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3 years ago

I have f(x)=x^2+x+5. Then (f(x)-f(a))/(x-a).

Mathematics

1 answer:

Salsk061 [2.6K]3 years ago

7 0

Answer:

(f(x) -f(a))/(x -a) = x +a +1

Step-by-step explanation:

(f(x) -f(a))/(x -a) = ((x^2 +x +5) -(a^2 +a +5))/(x -a) = (x^2 -a^2 +x -a)/(x -a)

= ((x -a)(x +a) +(x -a))/(x -a) = x +a +1

(f(x) -f(a))/(x -a) = x +a +1

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Rearrange the standard form of the equation below into y = mx + b by isolating y. <br> 5x − 2y = 6

Minchanka [31]

Answer:

y = $\frac{5}{2}$ x - 3

Step-by-step explanation:

5x - 2y = 6 ( subtract 5x from both sides )

- 2y = - 5x + 6 ( divide through by - 2 )

y = $\frac{5}{2}$ x - 3 ← in slope- intercept form

5 0

3 years ago

Can someone help me?

Lana71 [14]

Answer:

I'm not sure from my answer but I'm going to try

A = { a^2 - 4 = 0 }

A = { a^2 = 0+ 4 }

A = { a^2 = 4}

Take root of both sides

A = {a = 2}

A = {2}

B = { -2, -1, 0, 1, 2}

C = { 1, 2, 3, 4, 5, 6,7}

i) A\B

= {2} \ {-2,-1,0,1,2}

= ⌀ ( "null set" )

ii) (A\B) \C

= ( {2} \ {-2,-1,0,1,2} ) \ C

= ⌀ \ C

= ⌀ \ { 1, 2, 3, 4, 5, 6,7}

= ⌀ ( "null set" )

iii) (A ∪ B) \ C

= ( { 2 } ∪ { -2, -1, 0, 1, 2} ) \ C

= { -2, -1, 0, 1, 2} \C

= { -2, -1, 0, 1, 2} \ { 1, 2, 3, 4, 5, 6,7}

= { -2, -1, 0 }

iv) ( A\B) ∩ ( A\C)

= ( { 2 } \ {-2,-1,0,1,2} ) ∩ ( { 2 } \ { { 1, 2, 3, 4, 5, 6,7} )

= ⌀ ∩ ⌀

= ⌀

v) ( A ∩ B ) \ C

= ( { 2 } ∩ { -2, -1, 0, 1, 2 } ) \ C

= { 2 } \ { 1, 2, 3, 4, 5, 6, 7 }

= ⌀ "null set"

7 0

3 years ago

What is the quotient of 1/8 divided by 4

barxatty [35]

Answer:

0.03125

Step-by-step explanation:

1/8 would also equal to (1 divided by 8) which equals 0.125. The next step is to divide 0.125 by 4. you will get 0.03125

3 0

3 years ago

Read 2 more answers

Dentify the pattern for the following sequence. find the next three terms in the sequence. 5, 2, -1, -4, ____, ____, ____,...

kvasek [131]

Every time you are -3, the next terms would be -7, -10, -13

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3 years ago

Real Estate One conducted a recent survey of house prices for properties located on the shores of Tawas Bay. Data on 26 recent s

Ivanshal [37]

Answer:

Step-by-step explanation:

Hello!

Given the data for the variables:

Y: Selling price of a house on the shore of Tawas Bay

X₁: Number of bathrooms of a house on the shore of Tawas Bay.

X₂: Square feet of a house on the shore of Tawas Bay.

X₃: Number of bedrooms of a house on the shore of Tawas Bay.

The multiple regression model is Y= α + β₁X₁ + β₂X₂ + β₃X₃ + εi

a. Using software I've entered the raw data and estimated the regression coefficients:

^α= a= -5531.01

Represents the mean selling price of the houses when 0 bathrooms, 0 square feet and 0 bedrooms.

^β₁= b₁= -1386.21

Represents the modification of the mean selling price of the houses when the number of bathrooms increases in one unit and the square feet and number of bedrooms remain unchanged.

^β₂= b₂= 60.28

Represents the modification of the mean selling price of the houses when the square feet increase in one unit and the number of bathrooms and bedrooms remain unchanged.

^ β₃= b₃= 54797.08

Represents the modification of the mean selling price of the houses when the number of bedrooms increase in one unit and the number of bathrooms and square feet of the houses remain unchanged.

^Y= -5531.01 -1386.21X₁ + 60.28X₂ + 54797.08X₃

R²= 0.55

R²Aj= 0.49

The coefficient of determination gives you an idea of how much of the variability of the dependent variable (Y) is due to the explanatory variables. Each time you add another explanatory variable to the regression the coefficient increases regarding of real contribution of the new variable. This could lead to thinking (wrongly) that the new variables are good to explain the dependent variable.

The adjusted coefficient of determination is a correction made to the raw coefficient of determination to have a more unbiased estimation of the effect the independent variables have over the dependent variable.

⇒ As you can see both coefficient are around 50%, which means that these explanatory variables

The standard error estimate, this is the estimate of the population variance of the errors. In the ANOVA is represented by the Mean Square of the errors (MME)

Se²= MME= 3837640577.01

Se= 61948.6931

d) and f)

For the hypotheses tests for each slope the t- and p-values are:

α: 0.05

β₁: $t_{H_0}= \frac{b_1-\beta_1 }{Sb_1}$ t= -0.06; p-value: 0.9528 ⇒ Do not reject H₀, the test is not significant.

β₂: $t_{H_0}= \frac{b_2-\beta_2 }{Sb_2}$ t= 2.56; p-value: 0.0180 ⇒ Reject H₀, the test is significant.

β₃: $t_{H_0}= \frac{b_3-\beta_3 }{Sb_3}$ t= 2.28; p-value: 0.0326 ⇒ Reject H₀, the test is significant.

H₀: β₁= β₂= β₃

H₁: At least one βi is different from the others ∀ i=1, 2, 3

α: 0.05

F= 9.03

p-value: 0.0004

⇒ Reject H₀, the test is significant.

I hope it helps!

5 0

3 years ago