MATHEMATICS HIGH SCHOOL

Leo is running in a 5-kilometer race along a straight path. if he is at the midpoint of the path, how many kilometers does he have left to run?

Answers

Answer 1

Answer:

Let us assume Leo starts from a point (0,0)

Since the total length of the race is 5 km, he will be at (5,0) at the end of the race.

It is given that, he is at the mid point of the race.

Mid point formula is : $((x_(1) +x_(2) ))/(2) , ((y_(1) +y_(2) ))/(2)$

Present coordinate : $(5+0)/(2) , (0+0)/(2) = (2.5,0)$

He still needs to run 5-2.5 = 2.5 km

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Line SU bisects angle RST. Which statement is NOT true?A) ∠RST = ∠RSU
B) ∠RSU = ∠UST
C) ∠SQU = ∠SPU
D) PS = QS

Answers

In geometry, the angle bisector theorem is concerned with the relative lengths of the two segments that a triangle's side is divided into by a line that bisects the opposite angle. It equates their relative lengths to the relative lengths of the other two sides of the triangle.
so the answer is B

Answer : The incorrect option is, (A) ∠RST = ∠RSU

Step-by-step explanation :

As we are given that, line SU bisects angle RST and SPUQ is a rhombus.

First we have to determine that ΔSQU and ΔSPU are congruent triangles.

Proof:

Side SU = Side SU (common side)

∠SQU = ∠SPU (In rhombus opposite angle are always equal)

∠RSU = ∠UST (angle bisector)

ΔSQU ≅ ΔSPU (By ASA congruency)

So, Side PS = Side QS

∠RST = ∠RSU this option is wrong because $\angle RSU=(1)/(2)\angle RST$

Thus, the incorrect option is, (A) ∠RST = ∠RSU

140% of what number is 14?

Answers

140% of 19.6 is 14 and you are very welcome

140% of what number is 14
140% × number = 14
(140% = $(140)/(100)$ = 1.4)
1.4 × n = 14
Divide by 1.4 to isolate n
$(1.4n)/(1.4)$ = $(14)/(1.4)$
1.4 and 1.4 cancels out
n = 10

140% of 10 is 14

Check:
$(140)/(100)$ × 10 = 14
1.4 × 10 = 14
14 = 14

Simplify the expression. q+12q

a. -13q

b. -11q

c. 11q

d. 13q

Answers

Answer:

13q

Step-by-step explanation:

q is the same as 1q

1q + 12q = 13q

Can anyone plz help me plz this is the only question am asking ??:(

Answers

I think it is 1/7(3) but if I am wrong then sorry:)

A helicopter hovers at an altitude that is 1000 feet above a mountain of altitude 5210 feet. A second, taller peak is viewed from both the mountaintop and the helicopter. from the helicopter, the angle of depression is 43, and the mountaintop, the angle of depression is 18 degree. how far apart are the mountain peaks? what is the altitude of the taller peak?

Answers

x - horizontal distance from peak to peak
y – difference between the altitudes of two peaks

Equations:
y/x = tan(17°)
(1100 – y)/x = tan(46°)

Solution:
y = (1100 tan(17°)) / (tan(17°) + tan(46°)) = 250.74 ft
x = y / tan(17°) = 820.12 ft

Horizontal distance from peak to peak is 820 ft.
Altitude of the taller peak is 5300 + 250 = 5550 ft.

The direct distance from peak to peak is √(x²+y²) = 857.6 ft.

Answer:

the altitude of the taller peak is equal to 5468.4 ft

Step-by-step explanation:

given,

altitude of the helicopter = 1000 ft

height of the mountain = 5210 ft

Angle of depression from helicopter = 43°

Angle of depression from mountain = 18°

$tan 18 = (h)/(s)$