(2(3^2+1)^2÷(5^2×4÷2))^3÷2^4​

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:

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: 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

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:

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:

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:

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:

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

Answer:

8,3

Step-by-step explanation:

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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9514 1404 393

Answer:

  rules of signs apply

Step-by-step explanation:

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

  y -k = m(x -h)

If the point coordinates are positive, their values show up in the equation with a minus sign.

Example:

  slope 2, point (3, 4)

  y -4 = 2(x -3)

__

If a point coordinate is negative, its value shows up in the equation with a plus sign.

Example:

  slope 2, point (-3, 4)

  y -4 = 2(x -(-3)) . . . . fill in the given value

  y -4 = 2(x +3) . . . . . simplify according to sign rules

__

The slope keeps its sign.

Example:

  slope -1/2, point (-3, 4)

  y -4 = -1/2(x +3) . . . . we only changed the slope from the previous example

Answer:

teehee

Step-by-step explanation:

:)

Answer:

This is called a prepayment

Answer:

13 & 7.

Hope this helps.

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:

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:

I think it is either the first or second answer

Step-by-step explanation:

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.

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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:

6.40

Hope this helped somehow

Answer:

x = 1.25

Step-by-step explanation:

1.5 = X + 0.25

1.25 = x             you subtract 0.25 from both sides

Answer:

3n=m

Step-by-step explanation:

Answer:

3m=n

Step-by-step explanation:

m equals the number of months she watches multiply that by three because three plus three plus three is the same as three times three.  and n is the equal because that is our total of movies she is going to watch. so three times the number of months she watched three movies consecutively to equal the total number of movies

Answer:

2(5x+4)

2×5=10

2×4=8

so answer is 2(5x+4)

Answer:

You're answer is 4/7

Step-by-step explanation:

I hope this helps!

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:

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:

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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[tex]\huge\text{$(18x+15)$ units}[/tex]

Given the area, we need to find the side length. Let's start with the area equation for a square, where [tex]s[/tex] is the side length and [tex]A[/tex] is the area.

[tex]s^2=A[/tex]

Substitute in the known value.

[tex]s^2=324x^2+540x+225[/tex]

Now we need to factor the trinomial. The trinomial given for the area is a perfect square trinomial since [tex]324[/tex] ([tex]18^2[/tex]) and [tex]225[/tex] ([tex]15^2[/tex]) are both perfect squares.

We also know that [tex]a^2+2ab+b^2=(a+b)^2[/tex], which we can use to factor.

[tex]s^2=324x^2+540x+225\\s^2=(18x)^2+2(18x)(15)+15^2\\s^2=(18x+15)^2[/tex]

Now, take the square root of both sides to fully isolate [tex]s[/tex].

[tex]\sqrt{s^2}=\sqrt{(18x+15)^2}[/tex]

Keep in mind that the square root of any value squared is the original value.

[tex]s=\boxed{18x+15}[/tex]