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umka2103 [35]
3 years ago
6

Information reference tables what is the solution set of the equation log4 (x2 + 3x) − log4 (x + 5) = 1?

Mathematics
1 answer:
faust18 [17]3 years ago
5 0
Use this property of logarithms:

\log_b\left(\dfrac{x}{y}\right)=\log_b x-\log_b y

Your equation transforms into:

log_4\left(\dfrac{x^2+3x}{x+5}\right)=1

Now, you have to apply the definition of a logarithm to express the equation in exponential form:

\dfrac{x^2+3x}{x+5} = 4^1

In case you don't remember, this is the definition of a logarithm:

\log_b x = y \iff b^y = x

The log is the exponent (y) you have to raise the base (b) to in order to get the power (x).

Finally, solve the rational equation:

\dfrac{x^2+3x}{x+5} =4 \iff x^2+3x=4(x+5)
\iff x^2-x-20=0
\iff x=\dfrac{1\pm\sqrt{(-1)^2-4\cdot(-20)}}{2}= \left \{ {{5} \atop {-4}} \right.

The correct answer is d.
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a line segment has (x1,y1) as one endpoint and (xm,ym) as its midpoint. Find the other endpoint (x2,y2)of the line segment in te
svlad2 [7]

(x1,y1)

(x2,y2)

(xm,ym)

Midpoint formula is given as below.

((x1 + x2)/2 , (y1 + y2)/2 )

Where

(x1 + x2)/2 = xm ----------- (1)

(y1 + y2)/2 = ym ----------- (2)

Equation (1) implies that;

x1 + x2 = 2xm

x2 = 2xm – x1

Equation (2) implies that;

y1 + y2 = 2ym

y2 = 2ym – y1

Thus the end point is

<span>(x2,y2) = (2xm – x1, 2ym – y1)</span>

7 0
3 years ago
Read 2 more answers
Click on the number line below to show the approximate location of 19 on the number line.
dsp73

Answer:

Between 4 and 5

Step-by-step explanation:

The closest square numbers are 16 and 25, so it’s in between 4 and 5

8 0
2 years ago
Find the slope of the line through each pair of points.
Fudgin [204]
<h2>Answer:    slope = ¹¹/₁₃ </h2><h3>Step-by-step explanation:    </h3>

      The question gives us two points, (−13, −19) & (13, 3), from which we can find the slope and later the equation of the line.

Finding the Slope

The slope of the line (m) = (y₂ - y₁) ÷ (x₂ - x₁)      

                                          =  ((3 - (-19)) ÷ (13 - (-13))      

                                          =   22 ÷ 26

                                          =  ¹¹/₁₃

<em></em>

<em></em>

<em>Checking my answer:</em>

<em>We can now use the point-slope form (y - y₁) = m(x - x₁)) to write the equation for this line. If the line passes through both of the points then we calculated the slope correctly.</em>

                                ⇒  y + 19 =  ¹¹/₁₃ (x + 13)

<em>I have included a Desmos Graph that I graphed using the information equation (including the slope) and the points given. </em>

7 0
3 years ago
{{Geomotry}} <br> please I need help! My math grade depends on it! ;w;
lozanna [386]
This basically means that you have to multiply the x and y values by 3. So 2 time 3 is 6. And -7 times 3 is -21. So the new coordinations are (6, -21)

Hope this helped and pls mark as brainliest!

~ Luna
3 0
3 years ago
Find four consecutive integers with a sum of 106.
grandymaker [24]
4 consecutive integers...
x, x + 1, x + 2, x + 3

x + x + 1 + x + 2 + x + 3 = 106
4x + 6 = 106
4x = 106 - 6
4x = 100
x = 100/4
x = 25

x + 1 = 25 + 1 = 26
x + 2 = 25 + 2 = 27
x + 3 = 25 + 3 = 28

ur 4 integers are : 25,26,27,28
6 0
2 years ago
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