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trapecia [35]
3 years ago
14

How do you solve the equation -7/8k=21

Mathematics
1 answer:
loris [4]3 years ago
4 0
- \frac{7}{8} k = 21

First, simplify \frac{7}{8} k to \frac{7k}{8} / Your problem should look like: -\frac{7k}{8} = 21
Second, multiply both sides by 8. / Your problem should look like: -7k = 167
Third, divide both sides by -7. / Your problem should look like: k = \frac{168}{-7}
Fourth, simplify \frac{168}{-7} to \frac{168}{7} / Your problem should look like: k = - \frac{168}{7}
Fifth, simplify \frac{168}{7} to 24. / Your problem should look like: k = -24

Answer: k = -24

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4. What is the system of equations that describes the following graph?
GarryVolchara [31]

Answer:

The system of inequalities is

y

y>0.25x

Step-by-step explanation:

step 1

Find the equation of the dashed line with negative slope

The line passes through the points

(0,-2) and (-2,0)

Find the slope

m=(0+2)/(-2-0)=-1

Find the equation of the line in slope intercept form

y=mx+b

we have

m=-1\\b=-2

substitute

y=-x-2

The solution of the inequality is the shaded area below the dashed line

therefore

The equation of the inequality A is

y

step 2

Find the equation of the dashed line with positive slope

The line passes through the points

(0,0) and (4,1)

Find the slope

m=(1-0)/(4-0)=0.25

Find the equation of the line (direct variation)

y=kx

we have

k=0.25

substitute

y=0.25x

The solution of the inequality is the shaded area above the dashed line

therefore

The equation of the inequality B is

y>0.25x

therefore

The system of inequalities is

y

y>0.25x

4 0
3 years ago
Using the chart "Amount of $1 at Compound Interest" from previous reading section "More Compound Interest", find the total amoun
vitfil [10]

Answer:

Step-by-step explanation:

the formula used for any interest other then continuously is

A=P(1+r/n)^nt

so... r=rate in decimal form ONLY n=how often interest is paid t=time passed

A=3000(1+.08/1)^(1)(5) = annually

A=3000(1+.08/2)^(2)(5)

A=3000(1+.08/4)^(4)(5)

use you calculator to get the answer

it is good practice to use your calculator now because soon you will be using it for population questions and those need to be entered very carefully.

7 0
3 years ago
the parallel sides of a trapezium are such that the longer side is 4cm more than the shorter side of the distance between them i
saw5 [17]

Answer:

32cm and 28cm

Step-by-step explanation:

Area of a trapezium=0.5 ( sum of parallel sides ) × height

600=0.5( 4+a+a)×20

where a is the length of the shorter side

600÷0.5=(4+2a)×20

1200=(4+2a)×20

1200÷20=4+2a

60=4+2a

60-4=2a

56=2a

56÷2=a

28=a.

since the longer side is 4 cm more than th shorter side , 28 +4=32

4 0
3 years ago
Graph ​y<1−3x​. .......................... . .
Mkey [24]

Answer:

algobn tu jale

Step-by-step explanation:

yo digo q C es la megor opceon

4 0
3 years ago
Implicit differentiation Please help
Anvisha [2.4K]

Answer:

y''(-1) =8

General Formulas and Concepts:

<u>Pre-Algebra</u>

Order of Operations: BPEMDAS

  1. Brackets
  2. Parenthesis
  3. Exponents
  4. Multiplication
  5. Division
  6. Addition
  7. Subtraction
  • Left to Right

Equality Properties

<u>Algebra I</u>

  • Factoring

<u>Calculus</u>

Implicit Differentiation

The derivative of a constant is equal to 0

Basic Power Rule:

  • f(x) = cxⁿ
  • f’(x) = c·nxⁿ⁻¹

Product Rule: \frac{d}{dx} [f(x)g(x)]=f'(x)g(x) + g'(x)f(x)

Chain Rule: \frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)

Quotient Rule: \frac{d}{dx} [\frac{f(x)}{g(x)} ]=\frac{g(x)f'(x)-g'(x)f(x)}{g^2(x)}

Step-by-step explanation:

<u>Step 1: Define</u>

-xy - 2y = -4

Rate of change of the tangent line at point (-1, 4)

<u>Step 2: Differentiate Pt. 1</u>

<em>Find 1st Derivative</em>

  1. Implicit Differentiation [Product Rule/Basic Power Rule]:                            -y - xy' - 2y' = 0
  2. [Algebra] Isolate <em>y'</em> terms:                                                                               -xy' - 2y' = y
  3. [Algebra] Factor <em>y'</em>:                                                                                       y'(-x - 2) = y
  4. [Algebra] Isolate <em>y'</em>:                                                                                         y' = \frac{y}{-x-2}
  5. [Algebra] Rewrite:                                                                                           y' = \frac{-y}{x+2}

<u>Step 3: Find </u><em><u>y</u></em>

  1. Define equation:                    -xy - 2y = -4
  2. Factor <em>y</em>:                                 y(-x - 2) = -4
  3. Isolate <em>y</em>:                                 y = \frac{-4}{-x-2}
  4. Simplify:                                 y = \frac{4}{x+2}

<u>Step 4: Rewrite 1st Derivative</u>

  1. [Algebra] Substitute in <em>y</em>:                                                                               y' = \frac{-\frac{4}{x+2} }{x+2}
  2. [Algebra] Simplify:                                                                                         y' = \frac{-4}{(x+2)^2}

<u>Step 5: Differentiate Pt. 2</u>

<em>Find 2nd Derivative</em>

  1. Differentiate [Quotient Rule/Basic Power Rule]:                                          y'' = \frac{0(x+2)^2 - 8 \cdot 2(x + 2) \cdot 1}{[(x + 2)^2]^2}
  2. [Derivative] Simplify:                                                                                      y'' = \frac{8}{(x+2)^3}

<u>Step 6: Find Slope at Given Point</u>

  1. [Algebra] Substitute in <em>x</em>:                                                                               y''(-1) = \frac{8}{(-1+2)^3}
  2. [Algebra] Evaluate:                                                                                       y''(-1) =8
6 0
3 years ago
Read 2 more answers
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