kelly used 2.1 x 10^6 KB of data so far this month. her younger brother joseph used 7 x 10^5 KB of the data so far this month if their share family plan allows them to use 3,000,000 KB of the data each month, how much data usage o they have available for the remainder of this month?

Answer:  D. (-2, -1)

Step-by-step explanation:

Here we do two reflections to the point (-1, 2).

First, we do a reflection over the line x = y.  Remember that a reflection over a line keeps constant the distance between our point and the given line, so we have that for a pint (x, y), the reflection over the line y = x is:

Ry=x (x, y) = (y, x)

so for our point, we have:

Ry=x (-1, 2) = (2, -1)

Now we do a reflection over the y-axis, again, a reflection over a line keeps constant the distance between our point and the given line, so if we have a point (x,y) and we do a reflection over the y-axis, our new point will be:

Ry-axis (x,y) = (-x, y)

Then in our case:

Ry-axis (2, -1) = (-2, -1)

The correct option is D.

Answer:

[tex]\boxed{ \{7, 6, 5, 3 \} }[/tex]

Step-by-step explanation:

The domain is all possible values for x.

The range is all possible values for f(x) or y.

The domain given is {-3, -2, -1, 1}.

Plug x as {-3, -2, -1, 1} and find the f(x) or y values.

[tex]f(-3)=-(-3)+4=7\\f(-2)=-(-2)+4=6\\f(-1)=-(-1)+4=5\\f(1)=-(1)+4=3[/tex]

The range is {7, 6, 5, 3}, when the domain is {-3, -2, -1, 1}.

Answer:

For "Negative 23 greater-than x" , highlight the left half of the number line starting at -23 and use a parenthesis ) on -23.

For "x greater-than-or-equal-to negative 23", highlight the right half of the number line starting at -23, and use a square bracket [ on -23.

Step-by-step explanation:

Start by locating the number -23 on the number line. Please see attached image to accompany the explanation.

In the first case:  "Negative 23 greater-than x" , which is expressed mathematically as:

[tex]-23 >x[/tex]

notice that "x" has to be strictly smaller than the number -23, therefore those sought x values must reside to the left of the number -23, so we have to highlight that half of the number line. Apart from that, we need to include a symbol on top of the number -23, that indicates that -23 itself shouldn't be considered as part of the set, that symbol is by convention a parenthesis ).

In the second case: "x greater-than-or-equal-to negative 23", which is expressed mathematically as:

[tex]x\geq -23[/tex]

notice that "x" has to be greater than or equal to the number -23, therefore those sought x values must reside to the right of the number -23, so we have to highlight that half of the number line. Apart from that, we need to include a symbol on top of the number -23, that indicates that -23 itself should be considered as part of the set, that symbol is by convention a square bracket [.

Answer:

the answer is A

Step-by-step explanation:

Answer: 0.25

Step-by-step explanation:

To find :  decimal number represented by  point A on the given number line.

Given:  Vertical number line is shown from negative 2.00 to 0 to positive 2.00.There are tick marks to show increments of 1 over 4.

Point A is plotted at the third tick .

That means, Point A is marked at 1 over 4.

1 over 4 = [tex]\dfrac{1}{4}=0.25[/tex]    [divide 1 by 4]

Hence, the point A  represents 0.25 on the given number line.

Answer:

Step-by-step explanation:

Where is the picture

Answer: 15

Step-by-step explanation:

General terms in AP

f, f+d, f+2d, f+3d, ....  , where f= first term and d= common difference.

The given A.P. : 18, a, b, - 3

here, f= 18    

[tex]f+d= a ...(i)\\\\f+2d = b ...(ii)\\\\f+3d= -3 ...(iii)\\\\[/tex]

Put f= 18 in (iii) ,

[tex]18+3d=-3\\\\\Rightarrow\ 3d= -3-18\\\\\Rightarrow\ 3d= -21\\\\\Rightarrow\ d=-7[/tex]

Put f= 18 and d= -7 in (i) and (ii) , we get

[tex]a=18+(-7)=11\\\\b=18+2(-7)\\\\\Rightarrow\ b=18-14\\\\\Rightarrow\ b=4[/tex]

Now, [tex]a+b= 11+4=15[/tex]

Hence, the correct answer is "15".

Complete question:

A group of 8 friends went to lunch and spent a total of $76, which included the food bill and a tip of $16. They decided to split the bill and tip evenly among themselves. Which equations and solutions describe the situation? Check all that apply. The equation 1/8(x+16)=76/8 represents the situation, where x is the food bill. The equation 1/8 (x+16)=76 represents the situation, where x is the food bill. The solution x=60 represents the total food bill. The solution x=60 represents each friend’s share of the food bill and tip. The equation 8(x+16)=76 represents the situation, where x is the food bill.

Answer:

The equation 1/8(x+16)=76/8 represents the situation, where x is the food bill

The solution x=60 represents the total food bill

Step-by-step explanation:

Given the following :

Total amount spent = $76

Amount paid as tip = $16

Number of friends = 8

Total Cost of lunch consists of:

Actual Cost of food + amount of tip

Let actual cost of food = x

Total cost of lunch is thus :

x + $16 = $76

If the friends are to each the bill equally:

Then:

Divide both sides by 8:

(1/8)* (x + 16) = 76/8

Therefore,

(x + 16) / 8 = 76/8

x + 16 = 76 / 8

(x + 16)/8 = 9.5

x + 16 = 9.5 * 8

x + 16 = 76

x = 76 - 16

x = 60

Answer:

A

and

C

Step-by-step explanation:

Answer:

0.6

Step-by-step explanation:

0.6-0.45=0.15

The value of y from the given equation is 0.60.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

The given equation is 0.15=y-0.45.

The solution of an equation is the set of all values that, when substituted for unknowns, make an equation true.

Here, 0.15=y-0.45

y=0.15+0.45

y=0.60

Therefore, the value of y is 0.60.

To learn more about an equation visit:

https://brainly.com/question/14686792.

#SPJ2

Answer:

[tex]\huge\boxed{f = 5\ Hz}[/tex]

Step-by-step explanation:

Given:

Time period = T = 0.2 sec

Required:

Frequency = f = ?

Formula:

f = 1/T

Solution:

f = 1/0.2

f = 5 Hertz

Answer:

[tex] \boxed{\sf Frequency \ (f) \ of \ the \ wave = 5 \ Hz} [/tex]

Given:

Time Period (T) = 0.2 s

To Find:

Frequency (f) of the wave

Step-by-step explanation:

[tex] \sf Frequency (f) = \frac{1}{Time Period (T)} [/tex]

[tex] \sf f = \frac{1}{0.2} [/tex]

[tex] \sf f = \frac{1}{0.2} \times \frac{10}{10} [/tex]

[tex] \sf f = \frac{10}{2} [/tex]

[tex] \sf f = \frac{ \cancel{2} \times 5}{ \cancel{2}} [/tex]

[tex] \sf f = 5 \: Hz[/tex]

━━━━━━━☆☆━━━━━━━

▹ Answer

a = 8

▹ Step-by-Step Explanation

a/4 + 4 = 6

Multiply both sides:

a + 16 = 24

Subtract 16 from both sides:

16 - 16 = a

24 - 16 = 8

a = 8

Hope this helps!

CloutAnswers ❁

━━━━━━━☆☆━━━━━━━

Answer:

a = 8

Step-by-step explanation:

a/4 + 4 = 6

Subtract 4 from each side

a/4 + 4-4 = 6-4

a/4 = 2

Multiply each side  by 4

a/4 * 4 = 2*4

a = 8

Answer:

Step-by-step explanation:

The explicit rule for determining the nth term of a geometric sequence is expressed as Tₙ = arⁿ⁻¹ where;

a is the first term of the geometric sequence

r is the common ratio

n is the number of terms

If a geometric sequence has a common ratio of 2 and the 12th term is −12,288, then;

T₁₂ = ar¹²⁻¹

T₁₂ = ar¹¹

Given T₁₂ = -12,288 and r = 2, we can calculate the first term a

-12,288 = a2¹¹

a = -12,288/2¹¹

a =  -12,288/2048

a = -6

Since the explicit rule for determining the nth term of a geometric sequence is expressed as Tₙ = arⁿ⁻¹, then for the sequence given, the explicit rule will be;

Tₙ = -6(2)ⁿ⁻¹

Tₙ = -6 * 2ⁿ * 2⁻¹

Tₙ = -6 * 2ⁿ * 1/2

Tₙ = -3(2)ⁿ

Hence the explicit rule that describes this sequence is Tₙ = -3(2)ⁿ

Answer:

Solution : Degree 4

Step-by-step explanation:

We only have one variable in this case, x. Therefore we can take the degree of this variable to be our solution, 4. As you can see x^4 will have a degree of 4, as that is the exponent present.

Answer:

Below

Step-by-step explanation:

All figures are squares. The area of a square is the side times itself

Let A be the area of the big square and A' the area of the small one in all the 5 exercices

51)

● (a) = A - A'

A = c^2 and A' = d^2

● (a) = c^2 - d^2

We can express this expression as a product.

● (b) = (c-d) (c+d)

■■■■■■■■■■■■■■■■■■■■■■■■■■

52)

● (a) = A-A'

A = (2x)^2 = 4x^2 and A'= y^2

● (a) = 4x^2 - y^2

● (b) = (2x-y) ( 2x+y)

■■■■■■■■■■■■■■■■■■■■■■■■■■

53)

● (a) = A-A'

A = x^2 and A' = y^2

● (a) = x^2-y^2

● (b) = (x+y) (x-y)

■■■■■■■■■■■■■■■■■■■■■■■■■■

54)

● (a) = A-A'

A = (5a)^2 = 25a^2 and A' =(2b)^2= 4b^2

● (a) = 25a^2 - 4b^2

● (a) = (5a-2b) (5a+2b)

■■■■■■■■■■■■■■■■■■■■■■■■■■

55)

● (a) = A - 4A'

A = (3x)^2 = 9x^2 and A'= (2y)^2 = 4y^2

● (a) = 9x^2 - 4 × 4y^2

● (a) = 9x^2 - 16y^2

● (a) = (3x - 4y) (3x + 4y)

Answer:

Yes, you are correct.

Step-by-step explanation:

You are substituting the measure of angle x as the measure of angle a since they are congruent to each other.

Answer:

Tess wins the prize.

Step-by-step explanation:

[tex]\boxed{\text{Indi}: 2-3}[/tex]

[tex]\boxed{\text{Mark}: -7-(-4)}[/tex]

[tex]\boxed{\text{Tess}: -1-(-7)}[/tex]

The expression of Indi's card is 2 - 3 = -1

The expression of Mark's card is -7 - (-4) = -7+4= -3

The expression of Tess's card is -1 - (-7) = -1+7= 6

Answer: This is a periodic relation.

Step-by-step explanation:

This is a periodic relation, that can be modeled with a sinusoidal relation, that relates the height as a function of time.

Then we can write this as h(t) = A*sin(C*t + F) + B

Where A is the amplitude, C is a constant that depends on the period, F is a phase shift, and B is the midpoint of the function.

2*A is the distance between the maximum height and the minimum height.

B is the middle height of the Femis Wheel.

Answer:

U = x + 4 and V = 2y^5.

Step-by-step explanation:

Square root of (x + 4)^2 = x + 4

Square root of 4y^10 = 2y^5

U = x + 4 and V = 2y^5.

(U - V)^2 = U^2 - 2UV + V^2

= (x + 1)^2 - 2 (2y^5 (x + 1) + 4y^10

= (x + 1)^2 - 4y^5 (x + 4) + 4y^10

Answer:

U = x + 4 and V = 2y^5.

Step-by-step explanation:

Answer:

BH= 108 --> 1st until 6th space

so, 108/6 = 18 for each space

DE...?

DE only use 1 space so the answers is 18 unit

I hope this helps^_^

Answer:  4+2 x (14-3)

Step-by-step explanation:

Answer:

The correct option is;

B. s ≥ 12 - t, s ≤ 30 - t, s ≤ 24 - 0.66·t

Step-by-step explanation:

The given parameters are;

The number of T-shirts, t, and shorts, s, Tim must design a day = 12

The maximum number of T-shirts and shorts Tim can design a day = 30

The maximum number of hours Tim can work = 18 hours

Therefore, we have;

The number of shorts Tim designs in a day is ≥ The minimum number of T-shirts and shorts Tim must design a day less the number of T-shirts Tim designs

Which gives;

s ≥ 12 - t

Also the number of shorts Tim designs in a day is ≤ The maximum number of T-shirts, and shorts, Tim can design a day less the number of T-shirts Tim designs

Which gives;

s ≤ 30 - t

The number of 45 minute period for the design of shorts in 18 hours = 18×60/45 = 24

The fraction of 36 minutes in 45 minutes = 36/45 = 0.667

Therefore we have;

The number of shorts Tim designs in a day is ≤ The number of 45 minute periods in 18 hours less the number of 36 minutes periods used to design T-shirts

Which gives;

s ≤ 24 - 0.66·t

The correct option is s ≥ 12 - t, s ≤ 30 - t, s ≤ 24 - 0.66·t.

Answer:

B. s> 12-tss 30 - t Ss 24 -0.66t, s 2 0; t> 0

Step-by-step explanation:

Hope this helps!!

Answer:

3053.5517 cm^3 ; 1/8

Step-by-step explanation:

Given the following :

Volume (V) of sphere = (4/3)πr^3 where r = radius

Diameter of sphere = 18 ; radius(r) = diameter / 2 = 18/2 = 9cm

V = (4/3) × π × 9^3

V = 1.3333 × π × 729

V = 3053.5517 cm^3

When diameter(d) is reduced to half

d = d/2

Volume (V1) of sphere with diameter 'd' =

V1 = (4/3)π(d/2)^3

Volume (V2) of sphere with diameter 'd' reduced to half, d = d/2, d/2 * 1/2 = d/4

V2 = (4/3)π(d/4)^3

V1 / V2 = [(4/3)π(d/2)^3] / [(4/3)π(d/4)^3]

V1 / V2 = (d/2)^3 / (d/4)^3

V1 / V2 = [d^3 / 2^3] / [d^3 / 4^3]

V1 / V2 = 8 / 64

V1 / V2 = 1 / 8

Answer:

first blank is 972

second blank is 1/8

yup

Step-by-step explanation:

Answer:

three terms

Step-by-step explanation:

3x + 2y + 8z

Since we cannot simplify

There are three terms

3x, 2y, 8z

Step-by-step explanation:

Here,

radius (r)= 2cm

height(h)=5cm

now,

according to the question we must find the surface area of cylinder so,

by formulae ,

a= 2.pi.r(r+h)

now,

a= 2×3.14×2(2+5)

by simplifying it we get,

The surface area of cylinder is 87.92 cm^2.

Hope it helps

Answer:

  842, 743, 394, 305, 836

Step-by-step explanation:

We arbitrarily chose the ones digit to start with as 2. (It must be 5 or less.) The other two digits are chosen by a random number generator, as shown in the attached.

The 5 three-digit numbers we chose are ...

  842, 743, 394, 305, 836

Answer:

The only criteria the question gives are that there must be 5 numbers, and the numbers must have 3 digits. The ones digit in the numbers should go up by 1.

So, we can have 111, 112, 113, 114, and 115.

Hope this helps!

Answer:

19 throws.

Step-by-step explanation:

For her success rate to be 80% in 37 throws she must make  0.8 * 37

= 29.6 throw - that is 30 to nearest throw.

So for the next 20 throws she must make  30 - 11 = 19 throws.

Answer:

First mechanic worked for = 10 hours

Second mechanic worked for = 15 hours.

Step-by-step explanation:

Let the number of hours the First mechanic worked = X

Let the number of hours the Second mechanic worked = Y

The first mechanic charged = $85 per hour

The second mechanic charged = $90 per hour

We are told in the question that: The mechanic worked for a combined total of 25 hours, and together they charged a total of $2200

Hence, we have the following equations from the above question

85X + 90Y = 2200....... Equation 1

X + Y = 25 ........ Equation 2

X = 25 - Y

Substitute 25 - Y for X in equation 1

85(25 - Y) + 90Y = 2200

2125 - 85Y + 90Y = 2200

Collect like terms

5Y = 2200 - 2125

5Y = 75

Y = 15

Since Y is the number of hours the second mechanic worked, hence, the second mechanic worked for 15 hours.

X + Y = 25 ........ Equation 2

Y = 15

X + 15 = 25

X = 25 - 15

X = 10

Since X represents the number of hours that the first mechanic worked, hence, the first mechanic worked for 10 hours.

Therefore, the first mechanic worked for 10 hours and the second mechanic worked for 15 hours.

If [tex]x-a[/tex] is a factor of a polynomial [tex]P(x)[/tex] then, [tex]a[/tex] is its root.

So [tex]-2[/tex] is a root of [tex]x^3-19x-p[/tex]

[tex](-2)^3-19\cdot(-2)-p=0\\-8+38-p=0\\p=30[/tex]

Answer:

  x = {π/4, 7π/6, 5π/4, 11π/6} +2kπ . . . for any integer k

Step-by-step explanation:

  [tex]\dfrac{\sin^3{x}}{1+\cos{x}}+\dfrac{\cos^3{x}}{1+\sin{x}}=\cos{2x}+2\cos{x}-1\\\\\dfrac{\sin{x}(1-\cos^2{x})}{1+\cos{x}}+\dfrac{\cos{x}(1-\sin^2{x})}{1+\sin{x}}=\cos^2{x}-\sin^2{x}+2\cos{x}-1\\\\\sin{x}(1-\cos{x})+\cos{x}(1-\sin{x})=\cos^2{x}-\sin^2{x}+2\cos{x}-1\\\\\sin{x}+\cos{x}-2\sin{x}\cos{x}=2\cos{x}-2\sin^2{x}\qquad\text{use $1=s^2+c^2$}\\\\\sin{x}+2\sin^2{x}-\cos{x}-2\sin{x}\cos{x}=0\\\\\sin{x}(1+2\sin{x})-\cos{x}(1+2\sin{x})=0\\\\(\sin{x}-\cos{x})(1+2\sin{x})=0[/tex]

This will have solutions where the factors are zero.

sin(x) -cos(x) = 0

Dividing by cos(x), we have ...

  tan(x) -1 = 0

  x = arctan(1) = π/4, 5π/4

1 +2sin(x) = 0

  sin(x) = -1/2

  x = arcsin(-1/2) = 7π/6, 11π/6

The four solutions in the interval [0, 2π] are x = {π/4, 7π/6, 5π/4, 11π/6}. Solutions repeat every 2π radians.

_____

Additional comment

We have made use of the factoring of the difference of squares:

  (1 -a^2) = (1 -a)(1 +a)

and we have made use of the cosine double angle identity:

  cos(2x) = cos(x)^2 -sin(x)^2

The "Pythagorean" identity for sine and cosine was used several times:

  1 = sin(x)^2 +cos(x)^2