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3 years ago

Enter a range of values for x: A 12 D 35° 20° B 4X4 С 1

Mathematics

1 answer:

MArishka [77]3 years ago

7 0

Answer:

The correct answer to the question is;

1 < x < <u>4</u>

Step-by-step explanation:

The give parameters are;

ΔABC is an isosceles triangle, with the vertex angle = 35° + 20° = 55°

Therefore, the two base angles are 62.5° each by definition of isosceles triangle

Given that the angle subtended by 4·x - 4 which is 25° is lesser than the angle subtended by the 12 unit side length which is 35° we have;

4·x - 4 < 12

4·x < 12 + 4

∴ 4·x < 16

x < 16/4

x < 4

Therefore, the range is 1 < x < 4

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Triangle ABC has been rotated 90° to create triangle DEF. Write the equation, in slope-intercept form, of the side of triangle A

Ket [755]

the equation in the slope-intercept of the side of triangle ABC that is perpendicular to segment EF is y = x + 1

<h3>How to determine the equation</h3>

From the figure given, we can deduce the coordinates of the sides

For A

A ( 4,2)

For B

B ( 4, 5)

C ( 1, 2)

D ( 2, -4 )

E ( 5, -4)

F ( 2, -1)

The slope for BC

Slope = $\frac{y2 - y1}{x2 - x1}$

Substitute the values for both B and C coordinates, we have

Slope = $\frac{2- 5}{1 - 4}$

Find the difference for both the numerator and denominator

Slope = $\frac{-3}{-3}$

Slope = 1

We have the rotation for both point ( 0, 1)

y - y1 = m ( x - x1)

The values for y1 and x1 are 1 and 0 respectively and the slope m is 1

Substitute the values

y - 1 = 1 ( x - 0)

y - 1 = x

Make 'y' the subject of formula

y = x + 1

Thus, the equation in the slope-intercept of the side of triangle ABC that is perpendicular to segment EF is y = x + 1

Learn more about linear graphs here:

brainly.com/question/4074386

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4 0

2 years ago

What is the area of this figure?<br> 168<br> 102<br> 132<br> 340

JulsSmile [24]

Area of square =6*6= 36 cm^2
Area of trapezoid =1/2( base1+base2)*height
base 1=7
base2=21-6=15
height=6
Area of trapezoid =1/2( 7+15)*6= 66
whole area = area of square + area of trapezoid= 36+66=102
Answer 102

8 0

3 years ago

Complete the sentences below the radius of a circle is _____ the length of its diameter. the diameter of a circle is ______ the

son4ous [18]

Answer:

Half; twice

Step-by-step explanation:

In a circle, the radius is said to be the distance from the center of the circle to any point on the edge of the circle, it is denoted as "r". The radius is called a radii if it is more than one.. The radius of a circle is half the length of the diameter of a circle because the diameter of a circle is the distance of the line that passes through the center of a circle touching both edges of the circle. It is denoted as "d".

Thus,

2r = d

r = d/2

For example, if the radius of a circle is 10cm, the diameter of the circle will be calculated as: d = 2 * 10 = 20cm. Which means if the radius is 10cm, diameter will be 20cm.

Therefore, the radius of a circle is half the length of its diameter. the diameter of a circle is twice the length of its radius

5 0

3 years ago

The graph represents this system of equations:

Kipish [7]

Answer:

(2.5, - 2)

Step-by-step explanation:

The solution to a system of equations given graphically is at the point of intersection of the 2 lines, that is

(2.5, - 2 ) ← point of intersection

3 0

3 years ago