The side lengths of a triangle are given by the expressions 5x+3,5x+5,and3x-2.write and simplify a linear expression for the perimeter of the triangle.

Answer:

Therefore the value of x is 4.

Step-by-step explanation:

Given:

AO = 5x - 8

BO = 3x

AM ≅ BM

To Find :

x = ?

Solution:

In  Δ AMO and Δ BMO

AM ≅ BM     ……….{Given}

∠ AMO ≅ ∠ BMO    …………..{measure of each angle is 90° given}

MO ≅ MO      ……….{Reflexive property}

ΔAMO  ≅ Δ BMO ….{ By Side-Angle-Side test}

∴ AO ≅ BO ...{corresponding sides of Congruent triangles or CPCT}

on substituting the values we get

[tex]5x-8=3x\\\\5x-3x=8\\\\2x=8\\\\x=\frac{8}{2}=4[/tex]

Therefore the value of x is 4.

Answer:

-The ordered pair (-1, 5) is a solution to the first equation because it makes the first equation true.

-The ordered pair (-1, 5) is a solution to the second equation because it makes the  second equation true.

-The ordered pair (-1, 5) is a solution to the system because it makes both equations true

Step-by-step explanation:

The correct question is

Which statements are true about the ordered pair (−1, 5) and the system of equations?

x+y=4

x−y=−6

we know that

If a ordered pair is a solution of  a equation, then the ordered pair, must satisfy the equation (makes the equation true)

If a ordered pair is a solution of the system of equations, then the ordered pair, must satisfy the equations of the system (makes both equations true)

we have

[tex]x+y=4[/tex] ----> first equation

[tex]x-y=-6[/tex] ----> second equation

step 1

Verify if the ordered pair satisfy  the first equation

Substitute the values of x and y of the ordered pair in the first equation  

For x=-1, y=5    

[tex]-1+5=4[/tex]

[tex]4=4[/tex] ---> is true

The ordered pair satisfy the first equation

so

The ordered pair is a solution to the first equation because it makes the first  equation true

step 2

Verify if the ordered pair satisfy  the second equation

Substitute the values of x and y of the ordered pair in the second equation  

For x=-1, y=5    

[tex]-1-5=-6[/tex]

[tex]-6=-6[/tex] ---> is true

The ordered pair satisfy the second equation

so

The ordered pair is a solution to the second equation because it makes the second  equation true

therefore

The ordered pair (-1, 5) is a solution to the system because it makes both equations true

Answer:

D. Patel found the incorrect quotient and checked his work using multiplication incorrectly.

Step-by-step explanation:

The dividend is [tex]8,[/tex] the divisor is [tex]\dfrac{1}{6}.[/tex] Divide the dividend by the divisor (division by fraction means multiplication by its reciprocal):

[tex]8\div \dfrac{1}{6}=8\times \dfrac{6}{1}=8\times 6=48,[/tex]

so the quotient is 48, not [tex]\dfrac{1}{48}.[/tex]

To check the answer, Patel has to multiply the quotient by the divisor to get the dividend. Check answer:

[tex]48\times \dfrac{1}{6}=\dfrac{48}{6}=8[/tex]

Hence, Patel found the incorrect quotient and checked his work using multiplication incorrectly.

The most accurate description of Patel's work is option D. Patel found an incorrect quotient and checked his work using multiplication incorrectly. therefore, option D. Patel found an incorrect quotient and checked his work using multiplication incorrectly.

Patel initially calculated 8 divided by 1/6 as 1/48, which is incorrect.

The correct quotient is 48.

When Patel multiplied 1/48 by 6, he got 1/8, which is also incorrect.

The correct result should be 48, not 1/8.

So, Patel's division was incorrect, and his check using multiplication was also incorrect.

In summary, Patel made an error in the initial division and didn't accurately check his work using multiplication, leading to an incorrect final result in both cases.

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The total commission that will be paid during the two years is $ 225

Solution:

Given that insurance company pays its agents 40% commission on the first year’s premium and 5% on the second year’s premium for life insurance policies

The premiums are 500$ per year

Commission on first year:

40% commission on the first year’s premium

Thus 40 % commission on $ 500

[tex]\rightarrow 40 \% \text{ of } 500\\\\\rightarrow 40 \% \times 500\\\\\rightarrow \frac{40}{100} \times 500\\\\\rightarrow 200[/tex]

Thus commission paid for first year is $ 200

Commission on second year:

5 % commission on the second year’s premium

Thus 5 % commission on 500

[tex]\rightarrow 5 \% \text{ of } 500\\\\\rightarrow 5 \% \times 500\\\\\rightarrow \frac{5}{100} \times 500 = 25[/tex]

Thus commission paid for second year is $ 25

Total commission paid = $ 200 + $ 25 = 225

Thus Total commission paid is $ 225

Answer: 128.86cm²

Step-by-step explanation:

The circle is inscribed in the rectangle. To find the shaded portion, subtract he area of the circle from the are of the rectangle.

Area of the rectangle                                  =  11 x 12

                                                                     =  132cm²

Area of the circle with radius of 1cm          =  πr²

                                                                     = 3.142 x 1²

                                                                     = 3.142cm²

Therefore , area of the shaded  region      = 132cm²  -  3.142cm²

                                                                    = 128.86cm²

Answer:128.86

Step-by-step explanation: I got it correct on khan

Answer:

The area of each triangle face is 27 square feet .

Step-by-step explanation:

Given as :

The base area of square pyramid = A = 36 square feet

The total surface area of square pyramid = TSA = 144 square feet

Let The area of each triangle face = x square feet

Now, According to question

Total surface Area of square pyramid = Base area of square pyramid + Area of four triangle faces

Or, TSA = A + 4 × x

Or, 144 ft² = 36 ft² + 4 × x  ft²

Or, 4 × x = 144 ft² - 36 ft²

Or  4 ×  x = 108 ft²

∴     x = [tex]\dfrac{108}{4}[/tex]

i.e  x = 27   ft²

So, The area of each triangle face = x = 27 square feet

Hence, The area of each triangle face is 27 square feet . Answer

Answer:

Possible numbers for Joshua's house are #13 and #21.

Step-by-step explanation:

Given:

Vacation houses are equally spaced along a street.

The first house is marked with #10 and so on.

Maria lives in house marked as #17.

Joshua lives 4 houses away from Maria.

So, the difference between Joshua's house number and Maria's house number is 4.

Let 'x' be the house number of Joshua's house.

Case 1: If Joshua's house is after Maria's house. So, [tex]x> 17[/tex]

[tex]x-17=4\\x=17+4=21[/tex]

Case 2: If Joshua's house is before Maria's house. So, [tex]x<17[/tex]

[tex]17-x=4\\17-4=x\\13=x\ or\\x=13[/tex]

Therefore, the possible numbers for Joshua's house are #13 and #21.

Answer:

Step-by-step explanation:

Answer:

a. Fraction of games won by team is [tex]\frac{3}{4}[/tex].

b. Total games played by Katy as catcher is 17.

Step-by-step explanation:

Here is the complete question: A baseball team played 32 games and lost 8 Katy was the catcher in 5/8 of the winning games and 1/4 of the losing games.

a. What fraction of the games did the team win?

b. In how many games did Katy play catcher?

Given: Total number of games= 32

           Total games lost= 8.

           Katy was the catcher in 5/8 of the winning games.

           Katy was the catcher in 1/4 of the losing games.

Now, finding total number games that team won.

Winning total= [tex]32-8= 24[/tex]

∴ Total number of games that team won is 24.

Next finding fraction of the games did the team win.

Fraction of games won by team is [tex]\frac{Games\ won}{Total\ number\ of\ games}[/tex]

∴ Fraction of games won by team = [tex]\frac{24}{32} = \frac{3}{4}[/tex]

Fraction of games won by team is [tex]\frac{3}{4}[/tex]

Lets find out numbers of games Katy play chatcher.

We know, Katy was the catcher in 5/8 of the winning games.

∴ Katy was catcher= [tex]\frac{5}{8} \times 24= 5\times 3[/tex]

Katy was catcher in 15 of the wining games.

We also know, Katy was the catcher in 1/4 of the losing games.

∴ Katy was catcher= [tex]\frac{1}{4} \times 8= 1\times 2[/tex]

Katy was the catcher in 2 of the losing games.

Total games played by Katy as catcher= Catcher in wining games+ catcher in losing games.

∴ Total games played by Katy as catcher= [tex]15+2= 17 games.[/tex]

Hence, total games played by Katy as catcher is 17.

Answer: (1)  x²y (2) 7pqr  (3) a  (4) 6a²  (5) y³z²

Step-by-step explanation:

(1)  x^4y³ and x²y

     x^4y³ =  x²y(x²y²)

    x²y      = x²y

Therefore the Highest Common factor

               x²y which is the common factor.

(2) 14p²qr^4 = 2 x 7 x p² x q  x r^4

   49p²q²r    = 7 x 7 x p² x q² x r

   35pqr       = 5 x 7 x p x q x r

Therefore HCF =  7 x p x q x r

                         = 7pqr

(3) -a^5             = -( a x a x a x a x a )

                         = -(a^5)

       ab³            =   a x b x b x b

Therefore HCF =   a

(4)   6a²             = 2 x 3 x a x a

      -18a6          = -( 2 x3 x 3 x a x a x a x a x a x a)

     -12a²            = -( 2 x 2 x 3 x a x a )

Therefore HCF  = 2 x 3 x a²

                          = 6a²

(5)   3y³z²           = 3 x y x y x y x z x z , 3 x y³ x z²

      15y^4z²       =  3 x 5 x y x y x y x y x y x z x z, 3 x 5 x y^4 x z²

      y^6z³          = y^6 x z³

Therfore HCF  = y³ x z²

                         = y³z²

Answer: The second table

Step-by-step explanation:

For the table to show  proportional relationship between x and y , then they must have a common ratio. that is x/y must be the same throughout

Table 1

[tex]x_{1}[/tex] = 1                [tex]y_{1}[/tex] = 2

[tex]x_{2}[/tex] = 3               [tex]y_{2}[/tex] = 5

[tex]x_{3}[/tex] = 4               [tex]y_{3}[/tex] = 8

[tex]x_{4}[/tex] = 7               [tex]y_{4}[/tex] = 14

[tex]\frac{x_{1}}{y_{1}}[/tex] = 1/2

[tex]\frac{x_{2}}{y_{2}}[/tex] = 3/5

[tex]\frac{x_{3}}{y_{3}}[/tex] = 4/8 = 1/2

[tex]\frac{x_{4}}{y_{4}}[/tex]= 7/14 = 1/2

Since the ratio is not the same throughout , then x and y are not proportional

Table 2

[tex]x_{1}[/tex] = 7               [tex]y_{1}[/tex] = 1

[tex]x_{2}[/tex] = 14               [tex]y_{2}[/tex] = 2

[tex]x_{3}[/tex] = 28               [tex]y_{3}[/tex] = 4

[tex]x_{4}[/tex] = 35              [tex]y_{4}[/tex] = 5

[tex]\frac{x_{1}}{y_{1}}[/tex] = 7/1 = 7

[tex]\frac{x_{2}}{y_{2}}[/tex] = 14/2 = 7

[tex]\frac{x_{3}}{y_{3}}[/tex] = 28/4 = 7

[tex]\frac{x_{4}}{y_{4}}[/tex]= 35/5 = 7

Since the ratio is the same throughout , it means that x and y are proportional.

Doing the same for table 3 and 4 , x and y are not proportional

Answer:

P(x) =  (x-1)² (x-3)

Step-by-step explanation:

P(x)=x³- 5x² + 7x-3 = x² (x-1) - 4x(x-1) + 3(x-1) = (x²-4x+3)(x-1)

P(x) = (x-1)(x-3)(x-1) = (x-1)² (x-3)

Answer:

36 trees were infected with the virus.

Step-by-step explanation:

Given:

Total number of trees =  90

Percentage of tree that had virus  40%

To find:

Number of tress that were infected by virus = ?

Solution:

Let the number trees that was affected by the virus be X.

then

X = 40% of 90

X = [tex]\frac{40}{100} \times 90[/tex]

X = [tex] 0.4 \times 90[/tex]

X= 36

Answer:

[tex]\frac{49\sqrt3}{2}[/tex]

Step-by-step explanation:

30 60 90 Right Trianlge.

Answer:

21 mini-muffins

Step-by-step explanation:

7 multiplied by 3 equals 21

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Tony bought a total of 21 mini-muffins. This was calculated by multiplying the number of packages he bought (7) by the number of mini-muffins in each package (3).

This question is about a mathematical operation called multiplication. Tony purchases 7 packages of mini-muffins. There are 3 mini-muffins in each package. To find the total number of mini-muffins Tony buys, multiply the number of packages he bought (7) by the number of mini-muffins in each package (3). This calculation is written as 7 * 3. Therefore, Tony buys a total of 21 mini-muffins.

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Answer:

The standard form is [tex]7x^7 +6x^5-3x^3 + 8x[/tex]

Step-by-step explanation:

Given:

[tex]6x^5 + 8x-3x^3+7x^7[/tex]

To Find :

standard form of [tex]6x^5 + 8x-3x^3+7x^7[/tex]

Solution:

A polynomial is in standard form when its term of highest degree is first, its term of 2nd highest is 2nd etc.

In order to write any polynomial in standard form, you look at the degree of each term. You then write each term in order of degree, from highest to lowest, left to write.

Now lets check the degree of each term in the polynomial

The degree of 6x is 5

The degree of 8x is 1

The degree of 3x is 3

 The degree of 7x is 7

Now rewrite  the polynomial in the order of the degree, from highest to lowest

[tex]7x^7 +6x^5-3x^3 + 8x[/tex]

Answer:

She needs $8 more to buy a game that cost $45

Step-by-step explanation:

10 * 2 = 20

5 * 3 = 15

1 * 2 = 2

20+15+2 = 37

45-37 = $8

She needs $8 more to buy a game that cost $45

Answer:

Step-by-step explanation:

Convert to the slope-intercept form (y = mx + b):

[tex]2y=5x+11[/tex]             divide both sides by 2

[tex]\dfrac{2y}{2}=\dfrac{5x}{2}+\dfrac{11}{2}\\\\y=\dfrac{5}{2}x+\dfrac{11}{2}[/tex]

We choose any three x values ​​and calculate the y value:

for x = -1

[tex]y=\dfrac{5}{2}(-1)+\dfrac{11}{2}=-\dfrac{5}{2}+\dfrac{11}{2}=\dfrac{6}{2}=3\to A(-1,\ 3)[/tex]

for x = 1

[tex]y=\dfrac{5}{2}(1)+\dfrac{11}{2}=\dfrac{5}{2}+\dfrac{11}{2}=\dfrac{16}{2}=8\to B(1,\ 8)[/tex]

for x = -3

[tex]y=\dfrac{5}{2}(-3)+\dfrac{11}{2}=-\dfrac{15}{2}+\dfrac{11}{2}=-\dfrac{4}{2}=-2\to C(-3,\ -2)[/tex]

Mark the points on the coordinate plane and draw a line through the given points.

Answer:

[tex]f(1)=9[/tex]

Step-by-step explanation:

[tex]Given \ f(n+1)=f(n)\\f(3)=f(2)\\f(2)=f(1)\\f(1)=f(2)=f(3)\\f(1)=f(3)\\f(1)=9[/tex]

(-8,1) should be the correct answer! Good Luck and Happy Holidays!!

Option E

The numerator of fraction is 21

[tex]2\frac{5}{8}[/tex] is to be written as improper fraction in lowest terms

To find: numerator of fraction

An improper fraction is a fraction in which the numerator (top number) is greater than or equal to the denominator (bottom number).

To convert a mixed fraction to an improper fraction, follow these steps:

[tex]2\frac{5}{8} = \frac{8 \times 2 + 5}{8} = \frac{16 + 5}{8} = \frac{21}{8}[/tex]

Thus the numerator of fraction is 21. Option E is correct

There are probably some choices we're not being shown, but let's just do the whole procedure.

x² + 6x - 8 = 0

Step one: move the 8 to the other side.

x² + 6x = 8

Step two: add (6/2)²=9 to both sides.

x² + 6x + 3² = 8 + 9

Step three: Factor

(x + 3)² = 17

Step four: take the square root

x + 3 = ±√17

Step five: Solve for x,

x = -3  ± √17

Answer:

The Sum Of The Integers From -6 To 58 is 1690.

Step-by-step explanation:

Given,

[tex]a=-6[/tex]

[tex]T_n=58[/tex]

We have to find out the sum of integers from -6 To 58.

Firstly we will find out the total number of terms that is 'n'.

Here [tex]a_1=-6\ and\ a_2=-5[/tex]

[tex]\therefore d=a_2-a_1=-5-(-6)=-5+6=1[/tex]

Now we use the formula of A.P.

[tex]T_n=a+(n-1)d[/tex]

On substituting the values, we get;

[tex]58=-6+(n-1)1\\\\n-1=58+6\\\\n-1=64\\\\n=64+1=65[/tex]

So there are 65 terms in between  -6 To 58.

That means we have to find the sum of 65 terms in between  -6 To 58.

Now we use the formula of Sum of n_terms.

[tex]S_n=\frac{n}{2}(2a-(n-1)d)[/tex]

On substituting the values, we get;

[tex]S_{65}=\frac{65}{2}(2\times-6+(65-1)1)\\\\S_{65}=\frac{65}{2}(-12+64)\\\\S_{65}=\frac{65}{2}\times52\\\\S_{65}=65\times26=1690[/tex]

Hence The Sum Of The Integers From -6 To 58 is 1690.

Final answer:

The sum of the integers from -6 to 58 is calculated using the formula for the sum of an arithmetic series and is found to be 1,690.

Explanation:

To find the sum of the integers from -6 to 58, we can use the formula for the sum of an arithmetic series, which is S = n/2 * (a1 + an), where S is the sum of the series, n is the number of terms, a1 is the first term, and an is the last term.

We first need to determine the number of terms in our series. Since our series starts at -6 and ends at 58, we can find the number of terms by subtracting -6 from 58 and then adding 1 (because both ends are inclusive). That gives us 58 - (-6) + 1 = 65 terms.

Now, we can plug the values into the sum formula:

S = 65/2 * (-6 + 58) = 32.5 * 52 = 1690.

Therefore, the sum of the integers from -6 to 58 is 1,690.

Answer:

[tex]x^{4} -18x^{3}+104x^{2} -172x-100[/tex]

Step-by-step explanation:

The 3 roots are given out of which 2 are real and 1 is imaginary. For a polynomial of least degree having real coefficients, it must have a complex conjugate root as the 4th root. Therefore, based on 4 roots, the least degree of polynomial will be 4. Finding the polynomial having leading coefficient=1 and solving it based on multiplication of 2 quadratic polynomials, we get:  

[tex]\\\\x_{1} = 2-\sqrt{6} \\x_{2} = 2+\sqrt{6} \\x_{3}=7-i \\x_{4}=7+i \\\\P(x)=1(x-x_{1})(x-x_{2} )(x-x_{3} )(x-x_{4} ) \\\\=(x-(2-\sqrt{6}))(  x-(2+\sqrt{6} )) (x-(7-i))( x-(7+i))\\=((x-2)+\sqrt{6})( ( x-2)-\sqrt{6} ) ((x-7)+i)( (x-7)-i)\\=((x-2)^{2} -(\sqrt{6} )^{2} )((x-7)^{2}-(i)^{2})\\=(x^{2} -4x-2)(x^{2} -14x+50)\\=x^{4} -18x^{3}+104x^{2} -172x-100\\[/tex]

Answer:

X^4-16x^3+73x^2-30x-250

Step-by-step explanation:

Answer:

F is the mid point of BC. (Proved)

Step-by-step explanation:

See the attached diagram.

Given AB ║ CD and EF is drawn to be parallel to AB.

So, EF ║ AB ║ CD .......... (1)

Now, in Δ ABD, E is the midpoint of AD and EG is parallel to AB.

So, G must be the midpoint of BD.

Now, in Δ BCD, G is the midpoint of DB and GF is parallel to CD. {From relation (1)}

So, we can write F is the midpoint of BC. (Proved)

[Since we know the theorem that if we joint the midpoints of two sides of a triangle then the line formed will be parallel to the third side.]

Answer:

Step-by-step explanation:

7.56 × 10^3

= 7.56×1000

= 7560

Answer:

447,697.125

Step-by-step explanation:

multiply 7.65 by 10

76.5

76.5 to 3rd power is just 76.5 times 76.5 times 76.5

answer is 447,697.125

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Answer:

Step-by-step explanation:

a spinner with the colors orange, yellow, purple, and green.....so this spinner only has 4 spaces....and 1 of those spaces is purple...so the ratio of stopping on purple is 1/4 or 0.25

The spinner has 4 colors, and purple is one of these. To find the theoretical probability of it stopping at purple, we divide 1 by 4, resulting in 0.25. Therefore, the theoretical probability of the spinner stopping on purple rounded to nearest hundredth is 0.25.

The probability of the spinner stopping on the color purple can be calculated by dividing the number of ways this can happen (which is 1, as there's only one purple on the spinner) by the total number of outcomes in the sample space (which is 4, as there are 4 colors on the spinner).

So, the probability would be 1 ÷ 4 = 0.25.

To get the value as a rounded decimal to the nearest hundredth, it stays 0.25 as it is already to the nearest hundredth.

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Answer:

The radius of the given equation is 2 .

Step-by-step explanation:

The equation of a circle whose center (h, k) and radius is r,

(x - h)² + (y - k)² = r² ..............................(i)

Here given that-

x² + y² + 21 = 10 x

x² - 10 x + y² + 21 = 0

( To making perfect square, add and subtract 25 ) -

x² - 10 x + 25 - 25 + y² + 21 = 0

(x² - 10 x + 25) + y² -4 =0

[As we know that -

(x - 5)² = x² - 10 x + 25]

(x - 5 )² + y² = 4

(x - 5)² + (y - 0)² = 4

(x - 5 )² + (y- 0)² = 2² ................................(ii)

On comparing equation (i) and(ii)-

r = 2

Hence the radius of the given equation is 2 and center is ( 5, 0).

Answer:

Part 1) [tex]BC=68\ units[/tex]

Part 2) [tex]DE=36\ units[/tex]

Part 3) [tex]CE=34\ units[/tex]

Step-by-step explanation:

we know that

The Midpoint Theorem states that the segment joining two sides of a triangle at the midpoints of those sides is parallel to the third side and is half the length of the third side

so

Part 1) Find the length of  BC

Applying the Midpoint Theorem

[tex]DF=\frac{1}{2}BC[/tex]

we have

[tex]DF=34\ units[/tex]

substitute the given value

[tex]34=\frac{1}{2}BC[/tex]

solve for BC

[tex]BC=34(2)=68\ units[/tex]

Part 2) Find the length of  DE

Applying the Midpoint Theorem

[tex]DE=\frac{1}{2}AC[/tex]

we have

[tex]AC=72\ units[/tex]

substitute the given value

[tex]DE=\frac{1}{2}(72)[/tex]

[tex]DE=36\ units[/tex]

Part 3) Find the length of  CE

we know that

[tex]BC=CE+BE[/tex] ----> by addition segment postulate

The point E is the midpoint segment BC

That means

[tex]CE=BE[/tex]

so

[tex]BC=2CE[/tex]

we have

[tex]BC=68\ units[/tex]

substitute

[tex]68=2CE[/tex]

solve for CE

[tex]CE=68/2[/tex]

[tex]CE=34\ units[/tex]

Answer:

I'm not Certain but I'm thinking that it would be 4 boxes of the regular tea and 5 of the herbal tea.

Step-by-step explanation:

herbal- $1.50

regular- $1

$1*4 =$4

$1.50*5 = $7.50

$4.00+ $7.50=11.50

Answer:

Herbal tea box = 3

Regular tea box =  7

Step-by-step explanation:

Le x be the number of herbal tea box and y be the number of regular tea box.

The herbal tea variety cost $1.50 per box and the regular variety cost $1.00 per box they bought A total of 10 boxes and spent $11.50.

[tex]x+y=10\Rightarrow y=10-x[/tex]          .... (1)

[tex]1.50x+1.00y=11.50[/tex]             ... (2)

From (1) and (2) we get

[tex]1.50x+1.00(10-x)=11.50[/tex]

[tex]1.50x+10-1.00x=11.50[/tex]

[tex]0.50x=11.50-10[/tex]

[tex]0.50x=1.50[/tex]

[tex]x=\dfrac{1.50}{0.50}=3[/tex]

Substitute x=3 in equation (1).

[tex]y=10-x=10-3=7[/tex]

Therefore, the number of herbal tea boxes is 3 and the number of regular tea boxes is 7.