Compound Shapes
Find the area of each figure, round your answer to one decimal place if necessary
12 ya
30
1)
3)
2)
3
12 yd
18
12 ya
3
20 yd
24
Area
Area
Area
4)
5)
6)
17 cm
4 cm
7.5 m
8 orn
12 cm
10 m
5 m
Area:
Area:
Area:
9)
7)
8)
35 m
3.5 m
20 in
TO in
18 in
21 m
21 in
18 in
20 in
3.5 m
21 m
Area:
Area:
Area:

Answer:

[tex]f(x) = -x^2 - 2x + 8[/tex]

y-intercept is when x = 0:

[tex]\implies f(0) = -(0)^2 - 2(0) + 8=8[/tex]

So the y-intercept is (0, 8)

x-intercepts are when f(x) = 0:

[tex]\implies f(x)=0[/tex]

[tex]\implies -x^2 - 2x + 8=0[/tex]

[tex]\implies x^2 + 2x - 8=0[/tex]

[tex]\implies x^2 - 2x + 4x - 8=0[/tex]

[tex]\implies x(x - 2) + 4(x-2)=0[/tex]

[tex]\implies (x+4)(x - 2)=0[/tex]

Therefore:

[tex]\implies (x+4)=0 \implies x=-4[/tex]

[tex]\implies (x-2)=0 \implies x=2[/tex]

So the x-intercepts are (-4, 0) and (2, 0)

The vertex is the turning point of the parabola.  The x-value of the vertex is the x-value between the 2 zeros (x-intercepts).

Therefore, the x-value of the vertex is [tex]\sf \dfrac{x_1+x_2}{2}=\dfrac{-4+2}{2}=-1[/tex]

Substituting x = -1 into the function:

[tex]\implies f(-1) = -(-1)^2 - 2(-1) + 8=9[/tex]

So the vertex is (-1, 9)

The domain is the input values, so x = all real numbers.

The range is the output values, so the range is [tex]f(x)\leq 9[/tex]

Therefore, (-4, 0), (-1, 9), (0, 8) and (2, 0) are solutions of the function, HOWEVER they are not ALL the solutions.

All solutions of the function are:

[tex](x, -x^2 - 2x + 8)[/tex] for all real numbers of x

Answer:

See below for answers and explanations

Step-by-step explanation:

Problem 1

First, identify the three vectors in component form (remember to have the direction angle for each vector account for the quadrants they are in!):

[tex]u=\langle90\cos220^\circ,90\sin220^\circ\rangle\\v=\langle 60\cos110^\circ,60\sin110^\circ\rangle\\w=\langle 40\cos30^\circ,40\sin30^\circ\rangle[/tex]

Secondly, we add them:

[tex]u+v+w=\langle90\cos220^\circ+60\cos110^\circ+40\cos30^\circ,90\sin220^\circ+60\sin110^\circ+40\sin30^\circ\rangle\approx\langle-54.824,18.531\rangle[/tex]

Thirdly, find the magnitude of the new vector:

[tex]||u+v+w||=\sqrt{(-54.824)^2+(18.531)^2}\\||u+v+w||\approx57.871[/tex]

And finally, find the direction of the new vector:

[tex]\theta=tan^{-1}(\frac{18.531}{-54.824})\\\theta\approx-18.675^\circ\approx-19^\circ[/tex]

Because our new vector is in Quadrant II, our found direction angle is a reference angle, telling us that the actual direction of our vector is 19° clockwise from the negative x-axis, which would be 180°-19°=161°

Thus, B is the best answer

Problem 2

To find the component form of a vector, we simply subtract the initial point from the terminal point. In this case, our initial point is at (7,-1) and our terminal point is at (1,6). We subtract the horizontal and vertical components separately:

[tex]\langle1-7,6-(-1)\rangle=\langle-6,7\rangle[/tex]

Thus, A is the correct answer

Problem 3

Again, subtract the initial point from the terminal point to find the vector, and then apply scalar multiplication:

[tex]-\frac{1}{2}v=-\frac{1}{2} \langle-8-8,10-4\rangle=-\frac{1}{2}\langle-16,6\rangle=\langle8,-3\rangle[/tex]

Thus, C is the correct answer

Problem 4 (top one in 4th image)

Remember that scalar multiplication only affects the magnitude of the vector and not the direction. Thus, [tex]-3u=-3\bigr[20\langle\cos30^\circ,\sin30^\circ\rangle\bigr]=-60\langle\cos30^\circ,\sin30^\circ\rangle[/tex], which means our magnitude is -60 and our direction remains 30°.

Thus, B is the correct answer

Problem 5 (fake #6, bottom one in 4th image)

Basically, whatever is in front of the i represents the horizontal component, and whatever is in front of the j represents the vertical component, so:

[tex]u=-3i+8j=\langle-3,8\rangle[/tex]

Thus, B is the correct answer

Problem 6 (real one, 5th image)

Recall:

Knowing these facts, let us compute the dot product:

[tex]u\cdot v=(-4*28)+(7*-49)=(-112)+(-343)=-455[/tex]

Since the dot product of the two vectors is not 0, then the vectors are not orthogonal, so we can eliminate choices A and B

To check if the vectors are parallel, find the angle between them:

[tex]\displaystyle\theta=cos^{-1}\biggr(\frac{u\cdot v}{||u||\:||v||}\biggr)\\\\\theta=cos^{-1}\biggr(\frac{-455}{\sqrt{(-4)^2+(7)^2}\sqrt{(28)^2+(-49)^2}}\biggr)\\\\\theta=cos^{-1}\biggr(\frac{-455}{\sqrt{16+49}\sqrt{784+2401}}\biggr)\\\\\theta=cos^{-1}\biggr(\frac{-455}{\sqrt{65}\sqrt{3185}}\biggr)\\\\\theta=cos^{-1}\biggr(\frac{-455}{\sqrt{207025}}\biggr)\\\\\theta=cos^{-1}\biggr(\frac{-455}{455}\biggr)\\\\\theta=cos^{-1}(-1)\\\\\theta=180^\circ[/tex]

So, since the angle between the two vectors is 180°, this implies that cosθ=-1, and the two vectors must be parallel.

Thus, D is the correct answer

Answer: X+Y+5

Step-by-step explanation:

There is no single answer you have to write an equation.

Answer:

2^3 = 2 * 2 * 2 which equals 8

Step-by-step explanation:

Using translation concepts, it is found that the equation of the transformed function is:

y = |x + 3| - 2.

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.

The absolute value function is given by y = |x|, and has vertex at (0,0). After the transformations, the function has vertex (-3, -2), which means that:

Thus, the equation of the function is now given by:

y = |x + 3| - 2.

More can be learned about translation concepts at https://brainly.com/question/4521517

Answer:y = |x + 3| - 2.

Step-by-step explanation:  B on edge

Answer:

Step-by-step explanation:

The angle where chords cross is the average of the measures of the intercepted arcs. The angle that is the supplement of x° will be the average of interecepted arcs 60° and 80°.

  180° -x° = (60° +80°)/2

  180 -70 = x . . . . . . . . . . . divide by °, add x-70

  x = 110

__

The external angle where secants meet is half the difference of the intercepted arcs.

  59° = (180° -y°)/2

  118 = 180 -y . . . . . . . multiply by 2, divide by °

  y = 180 -118 . . . . . add y-118

  y = 62

Answer:

A. 5/10

Step-by-step explanation:

Because the 5 in 256 is ine in tength's place. And 5/10 is 0.5 or 50

Using an exponential function, supposing that the value decays 10% a year, it is found that the current market value is $9,087.

A decaying exponential function is modeled by:

[tex]A(t) = A(0)(1 - r)^t[/tex]

In which:

In this problem, supposing a decay of 10% a year, and the original value of $13,850, the parameters are A(0) = 13850, r = 0.1.

Hence, the value of the car in 4 years is given by:

[tex]A(t) = A(0)(1 - r)^t[/tex]

[tex]A(4) = 13850(0.9)^4[/tex]

A(4) =  9087.

More can be learned about exponential functions at https://brainly.com/question/25537936

Answer:

108 inches

Step-by-step explaination:
Looking at the picture I drew, we can assume that 24 = 4x
and so x=6 and 3x=18.
6 times 18 is 108.

Answer:

Brand A

Step-by-step explanation:

IN the end buying it for $3.75/lb would end up being cheaper then buying it for $0.18/oz. Hopethis helps!

Answer:

490.87 ft^3.

Step-by-step explanation:

Radius = 1/2 * 5 = 2.5 ft.

Volume = π r^2 L

= π*2.5^2*25

= 490.87 ft^3

we know that the multiplication comes first in the family then we start from left to right

4 x 5= 20

9-20 = -11

-11 + 6 = -5

there you go!

[tex]9 - 4 \times 5 + 6[/tex]

[tex]9 - 20 + 6[/tex]

[tex] - 11 + 6[/tex]

[tex] - 5[/tex]

Answer:

Vertex of y = − 3 x 2 + 18 x − 13 Ans: Vertex (3, 14)

Step-by-step explanation:

Explanation: x-coordinate of vertex: x = ( − b 2 a ) = − 18 − 6 = 3 y-coordinate of vertex: y = f(3) = -27 + 54 - 13 = 14 x-coordinate of the axis of symmetry is the same as the x-coordinate of the vertex: x = 3

Answer:

the answer ia true

Step-by-step explanation:

hope this helps

Answer:

What is the difference between entering a formula and entering data ??

Answer:

D) 576 cubic cm

Step-by-step explanation:

[tex]16 \times 9 \times 4 = 576[/tex]

Answer:

the answer is D

Step-by-step explanation:

volume =height × length × width

so 9×4×16= 576

Answer:

La masa atómica del carbono (C) es 12 g/mol; para el oxígeno (O) es de 16 g/mol. Esto significa que 6.022 x 1023 átomos de carbono pesan 12 gramos. Según esto, el peso molecular del CO2 es: 12 g/mol [C] + 2 x 16 g/mol [O2] = 44 g/mol.

1 molécula de Nitrógeno por su masa atómica de 14.01 más 3 moléculas de Hidrógeno por su masa atómica de 1.008 = (1 * 14.01) + (3 * 1.008) = 14.01 + 3.024 = 43.038 u = 17.03 masa molecular = 17.03 g/mol de masa molar en el amoníaco.

Answer:

the answer is d , sundiata!

Step-by-step explanation:

the

Answer:

0.9952076759

Step-by-step explanation:

Probability that all three survive

= 0.9984 × 0.9984 × 0.9984

= 0.9952076759

Answer: multiply 10 to both terms and subrtact products

Step-by-step explanation:

10(5 - 2x)

multipy 10 to both terms

50  20x

subtract products

50 - 20x

Answer:

1. subtract 2×from get 3.×= 682+ 4672

Answer:

42.5

Step-by-step explanation:

(180-95)÷2=42.5

{11, 17, 27}

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Explanation:

Let's go through the answer choices.

Now return back to choice C. Notice how adding any two sides leads to a sum larger than the third side

The three conditions of the triangle inequality theorem are met, so a triangle is possible for choice C.

Answer:

1. Last years middle school and highschool softball teams.

2. I can't see the last option

3. Every girl at the local middle school.

4. A group of students at a college.

5. Survey the students selected blindly put of a box containing every students names.

Step-by-step explanation:

I hope these are correct. comment the last option for #2.