Use the Law of sines or trigonometric ratios to find each length. Round your answer to 1 decimal place.

a. The length of the zip line

b. The height of the point on the tree where the top of the ladder rests against it.

c. The distance between the base of the ladder and the base of the tree.

d. The distance between the base of the tree and the spot where the zip line is anchored in the ground.

The range of the function the as given in the equation is; -∞ ≤ y < ∞.

It follows from the task content that the function given is; y=3√x+8.

On this note, it follows that the range of the function is the set of all possible outputs, y values and in this case is; -∞ ≤ y < ∞.

It therefore follows that the range of the function is as indicated above as all X-values (domain) must be positive and the square root of x yields a positive or negative real number.

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Answer:

90 grams

Step-by-step explanation

Full = 120

half filled + empty = 150

half of 120 = 60

Therefore, a jar weighs 150 - 60

= 90 grams

Answer:

Step-by-step explanation:

A relation is a function if there is only one y-value for each x-value. If you can draw a vertical line on the graph that intersect more than one point, the relation is not a function. (This is the "vertical line test.")

Graph A: there are 3 y-values associated with x=2. Not a function.

Graph B: passes the vertical line test: A function.

Graph C: there are 2 y-values at each of x=1 and x=2. Not a function.

Answer:

the distance is 10

Step-by-step explanation:

since the slope is the same you know they're parallel, but just find the difference from the two y intercepts (the +3/-7) the difference is 10, so 10.

Answer:

16

Step-by-step explanation:

A fraction that is divided by a number is just multiplication with the denominator. So with that 8(2)=16

Based on the fact that the snake was placing the mice one - by - one into a jar, this is A. Combining sets.

When sets are combined, it means that numbers from a certain set of variables are combined with those from another set.

The snake had captured the mice separately which means they were in different sets. Putting them into one jar means they are being combined so this is combining sets.

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The $1.25 one for 9 Oz box of rice would be the best buy.

To get the best buy among the given items and prices, we need to find the unit price. Thus, the formula is;

Unit price = Price/Quantity

A) Unit Price = 0.90/6 = 0.15

B) Unit Price = 1.93/12 = 0.15083

C) Unit price = 2.42/16

Unit Price = 0.15125

D) Unit Price = 1.25/9 = 0.138

The $1.25 one for 9 Oz box of rice would be the best buy.

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Answer: 841

Step-by-step explanation:

29×29=841

Answer:

2.7 is the answer!!

Step-by-step explanation:

hope this helps :)

Answer:

Step-by-step explanation:

The mnemonic SOH CAH TOA is intended to help you remember the relationships between sides of a right triangle and trig functions of the acute angles. It tells you ...

The given triangle shows values of an acute angle and its opposite side. You are to find the other two sides in the triangle, as well as the other acute angle.

X is the side adjacent to the given angle, so the relevant trig relation is ...

  Tan = Opposite/Adjacent

  tan(25°) = (4 ft)/X

Solving for X gives ...

  X = (4 ft)/tan(25°) . . . . . . . . multiply by X/tan(25°)

  X ≈ 8.58 ft

Y is the hypotenuse, so the relevant trig relation is ...

  Sin = Opposite/Hypotenuse

  sin(25°) = (4 ft)/Y

  Y = (4 ft)/sin(25°) . . . . . . multiply by Y/sin(25°)

  Y ≈ 9.46 ft

The sum of angles in a triangle is 180°, so if one of them is 90°, the sum of the other two is 90°.

  Z = 90° -25°

  Z = 65°

Answer:

No solutions

Step-by-step explanation:

Hello!

To solve for x, we should expand the parenthesis and isolate the variable x.

The are no solutions for x, as 6 does not equal to 5.

In this scenario, children are identifying measurable attributes such as length and weight and solve problems by making direct comparisons of objects.

Measurement refers to a process through which the dimensions, size (weight), or other physical quantities of magnitude that are associated with an object is taken, especially for use in a scientific research and experiment such as direct comparison.

In this scenario, we can infer and logically deduce that the children are identifying measurable attributes such as length and weight and solve problems by making direct comparisons of objects.

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Answer:

y ≤ 2.5x-3

Step-by-step explanation:

we know two points: (2 , 2 ) and ( 0 , -3)

[tex]Grad = \frac{2--3}{2-0} =\frac{5}{2} =2.5\\[/tex]

we also know the y intercept is -3

therefore equation in question is : [tex]y = 2.5x-3[/tex]

we take any point either above the line or below the line and substitute in the equation above. Let us try point (0,0) which is above the line and in the unwanted(shaded region):

y = 2.5x-3

0=2.5(0)-3

0=-3

Normally 0 can  never be equal to -3 but is ≥ -3.

Since the point taken was not in the wanted region we reverse ≥  to ≤  to show the wanted region. The inequality in question becomes :

y ≤ 2.5x-3

By de Moivre's theorem,

[tex]\left(\cos\left(\dfrac\pi6\right) + i \sin\left(\dfrac\pi6\right)\right)^{18} = \cos\left(\dfrac{18\pi}6\right) + i \sin\left(\dfrac{18\pi}6\right) \\\\ ~~~~~~~~ = \cos(3\pi) + i \sin(3\pi) = \boxed{-1}[/tex]

The value of the given complex number is -1

Given the polar form of a complex number expressed as:

[tex](cos\theta + isin\theta)^n\\[/tex]

This can also be expressed according to the de moivre's theorem as;

[tex]=(cos\theta + isin\theta)^n\\\\=(cosn\theta+isinn\theta)[/tex]

Given the expression below;

[tex](cos\frac{\pi}{6} + isin\frac{\pi}{6} )^{18}\\(cos18\cdot\frac{\pi}{6} + isin18\cdot\frac{\pi}{6} )\\(cos3\pi + isin3\pi)\\=-1[/tex]

Hence the value of the given complex number is -1

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Answer:

48 servings

Step-by-step explanation:

3tsp=tbsp

32*3=96

96/2=48

Answer:c

options A  and B

Step-by-step explanation:

the ratio between the lengths of the two legs of a 30-60-90 triangle

General ration of 30-6- 90 degrees triangle is

x : xsqrt(3) : 2x

When x=1 the ratio becomes 1 : 1 sqrt(3)

when x= 2sqrt(3) the ratio becomes

It becomes

Two sides of 30-60-90 triangle cannot be equal

so option c  and option D are not possible

sqrt(2) is also not possible  because we have sqrt(3) in general ratio

PLS MARK ME AS BRAINLIEST.

Step-by-step explanation:

2A and 2B are scalar multiplications : every item in the matrix has to be multiplied by that factor.

the subtraction then of 2A - 2B is simply to subtract every positive in B from the corresponding same position in A.

that is all.

2A =

4 0

-6 2

2B =

0 2

-4 6

2A - 2B =

4-0 0-2

-6--4 2-6

=

4 -2

-2 -4

Answer: $412.50

Step-by-step explanation:

The area of the square formed by combining the painting and the molding is [tex](25)(28)=700[/tex] square inches.

The area of the painting itself is [tex](22)(25)=550[/tex] square inches.

Therefore, the area of the molding is [tex]700-550=150[/tex] square inches, and thus costs [tex](150)(2.75)=\$412.50[/tex]

Answer: it should be this M=kb^3/B^2

Step-by-step explanation:

Answer:

B. 13

Explanation:

[tex]\sf\:Given\:expression: log(\dfrac{x^2 y^3}{z} )[/tex]

Logarithm rules:

[tex]\sf (i) \ \sf log(ab) = log(a) + log(b)\\ \\ (ii) \ log(a/b) = log(a) - log(b)\\\\ (iii) \ log(a^n) = n log(a)[/tex]

Breakdown of the expression:

[tex]\rightarrow \sf log\left(\dfrac{x^2y^3}{z}\right)[/tex]

[tex]\rightarrow \sf log\left(x^2\right) + log\left(y^3\right) - log(z)[/tex]

[tex]\rightarrow \sf 2\log\left(x\right)+3\log \left(y\right)-\log \left(z\right)[/tex]

insert given values

[tex]\rightarrow \sf 2(3)+3(2)-(-1)[/tex]

[tex]\rightarrow \sf 13[/tex]

Answer:

B.) The graph of m(x) is wider.

     Both graphs open upward.

     Both have the axis of symmetry x = 0.

     The vertex of m(x) is (0, 4); the vertex of n(x) is (0, 0).

Step-by-step explanation:

When the coefficient before x² is greater than 1, the curve of the graph is narrower. When the coefficient is less than 1, the curve of the graph is wider.

When the coefficient in front of x² is positive, the graph opens upwards. When the coefficient is negative, the graph opens downwards.

The axis of symmetry is the "x" value which divides the curve into two equal sections. Their axis of symmetry are both x = 0 because their vertexes (the lowest point of the curve) are both at x = 0.

The vertex can be found by plugging x = 0 into both of the equations and then solving. The resulting value is the "y" position of the vertex.

m(0) = 0.7(0)² + 4                        n(0) = (0)²

m(0) = 0 + 4                                 n(0) = 0

m(0) = 4

Therefore, the vertexes are m(x) =  (0,4) and n(x) = (0,0).

Answer:

Step-by-step explanation:

m(x) =.7x^2 + 4

n(x) = x^2

In the graph below

green = m(x)

blue = n(x)

Answer:

The true statements are:

The interquartile range is 10.

The data is skewed.

A box plot is used to study the distribution and level of a set of scores

The end of the first whisker represents the minimum number and the end of the second whisker represents the maximum number.

On the box, the first line to the left represents the lower (first) quartile. The next line on the box represents the median. The third line on the box represents the upper (third) quartile. The interquartile range is the difference between the first and third quartile.

Interquartile range = 9 - (-1) = 10

A box plot is negative skewed because the median is not at the center of the box.

An outlier would be within: (Q1 - 1.5 * IQR or Q3 + 1.5 * IQR).

- 1 - (1.5 x 10 ) = -16

9 + (1.5 x 10) = 24

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A ratio shows us the number of times a number contains another number. The elephant's weight on Planet B is 96 pounds.

A ratio shows us the number of times a number contains another number.

The ratio of the weight of an object on Planet A to the weight of the same object on Planet B is 100 to 3.

Weight on Planet A/ Weight on planet B = 100 / 3

Now, the weight of the elephant on planet A to Planet B will be,

elephant's weight on Planet A/elephant's weight on Planet B = 100 / 3

elephant's weight on Planet B = (3 ×3200)/100

elephant's weight on Planet B = 96 pounds

Hence, the elephant's weight on Planet B is 96 pounds.

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Answer:

See below

Step-by-step explanation:

=  (-7)(11)(√(3*10) ) =  - 77 √(30)  

Domain: [-4, ∞)

Range: (-∞, 0]

*Domain are all x-values listed. Here you can see the graph going the right (positive) of -4 (Doesn't go to the left)

*Range are all y-values listed. Here you can see the graph starts from zero and goes down (negative)

Hope it helps!

Answer: -2, 1, all real numbers, all real numbers

Step-by-step explanation:

g o f(n) is basically g(f(n))

Using the question as an example we can get that f(0) = 1 so

g(f(0)) = g(1) = -2

f(1) = 0 so g(f(1)) = g(0) = 1

The domain of f(x) is all real numbers and the range of g(x) is all real numbers

[tex]\huge\boxed{L^\prime(0, -1)}[/tex]

To rotate a point around the origin by 180 degrees, multiply both parts of the coordinate point by [tex]-1[/tex]. (This means you go from [tex](x, y)[/tex] to [tex](-x, -y)[/tex].)

[tex]L(0, 1)[/tex]

[tex]L^\prime(0*(-1), 1*(-1))\\\boxed{L^\prime(0, -1)}[/tex]

Answer:

y=2x-11

Step-by-step explanation:

arralel lines have same gradient

since gradient of the known line is 2( the coefficient of x), it therefore follows that the gradient of the second line we want to find is also 2

So we know the gradient of the second line is 2, and we have one known point (7,3). We can therefore apply the formula for finding gradient to come up with the line

[tex]2=\frac{y-3}{x-7} \\\\y-3=2(x-7)\\\\y-3=2x-14\\\\y=2x-14+3\\\\y=2x-11[/tex]

a) The point (2, -7/5) is not a point on the graph?

b)  The value of f(x) when x is 1 is -1/3 and the point on the graph is (1, -1/3)

c) The value of x for f(x) = 2 is 22 and the point on the graph is (22, 2)

d) The domain of x is all real values of x ≠ 10

e) The x intercept is -2

f) The y intercept is -1/5

Function is a relation from a set of inputs to a set of possible outputs where each input is related to exactly one output and not one input for two outputs.

Analysis:

a) To test if the point (2, -7/5) is a point on the graph, we put in x = 2 into the function,

f(2) = 2+2/2-10 = 4/-8  = -1/2 ≠ -7/5. Therefore (2, -7/5) is not a point on the graph.

b) if x = 1, f(1) = 1 +2 / 1-10 =  3/-9 = - 1/3

   The point on the graph is (1, -1/3)

c) if f(x) = 2, then 2 = x+2/x-10

     2(x-10) = x+2

     2x -20 = x+2

      2x-x = 2+20

      x = 22, the point on the graph is (22, 2)

d) The domain of the function is such that the denominator would not be zero.

so if x - 10 ≠ 0

Then the values of x ≠ 10 are the domain of the function.

e) The x intercept of the graph is the point at which f(x) = 0

  0 = x+2/x-10

   x+2 = 0

   x = -2. The x-intercept is -2.

f) the y-intercept is such that x = 0

   0+2/0-10 = 2/-10 = -1/5

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