f(x) = [tex]\sqrt{x+7} -\sqrt{x^2+2x-15}[/tex] find the domain

Answer:

see explanation

Step-by-step explanation:

Given

(x + 2)² = 25 ( take the square root of both sides )

x + 2 = ± [tex]\sqrt{25}[/tex] ← Step 1

x + 2 = ± 5 ← Step 2 ( subtract 2 from both sides )

x = - 2 ± 5 ← Step 3

Answer:

1/9 or 3^-2

Step-by-step explanation:

Ignore the value of 1/3 for now and just focus on the 3^2.

Find 3^2:

3*3 = 9

Now 9 is the denominator, therefore our answer would be 1/9 once you reassemble the fraction.

Because 1/9 is our new fraction, we can use a negative exponent to create the same result. This is because the negative exponent rule tells us that a number with a negative exponent should be put to the denominator. Therefore we can then use 3^-2.

Answer:

3^-2

Step-by-step explanation:

Answer:

[tex]$L=\frac{v^2}{2-2\cos(\theta)}$[/tex]

Step-by-step explanation:

Solve for [tex]L[/tex] in

[tex]$L-L \cos(\theta)=\frac{v^2}{2} \Longrightarrow L(1-\cos(\theta))=\frac{v^2}{2}$[/tex]

[tex]$L=\frac{v^2}{2(1-\cos(\theta))}=\frac{v^2}{2-2\cos(\theta)}$[/tex]

Answer:

h=7

Step-by-step explanation:

First we need to define the formula for surface area

2(wl+hl+hw)=100

Now we can replace length with x

That makes width .5x and height x+3

2(.5x^2+x^2+3x+.5x^2+1.5x)=100

2(2x^2+4.5x)=100

2x^2+4.5x=50

2x^2+4.5x-50=0

Insert into quadratic equation (a=2x^2, b=4.5, c=-50)

x=4 or -6.25

x can't be negative so x is 4

h=x+3=7

h=7

Answer:

V= 6,000 cm^3

Step-by-step explanation:

(15*20*10) + (10*20*15)

3000 + 3000

6000 cm^3

Answer:

6000 cm³

Step-by-step explanation:

20 * 10 * 15 + (20 * 10 * 15) = 6000 cm³

Answer:

2 cm^2/sec

Step-by-step explanation:

side of cube ---- x cm

volume = x^3

d(volume)/dt = 3x^2 dx/dt

when c = 20, d(volume)/dt = 10 cm^3/sec

10 = 3(20^2) dx/dt

dx/dt = 10/1200 = 1/120 cm/sec

Surface area = SA = 6x^2

d(SA)/dt = 12x dx/dt

so when x = 20, as above

d(SA)/dt = 12(20)(1/120) cm^2/sec

= 2 cm^2/sec

Answer:

5

Step-by-step explanation:

-32=-7n-12+3n

-32=-7n+3n-12

-32=-4n-12

-4n=-32+12

-4n=-20

n=-20/-4

n=5

Answer:

[tex]n=5[/tex]

Step-by-step explanation:

[tex]-32=-7n-12+3n\\\text{Combine Like Terms}\\-32=-7n+3n-12\\-32=-4n-12\\\text{Isolate the Variable}\\-32+12=-4n-12+12\\-20=-4n\\\text{Divide each side by -4}\\n=5[/tex]

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

Explanation:

Since we have a circle, the segments extending from the center outward to the edge of the circle are radius segments. Any two radii of the same circle are the same length. The triangle on the left with the 92 degree angle is isosceles. Any isosceles triangle has exactly two side lengths that are the same, which leads to the base angles being the same as well.

For the triangle on the left with angles a,b,92, the base angles are 'a' and 'b'. So a = b.

For any triangle, the angles add to 180

a+b+92 = 180

a+a+92 = 180 ... Replace b with 'a'

2a+92 = 180

2a = 180-92

2a = 88

a = 88/2

a = 44

angle b is also 44 as well

a+b+92 = 44+44+92 = 180

Answer:

cos x

Step-by-step explanation:

sin x = (sin x) / (1) and cot x = (cos x) / (sin x)

Put those fractions next to each other and multiply them out (numerator times numerator, denominator times denominator).

Cancel out the (sin x) in the numerator and denominator

You should be left with just (cos x) / (1), whoch equals just (cos x).

Hope this helps!

Answer:

2

Step-by-step explanation:

The number of oranges he has is a multiple of 6, so the number can be

6, 12, 18, 24, 30, 36, 42, 48, 54, etc.

He sells one orange, so now he an have:

5, 11, 17, 23, 29, 35, 41, 47, 53, etc.

All numbers above up to 53 are multiples of 1, so n can be 1.

Also 5 and 35 are multiples of 5, so n can be 5.

All numbers other than 5 and 35 are prime.

Answer: 2

Answer:

1. $64

2. 20%

3. 25%

4. $65.50

Step-by-step explanation:

1.   80 x 20% = ?  

method =  80 x 0.20 = 16 = $16 80-16 = 64 = $64

2. 14 x ? % = $11.20  

method = We divide 11.20/14 = 0.8  = 0.80 = 80% inverse of 80% = 20%

proof 14 x 0.20 = 2.80  so; 14 -2.80 = $11.20

3. 1000 x ? = $750

method = 1000/750 = 0.75   0.75 = 75%  inverse on original price = 25%

4. $55 x 10% = ?

method = 55 x 1.10 = 65.5  = $65.50

Answer:

At company for less than 2 years:

College degree: 0.24

No college degree: 0.76

At company for more than 2 years:

College degree: 0.7

No college degree: 0.3

Step-by-step explanation:

To find the relative frequency for those at the company for less than 2 years with a degree:

5 + 16 = 21

5 / 21 = 0.23809523809

≈ 0.24

To find the relative frequency for those at the company for less than 2 years with a degree:

5 + 16 = 21

16 / 21 = 0.7619047619

≈ 0.76

Check:

0.24 + 0.76 = 1

To find the relative frequency for those at the company for more than 2 years with a degree:

14 + 7 = 21

14 / 21 = 0.666..

≈ 0.70

To find the relative frequency for those at the company for less than 2 years with a degree:

14 + 7 = 21

7 / 21 = 0.333..

≈ 0.30

Check:

0.70 + 0.30 = 1

I really hope this helps! Tell me if I'm wrong!

Answer:

15 cm

Step-by-step explanation:

The area of an equilateral triangle is:

[tex]\frac{\sqrt{3} }{4}a^2[/tex], where a is the length of one side.

We can find the value of a (the length) by:

[tex]\frac{25\sqrt{3} }{4} = \frac{\sqrt{3} }{4}a^2[/tex]

[tex]a^2 = 25[/tex]

a = 5, so the side length of this triangle is 5 cm.

The perimeter of an equilateral triangle will be 3 times the length.

[tex]3\cdot5=15[/tex]

Hope this helped!

Answer:

Below

Step-by-step explanation:

● 7/25

Let' write this fraction as a decimal then convert it to a percentage

● 7/25 = 0.28

To get a percentage multiply it by 10

● 0.28 × 100

● 28 %

Answer:

0.28 or 28 percent

Step-by-step explanation:

1)The easiest way to solve this is with a calculator. Just enter in 7/25, and you get 0.28.

2) Now, 0.28 is out of 1, but we also want a percent, so you have to change it to make it out of 100. You do this by multiplying by 100, and to do that you simply move the decimal place 2 places back.

3) You would then get 28, so 28 percent.

Extra) You can also do the part I did with a calculator without, but it is much more time consuming. After you get 0.28, you would go through the steps listed above.

Answer:

7. 36     8. 1     9. 21

Step-by-step explanation:

You plug in the variables in the equation.

7.[tex]5^{2} +-4^{2} = 41[/tex]

8. [tex](5-4)^{2} = 81[/tex]

9. [tex]5+4^{2} =21[/tex]

Answer:

See explanation

Step-by-step explanation:

1. 8^5 = 32768

2. a^6

3. 5^5*9^3 = 2278125

5. (-3)^5 = -243

6. (3/4)³ = 27/64

7. a² + b² = 5² + (-4)² = 25 + 16 = 41

8. (a + b)² = (5 + 4)² = 9² = 81

9. a + b² = 5 + 4² = 5 + 16 = 21

Answer:

[tex]124.63[/tex]

Step-by-step explanation:

[tex]a = \pi \times r {}^{2} = \pi \times (6.3) {}^{2} = \pi \times 39.69[/tex]

[tex]\pi \times 39.6 = 3.14 \times 39.69 = 124.63[/tex]

Hope this helps ;) ❤️❤️❤️

The area of circle will be;

⇒ 124.63 cm²

What is Circle?

The circle is a closed two dimensional figure , in which the set of all points is equidistance from the center.

Given that;

The radius of circle = 6.3 cm

Now,

Since, The radius of circle = 6.3 cm

We know that;

Area of circle = π r²

Hence, We get;

⇒ Area of circle = 3.14 × 6.3²

                         = 3.14 × 39.69

                         = 124.63 cm²

Thus, The area of circle will be;

⇒ 124.63 cm²

Learn more about the circle visit:

https://brainly.com/question/24810873

#SPJ2

Answer:

ALL POSSIBLE DIMENSIONS OF THE RECTANGLE (whole numbers):

1 cm and 36 cm (Perimeter = 74 cm)

2 cm and 18 cm (Perimeter = 40 cm)

3 cm and 12 cm (Perimeter = 30 )

4 cm and 9 cm (Perimeter = 26)

6 cm and 6 cm Perimeter= 24 (squares are also considered rectangles, this is a square because of equal sides)

The rectangle with the greatest perimeter consists of the dimensions 1 cm and 36 cm.

EXPLANATION:

I listed all possible factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36

And have come up with 5 possible dimensions with numbers from the listed factors above (when the dimensions of each rectangle are multiplied the result will be 36/the area)

Multiplication is used because the area of a rectangle is length x width

And I used the formula for perimeter:

2 (l + w)

And found the greatest perimeter (74 cm) that belongs to the rectangle with the dimensions 36 cm and 1 cm.

Answer:

DE = 13.4 cm  (to 1 decimal place)

Step-by-step explanation:

Given: ABCD is a square

BC = AC = 12 cm    (opposite sides of a square are congruent)

E is midpoint of BC   (given)

BE = EC  = 12/2 = 6 cm

CD = AB = 12 cm   (opposite sides of a square are congruent)

angle ECD is a right angle (interior angles of a square are 90 deg.)

Consider right triangle ECD

DE = sqrt(EC^2+CD^2)    ............. pythagorean theorem

= sqrt(6^2+12^2)

= sqrt ( 36+144 )

= sqrt (180)

= 2 sqrt(45)

= 13.416 (to three dec. places)

Answer:

mean = 254.6

median = 120

mode = 60

midrange = 958

For average data sets i prefer by finding the mean

Step-by-step explanation:

mean :

(98+120+493+206+73+102+183+870+76+60+60+112+147+1018+201) ÷ 15 = 254.6

median : 60 60 73 76 98 102 112 120 147 183 201 206 493 870 1018

find the middle number

= 120

mode :

number that is more than one

= 60

midrange :

highest number - smallest number

= 1018 - 60

= 958

Answer:

b. 2:15

Step-by-step explanation:

oregano : pepper

1/6                1 1/4

Changing to an improper fraction

1/6                 5/4

Multiplying by 12 to get rid of the fractions

12 * 1/6           12*5/4

2                       15

Answer:

Let the height of the larger box = h

and length and width of the larger box = l and w , repectively

Now , Let find the volume of the larger box

Volume = length * width * height

So Volume of the larger box = l*w*h = lwh

Now the question says

the height of the smaller box is 80% of the height of the larger box

It means

Height of the smaller box = 80% of h = 0.80*h = 0.80h

and the other two dimensions are same so it means length and width of the smaller box = l and w

so, Volume of the smaller box = l*w*0.80h = 0.80lwh

So the Difference in the volume of the two boxes = Volume of larger box - Volume of smaller box

therefore , Difference in the Volume of two boxes = lwh - 0.80 lwh = 0.20lwh

Step-by-step explanation:

Answer:

Step-by-step explanation:

The system of equations is:

● 3x + 2y = 7

● 2x + 4y = 8

Where x is the price of a single coffee and y is the price of a single coffee

We will solve this simultaneous equations using the graphing method:

The solutions is the intersection point of to the lines.

(Picture below)

The intersection point is (1.5,1.25)

Answer:

x = 1.5

y =1.25

Step-by-step explanation:

3x+2y=7

2x+4y=8

Multiply the first equation by -2

-2(3x+2y=7 )

-6x-4y = -14

Add this to the second equation

-6x-4y = -14

2x+4y=8

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

-4x = -6

Divide by -4

-4x/-4 = -6/-4

x = 1.5

Now find y

3x+2y=7

3(1.5) + 2y = 7

4.5 +2y = 7

Subtract 4.5 from each side

2y = 2.5

Divide by 2

y = 1.25

The total depth covered  by the diver is 27(1/24) yards.

Yard is a unit to measure length. 1 yard is equal to 36 inches.

1 yard= 3 feet or (0.9144 meter)

What is

Given that,

First time depth reached by diver = 17(2/3) yards

In the second time, the depth reached by the diver is 9(3/8) yards more than the first time,

To find total depth,

Add depth covered by first time and second time,

Total depth = 17(2/3)+9(3/8)

                   =53/3+75/8

                   = 27(1/24)

The total depth covered by the diver is 27(1/24) yards.

To know more about Yard on

https://brainly.com/question/28365360

#SPJ5

Answer:

a=4

Step-by-step explanation:

When going from degrees to radians, 180 degrees is always going to equal π radians

That means 2π would be 360 degrees, and 4π would be 720

And since we're trying to find a in aπ when it's a 720 degree angle, we can conclude that a=4

Answer:

4

Step-by-step explanation:

We know that:

Then:

The value of a:

Answer: D) 48 inches by 64 inches

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

Explanation:

The scale factor is 1/4 = 0.25, meaning that the original preimage is larger and it is reduced to get the image. The reduced width is 12, so the original width is 12/0.25 = 48 inches. The reduced length is 16 making the original to be 16/0.25 = 64.

--------

note that

48*0.25 = 12

64*0.25 = 16

showing how a 48 by 64 rectangle is reduced to a 12 by 16 rectangle after applying the scale factor to each dimension

Answer: 8 hours

Step-by-step explanation:

Let x be the time before they meet ( in hours)

Speed of Sam = 12 mph

Sped of Fred = 9 mph

Distance = Speed × time

Distance covered by Sam in x hours = 12x

Distance covered by Fred in x hours = 9x

                                               (Distance)     (rate1) (time1)          (rate2) (time2)  

Total distance between them: 168             =     12      x        +      9    x

[tex]\Rightarrow\ 168= 21x\\\\\Rightarrow\ x=\dfrac{168}{21}=8[/tex]

Hence,  the number of hours before they meet if Sam runs 12 mph and Fred runs 9 mph. = 8

Answer:

Push-Ups: 15, 30, 45, 60, 75

Sit-Ups: 30, 60, 90, 120, 150

Step-by-step explanation:

Multiply the number of push-ups by 2 to find the number of sit-ups.

Answer: For the push ups fill them up with the numbers 45, 60, and 75/ For the sit-ups fill them up with 90, 120, and 150./ But I'm pretty confused to find the overall example would you try to explain a bit more.

Step-by-step explanation: