Answer:
4.5
Step-by-step explanation:
4x+6 = 6x-3
3+6 = 6x-4x
9 = 2x
X =4.5
Answer:
(d) m∠AEB = m∠ADB
Step-by-step explanation:
The question is asking you to compare the measures of two inscribed angles. Each of the inscribed angles intercepts the circle at points A and B, which are the endpoints of a diameter.
__
<h3>applicable relations</h3>
Several relations are involved here.
- The measures of the arcs of a circle total 360°
- A diameter cuts a circle into two congruent semicircles
- The measure of an inscribed angle is half the measure of the arc it intercepts
<h3>application</h3>
In the attached diagram, we have shown inscribed angle ADB in blue. The semicircular arc it intercepts is also shown in blue. A semicircle is half a circle, so its arc measure is half of 360°. Arc AEB is 180°. That means inscribed angle ADB measures half of 180°, or 90°. (It is shown as a right angle on the diagram.)
If Brenda draws angle AEB, it would look like the angle shown in red on the diagram. It intercepts semicircular arc ADB, which has a measure of 180°. So, angle AEB will be half that, or 180°/2 = 90°.
The question is asking you to recognize that ∠ADB = 90° and ∠AEB = 90° have the same measure.
m∠AEB = m∠ADB
_____
<em>Additional comment</em>
Every angle inscribed in a semicircle is a right angle. The center of the semicircle is the midpoint of the hypotenuse of the right triangle. This fact turns out to be useful in many ways.
Y=<span><span><span>(<span>x<span>−3</span></span>)^2</span></span><span>−<span>2 will be in vertewx form</span></span></span>
<h2>3x-4y-15=0 </h2><h2>Geometric figure: Straight Line</h2><h2> Slope = 1.500/2.000 = 0.750</h2><h2> x-intercept = 15/3 = 5</h2><h2> y-intercept = 15/-4 = -3.75000</h2><h2>Step by step solution :</h2><h2>Step 1 :</h2><h2>Equation of a Straight Line</h2><h2> 1.1 Solve 3x-4y-15 = 0 </h2><h2 /><h2>Tiger recognizes that we have here an equation of a straight line. Such an equation is usually written y=mx+b ("y=mx+c" in the UK). </h2><h2 /><h2>"y=mx+b" is the formula of a straight line drawn on Cartesian coordinate system in which "y" is the vertical axis and "x" the horizontal axis.</h2><h2 /><h2>In this formula :</h2><h2>y tells us how far up the line goes</h2><h2>x tells us how far along</h2><h2>m is the Slope or Gradient i.e. how steep the line is</h2><h2>b is the Y-intercept i.e. where the line crosses the Y axis</h2><h2>The X and Y intercepts and the Slope are called the line properties. We shall now graph the line 3x-4y-15 = 0 and calculate its properties</h2><h2>Calculate the Y-Intercept :</h2><h2>Notice that when x = 0 the value of y is 15/-4 so this line "cuts" the y axis at y=-3.75000</h2><h2> y-intercept = 15/-4 = -3.75000 </h2><h2>Calculate the X-Intercept :</h2><h2>When y = 0 the value of x is 5/1 Our line therefore "cuts" the x axis at x= 5.00000</h2><h2> x-intercept = 15/3 = 5 </h2><h2>Calculate the Slope :</h2><h2>Slope is defined as the change in y divided by the change in x. We note that for x=0, the value of y is -3.750 and for x=2.000, the value of y is -2.250. So, for a change of 2.000 in x (The change in x is sometimes referred to as "RUN") we get a change of -2.250 - (-3.750) = 1.500 in y. (The change in y is sometimes referred to as "RISE" and the Slope is m = RISE / RUN)</h2><h2> Slope = 1.500/2.000 = 0.750 </h2><h2>Geometric figure: Straight Line</h2><h2> Slope = 1.500/2.000 = 0.750</h2><h2> x-intercept = 15/3 = 5</h2><h2> y-intercept = 15/-4 = -3.75000</h2><h2>Hope This Helps!!!</h2>
