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4 years ago

Given: PQ= TQ, UQ: QS

Mathematics

1 answer:

joja [24]4 years ago

3 0

Answer:

The required prove is shown below.

Step-by-step explanation:

Consider the provided statement.

The required figure is shown below:

Statement Reasons

PQ ≅ TQ; UQ ≅ QS Given

PQ = TQ, UQ = QS Definition of Congruence

PQ + QS = PS; TQ+QU = TU Segment Addition Postulate

TQ + QS = PS Substitution (PQ = TQ)

TQ + QS = TU Substitution (QU = QS)

PS = TU Transitive Property

Prove: PS ≅TU Definition of Congruence

Hence, the required prove is shown above.

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An explosion causes debris to rise vertically with an initial speed of 120 feet per second. The formula h equals negative 16 t s

Novay_Z [31]

Answer:

The debris will be at a height of 56 ft when time is 0.5 s and 7 s.

Step-by-step explanation:

Given:

Initial speed of debris is, $s=120\ ft/s$

The height 'h' of the debris above the ground is given as:

$h(t)=-16t^2+120t$

As per question, $h(t)=56\ ft$ . Therefore,

$56=-16t^2+120t$

Rewriting the above equation into a standard quadratic equation and solving for 't', we get:

$-16t^2+120t-56=0\\\textrm{Dividing by -8 throughout, we get}\\\frac{-16}{-8}t^2+\frac{120}{-8}t-\frac{56}{-8}=0\\2t^2-15t+7=0$

Using quadratic formula to solve for 't', we get:

$t=\frac{-b\pm \sqrt{b^2-4ac}}{2a}\\\\t=\frac{-(-15)\pm \sqrt{(-15)^2-4(2)(7)}}{2(2)}\\\\t=\frac{15\pm \sqrt{225-56}}{4}\\\\t=\frac{15\pm\sqrt{169}}{4}\\\\t=\frac{15\pm 13}{4}\\\\t=\frac{15-13}{4}\ or\ t=\frac{15+13}{4}\\\\t=\frac{2}{4}\ or\ t=\frac{28}{4}\\\\t=0.5\ s\ or\ t=7\ s$

Therefore, the debris will reach a height of 56 ft twice.

When time $t=0.5\ s$ during the upward journey, the debris is at height of 56 ft.

Again after reaching maximum height, the debris falls back and at $t=7\ s$ , the height is 56 ft.

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3 years ago

How do I solve this Geometry problem?

tia_tia [17]

Answer:

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Step-by-step explanation:

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2 years ago

What is 3 over 2 divided by 1 over 4

laila [671]

That would be 6/1 which equals to 6 ~Eos

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4 years ago

Translate and solve using proportions 6.5% of what number is $3.77

marshall27 [118]

Answer:

The quantity is US$ 58, which 6.5% is US$ 3.77

Step-by-step explanation:

Number = x

6.5% of x = $ 3.77

6.5% = 0.065 = 65/1,000 = 13/200 (Dividing by 5)

3.77 = 3 + 77/100 (We can't simplify 77/100)

Thus,

13/200 * x = 3 77/100

13x/200 = 377/100

13x = 754 (Multiplying by 200 at both sides)

x = 754/13 (Dividing by 13 at both sides)

x = 58

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4 years ago

Solve the problem 5x-8<7x-4

kumpel [21]

Answer:

x>-2

Step-by-step explanation:

5x-7x<-4+8

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x>-2

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3 years ago