Geometry unit 1 lesson 1

Answer: Ist integer = 32

2nd integer = 34

Step-by-step explanation: SEE THE ATTACHED

Final answer:

Sara paid 55% of the original price of the dress when she bought it for $30. By dividing the sale price by 0.55, we calculate that the original price was approximately $54.55.

Explanation:

To answer the question of what the original cost of Sara's dress was before she saved 45% on the sale, we need to set up a simple percentage calculation. Since Sara saved 45%, this means she paid 55% of the original price (100% - 45% = 55%). The sale price of $30 is what represents this 55%.

To find the original price, we can write the equation:
30 = 0.55 × (original price).

Now we divide the sale price by 0.55 to find the original price:
(original price) = $30 / 0.55 = approximately $54.55.

So the original cost of the dress was approximately $54.55 before the sale.

The original price of the dress is approximately '54.55'

Sara bought a dress on sale for $30 and she saved 45% on the dress

Thus the price she paid for the dress is 100%−45%=55%

Now 55% of the original price of the dress is the amount she paid for the dress

Thus let 'P' be the original price of the dress

We can say that,

55% of P = 30

[tex]55*\frac{P}{100}=30\\ 55*P=30*100\\55*P=3000\\P=\frac{3000}{55}\\ P=54.55[/tex]

Thus '54.55' is the required answer

The value of i^{20}+1 is 2, which is calculated by recognizing that the powers of i repeat every 4 cycles and that i^20 simplifies to 1.

The value of i^{20}+1 can be determined by understanding the properties of the imaginary unit i, which is defined by i^2 = -1.

The powers of i follow a cyclical pattern: i^0 = 1, i^1 = i, i^2 = -1, i^3 = -i, and i^4 = 1, with this pattern repeating every 4 powers.

To find i^{20}, we observe that 20 is divisible by 4 (20 = 4 × 5), so i^{20} = (i^4)^5 = 1^5 = 1.

Add 1 to this result, and we get i^{20} + 1 = 1 + 1 = 2.

Answer:

$7.54 / hour to the nearest cent.

Step-by-step explanation:

This is 120.67 / 16

= $7.54 / hour,

The position of the diver relative to the surface is -9 feets

Using the parameters given for our Calculation;

Difference in distance

Since, we are expressing position relative to the surface , The diver is 9 feets below the surface , which would be expressed as -9 feets.

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Answer:

120

Step-by-step explanation:

Length of the rectangle = 120 feet

Given :

The width of a rectangle is 3/4 its length. The perimeter of the rectangle is 420 feet.

Let 'L' be the length of the rectangle

Width of the rectangle is 3/4 of its length

width = [tex]\frac{3}{4} \cdot length[/tex]

Perimeter of rectangle = 2(length ) +2(width )

[tex]P=2L+2W\\P=2L+2(\frac{3}{4}\cdot L) \\P=2L+(\frac{3}{2}t L) \\\\P=\frac{7}{2}L \\[/tex]

Given that perimeter of rectangle is 420 feet

Replace perimeter by 420 feet and solve for L

[tex]420= \frac{7}{2} L\\840=7L\\Divide \; by \; 7\\L=120[/tex]

Length of the rectangle = 120 feet

Width of the rectangle =[tex]\frac{3}{4} \cdot length= \frac{3}{4} \cdot 120=90[/tex]

Width of the rectangle = 90 feet

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Answer:

21meter

Step-by-step explanation:

because 1 min equal 60min and 1meter equal 100cm

Answer:  The answer is:  " 45  % "  .    

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               →    " Twenty-seven is 45 % of 60. "

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Step-by-step explanation:

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The question asks:

 " 27 is what % {percentage] of 60 " ?  ;

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So:  " 27 =  (n/100) * 60 " ;  Solve for "n" ;

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Method 1:

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  →   (n/100) * 60 = 27 ;

Divide each side by 60 :

 →   [ (n/100)  * 60 ] / 60 = 27 /60 ;

to get:

 →    (n/100) = 27/60 ;

Now:  Cross-factor multiply:

 →  60n = (27)*(100) ;

to get:

 → 60n = 2700 ;

Divide each side by "60" ;

→  60n = 2700/ 60 ;

to get:  n = 45 ;

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 →  The answer is:  45 % .    

   →  " Twenty-seven is 45 % of 60."

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Method 2:

________________________________________________

The question asks:

 " 27 is what % {percentage] of 60 " ?

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To solve this problem:

Rephrase this question as:

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" 27 is 60% of what number ? "

 →  The answer will be the same!

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→  27 = (60/100)* n ;   Solve for "n" ;

Multiply each side of the equation by "100" ; to eliminate the fraction:

→  100 * 27 = 100 * [ (60/100)* n ] ;

 to get:

   →   2700 = 60n ;

↔  60n = 2700 ;

Divide Each Side of the equation by "60" ;

    →   60n/60 = 2700 / 60 ;

to get:  n = 45 ;

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→  The answer is:  45 % .    

       →  " Twenty-seven is 45 % of 60."

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Method 2:  Variant 1 of 2:

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When we have:

→  27 = (60/100)* n ;   Solve for "n" ;

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Note that:  "(60/100) = (60÷ 100) = (6 ÷ 10)" ;   since:  in "(60/100)" ;  the "zero" from the "numerator" cancels out;  And:  the "last zero" in "100" — from the "denominator" cancels out;  since we are dividing "each side" of the fraction by "10" ;

  →   "(60÷10) / (600÷10)"  =  " 6/10 " ;  

  →   " (6/10)" ; that is;  "six-tenths"} ;  

  →     can be represented by:  " 0.6 " ;

  →  {by convention;  but specifically, here is the explanation} — as follows:

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  →   "(6/10)" =  " (6 ÷ 10) " ;  

Note:  When dividing a number by "10" ;  we take the original number; and move the decimal point to the left; & then we rewrite that number as the "answer".  

Note:  When multiplying or dividing by a positive, non-zero integer factor of "10" that has at least 1 (one) "zero" after that particular factor of "10".  We can get the answer by taking the original number & moving the decimal point the number of spaces as designated by the number of zeros following the particular [aforementioned factor of "10".].

We move the decimal point to the right if we are multiplying;  and to the left  if we are dividing.  In this case, we are dividing "6" by "10 " :

 →  " 6   ÷  10  =  ? " ;  

 →  " 6.  ÷ 10 =  ? " ;

   We take the: " 6. " ;  and move the decimal point "one space backward [i.e. "to the left"];  since we are dividing by "10" ;

 →  to get:  " .6 " ;  & we rewrite this value as "0.6" in a rewritten equation:

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So; we take our equation:

→  27 = (60/100)*n ;  And rewrite—substituting "0.6" for

"(60/100)"— as follows:

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→  27 = (0.6)n ;  ↔ (0.6) n = 27 ;

Multiply each side of the equation by "10" ; to eliminate the decimal:

   →  10 * [ (0.6)n ]  = 27 * 10 ;

to get:

  →  6n = 270 ;

Divide each side of the equation by "6" ; to isolate "n" on one side of the equation; & to solve for "n" ;

 →  6n / 6  =  270 / 6 ;

to get:   n = 45 ;

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→  The answer is:  45 % .    

      →  " Twenty-seven is 45 % of 60."

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Method 2 (variant 2 of 2):

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We have the equation:  27 = (60/100)* n ;   Solve for "n" ;

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Note:  From Method 2 (variant) 1 of 2— see above):

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Note:  Refer to the point at which we have:

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→   " {  (60÷10) / (600÷10)"  =  " (6/10) " ;  that is;  "six-tenths"} ;

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Note that the fraction— "(6/10)" ;  can be further simplified:

→  "(6/10)" =  "(6÷2) / (10÷2)" = "(3/5)" ;

Now, we can rewrite the equation;

→ We replace "(60/100)" ;  with:  "(3/5)" :

    →  27 = (3/5)* n ;   Solve for "n" ;

↔ (3/5)* n = 27 ;  

↔    (3n/5) = 27 ;

Multiply Each Side of the equation by "5" ;

→  5* (3n/5) = 27 * 5 ;  

to get:

→   3n = 135 ;

Divide Each side of the equation by "3" ;  to isolate "n" on one side of the equation;  & to solve for "n" ;

→  3n / 3 = 135 / 3  ;

to get:   n = 45 ;

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 →  The answer is:  45 % .    

       →  " Twenty-seven is 45 % of 60."

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Hope this answer is helpful!

        Wishing you the best in your academic endeavors

           — and within the "Brainly" community!

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Answer and Step-by-step explanation:

[tex]27[/tex] of [tex]60[/tex] is [tex]45[/tex]%

Working out in percentage :

[tex]27[/tex] of [tex]60[/tex] can be written as :

[tex]\frac{27}{60}[/tex]

Multiplying both the numerator and denominator by [tex]100[/tex] :

[tex]\frac{27}{60} *\frac{100}{100}= \frac{45}{100}=45[/tex]%

So the answer to your question is [tex]27[/tex] of [tex]60[/tex] is [tex]45[/tex] %

Gabriella got the better deal, as she paid slightly less per pound for the tomatoes.

To determine who got the better deal, we need to calculate the price per pound of tomatoes for each person.

For Clay:

Price per pound = Total price / Total pounds

Price per pound = $13.50 / 214 pounds ≈ $0.0631 per pound

For Gabriella:

Price per pound = Total price / Total pounds

Price per pound = $6.75 / 112 pounds ≈ $0.0607 per pound

Comparing the two, we see that Gabriella paid approximately $0.0607 per pound, while Clay paid approximately $0.0631 per pound.

Answer:

ley the different numbers be x&y

x+y=67

x-y=7

2y=54

y=27

substitute for x

x-27=7

x=7+27

x=34

The two unknown numbers 'a' and 'b' are 34 and 27.

A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.

Let the two numbers be 'a' and 'b'.

Given, The sum of two numbers is 61 which is (a + b) = 61...(i)

Also given the difference is 7 which is (a - b) = 7...(ii)

Adding the equations (i) and (ii) we get,

2a = 68          (+ b and - b cancel out)

a = 34 and hence 34 + b = 61 ⇒ b = 27.

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5^4÷ 5^6=5^-2

1 over 25

Answer:

the answer is 1 over 25

Step-by-step explanation:

i hope this helps

Final answer:

The absolute value equation that has solutions of 3 and -3 is |x| = 3. Substituting x = 3 or x = -3 into the equation both result in true statements, confirming they are the correct solutions.

Explanation:

The student is asking about solving an absolute value equation that has solutions of 3 and -3. To tackle this problem, you want to set up an equation where the absolute value is equal to both positive and negative 3. The most straightforward equation that satisfies this condition is |x| = 3. This equation means that the solution, x, can be either 3 or -3 because the absolute value of both numbers is 3. To verify that these are the correct solutions, you can substitute them back into the original equation:

For x = 3: |3| = 3, which simplifies to 3 = 3, confirming the solution.

For x = -3: |-3| = 3, which simplifies to 3 = 3, again confirming the solution.

This absolute value equation is an identity because substituting either solution results in a true statement.

Answer:

.083

Step-by-step explanation:

just divide by the number it says its times as

in this example divide .83 by 10

Answer:

0.083

Step-by-step explanation:

If you move the decimal once to the right from 0.083 you will get the answer .83

The number 3.249 rounded to nearest tenth is; 3.2

According to the question;

According to the place value concept in mathematics; the place values after the decimal point in a decimal number are identified from left to right, as tenths, hundredths, thousandths etc.

Evidently, the number which occupies the tenths position in 3.249 is the digit 2.

Since, 4 is less than 5, it is rounded off to 0 and added to the digit, 2 which occupies the tenths position in the number 3.249

Ultimately, the number 3.249 rounded to nearest tenth is 3.2.

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Answer:

17

Step-by-step explanation:

17 is the odd number because 17 cannot be split into 2 equal groups. However, 2,6, and 10 can be split into 2 even groups. So therefor, they are even numbers.

as you already know, to get the inverse of any expression we start off by doing a quick switcheroo on the variables and then solve for "y".

[tex]\bf \stackrel{f(x)}{y}=x^2-10\implies \stackrel{switcheroo}{x=y^2-10}\implies x+10=y^2\implies \sqrt{x+10}=\stackrel{f^{-1}(x)}{y}[/tex]

Hey!

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Answer: 7 14/18 has not been reduced to simplest form.

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Solution: 7 14/18 can be simplified to 7 7/9

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Hope This Helped! Good Luck!

Answer:

Yes

Step-by-step explanation:

Under a counterclockwise rotation about the origin of 270°

a point (x, y ) → (y, - x )

Thus

A(1, 1 ) → A'(1, - 1 )

B(1, 4 ) → B'(4, - 1 )

C(3, 4 ) → C'(4, - 3 )

D(6, 1 ) → D'(1, - 6 )

These are the correct coordinates for the diagram A'B'C'D'

A translation (x, y ) → (x + 4, y + 1 )

Add 4 to the x- coordinates and add 1 to the y- coordinates, that is

A'(1, - 1 ) → A''(1 + 4, - 1 + 1 ) → A''(5, 0 )

B'(4, - 1 ) → B''(4 + 4, - 1 + 1 ) → B''(8, 0 )

C'(4, - 3 ) → C''(4 + 4, - 3 + 1 ) → C''(8, - 2 )

D'(1, - 6 ) → D''(1 + 4, - 6 + 1 ) → D''(5, - 5 )

These are the correct coordinates for the diagram A''B''C''D''

Hence the composition of transformations is correct

Answer:

Step-by-step explanation:

You give characteristics about the polygons. Then you define then. For example, C is a rectangle because it has 4 right angles, it had 4 sides and corners, and it has two sets of parallel lines. For b, you just organise the polygons into the Venn diagram according to each polygons classification.

The red marble is farthest from the target.

Answer:

Consider two right triangles: 1. ΔABC with vertices A(0,0), B(0,2), C(6,0). Then AB is perpendicular to AC and AB=2 units (vertical leg), AC=6 units (horizontal leg).2. ΔXYZ with vertices X(6,-10), Y(6,0), Z(36,-10). Then XY is perpendicular to XZ and XY=10 units (vrrtical leg), XZ=30 units (horizontal leg).The equation of the line BC is Check whether points Y and Z lie on this line:Y(6,0):  - true;Z(36,-10):  - true.Answer:  the hypotenuses of these two triangles could lie along the same line

Answer:

ok honestly that wus super confusing, but i think its a trick question so the answer is 0

Step-by-step explanation:

Answer:

58 loaves

Step-by-step explanation:

22+17+19= 58

Answer:

Step-by-step explanation:

[tex]-3t+4=19\qquad\text{subtract 4 from both sides}\\\\-3t+4-4=19-4\\\\-3t=15\qquad\text{divide both sides by (-3)}\\\\\dfrac{-3t}{-3}=\dfrac{15}{-3}\\\\t=-5[/tex]

Answer:

-5

Step-by-step explanation:

19-4= 15

15/-3 = -5

t = -5

Answer: 44

Step-by-step explanation:

I’m assuming that the shape is a quadrilateral, meaning that it has 4 sides. All quadrilaterals need angles to add up to 360.

An obtuse angle is any angle larger than 90 degrees and less than 180 degrees. In other words, if the angle formed where two line segments meet goes beyond a right angle, it's obtuse.

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Answer:

$119.25

Step-by-step explanation:

$0.55.×45= $24.75

$0.80×45= +$36.00

$180.00- $ 60.75= $119.25

Hope it helps :)

The amount of money he has left to spend on art supplies is $119.25.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that an art teacher is hosting a summer art camp. He has a total of $180 to purchase snacks, drinks, and art supplies. He buys 45 bags of chips at $0.55 each and 45 juice boxes at $0.80 each.

$0.55.×45= $24.75

$0.80×45= +$36.00

$180.00- $ 60.75= $119.25

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Answer:I believe it’s 40 degrees

Step-by-step explanation:

70

-30

=

40

Answer:both are in thousandths place,in the thousandths place both have 4 as a value

Step-by-step explanation:

Answer:

Step-by-step explanation:

Given  :  0.004 and  0.444.

To find : How is 0.004 the same as and different from 0.444.

Solution : We have given 0.004 and  0.444.

In 0.004

We can see tenth place digit is 0.

Hundredth place digit is 0

Thousandth place digit is 0.

In 0.444.

We can see here tenth place is 4

Hundredth place digit is 4

Thousandth place digit is 4.

We can conclude that 0.444 is greater than 0.004.

Therefore, 0.444 is greater than 0.004.