find the lowest common denominator of and . A. x3y4 B. x2y3 C. xy4 D. x4y5

Blizzard [7]

Lowest Common Denominator refers to lowes t common multiple. These expressions have two terms 'x' and 'y' and we want to choose the expression that has the highest power such that the other expressions can be multiplied into the common denominator.

For the 'x' term, the highest power is x⁴ and for the 'y' term, the highest power is y⁵

Common denominator of A, B, C, and D: x⁴y⁵

5 0

4 years ago

You don't need to construct a Venn Diagram, it is just part of the instruction. Just determine whether or not the argument is va

icang [17]

Answer:

It is valid.

Venn Diagram is attached.

I also provided a truth table.

I also provided a couple of names this argument could be called.

Please let me know if you have any questions about this question.

Thank you kindly.

Step-by-step explanation:

If a person is a poet, then that person is a loner.

If a person is a loner, then that person is a taxi driver.

If a person is a poet, then that person is a taxi drive.

This is in the form:

p->q

q->r

Therefore, p->r.

This is an example of a hypothetical syllogism.

The first thing my mind goes to when seeing this is the transitive property which says if A is related to B and B is related to C then A is related to C.

So this syllogism also has another name and it is called the principle of transitivity of implication.

Let p=person is a poet, q=person is a loner, and r=person is a taxi driver.

I'm going to make a truth table and compare the truth values of the propositions to the conclusion.

Since we have 3 variables, we are going to need 2^3=8 rows.

p q r p->q q->r (p->q) and (q->r) conclusion=(p->r)

T T T T T T T

T T F T F F F

T F T F T F T

T F F F T F F

F F F T T T T

F F T T T T T

F T F T F F T

F T T T T T T

So we are trying to see if we ever have the preposition part true and the conclusion false.

That doesn't happen so the argument is valid.

5 0

4 years ago