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3 years ago

Find the value of x. A. 144 B. 44 C. 25 D. 50

Mathematics

1 answer:

Soloha48 [4]3 years ago

3 0

Answer:

Step-by-step explanation:

The angle formed by two secants = 1/2(difference of intercepted arcs)

x = 1/2 (72-22)

x = 1/2 (50)

x = 25

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Express in partial fraction

aksik [14]

Step-by-step explanation:

<u>There is one possible way:</u>

(4x² - 47x + 141)/(x² + 13x + 40) =
(4x² + 4*13x + 4*40 - 47x - 52x - 160 + 141)/(x² + 13x + 40) =
4 - (99x + 19)/(x² + 13x + 40)

No further simplification

8 0

3 years ago

Read 2 more answers

Solve the equation by graphing. If exact roots cannot be found, state the consecutive integers between which the roots are locat

zavuch27 [327]

Answer:

The equation contains exact roots at x = -4 and x = -1.

See attached image for the graph.

Step-by-step explanation:

We start by noticing that the expression on the left of the equal sign is a quadratic with leading term $x^2$ , which means that its graph shows branches going up. Therefore:

1) if its vertex is ON the x axis, there would be one solution (root) to the equation.

2) if its vertex is below the x-axis, it is forced to cross it at two locations, giving then two real solutions (roots) to the equation.

3) if its vertex is above the x-axis, it will not have real solutions (roots) but only non-real ones.

So we proceed to examine the vertex's location, which is also a great way to decide on which set of points to use in order to plot its graph efficiently:

We recall that the x-position of the vertex for a quadratic function of the form $f(x)=ax^2+bx+c$ is given by the expression: $x_v=\frac{-b}{2a}$

Since in our case $a=1$ and $b=5$ , we get that the x-position of the vertex is: $x_v=\frac{-b}{2a} \\x_v=\frac{-5}{2(1)}\\x_v=-\frac{5}{2}$

Now we can find the y-value of the vertex by evaluating this quadratic expression for x = -5/2:

$y_v=f(-\frac{5}{2})\\y_v=(-\frac{5}{2} )^2+5(-\frac{5}{2} )+4\\y_v=\frac{25}{4} -\frac{25}{2} +4\\\\y_v=\frac{25}{4} -\frac{50}{4}+\frac{16}{4} \\y_v=-\frac{9}{4}$

This is a negative value, which points us to the case in which there must be two real solutions to the equation (two x-axis crossings of the parabola's branches).

We can now continue plotting different parabola's points, by selecting x-values to the right and to the left of the $x_v=-\frac{5}{2}$ . Like for example x = -2 and x = -1 (moving towards the right) , and x = -3 and x = -4 (moving towards the left.

When evaluating the function at these points, we notice that two of them render zero (which indicates they are the actual roots of the equation):

$f(-1) = (-1)^2+5(-1)+4= 1-5+4 = 0\\f(-4)=(-4)^2+5(-4)_4=16-20+4=0$

The actual graph we can complete with this info is shown in the image attached, where the actual roots (x-axis crossings) are pictured in red.

Then, the two roots are: x = -1 and x = -4.

5 0

3 years ago

Please help asap 25 pts

guajiro [1.7K]

D because the y-intercept is at -5 like shown in the equation, and the slope equals to 1, and I do believe that the bold line means that it is less than or equal to, just like the equation says.

3 0

3 years ago

Find the area of a circle with a radius of 6 centimeters. Round to the nearest tenth

coldgirl [10]

Answer: 113.1 cm^2

Step-by-step explanation: The formula to find the area of a circle is 3.14r^2. R stands for radius which is 6 in this case so just plug that in for R. 3.14(6)^2=113.1

8 0

4 years ago

Mathew deposits 400800.00 kina with the bank which offers 5½% interest per annum. calculate the interest earned after four years

Sati [7]

Solution

For this case we can use the following formula:

$A=P(1+\frac{r}{n})^{nt}$

Where:

P= 400800 = present value

A= future value

r= 0.055 interest rate

n= 4, number of times that the interest is compund in a year (quarterly)

t= 4 years

Replacing we got:

$A=400800(1+\frac{0.055}{4})^{4\cdot4}=498679.58$

then the interest would be:

$I=A-P=498679.58-400800=97879.58$

4 0

1 year ago