Write an augmented matrix for the following system of equations and give its size.- 8x + 3y = 1 4x - 7y = 4What is the augmented matrix?

Answer

Selling price = $ 925

Mark percentage = 62%

The cost price is 570.

Answer:

Measure of Angle A is 100°

Step-by-step explanation:

The sum of interior angles of a polygon is given by the formula :

(n-2)×180  (where n is the number of sides)

n = 6

(6-2)×180 =  

4 × 180 = 720

So :

A + B + C + D + E + F = 720

Substitute values given in diagram (angle d is 90 as the little square indicates a right angle) (Calling angle a as x)  :

x + 135 + 115 + 90 + 110 + 170 = 720

Simplify :

x + 620 = 720

Subtract 620 from both sides :

x = 720 - 620

x = 100

Measure of Angle A is 100°

Hope this helped and have a good day

The bulb is 5 inches far from the vertex of the cross section.

A portion of the right cone known as a parabola is one that runs parallel to the generating line on one side of the conic figure.

The standard equation for a parabola is typically expressed as y² = 4ax if the directrix is parallel to the y-axis, and y² = 4ax if the parabola is in the negative quadrants. The conventional equation of a parabola is x² = 4ax if the parabola is sideways, or if the directrix is parallel to the x-axis. If the parabola is in the negative quadrants, the equation is x² = 4ax.

Given, The equation x = 1/20y² can be used to model the cross section of a parabolic spotlight (with units in inches).

We must determine the distance between the bulb and the cross section's vertex.

Equation x = 1/20y² is alternatively denoted by the expression y² = 20x.

Now, comparing the equation to the parabola's conventional form, y²=4ax

So, 4a=20

a=5

Consequently, a=5 represents the distance from the cross section's vertex to the bulb.

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Answer:

approximately 1,375 feet

Step-by-step explanation:

Set up and solve this proportion:

[tex] \frac{881}{66} = \frac{h}{103} [/tex]

[tex]66h = 90743[/tex]

[tex]h = 1375[/tex]

So the height of building b is about 1,375 feet.

Moving waves can be described either as a function of time or as a function of position

A wave is a dynamic disturbance of one or more quantities that propagates in physics, mathematics, and related sciences. When waves oscillate frequently around an equilibrium value at a certain frequency, they are said to be periodic.

In a medium, a wave is a disturbance or variation that gradually transfers energy from one point to another. It can be an elastic deformation or a change in pressure, electric or magnetic strength, electric potential, or temperature.

It should be noted that it can be a function of the position as well as the time.

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since the angles are opposite by the vertex, we have that the expression to find the value of x is:

and if we solve it, we obtain:

Answer:

switzerland was the leading country in chocolate consumption per capita in 2017, with citizens eating nearly nine kilos of the sweet stuff in that year. World renowned for the chocolate they produce, it seems the Swiss themselves can’t get enough of the candy. Germany, the country’s neighbor, is equally addicted, importing the largest share of Swiss chocolate of all countries in the world.

Step-by-step explanation:

Answer: a swede would consume 1.9 times as much chocolate as an American.

Step-by-step explanation: 9.1 / 4.7 = 1.93617021. round to the nearest tenth = 1.9.

1.93617021 times 4.7 equals 9.1

Answer:

[tex]-12w + x[/tex]

Step-by-step explanation:

question:

[tex]-3w - 3x - 7w + 4x - 2w[/tex]

first you add all the 'w' together.

(-3)+(-7)+(-2) = -10+(-2)=-12

so, [tex]-12w - 3x + 4x[/tex]

second you add all the 'x' together

(-3)+(4) = 1

so, [tex]-12w+1x[/tex]

then simplify:

[tex]-12w + x[/tex] <--answer

hope this helps!

The greatest number of crates that can safely be lifted  at one time without breaking the cable is 71.

What is GCF?

The biggest positive integer m that divides both x and y is the GCF of two or more non-zero integers, x, and y. The GCF stands for greatest common factor. In this case, greatest can be changed to highest, and factor to divisor. The highest common factor is often referred to as the biggest common factor, highest common factor, or highest common divisor (GCD). GCF is usually always utilised with fractions, which are frequently employed in daily life. You can obtain the necessary reduced form by determining the GCF of the denominator and numerator of a fraction or ratio.

A crane has a cable with a breaking strain of 6400 kg  measured to 2 significant figures.  It is used to lift crates which weigh 90 kg measured to the nearest 10 kg.

We need to calculate the greatest number of crates that can safely be lifted at one time without breaking the cable.

According to the question,

It is given that, the breaking strain of the crane is 6,400 kilograms and each crate is 90 kilograms.

Thus, to know the number of crates (n) that can safely lift is equal to the weight of the crane is 6,400 kilograms divided by is 90 kilograms.

thus,

[tex]n=\frac{weight of the crane}{weight of each crate}\\ \\n=\frac{6400}{90}[/tex]

so,  n= 71.111≈71

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Given the patient consumption rate on his diet:

(a) Average energy per day consumed will be since the number of days = 4

The average energy per day consumed = 850 Cal(b) The unit symbol for the answer = calorie

Answer:$346.8

Step-by-step explanation:

1. X - 70% = 204

Want to get the value of X

2. X + 70% = 204 + 70%

= X = 204 x 1.7

= X = $346.8

Answer:

Original Price = $680

Step-by-step explanation:

Think about what a 70% reduction in price means.

If the original price of an item is $100 then a 70% reduction would mean that it costs 70% less from the original price. This means you would be paying only 30% of the original price

Let the original price be $P

Then the price you pay after 70% reduction is 30% of P
= P x 30/100

= P x 0.3                  (30% = 30/100 = 0.3)

= 0.3P

We are given that this sale price = $204

--> 0.3P = 204

Dividing both sides by 0.3 gives us the value for P
0.3P/0/3 = 204/0.3

P = 204/0.3 = 680

So

Original Price = $680

We can double check our computations as follows

If original price = 680, then a reduction of 70% would be a discount of
0.7 x 680 = 476

Price after discount = Original Price - Discount

= 680 - 476 = 204

So our results are consistent

Answer:290

Step-by-step explanation:

first look at the ones place it is greater than 4 so round up  

286 to the nearest tenth is 290.

Place value, which is related to a digit's location in a number, is the amount that each digit is worth.

Given:

The number is 286.

The digit in tenth place is 6.

And the number 6 is greater than the number 4.

And 6 > 4.

So, the number will round off to the nearest tenth.

6 becomes zero.

And the number left to 6 will increase by 1.

That means 8 + 1 = 9.

So,

286 to the nearest tenth is 290.

Therefore, 290 is the nearest ten of the required number.

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Answer:

Explanation:

eight of the bush when it was first planted int he garden = 12cm

After 2 weeks, its height = 120% of Height when it was planted.

We solve for the result.

The bush was 14.4cm tall after two weeks.

Answer:

p = 18, q = 0

Step-by-step explanation:

The expression on the left side of the equation is
[tex]\large \text {$ \dfrac{\sqrt{5}+\:2}{\sqrt{5}-2}+\dfrac{\sqrt{5}-\:2}{\sqrt{5}+2} $}[/tex]

Multiply the denominators to get a common denominator:

[tex]\text{$\left(\sqrt{5}-2\right)\left(\sqrt{5}+2\right)$}[/tex]

= [tex]\left(\sqrt{5}\right)^2-2^2[/tex]                           ∵ (a + b)(a - b) = a² - b²

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

[tex]\large \text {$ \dfrac{\sqrt{5}+\:2}{\sqrt{5}-2}+\dfrac{\sqrt{5}-\:2}{\sqrt{5}+2} $}\\\\[/tex]

[tex]=\dfrac{\left(\sqrt{5}+2\right)\left(\sqrt{5}+2\right)}{\left(\sqrt{5}-2\right)\left(\sqrt{5}+2\right)} + \dfrac{\left(\sqrt{5} - 2\right)\left(\sqrt{5} - 2\right)}{\left(\sqrt{5}-2\right)\left(\sqrt{5}+2\right)}[/tex]

Since denominator
[tex]\text{$\left(\sqrt{5}-2\right)\left(\sqrt{5}+2\right)$} = 1,[/tex]

the expression becomes

[tex]=\left(\sqrt{5}+2\right)^2 + \left(\sqrt{5}-2\right)^2\\\\= 5 + 4\sqrt{5} + 4 + 5 - 4\sqrt{5} + 4\\\\[/tex]

[tex]= 10 + 8 = 18[/tex]

Therefore  
[tex]\large \text {$ \dfrac{\sqrt{5}+\:2}{\sqrt{5}-2}+\dfrac{\sqrt{5}-\:2}{\sqrt{5}+2} = p + q\sqrt{5}$}\\\\\\= > \large \text{$ 18 = p + q\sqrt{5}$}[/tex]

Now [tex]\sqrt{5}[/tex] is an irrational number and p = rational so since there is no [tex]\sqrt{5}[/tex] term on the left side, q = 0 and p = 18

Answer:

(0,7]

Step-by-step explanation:

It is an open circle at 0 and a closed circle at 7.

Answer:

-7/10

Step-by-step explanation:

First, we obviously need to convert 0.66 into a fraction.  Since -7/10 cannot be changed, we need to change AND simplify -0.66.

-0.66 is equal to -66/100, but we can still simplify this. We can divide the numerator and denominator by 2.

66 divided by 2 is 33.

100 divided by 2 is 50.

-33/50 CANNOT be simplified anymore.

So -7/10 _ -33/50. Which is greater?

-7/10 is closer to 0 on the number line. -33/50 isnt.

So -7/10 is the answer.

-7/10 > -0.66

Given expression is (a+b)^8 and we need to find the 5th term of this series.

Explanation -

The general binomial expression is given as

So the given expression can be written as

So the 5th term will be

Then we have

The non-real solutions are (2 + i√26)/3 and  (2 - i√26)/3

The equation of the polynomial expression is given as:

3x^3 + 14x^2 - 14x + 60 = 0

From the question, we have

x = -6

This gives

So, we have

x + 6 = 0

The next step is to divide the polynomial equation 3x^3 + 14x^2 - 14x + 60 = 0 by x + 6 = 0

This is represented as

3x^3 + 14x^2 - 14x + 60/x + 6

Using a graphing calculator, we have

3x^3 + 14x^2 - 14x + 60/x + 6 = 3x^2 - 4x + 10

Next, we determine the solution of the quadratic expression 3x^2 - 4x + 10 using a quadratic formula

So, we have

x = (-b ± √(b² - 4ac))/2a

This gives

x = (4 ± √((-4)² - 4 * 3 * 10))/2 * 3

So, we have

x = (4 ± √-104)/6

This gives

x = (4 ± 2√-26)/6

Divide

x = (2 ± √-26)/3

Rewrite as

x = (2 ± i√26)/3

Split

x = (2 + i√26)/3 and  x = (2 - i√26)/3

Hence, the non-real solutions of the polynomial expression are x = (2 + i√26)/3 and  x = (2 - i√26)/3

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tata:

• Blue paint (,: B,) 3

• ellow poaint (

• Mixture obtained ( ),O

• Total mixture (), T

• Total yellow paint (): , TY

Proportion f Y:

TY:

nswer: 8oz

ummary:

0. We got the proportion of yellow paint in the mixture

1. We multiply the proportion by the total mixture to know how many ounces of yellow paint is needed.

The expression for study hours of Francesca will be ( Z + 4 ) hours.

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 Jonah studied z hours for a big test. Francesca studied a fourth as long as Jonah studied.

The expression will be written as Francesca studied 4 hours more than Jonah.

Francesca's study time = ( Z + 4 ) hours

Therefore, the expression for study hours of Francesca will be ( Z + 4 ) hours.

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The most appropriate choice for sets, union and intesrsection of set will be given by

1) (A ∩ B) U C = {-2, 1, 5, 7, 9, 11}

2)  (B U C) ∩ A = {5, 7, 9, 11}

What is set and union and intersection of set?

Set is a well defined collection of distinct objects. Set can be empty as well as non empty.

Writing all the elements of two or more sets together in one set is known as union of sets.

Writing the common elements of two or more sets in one set is known as intersection of sets.

Given,

A= {0,3,5,7,9,11,12}

B={-3,5,8,9,11,14}

C={-2,1,5,7}

For 1)

(A ∩ B) = {5, 9, 11}

(A ∩ B) U C = {-2, 1, 5, 7, 9, 11}

For 2)

(B U C) = {-3, -2, 1, 5, 7, 8, 9, 11, 14}

(B U C) ∩ A = {5, 7, 9, 11}

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The correct graph that represents the solution set of the system of inequalities is in Option(b).

Inequality is a  statement of an order relationship (greater than, greater than, or equal to, less than, or less than or equal to) between two integers or algebraic expressions in mathematics.

The given system of inequalities are,

y < -3x - 2

y ≤ x - 2

We have to select the graph that represents the solution set of the system of inequalities.

y < -3x - 2

Let, y = -3x - 2

Now, plot the graph of the line y = -3x - 2 with a Dotted line ( as < is a strict inequality).

y ≤ x - 2

Let, y = x - 2

Now, plot the graph of the line y = x - 2 on the graph.

The area between the two lines of inequalities on the graph represent the solution set.

Upon comparison with the graphs in the options, the correct graph is present in Option(b).

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Answer:

Step-by-step explanation:

The first thing you need to do, is find the total amount of gorillas.
to do this, you are going to use the equation:

24 + g = 7g

Both sides are equal, since the wallabies and the buffalo are equal. This makes the equation true.
you subtract g from 7g, and you should get:

24= 6g

Divide by six:

4 = g  

That is the # of gorillas.

Now, if you add 24 + 4

You get the # of buffalo.

Which is: 28

Since the buffalo and wallabies are the same, the # of wallabies is also 28.
if you want to check, multiply 4x7 to get the amount of wallabies.

The surface area and volume of the solid are  104 in² and 60 in³

It is important to note that the figure takes the shape of a cuboid.

The formula for determining the surface area of a cuboid is expressed as;

SA = 2lw + 2lh + 2hw

Where;

Now, let's substitute the values into the formula, we have;

Surface area = 2(5× 2) + 2(5 ×6) + 2(6 × 2)

expand the bracket

Surface area = 2(10) + 2(30) +2 (12)

Surface area = 104 in²

The formula for volume is given as;

Volume = l × w × h

Volume = 5 × 2 × 6

Volume = 60 in³

Thus, the values are  104 in² and  60 in³

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We have the following:

To find the percent markup, we must calculate the profits, knowing that there are 300 shirts and they sell them for a total of $ 20

Now we subtract from what was initially spent and then divide by that same amount and multiplying by 100 we will know the percent markup

Which means that the percent markup is 67%

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

Explanation:

The unique digits are: 9, 6, 1

There are 1+3+3 = 7 digits with the repeats mentioned. If we could somehow tell the 6's apart and the 1's apart, then we'd have 7! = 7*6*5*4*3*2*1 = 5040 different permutations.

But because we can't tell the 6's apart, nor the 1's apart, this means we have to divide by (3!*3!). Each 3! represents the number of times the 6's show up and same goes for the 1's.

So (5040)/(3!*3!) = 5040/(6*6) = 5040/36 = 140 is the number of ways to rearrange the digits

Given the system of equations:

To solve it by substitution, follow the steps below.

Step 1: Solve one linear equation for x in terms of y.

Let's choose the second equation. To solve it for x, add 3y to each side of the equations.

Step 2: Substitute the expression found for x in the first equation.

Step 3: Isolate y in the equation found in step 2.

To do it, first, add 48 to both sides.

Then, divide both sides by 15.

Step 4: Substitute y by 5 in the relation found in step 1 to find x.

Answer:

x = -9

y = 5

or (-9, 5)

Also, you can graph the lines by choosing two points from each equation, according to the picture below.

The group of restrictions used to simulate the issue includes

The issue includes the following information.

The limitations for modeling the problem are as follows: The gap between the number of hours Savanah has reserved and those that John has is no more than five times.

Savanah will provide child care for a minimum of 40 hours, but no longer than that, indicating that it is less than; as a result.

,y<5x

Meaning "at least 40 hours" is "at least 40 hours." 40 hours or more may be expressed as

y ≥ 40 hours

The two necessary restrictions are represented as y< 5x and y=> 40 hours in an inequality model.

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Side BC is opposite to angle BAC, in the picture.

Answer: Angle BAC - first option