MATHEMATICS HIGH SCHOOL

Find the length of the third side. If necessary, write in simplest radical form

Answers

Answer 1

Answer:

Answer:

$√(19)$

Step-by-step explanation:

Pythagoras

c² = a² + b²

with c being the Hypotenuse (= the side opposite of the 90 degree angle).

10² = 9² + b²

100 = 81 + b²

19 = b²

b = sqrt(19) (≈ 4.36)

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If h(x) = 5x − 3 and j(x) = −2x, solve h[j(2)] and select the correct answer below.17
23
−17
−23

Answers

sub 2 for x in j(x) and evalueate
then sub that result for x in h(x)

j(2)=-2(2)
j(2)=-4

now sub-4 for x in h(x)

h(-4)=5(-4)-3
h(-4)=-20-3
h(-4)=-23

answer is -23

Find the midpoints of the points (-3,-2) and (1,-4)

Answers

Answer: (-1,-3)

Step-by-step explanation:

midpoint formula $\left((x_2+x_1)/(2),\:\:(y_2+y_1)/(2)\right)$

$\left(x_1,\:y_1\right)=\left(-3,\:-2\right),\:\left(x_2,\:y_2\right)=\left(1,\:-4\right)$

$\left((1-3)/(2),\:(-4-2)/(2)\right)$

$((-2)/(2),(-6)/(2))$

-2/2=-1

-6/2=-3

So the midpoint is (-1,-3)

Please mark brainliest

4. solve
e) 4^x-10.2^x+16=0
I think the dot means multiply?

Answers

$4^x-10\cdot2^x+16=0\Rightarrow(2^2)^x-10\cdot2^x+16=0\Rightarrow(2^x)^2-10\cdot2^x+16=0$

$subtitute\ 2^x=t > 0\n\nt^2-10t+16=0\nt^2-2t-8t+16=0\nt(t-2)-8(t-2)=0\n(t-2)(t-8)=0\iff t-2=0\ or\ t-8=0\n\nt=2\ or\ t=8\n\nt=2^1\ or\ t=2^3\n\ntherefore\ 2^x=2^1\ or\ 2^x=2^3\n\nAnswer:\boxed{x=1\ or\ x=3}$

2^x=a
4^x=(2^2)^x=(2^x)^2=a^2

a^2-10a+16=0
Δ=10^2-4*1*16=100-64=36
√Δ=6
a1=(10+6)/2=16/2=8
a2=(10-6)/2=4/2=2
2^x=8=2^3⇒ x=3 or
2^x=2=2^1⇒ x=1

There are 2 solutions : x=1 or x=3

A drive has a maximum speed of 10,000 revolutions per minute. If a disc has a diameter of 14 cm, what is the linear speed, in km/h, of a point 6 cm from the center if the disc is spinning at a rate of 6000 revolutions per minute?

Answers

The point 6 cm away from the center travels in a circle of circumference 2π*(6 cm) = 12π cm, so that it covers this distance per revolution, 12π cm/1 rev.

So the disk has a linear speed of

(6000 rev/min) * (12π cm/rev) = 72,000π cm/min

which is equivalent to

(72,000π cm/min) * (1/100,000 km/cm) * (60 min/h)

or approximately 135.7 km/h.

Which expression gives the solutions of -5+2x^2=-6x

Answers

Answer:

The solutions are

$x1=(-6+2√(19))/(4)$

$x2=\frac{-6-2√(19)} {4}$

Step-by-step explanation:

we have

$-5+2x^(2) =-6x$

rewrite the quadratic equation

$2x^(2)+6x-5=0$

The formula to solve a quadratic equation of the form $ax^(2) +bx+c=0$ is equal to

$x=\frac{-b(+/-)\sqrt{b^(2)-4ac}} {2a}$

in this problem we have

$2x^(2)+6x-5=0$

$a=2\nb=6\nc=-5$

substitute in the formula

$x=\frac{-6(+/-)\sqrt{6^(2)-4(2)(-5)}} {2(2)}$

$x=\frac{-6(+/-)√(76)} {4}$

$x=\frac{-6(+/-)2√(19)} {4}$

$x1=(-6+2√(19))/(4)$

$x2=\frac{-6-2√(19)} {4}$

-5 + 2x² = -6x
rearrange the equation to the form ax² + bx + c = 0

=> 2x² + 6x - 5

use the quadratic formula to solve for the value(s) of x $-b ± \sqrt{ (b^(2) - 4ac)/(2a) }$

=> $-6 ± \sqrt{ (6^(2) - 4(2)(-5))/(2(2)) }$

=> $-6 ± \sqrt{ (36 - (-40))/(4) }$

=> $-6 ± \sqrt{ (76)/(4) }$

∴ x = $-6 + √( 19) }$ OR x = $-6 - √(19)$

x = - 1.64 ; x = - 10.36

The Nelson family drank of a gallon of orange juice on Saturday morning and of a gallon of orange juice on Sunday morning. How much orange juice did they drink in All