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3 years ago

Find the value of x so that L is parallel to M. State the converse used!

Mathematics

1 answer:

galben [10]3 years ago

3 0

Answer:

<h3>6 degrees</h3>

Step-by-step explanation

Find the diagram attached. In Line geometry, there is a theorem that states that the sum of the adjacent interior angles is 180 degrees. According to the diagram, the adjacent interior angles are 7x- 15 and 24x + 9.

The sum of this angles must give 180 degrees as shown;

7x-15 + 24x + 9 = 180

7x+24x-15+9 = 180

31x-6 = 180

31x = 180+6

31x = 186

x = 186/31

x = 6

Hence the value of x is 6 degrees

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Consider the function f(x) = 3x2 + 7x + 2.

olga nikolaevna [1]

The discriminant:
D = b² - 4 a c = 7² - 4· 3 · 2 = 49 - 24 = 25
D > 0 This function has 2 x-intercepts ( 2 zeroes ).
x 1 = (-7+5)/6 =-1/3
x 2 = (-7-5) / 6 = - 2

5 0

3 years ago

Read 2 more answers

A parallelogram is shown below: A B A 2 foot D с 3 feet Part A: What is the area of the parallelogram? Show your work. (5 points

docker41 [41]

9514 1404 393

Answer:

Part A: 2 ft²

Part B: draw a diagonal (AC, for example); 1 ft²

Step-by-step explanation:

<u>Part A</u>:

The area of a parallelogram is given by the formula ...

A = bh

where 'b' is the length of the base, and 'h' is the perpendicular distance between the bases.

Using the numbers shown on the diagram, the area is ...

A = (3 ft)(2/3 ft) = 3·2/3 ft²

A = 2 ft² . . . . . area of the parallelogram

<u>Part B</u>:

Typically, a polygon is partitioned into triangles by drawing diagonals from one of the vertices. It does not matter which one. (In a quadrilateral, only one diagonal can be drawn from any given vertex.) Here, the "base" of each triangle is the same as the base of the parallelogram: 3 feet. The "height" of each triangle is the same as the height of the parallelogram: 2/3 ft.

The area of a triangle is given by the formula ...

A = 1/2bh

A = 1/2(3 ft)(2/3 ft) = (1/2)(3)(2/3) ft²

A = 1 ft² . . . . . . . . area of each triangle

_____

<em>Additional comment</em>

It should be no surprise that the area of each of the two congruent triangles is 1/2 the area of the parallelogram.

7 0

3 years ago

in a survey of Swami student it was found that 60% of student studies in math and 40% study science if 40% students study both t

EleoNora [17]

Answer:

Step-by-step explanation:

150% = 150 ÷ 100 150% = 1.5

7 0

3 years ago

People use water to cook, clean, and drink every day. An estimate of 15.5% of the water used each

Studentka2010 [4]

Answer:

260 gallons

Step-by-step explanation:

An estimate of 26.5% of the water used each day is for cleaning and a family uses 68.9 gallons of water a day for cleaning,

Percentage of water used for cleaning= 26.5%

Gallons of water used for cleaning= 68.9

Let the number of gallons used everyday be represented by g. This will give:

26.5% of g = 68.9

26.5/100 × g = 68.9

0.265 × g = 68.9

0.265g = 68.9

Divide both side by 0.265

0.265g/0.265 = 68.9/0.265

g= 260

260 gallons of water are used everyday

5 0

3 years ago

Help me please, this is really hard.

Snowcat [4.5K]

The points of new triangle is (3,-2), (6,-3) and (2,-5).

<u>Step-by-step explanation:</u>

The given points in the triangle A(-3,7), B(9,3) and C(-7,-5).

The scale factor is $\frac{1}{4}$ and centered at point (5,-5).

The formula to dilate a point that is not centered on a origin is given by,

D(x,y)=(h+t(x-h),k+t(y-t)).

where (h,k) is the center point.

To find A',

$D(-3,7)=(5+\frac{1}{4}(-3-5),-5+\frac{1}{4}(7+5)).$

$D(-3,7)=(5+\frac{1}{4}(-8),-5+\frac{1}{4}(12)).$

D(-3,7)=(5-2, -5+3).

D(-3,7)=(3,-2).

To find B',

$D(9,3)=(5+\frac{1}{4}(9-5),-5+\frac{1}{4}(3+5)).$

$D(9,3)=(5+\frac{1}{4}(4),-5+\frac{1}{4}(8)).$

D(9,3) = (5+1,-5+2).

D(9.3)=(6,-3).

To find C',

$D(-7,-5)=(5+\frac{1}{4}(-7-5),-5+\frac{1}{4}(-5+5)).$

$D(-7,-5)=(5+\frac{1}{4}(-12),-5+\frac{1}{4}(0)).$

D(-7,-5)=(5-3,-5+0).

D(-7,-5)=(2,-5).

∴ The points of new triangle is (3,-2), (6,-3) and (2,-5).

8 0

3 years ago