“use the converse of Pythagorean Theorem to tell whether the triangle is right, acute, or obtuse”

Answer:

200 children.

180 adults.

Step-by-step explanation:

let x=Children and y=Adults

create 2 equations.

x+y = 380

2.50x+5.80y = 1544

solve for x in the first equation and plug into the second equation.

x = 380-y

2.50(380-y) +5.80y = 1544

distribute and simplify.

950 + 3.3y = 1544

simplify

3.3y = 594

y = 180

plug y back into first equation and you get that there were 200 children.

The value of r is 6+ 2[tex]\sqrt{14}[/tex]

Algebraic equation in x that has a second degree. The quadratic equation in its conventional form is Ax2 + bx + c = 0 where a and b are the coefficients, x is the variable, and c is the constant term. To qualify as a quadratic equation, an equation must contain a non-zero term (a 0) for the coefficient of x2. In order to create a quadratic equation in standard form, the x2 term, the x term, and the constant term must be written first, second, and third, respectively. As opposed to fractions or decimals, integral values are typically used to express the numerical values of letters a, b, and c.

[tex]r^{2}-12r=51-31\\ r^{2}-12r-20=0\\ \frac{b^{2} }{4a} \\ =[/tex]

=36

= do ±36 in equation

=[tex]r^{2}-12r +36 -36 = 20\\ (r-6)^{2}=56[/tex]

=(r-6) = ±[tex]\sqrt{56}[/tex]

r = 6 ±[tex]\sqrt{56}[/tex]

r= 6+ 2[tex]\sqrt{14}[/tex]

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The distance between the point (-1,0) and (7,6) is 10.

Distance between the points:

Distance between two points is the length of the line segment that connects the two points in a plane.

The formula to find the distance between the two points is usually given by

d=√((x2 – x1)² + (y2 – y1)²).

Given,

(−1,0) and (7,6).

Here we need to find the distance between these points.

Apply the values on the formula , in order to solve it,

d = √(7 - (-1))² + (6 - 0)²

When we simplify it, then we get,

d = √(7 + 1)² + (6)²

d = √(8)² + 36

d = √64 + 36

d = √100

d = 10

Therefore, the distance is 10.

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[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]

[tex]\qquad\displaystyle \tt \rightarrow \: {y= -1/6(x⁴ +2x³-7x²-8x+ 12 } [/tex]

____________________________________

[tex] \large \tt Solution \: : [/tex]

The values of x for which curves cuts/touches the x - axis are the roots of that particular polynomial.

And that polynomial can be depicted in form :

[tex]\qquad \tt \rightarrow \: a(x - h1) (x - h2) (x - h3)........ (x - hn) = 0[/tex]

[ where, h1, h2, h3... hn represents roots of that polynomial, and " a " is the stretch of curve]

And by that, we can sort out the roots of given polynomial that are :

Since there are four roots, the least degree polynomial formed will have bi - quadratic polynomial.

And it will be represented as :

[tex]\qquad \tt \rightarrow \: y=a(x - ( - 3)) (x - ( - 2))(x - 1)(x - 2) [/tex]

[tex]\qquad \tt \rightarrow \:y=a (x + 3)(x + 2)(x - 2)(x - 1) [/tex]

And it can be further solved to get ~

[tex]\qquad \tt \rightarrow \: y=a(x + 3)( {x}^{2} - 4)(x - 1)[/tex]

[tex]\qquad \tt \rightarrow \:y= a( {x}^{2} - 4)( {x}^{2} + 2x - 3)[/tex]

[tex]\qquad \tt \rightarrow \: y=a( {x}^{4} + 2 {x}^{3} - 3 {x}^{2} - 4 {x }^{2} - 8x + 12)[/tex]

[tex]\qquad \tt \rightarrow \: y=a({x}^{4} + 2 {x}^{3} - 7{x }^{2} - 8x + 12)[/tex]

Now, it's time to evaluate the value of a, for that we can just use a point that satifys the curve ( i.e (0 , -2)

plug in the values :

[tex]\qquad\displaystyle \tt \rightarrow \: {-2= a(0⁴ +2(0)³-7(0)²-8(0) + 12 } [/tex]

[tex]\qquad\displaystyle \tt \rightarrow \: {-2= a(0 +0-0-0 + 12 } [/tex]

[tex]\qquad\displaystyle \tt \rightarrow \: {-2= a( 12 )} [/tex]

[tex]\qquad\displaystyle \tt \rightarrow \: {a= -2 ÷ 12 } [/tex]

[tex]\qquad\displaystyle \tt \rightarrow \: {a= -1/6} [/tex]

Therefore, the required equation is :

[tex]\qquad\displaystyle \tt \rightarrow \: {y= -1/6(x⁴ +2x³-7x²-8x+ 12 } [/tex]

Answered by : ❝ AǫᴜᴀWɪᴢ ❞

Answer:

VD; DV

Step-by-step explanation:

you can name the line in two ways

VD or DV

they are the two endpoints of the line

they are the same line

Answer: 3x^2−3x

Step-by-step explanation:

1.) Distribution

2.) Combine like Terms

3.) Combine like Terms.. again

4.) Common Factor

5.) GET UR SOLUTION!!

hello

to solve this problem, we need the formula of length of an arc

t find the value of angle JM, we should take into cognizance that the sum of angles in a circle is equal to 360 degree and angle on a straight line is equal to 180 degree

now we know the value of angle jm, let's find the length of the radius

with all the necessary informations or data required, we can now proceed to solve for the length of arc jm

from the calculations above, the length of the arc is equals to 12.87 miles

Answer:

12.9

Step-by-step explanation:

Jim can make interest-only payments until after 1 year and 6 months.

The interest-only payment enables students to avoid interest capitalization during their school years and during the next six months after graduation.

The six-month period is called the grace period.

Non-capitalization of interest lowers the monthly repayments when payments become due after the grace period.

Amount of student loan = $15,200

Interest rate = 4.29%

Loan period = 10 years

Interest-only period = 1 year and 6 months

Amount of interest per month = $54.34 ($15,200 x 4.29% x 1/12)

Total interest during the interest-only period = $978.12 ($54.34 x 18)

Thus, the interest-only payments last for 18 months.

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Answer:

Step-by-step explanation:

−2x−y−2z−4x−2y+3z

Combine −2x and −4x to get −6x.

−6x−y−2z−2y+3z

Combine −y and −2y to get −3y.

−6x−3y−2z+3z

Combine −2z and 3z to get z.

−6x−3y+z

DIFFERENTIATE W.R.T. X

−6

The equations of the lines that are perpendicular are y = 3x  and y = - 1 / 3 x - 2

The equation of a line can be represented as follows:

y = mx + b

where

Parallel line have the same slopes.

The products of the slopes of an equation of lines must be equals to negative one for it to be perpendicular.

Therefore,

m₁ m₂ = -1

The equation are as follows:

y = 3x

y = 4

y = - 1 / 3 x - 2

Hence, using m₁ m₂ = -1

3 × - 1 / 3 = -1

Therefore, y = 3x  and y = - 1 / 3 x - 2 are perpendicular.

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Answer:

percentage = 528/ 3,300*100= 16%

Step-by-step explanation:From the pie chart we can see that saving are 528 dollars, so

now we need to calculate total from the given pie chart, which is

3,300 dollars. So percentage is savings( 528 dollars) divided by total( 3,300 dollars) and then finally multiply by 100

Value of x is 16/91

How to Find value of x  ?

In question

(8/7)/(13/9) = x / (2/9)

72/91 =x/(2/9)

182* (72/91) = 182* (x/(2/9))

2 *72 = 819 * x

144 = 819 * x

(144/819) = 819 *x / 819

X = 16/91

The value of x is 16/91

Definition of Fraction :

There are in total six types of fractions such as:

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Answer: B

Step-by-step explanation:

Answer:

B. 81 / 100

Step-by-step explanation:

9 / 11 = 0.82

81 / 100 = 0.81

8 / 9 = 0.89

80 / 99 = 0.80

Hope this helps! :)

Answer:

x = 3

Step-by-step explanation:

x + .12x = 3.36  Combine like terms

1.12x = 3.36  Divide both sides of the equation by 1.12

x = 3

=======================================

Work Shown:

12% = 12/100 = 0.12

x + 12% of x = x + 0.12x = 1.12x = 3.36

1.12x = 3.36

x = 3.36/1.12

x = 3

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

Check:

12% of 3 = 0.12*3 = 0.36

x + 12% of x = 3 + 12% of 3 = 3 + 0.36 = 3.36

Or you could say 1.12x = 1.12*3 = 3.36

The answer is confirmed.

Answer:

70 ft

Step-by-step explanation:

To find the height of the building, we can use the trigonometric relationship between the angle of elevation, the distance from the object, and the height of the object.

In this case, we have a right triangle formed by the observer, the top of the building, and the base of the building. Therefore, we can use the tangent trigonometric ratio, since the height of the building is the opposite the angle of elevation, and the distance between the observer and the building is the side adjacent the angle.

[tex]\boxed{\begin{minipage}{7 cm}\underline{Tangent trigonometric ratio} \\\\$\sf \tan(\theta)=\dfrac{O}{A}$\\\\where:\\ \phantom{ww}$\bullet$ $\theta$ is the angle. \\ \phantom{ww}$\bullet$ $\sf O$ is the side opposite the angle. \\\phantom{ww}$\bullet$ $\sf A$ is the side adjacent the angle.\\\end{minipage}}[/tex]

Let "x" be the height of the building.

Let "d" be the initial distance from the observer to the building.

The angle of elevation changes from 15° to 30° as the observer advances 140 feet toward the building.

(See the attachment for a visual representation).

Based on this information, we can set up the following equations:

[tex]\tan 15^{\circ}=\dfrac{x}{d}[/tex]

[tex]\tan 30^{\circ}=\dfrac{x}{d-140}[/tex]

Rearrange both equations to isolate d:

[tex]d=\dfrac{x}{\tan 15^{\circ}}[/tex]

[tex]d=\dfrac{x}{\tan 30^{\circ}}+140[/tex]

Solve this system of equations by the method of substitution.

[tex]\dfrac{x}{\tan 15^{\circ}}=\dfrac{x}{\tan 30^{\circ}}+140[/tex]

[tex]\dfrac{x}{\tan 15^{\circ}}-\dfrac{x}{\tan 30^{\circ}}=140[/tex]

[tex]\dfrac{x\tan 30^{\circ}-x \tan 15^{\circ}}{\tan 30^{\circ}\tan 15^{\circ}}=140[/tex]

[tex]\dfrac{x(\tan 30^{\circ}- \tan 15^{\circ})}{\tan 30^{\circ}\tan 15^{\circ}}=140[/tex]

[tex]x=\dfrac{140\tan 30^{\circ}\tan 15^{\circ}}{\tan 30^{\circ}- \tan 15^{\circ}}[/tex]

[tex]x=\dfrac{140\cdot \frac{\sqrt{3}}{3}(2-\sqrt{3})}{\frac{\sqrt{3}}{3}- (2-\sqrt{3})}[/tex]

[tex]x=\dfrac{\dfrac{140(2\sqrt{3}-3)}{3}}{\dfrac{4\sqrt{3}-6}{3}}[/tex]

[tex]x=\dfrac{140(2\sqrt{3}-3)}{2(2\sqrt{3}-3)}[/tex]

[tex]x=\dfrac{140}{2}[/tex]

[tex]x=70[/tex]

Therefore, the height of the building is exactly 70 feet.

Parametric equation of the give cartesian equation x(y) = 3log(y)+y is

x(t) =3log(t)+t

y(t) = t

The given cartesian equation x(y) = 3log(y)+y

The cartesian equation is an equation of the curve in which variables are the Cartesian coordinates of a point on the curve or surface.

Here we have to convert the cartesian equation into parametric equation.

We can converting the cartesian equation into parametric equation by changing the independent variable in the cartesian equation to t.

The cartesian equation x(y) = 3log(y)+y

Here x is expressed as the function of y.

Define y = t

x(t) = 3log(t)+t

y(t) = t

Hence, the Parametric equation of the give cartesian equation x(y) = 3log(y)+y is

x(t) =3log(t)+t

y(t) = t

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I am going to draw a picture to ilustrate the solution

Now, we are going to use the trigonometric functions for the right triangle on the left to calculate h

Now we use the formula for the area of a triangle

SOLUTION

Given the question in the image, the following are the solution steps to answer the question.

STEP 1: Write out the given data for Team A

STEP 2: Find the mean

Hence, the mean of the data for production team A is 37375

When the graph of a relationship shows a line that passes through the origin, then it is proportional.

If a connection's graph is a line that runs through its origin, it is proportional. If there isn't a line or ray that does this, the ratio isn't proportional. The equation for the proportionality constant is K = y/x.The equation that describes the slope of a straight line in relation to its origin is identical to this one.

When the graph of a proportional connection passes through the origin, any ratio in the proportional relationship can be found.

A relationship is proportional if its graph is a line or ray that passes through the origin. It is not proportional if the line or ray does not go through the origin.

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Answer:

When data points are marked on the chart, all data points within a single dependent variable are connected with a line, making it very useful tool for analyzing changes over time for one or more variables.

Step-by-step explanation:

96622 is the total number of employees in the company.

Let x be the total number of employees in the company

we are given that, 28600 employees comprise 29.6% of the company's total employees

Thus,

x * 29.6% = 28600

x * 296/1000 = 28600

x * 296 = 28600 * 1000

x * 296 =28600000

x = 28600000/296

thus x = 96622 employees (approx)

What do you mean by "Percentage"?

"A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100."  Hence the percentage refers to parts per hundred.

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Answer:  [tex](r,\theta) = \left(\sqrt{6}, \frac{\pi}{4}\right)[/tex]

In other words, [tex]r = \sqrt{6} \ \text{ and } \ \theta = \frac{\pi}{4}[/tex] where theta is in radians.

=====================================================

Work Shown:

[tex](\text{x},\text{y}) = (\sqrt{3},\sqrt{3})\\\\r = \sqrt{\text{x}^2+\text{y}^2}\\\\r = \sqrt{(\sqrt{3})^2+(\sqrt{3})^2}\\\\r = \sqrt{3+3}\\\\r = \sqrt{6}\\\\[/tex]

and,

[tex]\theta = \tan^{-1}\left(\frac{\text{y}}{\text{x}}\right)\\\\\theta = \tan^{-1}\left(\frac{\sqrt{3}}{\sqrt{3}}\right)\\\\\theta = \tan^{-1}\left(1\right)\\\\\theta = \frac{\pi}{4} \text{ radians}\\\\[/tex]

Use a calculator or the unit circle to arrive at the last step. Keep in mind that (√3, √3) is in the first quadrant where [tex]0 < \theta < \frac{\pi}{2}[/tex] since both x and y are positive.

Answer:

It is forever, and it does not end.

Step-by-step explanation:

Infinity is the concept of no beginning and no end. It is the concept of all things and everything. So when you think of a deity ( Ex. God ) you think of them being infinite. They have no beginning or end, and have limitless possibilities. They live forever, and they can do anything. That is infinity in a nutshell.

Hope this helps.

Answer:

3:2

Step-by-step explanation:

The value of x (hypotenuse) using the Pythagorean Theorem is 5 units.

So, the formula of the Pythagorean Theorem:

Where a (AC) = 4 and b (CB) = 3 as the given figure is symmetric and so line CB will be equal to 3.

Now,

Therefore, the value of x using the Pythagorean Theorem is 5 units.

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Answer:

Approximately $18 each month.

Step-by-step explanation:

This is quite simple. So, we know that there are 12 months in a year. And we know that in a year, the store has given out discounts totaling up to $216. All we have to do is divide the total number by how many months there are in a year.

[tex]216\div12=18[/tex]

This means that the store gives out $18 of discounts per month.

(Also, you don't seem college level)