Mathematics High School

I have x N50 note and y N100 note. There are eight note altogether and their total value i N550. How many of each note do I have?

Answers

Answer 1

So I have 5 and 3 notes each

You need to use simultaneous equations to solve this problem since there are 2 variables.

50x + 100y = 550 (value of the notes x the number of each note)

x + y = 8 (the number of each note added).

Multiply the second equation by 50 so that it the x variables are the same in both equations. Thus, 50x + 50y = 400.

Subtract 50x + 50y = 400 from 50x + 100y = 550.

The subtraction results in 50y = 150.

Divide by 50. y = 3, so x must equal 5.

So I have 5 and 3 notes each

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Related Questions

Fill in the missing information in the table.

Note: The cylinder and cone in each row have the same dimensions.

(I already solved some of them just give me the answers to the parts where I put the zeros, and please hurry)

Answers

The missing information, considering the volume of the cone and the cylinder, is given as follows:

Second row: height = 13.3, volume of cylinder = 120π.Third row: Diameter = 12, radius = 6, height = 4, volume of cylinder = 144π.

How to obtain the volume of a cone and of a cylinder?

The volume of a cylinder of radius r and height h is given as follows:

Vcy = πr²h.

The volume of a cone is one third that of the cylinder, hence:

Vco = πr²h/3.

At the second row, the volume of the cylinder is three times that of the cone, hence:

40π x 3 = 120π.

Considering the volume of the cylinder and the radius, the height is obtained as follows:

πr²h = 120π

9h = 120

h = 120/9

h = 13.3.

For the third row, we have that the base area is of 36π squared units, hence the radius is obtained as follows:

πr² = 36π

r = 6. (as the base is circular).

Hence the diameter is of 12 units, as the length of the diameter is twice that of the radius.

The volume of the cylinder is three times that of the radius, hence:

3 x 48π = 144π

Meaning that the height is then calculated as follows:

πr²h = 144π

36h = 144

h = 144/36

h = 4.

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Tom got a Mr. Potato Head for his birthday. It came with $3$ hairstyles, $2$ sets of eyebrows, $1$ pair of googly eyes, $2$ sets of ears, and $2$ sets of lips, a pair of regular shoes, and a bonus pair of clown shoes. If a complete Mr. Potato Head personality includes eyebrows, eyes, ears, lips, shoes and optionally hair, how many different wacky personalities can Tom come up with? Note that Mr. Potato Head can be bald. Note: You cannot "mix and match". For example, you cannot take the left eyebrow from one pair and the right eyebrow from the other pair.

Answers

Answer: Tom can come up with 13 different wacky personalities for Mr Potato Head.

Step-by-step explanation:

Tom can come up with 3 different hairstyles for Mr Potato Head, 2 sets of eyebrows, 1 pair of googly eyes, 2 sets of ears, and 2 sets of lips. He also has 2 pairs of shoes to choose from. If Mr Potato Head can be bald, Tom can also choose to not include a hairstyle.

In total, Tom can come up with 3+2+1+2+2+2+1=13 different combinations of features for Mr Potato Head. Since each combination represents a different personality, Tom can come up with 13 different wacky personalities for Mr Potato Head.

What is the value of tan Î¸?

Answers

The value of tan 1 is 45 degree.

tangent is the trigonometric ratio.

we can find out the value of tangent by taking opposite side of the theta angle divided by the adjacent side of the theta angle.

tan Q = perpendicular of triangle /base of triangle.

sine theta divided by cos theta gives the value of tan theta.

tan Q = sin Q/ cos Q.

some formula of the tan Q are as follows,

1- tan Q = sin Q/cos Q

2- tan Q= 1 /cot Q

3-tan^2 Q =sec^2 Q -1

4- tan(90 - Q)=cot Q

5- tan (Q+π)=tan Q

6- tan (π-Q)=-tan Q

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Is (1,-2) a solution to this system of equations?
20x+20y=-2

2x+5y=-8
YES OR NO

Answers

The point (1, -2) is not a solution to the system of equation, 20·x + 20·y = -2, 2·x + 5·y = -8, the correct option is NO, the solution is (2.5, -2.6)

What is a system of equations?

A system of equations are two (or more) equations that have common variables.

The system of equation is presented as follows;

20·x + 20·y = -2

2·x + 5·y = -8

The specified possible solution of the equation is; (1, -2)

Making y the subject of each of the equations, and plugging in the value of x = 1, for the first equation, we get;

20·x + 20·y = -2

20·y = -2 - 20·x

y = (-2 - 20·x)/20

Therefore; y = (-2 - 20 × 1)/20 = -1.1

When x = 1, y = -1.1, therefore, the point (1, -2), is not a solution to the first equation, 20·x + 20·y = -2

Evaluating the second equation, we get;

2·x + 5·y = -8

5·y = -8 - 2·x

y = (-8 - 2·x)/5

Plugging in x = 1, we get;

y = (-8 - 2 × 1)/5 = -2

When x = 1, y = -2, therefore, the point (1, -2), is a point on the graph of the second equation, 2·x + 5·y = -8, but it is not a solution to the system of equation

The solution to the system of equation, 20·x + 20·y = -2, 2·x + 5·y = -8, can by found by equating both expressions for y as follows;

y = (-2 - 20·x)/20 and y = (-8 - 2·x)/5

Therefore; (-2 - 20·x)/20 = (-8 - 2·x)/5

-10 - 100·x = -160 - 40·x

60·x = 150

x = 150 ÷ 60 = 2.5

x = 2.5

y = (-2 - 20 × 2.5)/20 = -2.6

y = -2.6

The correct option is therefore, no, the solution to the system of equation is; (2.5, -2.6)

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Explain how you decided to divide your wholes into fractional parts and how you decided where your number scale should begin and end. Due 1-2-23

Answers

On solving the provided question, we can say that - on doing the fraction we have [tex]\frac{1}{10} ; \frac{1}{100} ; \frac{1}{10000}[/tex]

what is fraction?

Any number of equal portions, or fractions, can be used to represent a whole. Fractions in standard English indicate how many units of a certain size there are. 8, 3/4. A whole includes fractions. The ratio of the numerator to the denominator is how numbers are expressed in mathematics. Each of these is an integer in simple fractions. In the numerator or denominator of a complex fraction is a fraction. True fractions have numerators that are less than their denominators. A fraction is a sum that constitutes a portion of a total. By breaking the entire up into smaller bits, you can evaluate it. Half of a full number or item, for instance, is represented as 12.

here we have,

0.1 = 1/10

0.01 = 1/100

0.0001 = 1/10000

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What is the length of leg y of the right triangle?

Answers

Answer:

Step-by-step explanation:

Liliana used 444 dark power crystals to raise 141414 zombie soldiers. She wants to know how many zombie soldiers (z)(z)(, z, )she can raise with 101010 dark power crystals. How many zombie soldiers can Liliana raise with 101010 power crystals

Answers

On solving the provided question, we can say that by unitary method With ten power crystals, 35 zombie troops can be raised.

What is unitary method ?

The unit technique is an approach to problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value.

Liliana raised 14 zombie troops with the help of four dark power stones.

Zombie troops can be increased to a total of 14 with 4 Dark power crystals. Zombies can be raised with 1 Dark power crystal, or 14/4.

Zombie soldiers can be raised using 1 Dark power crystal, or 7/2.

Zombie troops can be generated with 1 Dark power crystal by adding 10 to 7/2. You can produce 5 * 7 zombie troops with 1 Dark power crystal.

35 zombie troops can be generated with 1 dark power crystal.

With ten power crystals, 35 zombie troops can be raised.

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Write the equation of the perpendicular bisector’s of the line AB given: A(1,3) & B(-3,5)

Answers

Answer:

y = 2x + 1

Step-by-step explanation:

[tex]\frac{5-3}{-3-1}[/tex] = [tex]\frac{2}{-4}[/tex] = [tex]\frac{1}{-2}[/tex]

Perpendicular slopes are the opposite reciprocals . So the slope of the line will be 2

slope (m) = 2

y = 3 You could use either point given. I chose (1,3)

x = 1 From the point given (1,3)

y = mx + b substitute in what you know and solve for b

3 = (2)(1) + b

3 = 2 + b Subtract 2 from both sides

1 = b

The y-intercept is 1.

y = mx + b

y = 2x + 1

What is the first step in a 2 step equation?

Answers

Answer:Use the following denomination (Ghana cedis 200,100,50 and 20)to find the quantities of notes

1.3584655000

2.85760000

3.146737000

4.5555627000

5.7777000

Step-by-step explanation:

What is a 123 triangle?

Answers

This is a triangle whose three angles are in the ratio 1:2:3 and respectively measure 30° ( π/6), 60° ( π/3), and 90° ( π/2) and the sides are in the ratio 1:√3: 2.

These triangles are also known as special right triangles, such as 30-60-90 triangles, and 45°-45°-90° triangles. Among all right triangles, the 45°–45°–90° degree triangle has the smallest ratio of the hypotenuse to the sum of the legs, √2/2 and the greatest ratio of the altitude from the hypotenuse to the sum of the legs, √2/4.

The 30°-60°-90° triangle is the right triangle whose angles are in an arithmetic progression. The proof of this fact is simple and follows the fact that if α, α + δ, α + 2δ are the angles in the progression then the sum of the angles 3α + 3δ = 180°. By dividing by 3, the angle α + δ must be 60°. The right angle is 90°, and the remaining angle is 30°.

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how do i do this question

Answers

Answer: Okay this is the formula for slope: y=mx+b 2 would be the slope and -1 would be the y intercept so select b.

Step-by-step explanation:

Saad yearly income is rs 236000.How much income tax he paid

Answers

Saad's income tax will be N.I.L.

Here, saad's yearly income is Rs 2,36,000.

The rate of income tax on his income will be nil because,

INCOME TAX RATE

0-2,50,000 NIL

2,50,000-5,00,000 5%

5,00,001-10,00,000 20%

More than 10,00,000 30%

Computation of tax liability of Saad

Tax on 1st 2,36,000 = N.I.L

As his income is less than 2,50,000 no income tax shall be charged to saad's income.

Therefore, the tax liability of saad would be 0.

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33
Problem 2
m, p, and z represent the lengths of the three sides of this right triangle.
m
i
Z
Р
Select all the equations that represent the relationship between m, p, and z.

Answers

Therefore , the solution of the given problem of equation comes out to bem² + p² =z².

Equation: What is it?

The Latin word equ has the meaning of equivalent. Many of the English language's changeable terms, including adequate, temperate, and equality, contain Latin roots in their base words. The Latin root word equ enters our lexicon rather easily because both sides of an equation are, by essence, "equal" to one another.

Here,

Given : a triangle of m,p,z of length of right triangle :

By using Pythagoras theorem :

The relationship comes out to be :

=> m² + p² =z²

Thus , relationship between m , p and z is m² + p² =z² as per Pythagoras theorem.

Therefore , the solution of the given problem of equation comes out to be m² + p² =z².

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Select the correct answer.
What is the reaction quotient for the following reaction; AB + 2C?
Q = [B][C], ²
[A].
OA.
OB.
O C. Q=
Q = BIC
[A].
OD. Q=
[A]
[B].[C].2
[A],
[B]. [C].

Answers

Slope Sales will be $-159.474 at 0 degrees Celsius, which is nonsensical to understand.

what is slope?

A line's steepness is determined by its slope. The "gradient overflow" is a mathematical expression for the gradient (the change in y divided by the change in x). The ratio of the vertical change (rise) between two points to the horizontal change (run) between the same two places is referred to as the slope. The slope-intercept form of an equation is used to represent each time a straight line's equation is stated as y = mx + b. The line's slope is m. b is b at the point where the y-intercept is, and (0, b). As an illustration, the equation y = 3x - 7 has a slope of 3, and its y-intercept is (0, 7).

given information,

Temperature=20 egression equation,

[tex]sales= 442.284\\ Slope=$ 30.0879[/tex]

temperature increases by 1 degree

$30.0879, on average.

[tex]y-intercept= -159.474[/tex]

At 0 degree celsius of temperature, Sales will be [tex]$-159.474[/tex]which is meaningless to interpret.

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GIVEN: GH (congruent JH and FH (congruent) HI

PROVE: FG (congruent) IJ

Answers

Hence proved that FG = IJ with CPCT theorem for ΔGHF ≅ ΔJHI by SAS Congruency rule.

What is Congruency of triangles?

Triangle congruence: Two triangles are deemed to be congruent if all three of their corresponding sides and angles have the same magnitude. Slides, rotations, flips, and turns can be used to make these triangles appear identical. They would be in alignment if they were moved. Congruence is represented by the letter "≅".

When two figures are similar to one another in terms of their size and shape, this is what mathematicians mean by congruence. It can be demonstrated that two triangles are congruent using four congruence rules in general. Finding all six dimensions is necessary, though.

Given that,

GH ≅ JH

FH ≅ HI

And,

∠GHF = ∠JHI

Therefore,

ΔGHF ≅ ΔJHI (SAS Congruency)

∴ FG = IJ (CPCT theorem)

Hence proved that FG = IJ with CPCT theorem for ΔGHF ≅ ΔJHI by SAS Congruency rule.

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The four-digit numeral $3AA1$ is divisible by $9$. What digit does $A$ represent?

Answers

When the four - digit numeral is divisible by nine is given by 3AA1 the digit A represents 7

Properties of numbers divisible by 9

A number itself is divisible by 9 if its digit's sum is also divisible by 9.

In mathematics, multiples are the results of multiplying an integer by a given number. number divisible by 9 is multiple of 9

using the above property we have that

3 + A + A + 1 = 9, OR 18, OR 27

4 +2A = 9, OR 18, OR 27

assuming 18

2A = 18 - 4

2A = 14

A = 7

hence the number is 3771

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8. On a map of scale 1:20 000 the area of a forest is 50 cm². On another map the area of the forest is 8 cm². Find the scale of the second map.

Answers

Answer: The scale of a map is a ratio that represents the relationship between distances on the map and distances in the real world. For example, a scale of 1:20 000 means that 1 unit on the map represents 20 000 units in the real world.

In this case, we are given that the area of the forest on the first map is 50 cm² and the area of the forest on the second map is 8 cm². We can use the scale of the first map to find the scale of the second map.

Since the area of the forest on the first map is 50 cm² and the scale is 1:20 000, the area of the forest in the real world is 50 cm² * 20 000 = 1 000 000 cm².

Similarly, since the area of the forest on the second map is 8 cm², the area of the forest in the real world is 8 cm² * x, where x is the scale of the second map.

Setting these two expressions equal to each other, we get:

1 000 000 cm² = 8 cm² * x

Dividing both sides of the equation by 8 cm², we get:

x = 125 000

Therefore, the scale of the second map is 1:125 000.

Step-by-step explanation:

What is .15 written as a rational number

Answers

Answer:

it is a rational number already

Step-by-step explanation:

15) 3x2 - x - 10 When this trinomial is factored completely, one of its factors is A) x 2 B) x - 5 C) 3x 5 D) 3x - 2

Answers

When the trinomial 3x² - x - 10 is factored completely, one of its factors is 3x+5.

Solving the given trinomial 3x² - x - 10.

=>3x² - 6x+5x - 10

=>3x(x-2)+5(x-2)

=>(3x+5)(x-2)

The two factors of the given trinomial 3x² - x - 10 is (3x+5) and (x-2), but according to the given options, the correct answer is option C - 3x+5.

Thus, When the trinomial 3x² - x - 10 is factored completely, one of its factors is 3x+5.

Complete question: 3x² - x - 10

When this trinomial is factored completely, one of its factors is

A) x + 2

B) x - 5

C) 3x + 5

D) 3x - 2

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The tip of a minute-hand travels 103. 62mm in one hour. Find the length of the minute

hand

Answers

Using the concept of circumference of a circle, the length of the minute hand is 16.5mm.

What is circumference of a circle?

The measurement of the circle's perimeter, also known as the circle's boundary, is called its circumference . The radius of the circle is considered when applying the formula to determine the circumference of the circle.

Circumference of circle(C) = 2πR

where,

R represents the radius of the circle

π is a constant with an approximate value of 3.14

Now, it is given that the tip of a minute-hand travels 103. 62mm in one hour which means that the minute hand moves 360 degrees.

This means that C= 103.62

So, using the concept of circumference of a circle,

C= 2πR

103.62= 2*3.14*R

So, R= 103.62/6.28

R=16.5mm

Hence, the length of the minute hand is 16.5mm.

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What is 648 rounded to the nearest ten

Answers

Answer: 640

Step-by-step explanation:

1. To help identify what place value to round write out the numbers with their place

the hundreds value in this question is 600

the tens value in this question is 40

and the ones value is 8

Since the questions asks to round to the nearest 10, you would look at the number after 4 and see if it is equal or greater than 5, if so, you would round it up to the next number, which would be 5 and write it like 640.

A vending machine has twice as many quarters in it as dollar bills if the quarters and dollar bills have a combined value of $96. 00 how many quarters are in the machine

Answers

According to question, we can say that there are 128 quarters in the machine.

What is fraction?

Any number of equal portions, or fractions, can be used to represent a whole. Fractions in standard English indicate how many units of a certain size there are. 8, 3/4. A whole includes fractions. The ratio of the numerator to the denominator is how numbers are expressed in mathematics. Each of these is an integer in simple fractions. In the numerator or denominator of a complex fraction is a fraction. True fractions have numerators that are less than their denominators. A fraction is a sum that constitutes a portion of a total. By breaking the entire up into smaller bits, you can evaluate it. Half of a full number or item, for instance, is represented as 12.

N = the number of dollars 2N the number of quaters.....so we have

25(2N) + 1N = 96

1.50N = 96

so, by fraction we have -

N = 96 / 1,50 = 64 dollars

2(64) = 128 quarters

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Quadrilateral ABCD below is reflected about line m. After the reflection, how is the perimeter of A'B'C'D' related to the perimeter of ABCD?
Quadrilateral ABCD below is rotated 180°. After the rotation, how is the area of A'B'C'D' related to the area of ABCD?

Answers

Reflection and rotation will not alter the perimeter of the quadrilateral

What is transformation?

Transformation is a term used in mathematics to refer to the movements made by objects.

Transformations has basically classifications

non rigid transformationRigid transformation

Non rigid transformation are the transformation where the dimension or size of the object will be different going from preimage to the image, example is dilation

In rigid transformation, the dimensions of the object is maintained or not altered through out the transformation process. instance of rigid transformations are

rotationreflectiontranslation

Because the transformation used are all rigid transformations then all the sides will remain same and the perimeter conserved

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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

Answers

The solution of the equation is x = -1 and y = -3.

And the intersection point is (-1, -3).

What is the system of equations?

One or many equations having the same number of unknowns that can be solved simultaneously called as simultaneous equation.

And simultaneous equation is the system of equation.

Given system of equations:

y = x-2 ...... equation 1

y = −3x−6 ...... equation 2

To solve the system of equations:

Substitute the value of y from the equation 1 to equation 2,

we get,

x - 2 = -3x - 6

x + 3x = -6 + 2

4x = -4

x = -1

Then y = -1 -2 = -3.

By graphically:

1). Draw the linear equation on the graph.

2). And the intersection point of the lines is a solution of the equation.

3). The solution is x = -1 and y = -3.

The complete graph is given in the attached image.

Therefore, the solution is x = -1 and y = -3.

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e:f =2:5 f:g=3:4 work out e:g in simpliest form

Answers

After a work out, the simplest form of e:g is 3:10.

What is a ratio?

Ratio is an expression which shows the relationship between two numbers or variables. It can generally be expressed in two forms, viz; a:b or a/ b.

To work out the simplest form of e:g as required in the question,

e/ f = 2/ 5

2f = 5e ........... 1

f/g = 3/ 4

3g = 4f ........... 2

From equation 1,

f = 5e/2

substitute the value of f in equation 2

3g = 4(5e/2)

3g = 10e

Therefore, e:g is given as;

3/ 10 = e/ g

3:10 = e: g

Thus in its simplest form, e:g = 3:10

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Charlotte has a loyalty card good for a 14% discount at her local grocery store. If the total cost, before tax and discount, of all the items she wants to buy is c, which expression represents the cost after the discount?

Answers

The expression that represents the cost after the discount is

y(c) = (7/50)c

What is expression?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.

Given is that Charlotte has a loyalty card good for a 14% discount at her local grocery store.

Let the total cost, before tax and discount, of all the items she wants to buy is {c}. Now, let the expression that represents the cost after the discount is given by y(c). We can write -

y(c) = 14% of c

y(c) = (14/100) x c

y(c) = (7/50)c

Therefore, the expression that represents the cost after the discount is

y(c) = (7/50)c.

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Jada earns $7 dollars per hour mowing her neighbors’ lawns. Name the two quantities in Jada’s situation that are in a functional relationship. Which did you choose to be the independent variable? What is the variable

Answers

The two quantities in Jada’s situation that are in a functional relationship are the number of hours she works (independent variable) and the amount of money she earns (dependent variable).

The two quantities in Jada’s situation that are in a functional relationship are the number of hours she works and the amount of money she earns. The number of hours worked is the independent variable because it is the variable that affects the amount of money earned. The amount of money earned is the dependent variable because this is the variable that is dependent on the number of hours worked.If she works 8 hours, she would earn $56.Jada earns $7 per hour, so if she works 3 hours, she would earn

$21 (3 x 7 = 21).

If she works 5 hours, she would earn

$35 (5 x 7 = 35).

If she works 8 hours, she would earn

$56 (8 x 7 = 56).

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Which of the following statements is not equivalent to the others?

16-34
|34 -16|
34-16
|16 -34

Answers

Answer:

the one that is not equivalent to the others would be 116-34

Step-by-step explanation:

because its 116 and the others dont have anything to do with 116 :)

Answer: The statement that is not equivalent should be D. |16-34

Before sending track and field athletes to the Olympics, the U. S. Holds a qualifying meet. The upper box plot shows the top 12 men's long jumpers at the U. S. Qualifying meet. The lower box plot shows the distances (in meters) achieved in the men's long jump at the 2012 Olympic games. Which pieces of information can be gathered from these box plots?

Answers

We require median, interquartile range, outliers, minimum and maximum value.

What are statistics?

Statistics is a branch of mathematics that deals with the collection, analysis, interpretation, presentation, and organization of data.

From the upper box plot representing the top 12 men's long jumpers at the U.S. Qualifying meet, we can gather the following pieces of information:

The median (middle value) of the data is around 7.6 meters, as indicated by the line in the center of the box.

The interquartile range (IQR), which is the range between the first and third quartiles, is approximately 0.4 meters, as indicated by the height of the box.

There are some outliers or values that fall outside the range of the box, which is represented by the dots or asterisks outside the box.

The minimum and maximum values for the data are around 7.3 meters and 8.0 meters, respectively, as indicated by the lower and upper ends of the whiskers.

From the lower box plot representing the distances achieved in the men's long jump at the 2012 Olympic games, we can gather the following pieces of information:

The median (middle value) of the data is around 8.0 meters, as indicated by the line in the center of the box.

The interquartile range (IQR), which is the range between the first and third quartiles, is approximately 0.5 meters, as indicated by the height of the box.

There are some outliers or values that fall outside the range of the box, which is represented by the dots or asterisks outside the box.

The minimum and maximum values for the data are around 7.5 meters and 8.4 meters, respectively, as indicated by the lower and upper ends of the whiskers.

The main difference between the two box plots is the median value, which is 0.4 meters apart and the IQR for the Olympic games is slightly bigger than the Qualifying meet.

Hence, we require median, interquartile range, outliers, and minimum and maximum values.

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We require median, interquartile range, outliers, and minimum and maximum values.

What are statistics?

Statistics is a branch of mathematics that deals with the collection, analysis, interpretation, presentation, and organization of data.