If each quadrilateral below is a rectangle find the missing measure in #3

Answers

Answer 1

Answer: You can solve this exercise as below (View the figure attached):

1.Divide the figure in four equals parts. Now we have 4 rectangles with the same dimensions.
2.Choose the rectangle that has the angle given in the problem, which we will call "α" (α=59°).
3. We must remember that the sum of the internal angles of a triangle is 180°. We have α=59° and the right angle, so we can find the other one, which we will call "β1":
β1=180°-90°-59° β1=31°
4. As we can see in the figure, "α" is alternate interior with α1 (α=α1=59°) and β1 is alternate interior with m∠11 (β1=m∠11=31°).
5. The others rectangles have the same dimensions of the rectangle we chose, so they have the same angles too.
We can notice in the figure that m∠7+m∠8+m∠9+m∠10= 360°

The answer is:
m∠1=59°
m∠2=31°
m∠3=59°
m∠4=31°
m∠5=31°
m∠6=59°
m∠7=118°
m∠8=62°
m∠9=62°
m∠10=118°
m∠11=31°

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if the letters of the word 'MOTHER'are written in all possible order and these words are written out as in dictionary ,find the rank of the word 'MOTHER'.

Answers

There are 6 letters, each different
Before MOTHER, words from E , H will come
Words from E = 5! (there are 5 letters to arrange)
Words from H = 5!( there are 5 letters to arrange)

Now words starting by M will come.
First ME will have = 4! (as 4 letters will be arranged)
Then MH = 4!
Now words with MO
First words starting with MOE... =3!
And words starting with MOH... =3!
the words starting with MOR... =3!

Now, words starting from MOT will come
words starting with MOTE.. = 2!
then after words starting from MOTH will come and first word will MOTHER

so, total no. of words before MOTHER = 5! + 5! + 2* 4! + 3 * 3!
= 120 +120 + 48 + 18
= 306
so, rank of MOTHER = 307

Subtract 14 inches from 4 feet, 2 inches.10 inches
3 feet
34 inches
5 feet

Answers

If you would like to subtract 14 inches from 4 feet 2 inches, you can calculate this using the following steps:

1 foot = 12 inches
4 feet 2 inches = 50 inches
4 feet 2 inches - 14 inches = 50 - 14 = 36 inches
36 inches = 3 feet

The correct result would be 3 feet.

3 ft. because 4 ft. converted to inches is 48 in. + 2 in. - 14 in. = 3 ft.

Which of the following is a example of perpendicular lines

Answers

The correct option is D.

Important information:

Each graph has two lines.

Perpendicular lines:

Two lines are called perpendicular lines if the angle between those lines at the intersection point is 90 degrees.

In option A, the lines are parallel because they have the same direction and slope.

In option B, if we increase the lines, then they can not make a 90-degree angle.

In option C, the lines are not making a 90-degree angle.

In option D, the lines are perpendicular because they are making a 90-degree angle.

Therefore, the correct option is D.

Find out more about 'Perpendicular lines' here:

brainly.com/question/2096532

Its option D. the first is parallel and the rest two will intersect at a point but not at 90 degree. Since, in the fourth one, the lines meet at 90 degree, it is a perpendicular line

7/8(-4/5)= the answer to this question

Answers

$(7)/(8) * (-4)/(5)$
let's simplify the terms now
so, we are let with

$(7)/(2) * (-1)/(5)$
Now lets multiply them together

$(-7)/(10)$

hope this helped... :)

The circumference of a circular painting is 28.26
feet. What is the diameter of the painting? Use
3.14
for
π
and do not round your answer.

Answers

Divide 28.26 by 3.14

The answer is 9

A landscaper is designing a flower garden in the shape of a trapezoid. She wants the shorter base to be 3 yards greater than the height, and the longer base to be 7 yards greater than the height. She wants the area to be 225 square yards. The situation is modeled by the equation . Use the Quadratic Formula to find the height that will give the desired area. Round to the nearest hundredth of a yard.

Answers

Let

x--------> shorter base in yards

y--------> the longer base in yards

z-------> the height in yards

we know that

the area of the flower garden in the shape of a tra-pezoid is

$A=(1)/(2) (x+y)z$

$A=225\ yd^(2)$

$225=(1)/(2) (x+y)z$ --------> equation $1$

$x=z+3$ --------> equation $2$

$y=z+7$ --------> equation $3$

Substitute equation $2$ and equation $3$ in equation $1$

$225=(1)/(2) ((z+3)+(z+7))z$

$225=(1)/(2) ((z+3)+(z+7))z\n \n450=[2z+10]z\n \n2z^(2)+10z-450=0$

Solve the quadratic equation for z

using a graphing tool

see the attached figure

the solution is

$z=12.71\ yd$

therefore

the answer is

the height of the flower garden in the shape of a tra-pezoid is $12.71\ yd$

The equation is to be given, judging by the tone problem given but apparently it's not given. The equation can be derived from the problem. The area of a trapezoid is given by the equation $A = ((a+b))/(2) h$ . Also, given that a, is the longer side, then a = h+7 and b (shorter side) = h+3 and h is the height. the equation is then $A = ((h+3)(h+7))/(2)h = 225$ . Solving this quadratic equation, h is 4.84.

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