Simplify the mathematical expression (a) 7 x 6 – 5 x 4 + 1 x 3
The order of operations is a collection of rules that gives the correct sequence of steps for doing a calculation. BIDMAS is an acronym used to tell you the correct order to complete a calculation when there are different operations . It stands for Brackets, Indices , Division, Multiplication, Addition and Subtraction.
Thus solving the expression;
we first solve all the multiplication parts:
7 x 6 - 5 x 4 + 1 x 3
Now addition:
= 42 - 20 + 3
Lastly subtraction:
= 42 - 23
= 19
A+b=7 and ab= 6 find a2+b2
Answer:
37
Step-by-step explanation:
a+b=7 and ab= 6 find a^2+b^2
a + b = 7ab = 6( a + b )² = a² + b² + 2ab =
7² = a² + b² + 2 × 6 =
49 = a² + b² + 12 =
a² + b² = 49 - 12 =
a² + b² = 37
There are 400 more men than women at a funfair in the morning. In the afternoon 2/5 of the men and 1/4 of the women left the funfair. As a result, there were 120 more men than women remaining at the funfair. How many men were there at the funfair at first
There was 1200 men and 800 women at the funfair in the morning
What is an equation?An equation consists of numbers and variables linked together by mathematical operations to form an expression.
Let x represent the number of men and y represent the number of women in the morning.
There are 400 more men than women at a funfair in the morning. Hence:
x = y + 400
x - y = 400 (1)
In the afternoon 2/5 of the men and 1/4 of the women left the funfair. hence:
number of men remaining = x - (2/5)x = (3/5)x
number of women remaining = y - (1/4)y = (3/4)y
There were 120 more men than women remaining at the funfair. therefore:
(3/5)x - (3/4)y = 120 (2)
From both equations:
x = 1200, y = 800
There was 1200 men in the morning
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Aditi and Kavita had 40 coins in total. Aditi gave 10 coins to Kavita. The product of the coins they now have is 375. Aditi had fewer than 30 coins when she started.
Aditi and Kavita had 40 coins in total. the coin share b/w them is
x=25, y=15
What is coin share?Generally, Aditi and Kavita's original coin total is 40.
x+y=40
Aditi gave 10 coins to Kavita.
(x-10)*(y+10)=375
Now solving a system of equations using a calculator
x=25, y=15
x=35, y=5
Since Aditi had fewer than 30 coins when she started.
The correct proportion is
x=25, y=15
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CQ
Aditi and Kavita had 40 coins in total. Aditi gave 10 coins to Kavita. The product of the coins they now have is 375. Aditi had fewer than 30 coins when she started.
How much coin did dey both have
determine if the two lines 7x-3y=-21 and y= "-3/7x+5" are parallel, perpendicular or neither
Answer:
They are perpendicular!
Step-by-step explanation:
Get 7x-3y=-21 into y=mx+b format.
7x-3y=-21 Bring 7x to the other side
-3y=7x-21 Divide -3 by both sides, it cancels out on the y's side.
y=-7/3x+7 Two negatives equal a positive, that it why 7 is positive.
y=-7/3x+7 is the line, the other is y=-3/7x+5
The slope of this line is -7/3 , the slope of the given line is -3/7.
Lines are perpendicular if the slopes are opposite reciprocals, such as this.
So, while they intercept at different points on the y-axis, they will intersect at some point! This makes them perpendicular.
What is the rule for a 45 45 90 special right triangle choices are given by the order of leg leg hypotenuse leg?.
For each 45-45-90 triangle, the period of the hypotenuse equals the length of the leg expanded via the square root of 2. That is the 45-45-90 Triangle Theorem.
A triangle is a polygon with three edges and 3 vertices. The terminology for categorizing triangles is greater than thousand years vintage, having been described at the very first web page of Euclid's elements.
In Euclidean geometry, any 3 elements, at the same time as non-collinear, determine a very precise triangle and simultaneously, a unique plane (i.e. a -dimensional Euclidean area). In special words, there's exceptional one plane that includes that triangle, and each triangle is contained in some plane. If the complete geometry is best the Euclidean plane, there is the fine one aircraft and all triangles are contained in it; however, in better-dimensional Euclidean areas, this isn't actual. this text is prepared triangles in Euclidean geometry, and specifically, the Euclidean plane, besides in which otherwise said.
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PLEASE HELP ASAP!!
Select the correct answer.
Simplify the following expression.
5-^3
Answer: A
Step-by-step explanation:
when you have a number to a negative power, putting it as a fraction under 1 will turn the negative power positive
What is the difference between greatest 6 digit number and smallest 6 digit number?.
The difference between the greatest 6-digit and smallest 6-digit numbers is 899999.
The aim is to find the smallest and largest 6-digit numbers, and then we need to find how many numbers are between these two values.
Let's start by finding the smallest 6-digit number.
We know that 0 is the smallest digit that can not be used in the highest place value, so we will consider the next smallest digit; that is, 1 and 1 can be used in the highest place value.
Thus, we can create the required 6-digit smallest number with 0 and 1.
Hence, the smallest 6-digit number is 100000.
Now, we will discover the largest 6-digit number.
As we know, the largest digit is 9, which can be used anywhere. So, we will form the largest 6-digit number with the digit 9.
Thus, the largest 6-digit number is 999999.
Next, we need to find the difference between these two values.
So, we can determine the difference between the smallest 6-digit number and the largest 6-digit number by subtracting the smallest from the largest.
Thus, we get,
⇒999999−100000
⇒899999
Hence, 899999 is the difference between the smallest 6-digit and the largest 6-digit numbers.
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Rectangle A B C D is transformed by a combination of two transformations so that all points on AB are invariant and there are no other invariant points.
The first transformation is
a reflection in the line with equation y = k, where ‘k’
is an integer and k ≠1
Describe fully the second transformation.
(2 marks)
It is a translation by vector
(?)
The second transformation that is applied to rectangle A B C D is a translation.
Explain about fully the second transformation:A translation is a transformation that moves an object a certain distance in a certain direction without changing its size or orientation. In this case, the translation is represented by a vector, which is a mathematical object that has both magnitude and direction. The vector for this translation would have the form (x, y), where x and y are the horizontal and vertical distances that the object is moved.In the case of rectangle A B C D, since all points on AB are invariant, it means that the translation vector has the same magnitude in the horizontal direction as it does in the vertical direction. This is why the vector for the translation is represented by (?), as the values of x and y are not given. The only thing that is specified in the problem is that the translation vector moves the rectangle in a direction that is different from the reflection line y = k, as there are no other invariant points.To learn more about second transformation refer to;
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can someone help me please
what is 2(1/3^2) ?
Step-by-step explanation:
0.22222222222222222222222222
What are the types of multiplication method?.
Different types of multiplication method is given by :
a. Addition method
b. Vertical method
c. Box method
d. Partial multiplication method
As given in the question,
Different types of the multiplication method are as follow :
a. Addition method :
In addition method if 4 × 3 it means add 4 three times.
4 + 4 + 4 = 12
b. Vertical method :
It is traditional way of multiplying the given numbers . Example : 12 × 4
1 2
×4
48
c. Box method :
In this box was formed as per the given numbers . Example 42 × 13
10 3
40 400 120
2 20 6
Add : 400 + 120 + 20 + 6 = 546
d. Partial multiplication method :
This method is based on distributive property to make the calculation easy.
45 × 6
= ( 40 + 5 ) × 6
= 40 × 6 + 5 × 6
= 240 + 30
= 270
Therefore, the different types of multiplication methods are:
a. Addition method
b. Vertical method
c. Box method
d. Partial multiplication method
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What is the lowest whole number side length in inches that would ensure the triangle is an obtuse triangle?.
Answer:
24 inches.
Step-by-step explanation:
In order for a triangle to be obtuse, one of its angles must be greater than 90 degrees. In a right triangle, the angle opposite the hypotenuse is always 90 degrees, so in order for the triangle to be obtuse, the hypotenuse must be the longest side.
To find the lowest whole number side length in inches that would ensure that the triangle is obtuse, we can use the Pythagorean theorem. The Pythagorean theorem states that the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.
a^2 + b^2 < c^2
If we take the base 48cm and convert it to inches, 48cm = 48*0.393701 = 18.897638 inches
So the base is 18.897638 inches.
Now we have to find the lowest whole number side length of c so that:
18.897638^2 + b^2 < c^2
358.565744 + b^2 < c^2
We can see that the lowest whole number of c is 24 inches.
So, the lowest whole number side length in inches that would ensure that the triangle is obtuse is 24 inches.
in anytown, 55% of the 20,000 inhabitants live in houses, 25% of the inhabitants live in apartments, the rest of the inhabitants live in condominiums, how many anytownians live in condominiums. HELP WILL GIVE BRAINLIST IF SHOW WORK
Answer: 4,000 people live in condominiums.
Step-by-step explanation:
First add 55%+25%=80%
Then subtract 100%-80%=20%
Then turn 20% to 0.2.
Last, multiply 0.2x20,000= 4,000
which neurotransmitter is released from the parasympathetic ganglion
The amount of neurotransmitter released from the parasympathetic ganglion is acetylcholine.
The parasympathetic nervous system is part of the autonomic nervous system which helps to regulate involuntary bodily functions such as heart rate, digestion and other processes.
The parasympathetic nervous system is responsible for calming the body and restoring it to its resting state. Parasympathetic ganglia are clusters of neurons that receive and transmit nerve signals from the brain to the organs and muscles.
The amount of neurotransmitter released from these ganglia is acetylcholine, which helps to slow the heart rate and promote relaxation.
The parasympathetic nervous system is part of the autonomic nervous system which helps to regulate involuntary bodily functions such as heart rate, digestion and other processes.
The parasympathetic nervous system is responsible for calming the body and restoring it to its resting state. Parasympathetic ganglia are clusters of neurons that receive and transmit signals from the brain to the organs and muscles.
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11. Find the value of x
Giving 75 points please help
1) Triangle Midsegment Theorem will be used to solve the given problem.
2) The value of x would be 10.
What is Triangle Midsegment Theorem?
A triangle midsegment is a segment that links the midpoints of two triangle sides. A midsegment joining two triangle sides is parallel to the third side and half the length.
1) Triangle Midsegment Theorem will be used to solve the given problem.
2) Here M is the midpoint of AB, and P is the midpoint of BC. So, PM is a midsegment.
Therefore by the Triangle Midsegment Theorem,
[tex]PM=\frac{1}{2} AC\\\\(x+5)=\frac{1}{2} 3x\\\\x=10[/tex]
Hence, The value of x would be 10.
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Gabe goes to the mall. If k is the number of items he bought, the expression 18.58k+30 gives the amount he spent in dollars at one store. Then he spent 22 dollars at another store. Find the expression which represents the amount Gabe spent at the mall. Then estimate how much Gabe spent if he bought 3 items.
The expression which represents the amount Gabe spent at the mall will be 18.58k + 52.
The amount that Gabe spent if he bought 3 items will be $107.74.
How to calculate the expression?From the information, Gabe goes to the mall. If k is the number of items he bought, the expression 18.58k+30 gives the amount he spent in dollars at one store and he spent 22 dollars at another store.
The expression which represents the amount Gabe spent at the mall will be:
= 18.58k + 30 + 22
= 18.58k + 52
The amount that Gabe spent if he bought 3 items will be:
= 18.58k + 52
= 18.58(3) + 52
= $107.74
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How do you draw a 100 degree angle?.
You can draw a 100 degree angle with the help of Protractor.
A degree is the name given to the mathematical unit of measurement for an angle. A protractor is a device used to determine the degree of an angle. Angles can be measured at different angles with different degrees, such as 30°, 45°, 60°, and so on. A complete circle rotates at 360°.
Each of the 360 equal segments that make up a rotation is referred to as a degree. We use a circle ° to represent a degree. 180°, for instance, denotes 180 degrees. An angle in degrees is an angle whose measure is expressed in degrees.
Follow the given steps to construct a 100-degree angle with the help of a protractor.
Step 1: Draw a line with the help of a ruler and name it AB.Step 2: Place protractor tip at A and choose a 100 degree mark on protractor.Step 3: Place the pencil tip on the mark of 100 and mark a small point.Step 4: Draw a line connecting the point A and the recently marked point.Learn more about Angle:
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What are the 3 types of multiplication?.
The three types of multiplication properties are given by :
1. Commutative property : a × b = b × a , a, b ∈R
2. Identity property : a × 1 = a , a ∈ R
3. Distributive property : a × ( b + c ) = a × b + a × c , a, b, c ∈R.
As given in the question,
Three types of multiplication property is given by :
Let us consider variable a, b, c belongs to real number R.
1. Commutative property :
Order of the multiplication having no affect on the final outcome.
a × b = b × a
Example : 5 × 4 = 20
4 × 5 = 20
2. identity property :
Multiplying one to any real number always gives the same number.
a × 1 = a
Example : 3 × 1 = 3
3. Distributive property :
Adding first two numbers and then multiplying or first multiplying each pair and then adding result remain same.
a × ( b + c ) = a × b + a × c
Example:
5 × ( 2 + 1 ) = 5 × 2 + 5 × 1
Therefore, the three types of multiplication property are given by :
1. Commutative property
2. Identity property
3. Distributive property
The above question is incomplete , the complete question is :
What are the 3 types of multiplication properties ?.
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Pine Grove High School has a total of one thousand and twenty
students. Ten percent of the students are out sick, and twenty-five
percent of the students are on a field trip. How many students are
currently in the school?
10 pointss!! Huryyyy nowww
663.
i found out what 35% of 1020 is and then subtracted that by 1020.
If all of the following are non-terminating decimals, which would be classified as a rational number?
A. 1.25468902
B. 12.4587984
C. 3.12541254
D. 2.15435321
Answer:c
Step-by-step explanation:
Solve for u.
–11u = 759
Answer:
u = -69
Step-by-step explanation:
Now we have to,
→ find the required value of u.
The equation is,
→ -11u = 759
Then the value of u will be,
→ -11u = 759
→ u = 759/-11
→ u = -(759/11)
→ [ u = -69 ]
Hence, the value of u is -69.
What is The quotient of anumber and nine is less than the number. In algebraic expressions
Answer: [tex]x-\frac{x}{9}[/tex]
Step-by-step explanation:
1) quotient is the answer of a division problem
with that in mind and letting "a number" = x . . .
"The quotient of a number and nine..." would be [tex]\frac{x}{9}\\[/tex]
2) "is less than" always means you but the previous statement BEHIND . . .
[tex]x-\frac{x}{9}[/tex]
Simplify $(4 - 5i) - (-2i - 8) + (-1 + 8i).$
The expression $(4 - 5i) - (-2i - 8) + (-1 + 8i) is simplified to $5i -11
What are algebraic expressions?Algebraic expressions are defined as expressions that are composed of variables, coefficients, factors, constants and terms.
These expressions are likely to consist of some arithmetic operations, such as;
AdditionSubtractionMultiplicationFloor divisionBracketParenthesesDivisionFrom the information given, we have that;
$(4 - 5i) - (-2i - 8) + (-1 + 8i)
expand the bracket
$4 - 5i + 2i +8 - 1 + 8i
Now, collect like terms
$-5i +2i + 8i +4 +8 - 1
Add or subtract the like terms
$5i -11
Hence, the expression is $5i -11
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What is the additive inverse of the polynomial –9xy2 + 6x2y – 5x3?
Answer:
9xy² -6x²y +5x³
Step-by-step explanation:
You want the additive inverse of –9xy² + 6x²y – 5x³.
Additive inverseThe additive inverse is the value that gives zero when added to the original. It can be formed by changing the signs of the terms in the sum:
9xy² -6x²y +5x³
What is the product of 3x3x3x3?.
The product of numbers , 3× 3×3×3 is equals to the eighty-one.
In mathematics, a product is a number or result that is obtained by multiplying two or more numbers together. So, 12 is the product of 3 and 4. For example product of 5 and 4 is represented by 5 × 4 = 20 , it is a multiplication expression. A multiplication expression has three parts, a multiplier ( i.e., 4) , a multiplicand ( i.e., 5), and the product ( i.e., 20). We have, a multiplication expression as 3×3×3×3. We can rewrite it in form 3¹× 3¹ ×3¹× 3¹ = 3¹⁺¹⁺¹⁺¹ = 3⁴ , it is an exponential form number. Therefore, results is equals to 81. So, the required product value is 81.
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Oakwood Elementary Fall Carnival gets bigger every year! Last year, they had 70 volunteers working 14 booths. This year, they want to have 42 booths.
If they use the same ratio of volunteers to booths, how many volunteers does Oakwood Elementary need this year?
Answer:
210
Step-by-step explanation:
70
14 booths
ratio = 70/14 =5
42 booths
by the same ratio = 42*5 = 210
The table shows a linear relationship between the height of a fast-growing bamboo plant and the number of days since it was planted.
Days Planted. x 0, 2,4,6
Height (in.), y 15,20,25,30
1. What do the variables x and y represent in this relationship?
2. Read the description of the relationship above the table. How do you know that the relationship can be represented by a linear equation?
3. Can you tell whether the relationship has a positive or negative slope just by looking at the data in the table? Explain.
4. What rate does the slope represent in this situation?
5. Choose two points from the table and calculate the slope.
6. Suppose you graph the points given in the table. Where does the point (0, 15) lie? Use this information to find the y-intercept.
7. Write an equation in slope-intercept form that represents this
Step-by-step explanation:
answer is 567
How many types of fractions are there Class 6?.
There are seven types of fractions.
We know that the fraction is used to represent the portion or part of the whole thing.
The fraction has two parts: numerator and denominator.
The top part of fraction is numerator and the bottom part is denominator.
consider a fraction 1/8.
Here, numerator is 1, denominator is 8
When certain thing is divided into 8 equal parts then each part of is represented by fraction1/8
The types of fractions are:
1) Proper fraction - the numerator is always less than the denominator
2) Unit Fractions - the numerator of fraction is always 1
3) Improper fraction - the numerator is greater than the denominator
4) Mixed fraction - it is a combination of a natural number and fraction
5) Like fractions - the fractions have the same denominators
6) Unlike fractions - the fractions have the different denominators
7) Equivalent fractions - the fractions have the same value when simplified.
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From the top of a tower, John ee hi friend Julie on the ground at an angle of depreion of 49. If the tower i 83 ft. In height, how far i Julie from the bae of the tower? Round your anwer to the nearet tenth
Julie is approximately 40.6 ft away from the base of the tower.
Trigonometry is a branch of mathematics that deals with the relationships between the angles and sides of triangles. One of the main uses of trigonometry is to calculate distances in a triangle when the lengths of two sides and the measure of the angle between them are known.
We can calculate this by using the formula:
Distance = (tower height) / (tan(angle of depression))
Distance = (83 ft) / (tan(49))
Distance = 40.6 ft (rounded to the nearest tenth)
Therefore, Julie is approximately 40.6 ft away from the base of the tower.
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Please help!! I NEED this by tmr!!
Find the length of the segment y =
2.5x+10 from x = 0 to x = 16.
The length of the segment is 10,12.5 , 15,.. when x is from x = 0 to x = 16.
What is algebraic expression ?
Algebraic expression can be defined as the combination of variables and constants .
From the given expression ,
y = 2.5 x + 10
So, we have to find the length of line segment from x = 0 to x = 16.
so when x = 0 ,
y = 0+10
y = 10
and when x=1
y = 2.5*1+10
y=12.5
and similarly
when x = 2
y = 2.5* 2 + 10
y = 15
So, like this the sequence will be goin on y = 10 , 12.5 , 15 , 17.5 and etc .
Hence, The length of the segment is 10,12.5 , 15,.. when x is from x = 0 to x = 16.
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