Find the area and the perimeter of the shaded regions below. Give your answer as a completely simplified exact value in terms of π (no approximations). The figures below are based on semicircles or quarter circles and problems b), c), and d) are involving portions of a square.

Answer:

(-6, 0) and (2, 0)

Step-by-step explanation:

To find the x-intercepts, we can factor the expression:

f(x) = x² + 4x - 12

2 factors of -12 that add up to 4 are 6 and -2

(x + 6)(x - 2)

Set each factor equal to 0 and solve for x:

x + 6 = 0

x = -6

x - 2 = 0

x = 2

So, the x intercepts are (-6, 0) and (2, 0)

Answer:

It's the first option, (-6, 0) (2, 0)

Step-by-step explanation:

100% on Edge

Answer:  8.94 is the length of GI

Step-by-step explanation: The two triangles are similar, so the ratios of the sides to each other will be the same.

the unknown length of GI in triangle FIG corresponds to the known length 20 of IH in Triangle GIH, and the known length 4 of side FI in triangle FIG corresponds to GI in Triangle GIH. So the ratio looks like 4:x as x:20

4/x = x/20  multiply both sides by x and 20 to "cancel" the denominators.

20x(4/x) = 20x(x/20)

80 = x²    Calculate the square roots  

√x² = x . √80 = 8.94

Answer:

Explanation:

sum of the power of 2x^2y=2+1=3

sum of the power of 4x^5=5

sum of the power of 6xy^3=1+3=4

Highest power=5

Therefore, The degree of given polynomial is 5.

Hope this helps...

Good luck on your assignment..

Step-by-step explanation:

This question requires the Pythagorean theorem.

Car A travels north 100km in two hours.

Car B travels west 160km in two hours.

Imagine a triangle the line going up is 100km

the line going left is 160km

the formula for the Pythagorean theorem is

a^2+b^2=c^2

100^2+160^2=c^2

10000+25600=c

35600=c

√35600=c

You can draw a diagram.

Answer:

30 cubes are added

Step-by-step explanation:

The image of the solid shape is attached.

From the Plan, Side elevation and Front elevation, the number of cubes needed to make the shape is 18 blocks. From the front elevation, 12 blocks is needed (4 * 3 blocks) while from the side elevation 6 blocks are needed given a total of 18 blocks.

The number of blocks needed to make the cuboid = 4 * 4 * 3 = 48 cm cubes.

Therefore the number of cubes to be added = 48 cubes - 18 cubes = 30 cubes.

30 cubes are added

The number of cubes that are added is 30.

What is Cube?

A cube's form is occasionally referred to as "cubic." Another way to put it is that a block with uniform length, width, and height is regarded to be a cube. It also contains 12 edges and 8 vertices, with 3 of the edges coming together at a single vertex point. Examine the illustration below, identifying the faces, edges, and vertices. It is also referred to as a right rhombohedron, an equilateral cuboid, and a square parallelepiped. One of the platonic solids, the cube is a convex polyhedron with all of its faces being square. The cube has either cubical symmetry or octahedral symmetry. The square prism is a specific instance of a cube.

From the Plan, Side elevation, and Front elevation, the number of cubes needed to make the shape is 18 blocks. From the front elevation, 12 blocks are needed (4 * 3 blocks) while from the side elevation 6 blocks are needed given a total of 18 blocks.

The number of blocks needed to make the cuboid

= 4 * 4 * 3 = 48 cm cubes.

Therefore the number of cubes to be added

= 48 cubes - 18 cubes

= 30 cubes.

30 cubes are added.

Hence, The number of cubes that are added is 30.

To learn more about, cubes, visit;

https://brainly.com/question/107100

#SPJ13

Answer:

The answer is "Option A"

Step-by-step explanation:

Given:

[tex]\to \frac{(a-5)+a}{2}=x.....(a)\\\\\to \frac{a+(a+9)}{2}=y.....(b)\\\\[/tex]

solve the above equation:

[tex]\to \bold{\frac{(a-5)+a}{2}=x}\\\\\to \frac{a-5+a}{2}=x\\\\\to \frac{2a-5}{2}=x\\\\\to \bold{\frac{a+(a+9)}{2}=y}\\\\\to \frac{a+a+9}{2}=y\\\\\to \frac{2a+9}{2}=y\\\\[/tex]

add both value (x and y):

[tex]\to \bold{x+y}\\\\\to \frac{2a-5}{2}+\frac{2a+9}{2}\\\\\to \frac{2a-5+2a+9}{2}\\\\\to \frac{4a+4}{2}\\\\\to \frac{2(2a+2)}{2}\\\\\to (2a+2)\\[/tex]

average of x and y:

[tex]\to \frac{x+y}{2}\\\\\therefore \bold{x+y= 2a+2}\\\\\to \frac{2(a+1)}{2}\\\\\to \boxed{(a+1)}\\[/tex]

Answer:

X^2-9=0 is x2 = 9

Step-by-step explanation:

Answer:

The result is 0.36b

Step-by-step explanation:

Here. we want to translate the wordings into an expression of algebra.

Firstly, we decrease b by 40%

40% is same as 40/100 = 0.4

So decreasing b by 40% = b-0.4(b) = b-0.4b = 0.6b

Now we want to decrease 0.6b by another 40%

= 0.6b -0.4(0.6b)

= 0.6b - 0.24b

= 0.36b

Answer:

(1, 0) and (3, 0)

Step-by-step explanation:

y=2x²-8x+6

x- intercept when y=0

Answer:

(1, 0) / (3, 0)

Step-by-step explanation:

Answer:

The estimated answer would be 9

Step-by-step explanation:

The answer I received in the calculator was 8.94422. Since the tenths, place value(9) is closer to 9.0 than 8.0, we round up. I hope this helps you.

Answer:

32

Step-by-step explanation:

tanx=opp/adj.=40/64=5/8=0.625

find tan^-1= 32 degrees

Answer:

A. 32°

Step-by-step explanation:

[tex] \tan \: x \degree = \frac{40}{64} \\ \\ \tan \: x \degree = \frac{5}{8} \\ \\ \tan \: x \degree =0.625 \\ x \degree = {\tan}^{ - 1}( 0.625) \\ \\ x \degree =32.005383208 \degree \\ \\ \huge \red { \boxed{ x =32 \degree}}[/tex]

Answer:

x = 1/2

Step-by-step explanation:

-3x + 1 + 10x = x + 4

7x + 1 = x + 4

6x + 1 = 4

6x = 3

x = 3/6

x = 1/2

Answer:

It's (A) [tex]x\frac{1}{2}[/tex]

Step-by-step explanation:

Answer:

assuming the graph is a 10 by 10 there would be 10 diffrent whole number coordinates.

Answer: [tex]1.6\pi[/tex]

Step-by-step explanation:

If a circle has a radius of 6, then the perimeter of the circle is 12pi, or about 37.68.  A circle has 360 degrees.  Thus, the arc takes up 48/360 of the circle.  Thus, simply multiply [tex]\frac{48}{360} * 12\pi[/tex] to get 5.024 or 1.6pi.

Hope it helps <3

Answer:

Part A:

Equation for Company A:

x = Number of days renting a car

35x + 15

Equation for Company B:

x = Number of days renting a car

42x + 10

Part B:

Company A will charge $ 37 less than Company B

Part C:

Company A will charge $ 65 less than Company B

Step-by-step explanation:

Part A:

Equation for Company A:

x = Number of days renting a car

35x + 15

Equation for Company B:

x = Number of days renting a car

42x + 10

Part B:

Renting a car for 6 days

Company A:

35 * 6 + 15 = 210 + 15 = $ 225

Company B:

42 * 6 + 10 = 252 + 10 = $ 262

Company A will charge $ 37 less than Company B

Part C:

Renting a car for 10 days

Company A:

35 * 10 + 15 = 350 + 15 = $ 365

Company B:

42 * 10 + 10 = 420 + 10 = $ 430

Company A will charge $ 65 less than Company B

Answer:

C

Step-by-step explanation:

Using the rule of radicals/ exponents

[tex]a^{\frac{m}{n} }[/tex] ⇔ [tex]\sqrt[n]{a^{m} }[/tex]

Given

[tex]5^{\frac{1}{3} }[/tex] = [tex]\sqrt[3]{5}[/tex] → C

Answer:

276

Step-by-step explanation:

∆y = 2y3

∆2 = 2(2)3 = 16

∆5 = 2(5)3 = 250

∆2 + ∆5 = 250 + 16 = 276

Answer:

12 in²

Step-by-step explanation:

The area of a triangle is base × height × 1/2.

b × h × 1/2

6 × 4 × 1/2

24 × 1/2

= 12

The area is 12 in².

Answer:

Solution,

Base(b)=6 inches

Height(h)=4 inches

Area of triangle=?

Now,

[tex]area \: of \: triangle \\ = \frac{bh}{2} \\ = \frac{6 \times 4}{2} \\ = \frac{24}{2} \\ = 12 \: {inches}^{2} [/tex]

hope this helps ..

Good luck on your assignment...

Answer:

B

using SOHCAHTOA

COS THETA WILL BE EQUALS TO ROOT 5/3 AND TAN THETA WILL BE EQUALS TO 2ROOT 5/3

Answer:

B.

Step-by-step explanation:

First, note that since [tex]sin(\theta)=2/3[/tex], this means that the opposite side is 2, the hypotenuse is 3, and the last, adjacent side is [tex]\sqrt{5\\[/tex].

Also note that we are told that [tex]sec(\theta)<0[/tex]. This means that [tex]\theta[/tex] cannot be in quadrants 1 nor 4 because (remember All Students Take Calculus?) in those quadrants cosine and secant are positive. Also, we know that sine is positive so we can conclude that [tex]\theta[/tex] is in the second quadrant.

In the second quadrant, sine is positive, cosine is negative, and tangent is negative. Now we can answer the question. We already know the side lengths: opposite=2, adjacent=[tex]-\sqrt{5}[/tex] (because it's in Quadrant II), and hypotenuse=3.

Therefore...

[tex]cos(\theta)=-\sqrt{5} /3[/tex]

[tex]tan(\theta)=2/(-\sqrt{5})=-(2\sqrt{5}/5)[/tex]

Answer:

49

Step-by-step explanation:

7 times 4 equals 49.

Answer:

(D)  [tex]\dfrac{27}{16}[/tex]

Step-by-step explanation:

Volume of a Cylinder =[tex]\pi r^2h[/tex]

Cylinder A

Height = 3 Units

Radius = 3 Units

[tex]Volume =\pi \times 3^2 \times 3 =27\pi$ cubic units[/tex]

Cylinder B

Height = 4 Units

Radius = 2 Units

[tex]Volume =\pi \times 2^2 \times 4 =16\pi$ cubic units[/tex]

[tex]\dfrac{\text{Volume of Cylinder A}}{\text{Volume of cylinder B}}=\dfrac{27\pi}{16\pi}\\\\=\dfrac{27}{16}[/tex]

The correct option is D

Question:

Found a picture which relates to the question asked. It can be found in the attachment below.

Answer:

b. c2 + b2 = a2

Step-by-step explanation:

According to Pythagoras rule :

The longest side of the triangle is the hypotenus

The opposite and adjacent sides depends on the particular angle provided or one which is to be calculated.

The opposite side is one drawn across a given angle, while the side next to the Given angle is called the adjacent side.

FROM △ABC ;

THE longest side is 'a' = hypotenus

Opposite side = c

Adjacent = b

From Pythagoras :

(Hypotenus)^2 = (Opposite)^2 + (adjacent)^2

Hence,

a^2 = c^2 + b^2

Answer:

m^2+m+1

Step-by-step explanation:

HCF= m^2+m+1 which is the factor of all three polynomials

Answer:

The answer is below

Step-by-step explanation:

From the diagram attached, to find the length of side AB, we need to use Pythagoras theorem on the right triangles. We can see that AB is the base of the two right triangle.

For the first right triangle with hypotenuse of 13 and height of 12, let x be the base, therefore using hypotenuse:

13² = 12² + x²

169 = 144 + x²

x² = 169 - 144

x² = 25

x = √25 = 5

For the second right triangle with hypotenuse of 15 and height of 12, let y be the base, therefore using hypotenuse:

15² = 12² + y²

225 = 144 + y²

y² = 225 - 144

y² = 81

y = √81 = 9

The length of AB = x + y = 9 + 5 = 14 unit

Since for a square all the sides are equal, therefore the length of each side of the square ABCD is 14 units.

In triangle ADC, the hypotenuse = AC, AD = DC = 14 unit. Using Pythagoras:

AC² = AD² + DC²

AC² = 14² + 14²

AC² = 196 + 196 = 392

AC = √392 = 19.8

The length of its diagonal is about 19.8 units

Answer:

1) Distributive Property of Multiplication (The terms are distributed)

2) Addition property of equality (Adding 14 to both sides)

3) Simplifying (We simplified the expression)

4) Division property of equality (Dividing both sides by 6)

Answer:

[tex]\boxed{\mathrm{view \: explanation}}[/tex]

Step-by-step explanation:

- 14 + 6m = 10

Distributive Property of Multiplication

2 is distributed to -7 and 3m

- 14 + 14 + 6m = 10 + 14

Addition Property of Equality

Adding 14 to both sides.

6m = 24

Simplifying

Simplifying the equation.

[tex]\displaystyle \frac{6m}{6} =\frac{24}{6}[/tex]

Division Property of Equality

Dividing both sides by 6.

Answer:

Third choice is correct

Step-by-step explanation:

-2x-y=-2

-y=2x-2

y=-2x+2

3x-y=-2

-y=-3x-2

y=3x+2

These two lines intersect at (0, 2)

Answer:

x = a(c + b)

Step-by-step explanation:

Step 1: Add b to both sides

x/a = c + b

Step 2: Multiply both sides by a

x = a(c + b)

Answer:

Area of a circle is πr²

where r is the radius

r = 7.29m

Area = π × 7.29²

= 166.957

= 166.96m² to 2 decimal places

Hope this helps you

Answer:

4=x

Step-by-step explanation:

1.5(x + 4) – 3 = 4.5(x – 2)   distribute

1.5x+6-3 = 4.5x-9                   subtract 1.5x from each side

3=3x-9                                 add 9 to both sides

12=3x                                    divide by on both sides

4=x                                        simplify

Answer:

x=4

Step-by-step explanation