two square regions have an area of 125 and 5 how many yards of fencing is needed to enclose? ( assume regions fenced separately)

[tex]x^2 + 20x + 99=x^2+9x+11x+99=x(x+9)+11(x+9)=(x+11)(x+9)[/tex]

Answer:

The measure of angle 1 is 35°

Step-by-step explanation:

we know that

The measurement of the outer angle is the semi-difference of the arcs it encompasses.

∠1=(1/2)[106°-36°]=35°

Answer:

C=K-273.15

Step-by-step explanation:

Here we are given the relation between the measurements of temperatures in Celsius C and Kelvin K . The relationship is as under

K=C+273.15

now we have to rewrite this equation so that we can evaluate C in terms of K

In  order to do so , we Subtract 273.15 from both sides.

K-273.15 = C + 273.15-273.15

K - 273.15=C

C=K-273.15

Answer:

A

Step-by-step explanation:

The common difference d is the difference between consecutive terms.

d = - 2 - (- 6) = - 2 + 6 = 4

d = 2 - (- 2) = 2 + 2 = 4

Answer:

4

Step-by-step explanation:

BIG BRAIN

Answer: Acute Angle

Step-by-step explanation:

Any angle 89 degrees or less will identify as an acute angle.  

A 43 degree angle can be classified as an acute angle.

A 43 degree angle is classified as an acute angle which means it measures less than 90 degrees. Acute angles are commonly found in many geometric shapes.

They are also often associated with sharp corners or narrow angles. In the case of a 43 degree angle, it is smaller than a right angle (90 degrees) but larger than a zero or null angle.

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Answer:

2

Step-by-step explanation:

The reason 2 is the Greatest Common Factor of 6 and 8 is because 2 is the only number (other than 1) that you can divide evenly by both numbers  without making a fraction. 6/2= 3 and 8/2= 4.

Answer:

Step-by-step explanation:

In general, factor the numbers given into their primes.

6: 2*3

8: 2 * 2 * 2

Take the most you can from the two numbers primes. In this case it is 2.

A slightly more interesting problem is the GCF of 12 and 18

12: 2 * 2 * 3

18: 2 * 3 * 3

Here the two numbers that are common to both factored numbers is 2 and 3

GCF = 2*3

GCF = 6

Answer:

Option A - Permutation; number of ways = 210

Step-by-step explanation:

Given : At a competition with 7 runners, medals are awarded for first, second, and  third places. Each of the 3 medals is different.

To find : How many ways are there to  award the medals?        

Solution :

There are 7 runners but medals are three.

The first runner up got first medal as one is locked.

The second runner up got second medal as second is locked.

The third runner up got the third medal.

So, There is a permutation.

Number of ways to award the medals is [tex]^7P_3[/tex]

We know, [tex]^nP_r=\frac{n!}{(n-r)!}[/tex]

Substitute the values,

[tex]^7P_3=\frac{7!}{(7-3)!}[/tex]

[tex]^7P_3=\frac{7\times 6\times 5\times 4!}{4!}[/tex]

[tex]^7P_3=210[/tex]

Therefore, Option A is correct.

Permutation; number of ways = 210

Answer:

0

Step-by-step explanation:

x+y=5

x^3+y^3+15xy-125

(x+y)(x^2-xy+y^2)+15xy-125

5(x^2-xy+y^2)+15xy-125

5x^2+5y^2-5xy+15xy-125

5x^2+5y^2+10xy-125

5[x^2+2xy+y^2]-125

5(x+y)^2-125

5(5)^2-125

125-125

0

Answer:

The worth of one bill is $20 and the worth of the other bill is $1

Step-by-step explanation:

Let

x----> the worth of one bill

y ---> the worth of the other bill

I assume x > y

we know that

x+y=21 ----> equation A

x=y+19 ---> equation B

Solve the system by elimination

Multiply equation B by -1 both sides

-x=-y-19 ----> equation C

Adds equation A and equation C

x+y=21

-x=-y-19

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

y=21-y-19

2y=2

y=1

Find the value of x

x=y+19 -----> x=1+19=20

therefore

The worth of one bill is $20 and the worth of the other bill is $1

Linear functions are "graphs with straight lines." The formula to solving a linear function is [tex]y=f(x)=a+bx[/tex] Linear functions also have one independent variable and one dependent variable.

Hope this helps.

Answer:    Im pretty sure it is D

Step-by-step explanation:  I don't really know how to explain it.

I hope it helps tho ;)

Tell me if im wrong.

Answer:  The correct option is

(D) rotation of 270 degrees counterclockwise and shifting 3 units up.

Step-by-step explanation:  We are given to select the correct transformations that were applied to triangle ABC to obtain triangle A'B'C'.

From the graph, we note that

the co-ordinates of the vertices of triangle ABC are A(3, 4). B(5, 6) and C(8, 1).

And, the co-ordinates of the vertices of triangle A'B'C' are A'(4, 0), B'(6, -2) and C'(1, -5).

We see that

if a point (x, y) is rotated 270 degrees counterclockwise and then shifted 3 units up, then its co-ordinates becomes

(x, y)   ⇒   (y, -x+3).

With this transformation rule,

A(3, 4)  ⇒  (4, -3+3) = (4, 0),

B(5, 6)  ⇒  (6, -5+3) = (6, -2)

and

C(8, 1)  ⇒  (1, -8+3) = (1, -5).

Since the resulting co-ordinates are the vertices of triangle A'B'C', so the required transformations rare

rotation of 270 degrees counterclockwise and shifting 3 units up.

Option (D) is CORRECT.

Answer:

k=-5 or k= -13

Step-by-step explanation:

lk+9l=4

k+9=4 or k+9=-4

k=-5 or k= -13

The solutions for the equation |k+9| = 4 are k = -5 and k = -13. We got these results by considering separately the positive and negative cases for the absolute value.

To find the solution to the equation |k+9| = 4, we need to think about what the absolute value operation represents. Absolute value takes the positive version of whatever is inside, no matter if it's positive or negative. So we actually need to consider two separate cases.

So the solutions to the equation are k = -5 and k = -13.

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Answer:

Option D. 3.73​

Step-by-step explanation:

we know that

[tex]tan(x+y)=\frac{tan(x)+tan(y)}{1-tan(x)tan(y)}[/tex]

and

[tex]sin^{2}(\alpha)+cos^{2}(\alpha)=1[/tex]

step 1

Find cos(X)

we have

[tex]sin(x)=\frac{1}{2}[/tex]

we know that

[tex]sin^{2}(x)+cos^{2}(x)=1[/tex]

substitute

[tex](\frac{1}{2})^{2}+cos^{2}(x)=1[/tex]

[tex]cos^{2}(x)=1-\frac{1}{4}[/tex]

[tex]cos^{2}(x)=\frac{3}{4}[/tex]

[tex]cos(x)=\frac{\sqrt{3}}{2}[/tex]

step 2

Find tan(x)

[tex]tan(x)=sin(x)/cos(x)[/tex]

substitute

[tex]tan(x)=1/\sqrt{3}[/tex]

step 3

Find sin(y)

we have

[tex]cos(y)=\frac{\sqrt{2}}{2}[/tex]

we know that

[tex]sin^{2}(y)+cos^{2}(y)=1[/tex]

substitute

[tex]sin^{2}(y)+(\frac{\sqrt{2}}{2})^{2}=1[/tex]

[tex]sin^{2}(y)=1-\frac{2}{4}[/tex]

[tex]sin^{2}(y)=\frac{2}{4}[/tex]

[tex]sin(y)=\frac{\sqrt{2}}{2}[/tex]

step 4

Find tan(y)

[tex]tan(y)=sin(y)/cos(y)[/tex]

substitute

[tex]tan(y)=1[/tex]

step 5      

Find tan(x+y)

[tex]tan(x+y)=\frac{tan(x)+tan(y)}{1-tan(x)tan(y)}[/tex]

substitute

[tex]tan(x+y)=[1/\sqrt{3}+1}]/[{1-1/\sqrt{3}}]=3.73[/tex]

Answer:

D. 3.73

Step-by-step explanation:

Answer:

7(10+5)

105

Step-by-step explanation:

Distributive property:

       ↓

A(B+C)=AB+AC

7*15=7(10+5)

7(10+5) is the correct answer.

105 is the correct answer.

I hope this helps you, and have a wonderful day!

By distributive property, 7·15 can be written as 7*(10 + 5) = 105 .

According to the distributive property, multiplying the sum of two or more variables by a number will give the same result as multiplying each variables individually by the number and then adding the products together.

Mathematically,

A*(B + C) = AB + AC

Given expression is 7·15 .

By distributive property, the expression can be written as -

⇒ 7·15 = 7*(10 + 5)

⇒ 7*(10 + 5) = 7*10 + 7*5

⇒ 70 + 35 = 105 .

Thus, by distributive property, 7·15 can be written as 7*(10 + 5) = 105

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f(x) and y are two different ways of denoting the same thing. Thus...

f(x) = 9x - 8 is the same as y = 9x - 8

Inverse: the inverse of a function is the resulting equation when x and y switch places and the equation is solved for x

Switch the places of x and y in the given equation:

y = 9x - 8 ---> x = 9y - 8

Solve the new equation for y (isolate y on the left side of the equation)

x = 9y - 8

x + 8 = 9y - 8 + 8

x + 8 = 9y

(x + 8) / 9 = 9y / 9

(x + 8)/9 = y

y = (x + 8) / 9

y = [tex]\frac{x+8}{9}[/tex]

Now you have the inverse of f(x) = 9x - 8:

A) [tex]f^{-1}[/tex] =[tex]\frac{x + 8}{9}[/tex]

inverse

Answer:

A. [tex]f^{-1}(x)=\frac{x+8}{9}[/tex]

Step-by-step explanation:

We have been given a function [tex]f(x)=9x-8[/tex]. We are asked to find the inverse function for our given function.

First of all, we will rewrite [tex]f(x)[/tex] as [tex]y[/tex] as:

[tex]y=9x-8[/tex]

To find the inverse function, we will interchange x and y variables and then solve for y.

[tex]x=9y-8[/tex]

Now, we will add 8 on both sides of our given equation.

[tex]x+8=9y-8+8[/tex]

[tex]x+8=9y[/tex]

Switch sides:

[tex]9y=x+8[/tex]

Now, we will divide both sides of our equation by 9.

[tex]\frac{9y}{9}=\frac{x+8}{9}[/tex]

[tex]y=\frac{x+8}{9}[/tex]

Now, we will replace [tex]y[/tex] with [tex]f^{-1}(x)[/tex] as:

[tex]f^{-1}(x)=\frac{x+8}{9}[/tex]

Therefore, the inverse function for our given function would be [tex]f^{-1}(x)=\frac{x+8}{9}[/tex] and option A is the correct choice.

Answer:

0.

Step-by-step explanation:

If log(a) x = b

Then by the definition of a logarithm x = a^b.

So let log(4) 1 = y

then 1 = 4^y

but 4^0 = 1

so y = log(4) 1 = 0.

Answer: 95°

Step-by-step explanation: We are given information for Angles 1 and 4, which happen to be vertical angles, meaning they are congruent. Because of this, we can say 3x+10=4x-15, therefore x=25. Angles 1,2,3 and 4 must add up to 360°, and since we know angles 1 and 4 are 85° (3*25 + 10 = 85), we can find angles 2 and 3. 360° - 85° - 85° = Angle 2 + Angle 3. Angle 2 + Angle 3 = 190, and because Angles 2 and 3 are vertical angles and therefore congruent, we can divide 190 by 2 and get that Angles 2 and 3 equal 95°. Because lines b and c are parallel, any corresponding angles created by a transversal are congruent. This basically means Angles 3 and 7 must be congruent, therefore Angle 7 = 95°

Congruent - same meaning as equal

Vertical Angles - each of the pairs of opposite angles made by two intersecting lines.

Answer:

{[tex](x,y)|(x=3,y=4)[/tex]}

Step-by-step explanation:

The given system of equations is;

[tex]y-4=0...(1)[/tex]

and

[tex]2x-y-2=0...(2)[/tex]

We rewrite the equations in the standard form to get:

[tex]y=4...(3)[/tex]

[tex]2x-y=2...(4)[/tex]

We now substitute equation (3) into equation (4) to get:

[tex]2x-4=2[/tex]

Group similar terms:

[tex]2x=2+4[/tex]

[tex]2x=6[/tex]

Divide both sides by 2

[tex]\frac{2x}{2}=\frac{6}{2}[/tex]

This implies that:

[tex]x=3[/tex]

Therefore the solution set is:

{[tex](x,y)|(x=3,y=4)[/tex]}

Answer:

9/32

Step-by-step explanation:

BC = black circle

BS = black square

WC = white circle

WS = white square

Given:

(WC + WS) / (BC + BS) = 5 / 11

WC / WS = 3 / 7

BC / BS = 3 / 8

Find: (BC + WC) / (BC + BS + WC + WS)

Solve for WC and BC in the last two equations, then substitute into the first:

WC = 3/7 WS

BC = 3/8 BS

WC + WS = 5/11 (BC + BS)

3/7 WS + WS = 5/11 (3/8 BS + BS)

10/7 WS = 5/8 BS

WS = 7/16 BS

Therefore:

WC = 3/7 WS

WC = 3/16 BS

Substitute:

(BC + WC) / (BC + BS + WC + WS)

(3/8 BS + 3/16 BS) / (3/8 BS + BS + 3/16 BS + 7/16 BS)

(9/16 BS) / (2 BS)

9/32

Answer:

B) 4, 8, 10

Step-by-step explanation:

4+8 is greater than 10

4+10 is greater than 8

10+8 is greater than 4

Answer:

The answer D is incorrect

I'm sorry I don't know the answer but I wanted to warn you so you can at least have a better chance

Step-by-step explanation:

Answer:

60

Step-by-step explanation:

i took the test i got it right (:

ANSWER

[tex] 12\pi[/tex]

EXPLANATION

The area of sector is calculated using

[tex] \frac{angle\:of \: sector }{360 \degree} \times \pi \: {r}^{2} [/tex]

The angle of the sector is 120° and the radius of the circle is 6 units.

We substitute the given values into the formula to obtain:

[tex] \frac{120 \degree}{360} \times \pi \times {6}^{2} [/tex]

[tex] = \frac{120 \degree}{360} \times \pi \times 36[/tex]

[tex]= \frac{120 \degree}{10} \times \pi = 12\pi[/tex]

Hence the area of the sector is [tex] 12\pi[/tex]

[tex]\bf (\stackrel{x_1}{2}~,~\stackrel{y_1}{11})\qquad (\stackrel{x_2}{4}~,~\stackrel{y_2}{17}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{17-11}{4-2}\implies \cfrac{6}{2}\implies 3 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-11=3(x-2)\implies y-11=3x-6[/tex]

[tex]\bf y=3x+5\qquad \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}[/tex]

Answer:

[tex]y = 3x + 5[/tex]

Step-by-step explanation:

First, find the rate of change [slope]:

-y₁ + y₂\-x₁ + x₂ = m

[tex]\frac{-11 + 17}{-2 + 4} = \frac{6}{2} = 3[/tex]

Now, plug the coordinates into the Slope-Intercept Formula instead of the Point-Slope Formula because you get it done much swiftly. It does not matter which ordered pair you choose:

17 = 3[4] + b

12

5 = b

[tex]y = 3x + 5[/tex]

__________________________________________________________

11 = 3[2] + b

6

5 = b

[tex]y = 3x + 5[/tex]

You see? I told you it did not matter which ordered pair you choose because you will always get the exact same result.

I am joyous to assist you anytime.

Answer:

A=384

Step-by-step explanation:

For this case we have by definition, that the surface area of a cube is given by:

[tex]SA = 6l ^ 2[/tex]

Where:

l: It's the side of the cube

We have as data, according to the figure, that:

[tex]l = 8ft[/tex]

Substituting in the figure:

[tex]SA = 6 (8) ^ 2\\SA = 6 * 64\\SA = 384 \ ft ^ 2[/tex]

Thus, the surface area of the cube is [tex]384 \ ft ^ 2[/tex]

Answer:

[tex]384 \ ft ^ 2[/tex]

Answer:

7y

Step-by-step explanation:

By cross multiplication

[tex] \frac{x}{7} = \frac{y}{5} \\ 5x = 7y[/tex]

Answer:

[tex]5x=7y[/tex]

Step-by-step explanation:

We have the following relationship

[tex]\frac{x}{7}=\frac{y}{5}[/tex]

Based on the relationship between the variables X and Y that we know, we must find out what the expression "5x" is in terms of the variable y.

Then we solve the equation for x

[tex]x=\frac{7y}{5}[/tex]

Now multiply by 5 both sides of equality

[tex]5x=\frac{5*7y}{5}[/tex]

[tex]5x=7y[/tex]

Finally we have that 5x equals 7y

For this case we have that by power properties it is fulfilled:

[tex](a ^ n) ^ m = a ^ {n * m}[/tex]

Now, we can rewrite the expression as:

[tex]\frac {64g ^ 9 * h ^ 6 * k ^ {12}} {8g ^ 3 * h ^ 2} -h ^ {25} k ^ {15} =[/tex]

We also have by definition of properties of powers that:

[tex]\frac {a ^ m} {a ^ n} = a ^ {m-n}[/tex]

So:

[tex]8g ^ {9-3} * h ^ {6-2} * k ^ {12} -h ^ {25} k ^ {15} =\\8g ^ 6 * h ^ 4 * k^{12} -h^{25} * k^{15}[/tex]

Answer:

Option D

Answer:

68

Step-by-step explanation:

i just took the test.

Answer:

5 + 2m = 23

Step-by-step explanation:

This equation can be solved as follows:

5 + 2m = 23

2m = 23 - 5

m = 18/2

m = 9 months

Answer:

20 rad/sec

Step-by-step explanation:

The formula we are going to use is  [tex]v=\omega r[/tex]

Where

v is the linear velocity (here given 60 ft/s)

[tex]\omega[/tex]  is the angular velocity (what we sought to find)

r is the radius (which is half of diameter, hence, 6/3 = 3 ft)

Plugging these numbers in, we find the angular velocity as:

[tex]v=\omega r\\60=\omega*(3)\\\omega=\frac{60}{3}=20[/tex]

Note: the units is radians per second (rad/s)

Correct answer 20 rad/sec

Answer:

[tex]20 \frac{rad }{sec}[/tex]

Step-by-step explanation:

Hello.

let's see this way.

if you know the distance(a circumference 2πr) and the speed(60 ftps) you are able to find the time it takes a whole spin( a circle)

Step 1

find the distance and time

Let

[tex]V=60 \frac{feet}{sec} \\distance= circumference= 2*\pi *r\\diameter=6 feet\\radius=\frac{Diameter}{2}\ so,r=\frac{6}{2} =3 feet\\Hence\\\\distance= circumference= 2*\pi *3\\\\distance=18.84\\\\time=\frac{distance}{velocity}\\ put\ the\ values\\time=\frac{18.84 feet}{60 \frac{feet}{sec} } \\\\time=0.314\ sec[/tex]

now, for obtain the  angular velocity , divide  the circumference (use radians  2π radians=360 degrees )by the time it takes to complete a lap

[tex]\alpha =\frac{(2 \pi rad)}{time\ per\ lap}\\\\ \alpha =\frac{(2\pi rad)}{0.314 sec}\\ \alpha =20 \frac{rad}{sec}[/tex]

Have a great day

Answer:

The answer in the procedure

Step-by-step explanation:

we have

[tex]\frac{1}{3}x^{2} +2[/tex]

This is a vertical parabola open upward with the the vertex at (0,2)

The vertex is a minimum

The y-intercept is the point (0,2) (value of y when the value of x is equal to zero)

The graph does not have x-intercepts, therefore the solutions of the quadratic equation are complex number

using a graphing tool

see the attached figure