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4 years ago

Given s(x) = 2x - 3 and t(x) = 5x + 4. find the formula and domain for s(x) over t(x) and w(x) = t(x) over s(x)

1 answer:

6 0

V(x) = (2x - 3)/(5x + 4) The domain is all Real numbers except x = -4/5, because if x = -4/5 the denominator would be zero and you cannot divide by zero.{x | x ∈ R, x ≠ -4/5} w(x) = (5x + 4)/(2x - 3)similarly, x ≠ 3/2so, {x| x ∈ R, x ≠ 3/2}

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Quadrilateral ABCD is similar to Quadrilateral EFGH. Diagonal AC has length 7 and diagonal EG has length 13. What is the scale f

olasank [31]

Answer:

$\large \boxed{\text{A. }\dfrac{13}{7}\text{; B. }\dfrac{17}{14} \text{; C. 507 in}^{2}}$

Step-by-step explanation:

A. Scale factor

When you dilate an object by a scale factor, you multiply its line lengths by the same number.

If EF/AB = 13/7, the scale factor is 13/7.

B. Length of EF

$\begin{array}{rcl}\dfrac{EF}{AB} & = & \dfrac{13}{7}\\\\\dfrac{EF}{\frac{17}{26}} & = & \dfrac{13}{7}\\\\EF & = & \dfrac{13}{7}\times\dfrac{17}{26}\\\\ & = &\dfrac{1}{7}\times\dfrac{17}{2}\\\\ & = & \mathbf{\dfrac{17}{14}}\\\end{array}\\\text{The length of EF is $\large \boxed{\mathbf{ \dfrac{17}{14}}}$}$

C. Area of EFGH

If the lengths in a shape are all multiplied by a scale factor, then the areas will be multiplied by the scale factor squared.

ABCD is dilated by a scale factor of 13/7, so its area is dilated by a scale factor of

$\left(\dfrac{13}{7} \right)^{2} = \dfrac{169}{49}$

The area of its dilated image EFGH is

$\text{Area of EFGH} = \text{147 in}^{2} \times \dfrac{\text{169}}{\text{49}} = 3 \times 169\text{ in}^{2} = 507 \text{ in}^{2}\\\\\text{The area of EFGH is $\large \boxed{\textbf{507 in}^{\mathbf{2}}}$}$

8 0

3 years ago

17.3152 to the nearest hundredth=

mamaluj [8]

Answer:

17.32

Step-by-step explanation:

since there is a 5 in the thousandths, we round the 1 in the hundredths up and get 17.32

3 0

2 years ago

8 times of the eight term of an arithmetic progression is equal to 12 times of the twelfth term. find its first term if the comm

Ilya [14]

Answer:

a₁ = 38

Step-by-step explanation:

Given AP, where:

8a₈ = 12a₁₂
d = -2,
a₁ = ?

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<h3>Solution</h3>

aₙ = a₁ + (n-1)d

a₈ = a₁ + 7d = a₁ + 7*(-2) = a₁ - 14
a₁₂ = a₁ + 11d = a₁ + 11*(-2) = a₁ - 22

8a₈ = 12a₁₂

8(a₁ - 14) = 12(a₁ - 22)
2(a₁ - 14) = 3(a₁ - 22)
2a₁ - 28 = 3a₁ - 66
3a₁ - 2a₁ = -28 + 66
a₁ = 38

6 0

3 years ago

The time, t, required to drive to a certain distance varies inversely with the speed, r. if it takes 12 hours to drive the dista

kap26 [50]

T = k/R where k is the constant of variation, T=time and R=speed.
Plug in the given values:-
12 = k/60
k = 12*60 = 720
So the equation of variation is T = 720/R

At 85 mph we have

T = 720 / 85 = 8.47 hours (answer)

8 0

3 years ago

M= 2²×3×5² N=2³×3²×7<br>find the largest Number that divides exactly into M and N

nevsk [136]

Answer:

Step-by-step explanation:

just find the HCF, which will be

2² × 3 = 12

5 0

2 years ago