Evaluate the expressions when a = 10, b = -2, and c = -5: (a) a * b (b) 10 * b² (c) -a * b² + (-c) (d) (a * c + a) / b

Answers

Answer 1

Answer: (a) ab
(10)(-2)
-20

(b) 10bsquared
10(-2)squared
10(4)
40

(c) -absquared
-(10)(-2)squared
-10(4)
-40

(d) ((10)(-5)+(10))/(-2)
(-50+10)/-2
(-40)/-2
20

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How to solve a mixed fraction?

Answers

To solve a mixed fraction you will have to multiply the mixed number by the denominator then add the numerator for example:
7 3/4 you are gonna go 7x4=28 then you are gonna take that 28 and add 3 to it so it would be 31. I hope that helped some c:

Which reason completes the proof in the picture A.alternate interior angles converse
B.opposite sides of a parallelogram are congruent
C.opposite angles of a parallelogram are congruent
D.alternate interior angles theorem

Answers

C. Opposite angles of a parallelogram are congruent.

Angle 1 is congruent to angle 2 because they are opposite angles of the larger parallelogram. Angle 2 is congruent to angle 3 because they are opposite angles of the smaller parallelogram.

The function f(x) = x2 – 9 is shifted 2 units up and 3 units to the left. Select the new function. A) g(x) = 2x2 – 6 B) g(x) = (x – 3)2 + 7 C) g(x) = 3x2 – 7 D) g(x) = (x + 3)2 – 7

Answers

We have the following function:
f (x) = x ^ 2 - 9
Applying the transformations we have:
Vertical translations
Suppose that k> 0
To graph y = f (x) + k, move the graph of k units up.
h (x) = x ^ 2 - 9 + 2
h (x) = x ^ 2 - 7
Horizontal translations
Suppose that h> 0
To graph y = f (x + h), move the graph of h units to the left.
g (x) = (x + 3) ^ 2 - 7
Answer:
D) g (x) = (x + 3) ^ 2 - 7

What's the perimeter of a regular heptagon if one side measures 3 inches? A. 10 in.
B. 21 in.
C. 18 in.
D. 11 in.
3. A polygon that has all sides the same measure and all angles the same measure is called what?
A. Irregular polygon
B. Convex polygon
C. Regular polygon
D. Concave polygon
4. The gazebo in the park is an octagon. Each side of the gazebo is 4 feet long. What is the perimeter of the gazebo?
A. 24 feet
B. 36 feet
C. 30 feet
D. 32 feet
5. Which of the following best describes a plane?
A. The surface of a flat table
B. A curve in a road
C. The edge of a desk
D. The point of intersection of two walls
6. Two angles are supplementary. The first angle measures 40°. What's the measurement of the second angle?
A. 120°
B. 50°
C. 140°
D. 60°
7. In order for a button to fit through its buttonhole, the hole needs to be the size of the button's diameter. What size buttonhole is needed for a button with a circumference of 9.42 centimeters?
A. 6 centimeters
B. 1.5 centimeters
C. 3 centimeters
D. 4 centimeters
8. The Pentagon in Washington DC is immense in size, with each outside wall 921 feet in length. What is the perimeter of the Pentagon?
A. 2,663,476.74 ft.
B. 3,684 ft.
C. 5,526 ft.
D. 4,605 ft.

Answers

B. 21 in. A heptagon has seven sides, each side has the same measure. 3x7 equals 21.C. Regular polygon. It is called regular because of the regularity of all the sides.D. 32 feet. An octagon has 8 sides. 4x8 equals 32.A.The surface of a flat table.C.140Â°. To have supplementary angles means to have two angles that joined together they add 180.7. The answer should be 9.42 centimeters, since the diameter is the same size of that of the bottom.D. 4,605 ft. A pentagon counts with 5 sides, these 5 sides of 921 each one, add 4,605.

Part 2) What's the perimeter of a regular heptagon if one side measures 3 inches?

we know that

The number of sides in a regular heptagon is equal to $7$

The perimeter is equal to

$P=7*a$

where

a is the length side

in this problem

$a=3\ in$

substitute

$P=7*3 =21\ in$

therefore

the answer Part 2) is the option

B. 21 in.

Part 3) A polygon that has all sides the same measure and all angles the same measure is called what?

we know that

When all angles are equal and all sides are equal, is a polygon that is equiangular and equilateral, so, is called a regular polygon

therefore

the answer part 3) is the option

C. Regular polygon

Part 4) The gazebo in the park is an octagon. Each side of the gazebo is 4 feet long. What is the perimeter of the gazebo?

we know that

The number of sides in a octagon is equal to $8$

The perimeter is equal to

$P=8*a$

where

a is the length side

in this problem

$a=4\ ft$

substitute

$P=8*4 =32\ ft$

therefore

the answer Part 4) is the option

D. 32 feet

Part 5) Which of the following best describes a plane?

we know that

--The edge of a desk is a piece of a straight or curved line.

-- A curve in a road is a piece of a curved line.

-- The intersection of two walls is a piece of a straight line

therefore

the answer Part 5) is the option

A. The surface of a flat table

Part 6) Two angles are supplementary. The first angle measures 40°. What's the measurement of the second angle?

we know that

Two angles are supplementary if the sum of their angles is equal to $180$ degrees

Let

x------> the measure of the second angle

$40+x=180\n x=180-40\n x=140\ degrees$

therefore

the answer Part 6) is the option

C. 140°

Part 7) In order for a button to fit through its buttonhole, the hole needs to be the size of the button's diameter. What size buttonhole is needed for a button with a circumference of 9.42 centimeters?

we know that

The circumference is equal to

$C= \pi D$

where

D is the diameter

solve for D

$D=(C)/(\pi)$

$D=(9.42)/(\pi)$

$D= 3\ cm$

therefore

the answer Part 7) is the option

C. 3 centimeters

Part 8) The Pentagon in Washington DC is immense in size, with each outside wall 921 feet in length. What is the perimeter of the Pentagon?

we know that

The number of sides in a pentagon is equal to $5$

The perimeter is equal to

$P=5*a$

where

a is the length side

in this problem

$a=921\ ft$

substitute

$P=5*921 =4,605\ ft$

therefore

the answer Part 8) is the option

D. 4,605 ft.

Recall, $\pi$ is defined as the ratio of the circumference (say c) of a circle to its diameter (say d). That is, $\pi$ =c/d. This seems to contradict the fact that $\pi$ is irrational. How will you resolve this contradiction?

Answers

Though $\pi$ = $(c)/(d)$ , it is an approximate value. As we get an approximate value and not a fixed one, there is no contradiction. Mathematically,
$(c)/(d)$ = $(2 \pi r)/(2r)$ = $\pi$ .
Hence, no contradiction.

Yes, it is true that π = c / d . However, note here that c or the circumference is known by the equation c = 2πr. In finding the circumference, we take value of pi approximately, and hence there is no contradiction. However, even if the circumference is accurate, it will be an irrational number. Recall that an irrational number operated in any way results again into an irrational number.

A map has a scale of 1 cm to 2.3 km. The real-life distance between two towns is 69 km. What is the distance between the two towns on the map?