Solve the following system of equations graphically on the set of axes below.
y= x-2
y=x−2
y= -3x-6
y=−3x−6

Answer:

x+7+3y

Step-by-step explanation:

You just remove the parentheses in this case since you don't have to change any of the operations.  

Answer:

Step-by-step explanation:

x+7+3y simplifed

The total amount for Elizabeth's purchase after 10 percent discount on her total bill is 33 dollars and 84 cents which is equivalent to 34 dollars.

What is percentage?

A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100.

Elizabeth bought the grocery for a total of 37 dollars and 60 cents.

She has a coupon of 10% discount.

Which means, she can get 10% discount on her total bill.

The amount of her total bill is $37.60.

So, calculate using percentage, the value of 10% of $37.60.

=(10 × 37.60/100)

= 376/100

= 3.76

So, Elizabeth would get a discount of $3.76 on her total bill -

= 37.60 - 3.76

= 33.84

Therefore, after the discount Elizabeth's total bill is $33.84 ≈ $34.

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A (A) histogram is a useful tool for condensing qualitative data.

An effective tool for summarizing qualitative data is a histogram.

The distribution of numerical data is roughly depicted by a histogram.

Karl Pearson was the person who first coined the phrase.  

The first stage in creating a histogram is to "bin" (or "bucket") the range of values, divide it into a series of intervals, and then count the number of values that fall into each interval.

The bins are often defined as a series of discrete intervals that don't overlap.

The bins (intervals) must be close together and frequently, though not always, have the same size.

Therefore, a (A) histogram is a useful tool for condensing qualitative data.

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Answer: B. 3750

Step-by-step explanation:

We start by converting the percentage 25% to the decimal 0.25.

Next, we multiply the original price by this decimal (5000*0.25=1250)

And Finally, Since it is a loss we subtract the 1250 from the original price.

5000 - 1250 = 3750

Therefore , the solution of the given question triangle comes out to be

triangle PQR to triangle ZXY is 3/2

You can link any three points in a plane to form triangles, which have three sides and three angles. They were among of the first geometric forms to be examined. Since triangles may be divided into any polygon, regardless of whether it has four, five, six, or n sides, they are very significant.

Here,

Consider PR and ZY as a point of comparison.

PR = 5

ZY = 14

Suppose the scaling factor is r and that

5 * r = 14

r = 14 / 5

r = 14/5

examining other sides

RQ to PR

right 5 * 12/3 = 20

To YX, QP

Correct answer is 4 * 9/3 = 12.

Thus,

triangle PQR to triangle ZXY

Therefore , Triangle PQR to Triangle ZXY equals 3/2, which is how the given question's solution is determined.

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Answer:

Yolanda's answer is incorrect because the recipe calls for 1 cup of almonds, 1 cup of pecans, and 1 cup of dried fruit, which totals 3 cups of nuts. The correct ratio of nuts to fruit in this recipe is 3:1. This means that for every 3 cups of nuts, there is 1 cup of fruit.

The potential solutions to the equation are x = -2 and x = -4

A logarithm is the power to which a number must be raised in order to get some other number .

The given expression is ln(x + 3) = 0

It can be rewritten as

[tex]ln _e (x + 3) = 0[/tex]

[Since base of a natural logarithm is considered as e]

[tex]e^0 = (x + 3)[/tex]

Since in a logarithmic function if log b with base e = c

Then we further solve the expression to get the possible roots.

x + 3 = 1

x =  1-3

x = -2

Therefore, the potential solutions are x = -2 and x = -4

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Answer:

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

We can see two angles marked as same, one of them is a right angle.

The included vertical side is common to both triangles so is a congruent side.

Since we have congruence of two angles and the included side, it is Angle-Side-Angle or ASA.

To complete the table, we can simply multiply the number of calories by 0.239 to find the equivalent amount of Joules.

The equation relates Joules to calories as j = 0.239c, where c stands for calories and j stands for joules. For example, 1 calorie is equal to 0.239 Joules, 2 calories is equal to 0.478 Joules, and so on.

Joules (j)              Calories (c)

0.239c                  1

0.478c                  2

0.717c                  3

0.956c                  4

1.195c                  5

1.434c                      6

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A reflex angle is an angle which measures more than 180 degrees and less than 360 degrees.

There are different types of angles in geometry, such as obtuse, acute and right angles, which all are under 180 degrees.

Assume, z is an acute or obtuse angle, and r is the reflex angle, then:

z + r = 360

r = 360 - z

Therefore, we can find the related reflex angle(r), if we know the value of the acute or obtuse angle(z).

A reflex angle equals the summation of 180 degrees and any of the primary angles (acute, right and obtuse angles). Therefore,

Reflex angle = 180° + Acute angle

Reflex angle = 180° + Right angle

Reflex angle = 180° + Obtuse angle

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What the height would need  for this curve to be a density curve is; One-half

The criteria for a curve to be a density curve is as follows;

1. The curve must always be non-negative. This tells us that the y-value of the curve must be greater than or equal to 0 at every given point.

2. The area under the curve must always be equal to 1.

Now, we are told that the curve starts at (-2, 0) and then goes to (5, question mark), and then goes down to (6, 0),.

This means that the area under the curve will be a trapezoid that has a height of question mark and then bases of length 3 (from -2 to 5) and length 1 (from 5 to 6).

The area of this trapezoid will be equal to the sum of the bases times the height divided by 2, or:

Area = ((3 + 1) × question mark)/2

Since the area under the curve must be equal to 1, we can set up the equation:

1 = ((3 + 1)  ×  question mark) / 2

Solving for question mark, we will:

The question mark = 2/4

The question mark = 1/2

Therefore, we can conclude that the height of the curve is  1/2

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Since the square root of a negative number does not exist in the real numbers, there are no real solutions for x. Therefore, the system of equations has no solutions.

An algebraic expression in mathematics is an expression created using variables, constant algebraic numbers, and algebraic operations. A good example of an algebraic expression is 3x2 2xy + c.

A constant has a fixed value and does not vary over time. For instance, the size of a shoe, a piece of clothing, or any other article of clothing will never alter. x+y = 8 is an algebraic equation, and 8 is a constant that cannot be altered. Variables are concepts that change or fluctuate throughout time.

To solve this system of equations algebraically, we can substitute y = x-3 into the first equation

y = x² - 15x + 60

x-3 = x² - 15x + 60

x² - 16x + 63 = 0

We know that this quadratic equation has no real solutions because its discriminant (b^2 - 4ac) is negative, so the system of equations has no real solutions.

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Answer: a) AE || BC     b)AB=BC      c)AE⊥ED &ED⊥CD

Step-by-step explanation:

a) The line segments that have the arrow sign on them mean that they are parallel, so AE || BC ( || = parallel to).

b) When two line segments have a dashed line on it, it shows that they are the same length, so AB is equal to BC.

c) when two segments intersect with a 90° angle, they are perpendicular, so AE⊥ED &ED⊥CD(⊥ = perpendicular to).

The Law of Cosines can be used to calculate the angles of an isosceles triangle given three side lengths. Two of the angles are equal, while the third can be found by subtracting the two known angles from 180°.

Since you are given three sides of an isosceles triangle, you can use the Law of Cosines to calculate the angles of the triangle. The Law of Cosines states that for a triangle with side lengths a, b, and c and angle C opposite side c, the following equation holds:

c² = a² + b² - 2abcosC

Therefore, you can rearrange the equation to solve for angle C:

C = arccos((a² + b² - c²) / (2ab))

For an isosceles triangle, two of the angles will be equal, so you can calculate those two angles using the equation above, and the third angle can be found by subtracting the two known angles from 180°.

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Perfect squares NEVER be irrational numbers.

Repeating decimals will ALWAYS be rational numbers.

Irrational numbers will NEVER be able to be written as fractions.

A square number, also known as a perfect square, is an integer that is the square of another integer, or the result of multiplying another integer by itself. For instance, 9 is a square number since it equals 3² and is represented by the symbols 3 × 3.

A number whose decimal representation eventually becomes periodic is known as a repeating decimal, also known as a recurring decimal.

All real numbers that are not rational are considered irrational numbers. In other words, it is impossible to express an irrational number as the ratio of two integers.

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Complete question

Fill in the following statements with either "sometimes ", "always ", or "never " in order to make it a true statement.

Perfect squares _______be irrational numbers

Repeating decimals will_____be rational numbers

Irrational numbers will____ be able to be written as fractions

The slope of the line through (-9,6) and (-6,-9) is -5

Now, According to the question:

Let's know:

What is slope and example?

Whenever the equation of a line is written in the form y = mx + b, it is called the slope-intercept form of the equation. The m is the slope of the line. And b is the b in the point that is the y-intercept (0, b). For example, for the equation y = 3x – 7, the slope is 3, and the y-intercept is (0, −7).

The formula for the slope of a line when two points (coordinate pairs)

[tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] are given is :

[tex]m = \frac{y_2-y_1}{x_2-x_1}[/tex] ,  where m denotes the slope of the line.

Applying this formula, we get:

[tex]m = \frac{-9-6}{-6-(-9)}[/tex]

[tex]m = \frac{-15}{-6+9}[/tex]

m = [tex]\frac{-15}{3}[/tex]

m = -5

Hence, The slope of the line through (-9,6) and (-6,-9) is -5.

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The complete question is this:

What is the slope of the line through (-9,6) and (-6,-9) ?

Check the picture below.

let's bear in mind that the -(1/3)x has a negative slope, namely going down, so a reflection over the x-axis will yield the same points pretty much, but instead of the IV Quadrant, on the I Quadrant, above, whilst the slope remains the same, it simply turns positive.

The volume of the cylinder on the image is:

v = 36,424 in³

So the correct option is the second one.

We know that for a cylinder of diameter D and height H, the volume is given by the formula:

V = pi*(D/2)²*H

Where pi = 3.14

Here we know that:

D = 40 inches.

H = 29 inches.

Replacing that in the formula for the volume we will get:

V = 3.14*(40 in/2)²*29 in = 36,424 in³

So the correct option is the second one.

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Recently, the Town of Aberdeen announced they were going to acquire a large parcel of land for a new park initiative.

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The range of the amount Tyrese makes each hour if he can only work a total of 8 hours is 20 ≤ x ≤ 24.80

The range is the space between the highest and lowest numbers.

Given: Tyrese works every day and gets paid more per hour the more time he puts in. Create a function to represent a starting wage of $20 that rises by 3% each hour.

To find: Establish the range of Tyrese's hourly pay if he can only work a total of 8 hours.

The beginning wage is $20.

Suppose x hours are in a day.

A $20 salary is offered, with a 3% hourly raise.

e.g., increment = (3/100)*20*x = (3/5)x

A function's maximum possible earnings are

y = 20 + (3/5)x

He is only allowed to work a total of 8 hours, per our instructions.

Therefore, the most money she can make in 8 hours is

y = 20 + (3/5)*8

y = 20 + 4.8

y = 24*8

$20 is the first sum.

As a result, if Tyrese can only work a total of 8 hours every day, the range of his hourly wage is .

Therefore, the correct answer is option B) 20 ≤ x ≤ 24.80.

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Answer: The teacher's claim is that there will be at least three numbers on the whiteboard whose digits have the same sum, no matter what the students write. To see if this claim is true, we can consider different cases for the number of students in the class.

If there are only two students in the class, the teacher's claim is not true. The two students can write any two different two-digit numbers, and it's not guaranteed that the digits in those numbers will have the same sum.

If there are three students in the class, the teacher's claim is true. The three students can write any three different two-digit numbers, and at least one of those numbers is guaranteed to have digits that have the same sum as one of the other numbers.

If there are more than three students in the class, the teacher's claim is true. No matter what numbers the students write, there will always be at least three numbers whose digits have the same sum.

Therefore, the smallest number of students for the teacher's claim to be true is three students.

It's worth mentioning that the teacher's claim is not necessarily true for all cases, it's only true that any three numbers picked out of the two-digit numbers set, will have digits with the same sum.

Step-by-step explanation:

Answer:

Step-by-step explanation:

9 - 3 = 6

6/10 = 3/5

Answer:

6/10 and/or 3/5(this is the answer simplified

Step-by-step explanation:

Subtract: 9/10 - 3/10

= 9 - 3/10

= 6/10

= 2 · 3/ 2 · 5

= 3/5

It is suitable to adjust both fractions to a common (equal, identical) denominator for adding, subtracting, and comparing fractions. The common denominator you can calculate as the least common multiple of both denominators - LCM(10, 10) = 10. It is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 10 × 10 = 100. In the following intermediate step, cancel by a common factor of 2 gives 3/5. In other words - nine tenths minus three tenths is three fifths.

The solution to the equations is

The value of first x = € 160

The value of second y = € 120

The value of third z = € 140

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.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

Let the first , second and third be represented as x , y , and z

The total amount to be distributed = € 420

So , x + y + z = € 420   be equation (1)

Now , first has €40 more than the second

So , x = y + 40   be equation (2)

And , third has half of what they have between the first two

So , z = ( 1/2 ) ( x + y )   be equation (3)

Substituting the value of x in the equation (3) , we get

z = ( 1/2 ) ( 2y + 40 )

z = y + 20   be equation (4)

Substituting the value of z and x in equation (1) , we get

( y + 40 ) + y + ( y + 20 ) = 420

On simplifying the equation , we get

3y + 60 = 420

Subtracting 60 on both sides of the equation , we get

3y = 360

Divide by 3 on both sides of the equation , we get

y = € 120

Therefore , the value of x = € 160

The value of z = € 140

Hence , the solution to the equation is € 160 + € 120 + € 140 = € 420

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The length of the spine will be;

⇒ 48.2 cm

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

Given that;

A kite is shaped like an isosceles triangle.

Now,

Since, A kite is shaped like an isosceles triangle.

Hence, Two sides of a triangle is equal to each other.

Let the length of the spine = x

So, We can formulate by the Pythagoras theorem,

⇒ Hypotenuse² = Base² + Perpendicular²

⇒ 62² = (78/2)² + x²

⇒ 3844 = 39² + x²

⇒ 3844 = 1521 + x²

⇒ 3844 - 1521 = x²

⇒ 2323 = x²

⇒ x = √2323

⇒ x = 48.2 cm

Thus, The length of the spine = 48.2 cm.

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Answer:

120

Step-by-step explanation:

3/5 of 200 = 120

3u^2-84 = 0 then u=5.29 is the nearest hundredth

The union of both rational and irrational numbers is known as a real number. They are represented by the letter "R" and can be either positive or negative.

This category includes all natural integers, decimals, and fractions.

In the number system, real numbers are only the fusion of rational and irrational numbers.

These numbers can generally be used for all arithmetic operations and can also be expressed on a number line.

Imaginary numbers, which are often known as unreal numbers since they cannot be stated on a number line, are frequently used to symbolize complex numbers. Examples of actual numbers include 23, -12, 6.99, 5/2, and so forth.

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Answer:

10 students are wearing shirts other than blue or white.

Step-by-step explanation:

1 10 of the students in the classroom are wearing blue shirts, which is 1/1020 = <<1/1020=2>>2 students.

2 5 of the students in the classroom are wearing white shirts, which is 2/5*20 = 8 students.

Altogether, 2+8 = <<2+8=10>>10 students are wearing either blue or white shirts.

There are 20 students in the classroom, so 20-10 = <<20-10=10>>10 students are wearing shirts other than blue or white.

The lengths of the sides of the kite LM is 13√2.

According to the Pythagorean theorem, the hypotenuse of a right-angled triangle's other two sides add up to a square whose length equals the hypotenuse's.

The hypotenuse (longest side) of a right-angled triangle's square is equal to the sum of its other two sides, according to the Pythagoras theorem (base and perpendicular). Hypotenuse2 = Base2 + Perpendicular2 is how this is expressed. A2 + B2 = C2 is the formula for the hypotenuse.

According to question:-

LM = 13√2

Hypotenuse = Base 2 + Perpendicular 2.

So,

LM = √7² + 17²

LM = √49 + 289

LM = √338

LM = 13√2.

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    Given ,

To Find : Maximum number of small cube shaped boxes that can fit in the cuboid

Volume of the Cuboid = [tex]2(lb+bh+lh)[/tex]

Volume of the cuboid = [tex]2(70X40+40X40+70X40)[/tex]

                                      = [tex]14400cm^{3}[/tex]

Now to find the volume of a cube,

[tex]V = a^{3}[/tex]

[tex]V = 10X10X10[/tex]

[tex]V = 1000cm^{3}[/tex]

Number of boxes that can fit in a cuboid = [tex]\frac{14400}{1000}[/tex]

                                                                    = [tex]14boxes[/tex]

Hence , the number of cube shaped boxes that can fit in a cuboid are 14