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3 years ago

What is the value of y?

Mathematics

1 answer:

sesenic [268]3 years ago

5 0

The lines through side AB and side AC tell us that both sides are congruent, and by the isosceles triangle theorem that means that m∠ABC = m∠ACB so
m∠ABC = 40
Since all 3 angles in a triangle always add up to 180, we know that
(40) + (5x) + (2y + 20) = 180
We substitute our known value for 5x and solve for y:
40 + 40 + 2y + 20 = 180
2y + 100 = 180
subtract 100 from both sides
2y = 80
divide both sides by 2 to get our answer:
y = 40

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The volume of a packing box is 5 – x cubic feet. The width of the box is x feet and the length is x – 2 feet. The height is give

photoshop1234 [79]

By definition we have that the volume is given by
V = h * w * l
where
V: Volume
h: height
w: width
l: length
Clearing the height we have:
h = V / (w * l)
h = (5 - x) / ((x) * (x - 2))
The expression is not defined for the values of x that make the denominator zero:
((x) * (x - 2)) = 0
x = 0
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Answer
h = (5 - x) / ((x) * (x - 2))
x = 0
x = 2

4 0

3 years ago

the line y=2x-4 is dilated bt a scale factor of 3/2 and centered at the origin. Write an equation that represent that image of t

Veseljchak [2.6K]

Answer: $y = 2x -6$

Step-by-step explanation:

Since, If (x,y) represents the coordinates of a line, then after dilation about the origin by the scale factor k, the coordinates of the resultant line will get by the rule,

$(x,y)\rightarrow (kx,ky)$

Here, The equation of the given line is,

y = 2x - 4

x-intercept and y-intercept of the line are (2,0) and (0,-4) respectively,

Hence, the line y = 2x - 4 will be passes through the points (2,0) and (0,-4),

By the above property,

The dilated line about the origin will be passes through the points (3,0) and (0,-6), ( Because (3/2× 2, 3/2×0) = (3,0) and (3/2×0, 3/2×-4) = (0,-6) )

Hence, the equation of transformed line after dilation,

$y-0 = \frac{-6-0}{0-3}(x-3)$

$y-0=2(x-3)$

$y-0=2x-6$

$y=2x-6$

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3 years ago

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3 years ago

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Yakvenalex [24]

Answer:-80

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3 years ago

Find the coordinates of point X that lies along the directed line segment from Y(-8, 8) to T(-15, -13) and partitions the segmen

Nataly_w [17]

Answer:

C. (-13, -7)

Step-by-step explanation:

The location of a point O(x, y) that divides a line AB with location A $(x_1,y_1)$ and B $(x_2,y_2)$ in the ratio m:n is given by:

$x=\frac{m}{m+n} (x_2-x_1)+x_1\\\\y=\frac{m}{m+n} (y_2-y_1)+y_1$

Therefore the coordinates of point X That divides line segment from Y(-8, 8) to T(-15, -13) in the ratio 5:2 is:

$x=\frac{5}{5+2} (-15-(-8))+(-8)\\\\x=\frac{5}{7} (-15+8)-8=\frac{5}{7}(-7)-8=-5-8=-13 \\\\\\y=\frac{5}{5+2} (-13-8)+8\\\\y=\frac{5}{7} (-21)+8=5(-3)+8=-15+8=-7$

Therefore the coordinates of point X is at (-13, -7)

6 0

3 years ago