A furniture store is having a 20% sale.

(a) A sofa usually costs £1200. Work out the sale price of the sofa.

(b) The sale price of a table is £480. Work out the original price of the table.

The solution for the system of equations of three variables is:

x = 4

y = -1

z = -3

Or (4, -1, -3) written as a point.

Here we have a system of equations on 3 variables, the system is:

3x + 2y + z = 7

5x + 5y +4z = 3

3x + 2y + 3z = 1

Notice that the "x" and "y" coefficients in the first and last equation are the same ones, so we can take the difference between these to get:

(3x + 2y + 3z ) - (3x + 2y + z ) = 1 - 7

2z = -6

z = -6/2 = -3

So the value of z is -3.

Replacing that in the first and second equation we get:

3x + 2y - 3 = 7

5x + 5y + 4*(-3) = 3

Now we can simplify these:

3x + 2y = 10

5x + 5y = 15

We can divide the second one by 5 to get:

(5x + 5y)/5 = 15/5

x + y = 3

Isolating x, we get:

x = 3 - y

Now we replace that in the other equation:

3*(3 - y) + 2y = 10

9 - y = 10

9 - 10 = y

-1 = y

Now we know the value of y, finally with:

x = 3 - y

We can get the value of x:

x = 3 - (-1) = 4

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The result of the expression given is 3x - 3

To solve this problem, we have to simplify the equation, and write the expression.

Given that

[tex]\sqrt{x^2}+ 2x -3[/tex]

For every square root having a square inside, they both cancel out each other to have the variable only.

Lets apply that in this expression

[tex]\sqrt{x^2} + 2x - 3\\x + 2x - 3[/tex]

To solve the expression, we would have the final answer to the question.

[tex]x + 2x - 3\\3x - 3[/tex]

The value of the expression given is 3x - 3

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Answer :- 60 cm^2

Step-by-Step Solution :-

Let ABCD be the Rectangle.

Given :

AD = 12 cm

BD = 13 cm

To Find : Area of ABCD

Solution :

In ∆ADB,

AD = 12 cm and BD = 13 cm

By Pythagoras Theorem,

(BD)^2 = (AD)^2 + (AB)^2

13^2 = 12^2 + (AB)^2

169 = 144 + (AB)^2

AB^2 = 169 - 144 = 25

AB = √25

Therefore, AB = 5 cm

Now, to find the Area,

Area of Rectangle = length × breadth

Area of ABCD = 12 × 5

Therefore, Area of ABCD = 60 cm^2

Answer:

x = 2

Step-by-step explanation:

The Question was:
7x + 14 = 28

Subtract 14 from both sides.

7x = 28 − 14

Subtract 14 from 28 to get 14.

7x = 14

Divide both sides by 7.

x = 14/7

​

Divide 14 by 7 to get 2.

x = 2

Answer:

x=2

Step-by-step explanation:

To solve a question like that, we have to isolate the variable.

What is the variable? A variable is a letter partaking in an equation that is in place of a number or solution that makes the equation true.

In this case, the variable is x.

To isolate the variable, we must do the opposite action that is being done to the number.

For example, if a number was added to one side by 28, we can subtract both sides by 28 so it negates the addition and does not alter the original equation.

7x+14=28                We can subtract the 14 on both sides to negate the                                -14  -14                     addition.

7x=14                      Divide each side by 7 to isolate x.

x=2

Answer:

x = 32

Step-by-step explanation:

-6(x-18) = -84

Divide both sides by -6

x - 18 = 14

Add 18 to both sides

x = 32

If the diameter of the Ferris wheel is 80 meters, then a rider will travel  251.2 meters in one complete rotation around the Ferris wheel.

The diameter of the Ferris wheel = 80 meters

The radius of the Ferris wheel = Diameter / 2

= 80/2

= 40 meters

The Total distance travelled by the rider in one revolution = The circumference of the wheel

The circumference of the wheel = 2πr

Where r is the radius of the wheel

Substitute the values in the equation

The circumference of the wheel = 2×3.14×40

= 251.2 meters

Hence, if the diameter of the Ferris wheel is 80 meters, then a rider will travel  251.2 meters in one complete rotation around the Ferris wheel

The complete question is :

If the diameter of the Ferris wheel is 80 meters, how far does a rider travel in one complete rotation around the Ferris wheel?

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Answer: 769 bottles ≤ 12x + 205, or 564 bottles ≤ 12x

Step-by-step explanation:

➜ They need at least 769 bottles, so our inequality will use either ≤ or ≥ depending on how we set it up.

➜ They currently have 205 bottles, so we will use addition to show there are some glasses currently owned

➜ If each set contains 12 glasses, we will multiply x, the number of sets bought, by 12

     With these details, we will write an inequality.

769 bottles ≤ 12x + 205

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Answer:

1/5, 30%, 0.8, 4/3

The container whose sugar water mixture is a darker shade of red is: A. the small bowl's mixture is a darker shade of red.

A ratio can be defined as a mathematical expression that's used to denote the proportion of two (2) or more quantities with respect to one another and the total quantities.

In this scenario, the ratio of the sugar water mixture in the small bowl (S) to the sugar water mixture in the large bucket (L) can be represented by this mathematical expression:

S:L = 1:3

Also, when red coloring is added to both containers, we have:

S:L = 1r:3r

In this context, we can reasonably and logically deduce that the mixture in the small bowl would have a darker shade of red because it is less diluted in comparison with the sugar water mixture in the large bucket.

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Complete Question:

For her science fair project, Madelyn is growing crystals with sugar water. She wants to know if the size of the container has an effect on crystal growth. To start, Madelyn pours a sugar water mixture into a small bowl. Then she pours triple the amount of the mixture into a large bucket. She decides to add red coloring so the crystals are more visible. Madelyn adds the same amount of red coloring to both containers. Which container's sugar water mixture is a darker shade of red?

answer choices

The small bowl's mixture is a darker shade of red.

The large bucket's mixture is a darker shade of red.

Neither. The mixtures are the same shade of red.

Based on the highest common factor, the number of kids that can decorate 30 pumpkins equally and make scarecrows from the materials without leftovers is 5.

The highest common factor (HCF) is the number that can divide between 30 and 36 without a remainder.

                          Pumpkins      Materials

Units                       30                 36

HCF                          6                   6

Average used          5                  6

Thus, dividing 30 and 36 by their HCF of 6, respectively, shows that 5 kids can decorate the 30 pumpkins using 6 materials each to make the scarecrows.

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The number of kids who can decorate 30 pumpkins equally and make scarecrows from the materials without leftovers would be; 5.

factorization is the method of breaking a number into smaller numbers that multiplied together will give that original form.

The highest common factor (HCF) is defined as the number which can divide between 30 and 36 without a remainder.

Given that they have 30 to decorate and 36 sets of material to make mini scarecrows.

Their HCF is 6. The averages used are 5  and 6 respectively.

Hence, their HCF of 6, shows that 5 kids can decorate the 30 pumpkins by using 6 materials each to make the scarecrows.

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The angles that are congruent to angle 6 in the given diagram are:

∠2, ∠3, and ∠5.

Interior angles that lie opposite to each other along a transversal that cut across the parallel lines they are found on are said to be congruent angles based on the alternate interior angles theorem.

Also, vertical angles have angle measure that are the same, that is, they are congruent as well, so also are corresponding angles.

In the image given, angles 3 and 6 are alternate interior angles. Therefore, they are congruent.

∠5 is congruent to ∠6 because they are vertical angles.

∠2 is congruent to ∠6 because they are corresponding angles.

The angles that are congruent to angle 6 are: angles 3, 5, and 2.

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Answer:

  y = 3x -4

Step-by-step explanation:

You want the slope intercept equation representing the relationship between x and y, given (x, y) = (1, -1) and (4, 8).

The slope can be found using the formula ...

  m = (y2 -y1)/(x2 -x1)

  m = (8 -(-1))/(4 -1) = 9/3 = 3

The y-intercept can be found using the equation ...

  b = y1 -m(x1)

  b = -1 -3(1) = -4

The slope-intercept equation of a line has the form ...

  y = mx + b

Using the above values of m and b, this becomes ...

  y = 3x -4

__

Additional comment

Attached is a graph showing the points and the line the equation represents.

<95141404393>

Solution

Given that

Area f small square = 40 inches squared.

Let the side of the large square be L

Since the large square has sides that are 8 times longer than the small square

=> L = 8l

Hence, the area of Large square is;

Hence, the area of the large square is: 256 inches squared.

The probability that their hospital stay is greater than 6 days is equal to 0.67724 and the probability that their hospital stay is from 5 to 6 days is equal to 0.108

Mean (μ) = 7.37

Standard deviation (σ) = 3

we need to calculate probability that their hospital stay is from 5 to 6 days i.e.

⇒ P(5 < X < 6) = P(X < 6)-P(X < 5)

Here we will use standard normal distribution where,

Z-score = (X -μ )/ σ = (6 - 7.37)/3 = -0.46

Z-score = (5 - 7.37)/3 = -0.79

from Z table we found p-value

⇒P(5<X<6) = P(X<6) - P(X<5) = 0.32276 - 0.21476 = 0.108

So there is 0.108 probability that their hospital stay is from 5 to 6 days.

we need to calculate probability that their hospital stay is greater than 6 days i.e.

We get: P(X > 6) = 1 − P(X < 6)

Here we will use standard normal distribution where,

Z-score = (X - μ)/σ = (6 - 7.37)/3 = -0.46

from Z table we found p-value

P(X > 6) = 1 - P(X<6) = 1 - 0.32276 = 0.67724

So there is 0.67724 probability that their hospital stay is greater than 6 days.

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The cost for children meal is $16 and the.cost for adult meal is $26.

Let cost of adult meal = a

Let cost of child meal = c

Lexi plans to have 63 adults and 59 children attend, so the total projected cost of her meals is $2,582.This will be:

63a + 59c = 2582 ...... i

Raymond has 63 adults and 93 children on her guest list, so he will pay the caterer $3,126. This will be;

63a + 93c = 3126 ...... ii

Collect both equations

63a + 59c = 2582 ...... i

63a + 93c = 3126 ...... ii

Subtract i from ii

34c = 544

Divide

c = 544 / 34

c = 16

The cost of children meal is $16.

From equation i, 63a + 59c = 2582

63a + 59(16) = 2582

63a + 944 = 2582

Collect like terms

63a = 2582 - 944

63a = 1638

a = 1638/63

a = 26

Adult meals is $26.

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Answer:

9 terms

Step-by-step explanation:

The sequence given is a geometric sequence

In a geometric sequence, the nth term of the sequence can be found by the formula

[tex]a_n = a_1r^{n-1}[/tex]

[tex]\text{where }\\\\ a_n = \text {nth term}\\\\\text{$a_1 = $ first term}\\\\\text{$r = $ common ratio}[/tex]

In the given sequence,

a₁ = 1

r = -4

aₙ = 65536

So we get the relation:
65536 =  1·  (-4)ⁿ⁻¹

65536  = (-4)ⁿ⁻¹

It is clear that n-1 has to be even so that the power of 4  is positive.
Substituting x = n -1 where x is even gives us
4ˣ = 65536

If we take logarithms to the base 4 on both sides we get

=> x = [tex]\log_465536 = 8\\\\[/tex]

Since x = n - 1 and x = 8, n = 9

So the 9th term in the series is 65536

0.8973 is the probability that the next tornado will occur within the next seven months.

Applying the rule of three, we can infer that since the average number of tornadoes in a year is 3.9, the average number of tornadoes in a nine-month period is 3.9*7/12 = 2.275. It is reasonable to believe that the distribution of tornadoes over time is Poisson. Let's refer to X as the number of tornadoes in a seven-month period. X has a Poisson distribution with a parameter of 2.27.

The probability of X being greater than or equal to 1 is equivalent to the likelihood that the next tornado will occur within the next seven months.. However P(X≥1) = 1-P(X=0), and

[tex]p(X=0) = (e^{2.275} * 2.275^{0}) / 0![/tex] = 0.1027  

Thus, the probability that the next tornado comes within the next 7 months is 1-0.1027  = 0.8973.

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Answer:

37

Step-by-step explanation:

Use PEMDAS, in this case, start with multiplication: (2)(-7), don't forget there is a minus sign in front of the two which is important later, then move on to dividing (-9) by (-3). Then you are left with 20-(-14)+3, which is the same as 20+14+3, which equals 37.

The value of p is $ 6.75.

It is given in the figure that the price of 6 apples in the grocery store is $ 4.50.

We have to find the value of p which is the price of 9 apples.

By unitary method, we can write,

Price of 1 apple = 4.5/6 = 3/4 =  $ 0.75.

Hence,

Price of 9 apples = 0.75*9 = 6.75 dollars  

Hence, the value of p is $ 6.75.

Unitary method

The unitary method is generally a way of finding out the solution of a problem by initially finding out the value of a single unit, and then finding out the essential value by multiplying the single unit value.

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Answer: Congruent angles are the angles that have equal measure. So all the angles that have equal measure will be called congruent angles. They are seen everywhere, for example, in equilateral triangles, isosceles triangles, or when a transversal intersects two parallel lines.

Step-by-step explanation:

The function is power function. The power of the function is -3, the constant of variation is k, and the independent variable is d.

In this question, we have been given a function y = k/d³

We need determine whether function is power function or not.

We know that, a power function is of the form y = x ^n where n is any real number.

We can write given function as,

y = k × d^(-3)

Given that, k represents a constant.

Here, the value of y depends on the value of d.

So, d is an independent variable and y is dependent variable.

also, the power of given function is -3

Therefore, the function is power function. The power of the function is -3, the constant of variation is k, and the independent variable is d.

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The largest possible value in the list is 35.

What is mean, median and mode?

Adding the numbers together and dividing the result by the total number of numbers in the list yields the arithmetic mean. An average is most frequently used to refer to this. The middle value in a list that is arranged from smallest to greatest is called the median. The value that appears the most frequently on the list is the mode.

Given: There is a list of 11 positive integers.

Has a mean of 10, a median of 9 and a unique mode of 8.

Since the mode (8) is less than the median (9), the mode can only appear (at most) 5 times since the mode is the 6th number in the list (assuming the list has been sorted in ascending order).

If so, the first five numbers can be 8, the following four numbers can be 9, and the next greatest number can be 10, which means the largest number must be 110 - (8 x 5 + 4 x 9 + 10) = 110 - 86 = 24.

The largest number must be 110 - 77 = 33 if the mode repeats just twice, in which case we can let the first ten numbers be 1, 2, 3, 8, 8, 9, 10, 11, and 13, totaling 77.

The biggest number in this scenario is 110 - 75 = 35 if the mode repeats itself three times. Alternatively, we can let the first ten numbers be 1, 1, 8, 8, 8, 9, 10, 10, and 11 totaling 75.

Therefore, the largest possible value of an integer in the list is, 35.

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When q = -17, the value of the equation, q - 7 would be: d. -24.

If we are given an equation to evaluate for a given value of a variable, we are to substitute the value of the variable into the equation and solve or simplify.

For example, if an equation is given as 3x + 4, and we are told that the x = 3, to determine the value of the equation, 3x + 4, substitute x = 3 into the equation as:

3(3) + 4

= 9 + 4

= 13

Here, we can now conclude that the value of the equation is 13.

Given the equation, q - 7, to find the value of the equation when q = -17, substitute the value of q into q - 7.

Therefore:

q - 7 = -17 - 7

= -24.

The value of the equation is: d. -24.

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The value of q - 7, when q = - 17 is - 24.

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

Given, q = - 17.

∴ q - 7.

To solve our expression we'll substitute the numerical value of q in the given expression.

= (-17) - 7.

= - 17 - 7.

= - 24.

We can also take negative sign common in the second step and distribute them later.

- 17 - 7.

= - (17 + 7).

= - (24).

= -24.

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Answer:

The amount invested at 8% was $11,000

The amount invested at 9% was $19,000

Step-by-step explanation:

Let the variable x represent the amount in $ invested at 8% and let y be the amount in $  invested at 9%

Total amount invested:
x + y = 30000   [1]

8% = 8/100 = 0.08

9% = 9/100 = 0.09

Interest at 8% on $x = 0.08x

Interest at 9% on $x = 0.09x

Total Interest :

0.08x + 0.09y = 2590  [2]

Using equations [1] and [2] we can solve for x and y

We have

x + y = 30000   [1]
0.08x + 0.09y = 2590  [2]

Multiply equation 1 by 0.08 to get
0.08x + 0.08y = 0.08(30,000)

0.08x + 0.08y = 2,400  [3]

Subtract [3] from [2] :

0.08x + 0.09y = 2590  
-
0.08x + 0.08y = 2400  
----------------------------------
       0x + 0.01y = 190

Divide both sides by 0.01
0.01y/0.01 = 190/0.01

y = = 19,000

Use [1] to get value of x

x + y = 30,000

x + 19,000 = 30,000

x = 30,000 - 19,000

x = 11,000

Answer:

203.5

Step-by-step explanation:

just divide 814 by 4

Answer:

203.5 miles per day

Step-by-step explanation:

divide 814 by 4= 203.5

Answer:

================

Find the midpoint of the segment and its slope to determine the perpendicular line passing through the midpoint.

The midpoint has coordinates:

The slope:

We know perpendicular lines have opposite/reciprocal slopes.

So the slope of the perpendicular bisector is:

Use the coordinates of the midpoint and point-slope equation to determine the line:

Answer:

[tex]y=-\dfrac{5}{2}x+9[/tex]

Step-by-step explanation:

A perpendicular bisector is a line that intersects another line segment perpendicularly and divides it into two equal parts.

Given endpoints of the line segment:

Substitute the given endpoints into the slope formula to find the slope of the line segment:

[tex]\implies \textsf{Slope $m$}=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{6-2}{7-(-3)}=\dfrac{4}{10}=\dfrac{2}{5}[/tex]

If two lines are perpendicular to each other, their slopes are negative reciprocals.  

Therefore, the slope of the perpendicular line is -⁵/₂.

Find the midpoint of the given line segment by substituting the given endpoints into the midpoint formula:

[tex]\implies \textsf{Midpoint}=\left(\dfrac{x_2+x_1}{2},\dfrac{y_2+y_1}{2}\right)[/tex]

[tex]\implies \textsf{Midpoint}=\left(\dfrac{7-3}{2},\dfrac{6+2}{2}\right)[/tex]

[tex]\implies \textsf{Midpoint}=\left(\dfrac{4}{2},\dfrac{8}{2}\right)[/tex]

[tex]\implies \textsf{Midpoint}=\left(2,4\right)[/tex]

To find the equation of the perpendicular bisector, substitute the found slope and midpoint into the point-slope form of a linear equation:

[tex]\implies y-y_1=m(x-x_1)[/tex]

[tex]\implies y-4=-\dfrac{5}{2}(x-2)[/tex]

[tex]\implies y-4=-\dfrac{5}{2}x+5[/tex]

[tex]\implies y=-\dfrac{5}{2}x+9[/tex]

Therefore, the equation for the perpendicular bisector of the line segment whose endpoints are (-3, 2) and (7, 6) is:

[tex]\boxed{y=-\dfrac{5}{2}x+9}[/tex]