which is the value of (1.8 x 10^8) (8.3 x 10^-3)

The value of the expression 13 + (2^2 x 7) - 10 is 31

The expression is given as

13 + (2^2 x 7) - 10

Evaluate the exponent

So, we have

13 + (2^2 x 7) - 10 = 13 + (4 x 7) - 10

Evaluate the product

So, we have

13 + (2^2 x 7) - 10 = 13 + 28 - 10

Evaluate the sum

So, we have

13 + (2^2 x 7) - 10 = 41 - 10

Evaluate the difference

So, we have

13 + (2^2 x 7) - 10 = 31

Hence, the value of the expression 13 + (2^2 x 7) - 10 is 31

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The distance from the line [tex]y=\frac{1}{6} x+6[/tex] to the given point (-6,5) is o units .

Distance Formula : the distance between the line ax+by+c=0 and the point (p,q) is given by the formula

[tex]d=\frac{|ap+bq+c|}{\sqrt{a^{2} +b^{2} } }[/tex]

In the given question the equation of line is [tex]y=\frac{1}{6} x+6[/tex]

taking LCM and solving further

[tex]y=\frac{x+36}{6} \\ \\ 6y=x+36\\ \\ x-6y+36=0[/tex] ⇒equation of the line .

Given point (-6,5)

from above values we found that a=1 , b = -6 , c=36, p=-6, q=5.

Substituting the values in distance formula we get

[tex]d=\frac{|1*(-6)-6*5+36}{\sqrt{1^{2} +(-6)^{2} } }[/tex]

[tex]=\frac{|-6-30+36|}{\sqrt{37} }[/tex]

[tex]=\frac{-36+36}{\sqrt{37} }[/tex]

[tex]=0[/tex]

Therefore , the distance from the line [tex]y=\frac{1}{6} x+6[/tex] to the given point (-6,5) is 0 units.

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(x + 100, y - 75) is the function notation used to characterise the translation to a bottom of the hill.

The Pythagorean theorem states that the sum of a squares on a legs of a right triangle equals the square on hypotenuse (this same side opposite this same right angle)—or, in recognizable algebraic notation, a² + b² = c².

Now, as per the given question;

From the shown diagram,

AC  = b

Ab  = c

We must find the coordinates of a point B. If C(x,y), then the coordinates of points A and B are:

A(x, y−b) and B(x+c, y−b)

We need to figure out b and c. To find c, we should use sine function.

sinC = perpendicular/hypotenuses

sinC = c/BC

​Thus, c = BC sinC

c = 125sin53°

  =125⋅0.79863551

c ≈100

To find b, we are using the Pythagorean Theorem.

BC² = AC² + AB²

125² = b² + 100²

b² = 125² - 100²

b = √5625

b = 75

The coordinates of a point B are as follows:

B(x+c, y−b)

B(x+100, y−75).

Therefore, the translation to the bottom of the hill defined by the function notation is B(x+100, y−75).

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Answer:

$138.45

Step-by-step explanation:

The original price was 100% of the original price since 100% is the whole thing.

The price was discounted by 9%.

100% - 9% = 91%

That means the discounted price is 91% of the original price.

Let x = original price.

91% of x = $125.99

0.91x = 125.99

x = 125.99/0.91

x = 138.45

Answer: $138.45

Answer:

DF=12√2

FG=12√2

DG=24

Step-by-step explanation:

Ratio of special Right Triangle (45:45:90): x:x:x√2

Triangle DEF: x:x:x√2

x=12

12: 12: 12√2

So, DF= 12√2

Opposite (if q, then p) Base angle theorem. So, FD≅FG.

FD=12√2

FG=12√2

Ratio of 45:45:90 Triangle: x:x::x√2

x in triangle FDG= 12√2

12√2:12√2:12√2(√2)

12√2*√2=24

=12√2: 12√2: 24

DG=24

Ricardo will be left with $23.92 after 3 hours of Jet ski riding

Ricardo is on vacation so he went jet skiing

The Jet ski has a rental flat rate of $25

They also charge $17.75 per hour

Ricardo had $102.17

The amount spent in 3 hours is

17.75(3) + 25

= 53.25 + 25

= 78.25

The amount left is

= 102.17 - 78.25

= 23.92

Hence Ricardo has $23.92 left after the Jet ski ride

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Answer:

Step-by-step explanation:

1. We know it travels 346 meters in a second, we now need to multiply 346 by 20. This equals 6920

2. Sound travels 5971 meters per second. We need to multiply this by 12 to find the distance it travels in 12 seconds. 71652 meters

3. We know sound travels 5971 meters per second in stone and 5000 meters per second from the chart. We need to find the difference between these and multiply that by 17 to find the distance covered in 17 seconds.

5971-5000=971

971*17=16507

Sound travels 16507 more meters in 17 seconds through stone than it would travel in aluminum

The equation that represents the linear relationship between the x- values and y-values in the table is y = 6x - 5 .

What is a linear equation?

An algebraic equation of the form y=mx+b is referred to as a linear equation. m is the slope, and b is the y-intercept, and all that is involved is a constant and a first-order (linear) term. The variables in the preceding equation are y and x, and it is occasionally referred to as a "linear equation of two variables."

The equation y = 6x - 5  can represent the linear relationship between the x- values and y-values because it satisfies all the given values for x and y.

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Answer:

Greater than

Step-by-step explanation:

2x2+7x+2

----------

The area of the cross section of the planet at the equator is 5. 92 × 10^9 square miles

From the information given, we have the formula for area to be;

A = 3.14r²

Where 'r' is the radius of the shape

The radius of Jupiter = 2 * 5^2 * 11 * 79

This is simplified to = 2 × 25 × 11 × 79 = 43, 450

Substitute into the formula

Area = 3. 14 × (43, 450)²

Area = 3. 14 × 1. 89 × 10^9

Area = 5. 92 × 10^9 square miles

Thus, the area of the cross section of the planet at the equator is 5. 92 × 10^9 square miles

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Answer:

5,928,013,850

Answer:

g(x) = |4x+3|

Step-by-step explanation:

g(x) = f(x) - 2

=|4x+3|

10. m∠HIK (2x+15)°, m∠LIJ = (5x-27)°, m∠HIK =

if they are vertice angles then they are equal to each other or

they both add up to 180°

A.

2x+15=5x-27

3x=42

x=14

B.

(2x+15)° + (5x-27)° = 7x-12

7x-12 = 180

7x=192

x = 27 3/7 or 27.43

If Edgar is a high school senior who has great grades and just received a notification that he was awarded a few scholarships in the amounts of $4,500, $7,500, and $750 while his expected tuition with books and fees is $25,000, then the amount of money Edgar will need to pay for the rest of his education bill is equal to $12,250.

The amount of money Edgar will need to pay can be determined by the subtraction of the total tuition with books and fees from the total amount of scholarships awarded to Edgar.

The total amount of scholarships awarded to Edgar can be determined by the sum of all of the scholarships.

Total amount of scholarships = 4500 + 7500 + 750

Total amount of scholarships = $12,750

Now the amount that Edgar will need to pay for the rest of his education bill can be determined by subtraction.

Amount to be paid by Edgar =  Tuition with books and fees - Total amount of scholarships

Amount to be paid by Edgar  = 25,000 - 12750

Amount to be paid by Edgar = $12,250

Hence, the amount of money Edgar will need to pay for the rest of his education bill is calculated to be $12,250.

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Answer:

-59

Step-by-step explanation:

use pemdas

1+10-70

11-70

-59

Answer:

Step-by-step explanation

Height for time = 8 seconds

h = -4.9t^2 + 259t + 423

h = -4.9(8)^2 + 259(8) + 423

h = -313.6 + 2072 + 423

h = 2181.4 meters at 8 seconds

Heoght for time = 0 seconds

h = -4.9t^2 + 259t +423

h = -4.9(0)^2 + 259(0) + 423

h = 0 + 0 + 423

h = 423 meters at 0 seconds

The solutions of the given equation 11/3x - 1/3 = -4/x² are x = -1 and x = 12

In this question, we have been given an equation.

11/3x - 1/3 = -4/x²

We need to solve given equation.

⇒ 11/3x - 1/3 = -4/x²

⇒ (33 - 3x)/9x = -4/x²

⇒(33 - 3x)/9 = -4/x

⇒ x(33 - 3x) = -36

⇒ -3x² + 33x + 36 = 0

⇒ x² - 11x - 12 = 0

⇒ x² - 12x + x - 12 = 0

⇒ x(x - 12) + 1(x - 12) = 0

⇒ (x - 12)(x + 1) = 0

⇒ x - 12 = 0           or       x + 1 = 0

⇒ x = 12           or          x = -1

Now we need to check above solutions.

Substitute x = 12 in given equation.

⇒ 11/3(12) - 1/3 = -4/(12)²

⇒ 1/3 (11/12 - 1) = 1/3(-4/48)

⇒ -1/12 = -1/12

⇒ LHS = RHS

Now substitute x = -1 in given equation.

⇒ 11/3(-1) - 1/3 = -4/(-1)²

⇒ -12/3 = -4/1

⇒ -4 = -4

⇒ LHS = RHS

Therefore, the solutions of the given equation 11/3x - 1/3 = -4/x² are x = -1 and x = 12

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The sentence describes the error is that A) Both terms aren’t multiplied by 8x, so 8x can’t go in front of the parentheses.

It should be noted that the expression given is illustrated as 32x and 16.

In this case, it should be noted that the common factor between the expression is 8.

Therefore, the sentence describes the error is that both terms aren’t multiplied by 8x, so 8x can’t go in front of the parentheses.

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Answer: Therefore, the sentence describes the error in that both terms aren’t multiplied by 8x, so 8x can’t go in front of the parentheses.

Step-by-step explanation:

Answer:

[tex]y - 2 = -\frac34(x - 4)[/tex]

Step-by-step explanation:

Hello!

The equation in #17 is written in Slope-Intercept Form: [tex]y=mx+b[/tex]

Point Slope form is the equation given slope and a point: [tex]y - y_1 = m(x - x_1)[/tex]

The point given to us is (4,-2), which we can use as x1 and y1.

The slope is given in the slope-intercept form equation: -3/4

Plug in the values to find the equation:

The equation is [tex]y - 2 = -\frac34(x - 4)[/tex].

Answer: y = -4x + 3

Step-by-step explanation:

Line touches at point 3 on the y axis

Goes up 4 and left by 1

The solution of the system of equations involving x + 3y = 5 and -2x - 4y = -5 is (-5/2 , 5/2).

A system of linear equations is a set of two or more equations which includes common variables. To solve system of equations, we must find the value of the unknown variables used in the equations that must satisfy both equations.

There are three methods that can be used to solve system of linear equations.

1. Elimination

2. Substitution

3. Graphing

Using substitution method, given two linear equations in x and y,

x + 3y = 5     (equation 1)

-2x - 4y = -5     (equation 2)

Using the first equation, find the value of one variable, lets say x, in terms of the other.

x + 3y = 5     (equation 1)

x = 5 - 3y

Substitute the equation of x to the second equation.

-2x - 4y = -5     (equation 2)

-2(5 - 3y) - 4y = -5

-10 + 6y - 4y = -5

Combining all terms containing the variable y on one side and the constants on the other side of the equality, and solving for y.

-10 + 6y - 4y = -5

6y - 4y = -5 + 10

2y = 5

y = 5/2

Substitute the value of y in the equation of x.

x = 5 - 3y

x = 5 - 3(5/2)

x = 5 - 15/2

x = -5/2

Hence, the solution of the given system of equations is (-5/2 , 5/2).

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According to the given statement The preceding population was =  62,500.

A % is a relative figure that represents the hundredth part of any amount. One percent (symbolized 1%) is a one-hundred part; consequently, 100 percent denotes the complete amount and 200 percent defines twice the supplied amount.

Percent originated from the Latin adverbial phrase per centum, which means "by the hundred." The Latin phrase made its way into English in the 16th century. Later, it was abbreviated to % with a period. The period was eventually eliminated, and the two components amalgamated to form the contemporary one-word form %.

The current population of a city = 80000

A city's population has grown by 28% since the last census.

measured.

We have to calculate the previous population before increasing 28%.

Let the previous population be p

p +(28% × p) = 80000

p + 0.28p = 80000

1.28p = 80000

p = 80000/1.28

p = 62,500

The preceding population was =  62,500.

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Answer:

Step-by-step explanation:

[5x+3x-(-2x)]+[-3-8]=9

10x+(-11)=9

10x=20

x=2

The sum of finite arithmetic series  8+9+10+. . . . . . +15 is 92

Suppose we are given an arithmetic series:

      a(1) + a(2) + ... + a(n)

Then the sum is:

      S(n) = n/2 (a(1) + a(n))

Where: a(1) = first term

a(n) = nth term

The given series is:

      8+9+10+. . . . . . +15

We need to find n such that a(n) = 15.

Recall that in an arithmetic sequence:

      a(n) = a(1) + (n -1) . d

where d = difference between 2 consecutive terms.

Substituting a(1) = 8, and  d = 9 - 8 =1 into the formula:

a(n) = 8 + (n -1) . 1

15 = 7 + n

n = 8

Substitute n = 8 into the sum formula:

S(n) = n/2 (a(1) + a(n))

S(8) = 8/2 . (8 + 15)

        = 4 . 23 = 92  

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The statement "The distance between a line and a plane can be found" is sometimes true.

Given,

The statement "The distance between a line and a plane can be found".

The distance between the point and the plane can be found by the taking a point on the line and finding the perpendicular distance from line to the plane.

But we can't apply this method in every case. We can only apply when either the line is parallel to the plane or the line intersects the plane.

Hence, the statement "The distance between a line and a plane can be found" is sometimes true.

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7 - The geocentric model says that the earth is at the center of the cosmos or universe, and the planets, the sun and the moon, and the stars circles around it. The early heliocentric models consider the sun as the center, and the planets revolve around the sun.

8 - Modele A is the most accurate cause the sun, earth, & moon are in a straight line & in the time and space all the planets are in one straight line.

There is need of total of 25 boxes of same size for the next lower level.

A sequence can be taken as the set of numbers having a particular order for all the terms or we can say that arrangement of numbers in some order is known as sequence.

Some examples for sequence are :

2,4,6,8,10,12

3,9,27,81,243

The recursive sequence is the sequence in which any term in the sequence can be find with the help of previous term of that sequence.

In a sequence , first term always known as initial term.

and difference between two terms are known as common difference. It is denoted by d.

General form of sequence is :

[tex]a_1,a_2,a_3,----,a_n[/tex]

where , [tex]a_n[/tex] = last term in sequence.

According to question,

The boxes in each of successive levels make a sequence.

Also, number of boxes at level n = [tex]n^2[/tex]

As upto four level the number of boxes are 16.

at level 5 , n = 25

Thus, the total  boxes of equal or same size need for next lower level is 25.

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The complete question is :

Suppose you're stacking boxes in levels which make squares. The numbers of boxes in each successive levels make a sequence. The figure show top four levels as view from top or above.

a. How many boxes of same size would need for next lower level?

b. How many boxes of same size would need to add the 3 levels?

c. Suppose you are stacking 285 boxes. Then, how many total levels will you have?

30x is the value of the given equation .

Algebraic expression multiplication is the operation of multiplying two given expressions made up of variables and constants. An algebraic expression is one that incorporates variables and integer constants.

x = 5

y = 3x

2xy = 2 * 5 * 3x ( plugging in the value )  

       = 30x

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Answer:|x| means “distance between a number and zero

Step-by-step explanation:

Also known as absolute value

ex l5l=5 & l5l=-5

Answer:

7.5

Step-by-step explanation:simply divide 30 and 4 and the answer is 7.5