Solve the problem.
The length of a rectangular room is 9 feet longer than twice the width. If the room's perimeter is
198 feet, what are the room's dimensions?

Answer:

(0, 7/12)

Step-by-step explanation:

to find the y intercept we equate x to 0.

hence,

f(0) = 7/12

the coordinate is (0, 7/12)

Answer:

[tex](0,\frac{7}{12})[/tex]

Step-by-step explanation:

In order to find the y-intercept of an equation, simply plug in 0 for x, as that's where the y-axis is.

[tex]\frac{(2(0)+1)(0+7)}{((0)+3)((0)+4)}[/tex]

Simplify:

[tex]\frac{7}{(3)(4)}=\frac{7}{14}[/tex]

Therefore, the y-intercept for the equation is:

[tex]\frac{7}{14}[/tex]

Applying the distance formula, the length of AB is: D. About 9.4 units.

Distance formula is given as: [tex]d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex].

Given the following:

A(4, 2) = (x1, y1)

B(9, 10) = (x2, y2)

Apply the distance formula

AB = √[(9−4)² + (10−2)²]

AB = √[(5)² + (8)²]

AB = √89

AB ≈ 9.4 units

Learn more about the distance formula on:

https://brainly.com/question/661229

#SPJ1

Answer:

6

Step-by-step explanation:

I presume you meant

[tex]g(x) = \sqrt{x + 32} \\ g(32) = \sqrt{32 + 4} \\ g(32) = \sqrt{36} \\ g(32) = 6[/tex]

Answer:

height = 8m

radius = 6m

Surface area of the cylinder = 2 Pie r h

= 2* 3.14 * 6 * 8

= 6.28 * 48

= 301.4 sq meters

Answer:

x = 35 and 100°

Step-by-step explanation:

the sum of the exterior angles of a triangle = 360° , then

2x + 10 + 3x + 15 + 4x + 20 = 360 , that is

9x + 45 = 360 ( subtract 45 from both sides )

9x = 315 ( divide both sides by 9 )

x = 35

then each exterior angle is

2x + 10 = 2(35) + 10 = 70 + 10 = 80°

3x + 15 = 3(35) + 15 = 105 + 15 = 120°

4x + 20 = 4(35) + 20 = 140 + 20 = 160°

the sum of an exterior angle and corresponding interior angle = 180°

then

180° - 80° = 100°

180° - 120° = 60°

180° - 160° = 20°

the largest interior angle of the triangle is 100°

Answer:

x = 35

largest interior angle = 100°

Step-by-step explanation:

The exterior angles of a triangle sum to 360°

⇒ (2x + 10) + (3x + 15) + (4x + 20) = 360

⇒ 2x + 10 + 3x + 15 + 4x + 20 = 360

⇒ 9x + 45 = 360

⇒ 9x = 315

⇒ x = 35

Therefore, the three exterior angles are:

If the side of a triangle is extended, the angle formed outside the triangle is the exterior angle.  As angles on a straight line sum to 180°:

⇒ interior angle + exterior = 180°

So the largest interior angle will be the supplementary angle to the smallest exterior angle.

The smallest exterior angle is 80°, so:

⇒ largest interior angle + 80° = 180°

⇒ largest interior angle = 180° - 80°

⇒ largest interior angle = 100°

Answer:

the graph has a parent function of f(x) = x²

The (x - 5)² tells us that the graph is shifted to the right 5 units.

The +2 tells us that the graph is shifted up 2 units.

basically you treat y like a number and not a variable

Answer:

a is 4

b is 2y

c is -10y²+9

discriminant is 4(41y²-36)

Step-by-step explanation:

4x²+2xy-10y²+9=0

rewrite in standard form of a quadratic equation like ax² + bx + c = 0

4x²+2yx-10y²+9=0

basically you treat y like a number and not a variable

a is the number with the x²

right away we know a is 4 because of 4x²

b is the one with x so in this formula b is 2y

c is the number without the x which in this case is -10y²+9

discriminant is

b² - 4ac

(2y)²- (4)(4)(-10y²+9)

4y²-(16)(-10y²+9)

4y²-(16)(-10y²+9)

4y²+160y²-144

164y²-144 =

4(41y²-36)

Given:

Formula:

AB × AD = AC × AE

Here if applied:

EA × EB = EC × ED

2 × 12 = 3 × (3 + y)

24 = 9 + 3y

3y = 15

y = 5

Answer:

y = 5

Step-by-step explanation:

Secant: a straight line that intersects a circle at two points.

Segment: part of a line that connects two points.

The given diagram shows two secant segments EB and ED drawn to the circle from one exterior point E.  Therefore, using the Intersecting Secants Theorem,  the product of the measures of one secant segment and its external part is equal to the product of the measures of the other secant segment and its external part.

⇒ EB · EA = ED · EC

⇒ (2 + 10) · 2 = (3 + y) · 3

⇒ (12)2 = 3(3 + y)

⇒ 24 = 9 + 3y

⇒ 15 = 3y

⇒ y = 5        

Answer:

First option.

Step-by-step explanation:

Step-by-step explanation:

I'm going to assume you meant to write [tex]\sqrt{r+1}[/tex] in the equation as +1 - 1 wouldn't make much sense since they would just cancel out.

a. [tex]f(-1) = \sqrt{-1 + 1} - 1\\ f(-1) = \sqrt{0} - 1\\f(-1) = 0-1\\f(-1) = -1[/tex]

b. [tex]f(24) = \sqrt{24 + 1} - 1\\ f(24) = \sqrt{25} - 1\\f(24) = 5 - 1\\f(24) = 4[/tex]

c. [tex]f(x-1) = \sqrt{(x-1)+1} -1\\f(x-1) = \sqrt{x} - 1[/tex]

Using translation concepts, the graph of function g(x) = f(x) - 2 = x² - 2 is given at the end of the question.

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.

In this problem, the functions are given as follows:

Which means that g(x) is a shift down of 2 units of f(x), as given by the graph in the end of the question.

More can be learned about translation concepts at https://brainly.com/question/4521517

#SPJ1

Answer: K

Step-by-step explanation:

The subtraction with the negatives can cancel out, resulting in a possible positive answer.

Answer:

k

Step-by-step explanation:

K      you CAN get a positive number....

        example  :

     -3   - (-5)   = -3 + 5 = + 2

Answer:

[tex]x^{2}-\frac{3}{2} x-\frac{7}{16} =0[/tex]

Step-by-step explanation:

[tex]\begin{cases}\alpha -\beta =2\\ \alpha^{2} -\beta^{2} =3\end{cases}[/tex]

[tex]\Longleftrightarrow \begin{cases}\alpha -\beta =2&\\ \left( \alpha +\beta \right) \left( \alpha -\beta \right) =3&\end{cases}[/tex]

[tex]\Longleftrightarrow \begin{cases}\alpha -\beta =2&\\ \alpha +\beta =\frac{3}{2} &\end{cases}[/tex]

Then

2α = 2 + 3/2 = 7/2

2β = (3/2) - 2 = -1/2

Then

Then

α = 7/4

β = -1/4

Then

a quadratic equation with root α and β can be :

[tex]\left( x+\frac{1}{4} \right) \left( x-\frac{7}{4} \right) =0[/tex]

[tex]\Longrightarrow x^{2}-\frac{3}{2} x-\frac{7}{16} =0[/tex]

Answer: [tex](-\infty, -8) \cup (-8, \infty)[/tex]

Step-by-step explanation:

I'm assuming you meant [tex]f(x)=\frac{x-9}{x+8}[/tex]

For this function, we need to make sure the denominator is not equal to 0, because if it was, then the fraction would be undefined.

Thus, [tex]x+8 \neq 0 \longrightarrow x \neq -8[/tex]

In interval notation, this is [tex](-\infty, -8) \cup (-8, \infty)[/tex]

Answer:

The cosine function is f(t) = -30sin(π÷3)t + 20

Step-by-step explanation:

Given : The temperature of a chemical reaction ranges between −10 degrees Celsius and 50 degrees Celsius. The temperature is at its lowest point when t = 0, and the reaction completes 1 cycle during a 6-hour period.

To find : What is a cosine function that models this reaction?

General form of cosine function is f(x) = A cos(Bx)+C

Where A is the amplitude

B=2π÷Period

C is the midline    

Now, We have given

The temperature of a chemical reaction ranges between −10 degrees Celsius and 50 degrees Celsius.

A is the average of temperature,

i.e,

A=(-10-50)÷2 = -30

Period of 1 cycle is 6 hour

So,

B = 2π÷6 = π÷3

The temperature is at its lowest point when t = 0 and we know lowest point is -10

So,

f(t) = A cos t + C

-10 = -30 cos 0 + C

Therefore, C = 20

Substituting the values, we get

The cosine function is f(t) = -30sin(π÷3)t + 20

Read more at:

https://brainly.com/question/4411386

#SPJ10

Answer:

17cm Squared

Step-by-step explanation:

Get the area of the whole triangle, then the area of the white part. Then subtract the white from the whole area

Answer:

1277

Step-by-step explanation:

350 * (1.04)^33 =

1276.93338385

algebracom

theo(12211)

Answer:

[tex] \frac{45}{55} = \frac{3}{11} [/tex]

Step-by-step explanation:

I think that is the right answer

Answer:

z = -2

Step-by-step explanation:

Answer:

[tex]\boxed{\bf z = - 2}[/tex]

Step-by-step explanation:

[tex]\bf 6z + 10 = - 2[/tex]

Subtract 10 from both sides.

Simplify.

Divide both sides by 6.

Simplify.

_________________________

The Function models Jay's total monthly salary s(x) in dollars would be s(x) = 0.03s - 1060.

A function is a type of relation, or rule, that maps one input to a specific single output.

Given

Base salary = $2500 per month

Commision = 3% on Sales over 48000

Determine the function s(x) for sales over $48000

Let's Represent the total sales in a month with s.

So, the function s(x) is:

s(x)  = Base Amount + Commission x Sales over $48000

s(x) = 2500  + 3% (s - 48000)

s(x) = 2500  + 0.03(s - 48000)

s(x) = 2500  + 0.03s - 1440

s(x) = 0.03s - 1060

Hence, the Function models Jay's total monthly salary s(x) in dollars would be s(x) = 0.03s - 1060.

Learn more about function here:

https://brainly.com/question/2253924

#SPJ1

Answer:

78

Step-by-step explanation:

plug in -3 as x

6(2(-3)^2-5)

6(2(9)-5)

6(18-5)

6(13)

78

Answer:

CI = (71.41%, 78.99%)

Step-by-step explanation:

[tex] \frac{376}{500} - 1.96 \sqrt{ \frac{ (\frac{376}{500} )( \frac{124}{500} )}{500} } = 71.415\%[/tex]

[tex] \frac{376}{500} + 1.96 \sqrt{ \frac{ (\frac{376}{500} )( \frac{124}{500}) }{500} } = 78.985\%[/tex]

If 500 high school students, 376 said they would prefer to have computers in every classroom then the confidence interval at 95% is (71.41%,78.99%)  Since option (a) is correct.

Given x= 376, n = 500

The (71.41%,78.99%)  

[tex]\hat{p}=\frac{x}{n}\\ =\frac{376}{500} \\=0.752[/tex]

Critical values

Using the z-table the z-critical value at the given significance level at α=0.05 is,[tex]z_{a/2} =1.96[/tex]

Construct a 95% confidence interval

That is,

[tex]\hat{p}= z_{a/2}\sqrt{\frac{\hat{p}(1-\hat{p})}{n} }[/tex]

  [tex]=0.752\pm 1.96\sqrt{\frac{0.752(1-0.752)}{500} }[/tex]

  [tex]=0.752\pm 0.0379[/tex]

  = (71.41%,78.99%)  

Learn more about confidence intervals here: https://brainly.com/question/15712887

#SPJ10

The standard deviation is a measure of a collection of values' variance or dispersion. The correct option is B.

The standard deviation is a measure of a collection of values' variance or dispersion. A low standard deviation implies that the values are close to the set's mean, whereas a high standard deviation shows that the values are spread out over a larger range.

For the last summer,

Mean = (140 + 220 + 190 + 180 + 190) / 5 = 920/5 = 184

[tex]\sigma={\sqrt {\dfrac{(140-184)^2+ (220-184)^2+(190-184)^2+(180-184)^2+(190-184)^2}{5}}}\\\\\sigma = 25.7682[/tex]

For this summer,

Mean = (150 + 170 + 150 + 190 + 180) / 5 = 840/5 = 168

[tex]\sigma={\sqrt {\dfrac{(150-168)^2+ (170-168)^2+(150-168)^2+(190-168)^2+(180-168)^2}{5}}}\\\\\sigma = 16[/tex]

Hence, The number of pages in each book varied more last summer than this summer. Thus, the correct option is B.

Learn more about Standard Deviation:

https://brainly.com/question/16555520

#SPJ1

[tex] {x}^{2} + 5x + 6 = 0 \\ \\ {x}^{2} + 2x + 3x + 6 = 0 \\ \\ x(x + 2) + 3(x + 2) = 0 \\ \\ (x + 2)(x + 3) = 0 \\ \\ x + 2 = 0 \\ \\ x = - 2 \\ \\ x + 3 = 0 \\ \\ x = - 3.[/tex]

The value of x = -2 and -3 .

Answer:

hope it helps...

it has both co ordinate and factorization

Answers:

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

Work Shown:

n = number of sides = 26

S = sum of the interior angles of a polygon with n sides

S = 180(n-2)

S = 180(26-2)

S = 180(24)

S = 4320 degrees is the sum of the interior angles.

i = measure of one interior angle of a regular polygon

i = S/n

i = 4320/26

i = 166.1538 approximately

i = 166.15 degrees is the approximate measure of each interior angle.

Side note: The formula to determine the interior angle i only works for regular polygons. This is because each angle is the same measure.

[tex]DE=\sqrt{13^{2}+12^{2}-2(13)(12)(\cos 59^{\circ})} \approx \boxed{12.3}[/tex]

Answer:

Step-by-step explanation:

The answer is -0.18

when you convert 43% to decimal, it is 0.43

And the z-score of 0.43 is closest to -0.18

Hope it helps!

Answer:

cuantos billetes de 100.son en .100000?