Consider the function f(x) = 5(x - 4) + 9. Determine f(2b).

What is is distance between (0,2) and (5,2)

likoan [24]

5 units. The only variable changing is x so it's just 5 units up from the second coordinate

3 0

3 years ago

What is the area of the model in the problem?

nata0808 [166]

Answer:

$A=x^2+12x+27\ units^2$

Step-by-step explanation:

we know that

The area of the model is equal to the area of a rectangle

The area of a rectangle is equal to

$A=LW$

we have

$L=x+9\ units$

$W=x+3\ units$

substitute

$A=(x+9)(x+3)$

Apply distributive property

$A=x^2+3x+9x+27$

Combine like terms

$A=x^2+12x+27\ units^2$

4 0

4 years ago

A right-angled triangle has shorter side lengths exactly c^2-b^2 and 2bc units respectively, where b and c are positive real num

yKpoI14uk [10]

Answer: hypotenuse = $c^{2} + b^{2}$

Step-by-step explanation: Pythagorean theorem states that square of hypotenuse (h) equals the sum of squares of each side ( $s_{1},s_{2}$ ) of the right triangle, .i.e.:

$h^{2} = s_{1}^{2} + s_{2}^{2}$

In this question:

$s_{1}$ = $c^{2}-b^{2}$

$s_{2} =$ 2bc

Substituing and taking square root to find hypotenuse:

$h=\sqrt{(c^{2}-b^{2})^{2}+(2bc)^{2}}$

Calculating:

$h=\sqrt{c^{4}+b^{4}-2b^{2}c^{2}+(4b^{2}c^{2})}$

$h=\sqrt{c^{4}+b^{4}+2b^{2}c^{2}}$

$c^{4}+b^{4}+2b^{2}c^{2}$ = $(c^{2}+b^{2})^{2}$ , then:

$h=\sqrt{(c^{2}+b^{2})^{2}}$

$h=(c^{2}+b^{2})$

Hypotenuse for the right-angled triangle is $h=(c^{2}+b^{2})$ units

3 0

3 years ago

If a woodchuck could chuck 2<br> pieces of wood every hour, how big is a beavers dam?

Nataly_w [17]

Answer:

How many hours?

Step-by-step explanation:

the answer to this is 2x

X is the number of hours and you multipy it by 2 wood

6 0

4 years ago

Listed below are the overhead widths (in cm) of seals measured from photographs and the weights (in kg) of the seals. Construc

Anarel [89]

Answer and Step-by-step explanation: Scaterplot is a type of graphic which shows the relationship between to variables. In this question, you want to determine if there is a linear relationship between overhead widths of seals and the weights. So, the hypothesis are:

H₀: no linear correlation;

H₁: there is linear correlation;

In this hypothesis test, to reject H₀, the correlation coefficient r of the data set has to be bigger than the critical value from the table.

With α = 0.05 and n = 6, the critical value is 0.811.

The linear correlation is calculated as:

r = n∑xy - ∑x.∑y / √[n∑x² - (∑x)²] [n∑y² - (∑y)²]

r = $\frac{6.9632 - 51.1108}{\sqrt{6.439 - (51^{2} )}.6.14482 - (1108^{2} ) }$

r = 0.9485

Since r is bigger than the critical value, H₀ is rejected, which means there is enough evidence to conclude that there is linear correlation between overhead widths and the weights.

In the attachments is the scaterplot of the measurements, also showing the relationship.

5 0

4 years ago