The sum of the digits of a two-digit number is 5. When the digits are reversed, the number increases by 27. Find the original number. The original number is

Answer:

[tex]y=5x+7[/tex]

Step-by-step explanation:

step 1

Find the slope of the line parallel to the given line

we know that

If two lines are parallel, then their slopes are equal

The equation of the given line is [tex]y=5x+4[/tex]

The slope of the given line is [tex]m=5[/tex]

so

The slope of the line parallel to the given line is also [tex]m=5[/tex]

step 2

Find the equation of the line parallel to the given line

The equation of the line in point slope form is

[tex]y-y1=m(x-x1)[/tex]

we have

[tex]m=5[/tex]

[tex]point\ (-1,2)[/tex]

substitute

[tex]y-2=5(x+1)[/tex]

step 3

Convert to slope intercept form

Isolate the variable y

[tex]y-2=5x+5[/tex]

[tex]y=5x+5+2[/tex]

[tex]y=5x+7[/tex]

Answer:

200 KM  about 124 miles

Step-by-step explanation:

200 m is only 0.12 miles

200 cm is 78 inches

200 mm is 20 cm or 7.8 inches

Answer:

-2 - the square root of 3i is a known root

Step-by-step explanation:

we know that

The conjugate root theorem states that if the complex number a + bi is a root of a polynomial P(x) in one variable with real coefficients, then the complex conjugate a - bi is also a root of that polynomial

we have that

The root of a function is [tex]-2+\sqrt{3}i[/tex]

so

Applying the conjugate root theorem

[tex]-2-\sqrt{3}i[/tex] ---> is also a root of the function

therefore

-2 - the square root of 3i is a known root

Answer:

-2 - Squared 3i is a known root

Step-by-step explanation:

We have the following function

[tex]f(x)=\frac{3}{x+2}-\sqrt{x-3}[/tex]

We want to know what is the value of f(x) when x is 19

[tex]f(19)=\frac{3}{19+2}-\sqrt{19-3}=1/7-4=\boxed{-27/7}[/tex]

If you have additional questions feel free to ask.

Hope this helps.

Answer:

8 inches

Step-by-step explanation:

90 miles -------------> represented by 3 inches

1 mile -------------> represented by 3/90 inches

240 miles ----------> represented by 3/90 x 240 = 8 inches

To determine the length of a line segment that represents 240 miles on a scale drawing, set up a proportion using the information given. The line segment would be 8 inches long.

To determine the length of a line segment that represents 240 miles on a scale drawing, we can set up a proportion using the information given. The scale in the drawing states that 3 inches represent 90 miles. We can cross-multiply and solve for the unknown length as follows:

3 inches / 90 miles = x inches / 240 miles

To solve for x, we can multiply both sides of the equation by 240 and then divide by 90:

x inches = (3 inches / 90 miles) * 240 miles

x inches = 8 inches

Therefore, a line segment that represents 240 miles on the scale drawing would be 8 inches long.

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Answer:

x-intercept: (18/5,0)

y-intercept: (0,-2)

Step-by-step explanation:

btw .. you put the equation twice it's supposed to be " -5x+9y=-18 "

Write an algebraic expression that is the quotient of a variable term and a constant

The algebraic expression that is the quotient of a variable term and a constant is [tex]quotient = \frac{x}{5}[/tex]

In arithmetic, a quotient is the quantity produced by the division of two numbers

Here given in question that quotient of a variable term and a constant

So the quotient produced by division of variable term and constant

A variable is a special type of amount or quantity with an unknown value. Though it can be anything, you often see letters like x or y as variables in algebraic equations

Let the variable term be "x"

Constants are the terms in the algebraic expression that contain only numbers

Let the constant be "5" (Note that it can be any number, here we choose 5)

So the quotient of a variable term and a constant is:

An algebraic expression is a mathematical expression that consists of variables, numbers and operations.

[tex]quotient = \frac{\text{ variable term}}{constant}[/tex]

[tex]quotient = \frac{x}{5}[/tex]

[tex]quotient = x \div 5[/tex]

Each side of a square has a length of 5x. Use your area expression to find the area of the square when x = 2.2 centimeters. Show your work.

The area of square is 121 square centimeter

Solution:

Given that each side of square has length of 5x

The area of square is given as:

[tex]\text{ area of square }= (side)^2[/tex]

[tex]\text{ area of square} = (5x)^2\\\\\text{ area of square} = 25x^2[/tex]

Given x = 2.2 centimeter

[tex]\text{ area of square} = 25(2.2)^2 = 25 \times 4.84 = 121[/tex]

Thus area of square is 121 square centimeter

Final answer:

An algebraic expression x/3 is provided as an example, and the area of a square with side length 5x is calculated when x = 2.2 cm.

Explanation:

Algebraic expression: An example of an algebraic expression that is the quotient of a variable term and a constant is x/3, where x is the variable term and 3 is the constant.

Finding the area of a square: Given that each side of a square is 5x, the area is found by squaring the side length. So, Area = (5x)^2 = 25x^2.

Calculating the area when x = 2.2 cm: Substituting x = 2.2 into the area expression gives 25*(2.2)^2 = 25*4.84 = 121 cm².

Answer:

A: 34574+3280x-24x^2

Answer:

A

Step-by-step explanation:

took test

Answer:

I think its like $6.67

Step-by-step explanation:

divide 1000 by 375 then multiply the answer to that by 2.50 u should get 6.666666666666667 round it to 6.67

Answer:

Step-by-step explanation:

a deck of cards labeled 1 thru 10......probability of picking a 5 are 1/10 because there is 1 five card out of a deck of 10 cards.

number cube is rolled, probability of rolling an even number is 3/6 or 1/2....because u have 3 even numbers and ur number cube has 6 total numbers.

probability of both events happening are : 1/10 * 1/2 = 1/20 or 1:20 <==

The probability Megan chooses a card with a 5 and rolls an even number is 1 out of 20.

The probability of choosing a card with a 5 is 1 out of 10, since there is only one card numbered 5 out of the 10 cards in the deck.

To find the probability of both events happening, we multiply the individual probabilities together.

Therefore, the probability Megan chooses a card with a 5 and rolls an even number is 1 out of 20.

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Answer:

The 3rd picture.

Hope this helps :)

Answer:

yeah its the third picture hope this helped you

All you must do is multiply 4 by 1 and 1/4, so 5 total pounds.

Hope this helps, if not, comment below please!!!!

1st draw probability = 5/8

2nd draw probability = 4/7

probability of drawing two blue cards: 5/8 x 4/7 = 5/14

answer: 5/14

Answer: c  

Step-by-step explanation:

Answer:

f(x)=3/2(8/7)^-x

Step-by-step explanation:

If you turn the fractions into decimals ([tex]\frac{3}{2}(\frac{8}{7} )[/tex]^-x = 1.5(1.14)^-x), put that number into y= in your graphing calculator and press graph you will be able to see, verses the other functions, that the line decreases.

Answer:

[tex]\frac{(\frac{3}{5}*1000) }{6}[/tex]

Step-by-step explanation:

First, let's find out how many words Maria has left to write. If she has already finished 2/5 of her essay, she has 3/5ths left to write. We can do 3/5 times 1000 to find out how many words are left.

[tex]\frac{3 }{5} * \frac{1000}{1}[/tex]

[tex]\frac{3000}{5}[/tex]

[tex]600[/tex]

Thus, there are 600 words left to write.

Now to find the amount of time, we can find how take to write 600 words at a pace of 6 words per minute by dividing 600 by 6.

[tex]\frac{600}{6}[/tex]

[tex]100[/tex]

It will take 100 minutes for Maria to write the rest of her essay. Now let's think about an expression that tells us this information. It sounds like your questions is supposed to have options, but I doesn't seem like you've posted them, no worries however.

So first, the amount she has left to write.

[tex](\frac{3}{5} * 1000)[/tex]

We know this is 600, but we don't have to simplify it for the expression.

Now thinking back to how we found the time, we can divide this '600' by 6.

[tex]\frac{(\frac{3}{5}*1000) }{6}[/tex]

This is the expression that shows the amount of time it will take to write the rest of the essay.

[tex]\frac{((1-(\frac{2}{5})*1000) }{6}[/tex] is also a valid solution.

Final answer:

Maria has 600 words left to write in her essay, and at 6 words per minute, it will take her 100 minutes to finish writing the remaining part.

Explanation:

Maria has written 2/5 of her essay, which means she has written 400 words (2/5 of 1,000 words). To find out how long it will take her to write the remaining 3/5 of her essay, we need to calculate 3/5 of 1,000 words, which is 600 words. If she writes at a pace of 6 words per minute, we can find the time by dividing the remaining number of words by her writing pace.

The expression that shows the amount of time it will take her to finish the essay is:
 (Total remaining words) / (Words per minute)
 = (3/5  of 1,000) / 6
 = 600 / 6
 = 100 minutes

Question is not proper, Proper question is given below.

Denzel is comparing websites for downloading music. One charges a $5 membership fee plus $0.50 per song. Another charges $1.00 per song, but has no membership fee. Write and solve an equation to find how many songs Denzel would have to buy to spend the same amount at both websites.

Answer:

Denzel would have to buy 10 songs to spend the same amount at both websites.

Step-by-step explanation:

Let the number of songs be 'x'.

Given:

One charges a $5 membership fee plus $0.50 per song.

So the total cost at one site will be membership cost plus charges per song multiplied by number of songs.

framing in equation form we get;

Total Cost at one site = [tex]5+0.5x[/tex]

Another website charges $1.00 per song, but has no membership fee.

So the total cost at Another site will be charges per song multiplied by number of songs.

framing in equation form we get;

Total Cost at Another site = [tex]1\times x=1x[/tex]

To find the number of songs that results in same cost we should equate the two expression and solve.

[tex]5+0.5x=x[/tex]

Combining like terms we get;

[tex]5 = x-0.5x\\\\5=0.5x[/tex]

Now Dividing both side by 0.5 we get;

[tex]\frac{0.5x}{0.5} = \frac{5}{0.5} \\\\x=10\ songs[/tex]

Hence Denzel would have to buy 10 songs to spend the same amount at both websites.

Answer:

Step-by-step explanation:

-9z=-207

Dividing each term by -9

z = -207/-9

z = 23

Answer:

23

Step-by-step explanation:

-9z=-207

divide by 9 on both sides

z=23

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3 x 1/10 is 0.3 because it represents one tenth of 3, while 3 x 10 is 30 as it increases the value of 3 tenfold. Powers of ten and negative exponents demonstrate that each step in exponent changes the scale of the number by a factor of ten.

The reason why 3 x 1/10 is less than 3 x 10 is due to the values being multiplied by 3. When multiplying 3 by 1/10, you are essentially taking one tenth of 3, which gives you 0.3. However, when multiplying 3 by 10, you are increasing 3 tenfold, which results in 30.

To understand the scale, considering that each positive power of 10 is ten times bigger than the previous one, for instance from 3.2 to 3.2 x 10, and each negative power is ten times smaller, like from 3.2 to 3.2 x 1/10 . Powers of ten and their associated exponents allow us to easily compare and calculate with vastly different magnitudes, and this concept underlies the multiplication comparisons posed in the initial question.

Answer:

684 tickets were sold for each performance

Step-by-step explanation:

8,208 divided by 12 = 684

Answer:

684 tickets

Step-by-step explanation:

having been sold out means that all seats for 12 nights were sold with none left over.

given a total of 8,208 tickets were sold out for 12 nights,

number of tickets sold each night

= 8208 ÷ 12

= 684 tickets

Answer:

$1,330.26

Step-by-step explanation:

The solution is, Devonte’s actual account balance is $1,330.26.

A checking account gives smooth get admission to your money on your everyday transactional needs and facilitates keeping your coins cozy. clients can commonly use a debit card or exams to make purchases or pay payments. money owed may have special alternatives to help keep away from the month-to-month provider fee.

here, we have,

A transaction account, also called a bank account, chequing account, present-day account, call for a deposit account, or share draft account at credit score unions is a deposit account held at a financial institution or other monetary organization.

given that,

Devonte is balancing his checking account. His account statement does not include a deposit of $107.00 that he made on November 1st.

from the given data ,

so, we get,

Devonte’s actual account balance is $1,330.26.

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Answer:

Graph the solution of the inequality on a number line is attached in figure a that satisfies the graph of the solution set x > -1.

Step-by-step explanation:

The inequality is given as follows:

                             [tex]2\left(x-3\right)-5x<x-2[/tex]

Let's solve your inequality step-by-step

[tex]2\left(x-3\right)-5x<x-2[/tex]

[tex]2x-6\right)-5x<x-2[/tex]

[tex]-3x-6<x-2[/tex]

[tex]-6+2<x+3x[/tex]

[tex]-4<4x[/tex]

Divide both sides by -4.

[tex]x>-1[/tex]

Graph the solution of the inequality on a number line is attached in figure a that satisfies the graph of the solution set x > -1.

Keywords: inequality, graph solution

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Answer:

all the constants

Step-by-step explanation:

Answer:

[tex] \: \: \: \: \: \: \: \: 5n + ( - 3n) = - 18 \\ = > 5n - 3n = - 18 \\ = > 2n = - 18 \\ = > n = \frac{ - 18}{2} \\ = > n = - 9[/tex]

Answer:

data collection error

Answer:

B. Data Collection Error.

Step-by-step explanation:

Answer:

The second choice

Step-by-step explanation:

Answer:

|4x-2| = -6

Step-by-step explanation:

recall that the absolute value of anything must be greater or equal to zero (i.e 0 or positive).

in the first option, we can see that the absolute value of the expression (4x-2) gives a negative number. This violates our definition above hence it cannot be true.

Answer:

1.35

Step-by-step explanation:

$9=100%

15%        x

-----  =   ----

100%     9

Cross multiply:

100x=135

Solve:

x=1.35

15% of $9 is $1.35

:)

Answer: $1.35

Step-by-step explanation: To find 15% of $9, first write 15% as a decimal by moving the decimal point 2 places to the left to get .15.

Next, "of $9" means times 9 so we multiply .15 times 9 or (.15)(9) which gives us 1.35. So 15% of $9 is $1.35.

Answer:

[tex]\displaystyle \mathbb{R}-\left \{ -6,\ 6 \right \}[/tex]

Step-by-step explanation:

Domain of Functions

Given a function h(x), we call the domain of h, all the values x can take so h exists. It's commonly easier to find the values of x for which h does NOT exist and then exclude them from the general domain of the real numbers.

The question provides us with the following functions

[tex]\displaystyle f(x)=x^2-3x-18[/tex]

[tex]\displaystyle g(x)=x^2-36[/tex]

[tex]\displaystyle h(x)=\frac{x^2-3x-18}{x^2-36}[/tex]

We called h(x) to the newly created function f/g(x)

To investigate the possible points of nonexistence for h, we factor h(x)

[tex]\displaystyle h(x)=\frac{(x-6)(x+3)}{(x-6)(x+6)}[/tex]

We can clearly see the denominator has two zeros at

[tex]\displaystyle x=6,\ x=-6[/tex]

A rational function cannot exist where the denominator is zero, regardless of the possible simplification with the numerator, as in this case. For example, for x=6 the function gets the value 0/0 and it's not defined there. We cannot simplify the common factor because they are part of the original function.

So, the domain of h is

[tex]\displaystyle (-\infty,\ -6 )\bigcup (-6,\ 6)\bigcup (6,+\infty )[/tex]

Or equivalently

[tex]\displaystyle \mathbb{R}-\left \{ -6,\ 6 \right \}[/tex]

The domain of the function (f/g)(x), given f(x)=x^2-3x-18 and g(x)=x^2-36, is all real numbers except x = 6 and x = -6. This is because we can't have g(x) equals to zero in (f/g)(x). Hence the domain is (-∞, -6) U (-6, 6) U (6, ∞).

In Mathematics, when dealing with the domain of the function (f/g)(x) it is important to understand that the domain is the set of all possible x values that we can input into the function. For the function (f/g)(x), given f(x)=x^2-3x-18 and g(x)=x^2-36, the denominator g(x) cannot be zero as this would mean dividing by zero, which is undefined in Mathematics. So we need to find the values of x for which g(x) ≠ 0. To do this, we set g(x) equal to zero and solve for x. So, x^2-36=0. Simplifying this, we get (x+6)(x-6) = 0. Hence the roots of the equation are  x = 6, x = -6.

These are the values for which g(x) will become zero. Since we can't have g(x)=0 in (f/g)(x), the domain of the function (f/g)(x) is all real numbers except x = 6, x = -6. So, the domain of (f/g)(x) is (-∞, -6) U (-6, 6) U (6, ∞).

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Answer:

The length of the ladder is 9.2 meters

Step-by-step explanation:

Given as :

The angels of elevation of a ladder against a wall = 60°

The Distance of the foot of the ladder fro the wall = d = 4.6 meters

Let The length of the ladder = h meters

Now, According to question

cos angle = [tex]\dfrac{\textrm base}{\textrm hypotenuse}[/tex]

Or, cos 60° = [tex]\dfrac{\textrm d}{\textrm h}[/tex]

Or, 0.5 = [tex]\dfrac{\textrm 4.6}{\textrm h}[/tex]

∴  h = [tex]\dfrac{\textrm 4.6}{\textrm 0.5}[/tex]

i.e h = 9.2

So,The length of the ladder = h = 9.2 meters

Hence The length of the ladder is 9.2 meters Answer

Answer:

Here's what I get  

Step-by-step explanation:

CPCTC is an acronym for Corresponding Parts of Congruent Triangles are Congruent.

If ΔRST ≅ ΔXYZ then

∠R = ∠X

∠S = ∠Y

∠T = ∠Z

RS  = XY

ST  = YZ

RT  = XZ

To prove ΔRST ≅ ΔXYZ, perform a sequence of transformations and apply CPCTC to identify congruent parts.

To prove that ΔRST ≅ ΔXYZ, we need to perform a sequence of transformations that move ΔRST onto ΔXYZ. Once the triangles are superimposed, we can use the Corresponding Parts of Congruent Triangles are Congruent (CPCTC) to identify congruent parts.

CPCTC states that if two triangles are congruent, then their corresponding parts (sides and angles) are also congruent. In this case, the parts of ΔRST that are congruent to the corresponding parts of ΔXYZ are:

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Answer:

10.

Divide b into thirds, and then add together 2 of those thirds.

15/3 = 5

5x2 is 10.

Sorry if that doesn't make sense but it's how I do it in my head lol.