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2 years ago

15

Mathematics

1 answer:

Evgesh-ka [11]2 years ago

8 0

Answer:

Height = 14.4

Step-by-step explanation:

The diagonals meet at right angles. Interesting property.

The hypotenuse is the side of the rhombus = 15 cm

One of the sides of the small triangles created by the intersection of the diagonals = 24/2 = 12

You can find the other side of the the triangle by using the Pythagorean Theorem

a^2 + b^2 = c^2

c = 15

a = 12

b = ?

12^2 + b^2 = 15^2

144 + b^2 = 225

b^2 = 225 - 144

b^2 = 81

b = 9

The area of this right angle = 9 * 12/2 = 54

There are 4 of them so 4 * 54 = 216

That's the area of the rhombus.

The h= Area / b

b = 15

h = 216/15

h = 14.4

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1. Write the standard form of the line that passes through the given points. (7, -3) and (4, -8)

Sveta_85 [38]

Answer:

1. $-5x+3y+44=0$

2. $2x+y-2=0$

3. $2x+y-4=0$

Step-by-step explanation:

Standard form of a line is $Ax+By+C=0$ .

If a line passing through two points then the equation of line is

$y-y_1=m(x-x_1)$

where, m is slope, i.e., $m=\dfrac{y_2-y_1}{x_2-x_1}$ .

The line passes through the points (7,-3) and (4,-8). So, the equation of line is

$y-(-3)=\dfrac{-8-(-3)}{4-7}(x-7)$

$y+3=\dfrac{-5}{-3}(x-7)$

$y+3=\dfrac{5}{3}(x-7)$

$3(y+3)=5(x-7)$

$3y+9=5x-35$

$-5x+3y+9+35=0$

$-5x+3y+44=0$

Therefore, the required equation is $-5x+3y+44=0$ .

We need to find the equation of the line, in standard form, that has a y-intercept of 2 and is parallel to $2 x + y =-5$ .

Slope of the line : $m=\dfrac{-\text{Coefficient of x}}{\text{Coefficient of y}}=\dfrac{-2}{1}=-2$

Slope of parallel lines are equal. So, the slope of required line is -2 and it passes through the point (0,2).

Equation of line is

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

$y-2=-2x$

$2x+y-2=0$

Therefore, the required equation is $2x+y-2=0$ .

We need to find the equation of the line, in standard form, that has an x-intercept of 2 and is parallel to $2x + y =-5$ .

From part 2, the slope of this line is -2. So, slope of required line is -2 and it passes through the point (2,0).

Equation of line is

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

$y=-2x+4$

$2x+y-4=0$

Therefore, the required equation is $2x+y-4=0$ .

5 0

3 years ago

Where is each answer

storchak [24]

Answer:

1.(D)

2.(A)

3.(C)

4.(B)

4 0

3 years ago

Properties of isosceles triangle

Degger [83]

Answer:

Had two congruent sides

Has congruent base angles

8 0

3 years ago

What is the equation for the line?<br><br><br><br> Enter your answer in the box.

laila [671]

(0,0),(2,16)
slope = (16 - 0) / (2 - 0) = 16/2 = 8

y = mx + b
slope(m) = 8
and since the line goes thru the origin, the y int is 0

in y = mx + b form, the slope is in the m position and the y int is n the b position....so ur equation is :
y = 8x + 0 which can be written as y = 8x <==

5 0

3 years ago

Read 2 more answers

Jerry has a miniature model of a boat. He knows that the model is 3 3/4 inches wide and 5 1/2 inches long. What is the actual le

mylen [45]

Answer:

22 feet

Step-by-step explanation:

Change 15 feet into inches using the conversion

1 foot = 12 inches, thus

15 ft = 15 × 12 = 180 inches

scale factor = 180 ÷ 3.75 = 48

Thus the actual dimensions of the boat are 48 times the model.

actual length = 48 × 5.5 = 264 inches = 264 ÷ 12 = 22 feet

6 0

3 years ago