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3 years ago

Lines AB and CD are perpendicular to each other. If 3 measures (4x + 4)°, and 4 measures 26°, what is the value of x?

Mathematics

1 answer:

Misha Larkins [42]3 years ago

6 0

9514 1404 393

Answer:

A x = 15

Step-by-step explanation:

Lines AB and CD being perpendicular means the angles where they meet are all 90°. The diagonal line divides two of those 90° angles into two parts (each). The whole (90°) is the sum of the parts into which the angle has been divided.

The sum of angles 3 and 4 is 90°. Once you understand this relationship, you can write an equation based on the relationship. The equation can be solved in the usual way.

(4x +4)° +26° = 90°

4x = 60 . . . . . . . . . . . . divide by °, subtract 30

x = 15 . . . . . . . . . . divide by 4

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2 years ago

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3 years ago

Cylinder A has a radius of 10 inches and a height of 5 inches. Cylinder B has a volume of 750π. What is the percentage change in

Firlakuza [10]

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50% change in volume

Step-by-step explanation:

<h2>This problem bothers on the mensuration of solid shapes.</h2>

In this problem we are to find the volume of the first cylinder and compare with the second cylinder.

Given data

Volume v = ?

Diameter d= ?

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Height h= $5 in$

we know that the volume of a cylinder is expressed as

$volume = \pi r^{2}h$

Substituting our given data we have

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3 years ago

Read 2 more answers

F(x) = 4x^2 - 3x + 2kx + 1

dybincka [34]

$f(x)=4x^2-3x+2kx+1=4x^2+(2k-3)x+1\\\\a=4;\ b=2k-3;\ c=1\\\\function\ has\ two\ zeros\ when\ \Delta=b^2-4ac > 0\\\\\Delta=(2k-3)^2-4\cdot4\cdot1=4k^2-12k+9-16=4k^2-12k-7 > 0\\\\a_k=4;\ b_k=-12;\ c_k=-7\\\\\Delta_k=(-12)^2-4\cdot4\cdot(-7)=144+112=256\\\\k_1=\frac{-b_k-\sqrt{\Delta_k}}{2a_k};\ k_2=\frac{-b_k+\sqrt{\Delta_k}}{2a_k}$

$\sqrt{\Delta_k}=\sqrt{256}=16\\\\k_1=\frac{12-16}{2\cdot4}=\frac{-4}{8}=-\frac{1}{2};\ k_2=\frac{12+16}{2\cdot4}=\frac{28}{8}=\frac{7}{2}\\\\a_k=4 > 0\ (up\ parabola\ arms-see\ the\ picture)\\\\Answer:k\in(-\infty;-\frac{1}{2})\ \cup\ (\frac{7}{2};\ \infty)$

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2 years ago