which choice is equivalent to the quotient below when -2<=x<2
square root of 4-x^2 divided by square root of 2-x

Answer:

b. x=2, -3

Step-by-step explanation:

So I'm assuming the two equations are: [tex]y=4-x^2[/tex] and [tex]x-y=2[/tex]

Since it's asking to solve to solve for x. Then we need to solve for y in one of the equations, so that's it's defined using x, then substitute that into the other equation, that way the only variable left is going to be the x variable.

So since y is already solved for in the first equation. I'll plug that into the second equation.

Original equation:

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

Substitute 4-x^2 in as y

[tex]x-(4-x^2)=2[/tex]

Distribute the negative sign

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

Organize it so it's in order by degree

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

Subtract 2 from both sides

[tex]x^2+x-6=0[/tex]

So now we have a quadratic equation and we're trying to find the zeroes. You can use the quadratic equation, but since the only options are integers, we can easily factor this equation. So you need to look for factors of -6, which add up to 1. I like to think about it as find two numbers with a difference of 1, and then figure out which is going to be positive and which is going to be negative after. So knowing this you can easily see 3 and 2 have a difference of 1. Since the 1 is positive, that means the 3 has to be positive and the 2 has to be negative

Use the factors: 3 and -2 to rewrite the equation:

[tex](x+3)(x-2)[/tex]

Now set each factor equal to 0

x+3 = 0

x=-3

x-2=0

x=2

this gives you the two solutions: -3, and 2

From the given recursive definition,

[tex]a_1 = 3[/tex]

[tex]a_2 = a_1 + 5 = 3 + 5 = 8[/tex]

[tex]a_3 = a_2 + 5 = 8 + 5 = 13[/tex]

[tex]a_4 = a_3 + 5 = 13 + 5 = 18[/tex]

[tex]a_5 = a_4 + 5 = 18 + 5 = 23[/tex]

Answer:

It's A and C

Step-by-step explanation:

the angles are 45, which is less than 90

Answer:

[tex](a)1600f+600w\\\\(b)1600\times2f+600\times2w[/tex]

The equation to model the situation is [tex]\mathbf{y = \dfrac{k}{x^2}}[/tex]. The constant for the variation is 2250.

The intensity of light from a lantern varies inversely to the square of the distance from the lantern.

From the given information:

Then:

[tex]\mathbf{y \alpha \dfrac{1}{x^2} }[/tex]

[tex]\mathbf{y = \dfrac{k}{x^2} }[/tex]   here, k = constant.

2.

If y = 90 W/m² when the distance x = 5m

Then:

[tex]\mathbf{90 = \dfrac{k}{(5)^2}}[/tex]

k = 90 × 25

k = 2250

c.

The equation to model the situation by using the constant variation is:

[tex]\mathbf{y = \dfrac{2250}{x^2}}[/tex]

d.

If the light intensity y = 40, then x is determined as:

[tex]\mathbf{40 = \dfrac{2250}{x^2}}[/tex]

[tex]\mathbf{x = \sqrt{\dfrac{2250}{40}}}[/tex]

x = 7.5 m

e.

The light is needed in (225 × 1000)m = 225000 km of illumination.

f.

The lantern required for the new light estimation is:

y = 2250/225000

y = 0.01 intensity

Therefore, we can conclude that to get an intensity of 1 W/m², we need to put 100 lanterns.

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Answer:

A. 19

Step-by-step explanation:

Slove this expression using the order of operation PEMDAS.

12 + 2x -5

Replace x with 6

12 + 2(6) - 5

12 + 12 - 5

24 -5

19

Therefore the answer is the first option A.19 .

Answer:

19 inches

Step-by-step explanation:

So the perimeter of a triangle is the sum of the three sides. So the perimeter is [tex]\sqrt{65} + \sqrt{35} + \sqrt{26}[/tex] which is approximately 19.077 inches but in this case the answer is 19 inches

the constant variation, K= 4

Step-by-step explanation:

i have replace the constant variation by the letter K

First step is to write down the information

y directly proprotional to x

So, y= Kx

Replace the value given for x and y to find k

y= -4 and x = -1

Kx= y

K( -1) = -4

K = -4 ÷ -1

K= 4

Further answer

if you are asked the connecting equation between y and x just replace the value of K in the equation

y= Kx

y= 4x

Maribel leaves school at 3:10 to walk home, spent 20 minutes shopping and spent 30 minutes walking

An equation is an expression that shows the relationship between two or more variables and numbers.

Let us assume that Maribel reaches home at 4:00, hence:

Time spent walking = 4:00 - (3:10 + 20 minutes) = 4:00 - 3:30 = 30 minutes

Maribel leaves school at 3:10 to walk home, spent 20 minutes shopping and spent 30 minutes walking

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Answer:

x = - 3 ± [tex]\sqrt{2}[/tex]

Step-by-step explanation:

x² + 6x + 7 = 0 ( subtract 7 from both sides )

x² + 6x = - 7

using the method of completing the square

add ( half the coefficient of the x- term )² to both sides

x² + 2(3)x + 9 = - 7 + 9

(x + 3)² = 2 ( take square root of both sides )

x + 3 = ± [tex]\sqrt{2}[/tex] ( subtract 3 from both sides )

x = - 3 ± [tex]\sqrt{2}[/tex]

The missing step in the given solution to the inequality -x-3 < 13 + 3x is - 4x - 3 < 13

Incorrect steps:

- x - 3 < 13 + 3x

-4x < 16

X > -4

Correct steps:

- x- 3 < 13 + 3x

-x - 3x - 3 < 13

- 4x - 3 < 13

- 4x < 13 + 3

- 4x < 16

x < 16/-4

x > -4

Therefore, the missing step in the given solution to the inequality -x-3 < 13 + 3x is - 4x - 3 < 13

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Answer: $233

Step-by-step explanation:

- A flat fee is an amount that is charged or paid that doesn’t account for hourly use or work

- Then, you must pay by the hour for use

- So you would use the equation:

(22 • 9) + 35

- 22 is the maximum hours and 9 is the hourly rate

- 35 is your flat fee

- So, (22 • 9) + 35 = $233

hope this helps :)

Answer:

$233

Step-by-step explanation:

We can make up a linear equation. We already know that it costs $35 to rent a small auger.

Every hour there is a extra fee of 9$.

So, 9 can be the slope, while 35 can be the x intercept.

y=9x+35

x=22; maximum hours

y=9(22)+35

y=198+35

y=$233

Here is a more simple way

multiply 22 hours with 9 dollars, =$198

then add the 35 dollars; 198+35=$233

Answer: 36

Step-by-step explanation:

[tex]\overline{AB} \cong \overline{BC}[/tex] (Triangle ABC is isosceles)

[tex]m\angle CAB=m\angle CBA=30^{\circ}[/tex] (base angles of an isosceles triangle are congruent)

[tex]\angle MCB=90^{\circ}[/tex] (In triangle CMB, angles in a triangle add to 180 degrees)

[tex]\angle ACM=30^{\circ}[/tex] (triangle sum theorem)

[tex]MB=24[/tex] (30-60-90 triangle CMB)

[tex]AB=12[/tex] (sides opposite congruent angles in a triangle are congruent)

[tex]AB=36[/tex] (segment addition postulate)

Answer:

60 for both

Step-by-step explanation:

Since these angles are parallel, they are equal to each other :

6x = 5x + 10

Subtracting 5x from both sides gives us :

x = 10

Substituting this value back into both angles gives us

6x = 60

5x+10 = 60

The function is C(F) = (F-32) * 5/9
This means the function C, is using variable F to get the output.
C is Celsius, F is Fahrenheit, so the answer is "the temperature of 76.1 degrees Fahrenheit converted to degrees Celsius"

Answer:

a

Step-by-step explanation:

Hello,

Answer:

x = 13

Step-by-step explanation:

    7x + 5 + 5x + 19 = 180

⇔ 12x + 24 = 180

⇔ 12x = 180 - 24

⇔ 12x = 156

⇔ x = 156/12

⇔ x = 13

Answer:

25.5 mph

Step-by-step explanation:

So Bradley's speed can be modeled by the equation y=2x+40 where y=speed, x=time in hours after noon, and b=initial speed

So 12:15 is 15 minutes after noon, which is also 0.25 or 1/4 of an hour after noon. This is the x-value. Plug this into the equation to get his speed at 12:15

y=2(0.25)+40

y=0.5+40

y=40.5

So his speed was 40.5 at the time and since he was going 15 miles over the speed limit, the speed limit is 15 less than his speed

40.5 - 15 = 25.5

Answer:

25.5 mph

Step-by-step explanation:

Given information:

Calculate Bradley's speed at 12.15 pm:

60 minutes = 1 hour

⇒ 15 minutes = 1/4 hour

⇒ speed at 12.15 pm = speed at 12.00pm + 1/4 of 2 mph

                                  = 40 mph + 0.5 mph

                                  = 40.5 mph

If he was 15 miles over the speed limit at 12.15 pm then:

⇒ speed limit = speed at 12.15pm - miles over the limit

                       = 40.5 mph - 15

                       = 25.5 mph

Therefore, the speed limit was 25.5 mph.

The amount of bbd received for the given currency exchange rate is 6050  bbd.

The value of one country's currency in relation to the currencies of other countries or economic zones is known as the currency exchange rate.

The majority of currency exchange rates are free-floating and fluctuate according to market supply and demand.

There may be restrictions on some currency exchange rates since they are fixed to the value of other currencies.

According to the question,

Currency exchange rate: $1.00=5.50bbd

So, $1100=1100*5.50 bbd

               =6050 bbd

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Answer:

See below

Step-by-step explanation:

x^2 +2x -8   =   (x-2)(x+4)

x^2 + 6x  - 16 = (x + 8)(x-2)        now you can cancel the ( x-2 ) to get

(x+4) / (x+ 8)

Answer:

A. 0.068

Step-by-step explanation:

First, 3 inches to miles. 3 inches in a mile is 0.00004735.

The snail moves 0.00004735 miles per minute.

Next, search how many minutes are there in a day. There is 1440 minutes in a day.

Multiply the 1440 and 0.00004735.

1440*0.00004735=0.068

The snail can move 0.068 miles per day if it doesn't take a break.

Hope this helps!

If not, I am sorry.

Answer:

18.75

Step-by-step explanation:

[tex]Area=\pi r^{2} \\Area=3(\frac{5}{2} )^{2} \\Area=18.75[/tex]

Answer:

n = 8 or n = −6

Explanation:

First, isolate the absolute value:

5 − |n − 1| = −2

7 − |n − 1| = 0

7 = |n − 1|

Then, split this into two equations, since the result of the absolute value could be positive or negative:

7 = n − 1                           7 = −(n − 1)

8 = n                                7 = −n + 1

                                       n = −6

Answer:

[tex]\{-6\} \cup \{8\}[/tex]

Step-by-step explanation:

[tex]5 - |n - 1| = -2; \\ -|n - 1| = -2 - 5 \\ -|n - 1| = -7 \\ |n - 1| = 7 \\ \left \ [ {{n - 1 = 7} \atop {n - 1 = -7}} \right. \Leftrightarrow \left \ [ {{n = 7 + 1} \atop {n = -7 + 1}} \right. \Leftrightarrow \left \ [ {{n = 8} \atop {n = -6}} \right.[/tex]

Question 5

Vertical angles are congruent. Therefore, [tex]3y=\boxed{150}[/tex]. The sum of two supplementary angles equals [tex]\boxed{180^{\circ}}[/tex].

Therefore, [tex]6x+150=\boxed{180}[/tex]

Question 6

[tex]\angle b-14=90-\angle b\\\\2\angle b=104\\\\\angle b=\boxed{52^{\circ}}[/tex]

Question 7

[tex]\angle d+32=180-\angle d\\\\2\angle d=146\\\\\angle d=\boxed{73^{\circ}}[/tex]

Question 8

[tex]7x-80=3x\\\\-80=-4x\\\\x=20\\\\\implies \boxed{m\angle 1=m\angle 3=60^{\circ}}[/tex]

Answer:

x = 34 degrees

Step-by-step explanation:

Corresponding Angles Theorem: If 2 parallel lines are cut by a transversal, their corresponding angles are congruent.

Angle RNM = 78 degrees

Triangle RMN = 180 degrees

180 = 78 + 2x + x

102 = 3x

x = 34

The equation of line passing through points (4.5. 0) and (0, 9) is y = -2x + 9.

Suppose the given points are (x_1, y_1) and (x_2, y_2), then the equation of the straight line joining both two points is given by

[tex](y - y_1) = \dfrac{y_2 - y_1}{x_2 - x_1} (x -x_1)[/tex]

The graph of the picture shows two clear points (4.5. 0) and (0, 9)

[tex](y - 0) = \dfrac{9 - 0}{0 - 4.5} (x -4.5)\\\\\\(y - 0) = \dfrac{9 }{- 4.5} (x -4.5)\\\\\\-4.5y = 9(x -4.5)\\\\-4.5y = 9x - 40.5\\\\y = -2x + 9[/tex]

Hence, the equation of line passing through points (4.5. 0) and (0, 9) is y = -2x + 9.

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The amount Cindy should increase for each dimension of the scaled model will be 12 meters.

The scale factor is defined as the proportion of the new image's size to that of the previous image. decision-making.

Given that:-

The scale model will be solved as follows:-

Present volume = 2 x 4 x 6 = 48 cubic meters

Let the lengths be increased by x meters now the new volume will be:-

( 2 + x ) ( 4 + x ) ( 6 + x ) = 48 x 84

( x² + 6x + 8 ) ( 6 + x ) = 48 x 84

( x³ + 44x + 12x² - 3984 ) = 0

By solving the cubic equation we will get the value of x = 12 meters.

Therefore the amount Cindy should increase for each dimension of the scaled model will be 12 meters.

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The value of a is  0.10.

The value of b is 20.78.

The value of c is 0.02.

When two variables have inverse variation, the two variables move in opposite directions. If one variable increases, the other decreases.

p = 8.31 / V

V = 8.31 / p

a = 8.31 / 83.1 = 0.10

b = 8.31 / 0.4 = 20.78

c = 8.31 / 415.5 = 0.02

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Answer:

a= 0.1

b=20.775

c=0.10

Step-by-step explanation:

edge 2023

Answer:

-6,0 & -3,0

Step-by-step explanation:

The slope of the perpendicular line passes through C in GeoGebra.

GeoGebra is the software for the mathematical question for all levels of academics.

GeoGebra brings many mathematical problem solutions like geometry, algebra, spreadsheets, graphing, statistics, and calculus in one search engine.

Display the slope of and the slope of the perpendicular line passing through C.

Hence, the slope of the perpendicular line passes through C in GeoGebra.

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