4.1: Angle Articulation

Triangle A'B'C' is a dilation of triangle ABC using center P and scale factor 2.

1. What do you think is true about the angles in A' B'C' compared to the angles in ABC?

2. Use the tools available to figure out if what you thought was true is definitely true for
these triangles.

3. Do you think it would be true for angles in any dilation?

Answer:

so whats the question now?

Step-by-step explanation:

Answer:

See below

Step-by-step explanation:

Ina right traingle   tan (angle) = (opposite side) / (adjacent side)

So  tan A  = sqrt (161)/8       exactly

Answer:

Step-by-step explanation:

12y-19= 6y+1

12y-6y = 1 +19

6y = 20

y = 20/6

y= 10/3 or 3.33..

Answer:

Yes, if you know the coordinates of a point PP in your original figure as (x,y)(x,y), you can figure out the coordinates of PP following rotation and given by (x′,y′)(x′,y′) as

x′=−yx′=−y

y′=xy′=x

that is the circumference of its circular base.

[tex]\textit{volume of a cone}\\\\ V=\cfrac{\pi r^2 h}{3}~~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ h=9\\ V=27\pi \end{cases}\implies 27\pi =\cfrac{\pi r^2 (9)}{3}\implies 27\pi =3\pi r^2 \\\\\\ \cfrac{27\pi }{3\pi }=r^2\implies 9=r^2\implies \sqrt{9}=r\implies \underline{3=r} \\\\[-0.35em] ~\dotfill\\\\ \textit{circumference of a circle}\\\\ C=2\pi r\qquad \qquad \qquad C=2\pi (\underline{3})\implies C=6\pi[/tex]

The circumference of the cone will be;

⇒ 6π

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The volume of a right cone = 27π units³

And, The height = 9 units

Now,

Since, We know that;

The volume of cone = πr²h / 3

⇒ 27π = π × r² × 9 / 3

⇒ 27 = r² × 3

⇒ r² = 27/3

⇒ r² = 9

⇒ r = 3

Since, The circumference of the cone = 2πr

                                                            = 2 × π × 3

                                                            = 6π

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Answer:

A = 5x³ + 17x² - 35x - 30

Step-by-step explanation:

the shaded area (A) is calculated as

A = outer area - inner area

   = (5x + 3)(x² + 4x - 10) - 3x(2x - 1) ← distribute parenthesis

   = 5x³ + 20x² - 50x + 3x² + 12x - 30 - (6x² - 3x)

  = 5x³ + 23x² - 38x - 30 - 6x² + 3x ← collect like terms

  = 5x³ + 17x² - 35x - 30

Answer:

5x^3+ 17x^2- 35x-30 Or x=-4.63 or 1.9

Step-by-step explanation:

Area of rectangle =L×B

for smaller rectangle :

after applying the formula, the equation becomes:

6x^2 - 3x

For bigger rectangle:

Applying the same formula, the equation becomes:

5x^3+ 23x^2- 38x- 30

Area of shaded region =

Area of bigger rectangle- Area of smaller rectangle

= 5x^3+17x^2 -35x-30

going further solving the above equation

Area of shaded region: -4.96 or 1.9

Answer:

Step-by-step explanation:

Answer:

9 weeks :)

Step-by-step explanation:

First we subtract :)

2145 - 952.50 = 1192.50

Now we divide :)

265/2 = 132.5

Now we divide 1 more time :)

1192.50/132.50 = 9

It will take 9 weeks :)

Have an amzing day!!

Please rate and mark brainliest!!

Answer:

2 2/5 (For the word problem)

For the graph (In order)

4/5

1 1/4

12/30 (Or 2/5)

2 6/12 (or 2 1/2)

Step-by-step explanation:

1:

12 pounds make 5 pies, turn it into a fraction.

12/5

Now turn it into a mixed number. How many fives can go into 12?

Two fives equal ten, subtract it from twelve. Bring the amount of fives to the left.

2 2/5

2: Oh, that's really easy.

Four divided by five is 4/5

Five divided by four is 5/4 which as a mixed number is 1 1/4

3: 12 divided by thirty is 12/30, you can simplify it by dividing both sides of the denominator by three, then two. But if it's not required then just don't 12/30

4: 30 divided by 12 is 30/12, how many twelves can go into 30? Two.

30 - 24 = 6

2 6/12

Answer:

1390 cm^3

Step-by-step explanation:

9 x 7 x 10 = 630 cm^3 for the rectang prism top

area * 10 for the bottom

8 x ( 12 + 7)/2   * 10 = 760 cm^3  for the trap base

total = 1390 cm^3

Answer:

9.8 feet

Step-by-step explanation:

let area of triangular base be A square feet.

volume of prism = A x height(or length in this case)

498.33 = A x 9

A = 498.33 / 9 = 1/2 x 11.3 x base

...

thus, base = 9.8 feet

charlotte buys a rectangular rug with an area of 27/4 square meters.

The width of the rug is 3/2 meters. So the length of the rectangular rug is 9/2 meters.

The area of the rectangle is the product of the length and width of a given rectangle.

The area of the rectangle = length × Width

charlotte buys a rectangular rug with an area of 27/4 square meters.

The width of the rug is 3/2 meters.

Area of the rectangular rug = 27/4 square meters

Let us assume the length of the rug = x meters

Then,

Area of the rug =  length × Width

[tex]27/4 = (3/2) \times x\\\\x = (27/4) \times (2/3) \\x = 9/2[/tex]

So the length of the rectangular rug is 9/2 meters.

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Answer:

[tex]f(x)=x^2+2x-3[/tex]

Step-by-step explanation:

[tex]\textsf{General form of a quadratic function}:f(x)=ax^2+bx+c[/tex]

Equation 1

[tex]\begin{aligned}f(1) &=0\\ \implies a(1)^2+b(1)+c &=0\\ a+b+c &=0 \end{aligned}[/tex]

Equation 2

[tex]\begin{aligned}f(-1) &=-4\\ \implies a(-1)^2+b(-1)+c &=-4\\ a-b+c &=-4 \end{aligned}[/tex]

Equation 3

[tex]\begin{aligned}f(2) &=5\\ \implies a(2)^2+b(2)+c &=5\\ 4a+2b+c &=5 \end{aligned}[/tex]

Add Equation 1 and Equation 2:

[tex]\begin{array}{r l}a+b+c & =0 \\+\quad a-b+c & =-4 \\\cline{1-2} 2a+2c & =-4 \end{array}[/tex]

[tex]\implies a+c=-2[/tex]

Substitute [tex]a+c=-2[/tex] into Equation 1 and solve for b:

[tex]\begin{aligned}\implies a+b+c &=0\\ b-2 &=0\\ b &=2\end{aligned}[/tex]

Substitute [tex]a=-2-c[/tex]  and  [tex]b=2[/tex]  into Equation 3 and solve for c:

[tex]\begin{aligned} \implies 4a+2b+c&=5\\ 4(-2-c)+2(2)+c &=5\\-8-4c+4+c &=5\\ -3c &=9\\ c &=-3\end{aligned}[/tex]

Substitute found value of c into [tex]a=-2-c[/tex] and solve for a:

[tex]\implies a=-2-(-3)=1[/tex]

Therefore, a = 1, b = 2 and c = -3

Substitute the found values into the general form of a quadratic function to form the final equation:

[tex]f(x)=x^2+2x-3[/tex]

Answer: 58/19 or 3¹/119

Step-by-step explanation: Area = 58

Length is 19 Width is Area/ Length

By looking at the graph, we can see that:

For a function:

y = f(x)

We define the domain as the set of the possible inputs x, and the range as the set of the possible outputs y.

Here, to find the domain, we need to see the range of "horizontal values" that the graph takes. We can see that it goes from -7 to 6, then the domain is:

-7 ≤ x ≤ 6

The range goes from -4 to 5, so the range is: -4 ≤ y ≤ 5.

Then the correct option is the first one.

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Answer:

be specific

Step-by-step explanation:

which shaded eing

Answer:

90/140.

Step-by-step explanation:

75 + 15 = 90. Then 90 + 50 is 140.

Answer:

The answer would be 48 cm^2

Step-by-step explanation:

You have to do 9x4 and then add 6x2 to that.
9x4 is 36 and 6x2 is 12.
36+12 is 48. Hope this helps! :)

Answer:

The answer would be 48 cm^2

Answer: 10

Step-by-step explanation:

Given that a circle has the center at

(6.0) and the circle passes through the point (2,−3).So the distance between these two points will give us the measure of the radius.So(x1,y1)=(6

So by using the distance formula the radius of the given circle is-r=√(x2−x1)2+(y2−y1)2r=√(2−6)2+(−3−0)2r=√16+9r=√25=5 unitsSo the diameter of the given circle is=2rd==2(5)d=10units

Let's see

Find distance between these points and radius

The equation that correctly uses the law of cosines to solve for the missing side length of trianglepqr is 8^2 = 7^2 +11^2 - 2(7)(11) cos <P

For us to use the cosine formula, an angle must be situated between two sides of the triangle.

According to the rule;

c^2 = a^2 + b^2 - 2ab cos C

From the given diagram, if cos<P is the reference angle, then;

a = 11

b = 7

c = 8

Substiute

8^2 = 7^2 +11^2 - 2(7)(11) cos <P

Hence the equation that correctly uses the law of cosines to solve for the missing side length of trianglepqr is 8^2 = 7^2 +11^2 - 2(7)(11) cos <P

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Answer:

8,13,48

Step-by-step explanation:

Third = A(3) = -2 + (3-1)(5) = -2 + 10 = 8

Fourth = A(4) = -2 +(4-1)(5) = -2 + 15 = 13

Eleventh = A(11) = -2 + (11-1)(5) = -2 + 50 = 48

[tex]\qquad\qquad\displaystyle \huge Answer[/tex]

Let's check if (3 , 6) is the point of intersection of the given lines ~

[tex] \qquad \displaystyle \: y = 4x - 2[/tex]

and

[tex] \qquad \displaystyle \: y = \frac{1}{2} x + 5[/tex]

If the point is the point of intersection of these two lines, then it should satisfy both the equations ~

let's try each of them, using x coordinate of point.

[tex] \qquad \displaystyle \: y = 4(3) - 2[/tex]

[tex] \qquad \displaystyle \: y = 12 - 2[/tex]

[tex] \qquad \displaystyle \: y = 10[/tex]

So, the point didn't actually satisfy one of the equation. hence we can infer that the given statement is wrong.

Answer:A, commutative

Step-by-step explanation: The commutative property of multiplication states that

the order in which we multiply numbers does not change the product.

Answer:

A. Commutative

Step-by-step explanation:

I believe it's a because you didn't use +/- so I assumed it was multiplication in which case, the commutative property of multiplication, which states that the order we multiply in does not affect the product.

Let's see

#a

Take 28

#2

Take 9,10

Answer:

Two-digit number greater than 25:   32

Rewrite 32 as the difference of 2 numbers: 40 - 8

Therefore, x = 40  and  y = 8

[tex]\begin{aligned}\implies (40-8)^2 & =40^2-2(40)(8)+8^2\\ & = (4 \cdot 10)^2-(80)(8)+64\\ & = 4^2 \cdot 10^2-640+64\\ & = 16 \cdot 100-640+64\\ & = 1600-640+64\\ & = 960+64\\ & = 1024\end{aligned}[/tex]

Let a = 10

Let b = 11

[tex]\begin{aligned}\implies 10^3+11^3 & =(10+11)(10^2-10 \cdot 11+11^2)\\& = 21(100-110+121)\\ & = 21(-10+121)\\ & = 21(111)\\& = 21 (100 + 10 + 1)\\ & = (21 \cdot 100)+(21 \cdot 10)+(21 \cdot 1)\\ & = 2100 +210+21\\ & = 2310 + 21\\ & = 2331\end{aligned}[/tex]

[tex]2(x - 9) = 9 \div ( - \frac{1}{3} ) \\ [/tex]

[tex]2(x - 9) = 9 \times ( - 3)[/tex]

[tex]2(x - 9) = - 27[/tex]

[tex] \frac{2(x - 9)}{2} = \frac{ - 27}{2} \\ [/tex]

[tex]x - 9 = - 13.5[/tex]

[tex]x - 9 + 9 = - 13.5 + 9[/tex]

[tex]x = - 4.5[/tex]

Thus option B is the correct answer.