Write the system as a matrix equation.
2y + 7z = -3 -3x - 3y = 3
7x - 8z = 3

the maximum area of such a rectangle will be 144 unit²

What is a rectangle?

Rectangles are quadrilaterals having four right angles in the Euclidean plane of geometry. Various definitions include an equiangular quadrilateral, A quadrilateral with parallel sides that are equal to one another and four equal vertices is known as a rectangle. It is also known as an equiangular quadrilateral for this reason.

Rectangles can also be referred to as parallelograms because their opposite sides are equal and parallel.

The area of rectangle is A = a*b

A = 2x*(48-x²) = 96x - 2x³

We are asked to maximize the Area as changes so hopefully, we can identify a critical point of

It an associated with a maximum, So we need to find [tex]\frac{dA}{dx}[/tex] = 0

96 - 6x² = 0

x² =96/6 = 16

x = ±6

So the width = 12

Height = 48 - 36 = 12

So the area = 144 unit²

Hence the maximum area of such a rectangle will be 144 unit²

Learn more about rectangular by following the link below.

brainly.com/question/25292087

#SPJ4

Answer:

3! = 3*2*1 = 6

Step-by-step explanation:

! is factorial meaning that you multiply that number by all of the number below it

9! = 9*8*7*6*5*4*3*2*1

1011 = 1011*1010*1009*1008...3*2*1

The equation representing the normal cost (x), for an individual, is 6(x - 3) = 54, so option A is correct.

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side. It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Given:

Costs $54 for 6 people of the package, and $3 less per person than the normal cost for an individual.

The individual cost = 54 / 6 = $9, so the normal cost will be = 9 + 3 = $12

Apply the hit and trial method in the option,

(2)

3(x - 6) = 54

x - 6 = 54 / 6

x = 9 + 6 = 15

(1)

6(x - 3) = 54

x - 3 = 54 / 6

x = 9 + 3 = 12

Therefore, the equation representing the normal cost (x), for an individual is 6(x - 3) = 54.

To know more about equation:

https://brainly.com/question/12788590

#SPJ1

The value of car after 6 years is £498.53

Define Modeling Exponential Decay

Given that,

Dan buys a car =  £700

Depreciates at a rate of = 5.5% per year

The value after 6 years = 700 (1 - 5.5 / 100) ^6

                                       = 498.527 or 498.53

Therefore, the value of car after 6 years is £498.53

To read more about Modeling Exponential Decay

brainly.com/question/25297296

#SPJ9

the probability of the committee consisting of all women is 6.53%.

What is probability?

By simply dividing the favorable number of possibilities by the entire number of possible outcomes, the probability of an occurrence can be determined using the probability formula. Because the favorable number of outcomes can never exceed the entire number of outcomes, the chance of an event occurring might range from 0 to 1.

number of women = 20

number of men = 13

Total number of persons = 20+ 13 = 33

A committee of 5 people is chosen at random. Total number of ways in which the committee of 5 can be chosen N

N = C(33 5) = 33! / 5!*28!

N = 237336

p(the committee consists of all women) = C (20 3)*C(13 0)/N

p = 15504 / 237336

p = 0.0653

Hence, the probability of the committee consisting of all women is 6.53%

Learn more about probability, by the following link.

brainly.com/question/24756209

#SPJ4

Answer:

C

Step-by-step explanation:

If we use the distributive property for 4 (2x + 1), we see that 4 (2x) = 8x and that 4 (1) = 1. That means 4 (2x + 1) = 8x + 4 which is not equivalent to 2x + 4y. So this limits our answer to either C or D. C is the correct answer because if we use the distributive property again here for 4 (2x + y), we see that 4 (2x) = 8x and 4 (y) = 4y. That means that 4 (2x + y) = 8x + 4y which is the answer we're looking for.

May I please have brainliest for this? Thank you very much!

When the denominator is bigger than the numerator, a fraction is expressed as one with a numerator and a denominator. 55 cups of jam divided equally into 4 containers yields 13.75 cups per container. 13.75 cups of jam are contained in each container.

We have,

55 cups of blueberry jam were produced by Jada, who then evenly distributed the jam across 4 containers.

jam content of each container.

= 55 cups / 4 container

= 13.75 cups / 1 container

This indicates that there are 13.75 cups of jam in each container.

55 cups of jam are divided into 4 equal containers in this manner.

13.75 cups / 1 container

The amount of jam in each container is 13.75 cups of jams.

To learn more about fraction, refer to:

https://brainly.com/question/78672

#SPJ1

The expression "(-3 1/4d + 3/5) - (2 7/8d + 7/10) is equivalent to "negative forty nine over 8 times d minus one tenth" or -49/8d - 1/10.

An algebraic expression is a number, variable, or the combination of both and operational symbols.

To determine the equivalent of the expression "quantity negative three and one fourth times d plus three fifths end quantity minus quantity two and seven eighths times d plus seven tenths end quantity" or simply (-3 1/4d + 3/5) - (2 7/8d + 7/10), combine all like terms and perform the necessary operations.

(-3 1/4d + 3/5) - (2 7/8d + 7/10)

⇒ -3 1/4d + 3/5 - 2 7/8d - 7/10

⇒ (-3 1/4 - 2 7/8)d + 3/5 - 7/10

⇒ (-13/4 - 23/8)d + 6/10 - 7/10

⇒ (-26/8 - 23/8)d - 1/10

⇒ -49/8 d - 1/10

Hence, the equivalent expression is "negative forty nine over 8 times d minus one tenth" or -49/8d - 1/10.

Learn more about algebraic expression here: brainly.com/question/723406

#SPJ4

The equation of the line that passes through the points (4, -8) and (7,-8) is 5.33x + y = 13.22.

What is linear equation?

A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. Sometimes, the aforementioned is referred to as a "linear equation of two variables," with y and x serving as the variables.

Given two points,

(x1 = 4 ,y1 = -8) and (x2 = 7, y2 = -8)

The equation's general form will be written first:

y = mx + c

We may compute the slope of the equation (m) as follows:

[tex]m = \frac{y_2-y_1}{x_2-x_1}[/tex]

[tex]m = \frac{-8-8}{7-4}[/tex]

m = -16/3

m = -5.33

equation is y = -5.33x + c.

By entering the values of the x and y coordinates, we can now determine the value of the y-intercept (c):

For the point (4,-8),

-8 = -5.33(4) + c

-8 = -21.32 + c

c = 13.32

So the equation become ;

y = -5.33x + 13.32

or, 5.33x + y = 13.22

Learn more about linear equation click here:

https://brainly.com/question/1884491

#SPJ4

Force applied on the piston is 8π.

Given , Radius = 1 , Pressure = 8

Since , the units of pressure and radius are not given, let us assume radius is in cm and pressure is in [tex]\frac{Newton}{cm^{2} }[/tex].

Now , it becomes

Radius(r) = 1 cm

Pressure(p) = 8 [tex]\frac{Newton}{cm^{2} }[/tex]

Now , We know that

Force = Pressure × Area

∴ F = p × a

or F = 8 × π×[tex]1^{2}[/tex]         [∵ Area of Piston = π[tex]r^{2}[/tex]]

∴ F = 8π

Hence ,Force applied on the piston is 8π.

Learn more about Force at

https://brainly.com/question/8033367

#SPJ1

The temperature decrease for every meter that the mountain climber's altitude increases is given by:

-100 ºF.

The function that models this situation is a linear function, which has the format defined as follows:

y = mx + b.

In which the coefficients are given as follows:

In the context of this problem, the function is defined as follows:

f(a) = -100a + 75.

Hence the slope of the function is of:

-100.

Representing the temperature decrease for each meter of altitude increase of the climber.

The function is defined as:

f(a) = -100a + 75.

More can be learned about linear functions at https://brainly.com/question/24808124

#SPJ1

These are the general steps that every experiment takes, however no two research programs are the same. The aforementioned steps can be changed.

What is hypothesis in math?

A hypothesis is a proposition that makes sense in light of the available information but has neither been confirmed nor refuted.

                             A statement on which hypothesis testing will be based is referred to as a hypothesis in statistics (also known as a statistical hypothesis).

Of the 10 targets, you mislabeled two. Both the forecast and the hypothesis were messed up by you. Remember that a hypothesis usually offers less detail than a prediction.

Learn more about hypothesis

brainly.com/question/29519577

#SPJ4

Answer:

x≥4

Step-by-step explanation:

2x + 1  ≥ 5 + x  Subtract x from both sides

x + 1 ≥ 5  Subtract 1 from both sides

x ≥ 4

Answer:

D. The sixth root of three

Step-by-step explanation:

Translate from words to math symbols:

three to the one third power all over three to the one sixth power

[tex]\frac{3^{\frac{1}{3} } }{3^{\frac{1}{6} } } \\[/tex]

Rewrite the expression with rational exponents as a radical expression by extending the properties of integer exponents:

[tex]\frac{\sqrt[3]{3} }{\sqrt[6]{3} }[/tex]

Simplify:

[tex]\frac{\sqrt[3]{3} }{\sqrt[6]{3} } = \frac{\sqrt[3]{3} }{\sqrt[6]{3} } * \frac{\sqrt[6]{3^{5} } }{\sqrt[6]{3^{5} } } = \frac{\sqrt[3]{3} *\sqrt[6]{3^{5} } }{\sqrt[6]{3^{6} } } = \frac{3^{\frac{1}{3} }*3^{\frac{5}{6} } }{3^{\frac{6}{6} } } = \frac{3^{(\frac{1}{3} +\frac{5}{6} )} }{3} = \frac{3^{(\frac{2}{6} +\frac{5}{6} )} }{3} = \frac{3^{\frac{7}{6} } }{3} = \frac{3^{\frac{1}{6} } *3}{3} = \\\\3^{\frac{1}{6} } = \sqrt[6]{3}[/tex]

Answer:

[tex]\sqrt[6]{3}[/tex]

D. the sixth root of three

Answer: -1/4

Step-by-step explanation:

     We will use "rise over run" to find the slope of this line.

     Starting at (0, 1) we will count down (negative slope) one unit and 4 units to the right and arrive at point (4, 0) for a slope of -1/4.

Answer: 50% of her average running speed is her average walking speed

Step-by-step explanation:

60 ÷ 4 = 15
60 ÷ 8 = 7.5
7.5 is half of 15, making it 50% of her running speed.

The variables of the test statistic may be determined to be [tex]$s _1$[/tex], [tex]$s _2$[/tex], [tex]$n_ 1, n _2$[/tex], t, which is the t - distribution test statistic, and [tex]$x _1, x _2$[/tex], which is the mean of the two samples.

When the variances of the two groups are not equal, pooled standard deviation estimations cannot be used. As an alternative, we must determine the standard error for each group separately. The variables of the test statistic may be determined to be [tex]$s _1$[/tex], [tex]$s _2$[/tex], [tex]$n_ 1, n _2$[/tex], t, which is the t - distribution test statistic, and [tex]$x _1, x _2$[/tex], which is the mean of the two samples.

The formula for this type of test statistic is given by -

[tex]$t=\frac{x_1-x_2}{\sqrt{\frac{s_1^2}{n_1}+\frac{x_2}{n_2}}}$$[/tex]

Here, the variables can be defined as below -

[tex]$s_1^2, s_2^2=$[/tex] variance of two samples

[tex]$n_1, n_2=$[/tex] respective sizes of the two samples

t = t - distribution test statistic

[tex]$x_1, x_2=$[/tex] Mean of the two samples

As a result, the variables of the test statistic can be determined to be [tex]$s _1, s _2$[/tex], which represents the variance of two samples, [tex]$n _1, n _2$[/tex], which represents the size of the two samples, t, which represents the t-distribution test statistic, and [tex]$x _1, x _2$[/tex], which represents the mean of the two samples.

The complete question is:

The formula for the test statistic used for a two sample test of means where the population variances are unknown and unequal is:

t = X1−X2√s12/n1+s22/n2X1-X2s12/n1+s22/n2

Match the variables to their description.

To learn more about test statistic refer to:

brainly.com/question/14128303

#SPJ4

The y-intercept of the line that parallel is y = 4.

What is the y-intercept of the line?

The point on a line where it crosses the y-axis is known as the y-intercept. To put it another way, it is the value of y when x is equal to 0. This can sometimes have real significance for the model that the line offers, but it can also have no significance. In this section, we will see examples of both categories.

Use the slope-intercept form to find the slope.

The slope-intercept form is

y = mx + b,

where,

m is the slope and b is the y-intercept.

y = mx + b

Using the slope-intercept form, the slope is 0.

m = 0

To find an equation that is parallel, the slopes must be equal. Find the parallel line using the point-slope formula.

Use the slope 0 and a given point (-3, 4) to substitute for x1 and y1 in the point-slope form in the point-slope form y − y1 = m(x − x1),  which is derived from the slope equation

[tex]m = \frac{y_2 - y_1}{x_2 - _1}[/tex]

y - 4 = 0⋅(x - 3)

Simplify the equation,

y = 4.

hence, the y-intercept of the line that parallel is y = 4.

To learn more about the y-intercept of the line visit,

https://brainly.com/question/25722412

#SPJ4

Answer:

$722.5

Step-by-step explanation:

Since $225 is 30 students we can do 85/30 and multiply 225 by that.

For the proportion, it would be: 255/30=x/85

85/30=2.8 1/3

2.8 1/3*255=722.5

So it would be $722.5 for 85 students

Answer:

$722.5

Step-by-step explanation:

$255/ 30= 8.5

8.5* 85= $722.5

Answer:

y=3x+11

Step-by-step explanation:

y=mx+b is slope intercept form

m is slope and b is y intercept

parallel lines have the same slope so we know the slope will be 3 so to find the y intercept we plug in what we know

y=3x+b

5=3(-2)+b

5=-6+b

+6 +6

11=b

y=3x+11

hopes this helps please mark brainliest

The additional information that could be used to prove that ΔXYZ ≅ ΔFEG by ASA or AAS are:

∠Z ≅ ∠G and XZ ≅ FG

∠Z ≅ ∠G and XY ≅ FE .

The AAS is a theorem that states that we can prove that two triangles are congruent if they have two pairs of congruent angles and a pair of non-included sides.

The SAS is also another theorem that states that we can prove that two triangles are congruent if they have two pairs of congruent sides and a pair of included congruent angles.

From the image attached below, we are only given one pair of congruent angles, which is ∠X ≅ ∠F.

Therefore, for both triangles to be congruent by AAS or SAS, the additional information needed are:

∠Z ≅ ∠G and XZ ≅ FG or ∠Z ≅ ∠G and XY ≅ FE .

Learn more about the AAS and SAS on:

https://brainly.com/question/3999145

#SPJ1

Answer:

Step-by-step explanation:

Ok:

If the two books together costs $28.48 and one of them cost $7.44 Subtract to get the other book's price

2. 28.45-7.44=$21.01

3. Answer: The cost of the other one is $21.01

The y-intercept of the line that passes through the two points (-3, -5) and (3, -1) is -3.

What is the y-intercept of the line?

A line's y-intercept is the value of y at which the line crosses the y-axis. In other words, it is the value of y when x is equal to zero.

The given points are (-3, -5) and (3, 1).

By using a two-point form of the line

     [tex]\frac{x-x_1}{x_1-x_2} = \frac{y-y_1}{y_1-y_2}\\[/tex]

    [tex]\frac{x-(-3)}{-3-3} = \frac{y-(-5)}{-5-(-1)}\\\\\frac{x+3}{-6}=\frac{y+5}{-4}\\\\-4x-12=-6y-30\\\\6y=4x-30+12\\\\6y=4x-18[/tex]

This equation can be written as

      [tex]y =\frac{4x}{6}-\frac{18}{6}\\\\y=\frac{2x}{3}-3[/tex]

Now comparing with the slope-intercept form of the line 'y = mx + c'

then y-intercept (c) = -3.

Hence, the y-intercept of the line that passes through the two points (-3, -5) and (3, -1) is -3.

To learn more about y-intercept of the line, visit:

https://brainly.com/question/25722412

#SPJ4

Answer:

37

Step-by-step explanation:

4b+10-b = 3b + 10 = 3(9) + 10 = 27 + 10 = 37

Randall needs 3 quarts of ice cream.

What is the quarts?

An English measurement of volume equal to one-quarter gallon is the quart. There are now three different types of quarts in use: the liquid quart, dry quart, and imperial quart of the British imperial system. One litre is roughly equivalent to each. It is divided into either four cups or two pints.

If Randall needs 24 servings, that means that there would be 24 kids in his class.

If each kid in his class would have 1/8 quart,

you would do 24 x 1/8 which is 3 quarts.

3 quarters

Hence, Randall needs 3 quarts of ice cream.

To learn more about the quarts visit,

https://brainly.com/question/2683887

#SPJ4

Answer:

A, B, D, E

Step-by-step explanation:

Given expression:

When multiplying decimals, multiply as if there are no decimal points:

[tex]\implies 6 \times 154 = 924[/tex]

Count the number of digits after the decimal in each factor:

Therefore, there is a total of 5 digits.

Put the same number of total digits after the decimal point in the product:

[tex]\implies (0.06) \cdot (0.154)=0.00924[/tex]

-----------------------------------------------------------------------------------------------

Answer option A

[tex]\boxed{6 \cdot \dfrac{1}{100} \cdot 154 \cdot \dfrac{1}{1000}}[/tex]

When dividing by multiples of 10 (e.g. 10, 100, 1000 etc.), move the decimal point to the left the same number of places as the number of zeros.

Therefore:

[tex]\implies 6 \cdot \dfrac{1}{100} \cdot 154 \cdot \dfrac{1}{1000}=(0.06) \cdot (0.154)[/tex]

Therefore, this is a valid answer option.

Answer option B

[tex]\boxed{6 \cdot 154 \cdot \dfrac{1}{100000}}[/tex]

Multiply the numbers 6 and 154:

[tex]\implies 6 \times 154 = 924[/tex]

Divide by 100,000 by moving the decimal point to the left 5 places (since 100,000 has 5 zeros).

[tex]\implies 6 \cdot 154 \cdot \dfrac{1}{100000}=0.00924[/tex]

Therefore, this is a valid answer option.

Answer option C

[tex]\boxed{6 \cdot (0.1) \cdot 154 \cdot (0.01)}[/tex]

Again, employ the technique of multiplying decimals by first multiplying the numbers 6 and 154:

[tex]\implies 6 \cdot 154 = 924[/tex]

Count the number of digits after the decimal in each factor:

Therefore, there is a total of 3 digits.

Put the same number of digits after the decimal point in the product:

[tex]\implies 0.924[/tex]

Therefore, as (0.06) · (0.154) = 0.00924, this answer option does not equal the given expression.

Answer option D

[tex]\boxed{6 \cdot 154 \cdot (0.00001)}[/tex]

Again, employing the technique of multiplying decimals.

As there are a total of 5 digits after the decimals:

[tex]\implies 6 \cdot 154 \cdot (0.00001)=0.00924[/tex]

Therefore, this is a valid answer option.

Answer option E

[tex]\boxed{0.00924}[/tex]

As we have already calculated, (0.06) · (0.154) = 0.00924.

Therefore, this is a valid answer option.

The value of z = 0 + 0i

What is complex numbers ?

A complex number can be represented in the form a + bi, where a and b are real numbers. A complex number is a part of a number system that extends the real numbers by adding an element designated by the symbol I sometimes known as the imaginary unit, and meeting the equation displaystyle i2=-1.

( x + iy ) - 4i ( x - iy ) = 0

x + iy - 4ix + 4i²y = 0

x + i (-4x + y ) + 4y = 0

x + 4y + ( - 4x + y )i = 0

Now two complex numbers are equal if both the real and imaginary parts are equal, which gives you the system of equation

x + 4y = 0 ⇒(1)

-4x + y = 0 ⇒ (2)

Multiplying equation (1) with 4

4x + 16y = 0

Solving the equations

4x + 16 y = 0

-4x + y = 0

      17 y = 0

          y = 0

Putting the value of y in (1)

x + 4(0) = 0

x = 0

To learn more about complex numbers from the given link  

https://brainly.com/question/10662770

#SPJ9

Answer:

Step-by-step explanation:

i think its 1

The number of minutes which contains 9 five- minute segments as required in the task content is; 45 minutes.

It follows from the task content that there are 9 five minutes segments in how many minutes.

The question posed in the task content can be interpreted as determining the total number of minutes in 9 five minutes segments.

On this note, it can be evaluated as follows;

9 × 5 minutes

= 45 minutes.

On this note, it can be concluded that the number of minutes which contains 9 five minutes segments is; 45 minutes.

The blank in the task content can therefore be filled with; 45 minutes.

Read more on multiplication;

https://brainly.com/question/28773316

#SPJ1

The 600 chairs capacity of the hall and the arrangement such that an increase in the number of rows by 5 decreases the number of chairs per row by 6 is a word problem that indicates;

(a) There are originally 20 rows of chairs in the hall

(b) The number of empty chairs per row is 6 empty chairs

A word problem is a question in which the information required to find the solution and the description of the situation is provided using sentences, or regular verbal statements rather that symbols, expressions or operators.

(a) The number of chairs the hall can accommodate = 600

Let x represent  the number of rows of chairs, therefore;

The number of chairs per row = 600/x

When the number of rows is increased by and the number of shares per row is decreased by 6, we get;

New number of rows = x + 5

New number of chairs per row = (600/x) -6

The equation for the number of chairs in the hall becomes;

(x + 5) × ((600/x) - 6) = 600

600·x + 6·x² - 570·x - 3000 = 0

6·x² + 30·x - 3000 = 0

x² + 5·x - 500 = 0

(x + 25)·(x - 20) = 0

x = -25 and x = 20

The number of rows is a positive number, therefore;

(b) After re-arrangement, the number of rows, x = 20

The new number of chairs per rows = (600/20) - 6 = 24

The new number of rows = 20 + 5 = 25

Let E represent the number of empty chairs, the number of people in each row becomes 24 - E, which indicates;

25 × (24 - E) = 450

450 ÷ 25 = 18 = 24 - E

E = 24 - 18 = 6

The number of empty chairs per row, E = 6

Learn more about word problems here:

https://brainly.com/question/13818690

#SPJ1