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2 years ago

5

Directions: Solve for x. 1. X 32 9 24

1 answer:

ki77a [65]2 years ago

8 0

Answer:

x = 12

Step-by-step explanation:

set up a proportion:

<u> 24 </u> = <u> 32 </u>

33 32+x

24(32 + x) = 32(33)

768 + 24x = 1056

24x = 288

x = 12

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What is the sum if the first 22 terms of the following series? 86 + 79 + 72 + 65 +58+...

Arturiano [62]

Seems to be an arythmetic sequence
Sn=[n(a1+an)]/2
where
Sn means sum of all terms up the nth term
n=number of terms
a1=first term
an=nth term

so from 86 to the 22th term is from a1 to a22

find teh sequence
miknus 7 each time
an=a1+d(n-1)
an=87-7(n-1)
find 22n term
a22=87-7(22-1)
a22=87-7(21)
a22=87-147
a22=-60

S22=[22(87-60)]/2
S22=[22(27)]/2
S22=594/2
S22=297

the sum is 297

5 0

3 years ago

Value of the expression 6x-2y 5y when x=10 and y=3.

vfiekz [6]

Answer:

-150

Step-by-step explanation:

Multiply & Divide left to right

$60-2*35*3$

Once again Multiply & Divide

$60-210$

Add & Subtract

Final Answer: $-150$

6 0

2 years ago

You are given the parametric equations x=2cos(θ),y=sin(2θ). (a) List all of the points (x,y) where the tangent line is horizonta

vladimir1956 [14]

Answer:

The solutions listed from the smallest to the greatest are:

x: $-\sqrt{2}$ $-\sqrt{2}$ $\sqrt{2}$ $\sqrt{2}$

y: -1 1 -1 1

Step-by-step explanation:

The slope of the tangent line at a point of the curve is:

$m = \frac{\frac{dy}{dt} }{\frac{dx}{dt} }$

$m = -\frac{\cos 2\theta}{\sin \theta}$

The tangent line is horizontal when $m = 0$ . Then:

$\cos 2\theta = 0$

$2\theta = \cos^{-1}0$

$\theta = \frac{1}{2}\cdot \cos^{-1} 0$

$\theta = \frac{1}{2}\cdot \left(\frac{\pi}{2}+i\cdot \pi \right)$ , for all $i \in \mathbb{N}_{O}$

$\theta = \frac{\pi}{4} + i\cdot \frac{\pi}{2}$ , for all $i \in \mathbb{N}_{O}$

The first four solutions are:

x: $\sqrt{2}$ $-\sqrt{2}$ $-\sqrt{2}$ $\sqrt{2}$

y: 1 -1 1 -1

The solutions listed from the smallest to the greatest are:

x: $-\sqrt{2}$ $-\sqrt{2}$ $\sqrt{2}$ $\sqrt{2}$

y: -1 1 -1 1

6 0

2 years ago

−|9| = −9 True or False

Ket [755]

Answer:

false

Step-by-step explanation:

7 0

3 years ago

Read 2 more answers

Determine if events A and B are mutually exclusive.

gladu [14]

Answer:

A) Not mutually exclusive

Step-by-step explanation:

Given

$P(A) = \frac{1}{4}$

$P(B) = \frac{3}{5}$

$P(A\ or\ B) = \frac{7}{10}$

Required

Determine if they are mutually exclusive or not

Mutually exclusive are defined by:

$P(A\ or\ B) = P(A) + P(B)$

So, we have:

$P(A\ or\ B) = \frac{1}{4} + \frac{3}{5}$

Take LCM

$P(A\ or\ B) = \frac{5+12}{20}$

$P(A\ or\ B) = \frac{17}{20}$

By comparing:

$P(A\ or\ B) = \frac{17}{20}$ ---- Calculated

$P(A\ or\ B) = \frac{7}{10}$ ---- Given

We can conclude that A and B are not mutually exclusive because:

$\frac{17}{20} \ne \frac{7}{10}$

6 0

3 years ago