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ASHA 777 [7]
3 years ago
11

Which equation represents the relationship “4 less than a number is 10?”

Mathematics
2 answers:
DochEvi [55]3 years ago
8 0

Answer:

x - 4 = 10

x = 14

Step-by-step explanation:

Any variable can be used to represent the number, I choose to use "x" in this case.

x - 4 = 10

Inverse operations;

x - 4 = 10

  +4    +4

x = 14

Naily [24]3 years ago
6 0
X+3=7
Which 7-3 would be 4
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Let g(x) be the reflection of f(x)=x2+5 jn the x axis. what is a function rule for g(x)
Pie
X axis
means y turns to -y
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g(x)=-(x^2+5)
g(x)=-x^2-5

4 0
3 years ago
SOMEONE, PLEASE HELP!!!!!!
andrezito [222]

Answer:

I think its y^-3

Step-by-step explanation:

Since y^-3/y^-2 are both negatives they would swap places to become positive - y^2/y^3

then using rules of exponents you would subtract the exponents witch would be y^-3

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Which expdession is equivalent to 4-2(3x-5)​
GalinKa [24]

Answer:

4

Step-by-step explanation:

Your answer would be 0 because you have to subtract 3 by 5 you get the answer 2. Then you subtract 4 by 2 and you 2. After that you multiply 2 by 2 getting the answer 4.

7 0
3 years ago
Show all of your work, even though the question may not explicitly remind you to do so. Clearly label any functions, graphs, tab
Leona [35]

Answer:

a. 5 b. y = -\frac{3}{4}x + \frac{1}{2} c. 148.5 d. 1/7

Step-by-step explanation:

Here is the complete question

Show all of your work, even though the question may not explicitly remind you to do so. Clearly label any functions, graphs, tables, or other objects that you use. Justifications require that you give mathematical reasons, and that you verify the needed conditions under which relevant theorems, properties, definitions, or tests are applied. Your work will be scored on the correctness and completeness of your methods as well as your answers. Answers without supporting work will usually not receive credit. Unless otherwise specified, answers (numeric or algebraic) need not be simplified. If your answer is given as a decimal approximation, it should be correct to three places after the decimal point. Unless otherwise specified, the domain of a function f is assumed to be the set of all real numbers for which f() is a real number Let f be an increasing function with f(0) = 2. The derivative of f is given by f'(x) = sin(πx) + x² +3. (a) Find f" (-2) (b) Write an equation for the line tangent to the graph of y = 1/f(x) at x = 0. (c) Let I be the function defined by g(x) = f (√(3x² + 4). Find g(2). (d) Let h be the inverse function of f. Find h' (2). Please respond on separate paper, following directions from your teacher.

Solution

a. f"(2)

f"(x) = df'(x)/dx = d(sin(πx) + x² +3)/dx = cos(πx) + 2x

f"(2) = cos(π × 2) + 2 × 2

f"(2) = cos(2π) + 4

f"(2) = 1 + 4

f"(2) = 5

b. Equation for the line tangent to the graph of y = 1/f(x) at x = 0

We first find f(x) by integrating f'(x)

f(x) = ∫f'(x)dx = ∫(sin(πx) + x² +3)dx = -cos(πx)/π + x³/3 +3x + C

f(0) = 2 so,

2 = -cos(π × 0)/π + 0³/3 +3 × 0 + C

2 = -cos(0)/π + 0 + 0 + C

2 = -1/π + C

C = 2 + 1/π

f(x) = -cos(πx)/π + x³/3 +3x + 2 + 1/π

f(x) = [1-cos(πx)]/π + x³/3 +3x + 2

y = 1/f(x) = 1/([1-cos(πx)]/π + x³/3 +3x + 2)

The tangent to y is thus dy/dx

dy/dx = d1/([1-cos(πx)]/π + x³/3 +3x + 2)/dx

dy/dx = -([1-cos(πx)]/π + x³/3 +3x + 2)⁻²(sin(πx) + x² +3)

at x = 0,

dy/dx = -([1-cos(π × 0)]/π + 0³/3 +3 × 0 + 2)⁻²(sin(π × 0) + 0² +3)

dy/dx = -([1-cos(0)]/π + 0 + 0 + 2)⁻²(sin(0) + 0 +3)

dy/dx = -([1 - 1]/π + 0 + 0 + 2)⁻²(0 + 0 +3)

dy/dx = -(0/π + 2)⁻²(3)

dy/dx = -(0 + 2)⁻²(3)

dy/dx = -(2)⁻²(3)

dy/dx = -3/4

At x = 0,

y = 1/([1-cos(π × 0)]/π + 0³/3 +3 × 0 + 2)

y = 1/([1-cos(0)]/π + 0 + 0 + 2)

y = 1/([1 - 1]/π + 2)

y = 1/(0/π + 2)

y = 1/(0 + 2)

y = 1/2

So, the equation of the tangent at (0, 1/2) is

\frac{y - \frac{1}{2} }{x - 0} = -\frac{3}{4}  \\y - \frac{1}{2} = -\frac{3}{4}x\\y = -\frac{3}{4}x + \frac{1}{2}

c. If g(x) = f (√(3x² + 4). Find g'(2)

g(x) = f (√(3x² + 4) = [1-cos(π√(3x² + 4)]/π + √(3x² + 4)³/3 +3√(3x² + 4) + 2

g'(x) = [3xsinπ√(3x² + 4) + 18x(3x² + 4) + 9x]/√(3x² + 4)

g'(2) = [3(2)sinπ√(3(2)² + 4) + 18(2)(3(2)² + 4) + 9(2)]/√(3(2)² + 4)

g'(2) = [6sinπ√(12 + 4) + 36(12 + 4) + 18]/√12 + 4)

g'(2) = [6sinπ√(16) + 36(16) + 18]/√16)

g'(2) = [6sin4π + 576 + 18]/4)

g'(2) = [6 × 0 + 576 + 18]/4)

g'(2) = [0 + 576 + 18]/4)

g'(2) = 594/4

g'(2) = 148.5

d. If h be the inverse function of f. Find h' (2)

If h(x) = f⁻¹(x)

then h'(x) = 1/f'(x)

h'(x) = 1/(sin(πx) + x² +3)

h'(2) = 1/(sin(π2) + 2² +3)

h'(2) = 1/(sin(2π) + 4 +3)

h'(2) = 1/(0 + 4 +3)

h'(2) = 1/7

7 0
3 years ago
A sociologist wants to know the opinions of employed adult women about government funding for day care. The women were asked to
Zarrin [17]

Answer:

The correct option is C 20.1%.

Step-by-step explanation:

The probability distribution chart representing the opinions of employed adult women about government funding for day care is as follows:

Rating (<em>X</em>)        Probability (<em>p</em>)

     1                      0.110

     2                      0.206

     3                      0.464

     4                      0.201

     5                      0.119

The ratings are defined as follows:

1: too little

2: helpful but not enough

3: make a difference but insufficient

4: sufficient

5: generous

The probability of women who think that the support is sufficient is, 0.201.

The percentage is: 0.201 × 100 = 20.1%

Thus, the percentage of women who think that the support is sufficient is 20.1%.

The correct option is C.

5 0
3 years ago
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