A tree casts a shadow of 20 meters when the angle of elevation of the sun is 24°
Find the height of the tree to the nearest meter.

A second-degree polynomial takes the form

[tex]f(x) = ax^2 + bx + c[/tex]

for some constants a, b, and c. Such a function is continuous and differentiable everywhere in its domain.

Differentiating f(x) with respect to x gives

[tex]\dfrac{df}{dx} = 2ax + b[/tex]

We're told that

• f(x) is increasing on [0, 8]

• f(x) is decreasing on ]-10, 0]

and since df/dx is continuous, this tells us that df/dx = 0 when x = 0. It follows that b = 0, and we can write

[tex]f(x) = ax^2 + c[/tex]

We're also given that the curve passes through the point (-8, 4), which gives rise to the constraint

[tex]f(-8) = 64a - 8b + c = 4 \implies 64a + c = 4[/tex]

Since f(x) is decreasing on ]-10, 0], we have df/dx < 0 when x = -8, so

[tex]2ax+b < 0 \implies -16a < 0 \implies a > 0[/tex]

This means f(x) is minimized when x = 0, with min{f(x)} = c, so the co-domain of f(x) is the set {f(x) ∈ ℝ : f(x) ≥ c}.

Without another condition, that's all we can say about the co-domain. There are infinitely many choices for the constants a and c that satisfy the given conditions. For example,

a = 1, c = -60   ⇒   f(x) = x² - 60   ⇒   f(-8) = 4

⇒   co-domain = {f(x) ∈ ℝ : f(x) ≥ -60}

a = 2, c = -124   ⇒   f(x) = 2x² - 124   ⇒   f(-8) = 4

⇒   co-domain = {f(x) ∈ ℝ : f(x) ≥ -124}

etc.

Answer:

5 minutes.

44 x 5 = 220,

since 44 x 4 = 176 < 209

The match up  are:

The square root, in mathematics is known to be the factor of a number that, is said to be multiplied only by itself and thus it gives the original number.

For example:

[tex]\sqrt{4}[/tex] will give you 2.

Therefore, The match up  are:

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Answer:

C. 2

Step-by-step explanation:

Gradient = [tex]\frac{change in y}{change in x}[/tex]

Gradient = [tex]\frac{6}{3}[/tex]

Gradient = 2

The fill up for the 3rd  step is y - 250 =  340x.

Note that:

y-250 = 250 + 340 x - 250

y = 250 + 340x.

Make x the subject of the formula:

y - 250 =  340x.

then y-250/340 = x

Then  [tex]x = \frac{y-250}{340}[/tex]

The justification for the second step is subtraction property of equality because it undergoes subtraction and the collection of like terms and then subtracting them from one another as shown below:

y-250 = 250 + 340 x - 250

y= 250 + 340x - 250 + 250

Note that (-250 + 250) = 0

y = 250 + 340x.

Lastly, The fill up of the 6th step is substitution of the amount of money  saved and  then simplifying it.

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[tex](-4x+12)^{1/2}=x\\\sqrt{-4x+12}=x\\\\D:-4x+12\geq0\wedge x\geq0\\D:4x\leq12\wedge x\geq0\\D:x\leq3\wedge x\geq0\\D:x\in\langle0,3\rangle\\\\\sqrt{-4x+12}=x\\-4x+12=x^2\\x^2+4x-12=0\\x^2-2x+6x-12=0\\x(x-2)+6(x-2)=0\\(x+6)(x-2)=0\\x=-6 \vee x=2\\\\-6\not \in D\\\\\boxed{x=2}[/tex]

The point at which the graph of the function has a tangent line with the given slope is (-5,15)

A tangent is a straight line that touches any point on a curve.

Analysis:

slope of the curve [tex]x^{2}[/tex] + 2x is equal to dy/dx = d/dx( [tex]x^{2}[/tex] + 2x) = 2x+2

Which is equal to -8

2x+2 = -8

2x = -8-2

2x = -10

x = -5

substitute x into the equation

y = [tex](-5)^{2}[/tex] + 2(-5) = 25 - 10 = 15

In conclusion, the point at which the graph of the function has a tangent at -8 is (-5,15)

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The answer should be A. :)

The correct rational function of the graph is,

⇒ f (x) = 1 /(x + 5)²

A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

Given that;

The graph is shown in fgigure.

Now, By graph of function,

The graph is not defined at x = - 5.

Hence, From equation (i);

⇒ f (x) = 1 /(x + 5)²

Clearly, Function is noy defined at x = - 5.

Hence, The correct rational function of the graph is,

⇒ f (x) = 1 /(x + 5)²

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Answer:

y=3x+1

Step-by-step explanation:

From the table when X=0,y=1 thus b=1.

When

Answer: 3240-755

Step-by-step explanation:

We know that:

[tex](1+2+\cdots+80)-(71+72+\cdots+80)=1+2+\cdots+70[/tex]

Thus, [tex]1+2+\cdots+70=\boxed{3240-755}[/tex]

48.

Because 46+48 equals 94.

You can easily find out equations to this by subtracting the 46 from 94 to see what p is equal to.

HAVE A NICE DAY!

Answer:

Zoe's number is 6

Step-by-step explanation:

Let the number be 'n'

a) Multiply 'n' by 3 ⇒ n*3 = 3n

  Add 4 to '3n' ⇒ 3n + 4

Add 5 to 'n' ⇒  n +5

Multiply (n+ 5) by 2 ⇒ (n +5)*2 = 2n + 5*2 = 2n + 10

    3n + 4 = 2n + 10

b) 3n + 4 = 2n + 10

Subtract 4 form both sides

       3n = 2n + 10 - 4

       3n = 2n + 6

Subtract 2n from both sides

    3n - 2n = 6

          [tex]\sf \boxed{\bf n = 6}[/tex]

Answer:

21 is probably the best answer

Answer:

Answer: Original price = $150   Amount Paid = $90

Step-by-step explanation:

First we make a proportion 60/x = 40/100. When we cross multiply and divided to get x by itself we get $150 dollars. This is the original price of the dress. Now we take $150-$60 and we get $90. This is what Victoria paid for the dress after the 40% discount.

Hope this helps! :)

We are going to multiply the fraction 3/4, to the power of 2.

This means that:

Therefore:

[tex]\bf{\left(\dfrac{3}{4}\right)^{2}=\dfrac{3\times3}{4\times4}=\dfrac{9}{16} }[/tex]

Therefore, the answer of the fraction (3/4)^2, is equal to 9/16.

[tex]\red{\boxed{\green{\boxed{\boldsymbol{\purple{Pisces04}}}}}}[/tex]

The exact area of the isosceles trapezoid inscribed in a circle is determined as 196 sq units.

The height of the trapezoid is calculated as follows;

From the image, the sum of h1 and h2 is the height of the trapezoid.

Each of the height will be calculated using Pythagoras theorem as follows;

h1² = r² - (b1/2)²

h1² = 10² - 6²

h1² = 64

h1 = √64

h1 = 8

h2² = r² - (b1/2)²

h2² = 10² - 8²

h2² = 36

h2 = √36

h2 = 6

Total height = 8 + 6 = 14

A = ¹/₂(b₁ + b₂)H

A = ¹/₂(12 + 16) x 14

A = 196 sq units.

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The probability of drawing a black ball on the second draw will be 3/5.

From the information given, the total number of balls will be:

= 2 + 3 = 5 balls.

When the first ball is black and the second is red. This will be:

= 2/5 × 3/4

= 3/10

When the first is red and the second is black, this will be:

= 3/5 × 2/4

= 3/10

Therefore, the probability of drawing a black ball on the second draw will be:

= 3/10 + 3/10

= 3/5.

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Answer:

2

Step-by-step explanation:

Step-by-step explanation:

if there is no typo, or there are no parts missing, then

-1 <= 2-j < -5

cannot have any solution, because already for the outside limits -1 < -5 is impossible. -1 is larger than -5 !

Using translation concepts, the graph that represents [tex]y = \sqrt[3]{x} + 2[/tex] is given at the end of the question.

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

[tex]y = \sqrt[3]{x} + 2[/tex] is a shift up of 2 units of [tex]y = \sqrt[3]{x}[/tex], hence the graph is given at the end of this question.

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Answer:

18

Step-by-step explanation:

mack has 18cats because she has 2×9 cats as Wayne 2×9 is 18

Answer:

18

Step-by-step explanation:

[tex]\sf Twice = *2\\9 * 2 = 18[/tex]

The value of this equation is x = 0

The representation of an equation of the first degree - is given by:

[tex] \boxed{ \large \sf ax + b = 0}[/tex]

This representation is also defined in a first degree function.

— To solve this expression, let's: add or subtract the real terms. Then we will do the division.

⚘ Resolution

[tex] \large \sf{-3+8x-5=-8}[/tex]

[tex] \large \sf{-8+8x=-8}[/tex]

[tex] \large \sf{8x=0}[/tex]

[tex] \large \sf{x=0 \div 8}[/tex]

[tex] \green{ \boxed{ \boxed{ \blue{ \large \sf{x=0}}}}} \\ [/tex]

Therefore, the value of this equation will be x = 0

The number of dots tells us how many times we need to add the actual number underneath the dots. So you need to use both.

Let's suppose we have the next set:

{2, 2, 2, 4, 5, 5, 6}

If you graphed it in a dot plot, then you will have:

A total of 7 dots.

To find the mean, we just compute:

[tex]M = \frac{2 + 2 + 2 + 4 + 5 + 5 + 6}{7} = 3.7[/tex]

So the number of dots tells us how many times we need to add the actual number underneath the dots. In conclusion, to find the mean you need to use both, the number of dots and the number underneath.

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[tex]A = B \log_x C\\\\\text{Given that,}~~ A = 11, ~B = 4~ C = 190\\\\~~~~~~~~11 = 4 \log_x (190)\\\\\implies \log_x (190) = \dfrac{11}4\\\\\implies x^{\tfrac{11}4} = 190\\\\\implies x = 190^{\tfrac 4{11}}\\\\ \implies x \approx 6.7397[/tex]

Answer: 41.51

Step-by-step explanation:

[tex]\sin 49^{\circ}=\frac{x}{55}\\x=55 \sin 49^{\circ} \approx \boxed{41.51}[/tex]

Answer:

Step-by-step explanation:

Note that in this diagram, point A represents point X, point B represents point Y, and point C represents point Z.

From the diagram, it appears as if [tex]\overline{XZ} \perp \overline{XY}[/tex]. To determine if this is the case, we can find the slopes of both segments.

[tex]m_{\overline{XZ}}=\frac{4-1}{4-1}=1\\m_{\overline{XY}}=\frac{-1-1}{3-1}=-1[/tex]

Since these slopes are negative reciprocals, we know that they are perpendicular.

This means we can use the formula [tex]A=\frac{1}{2}bh[/tex], where b is the base (XY) and h is the height (XZ).

Using the distance formula,

[tex]XY=\sqrt{(3-1)^{2}+(-1-1)^{2}}=2\sqrt{2}\\XZ=\sqrt{(4-1)^{2}+(4-1)^{2}}=3\sqrt{2}[/tex]

This means the area is [tex]\frac{1}{2}(2\sqrt{2})(3\sqrt{2})=\boxed{6}[/tex]

Answer:

[tex]y= -\dfrac 17 x +\dfrac{48}7[/tex]

Step-by-step explanation:

[tex]~~~~~~~x+7y = 48\\\\\implies 7y = 48-x\\\\\implies y = \dfrac 17(48-x)\\\\\implies y= -\dfrac 17 x +\dfrac{48}7\\\\\text{It now in the slope-intercept form (y = mx+c).}[/tex]

(-3 - y) / (x - 4)

(-3 - (-3)) / ((-5) - 4)

(0)/(-9)

0

hope it helps...!!!

Answer:

0

Step-by-step explanation:

[tex] \frac{ (- 3 - y)}{(x - 4)} \\ when \: x = - 5 \: \: y = - 3 \\ \frac{( - 3 - - 3)}{ (- 5 - 4)} = \frac{ - 3 + 3}{ - 9} \\ = \frac{0}{ - 9} \\ 0[/tex]

Answer:

Area of the triangle = 210 cm^2 .

Step-by-step explanation:

Perimeter of triangle = 4x + 1 + 3x - 1 + 3x = 70

10x = 70 - 1 + 1 = 70

x = 7.

Area A = 1/2 * base * height

= 1/2 * 3x * (3x - 1)

= 1/2 * 3(7) * (3(7)  -1)

= 1/2 * 21 * 20

= 210.