As the planets revolve around the Sun, sometimes Earth is between the Sun and Mars (Point A) and sometimes the Sun is between Earth and Mars (Point B). The distance from the Sun to Mars is approximately 2.3 times 10 Superscript 8 km, and the distance from the Sun to Earth is approximately 1.5 times 10 Superscript 8 km.

The rotations of Earth and Mars around the sun.
Which statements are true? Check all that apply.

The value for the hotspots of the similar triangles ∆ABC and ∆PWR are:

(1). angle B = 68°

(2). PQ = 5cm

(3). BC = 19.5cm

(4). area of ∆PQR = 30cm²

Similar triangles are two triangles that have the same shape, but not necessarily the same size. This means that corresponding angles of the two triangles are equal, and corresponding sides are in proportion.

(1). angle B = 180 - (22 + 90) {sum of interior angles of a triangle}

angle B = 68°

Given that the triangle ∆ABC is similar to the triangle ∆PQR.

(2). PQ/7.5cm = 12cm/18cm

PQ = (12cm × 7.5cm)/18cm {cross multiplication}

PQ = 5cm

(3). 13cm/BC = 12cm/18cm

BC = (13cm × 18cm)/12cm {cross multiplication}

BC = 19.5cm

(4). area of ∆PQR = 1/2 × 12cm × 5cm

area of ∆PQR = 6cm × 5cm

area of ∆PQR = 30cm²

Therefore, the value for the hotspots of the similar triangles ∆ABC and ∆PWR are:

(1). angle B = 68°

(2). PQ = 5cm

(3). BC = 19.5cm

(4). area of ∆PQR = 30cm²

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To simplify the expression (2x²-3x² +1)(x+2)²-4, we first combine like terms within the parentheses and then expand the resulting expression.

1. Simplifying (2x²-3x² +1)(x+2)²-4:

We combine like terms within the parentheses:

(-x² + 1)(x+2)² - 4

Expanding the expression using the distributive property:

(-x² + 1)(x² + 4x + 4) - 4

Now, multiply each term:

- x⁴ - 4x³ - 4x² + x² + 4x + 4 - 4

Combining like terms:

- x⁴ - 4x³ - 3x² + 4x

Therefore, the simplified expression is -x⁴ - 4x³ - 3x² + 4x.

2. Expanding (x+1)(x+2)(x+3)-(x-2)(x+3):

Using the distributive property, we multiply each term:

(x² + 3x + 2)(x+3) - (x² + x - 6)

Expanding further:

x³ + 3x² + 2x + 3x² + 9x + 6 - x² - x + 6

Combining like terms:

x³ + 4x² + 10x + 12 - x² - x + 6

Simplifying:

x³ + 3x² + 9x + 18

Therefore, the expanded expression is x³ + 3x² + 9x + 18.

3. Finding A, B, and C in Ax²+2x+3=x²-Bx+C:

Comparing the coefficients of corresponding terms on both sides of the equation, we have:

A = 1

B = -2

C = 3

Therefore, A = 1, B = -2, and C = 3 in the given equation Ax²+2x+3=x²-Bx+C.

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Answer:

19 inches total

Step-by-step explanation:

the value of x will be 25.

What is an Equations?

Equations are mathematical statements with two algebraic expressions on either side of equals (=) sign. It illustrates the equality between the expressions written on the left and right sides. To determine the value of a variable representing an unknown quantity, equations can be solved. A statement is not an equation if there is no "equal to" symbol in it. It will be regarded as an expression.

D- 25

120-70=50

2x=50

50/2=25

Hence the value of x will be 25.

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Answer:

5y^5

Step-by-step explanation:

there is no real solution. really i just simplified. if you wanted a real answer y would have to be giving. if not then this is all the question is asking. for you to simplify

Answer:bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb

Step-by-step explanation:

The narrator of Fever 1793 helps compendiums imagine Philadelphia summers by describing about mosquitoes, blowflies, and hornets buzzing.

This refers to the liar of an event to talk about an event in the order of circumstance.

Given

The opening judgment of Fever 1793," From the moment Colette Ogilvie passed out, Philadelphia's church bells chimed continuous.

The narrator of Fever 1793 makes it easy for readers to picture her upbringing by expressing her love for the nation, describing how it felt to see her words printed, confessing to counting on her fingers, and describing how it felt to voice her anger with front-of-the-house service.

On the road corners, shots were fired, and a cannon was fired in the public forecourt to clear the air. In addition to that, hornets, blowflies, and mosquitoes swarmed about us continuous.

The noise was annoying." Illustration demonstrates how mosquitoes, blowflies, and hornets agonized Philadelphians with unheroic fever in 1793.

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Answer:

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

General equation for inverse variation is:

Find the value of k by substituting values of x and y:

Substitute the value of k to get the equation:

Answer:

  (a)  135

  (b) 28%

Step-by-step explanation:

We can write equations relating pears to oranges, solve them, and then find the number of apples. Let p, o, and 'a' represent the numbers of pears, apples, and oranges.

  p/o = 5/3 . . . . . the ratio of pears to oranges is 5:3

  p -o = 54 . . . . . there are 54 more pears than oranges

  a -o = 3 . . . . . .  there are 3 more apples than oranges

__

Multiply the first equation by 3/5o to get ...

  3/5p = o

Substitute that into the second equation:

  p -(3/5)p = 54

  2/5p = 54 . . . . . . simplify

  p = 54(5/2) = 135 . . . . multiply by 5/2 to get the number of pears

There are 135 pears in the basket.

__

  a = 3 +o = 3 +3/5p = 3 +3/5(135) = 3 +81 . . . . solve for the number of apples

  a = 84

The percentage of fruits that are apples is ...

  apples/total = 84/(135 +81 +84) = 84/300 = 28/100 = 28%

  28% of the fruits are apples

Answer:

This is your answer 360 degrees.

Step-by-step explanation:

Mark as brainlest makes my day

f(w) = 100 + 15t is the function that represents the relationship between w, the number of weeks Jordan kept his money in the account, and t, the total amount in the savings account

It is given to us that Jordan received $100 for a graduation present and deposited it in a savings account. Each week thereafter, he added $15 to the account but no interest was earned.

We need to write an equation represents the relationship between w, the number of weeks Jordan kept his money in the account, and t, the total amount in the savings account:

Graduation present = $100

Amount deposited per week = $15

Let, w be the number of weeks, and t, the total amount in the savings account, therefore, the function is:

f(w) = 100 + 15t

Therefore, f(w) = 100 + 15t represents the relationship between w, the number of weeks Jordan kept his money in the account, and t, the total amount in the savings account

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Point p is deflected across the y axis to obtain point q (5,-6) and across the x axis to obtain point r (-5,6).

A point on a grid has two numbers to identify its position. These numbers are known as coordinates. Coordinates are always written as the number of steps across first, then the number of steps up or down. Grids have two axes. The horizontal axis is called the x-axis and the vertical axis is called the y-axis.

We know that,

if point (x, y) deflected across y axis then the y coordinate remain same but the polarity of x gets change then

r(x, y) → (-x, y)

Similarly, if point (x, y) deflected across x axis then the x coordinate remain same but the polarity of y gets change then

r(x, y) → (x,-y)

Now, we have : p = (-5,-6)

As Point p is deflected across the y-axis to obtain point q , thus

r(-5,-6) → (5,-6)

point p is deflected across the x-axis to obtain point r, thus

r(-5,-6) → (-5,6)

Thus,  q=(5,-6) and r=(-5,6).

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Part a

There will be $2850 in the account after 8 years

Part b

The amount of interest earned in 5 years is $218.75

The principal amount = $2500

The interest rate = 1.75%

The time period = 8 years

Part a

The simple interest

A = P(1  + rt)

Substitute the values in the equation

A = 2500(1 + (1.75/100)×8)

A = 2500( 1 + 0.14)

A = 2500( 1.14)

A = $2850

Part b

The time period = 5 years

Simple interest = Prt

= 2500 × (1.75/100) × 5

= 2500 × 0.0175 × 5

= $218.75

Hence,

Part a

There will be $2850 in the account after 8 years

Part b

The amount of interest earned in 5 years is $218.75

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you don't multiply

Step-by-step explanation:

you must divide it by itself to get the variable alone and then divide the other side hope this helps!

Answer:

a\(\geq\)16

Step-by-step explanation:

3+a\(\geq\)19

-3    -3

a\(\geq\)16

(see below) (The line I drew represents where a is and if it is to be greater or equal to it must be 16 or over)

Answer: (16,-12)

Step-by-step explanation: just cuz... just listen linda

Answer:

(16,-12)

Step-by-step explanation:

I used a graph to get this answer

A sample size of 60 is required to estimate a population mean with a 98% confidence interval, assuming that the population standard deviation is approximately .

To calculate the required sample size to estimate a population mean with a 98% confidence interval, based on previous evidence that the population standard deviation is approximately , and a margin of error of 1.5, the following formula can be used:

n = [Z-score * (Population Standard Deviation / Margin of Error)]²

where Z-score is the critical value for a 98% confidence level, which can be found using a Z-table or a calculator.

For a 98% confidence level, the Z-score is approximately 2.33.

Substituting the values, we get:

n = [2.33 * () / 1.5]²

n = [2.33 * ] / 1.5]²

n ≈ 59.3

Rounding up to the nearest whole number, the required sample size is approximately 60.

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SOLUTION

Write out the equation given

To find y-intercept, we replace x with 0, hence

Hence

Y - intercept is ( 0, 8/7 )

Similarly, for x-intercept, we replace y with 0 and find x

Hence

x- intercept is ( - 8/5 , 0 )

Answer:

\((3^6)^{18}=3^{108}=3.38139191\times10^{51}\)

Answer:

109

Step-by-step explanation:

Combine like terms, then solve

Step-by-step explanation:

let's just write the equations on top of each other as in a large subtraction, then transform one of them so that at least one term is the range in both equations, and then do the subtraction.

a)

I automatically write rational numbers as the total fractions (14 1/4 = 57/4, 3 3/4 = 15/4)

15x - 7y = 57/4

- 5x - y = 15/4

15x - 7y = 57/4

- 15x - 3y = 45/4

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

0 -4y = 12/4

y = -(12/4)/4 = -12/16 = -3/4

then we use that in the simpler second equation

5x - -3/4 = 15/4

5x + 3/4 = 15/4

5x = 12/4

x = (12/4)/5 = 12/20 = 3/5

b)

we don't need to transform any equation, as the x terms are already equal.

3x - 4y = 2

- 3x - 7y = -1

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

0 3y = 3

y = 3/3 = 1

using this in e.g. the first equation

3x - 4×1 = 2

3x - 4 = 2

3x = 6

x = 6/3 = 2

The ratio of the price of pints of beer to the price of cups of coffee if Jim chooses to buy 4 pints of beer and 9 cups of coffee is: b/c = 4b/9c , b/c = 1.125

Jim bought 3 pints of beer and 7 cups of coffee for $14, and the ratio of the price of pints of beer to the price of cups of coffee is 2:3,

To determine the cost of one pint of beer and one cup of coffee, let's solve the system of equations.

                     2b + 3c = 7 (dividing both sides of the equation by 7)

                                    2b/7 + 3c/7 = 1b/3.5 + c/2.333

                  = 1b + 1.5c

                  = 4.666... (dividing both sides of the equation by 3.5)

                              b/3.5 × 4 + c/2.333 × 9

                            = 14b/0.875 + c/0.259

                                       = 14.666...

Therefore, the ratio of the price of pints of beer to the price of cups of coffee if Jim chooses to buy 4 pints of beer and 9 cups of coffee is:

                       b/c = 4b/9c (multiplying both sides by 9c)

                                       b/c = 1.125

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Answer:

-3

Step-by-step explanation:

9(2x + 5) + 6 = 6 + 3x

Do the distributive property first.

18x + 45 + 6 = 6 + 3x

Simplify the left side by adding like terms.

18x + 51 = 6 + 3x

Move the variables (x) to one side of the equation. I'm going to move the 3x to the left side by subtracting.

18x - 3x + 51 = 6

15x + 51 = 6

Move the constants to the others side. I'm going to subtract 51 from both sides.

15x + 51 - 51 = 6 - 51

15x = -45

Divide both sides by 15

15x/15 = -45/15

x = -3

Answer:

x = -3

Step-by-step explanation:

[Given]

9(2x + 5) + 6 = 6 + 3x

[Distrbute the 9]

18x + 45 + 6 = 6 + 3x

[Combine like terms on the left using addition]

18x + 51 = 6 + 3x

[Subtract 3x from both sides]

15x +51 = 6

[Subtract 51 from both sides to isolate the variable]

15x = -45

[Divide both sides by 15]

x = -3

Have a nice day!

     I hope this is what you are looking for, but if not - comment! I will edit and update my answer accordingly. (ノ^∇^)

- Heather

After simplifying each expression, we get (2+5a - 10 b), (8a² - 15ca +2c),

(11- 2a+b) and (a+ b) respectively.

The word simplify means to write an expression, equation or problems

in the simplest form so as to easy to evaluate it. we simplify an expression by removing the parenthesis and collecting like terms.

exercise 1.

given, A = 7 - 4a + 7a - 3b -5 -7b +2a

We collect the like term and get

A= 7 - 5 -4a +7a +2a -3b- 7b

A = 2 + 5a -10b

next, given B = 4a × 2a -5c - c +8c -3c × 5a

             B = 8a² -6c +8c - 15ca

        B = 8a² -15ca +2c

exercise 2.

given, A = 7 + [(2- a) -( 2+a) +9] + (b-5)

at first, we remove the parenthesis and get

A= 7 + [2-a - 2 -a+ 9] +b- 5

A = 7 + 9- 2a +b- 5

after collecting the like term

A = 11- 2a + b

given, B = 15 - [(7-b) - 9- (a-17)]

  B = 15 - [7- b- 9 - a+17]

 B = 15 - [15 - b -a]

after removing the parenthesis

B = b +a

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Answer:

h = A*2/a+b

Step-by-step explanation:

Answer:  <1 = 105° and <2 = 75°

Step-by-step explanation:

The information we have is the 75 degree angle already provided. Using our knowledge on transverses we know a 180 degree angle is a straight line (we happen to have two of these (c and d)). Using the corresponding angle theorem we know angle 2 is equivalent to 75 degrees. Supplementary angles refer to angles that add up to 180 degrees. Angle 1 and 2 are supplementary so from there we solve.

180 - 75 = 105

<1 = 105 degrees