Solve for x in the diagram. A. 25 B. 37 C. 14 D. 15

Find the values of a and b such that

Varvara68 [4.7K]

Answer:

a = 1.5

b = 1.75

Step-by-step explanation:

First, we need to solve $(x+a)^2$ and replace the result in the initial equation as:

$x^2+3x+4=(x+a)^2+b\\x^2+3x+4=x^2+2ax+a^2+b$

Then, this equality apply only if the coefficient of $x$ is equal in both sides and the constant is equal in both sides.

It means that we have two equations:

$3x=2ax\\4=a^2+b$

So, using the first equation and solving for a, we get:

$3x=2ax\\3=2a\\a=\frac{3}{2}=1.5$

Finally, replacing the value of a in the second equation and solving for b, we get:

$4=a^2+b\\4=1.5^2+b\\b=4-1.5^2\\b=4-2.25\\b=1.75$

3 0

3 years ago

Molly and James tracked the average temperature in their city for the past 8 days. They recorded their temperature findings in t

Katyanochek1 [597]

Add all the numbers then divde by how many numbers there are so the total divde by 8

5 0

3 years ago

What is the circumference of the circle? Use a = 3.14. Round your answer to the

larisa [96]

Answer: 53.4 cm

Step-by-step explanation:

The formula for circumference is C=2πr or C=πd. These equations are the same. Since the problem gives us the diameter, we'll go ahead and use C=πd.

C=(3.14)(17)

C=53.38=53.4 cm

3 0

2 years ago

A spinner has three sections. The table shows the results of spinning the arrow on the spinner 80 times.

Andrew [12]

The answer to your question is D: 45

4 0

3 years ago

Read 2 more answers

The point (8,-4) lies on a circle. What is the length of the radius of this circle if the center is located at (5,-7)

Kamila [148]

Notice the picture, the radius is just the distance from the
center to a point on the circle, thus

$\bf \textit{distance between 2 points}\\ \quad \\\\
\begin{array}{lllll}
&x_1&y_1&x_2&y_2\\
% (a,b)
&({{5}}\quad ,&{{ -7}})\quad 
% (c,d)
&({{ 8}}\quad ,&{{ -4}})
\end{array}\qquad 
% distance value
\\\\\\
\begin{array}{llll}
d = &\sqrt{({{ x_2}}-{{ x_1}})^2 + ({{ y_2}}-{{ y_1}})^2}\\
&\qquad \uparrow \\
&radius
\end{array}$

$\bf \begin{array}{llll}
d = &\sqrt{({{ 8}}-{{ 5}})^2 + ({{ -4}}-{{(-7)}})^2}\\
&\qquad \uparrow \\
&radius
\end{array}
\\\\\\
d=\sqrt{(3)^2+(-4+7)^2}\implies d=\sqrt{3^2+3^2}\implies d=\sqrt{18}
\\\\\\
d=\sqrt{9\cdot 2}\implies d=\sqrt{3^2\cdot 2}\implies d=3\sqrt{2}$

4 0

3 years ago