Which inequality describes all the solutions to 5(3-x)<-2x+6

Answer:

A. a. 34.5 feet

b. 60 feet

Step-by-step explanation:

Parabola equation

[tex]y=-0.005x^2+0.3x[/tex]

Differentiating with respect to x we get

[tex]\dfrac{dy}{dx}=-0.01x+0.3[/tex]

Equating with zero

[tex]-0.01x+0.3=0\\\Rightarrow -0.01x=-0.3\\\Rightarrow x=\dfrac{0.3}{0.01}\\\Rightarrow x=30[/tex]

Double derivative of the parabolic equation

[tex]\dfrac{d^2y}{dx^2}=-0.01<0[/tex]

So, [tex]x=30[/tex] is maximum.

[tex]y=-0.005\times 30^2+0.3\times 30\\\Rightarrow y=4.5[/tex]

So, the maximum height of the arch will be 4.5 feet.

From the ground the highest point of the arch will be [tex]30+4.5=34.5\ \text{ft}[/tex]

We are taking the x axis as the width of the bank.

[tex]0=-0.005x^2+0.3x\\\Rightarrow 0.005x^2=0.3x\\\Rightarrow x=\dfrac{0.3}{0.005}\\\Rightarrow x=60[/tex]

So, the width of the bank will be 60 feet.

Answer:

Option B

Step-by-step explanation:

In order to find the answer to this question you need to use the slope formula and solve by subtracting the numerator and the denominator.

[tex]slope=\frac{y^2-y1}{x^2-x^1}[/tex]

[tex]x^1,x^2=(2,5)[/tex]

[tex]y^2,y^1=(8,7)[/tex]

Substitute:

[tex]\frac{8-7}{2-5}[/tex]

Subtract:

[tex]8-7=1[/tex]

[tex]2-5=-3[/tex]

[tex]=\frac{-1}{3}[/tex]

Hope this helps.

Step-by-step explanation:

x^2+5x+7x+35=0

x*x+5x+7x+5*7=0

x(x+5)+7(x+5)=0

(x+7)*(x+5)=0

x=-7 or x=-5

So the function is positive (>0) when

x<-7 and when x>-5

Answer:

| x + 4 | = 1/2

Step-by-step explanation:

We want the numbers on the number line that are at a distance of 1/2 from "-4".

We can express such via the absolute value as :

| x - (-4) | = 1/2

| x + 4 | = 1/2

Answer:

17.5 ft

Step-by-step explanation:

6.25/10 = x/28

x = 28(6.25/10)

x = 17.5 ft

The tangent or tanθ in a right-angle triangle is the ratio of its perpendicular to its base. The height of the tree is 17.5 feet

The tangent or tanθ in a right angle triangle is the ratio of its perpendicular to its base. It is given as,

[tex]\rm Tangent(\theta) = \dfrac{Perpendicular}{Base}[/tex]

where,

θ is the angle,

Perpendicular is the side of the triangle opposite to the angle θ,

The base is the adjacent smaller side of the angle θ.

Given that George casts a 10-foot tall shadow when the tree casts a 28-foot shadow. Also, George's height is 6.25 feet. Therefore, the tan angel can be written as,

tan(θ)= George's height/George's shadow = Tree's height/Tree's shadow

George's height/George's shadow = Tree's height/Tree's shadow

6.25 feet / 10 feet = Tree's height/28 feet

Tree's height = 17.5 feet

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Answer:

4350

Step-by-step explanation:

Linda's net and first term of the expression is correct and the surface area of the attic is 4425 square feet.

The area of a three dimensional object on it's outer surface is called the surface area of the object.

Given the attic of Linda's home.

Attic is in the shape of triangular prism.

The net that Linda drawn is correct since she expresses all the measurements right in the net.

So, the net Linda drew is correct.

We can find the surface area from the net of the prism.

Net of the prism consists of 2 identical triangles, 2 identical rectangles and a rectangle.

Area of triangle is  [tex]\frac{1}{2}[/tex] × base × height and that of rectangle = length × width

Area of 2 triangles = 2 × [tex]\frac{1}{2}[/tex] × 25 × 15 = 25 × 15

Area of rectangles = (45 × 40) + (45 × 25) + (45 × 25)

                               = 45(40 + 25 + 25)

Total surface area = 45(40 + 25 + 25) + (25 × 15)

The first term of Linda's expression, 45(40 + 25 + 25) is correct.

The second term of Linda's expression, ([tex]\frac{1}{2}[/tex] × 25 × 15) is not correct.

Surface area of the attic = 45(40 + 25 + 25) + (25 × 15)

                                        = 4425 square feet

Hence the surface area of the attic is 4425 square feet.

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The complete question is given below.

The value of x from the figure is 13

The sum of angles on a straight line is 180 degrees.

From the given diagram;

Simplify

15x - 15  = 180

Add 15 to both sides

15x - 15 + 15 = 180 + 15

15x = 195

x = 195/15

x = 13

Hence the value of x from the figure is 13

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Answer:

D.5

Step-by-step explanation:

An angle bisector makes both sides of the angle equal (usually). Set the equation to 6x+4=8x-6. Solve for x by subtracting 6x from both sides so you get 4=2x-6. Add 6 to both sides so the equation is now 2x=10 and divide by 2.

Answer:

2(5x+4)

2×5=10

2×4=8

so answer is 2(5x+4)

Answer:

6.40

Hope this helped somehow

Answer:

13 & 7.

Hope this helps.

Answer:

This is called a prepayment

Answer:

Step-by-step explanation:

surface area of a square pyramid

= Area of base + 1/2 base perimeter * slant height

= (1 x 1) + (1/2 x 4 x 4)

= 1 + 8

= 9 yd²

9514 1404 393

Answer:

  A, D, E

Step-by-step explanation:

When the graph of a relation is a straight line, the relation is said to be "linear." When the graph of the line goes through the origin (x, y) = (0, 0), then the relation is both "linear" and "proportional."

The "rate of change" of a line is the ratio of "rise" to "run". On a graph of a line, it is convenient to determine "rise" and "run" using points where the line crosses grid intersections. Of course, there is a crossing here at (0, 0). We notice another grid intersection crossing at the point corresponding to x=2 and y = -6. Then the "rise" (y-change) divided by the "run" (x-change) is ...

  rate of change = rise/run = -6/2 = -3

__

The equation of a line representing a proportion is of the form ...

  y = kx

for some constant k. That constant is the "rate of change" of the proportion. Here, we found that rate of change to be -3, so the equation of the line is ...

  y = -3x

Answer:

x = 62

y = 31

Step-by-step explanation:

x+(0)+(0-2)=60

x-2=60

x=62

(0)+y+(y-2)=60

y+y=62

y= 31

Answer:

it is 5.25

Step-by-step explanation:

ignore this i just need more letters XD

Answer : 5.25

explanation : 1/4 automatically is 25 because it's 1/4 of 100. 5 stays the same. 5.25

Answer:

f we are talking about months of births its qualitative, if numbers such as 11, 10, 5, representing days or months or years is involved as data then it is quantitative.

Step-by-step explanation:

Answer:

x = 1.25

Step-by-step explanation:

1.5 = X + 0.25

1.25 = x             you subtract 0.25 from both sides

Answer:

no

Step-by-step explanation:

Answer: 4/20, or 1/5

Step-by-step explanation: since there are 4 orange, and 20 total, then if you were to draw an orange it would be 4/20(this is very basic probability)

Answer:

A

Step-by-step explanation:

pretty sure thats it

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Answer:

8,3

Step-by-step explanation:

Answer:

The correct answers are 120°, 180°

An equation is formed of two equal expressions. The solutions for the interval 0° ≤ x < 360° are 120° and 180°.

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

cos(x/2) = cos(x) + 1

cos(x/2) - cos(x) - 1 = 0

Let u=(x/2), therefore, the equation can be rewritten as,

cos(u) - cos(2u) - 1 = 0

cos(u) - 2cos²(u) + 1 - 1 = 0

cos(u) - 2cos²(u) = 0

-2cos²(u) = -cos(u)

2cos²(u) / cos(u) = 1

2 cos(u) = 1

cos(u) = 1/2

u = cos⁻¹ (1/2)

u = 60°

Since u=(x/2), therefore, the value of x is,

u=(x/2)

x = 120°

Hence, the solutions on the interval 0° ≤ x < 360° are 120° and 180°.

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Answer:

1

Step-by-step explanation:

The point is located in the first quadrant because x and y are both positive. The quadrants are labeled in counter-clockwise order, starting in the upper-right.

Answer:

I think it is either the first or second answer

Step-by-step explanation:

Answer:

The area is 3.9375 cubic ft, so yes, the area will greater than 3 and 1/2 ft.

Hope this helps:)

Step-by-step explanation:

Length of a rectangular sign :-

[tex] = 3 \frac{1}{2} \: \: m[/tex]

Width of a rectangular sign :-

[tex] = 1 \frac{1}{8} \: \: m[/tex]

The formula for finding the area of a rectangle is :-

[tex] =\bold{ length \times breadth}[/tex]

The area of the rectangular sign:-

[tex] =3 \frac{1}{2} \times 1 \frac{1}{8} [/tex]

[tex] = \frac{(2 \times 3 )+ 1}{2} \times \frac{(8 \times 1) + 1}{8} [/tex]

[tex] = \frac{6 + 1}{2} \times \frac{8 + 1}{8} [/tex]

[tex] = \frac{7}{2} \times \frac{9}{8} [/tex]

[tex] = \frac{7 \times 9}{2 \times 8} [/tex]

[tex] = \frac{63}{16} [/tex]

[tex] ={3 \frac{15}{6} \: \: }[/tex]

[tex] = 3 \frac{15 \div 3}{6 \div 3} [/tex]

[tex] ={ 3 \frac{5}{2} \: m}[/tex]

Thus, the area of the rectangular sign is:-

[tex] =\bold{ 3 \frac{5}{2} \: m}[/tex]

[tex]\bold{3 \frac{5}{2} \: > 3 \: \frac{1}{2} \: }[/tex]

Which will mean that the area of the rectangular sign is greater than [tex] { 3 \frac{1}{2} \: m}[/tex].

Therefore, the area of the rectangular sign is = [tex] \bold{ 3 \frac{5}{2} \: m}[/tex] and it is greater than [tex] \bold{ 3 \frac{1}{2} \: m}[/tex] .

Answer:

Step-by-step explanation:

first we need to get the side length of a square.

Area of a square A = L²

1 = L²

L = √1

L = 1 unit

The shaded portion is a circle.

Area of a circle = πd²/4

The diameter of the circle = 4L = 4(1) = 4units

Substitute into the formula;

A =πd²/4

A = π(4)²/4

A = 4(3.14)

A = 12.56inits²

B) The area of the whole shape = Length * width

Length = 6

Width = 6 (6 squares)

Area of the shape = 6*66 = 36units²

Percentage of the area shaded = 21.56/36 * 100

Percentage of the area shaded = 2156/36

Percentage of the area shaded = 59.9%

Answer:

You're answer is 4/7

Step-by-step explanation:

I hope this helps!