Determine whether the graph below is that of a function by using the vertical-line
test. If it is, use the graph to find
(a) its domain and range.
(b) the intercepts if any.
(C) any symmetry with respect to the x-axis, y-axis, or the origin.

The vertical distance from the ground to your eye is 10.9 feet and the height of the tree is 20.5 feet.

Pythagoras theorem is used to show the relationship between the sides of a right angled triangle. It is given by:

Hypotenuse² = Adjacent² + Opposite²

From the diagram, let d represent the horizontal distance, hence:

d² = 9.2² + 4.8²

d = 10.9 feet

Let h represent the height of the tree, hence:

h / 10.9 = 10.9 / 5.8

h = 20.5 feet

The vertical distance from the ground to your eye is 10.9 feet and the height of the tree is 20.5 feet.

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Answer:

63.7°

Step-by-step explanation:

supplementary_interier angle 180_116.3=63.7

Answer:

4

Step-by-step explanation:

[tex] ln(x) = ln(16) + ln(4) [/tex]

Use the Produxt Rule

[tex] ln(a) + ln(b) = ln(a + b) [/tex]

Remeber that Ln is a log function with base e,

so know we have

[tex]3 ln(x) = ln(64) [/tex]

[tex] ln(a) = ln(b) [/tex]

Only if a=b So we have

x^3=64

x=4

[tex]x = 64[/tex]

Step-by-step explanation:

See the picture for steps

!Answer:

Mrs. Thomas put 1/4 icing on the remaining cupcakes

Step-by-step explanation

Answer:

The length of the field = 24.5 yards

The width of the field = 12 yards.

Step-by-step explanation:

If "w" is the width, then the length is 49 - 2w.

The area of the rectangle field = length × width

= w(49 - 2w)

Area =

This a quadratic equation, the vertex of x coordinate is w

w =

Here a = -2 and b = 49

w = .

So width of the field is 12.25 yards.

The length of the filed = 49 - 2(12.25) = 24.5

Area = 12.25 × 24.5 = 300.125 square yards.

The field has an area of 294.

Therefore, the length must be 24.5 yards and width must be 12 yards.

24.5 × 12 =294 square yards.

Therefore, the length of the field = 24.5 yards

the width of the field = 12 yards.

Answer:

See below for answers and explanations

Step-by-step explanation:

Problem 1

[tex]u\cdot v=\langle4,-7\rangle\cdot\langle-6,9\rangle=(4*-6)+(-7*9)=-24-63=-87[/tex], so A is correct. Remember to multiply the horizontal components with each other and then add that to the product of the vertical components to get the dot product.

Problem 2

Two vectors are orthogonal if their dot product is 0, which also means that they must be perpendicular to each other, so we can check this:

[tex]u\cdot v=(6*-24)+(-9*36)=-144-324=-468[/tex]

Since the dot product of the two vectors is 0, they aren't orthogonal. Therefore, they are parallel since [tex]v=4u[/tex], making A the best choice.

Problem 3

Recall that the angle between two vectors is [tex]\theta=cos^{-1}(\frac{u\cdot v}{||u||*||v||})[/tex] where [tex]u\cdot v[/tex] is the dot product of vectors [tex]u[/tex] and [tex]v[/tex] while [tex]||u||[/tex] and [tex]||v||[/tex] are the magnitudes of vectors [tex]u[/tex] and [tex]v[/tex] respectively. If we let [tex]F_1=u[/tex] and [tex]F_2=v[/tex], we can then continue on:

[tex]u\cdot v=(190*128)+(160*-121)=24320+(-19360)=4960[/tex]

[tex]||u||=\sqrt{190^2+160^2}=\sqrt{61700}=10\sqrt{617}[/tex]

[tex]||v||=\sqrt{128^2+(-121)^2}=\sqrt{31025}=5\sqrt{1241}[/tex]

[tex]\theta=cos^{-1}(\frac{u\cdot v}{||u||*||v||})\\\\\theta=cos^{-1}(\frac{4960}{10\sqrt{617}*5\sqrt{1241}})\\\\\theta\approx83.49^\circ\approx83^\circ[/tex]

Therefore, B is the correct answer

Problem 4

We observe that [tex]u=\langle-8,-9\rangle[/tex] and [tex]v=\langle3,7\rangle[/tex], so [tex]-3(u\cdot v)=-3[(-8*3)+(-9*7)]=-3[-24+(-63)]=-3(-87)=261[/tex]. This means that B is the correct answer.

Problem 5

Recall that the projection of a vector [tex]u[/tex] onto [tex]v[/tex] is [tex]proj_vu=(\frac{u\cdot v}{||v||^2})v[/tex], thus:

[tex]proj_vu=(\frac{u\cdot v}{||v||^2})v\\\\proj_vu=(\frac{(-10*4)+(-3*8)}{\sqrt{4^2+8^2}^2})\langle4,8\rangle\\\\proj_vu=(\frac{-40+(-24)}{\sqrt{80}^2})\langle4,8\rangle\\\\proj_vu=(\frac{-64}{80})\langle4,8\rangle\\\\proj_vu=(-\frac{4}{5})\langle4,8\rangle\\\\proj_vu=\langle-\frac{16}{5},-\frac{32}{5}\rangle[/tex]

Therefore, D is the correct answer

Answer:

  (b)  y -5 = 3/4(x -6)

Step-by-step explanation:

The point-slope form of the equation for a line with slope m through point (h, k) is ...

  y -k = m(x -h)

Your graph has two points marked: (-2, -1) and (6, 5). Even if you don't know the slope, these tell you the form of the equation will be ...

  y +1 = m(x +2) . . . . no match

  y -5 = m(x -6) . . . . matches choice B

__

If you like, you can figure out the slope to be ...

  m = (y2 -y1)/(x2 -x1)

  m = (5 -(-1))/(6 -(-2)) = 6/8 = 3/4

All the answer choices agree that this is the slope of the line.

Answer:

That its a problem there u go

Step-by-step explanation:

Answer:

I am not sure but the answer may be 36 w

Answer:

A.1600

Step-by-step explanation:

I hope its help keep safe

Answer:

1920

Step-by-step explanation:

64 x 5/6

Multpying each side by the LCM which is 6

u will get (64 x 6) x 5

384 x5

1920

A 5th point that would maintain the function is (11, 31)

Given the following pairs of coordinates

Four of the points are given as (1,3) (2,5), (6, 13), (9,27)

Using the coordinates  (1,3) (2,5), to determine the slope

[tex]Slope=\frac{5-3}{2-1} = \frac{13-5}{6-2}=2\\[/tex]

Let the required coordinate be (x, y) to have:
[tex]2 = \frac{y - 27}{x - 9} \\[/tex]

Since the x coordinate of (9, 27) is greater than 8, hence the best x-coordinate will be 11. Substitute to get the y-coordinate

[tex]2 = \frac{y - 27}{11- 9}\\2(2) = y - 27 \\4 = y - 27\\y=27 + 4\\y=31[/tex]

Hence a 5th point that would maintain the function is (11, 31)

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Answer:

40 minutes later

Step-by-step explanation:

6:15 + 40 minutes = 6:55

Consider the given quadratic equation that we have :

[tex]{:\implies \quad \sf -5x^{2}+5=-2x}[/tex]

Multiplying both sides by -1 will yield ;

[tex]{:\implies \quad \sf 5x^{2}-5=2x}[/tex]

Write the above quadratic equation in the form of standard quadratic equation ax² + bx + c = 0 ,

[tex]{:\implies \quad \sf 5x^{2}-2x-5=0}[/tex]

Now , comparing this with the standard form of quadratic equation we will get a = 5 , b = -2 , c = -5 . So now , Discriminant (D) = (-2)² - 4 × 5 × -5 = 4 + 100 = 104

Now , by the quadratic formula ;

[tex]{:\implies \quad \sf x=\dfrac{-(-2)\pm \sqrt{104}}{2\times 5}}[/tex]

[tex]{:\implies \quad \sf x=\dfrac{2\pm 2\sqrt{26}}{2\times 5}}[/tex]

[tex]{:\implies \quad \sf x=\dfrac{\cancel{2}(1\pm \sqrt{26})}{\cancel{2}\times 5}}[/tex]

[tex]{:\implies \quad \bf \therefore \quad \underline{\underline{x=\dfrac{1\pm \sqrt{26}}{5}}}}[/tex]

For any quadratic equation of the form ax² + bx + c , the Discriminant (D) is given by D = b² - 4ac , and the root [tex]\bf x[/tex] of the quadratic equation is given by the quadratic formula as

Answer:

17

Step-by-step explanation:

Seeing that traingle ABC is = to triangle DEF.

It means that the angles are equal too.

So you would equate them to each other.

Hence 5X+2=87

5X=87-2

5X=85 (divide by 5)

X=17

Hope that helps :)

Step-by-step explanation:

Bro who give 5 point for this type of questions. This question deserve 50 points.

Answer:

The rule says that to find the number of years required to double your money at a given interest rate, you just divide the interest rate into 72. For example, if you want to know how long it will take to double your money at eight percent interest, divide 8 into 72 and get 9 years

Answer:

Step-by-step explanation:

Distance = d

d² = [1 - (-3)]² + [y - (-6)]²

5² = 16 + (y + 6)²

25 = 16 + (y + 6)²

(y + 6)² = 25 - 16 = 9

y + 6 = ±3

y = -6 ±3

so

y = -3 or -9

For the triangle, the following statements are correct: The third angle measures 50° and all sides have different lengths.

A triangle is a polygon with three sides and three angles. Types of triangles are isosceles, equilateral, scalene and right angled triangle.

Let x represent the third angle. The other angles measures of 100° and 30°. Hence:

x + 100 + 30 = 180° (sum of angles in a triangle)

x = 50°

Since the angles are different, hence all the sides have different lengths.

The third angle measures 50° and all sides have different lengths.

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Answer:

D : -14

Step-by-step explanation:

(5+4-2)(-2) = x

7(-2) = x

-14 = x

x = -14

Step-by-step explanation:

[tex]2 ln(3) = ln(x - 4) [/tex]

For logarithms, this is a property

[tex] ln(x {}^{n} ) = n ln(x) [/tex]

So we have

[tex] ln( {3}^{2} ) = ln(x - 4) [/tex]

[tex] ln(9) = ln(x - 4) [/tex]

If

[tex] ln(a) = ln(b) [/tex]

a=b

So

[tex]9 = x - 4[/tex]

[tex]13 = x[/tex]

Step-by-step explanation:

there is an official formula for this. this can be truly found very easily on the internet ...

the formula for the sum of all angles in a regular polygon with n sides or vertices is

(n-2)×180

so, since an octagon has 8 sides and vertices, this gives us

(8-2)×180 = 6 × 180 = 1080°

that's it ...

Answer:

(8-2)×180 = 6 × 180 = 1080°

Step-by-step explanation:

hope this help

Answer:

131

Step-by-step explanation:

When we attempt to find the square root of 5607, we get a remainder of 131. (5607=74^2 + 131) That means 5607-131 is a perfect square. (Which is 5476=74^2)    

Answer:

Line D

Step-by-step explanation:

Two points that passes through line D :  (0,-2) & ( -4 , 0)

[tex]Slope =\dfrac{y_{2}-y_{1}}{x_{2}-x_{1}}\\\\\\=\dfrac{0-[-2]}{-4-0}\\\\\\=\dfrac{0+2}{-4}\\\\\\=\dfrac{2}{-4}\\\\\\=\dfrac{-1}{2}[/tex]

Answer:

let

custard pie be x

Step-by-step explanation:

1/7 x = 185

x=185× 7

x=1395

1/8 of x= 1395/8

1/8 of x=174.3

1/4 of x = 1395/4

=348.75

1/6 of x =1395/6

=232.5

[tex]\fbox{Answer ~}[/tex]

Here ,

[tex]\bold\purple{3x + 12 + 7 = - 5x - 5} \\\\\bold{3x + 19 = - 5x - 5}[/tex]

gather and solve the like terms together ,

[tex]\bold{3x + 5x = - 5 - 19} \\\\ \bold{8x = - 24} \\\\\bold{ x = \cancel{ \frac{ - 24}{8} }} \\ \\\bold\red{ x = - 3}[/tex]

hope helpful~

Answer: 592330

Step-by-step explanation:

Answer:

[tex]\frac{20r^5}{c}[/tex]

Step-by-step explanation:

[tex]4c^{4}[/tex]·[tex]5c^{-5} r^{5}[/tex]

=[tex]4c^{4}[/tex]·[tex]\frac{5 r^{5}}{c^{5} }[/tex]

=[tex]\frac{20c^{4}r^{5} }{c^5}[/tex]

=[tex]\frac{c^4}{c^4} \frac{20r^5}{c}[/tex]

=[tex]\frac{20r^5}{c}[/tex] or =[tex]20c^{-1}r^5[/tex]