If a+b+c=7 and ab+bc+ca=20 find the value of a^2+b^2+c^2

Answer:

The answer is: 3(x+4)

Step-by-step explanation:

Oof

Answer:

The correct option is 2.

Step-by-step explanation:

The given statement is "three times the sum of a number and 4".

We need write the mathematical expression for the given statement.

Let the unknown number be x.

The sign " + " is used for addition and sum.

The sign " × " is used for multiplication, times and product.

Sum of a number and 4 = [tex](x+4)[/tex]

Three times the sum of a number and 4 = [tex]3\times (x+4)=3(x+4)[/tex]

The required expression is 3(x+4). Therefore, the correct option is 2.

Answer:

58 loaves

Step-by-step explanation:

22+17+19= 58

Answer: 1 and 11/12

Step-by-step explanation: (4 1/4) - (7/3)= 4 3/12- 2 4/12=1 and 11/12

Answer:

Step-by-step explanation:

f(n) = 3n + 2, n ≥ 1

Substitute n = 3:

f(3) = 3(3) + 2 = 9 + 2 = 11

The third term of the sequence is 11 given that that the sequence has a domain of n ≥ 1 and f(n) = 3n + 2. This can be obtained by substituting 3 in the sequence since we have to find the third term.

Given that, the sequence ⇒ f(n) = 3n + 2

Since n ≥ 1, first term will be ⇒ f(1) = 3(1) + 2 = 5

Second term will be f(2) = 3(2) + 2 = 8

Third term will be f(3) = 3(3) + 2 = 11

Thus the sequence is 5, 8, 11, ... and the third term is 11.

Hence the third term of the sequence is 11 given that that the sequence has a domain of n ≥ 1 and f(n) = 3n + 2.

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Answer: (-4,9)

Step-by-step explanation:

After applying the sequence of transformations, the coordinates of the final point are (-4, 9).

In Mathematics and Geometry, a reflection over or across the y-axis would maintain the same y-coordinate while the sign of the x-coordinate changes from positive to negative or negative to positive.

By applying a reflection over the y-axis to the coordinates of the point (4, -9), we have the following new coordinates for the image;

(x, y)                →      (-x, y)

(4, -9)           →     (-4, -9)

By applying a reflection over the x-axis to the coordinates of the point (-4, -9), we have the following new coordinates for the image;

(x, y)                →      (x, -y)

(-4, -9)           →     (-4, -(-9)) = (-4, 9)

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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:

B.

x-axis scale, 0–30; label, Months

Y-axis scale, 0–9,000; label, Total Remaining Debt ($)

Step-by-step explanation:

According to given data

Debt = $8950

Monthly payment = $360

Now we can calculate the total period required to eliminate the debt

Total months to eliminate debt = Total Debt/Monthly installment

Total months to eliminate debt = 8950/360

Total months to eliminate debt = 24.8 months

Now, by this calculate, we can say that it is only logical to plot time in graph with months, not years or days. Because if we plot graph with days, it will be too lengthy, on the other hand, if we plot graph with years, it will shrink to much and it will become very difficult to read it and estimate the progress. So all options with time in other than month will be eliminated and we will be left with option B. Notice that option a will be eliminated because we need to plot graph for 24.8 months but it contains 9000 months, which means 750 years. So it will be illogical to plot graph on this scale.

Answer:

x-axis scale, 0–30; label, Months

y-axis scale, 0–9,000; label, Total Remaining Debt ($)

Step-by-step explanation:

For the time scale you must have a value that goes over 25, and the units of months, not years.  For the Remaining Debt scale the value needs to be in a range that goes over $8950

Answer: C

Step-by-step explanation:

2x3= 6

55 x -4=  -220

6 + -220= -214

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: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.

Answer:

29 degrees Celsius are 84.2 Fahrenheit.

Step-by-step explanation:

In order to convert Celsius to Fahrenheit you can use this formula: [tex]F = C * 1.8 + 32[/tex].

Here we have [tex]F = 29 * 1.8 + 32[/tex] which equals 84.2. Instead of 1.8 you can use the fraction [tex]\frac{9}{5}[/tex] if you wish so.

Answer:

[tex]\large\boxed{29^oC=84.2^oF}[/tex]

Step-by-step explanation:

Formula for converting Celsius (C) to Fahrenheit (F):

[tex]F=32+\dfrac{9}{5}C[/tex]

We have C = 29. Substitute:

[tex]F=32+\dfrac{9}{5}(29)=32+\dfrac{261}{5}=32+52.2=84.2[/tex]

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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Answer:

Step-by-step explanation:

2/3 = 6/9 because to get to nine from three you need to multiply by three so you multiply the 2 by three to and you get 6 so the answer is 6/9

2/3 written as a sum of unit fractions with the denominator of nine is 6/9.

Equivalent fractions are two or more fractions that are all equal even though they different numerators and denominators.

The given fraction is 2/3.

2/3 written as a sum of unit fractions with the denominator of nine

Now, multiply both numerator and denominator by 3

2×3/3×3

= 6/9

Therefore, 2/3 written as a sum of unit fractions with the denominator of nine is 6/9.

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The red marble is farthest from the target.

The most appropriate price per stick of gum should be $0.5966.

Given that,

Based on the above information, the calculation is as follows:

[tex]= 30\div 1.79[/tex]

= 0.5966

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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.

Answer:

The new dimensions of the rectangle, after a dilation will be 72 ft by 18 ft

Step-by-step explanation:

we know that

The new dimensions of the rectangle, after a dilation will be equal to the original dimensions multiplied by the scale factor

we have

The scale factor is 9/4

Original length =32 ft

Original width=8 ft

Find the new dimensions after dilation

New length=(9/4)32=72 ft

New width=(9/4)8=18 ft

therefore

The new dimensions of the rectangle, after a dilation will be 72 ft by 18 ft

Answer:

The scale factor is 9/4

Original length =32 ft

Original width=8 ft

New length=(9/4)32=72 ft

New width=(9/4)8=18 ft

The new dimensions of the rectangle, after a dilation will be 72 ft by 18 ft

Step-by-step explanation:

Answer: Common

Step-by-step explanation:

The answer is with a multiplication of denominators, because when you multiply the denominator of one fraction with the denominator of the other fraction, we will get product which could divide between both denominator

for example if you have the following equation:

2/3+2/4

and you multiply 3*4 =12

and you can use it to complete the equation as a common denominator

Answer:see explanation

Step-by-step explanation:

first look at the abosloute value of the number, then go back to the question and look at the sign of that number. That sign should be the same sign as the sum.

for example

73+(-54)=

the absolute value of 73 is 73

the absolute value of -54 is 54

73 is bigger

go back to look at the sign of 73 in the eq.

it is positive, thus the answer should be positive too.

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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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:I believe it’s 40 degrees

Step-by-step explanation:

70

-30

=

40

Answer:  The answer is:  " 45  % "  .    

________________________________________________

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

________________________________________________

Step-by-step explanation:

________________________________________________

The question asks:

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

________________________

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

________________________________________________

Method 1:

________________________________________________

  →   (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 ;

________________________

 →  The answer is:  45 % .    

   →  " Twenty-seven is 45 % of 60."

________________________________________________

Method 2:

________________________________________________

The question asks:

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

________________________

To solve this problem:

Rephrase this question as:

________________________

" 27 is 60% of what number ? "

 →  The answer will be the same!

________________________

→  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 ;

________________________________________________

→  The answer is:  45 % .    

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

________________________________________________

Method 2:  Variant 1 of 2:

________________________________________________

When we have:

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

________________________

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:

________________________

  →   "(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:

________________________

So; we take our equation:

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

"(60/100)"— as follows:

________________________

→  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 ;

________________________________________________

→  The answer is:  45 % .    

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

________________________________________________

Method 2 (variant 2 of 2):

________________________________________________

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

________________________

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

________________________

Note:  Refer to the point at which we have:

________________________

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

________________________

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 ;

________________________________________________

 →  The answer is:  45 % .    

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

________________________________________________

Hope this answer is helpful!

        Wishing you the best in your academic endeavors

           — and within the "Brainly" community!

________________________________________________

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] %

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:

$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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