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2 years ago

Abbie is 5 years older than Cathy.

Mathematics

1 answer:

nlexa [21]2 years ago

5 0

14 because 14 times 2 is 28 which is less than 30

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Which statement describes the inverse of m(x) = x^2 – 17x?

DochEvi [55]

Given:

The function is

$m(x)=x^2-17x$

To find:

The inverse of the given function.

Solution:

We have,

$m(x)=x^2-17x$

Substitute m(x)=y.

$y=x^2-17x$

Interchange x and y.

$x=y^2-17y$

Add square of half of coefficient of y , i.e., $\left(\dfrac{-17}{2}\right)^2$ on both sides,

$x+\left(\dfrac{-17}{2}\right)^2=y^2-17y+\left(\dfrac{-17}{2}\right)^2$

$x+\left(\dfrac{17}{2}\right)^2=y^2-17y+\left(\dfrac{17}{2}\right)^2$

$x+\left(\dfrac{17}{2}\right)^2=\left(y-\dfrac{17}{2}\right)^2$ $[\because (a-b)^2=a^2-2ab+b^2]$

Taking square root on both sides.

$\sqrt{x+\left(\dfrac{17}{2}\right)^2}=y-\dfrac{17}{2}$

Add $\dfrac{17}{2}$ on both sides.

$\sqrt{x+\left(\dfrac{17}{2}\right)^2}+\dfrac{17}{2}=y$

Substitute $y=m^{-1}(x)$ .

$m^{-1}(x)=\sqrt{x+(\dfrac{189}{4}})+\dfrac{17}{2}$

We know that, negative term inside the root is not real number. So,

$x+\left(\dfrac{17}{2}\right)^2\geq 0$

$x\geq -\left(\dfrac{17}{2}\right)^2$

Therefore, the restricted domain is $x\geq -\left(\dfrac{17}{2}\right)^2$ and the inverse function is $m^{-1}(x)=\sqrt{x+(\dfrac{189}{4}})+\dfrac{17}{2}$ .

Hence, option D is correct.

Note: In all the options square of $\dfrac{17}{2}$ is missing in restricted domain.

7 0

3 years ago

Which is the definition of a ray?

zlopas [31]

Answer:

a part of a line that has one endpoint and extends indefinitely in one direction

Step-by-step explanation:

a ray has one endpoint, then has an arrow going indefinitely in one direction.

8 0

2 years ago

Simplify the expression 9m-7m+2m

tatuchka [14]

Simplify step-by-step.

9m−7m+2m

=9m+−7m+2m

Combine Like Terms:

=9m+−7m+2m

=(9m+−7m+2m)

=4m

4 0

2 years ago

The angles of elevation froma point X to the top of flagpoles A and B are 35* and 45* respectively. If X lies in the middle of t

BartSMP [9]

Let AB = t. And since X lies in the middle, so AX=BX = t/2 .

Let the height of the smaller flagpole is AO and of larger flagpole is BP .

Using tangent ratio rule in each triangle, we will get

$tan 35 =\frac{AO}{t/2} , tan 45= \frac{BP}{t/2} // AO = \frac{t*tan35}{2}, BP=\frac{t*tan45}{2}$

And there ratio is

$\frac{AO}{BP}= \frac{tan 35}{tan 45}=\frac{0.7}{1}$

5 0

2 years ago

Jane Marko buys a car for $43,900. In three years, the car depreciates 48% in value. How much is the car worth in 3 years

Marina86 [1]

$21,072 is the answer since you the original price is 43,900 and it has decreased 48% therefore using .48 to multiply with 43,900 to find the value after 3 years

4 0

2 years ago