Determining angle side relationships What are the angle measures in trainable ABC?

Answer:

A. 1/x = 2/6

Step-by-step explanation:

Given the sides of the smaller parallelogram:

1 in and 2 in

Given the sides of the bigger parallelogram:

x in and 6 in

By Comparison of similar sides

I.e. the slant sides (1in and x in) and the base (2in and 6in) of both parallelogram.

1/x = 2/6

Hence, the scale factor proportion for the enlargement is 1/x = 2/6.

Solving further to get the value of x

Simplify both sides

1/x = ⅓

Multiply both sides by x

1/x * x = ⅓ * x

1 = ⅓x

Multiply both sides by 3

1 * 3 = ⅓x * 3

3 = x

So x = 3 in

Answer:

A. 1/x = 2/6

Step-by-step explanation:

Answer:x=12

Step-by-step explanation:

5x+9-3x=18+15

First of all, in the case of a equation that has one vatiable having one power ,you need to bring all the variable together in one side.

5x-3x=18+15-9

0r,2x=18+6

Or,2x=24

Or,x=24/2

Or,x=12

So it's the solution..

To solve the equation 5x + 9 - 3x = 18 + 15, you simplify both sides of the equation to get 2x + 9 = 33. Then, you isolate x by subtracting 9 from both sides to get 2x = 24, and further divide by 2 to get x = 12. Therefore, x = 12 is the solution.

The question requires the solution for the equation 5x + 9 - 3x = 18 + 15. To start solving this, first simplify both sides of the equation. The left side simplifies to 5x - 3x + 9, which equals 2x + 9. The right side simplifies to 18 + 15, which equals 33.

So, 2x + 9 = 33. To isolate x, subtract 9 from both sides of the equation, and you'll get 2x = 24. Then divide both sides by 2, and you'll get x = 12.

This means that the solution to the equation 5x + 9 - 3x = 18 + 15 is x = 12.

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The correct answer is 12

Set up a ratio and then solve. See paper attached. (:

Final answer:

H varies directly as L, and using the constant of direct variation from the given values (H=20 when L=50), we calculated the value of H to be 12 when L is 30.

Explanation:

The concept we are dealing with here is direct variation, which means we can set up a proportion based on the relationship that H varies directly as L. Given that H=20 when L=50, we can determine the constant of variation k by dividing H by L (H = k*L), which gives us k = 20/50 or k = 0.4. With the constant of variation, we can then find the value of H when L=30.

To do this, we use the formula for direct variation again with our constant k and the new value of L:

H = k * L = 0.4 * 30 = 12

Therefore, when L is 30, H is 12.

Answer:

1. Option C is correct

2. Option A is correct

3. Option C is correct

4. Option B is correct

5. Option D is correct

Step-by-step explanation:

1. x^2-3x-18/x+3

Factorize the numerator

x^2-6x+3x-18/x+3

x(x-6)+3(x-6)/x+3

(x+3)(x-6)/x+3

x-6

x-6 where x≠6

Option C is correct.

2. x-2/x^2+4x-12

Factorizing the denominator

x-2/x^2+6x-2x-12

x-2/x(x+6)-2(x+6)

x-2/(x-2)(x+6)

1/x+6

1/x+6 where x≠-6

Option A is correct.

3. 5x^3/7 x^3+x^4

5x^3/7x^3+x^4

5x^3/x^3(7+x)

5/7+x

Option C is correct

5/7+x where x≠-7

4. Simplify x/6x-x^2

x/6x-x^2

x/x(6-x)

1/6-x

Option B is correct

1/6-x where x≠6

5. 2/3a * 2/a^2

Multiplying both terms

4/3a^3

Option D is correct.

4/3a^3 where a≠0

For this case we must subtract the following expression:

[tex](-2x ^ 2 + 9x-3) - (7x ^ 2-4x + 2) =[/tex]

We must bear in mind that:

[tex]- * + = -\\- * - = +[/tex]

We rewrite the expression:

[tex]-2x ^ 2 + 9x-3-7x ^ 2 + 4x-2 =[/tex]

We add similar terms taking into account that equal signs are added and the same sign is placed, while different signs are subtracted and the sign of major is placed:

[tex]-2x ^ 2-7x ^ 2 + 9x + 4x-3-2 =\\-9x ^ 2 + 13x-5[/tex]

Answer:

[tex]-9x ^ 2 + 13x-5[/tex]

Answer: [tex]=-9x^2+13x-5[/tex]

Step-by-step explanation:

First, you need to remember the multiplication of signs:

[tex](+)(+)=+\\(-)(-)=+\\(-)(+)=-[/tex]

Then, to subtract the polynomials given, the first step is to distribute the negative sign:

[tex](-2x^2+9x-3)-(7x^2-4x+2)=-2x^2+9x-3-7x^2+4x-2[/tex]

And finally, you need to add the like terms.

With this procedure,  you get the following result:

[tex]=-9x^2+13x-5[/tex]

answer is 2nd equation

30x 6/100x6=180/600

Answer:

0.05 oz

Step-by-step explanation:

Usually, the greatest number that is allowed for approximation, assuming that the number itself is obtained by approximation, is the greatest possible error of it.

It is usually half the place value of the last digit of the number.

Here we are given [tex]4\frac{1}{2}[/tex] oz which is equal to [tex]4.5[/tex] oz. The last digit is 5 which is at the tenth place (0.1) so the greatest possible error for this would be its half.

[tex]\frac{0.1}{2}[/tex] = 0.05 oz

The average rate of change in f(x) over the interval [1, 5] is -1

Hi! Let me help you to understand this problem. Here we have the following function:

[tex]f(x) = 17-x[/tex]

We need to compute the Average Rate of Change (ARC) in [tex]f(x)[/tex] over the interval [tex][1, 5][/tex]. So what is the average rate of change of a function? In general, for a nonlinear graph whose slope changes at each point, the average rate of change between any two points [tex](x_{1},f(x_{1}) \ and \ (x_{2},f(x_{2})[/tex] is defined as the slope of that line through that two points. Here we have a linear function, so the average rate of change will be the slope of the line:

So:

[tex]ARC=m=-1[/tex]

This can also be calculated as:

[tex]ARC=\frac{f(x_{2})-f(x_{1})}{x_{2}-x_{1}} \\ \\ ARC=\frac{17-5-(17-1)}{5-1} \\ \\ ARC=-1[/tex]

Here is your answer in the picture

Answer:

6

Step-by-step explanation:

Divide -12/-2 to get 6.

Simplify -12\div -2−12÷−2 to 66.

Answer:

Vertical= 61.43 miles

Horizontal=43.02 miles

Step-by-step explanation:

We use the trigonometric ratios for a right angled triangle to calculate the components.

The vertical is the adjacent while the horizontal is the opposite.

The vertical is calculated as follows:

V= 75 Cos 35° =61.43 Miles

The magnitude of the horizontal H is calculated as follows:

H= 75 Sin 35° = 43.02 miles

Final answer:

Using trigonometric functions, the horizontal component of the ship's journey is found to be 61.44 miles to the east, and the vertical component is 43.02 miles to the north.

Explanation:

A ship leaving port sails for 75 miles in a direct 35° north of due east. To find the magnitude of the vertical and horizontal components, one can use trigonometric functions based on the angle provided. The horizontal (east) component can be found using the cosine function, and the vertical (north) component can be calculated using the sine function.

To calculate the horizontal (east) component: Horizontal Component = 75 miles * cos(35°) = 75 * 0.8192 = 61.44 miles.

To calculate the vertical (north) component: Vertical Component = 75 miles * sin(35°) = 75 * 0.5736 = 43.02 miles.

Therefore, the ship’s vertical component of movement is 43.02 miles to the north, and the horizontal component is 61.44 miles to the east.

Answer:

C. Distributive property

Step-by-step explanation:

The options to your question can be found in the image below.

the correct option is C. Distributive property

(to clear the parenthesis)

(–2) + 5(x – 3) – 4x(6 + 1)

= -2 + 5x -15 -24x -4x

= -17 +5x -28x

= -23x -17

Answer:

4

Step-by-step explanation:

-3.5/-0.875 = 4

Answer:

The answer is 4 or C

Step-by-step explanation:

Since its a negative-negative equation, the result is a positive number. So take this equation as 3.5/0.875. Your result will be four or C. Hope this helps!

Your question asks to find what was the size of the population in 2017

In order to solve this problem, we're going to need to use the given information in the question in order to find the population in 2017.

Key information:

In 2010, population was 6500

In 2014, population increased by 10% from 2010

In 2017, population decreased by 6% from 2014.

With the information above, we can solve the problem.

We're going to start with 6500 as our starting population.

We know that the population increased by 10% in 2014, so we would multiply 6500 by 1.10.

[tex]6500*1.10=7,150[/tex]

The population in 2014 was 7,150.

We know that in 2017, the population decreased by 6% from the population in 2014. So we would find how much 6% is from 7,150 and then subtract that number.

[tex]7,150*.06=429\\\\7,150-429=6,721[/tex]

When you're done solving, you sohuld get 6,721.

The population in 2017 would be 6,721.

Answer:

6721

Step-by-step explanation:

the answer is 6721

Answer:

x=0

Step-by-step explanation:

7x - 42x = 0

Combine like terms

-35x = 0

Divide each side by -35

-35x/-35 = 0/-35

x = 0

Answer:

X=6

X=0

Step-by-step explanation:

On aP Ex

Answer:

x = 10

Step-by-step explanation:

The axis of symmetry is the vertical line that passes through the vertex.  We can readily see that the x-coordinate of the vertex is 10.

Therefore, the axis of symmetry here is x = 10.

We must find the slope of the graph first, we can do this by finding two perfect points and inputting those points into the formula y2 - y1/x2 - x1

Perfect point #1: (0,1)

Perfect point #2: (2,5)

As mentioned above, input these numbers into our formula.

5-1 = 4

2 - 0 = 2

4/2 = 2

So, the slope of the graph is 2.

Now, we must find the y-intercept which can be found based on where the line intersects with the y-axis. As we can see, the line intersects at (0,1) therefore the y-intercept of the graph is 1.

We now form a linear equation:

y = 2x + 1

However, since this is linear equality graph we will replace the equal sign with an inequality symbol. The inequality symbol we can use is based on the direction of the shaded area. If shaded up, we use the "greater than symbol", if down then we use the "less than symbol".

The line also matters, if the line is dotted we use the normal inequality symbol, but if it is straight then we use one of the "equal to" inequality symbols.

As for our graph, we have a dotted line with the shaded area upwards. Therefore, we will be using the greater than symbol and not a "equal to" symbol.

So, our answer would be y > 2x + 1

Answer:

336 ft^2

Step-by-step explanation:

We are given the dimensions of a rectangle, length 24 feet and width 14 feet, and we are to find the area of this rectangle.

We know that the formula of area of rectangle is given by:

Area of a rectangle = l × w

Substituting the given values in the above formula to get:

Area of rectangle = 24 × 14 = 336 ft^2

Answer:

Area = 336 ft^2

Step-by-step explanation:

Given

Width of rectangle = w = 14 ft

Length of rectangle = l = 24 feet

The formula for finding the area of rectangle is:

Area = Length * width

It can also be denoted as:

A = l*w

Putting the given values of length and width, the area of given rectangle will be:

A = 24 ft * 14 ft

A = 336 ft^2

So, the area of given rectangle is 336 ft^2 ..

Answer:

for value 36

c makes the perfect square

x2 - 12x +36

= x2 - 2*6x +6^2

= (x-6)^2 #

Answer:  The required value of c is 36.

Step-by-step explanation:  We are given to find the value of c so that the following expression becomes a perfect square trinomial :

[tex]E=x^2-12x+c~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]

To find the value of c, we proceed as follows :

[tex]E\\\\=x^2-12x+c\\\\=(x^2-2\times x\times6+6^2)+c-6^2\\\\=(x-6)^2+c-36.[/tex]

So, for E to be a perfect square trinomial, we must have

[tex]c-36=0\\\\\Righatrrow c=36.[/tex]

Thus, the required value of c is 36.

Answer: c. getting heads on a coin toss and rolling a 5 on a die

Step-by-step explanation:

Answer:

Part 1) [tex]24,000(0.908)^{5}> 15,000[/tex]

Part 2) No

Step-by-step explanation:

step 1

Let

x ----> the time in years

y ----> the area of the forests is square miles

we know that

The equation that represent this situation is a exponential function of the form

[tex]y=a(b)^{x}[/tex]

where

a is the initial value

b is the base

we have

[tex]a=24,000\ mi^{2}[/tex]

[tex]b=100\%-9.2\%=90.8\%=90.8/100=0.908[/tex]

substitute

[tex]y=24,000(0.908)^{x}[/tex]

The inequality that represent the situation is

[tex]24,000(0.908)^{x}> 15,000[/tex]

step 2

Verify if the state will be  able to keep their funding from the nonprofit wildlife organization in 5 years

For x=5 years

[tex]24,000(0.908)^{5}> 15,000[/tex]

[tex]14,813> 15,000[/tex] ----> is not true

therefore

The state will be not able to keep their funding from the nonprofit wildlife organization in 5 years

Answer:

24,000(0.908) > 15,000; no

Step-by-step explanation:

Answer:

See below in bold.

Step-by-step explanation:

The 40 is the adjacent side of the triangle that can be drawn and the 9 is the opposite side.

The hypotenuse =  sqrt (40^2 + 9^2) = 41.

sine = opp/hyp = 9/41 = 0.2195.

cosine = 40/41 = 0.9756.

tangent = 9/40 =0.2250.

cosec = 1/ sine =  41/9 = 4.5556.

secant = 1  / cosine = 41/40 = 1.0250.

cotangent = 1 / tangent =  40/9 = 4.4444.

The decimal forms are  correct to the nearest ten thousandth.

The values of the six trigonometric functions are:

sin θ = 9/41, cos θ = 40/41, tan θ = 9/40, cot θ = 40/9, sec θ = 41/40, cosec θ = 41/9.

The values of all trigonometric functions dependent on the value of the ratio of sides of a right-angled triangle are known as trigonometric ratios. The trigonometric ratios of a right-angled triangle's sides with regard to any of its acute angles are known as that angle's trigonometric ratios.

The three sides of the right-angled triangle are:

Hypotenuse (the longest side)

Perpendicular (opposite side to the angle)

Base (Adjacent side to the angle)

The six trigonometric ratios are sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec), and secant (sec).

The trigonometry ratios for a specific angle ‘θ’ is given below:

Trigonometric Ratios:

Sin θ =  Perpendicular/Hypotenuse

Cos θ = Base/Hypotenuse

Tan θ = Perpendicular/Base or Sin θ/Cos θ

Cot θ = Base/Perpendicular or 1/tan θ

Sec θ = Hypotenuse/Base or 1/cos θ

Cosec θ = Hypotenuse/Perpendicular or 1/sin θ

According to the Pythagoras theorem, we can say that in a right-angled triangle:

Hypotenuese² = Base² + Perpendicular²

We have to find the six trigonometric functions of an angle in standard position if the point with coordinates (40, 9) lies on its terminal side.

With the angle being θ, we have drawn a figure of the case. (attached)

In the right-angled triangle AOB, with respect to angle θ,

Hypotenuse: AO, Perpendicular: AB, and Base: BO

First we derive the value of AO, using the Pythagoras theorem,

AO² = AB² + BO² = 9² + 40² = 81 + 1600 = 1681 = 41²

∴ AO = 41 units.

Now we find the value of the six trigonometric functions, with respect to the angle θ.

sin θ = Perpendicular/Hypotenuse = AB/AO = 9/41

cos θ = Base/Hypotenuse = BO/AO = 40/41

tan θ = sin θ/cos θ = (9/41)/(40/41) = 9/40

cot θ = 1/tan θ = 1/(9/40) = 40/9

sec θ = 1/cos θ = 1/(40/41) = 41/40

cosec θ = 1/sin θ = 1/(9/40) = 40/9.

∴ The values of the six trigonometric functions are:

sin θ = 9/41, cos θ = 40/41, tan θ = 9/40, cot θ = 40/9, sec θ = 41/40, cosec θ = 41/9.

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Answer:

V= 32340cm^3

A= 5082cm^2

Step-by-step explanation:

Solution is in the picture. The area of the base of cone is not counted

The formulas for volume and surface area largely depend on the type of solid. For a cylinder, the volume is computed by πR²h and the surface area is 2πr(h + r) where Pi (π) is 22/7. Apply these formulas using consistent units such as meters.

To compute the volume of a particular solid shape, you would first need to know the specific formula that applies to that shape. For example, the volume of a cylinder can be calculated using πR²h (where R is the radius, and h is the height), and the calculation would use the value 22/7 for Pi (π). The volume of a pillar segment where the cross-sectional area A is given and height h is known could be calculated by multiplying A by h.

Surface area calculations would also depend on the specific shape. The surface area of a cylinder, for example, is 2πr(h + r), with r as radius, h as height, and Pi as 22/7.

Without knowledge of the specific type of solid in question, more detailed steps cannot be provided. However, once the shape is identified, application of the right formulas with consistent units (such as meters) will yield both the volume and surface area of the solid.

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The formula for surface area of a sphere is: A = 4 x PI x r^2

Replace r with the given radius and calculate the area:

Area = 4 x PI x 100^2

Area = 4 x PI x 10,000

Area = 40,000PI

Answer:

[tex]x=n \pi[/tex] or [tex]x=2\pi n+\frac{\pi}{2}[/tex]

Step-by-step explanation:

The given trigonometric equation is;

[tex]\sin x(\sin x-1)=0[/tex]

By the zero product property;

[tex]\sin x=0[/tex] or [tex]\sin x-1=0[/tex]

For [tex]\sin x=0[/tex], the general solution is [tex]x=n \pi[/tex]

[tex]\sin x-1=0[/tex], [tex]\sin x=1[/tex], the general solution is [tex]x=2\pi n+\frac{\pi}{2}[/tex]

Therefore the general solution is:

[tex]x=n \pi[/tex] or [tex]x=2\pi n+\frac{\pi}{2}[/tex]

The solutions to the equation sin(x)(sin(x)-1) = 0 are:

x = 0, π, 2π, 3π, π/2, 3π/2, 5π/2, and so on.

We have,

To solve the equation sin(x)(sin(x)-1) = 0, we can apply the zero-product property, which states that if a product of factors is equal to zero, then at least one of the factors must be equal to zero.

So, we set each factor equal to zero and solve for x:

sin(x) = 0

To find the solutions for this equation, we look for x values where the sine function equals zero.

The solutions are x = 0, π, 2π, 3π, and so on.

sin(x) - 1 = 0

Adding 1 to both sides:

sin(x) = 1

The solutions for this equation occur when the sine function equals 1, which happens at x = π/2, 3π/2, 5π/2, and so on.

Therefore,

The solutions to the equation sin(x)(sin(x)-1) = 0 are:

x = 0, π, 2π, 3π, π/2, 3π/2, 5π/2, and so on.

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Answer:

y = -x - 2.

Step-by-step explanation:

The function rule that describes the patter in the table is: y = -x - 2.

To prove that, we're going to test each given point:

For x= -2 ⇒  y = -(-2) - 2 = 0  ✅

For x = -1 ⇒ y = -(-1) - 2 = -1 ✅

For x = 0 ⇒ y = -(0) - 2 = -2 ✅

For x = 1 ⇒ y = -(1) - 2 = -3 ✅

For x = 2 ⇒ y = -(2) - 2 = -4 ✅

Then, we have just proved that the function rule that describes the patter in table is y = -x - 2

Answer:

D=[tex]\sqrt{(147-30\sqrt{10}}[/tex]

Step-by-step explanation:

Here we are required to find the distance between two coordinates. We will use the distance formula to find the distance

The distance formula is given as

[tex]D=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

Here we are given two coordinates as

[tex](6,5\sqrt{5} ) , (4,3\sqrt{2} )[/tex]

Substituting these values in the Distance formula given above we get

[tex]D=\sqrt{(6-4)^2+(5\sqrt{5} -3\sqrt{2}) ^2}[/tex]

[tex]D=\sqrt{(2)^2+(5\sqrt{5})^2+(3\sqrt{2})^2-2*5\sqrt{5}*3\sqrt{2}}\\[/tex]

[tex]D=\sqrt{4+125+18-2*15\sqrt{10}}\\D=\sqrt{147-30\sqrt{10}}\\[/tex]

Hence this is our answer

answer :

2 square of 3 is the answer

step-by-step explanation :

[tex]\sqrt({x} _{2} - x_{1})^{2} + (y_{2} - y_{1})^{2} \\\\\sqrt({4} - 6})^{2} + (3\sqrt{2} - 5\sqrt{2} )^{2} \\\\= \sqrt(-2})^{2} + (-2\sqrt{2} )^{2} \\\\\\= \sqrt4 + 8 \\\\\\\\\\= \sqrt12 \\\\\\\\= 2\sqrt{3}[/tex]

Answer:

It is b.

Step-by-step explanation:

When x is negative x^5 will also be negative.

f(x) = x^5 - 3x^3 + 2x + 4

As x  --> -∞ x^5 will  be the main factor for f(x) --->  -∞ .

Similarly  x^5 will have the greatest influence when x ---> ∞, so f(x) ---> ∞.

Answer:

b

Step-by-step explanation:

The end behaviour is what happens when x gets larger and positive ( right hand end ) or larger and negative ( left hand end ) Tis is called the end behaviour as x → + ∞ and x → - ∞ respectively

For a polynomial the end behaviour is determined by the term of greatest degree.

For the given function

f(x) = [tex]x^{5}[/tex] - 3x³ + 2x + 4 ← degree 5 polynomial

The leading coefficient is positive

• Odd degree, positive leading coefficient, then

as x → - ∞, f(x) → - ∞

as x → + ∞, f(x) → + ∞

----------------------------------------------------------------------

• Odd degree, negative leading coefficient, then

as x → - ∞, f(x) → f(x) → + ∞

as x → + ∞, f(x) → - ∞

Answer:

2,085

Step-by-step explanation:

multiply 3 by 600 then 90 then 5 and then u add them all and u get ur answer