Answer:
Step-by-step explanation:
The slope of a graph is also known as its gradient, which is the steepness of the graph.
If we are given two points on the line, we can find the slope by taking rise/ run, which is the ratio of the change in y-coordinate against the change in the x-coordinate. This can also be written as a formula:
☆ (x₁, y₁) is the first coordinate and (x₂, y₂) is the second coordinate
In this question, we are given the equation of the line. This equation is already in the slope-intercept form (y= mx +c) since the coefficient of y is 1 and all the other terms are on the other side of the equal sign. In the slope-intercept form, m is the slope while c is the y-intercept.
m= ⅘ since the coefficient of x is ⅘ in the given equation (when the equation is in the slope-intercept form).
Answer:
75°
Step-by-step explanation:
∠ESK is the supplement of ∠EDK, so is 100°. ∠ESD = 1/2·arc ED, so is 25°. Since ...
∠ESK = ∠ESD + ∠DSK
you have ...
100° = 25° + ∠DSK . . . . fill in known values
75° = ∠DSK . . . . . . . . . . subtract 25°
_____
Regarding opposite angles of an inscribed quadrilateral
Chord EK divides the 360° circle into two arc: major arc EDK and minor arc ESK. The sum of those arcs is 360°. Each of the inscribed angles that intercepts those arcs has half the measure of the arc. That is, ∠ESK intercepts arc EDK, so has half its measure. Likewise, ∠EDK intercepts arc ESK, so has half its measure. The sum of those opposite angles will be the sum of half the measures of the arcs, so half the sum of the arcs, or 1/2·360° = 180°.
This is why we can say ∠ESK is the supplement of ∠EDK.
Answer:
B) 25°
Step-by-step explanation:
Assuming the quadrilateral is the one shown in the picture attached, then a triangle ADC is form, where m∠ADC = 125° and m∠1 = 30°. The addition of the three angles of a triangle is equal to 180°, so:
m∠ADC + m∠1 + m∠2 = 180°
Replacing with the known values and isolating m∠2 we get:
125° + 30° + m∠2 = 180°
m∠2 = 180° - 125° - 30°
m∠2 = 25°
The long, straightforward, brute-force way to slog through the problem:
The prism is 12cm x 6cm x 9cm.
Volume of the prism = (12 x 6 x 9) = 648 cm³
Volume of each little cube = (1.5 x 1.5 x 1.5) = 3/375 cm³
Number of little cubes that fit into the prism = (648 cm³) / (3.375 cm³) = <em>
192 of them</em>
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The elegant but almost equally long way to master the problem:
The prism is 12cm x 6cm x 9cm.
If each dimension of your measuring cubie is 1.5cm,
then the prism measures
(8 cubie lengths) x (4 cubie widths) x (6 cubie heights) .
Its volume is (8 x 4 x 6) = <em>192 measuring cubies</em>.
