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2 years ago

12

Triangles BAD and BDC are right triangles with AB = 12 units, BD = 15 units, and BC = 17 units. What is the area, in square unit

s, of quadrilateral ABCD?

1 answer:

Irina18 [472]2 years ago

7 0

Answer:

The area of the quadrilateral ABCD is 114 square units

Step-by-step explanation:

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what is the volume of the hamsta snack box with a width of 1 1/2 inches, a length of2 1/2 inches, and a height of 4 inches

jenyasd209 [6]

<u>Given:</u>

The width of the snack box is $1 \frac{1}{2} \ inches=\frac{3}{2} \ inches$

The length of the snack box is $2 \frac{1}{2} \ inches=\frac{5}{2} \ inches$

The height of the snack box is 4 inches.

We need to determine the volume of the hamsta snack box.

<u>Volume of the box:</u>

The volume of the box can be determined using the formula,

$V=L \times W \times H$

where L is the length, W is the width and H is the height of the box.

Substituting the values, we get;

$V=4 \times \frac{3}{2} \times \frac{5}{2}$

Simplifying, we get,

$V=\frac{60}{4}$

$V=15 \ in^3$

Thus, the volume of the Hamsta snack box is 15 cubic inches.

3 0

3 years ago

Find an equation of the plane. The plane that passes through the line of intersection of the planes x − z = 3 and y + 2z = 3 and

IgorLugansk [536]

Answer:

x-y-3=0

Step-by-step explanation:

Choose two common points on the line of intersection of the planes x − z = 3 and y + 2z = 3:

1st point: if x=0, then z=-3 and y=3-2z=3+6=9, so the 1st point is (0,-3,9);
2nd point: if x=3, then z=0 and y=3-2z=3-0=3, so the 2nd point is (3,0,3).

The perpendicular plane to the plane x+y-4z=6 is parallel to the vector with coordinates (1,1,-4) (normal vector of the given plane).

Hence, the equation of needed plane is

$\left\|\begin{array}{ccc}x-0&y-(-3)&z-9\\3-0&0-(-3)&3-9\\1&1&-4\end{array}\right\|=0\Rightarrow \left\|\begin{array}{ccc}x&y+3&z-9\\3&3&-6\\1&1&-4\end{array}\right\|=0$

Thus,

$\left\|\begin{array}{ccc}x&y+3&z-9\\3&3&-6\\1&1&-4\end{array}\right\|=0\Rightarrow \\\\-12x-6(y+3)+3(z-9)-3(z-9)+6x+12(y+3)=0\\ \\-6x+6(y+3)=0\\ \\-x+y+3=0\\ \\x-y-3=0$

4 0

4 years ago

Mark has 312 books in his bookcase . he has 11 times as many fiction than non fiction. how many fiction does he havr

maw [93]

11x + x = 12x
312 / 12 = 26
26 nonfiction
312 - 26 = 286.
He has 26 non fiction books and 286 fiction books.

<span>Hope This Helps You!
</span>Good Luck Studying :)

4 0

3 years ago

Given a triangle with 3 angles that sum to 180o, can the lengths of the sides be determined? Explain.

amm1812

No. For example, the angles of every equilateral triangle ... whether its sides
are 1 nanometer, 1 inch, 1 mile, or 1 light-year long ... are always 60 degrees
each. The angles alone may reveal the <u>ratios</u> of the sides, but they tell nothing
about the actual length of any of the sides.

5 0

3 years ago

Plot the axis of symmetry and the vertex for this function: h(x) = (x − 5)2 − 7.

jeka94

Answer:

The vertex and the axis of symmetry in the attached figure

Step-by-step explanation:

we know that

The equation of a vertical parabola written in vertex form is equal to

$f(x)=a(x-h)^2+k$

where

a is the leading coefficient

(h,k) is the vertex of the parabola

and the equation of the axis of symmetry is equal to the x-coordinate of the vertex

$x=h$

In this problem

we have

$h(x)=(x-5)^2-7$

This is a vertical parabola written in vertex form open upward

The vertex is a minimum

where

the vertex is the point (5,-7)

the x-coordinate of the vertex is 5

so

the equation of the axis of symmetry is equal to

$x=5$

The graph in the attached figure

7 0

3 years ago