The area of this figure 20 in. is square inches. 28 in. 30 in. 7 in. 25 in.

Explanation

The first step is to draw a representation of the given parameters.

Since this is a right-angle triangle, the Pythagorean theorem applies. This can be seen below;

We can then apply it to the sides of the triangle.

DF is the longest side. Therefore,

Answer

It is said that the dressmaker bought 5 yards of cotton and silk. Let's see the first equation of the system:

And that he spent $46 on those 5 yards. Also, it is said that silk costs $17 per yard and cotton $4 per yard. Let's see the second equation of the system:

If 46 is how much the dressmaker spent, and 17 and 4 represent how much silk and cotton cost PER YARD then we know that x and y represent how much of each fabric did the dressmaker bought. Also, in the first equation you see that the total is 5 yards. So, if you solve this system you will find that 'x' is how many yards of silk the dressmaker bought and 'y' is how many yards of cotton he bought.

In summary, the solution of this system represents how may yards of silk (x) and cotton (y) the dressmaker bought.

The simplified expression is as follows:

[tex]\frac{\frac{3x^{6} }{14y^{9} } }{\frac{33x^{4} }{10y^{2} } } = \frac{5x^{2} }{77y^{7} }[/tex]

The expression can be simplified as follows:

To simplify an expression means to write an equivalent expression which contains no similar terms.

This means that we will rewrite the expression with the fewest terms possible.

Therefore,

[tex]\frac{\frac{3x^{6} }{14y^{9} } }{\frac{33x^{4} }{10y^{2} } }[/tex]

The expression can be represented as follows:

3x⁶ / 14y⁹ ÷ 33x⁴ / 10y²

3x⁶ / 14y⁹ × 10y² / 33x⁴

Hence,

3x⁶ / 14y⁹ × 10y² / 33x⁴  = 30x⁶y² / 462x⁴y⁹

Therefore,

30x⁶y² / 462x⁴y⁹ = 10x² / 154y⁷ = 5x² / 77y⁷

Hence,

[tex]\frac{\frac{3x^{6} }{14y^{9} } }{\frac{33x^{4} }{10y^{2} } } = \frac{5x^{2} }{77y^{7} }[/tex]

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Given

-y+9x=0

Find

check if equation model direct variation

Explanation

Equations with direct variation has a general form of y=kx

Given Equation

-y+9x=0

y=9x

whick is in the form of y=kx

Hence this equation is in direct variation with k=9

Final Answer

This equation is in direct variation with k=9

Unknown, the correct equation is:

- 4,863 + 81.1m = - 3,645 + 76.9m

And to solve for m, you use the standard form:

Like terms:

81.1m - 76.9m = -3,645 + 4,863

4.2m = 1,218

Answer:Nuts

Step-by-step explanation:

green on green

In the given triangle :

FD = 25, FE = 7, DE = 24

SinD

From the trignometric ratio of sin: It express as the ratio of measurement of the side opposite to the angle to the measurement of hypotenuse of triangle DEF,

So, the SinD is express as :

sin D = 7/25

cos F

From the trignometric ratio of cos : It expresses as the ratio of measurement of the side adjacent to the angle and to the hypotenuse of the triangle

So, the Cos F is express as :

cos F = 7/25

Sin F

From the trignometric ratio of sin: It express as the ratio of measurement of the side opposite to the angle to the measurement of hypotenuse of triangle DEF,

so, Sin F is express as :

sin F = 24/25

Answer :

sin D = 7/25

cos F = 7/25

sin F = 24/25

The temperature of the object is -456.97 degrees

From the details provided, we know that the population of the town gets smaller, that is, a decline and not a growth. The annual rate of decline (or decay) is 6% (or 0.06). The formula for this is given as shown below;

The variables here are;

The equation to represent the decline of this town's student population shall be;

When the population ofnthe town becomes 100, then we can replace variable y with 100. Since the formula is used to find the current population, and we have been given the population after a certain number of years, then our y is now 100.

We can now determine the number of years (variable n) that it takes before the population declines to 100 as shown below;

then our y is now 100.

We can now

In general, a quadratic equation can be written in terms of its solutions:

Now, notice that:

when x= -1/2, and it is equivalent to:

Therefore, you can write the quadratic equation as:

Computing the above multiplication, you get:

Simplifying the above equation you get:

We have to find the midpoint coordinates (D) of segment AB.

We can calculate the coordinates of the midpoint as:

Answer: D = (-4x, 0)

Solution

- The solution steps are given below:

Final Answer

111 ft

Given 25 pieces of repertoire, if a pianist plans to play 4 pieces at a recital and is considering playing which song to play first, second, etc, the possible ways is,

Hence, the different recital programs possible is 303600

Explanation

A trinagular prism has two bass and theree side surfaces.

Therefore, the suface area pf the prism is

Answer: Option C

The values of s in the interval [0, 2π) such that tan s = -(√3)/3 are 5π/6 and 11π/6.

What is trigonometry and how is it assessed?
Simply put, trigonometric functions—also referred to as circular functions: are the functions of a triangle's angle. This means that these trig functions provide the relationship between the angles and sides of a triangle. Sine, cosine, tangent, cotangent, secant, and cosecant are the fundamental trigonometric functions. Numerous trigonometric identities and formulas indicate the relationship between the functions and aid in determining the triangle's angles.
The quadrants determine the values of the trigonometric functions.


Given, tan s = -(√3)/3 ⇒ tan s = -(√3)/(√3)² ⇒ tan s = (-1)/(√3)
Therefore, the simplified value of tangent of s is tan s = (-1)/(√3)
Again the interval of the function is [0, 2π), so only the second and fourth quadrants can contain the given value of tangent being negative.
For the value of s in second quadrant, we have:
tan s = (-1)/(√3) ⇒ tan s = tan (π - (π/6)) ⇒ tan s = tan (5π/6) ⇒ s = 5π/6
For the value of s in the fourth quadrant, we have:
tan s = (-1)/(√3) ⇒ tan s = tan (2π - (π/6)) ⇒ tan s = tan (11π/6) ⇒ s = 11π/6
Thus, the values of s in the interval [0, 2π) such that tan s = -(√3)/3 are 5π/6 and 11π/6.

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Answer:

2

Step-by-step explanation:

Given:

Solve :

The function g(x) convert then x is equal to h(x) then:

B: The data collection method used was nonrandom since the athletes using Fastex shoes may have trained better.

This is false because they followed the same nutrition plan and training program during the study.

C. The data collection method used was unfair since the athletes given Fastex shoes may have been better runners than the athletes given SportsPlus shoes.

This is also false because members of both groups were pretested and determined to have equal athletic ability

D. Each group used one shoe design.

So, the correct option is A

The equation of the word is,

The distance on the x-coordinate from N to M is:

distance = 2 - (-3) = 2 + 3 = 5

Because 2 is the x-coordinate of M and -3 is the x-coordinate of N

Then, 1/4 of the distance is:

1/4*distance = (1/4)*5 = 5/4 = 1.25

So, the x-coordinate of R is:

(x-coordinate of N) + (1/4*distance) = -3 + 1.25 = -7/4 = -1.75

At the same way, the distance on the y-coordinae from N to M is:

distance = 3 - (-3) = 3 + 3 = 6

Then, 1/4 of the distance is:

1/4*distance = (1/4)*6 = 6/4 = 1.5

So, the y-coordinate of R is:

(y-coordinate of N) + (1/4*distance) = -3 + 1.5 = -1.5

Answer: R(x, y) = (-1.75, -1.5)

We have to solve this inequality:

We now use the properties of the absolute value. We will have two boundaries: one corresponding to when 4x+5 is negative and the other is when 4x+5 is positive.

When 4x+5 is negative, the absolute value function will change the sign of the expression, so we will have:

The other interval will be defined when 4x+5 is positive. In this case, the absolute function does not change the sign and we get:

Then, the solution set is the union of the intervals x < -3.25 and x > 0.75.

We can express the interval as (-∞, -3.25) ∪ (0.75, ∞).

Answer: (-∞, -3.25) ∪ (0.75, ∞)

The quadrants on the coordinate plane are the following:

then, we have that the upper left quadrant is quadrant II

The value of the function f(x) at x = 0 is found as -1.

For the given question,

The graph of the function f(x) = -x² + 4x - 1 is given.

For finding the value of f(x) at x = 0, check the y-coordinate of the graph when x = 0.

Put x = 0 in the given function.

f(0) = -0² + 40 - 1

f(0) = - 1

Thus, the value of the function f(x) at x = 0 is found as -1.

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EXPLANATION

Since 150% represents a percentage bigger than 156, the appropiate relationship would be as follows:

Where the whole number is 156 and the percentage is 150%:

In conclusion, the solution is 234

Hello there. To solve this question, we'll have to remember some properties about triangles.

Given the triangle:

Notice in this case we have two consecutive angles and a side between them. This is a case of ASA (angle-side-angle).

With respect to the side with measure x, we have two consecutive angles then the side, hence AAS.

To find x, we'll have to apply the law of sines:

In this case, the angle opposite to x measures 73º and the angle opposite to 4 measures 85º, hence:

Multiply both sides by a factor of sin(73º)

Using a calculator, we get the following approximation (rounding to the nearest tenth):

This is the measure of x we're looking for.

Answer:

f(x) = 1(x - 4.5)² - 6.25

Step-by-step explanation:

Hello!

Let's find the Vertex Form of the quadratic by Completing the Square.

The formula for a Perfect Square Trinomial is (a+b)² = a² + 2ab + b².

To find b², we need to divide -9 by 2 and square it.

Add this number to both sides and factor. Remember, the b term here is simply half of the b term in the equation (-4.5).

Convert this back to function form:

The equation is f(x) = 1(x - 4.5)² - 6.25.

Simplify the numerical expression

From the given circle, the measure of the arc or the central angle indicated is as shown at the center of the circle is subtended by the arc

Hence, the measure of the arc or central angle indicated is 65° ,Option B

Car B was 5 miles east of car A, Option A

We know that an inch is equivalent to 2.54 centimeters, then if we want to know how many inches are in a centimeters we do this:

In this case, we have 20 centimeters, then replacing a by 20 we find the equivalent inches to 20 like this: