MATHEMATICS HIGH SCHOOL

Pls include explanation

Answers

Answer 1

Answer:

Answer:

See below

Step-by-step explanation:

Corresponding sides have equal ratios:

OB / OP = OK / OS

Let the y-coordinate of the point K is y, then we have:

5 / 8 = y / - 12
y = - 12*5/8
y = - 7.5

Note, taken the coordinates of end points not the absolute distance.

The coordinates of the point K are (0, - 7.5)

The scale factor is:

k = OP / OB = 8/5 = 1.6 or
k = OS / OK = -12 / -7.5 = 1.6

Answer 2

Answer:

Answer:

K = (0, -7.5)

Scale factor = 1.6

Step-by-step explanation:

If ΔBOK is similar to ΔPOS then the ratios of their corresponding sides are the same.

Given side lengths:

OP = 8 units
OB = 5 units
OS = 12 units

Therefore:

$\sf \implies OP:OS = OB:OK$

$\sf \implies 8:5= 12:OK$

$\implies \sf (8)/(5)=(12)/(OK)$

$\implies \sf 8 \cdot OK = 12 \cdot 5$

$\implies \sf OK=(60)/(8)$

$\implies \sf OK=7.5$

Therefore, the coordinates of K are (0, -7.5).

To find the scale factor, simply divide the corresponding side lengths of the larger triangle by the smaller triangle:

$\implies \sf scale\:factor=(OP)/(OB)=(8)/(5)=1.6$

Learn more about similar triangles here:

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Prove that

Factor 35v–7w +42x. Write your answer as a product with a whole number greater than 1.

Answers

Answer: 7(5v-w+6x)

Step-by-step explanation:

GCD/HCF = 7

Which of the following expressions is equivalent to 3?7 + (-4)
-7 + 4
7 - (-4)
-7 - (-4)

Answers

-7 - (-4)

is your answer. hope I helped

Answer:

first one

Step-by-step explanation: 7 + (-4) = 3

hope this helps.

Estimate the solution of the equation x - 8.1=5.3 to the nearest whole number

Answers

Answer is about 13. i hope this helps.

A runner has a track lap of one minute while at a run, five minutes while at a jog, 7 minutes while at a walk. If 2/5 of the lap is paced at a run, 1/2 at a jog and 1/10 at a walk what is the total track lap time of the runner. Write the solution as a mixed number or a fraction in lowest terms

Answers

24 seconds running
2 minutes 30 seconds jogging
42 seconds walking
3 minutes 36 seconds in that lap

Final answer:

The total track lap time of the runner is 2 2/5 minutes or 2.4 minutes.

Explanation:

The total track lap time of the runner can be calculated by summing up the individual time spent at each pace (run, jog, walk). Each pace's time is first multiplied by the fraction of the lap completed at that pace.

For the run, the calculation is 2/5 of 1 minute which is 2/5 minute.

For the jog, the calculation is 1/2 of 5 minutes which is 5/2 = 2 1/2 minutes or 2.5 minutes in decimal form.

For the walk, the calculation is 1/10 of 7 minutes which is 7/10 = 0.7 minutes.

Adding these times together gives a total of (2/5) + (5/2) + (7/10) = 12/5 = 2 2/5 minutes or 2.4 minutes in decimal form.

Learn more about Total Track Lap Time Calculation here:

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#SPJ2

Find the remainder when f(x) = x3 − 14x2 51x − 22 is divided by x − 7.

Answers

We can use at least two approaches in answering this question. But the easiest way is to use the $<b>Remainder Theorem</b>$

According to the Remainder Theorem, if
$(x - a)$
is not a factor of
$f(x)$
then evaluating the function at
$x = a$
gives us the Remainder when
$f(x)$
is divided by
$(x - a)$
That is
$f(a) = R$

For the given question, we have

$f(x) = {x}^(3) - 14 {x}^(2) + 51x - 22$
When this function is divided by
$x - 7$
The remainder is given by
$f(7) = R$
$f(7) = {7}^(3) - 14( {7})^(2) + 51(7) - 22$
$f(7) = 343 - 14( 49) + 51(7) - 22$
$f(7) = 343 - 686+ 357 - 22$
$f(7) = - 8$
$<b>Hence the remainder is -8</b>$

The remainder is -8.

Find the volume of a cube whose diagonal measures 36√3 cm.

Answers

Answer:

$46656 cm^3$

Step-by-step explanation:

If a cubes diagonal measures you can solve for its sidelength by creating a triangle. Visualize the diagonal as the hypotenuse of our triangle inside the cube. Then, one of the legs would be the side of the cube itself, and the other leg would be the diagonal of the bottom side of the cube. Knowing this is a cube, we can call each side s. If each side is s, then the diagonal of the bottom face is $s√(2)$ ( this is a special triangle property, $45-45-90$ triangle.) Then we know our triangle is a right triangle, so we can use the Pythagorean theorem to solve for s.

$s^(2) + (s√(2) )^(2) = (36√(3))^2$

Solve this equation for s.

$s^(2) + 2s^(2) = 3888$

$3s^(2) = 3888$

$s^(2) = 1296$

$s = 36$

Since we now found the side length of the cube, we can find its volume by cubing the side length:

$s^3 = (36)^3 = 46656$ $cm^3$