What do x square equal

Solve.and show your work

Marysya12 [62]

Answer:

a) x > − 24 $\frac{3}{4}$

b) x < − 3

c) q < 56

Step-by-step explanation:

a) −2/5x−9<9/10

<=> 2/5x + 9 > − 9/10

<=> 2/5x > − 9/10 − 9

<=> 2×2/2×5x > − 9/10 − 9×10/10

<=> 4/10x > − 99/10

<=> x > − 99/4

<=> x > − 24 $\frac{3}{4}$

b) 4x+6<−6

<=> 4x < − 6 − 6

<=> 4x < − 12

<=> x < − 12/4

<=> x < − 3

c) q+12−2(q−22)>0

<=> q+12−2q −2×(−22)>0

<=> (q−2q) + (12+ 44) >0

<=> −q + 56 >0

<=> q < 56

8 0

3 years ago

Write an equation for an ellipse centered at the origin, which has foci at (\pm\sqrt{8},0)(± 8 ,0)(, plus minus, square root o

Alchen [17]

Answer:

The equation of ellipse centered at the origin

$\frac{x^2}{18} +\frac{y^2}{10} =1$

Step-by-step explanation:

given the foci of ellipse (±√8,0) and c0-vertices are (0,±√10)

The foci are (-C,0) and (C ,0)

Given data (±√8,0)

the focus has x-coordinates so the focus is lie on x- axis.

The major axis also lie on x-axis

The minor axis lies on y-axis so c0-vertices are (0,±√10)

given focus C = ae = √8

Given co-vertices ( minor axis) (0,±b) = (0,±√10)

b= √10

The relation between the focus and semi major axes and semi minor axes are $c^2=a^2-b^2$

$a^{2} = c^{2} +b^{2}$

$a^{2} = (\sqrt{8} )^{2} +(\sqrt{10} )^{2}$

$a^{2} =18$

$a=\sqrt{18}$

The equation of ellipse formula

$\frac{x^2}{a^2} +\frac{y^2}{b^2} =1$

we know that $a=\sqrt{18} and b=\sqrt{10}$

Final answer:-

The equation of ellipse centered at the origin

$\frac{x^2}{18} +\frac{y^2}{10} =1$

8 0

3 years ago

Read 2 more answers

Gary just started a new job as a nurse. he is given a starting salary of $58,550 per year. he is also told that his salary will

IRINA_888 [86]

Firts we need to find the rate of change, or in other words, the slope of the line.

Question 1:

a)

For this we can take two points in the form (years, salary). Then we can define as year 0 the year when Gary starts to work. In this year the salary is $58,550. The first point is (0, $58,550)

The next point we can take is at the year 10, when the salary of Gary will be $71,950. The second point is (10, $71,950)

b) Now that we have the two points, we can use the slope formula to get the rate of change. The slope formula is, for two points A and B:

$\begin{gathered} \begin{cases}A(x_a,y_a) \\ B(x_b,y_b)\end{cases} \\ m=\frac{y_a-y_b}{x_a-x_b} \end{gathered}$

In this case, we can call the points A(0, $58,550) and B(10, $71,950). Using the formula:

$m=\frac{58,550-71,950}{0-10}=\frac{-13400}{-10}=1340$

c) "The rate of change in Gary's salary is $1340 per year."

Question 2:

a) The slope intercept form of a line is:

$y-y_1=m(x_{}-x_1)$

Where:

y is the output of the function.

x is the input of the function. (we provide the function with a value for x and the function give us a value of y)

m is the slope of the line. We calculate it in question 1.

x1 is the x coordinate of a point we choose.

y1 is the y-coordinate of the same point of x1.

In this case, we know:

m = 1340;

And we can take the point (0, $58,550), thus:

x1 = 0

y1 = 58,550

b) Now we need to use all this values and use the slope-intercept form:

$y-58,550=1340(x-0)$

And solve to get:

$y=1340x+58,550$

Question 3:

a) Now we have a equation for the salary, we can use this to find the salary in 13 years. We just need to replace x = 13 in the equation:

$\begin{gathered} \begin{cases}y=1340x+58,550 \\ x=13\end{cases} \\ y=1340\cdot13+58,550 \\ y=75,970 \end{gathered}$

B) The salary of Gary in 13 years will be $75,970.

6 0

1 year ago

8.234 E14 in standard form

insens350 [35]

Answer:

8234.000 x 10^3

Step-by-step explanation:

5 0

3 years ago

Read 2 more answers

2. Lani opened a savings account with $450. She

lidiya [134]

Answer: C

Step-by-step explanation:

450 is her initial value

225 is her rate of change or constant rate

5 0

3 years ago