A garden table and a bench cost $741 combined. The garden table costs $91 more than the bench. What is the cost of the bench?

X=1 and

Y=3

Look at the image attached to see what I did

X = 1

Y = 3

Hope this helps!

Answer:

50 tickts

Step-by-step explanation:

We want to spread 1,000 tickets equally over 20 concerts. This calls for division

1000/20=50

50 tickets are sold each concert

Answer:

use foil method-first inside outside last

Step-by-step explanation:

Answer:

X = -10

Step-by-step explanation:

Adding negative ten and ten results in zero, and zero multiplied by anything is, of course, still zero.

(-10 + 10) * (-10 + 10) = 0

0 * 0 = 0

X=-10

Because (x+10)(x+10)=0

So it becomes (x+10)^2=0

And therefore x=-10

Answer:

B) $5.00,$1.00,$123

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

C would be the correct answer. You caanot multiply just one part of an equation, you must multiply the whole thing. All of the other steps follow this rule, so C is an incorrect step, and is therefore the correct choice.

Hope this helps!

Answer:

C) Multiply 3x by 6 in the first equation and subtract the second equation.

Step-by-step explanation:

We have been given a system of equations.[tex]3x+3y = 4[/tex] and [tex]18x-9y = 12[/tex]. We are asked to choose the "incorrect" step that will make "not" produce a system with the same solution.

Let us see our give choices one by one.

A) multiply the first equation by 6 and subtract the second equation.

When we will multiply 1st equation by 6, the coefficient of x would be 18. When we will subtract 2nd equation the both x's will cancel out. Therefore, option A is correct.

B) multiply the first equation by −6 and add the second equation.

When we will multiply 1st equation by -6, the coefficient of x would be -18. When we will add 1st equation to 2nd equation the both x's will cancel out. Therefore, option B is correct as well.

C) Multiply 3x by 6 in the first equation and subtract the second equation.

We need to remember that we cannot multiply only one term of equation by some quantity as it will make the whole equation false, therefore, option C is incorrect.

[tex]\frac{3n-7}{6}=\frac{2n+5}{3}[/tex]   Multiply 3 and 6 on both sides to get rid of the fraction (or cross multiply)

[tex]\frac{3n-7}{6}(3)=\frac{2n+5}{3} (3)[/tex]

[tex]\frac{3n-7}{6}(3)(6)=(2n+5)(6)[/tex]

3(3n - 7) = 6(2n + 5)    Distribute/multiply 3 into 3n-7, and 6 into 2n+5

(3)3n - (3)7 = (6)2n + (6)5

9n - 21 = 12n + 30    Subtract 9n on both sides

-21 = 3n + 30        Subtract 30 on both sides

-51 = 3n     Divide 3 on both sides

-17 = n

Answer:

n = 17/6 = 2.833

Step-by-step explanation:

Step by step solution :

Step 1 :

5

Simplify —

3

Equation at the end of step 1 :

7 5

(3n - —) - (2n + —) = 0

6 3

Step 2 :

Rewriting the whole as an Equivalent Fraction :

2.1 Adding a fraction to a whole

Rewrite the whole as a fraction using 3 as the denominator :

2n 2n • 3

2n = —— = ——————

1 3

Equivalent fraction : The fraction thus generated looks different but has the same value as the whole

Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator

Adding fractions that have a common denominator :

2.2 Adding up the two equivalent fractions

Add the two equivalent fractions which now have a common denominator

Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

2n • 3 + 5 6n + 5

—————————— = ——————

3 3

Equation at the end of step 2 :

7 (6n + 5)

(3n - —) - ———————— = 0

6 3

Step 3 :

7

Simplify —

6

Equation at the end of step 3 :

7 (6n + 5)

(3n - —) - ———————— = 0

6 3

Step 4 :

Rewriting the whole as an Equivalent Fraction :

4.1 Subtracting a fraction from a whole

Rewrite the whole as a fraction using 6 as the denominator :

3n 3n • 6

3n = —— = ——————

1 6

Adding fractions that have a common denominator :

4.2 Adding up the two equivalent fractions

3n • 6 - (7) 18n - 7

———————————— = ———————

6 6

Equation at the end of step 4 :

(18n - 7) (6n + 5)

————————— - ———————— = 0

6 3

Step 5 :

Calculating the Least Common Multiple :

5.1 Find the Least Common Multiple

The left denominator is : 6

The right denominator is : 3

Number of times each prime factor

appears in the factorization of:

Prime

Factor Left

Denominator Right

Denominator L.C.M = Max

{Left,Right}

2 1 0 1

3 1 1 1

Product of all

Prime Factors 6 3 6

Least Common Multiple:

6

Calculating Multipliers :

5.2 Calculate multipliers for the two fractions

Denote the Least Common Multiple by L.C.M

Denote the Left Multiplier by Left_M

Denote the Right Multiplier by Right_M

Denote the Left Deniminator by L_Deno

Denote the Right Multiplier by R_Deno

Left_M = L.C.M / L_Deno = 1

Right_M = L.C.M / R_Deno = 2

Making Equivalent Fractions :

5.3 Rewrite the two fractions into equivalent fractions

Two fractions are called equivalent if they have the same numeric value.

For example : 1/2 and 2/4 are equivalent, y/(y+1)2 and (y2+y)/(y+1)3 are equivalent as well.

To calculate equivalent fraction , multiply the Numerator of each fraction, by its respective Multiplier.

L. Mult. • L. Num. (18n-7)

—————————————————— = ———————

L.C.M 6

R. Mult. • R. Num. (6n+5) • 2

—————————————————— = ——————————

L.C.M 6

Adding fractions that have a common denominator :

5.4 Adding up the two equivalent fractions

(18n-7) - ((6n+5) • 2) 6n - 17

—————————————————————— = ———————

6 6

Equation at the end of step 5 :

6n - 17

——————— = 0

6

Step 6 :

When a fraction equals zero :

6.1 When a fraction equals zero ...

Where a fraction equals zero, its numerator, the part which is above the fraction line, must equal zero.

Now,to get rid of the denominator, Tiger multiplys both sides of the equation by the denominator.

Here's how:

6n-17

————— • 6 = 0 • 6

6

Now, on the left hand side, the 6 cancels out the denominator, while, on the right hand side, zero times anything is still zero.

The equation now takes the shape :

6n-17 = 0

Solving a Single Variable Equation :

6.2 Solve : 6n-17 = 0

Add 17 to both sides of the equation :

6n = 17

Divide both sides of the equation by 6:

n = 17/6 = 2.833

One solution was found :

n = 17/6 = 2.833

Answer:

7/12

Step-by-step explanation:

1 1/3 - 3/4

= 4/3 - 3/4

= 16/12 - 9/12

= 7/12

Answer:

[tex]1\frac{1}{3}-\frac{3}{4}=\frac{7}{12}[/tex]

change [tex]1\frac{1}{3}[/tex] into [tex]\frac{4}{3}[/tex]

[tex]=\frac{4}{3}-\frac{3}{4}[/tex]

get like denominators:

12

[tex]\frac{16}{12}-\frac{9}{12}[/tex]

16 - 9 = 7

Hope this helps and have a great day!!!

Okay so if the regular price of the shirt is 100% as $25 and you have a 30% discount you are still paying 70% (100-30=70) so 70% as a decimal is .70 and $25 x .70 is $17.50. Therefore the shirt is $17.50 after the discount.

Alright so, what it’s basically asking for is 70% of 25. This is the price of the shirt after you’ve accounted for the 30% discount

Then you would multiply 25 by .70, giving you $17.50

Hope this helps!

Answer:

D) -110

Step-by-step explanation:

x and y are variables, and any number that is in front of a variable (multiplication) is called a coefficient. 4 is the coefficient. x can be substituted. A constant is a number that does not change.  -110 is the constant.

Answer:

x1=4

x2=8

Step-by-step explanation:

1- Factor the equation.

2- solve a  Single Variable Equation

3- Parabola, Finding the Vertex

2x+4= 3x-6+2

2x+4=3x-4

2x-3x+4=3x-3x-4

-x+4=-4

-x+4-4= -4-4

-x=-8

Need to multiply by -1 for x to be positive and also for -8

-1(-x)= -1(-8)

x=8

Answer:

Step-by-step explanation:

2x+4=3(x-2)

2x+4=3x-6

+6 -2x

10 = 1x

1 = 1x

10= x

39. each term is ten more than the term before it :)

Answer:

39, 49, 59

Step-by-step explanation:

Note the difference between consecutive terms

9 - (- 1) = 9 + 1 = 10

19 - 9 = 10

29 - 9 = 10

The difference is a constant + 10

To obtain the next term in the sequence add 10 to the previous term

29 + 10 = 39

39 + 10 = 49

49 + 10 = 59

The next 3 terms are 39, 49, 59

Answer:

His money earned $36 after 3 months

Step-by-step explanation:

* Lets revise the rules of simple interest

- Simple Interest Equation (Principal + Interest)

 A = P(1 + rt)

- Where:

• A = Total amount (principal + interest)  future amount

• P = Principal Amount

• I = Interest Amount

• r = Rate of Interest per year in decimal; r = R/100

• t = Time Period involved  

* To calculate the interest I use the formula

  I = P × r × t

* Lets solve the problem

- The rate is annual

- The interest calculated after 3 months

∴ I = P × R/100 × t/12

∵ P = $3600.00

∵ R = 4%

∵ t = 3 month

∴ I = 3600.00 × 4/100 × 3/12 = $36

* His money earned $36 after 3 months

There are 720 different 6-letter arrangements that can be formed using the letters in the word QUASAR, calculated by 6 factorial (6!).

The question asks for the total number of different 6-letter arrangements that can be formed using the letters in the word QUASAR. This is a problem of permutations where all the letters are distinct. To find the number of different permutations of the letters in QUASAR, we multiply the number of choices available at each position. There are 6 choices for the first letter, 5 for the second, and so on, until 1 choice for the last letter.

Therefore, the permutations are calculated as 6 × 5 × 4 × 3 × 2 × 1, which is equal to 6! (6 factorial).

The calculation of 6! is as follows:

So, there are 720 different 6-letter arrangements that can be formed from the word QUASAR.

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Answer:

the answer is 25%

Step-by-step explanation:

100% : 4 =25

Answer:

%88 i believe

Step-by-step explanation:

hope this helps!

Answer: $43786.22 (Round)

Step-by-step explanation: Use this formula: A= P(1+r/n)^nt

We are trying to find A in this problem.

Plug it in:

A= 19,000(1+0.11/1)^(1)(8)

Answer:

The function is linear

Step-by-step explanation:

* Lets check from the table the type of the function

- At first check if it is linear or not

- The points are:

  (165 , 198) , (168 , 201.6) , (170 , 204) , (172 , 206.4) , (175 , 210)

* Find the slope for each two points if the value of the slop is

 constant, then the function will be linear

∵ The slop = (y2 - y1)/(x2 - x1)

∴ m1 = (201.6 - 198)/(168 - 165) = 1.2

∴ m2 = (204 - 201.6)/(170 - 168) = 1.2

∴ m3 = (206.4 - 204)/(172 - 170) = 1.2

∴ m4 = (210 - 206.4)/(175 - 172) = 1.2

∵ m1 = m2 = m3 = m4

# Note: You can use any to points to find the slope you will

  have the same value

∴ The graph of the points is a line with slope 1.2

* The function is linear

Answer:

A linear function is the best model.

The ratio of y to x for the ordered pairs is constant, so the relationship is a direct variation. A direct variation is a type of linear function.

When the data set is plotted, it forms a line.

Step-by-step explanation:

Answer:

20

Step-by-step explanation:

Set up ratios

for the shadows- 12:3, or 4:1

then height=4*5, or 20

Answer:20 feet

Step-by-step explanation:

5/3 = x/12

Use butterfly method.

3x = 60

x = 20

After 3 seconds and at 60 feet, the bolt hit the elevator if the height in feet after t second is given by the formula h(t)=20t.

Any equation of the form [tex]\rm ax^2+bx+c=0[/tex] Where x is variable and a, b, and c are any real numbers where a ≠ 0 is called a quadratic equation.

As we know, the formula for the roots of the quadratic equation is given by:

[tex]\rm x = \dfrac{-b \pm\sqrt{b^2-4ac}}{2a}[/tex]

When the bolt hit the elevator, they would be at the same height.

∴ 16t²+200 = 20t

16t² -20t + 200 = 0

It is a quadratic equation:

a = 16, b = -20, and c = 200 plug this values in the formula.

After calculating, we will get:

t = -4.2 or t = 3

Time cannot be negative.

So t = 3 seconds

And height h(3) = 20(3) = 60 feet

Thus, after 3 seconds and at 60 feet, the bolt hit the elevator if the height in feet after t second is given by the formula h(t)=20t.

Learn more about quadratic equations here:

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Answer:

There are infinitely many solutions.  It is the same line.

Step-by-step explanation:

If you start by multiplying the first equation by 2 to get rid of the fractions, you get -x + y = -2.  If you solve it for y, you get y = x - 2.  The second equation can be solved for y also, giving you y = x - 2.  That means they are the same line and the solution to this situation is infinitely many solutions because all the points on one line are identical to the points on the other line because they are the same line.

Answer:

C

Step-by-step explanation:

plato gang

Answer:

B

Step-by-step explanation:

The range of the function are the corresponding values of y for the given points

x = 1,3 → y = 5

x = 4 → y = 2

x = 6 → y = - 2

The range of the graphed function is { - 2, 2, 5 } → B

41 there are 12 numbers take middle

Hi

The answer is 41

11 18 23 32 33 =41= 54 56 58 67 70

Answer:

42

Step-by-step explanation:

23+18+67+32+54+41+70+11+56+33+41+58=504

(There's 12 sets of numbers)

504/12=42

Answer:

(1/2)(x³ - 3)

Step-by-step explanation:

That would be   (1/2)(x³ - 3).

The expression ' one-half difference of a number cubed and one' is written as [tex]\frac{1}{2} (x^3 - 1)[/tex].

Let the number be [tex]x[/tex].

The cube of the number is [tex]x^3[/tex].

Difference of the cube of the number with [tex]1[/tex] is [tex]x^3 - 1[/tex].

Now, one-half difference of a number cubed and one is represent as,

[tex]\frac{1}{2} (x^3 - 1)[/tex].

So, the expression ' one-half difference of a number cubed and one' is written as [tex]\frac{1}{2} (x^3 - 1)[/tex].

Learn more about expressions here:https:

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Volume of a sphere:

(4/3)(pi)r^3

.

radius (r) is half the diameter or 8 inches.

(4/3)(3.14)8^3

2144 cubic inches

The volume of the sphere would be 2144 cubic inches

A sphere is a three-dimensional shape analouge of a circle.

The Volume of a sphere = 4/3πr^3

We are given that the diameter of the sphere as 16 cm.

Since radius (r) is half the diameter or 8 inches.

Volume of a sphere:

= 4/3πr^3

= (4/3)(3.14)8^3

2144 cubic inches

Learn more about sphere;

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Answer: parallel because the slopes are the same

Step-by-step explanation:

Answer:

10 uniforms

Step-by-step explanation:

You will start by subtracting 250 from 550 to get 300. You will then divide 300 by 28 to get the total number of uniforms. You will get the answer 10.7, but because we are dealing with uniforms, we will remove the decimal and just use 10.

Answer:

4=2/3 . 7/9=14/21

4/5.  /5/6=20/30=2/5

Step-by-step explanation:

Answer:

Step-by-step explanation:

The segment 20.2 cm is the tangent. Therefore x and 20.2cm are perpendicular.

Use the Pythagorean theorem:

[tex]leg^2+leg^2=hypotenuse^2[/tex]

We have

[tex]leg=x,\ leg=20.2cm,\ hypotenuse=(14.7+x)cm[/tex]

Substitute:

[tex]x^2+20.2^2=(14.7+x)^2[/tex]           use (a + b)² = a² + 2ab + b²

[tex]x^2+408.04=14.7^2+(2)(14.7)(x)+x^2[/tex]          subtract x² from both sides

[tex]408.04=216.09+29.4x[/tex]        subtract 216.09 from both sides

[tex]191.95=29.4x[/tex]         divide both sides by 29.4

[tex]x\approx6.5\ cm[/tex]

Answer:

See explanation

Step-by-step explanation:

The given complex number are:

[tex]z_1=-3\sqrt{3}+3i[/tex]

and

[tex]z_2=6\cos 150\degree+6i\sin 150\degree[/tex]

When we rewrite [tex]z_1=-3\sqrt{3}+3i[/tex] in complex form, we obtain;

[tex]z_1=r(\cos \theta+i\sin \theta)[/tex]

where

[tex]r=\sqrt{(-3\sqrt{3})^2+3^2 }=\sqrt{36}=6[/tex]

and

[tex]\theta=tan^{-1}(\frac{y}{x})[/tex]

[tex]\implies \theta=tan^{-1}(\frac{-3\sqrt{3}}{3})=150\degree[/tex]

Hence,

[tex]z_1=6(\cos 150\degree+i\sin 150\degree)[/tex]

[tex]z_1=6\cos 150\degree+6i\sin 150\degree[/tex]

Hence

[tex]z_1=z_2[/tex]

Answer:

C- graph III

Step-by-step explanation:

The only graph showing a positive trend. If your selling tickets, you'll have an increased profit.