The larger of the two integers is 18 and the smaller integer is 17.
Integers are collection of whole numbers and negative numbers. Integers are not fractional numbers or decimal. Some examples of integers are -5,-25,0,13,9 .
Let us consider the smaller integer be x.
As the integers are consecutive, the larger integer is (x+1).
Now according to the given condition:
Twice the large integer=2(x+1)
15 less than the 3 times the smaller integer=3x-15
Now the value of these two expressions is equal.
Therefore: [tex]2(x+1)=3x+-15[/tex]
Solving the above equation to find the value of x:
[tex]or,2(x+1)=3x-15\\or,2x+2=3x-15\\or,2x-3x=-15-2\\or,-x=-17\\or,x=17[/tex]
Therefore the smaller integer is 17.
Larger integer(x+1) : 17+1=18
Therefore the integers are 17 and 18.
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ABC = 25x + 34
CBD= 11x +23
Find ABD CBD and ABC
The measure of <ABD, <DBC and <ABC are 67, 67 and 134 degrees respectively.
Bisection of anglesAngles are bisected if they are divided into two equal parts.
If the angle BC bisects <ABC, hence <ABD and <DBC are equal, hence;
2(11x + 23) = <ABC
Given the following parameters
<ABC = 25x + 34
2(11x + 23) = 25x + 34
Expand
22x +46 = 25x + 34
22x-25x = 34 - 46
-3x = -12
x = 4
Determine the measure of the angles
<ABD = 11x + 23 = <DBC
<ABD = 11(4) + 23
<ABD = 44 + 23
<ABD = 67 degrees
<ABC = 2(67)
<ABC = 134 degrees
Hence the measure of <ABD, <DBC and <ABC are 67, 67 and 134 degrees respectively.
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Select the set of ordered pairs that does not satisfy the requirements of a function.
O {(1, 1), (2, 2), (3, 3), (4,4)}
O {(1,4), (2,4), (3, 4), (4,4)}
O {(1, 1), (1, 2), (1, 3), (1,4)}
O {(1, 2), (2, 3), (3, 4), (4,1)}
A relation will be only a function if and if only for every single value of x there must be only one output thus {(1,1),(1,2), (1,3), (1,4)} will not be a function, therefore, option (C) will be correct.
What is a function?A certain kind of relationship called a function binds inputs to essentially one output.
A function can be regarded as a computer, which is helpful.
Given the coordinates,
In option (B) {(1,4),(2,4),(3,4),(4,4)} in this for y = 4 → x = 1,2,3,4 so it will be a function becuase for every single x value there is a single y value but for a single y value, there could be two x.
In option (D) {(1,1),(1,2), (1,3), (1,4)} for x = 1 → y = 1,2,3,4 so it will not a function.
Hence "{(1,1),(1,2), (1,3), (1,4)} will not be a function".
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Evaluate.
7- 24 ÷ 8 × 4 + 6
Answer:
-35
Step-by-step explanation:
Question =7-24÷8×4+6
=7-192÷4+6
=7-49+6
=-41+6
=-35
Therefore,right answer is (-35)
PLEASE MARK ME AS THE BRAINIEST.
Is the following statement true or false?
The intersection of three planes can be a point
Answer: Sometimes true
Step-by-step explanation:
This statement is sometimes true. If three planes intersect, then their intersection can be a line or a point.
If a closet organizer has a total width of 69 1/8 inches and the closet is 69 3/4 inches wide, will the organizer fit?
Yes the organizer will fit. See the explanation of the word problem below.
How do you know that the organizer will fit?Because 3/4 = 6/8,
69 6/8 is larger than 69 1/8 by 5/8".
That is 6 eighths minus 1 eighth is 5 eighths).
Hence, we may disregard the 69 inches because there is no difference in total inches.
The only distinction is in fractions of an inch.
Hence the organizer will be able to fit inside the closet.
What is a word problem?A word problem in mathematics is a math question expressed in one or more sentences that demands students to apply their arithmetic skills to a'real-life' setting.
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Which shows the expression below simplified?
A. 8 × 10-3
B. -1.4 x 10-3
C. 8x10-1
D. 8×104
0.00056+ (7 x 10-²)
Answer:
A.77
B.-17
C.79
D.832
E.0.07056
Step-by-step explanation:
A.=8×10-3
=80-3
=77
B.=-1.4×10-3
=-14-3
=-17
C.=8×10-1
=80-1
=79
D.=8×104
=832
E.=0.00056+(7×10^-2)
=0.00056+0.07
=0.07056
A small publishing company is planning to publish a new book. The production costs will include one-time fixed costs (such as editing) and variable costs (such as printing). There are two production methods it could use.
With one method, the one-time will total $13,238, and the variable costs will be $24.75 per book.
With the other method, the one time fixed costs will total 50,107, and variable costs will be 11.75 per book. For how many books produced will the costs from the two methods be the same?
2836 numbers books produced will the costs from the two methods be the same.
From the given data
There are two production methods could be used so we can get two equations for cost (c) from two methods
Let x be the numbers of books produced.
Now, To calculate the total production cost.
Total production cost by selling books = Fixed one time cost + Cost for production of books.
From method 1 the equation we get
C = 24.75x + 13238
and from method 2 the equation we get
C = 11.75x + 50107
Method 1 cost = Method 2 cost
24.75x + 13238 = 11.75x + 50107
24.75x - 11.75x = 50107 - 13238
13x = 36869
x = 36869/13
x = 2836
x = 2836 numbers of books will have same cost.
How can I create a mathematical expression using the provided description?By using variables, you may represent the unknowable amounts. As you follow the description, perform each mathematical conversion individually. For instance, if you are asked to increase an item by 4, you can do it by adding 4 to the item. There are various ways to translate descriptions into mathematical formulas, such as multiplying something by 2 if it is, for instance, doubled.
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Help !!! With this please !!!
Answer: $48.17
Step-by-step explanation:$148.68-$24.32= $124.36
$124.36-$37.53= $86.83
$135 -$86.83=$48.17
So he needs forty-eight dollars and 17 cents.
Identify the property that justifies the statement. ∠LMN ≅ ∠LMN
Please Hurry!!
The property which justifies the statement, ∠LMN ≅ ∠LMN is: C. reflexive property of ≅.
Corresponding parts of two congruent figures.In Mathematics, two geometric figures are considered to be congruent only when their corresponding side lengths are congruent and the magnitude of their angles are congruent.
What is the reflexive property of congruence?The reflexive property of congruence states that a line segment, an angle, or geometric shape (geometric figure) is always congruent to itself.
This ultimately implies that, for all angles M , ∠M ≅ ∠M. In this context, we can reasonably infer and logically deduce that the property which justifies the statement, ∠LMN ≅ ∠LMN is reflexive property of ≅.
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Q/R = g/F solve for F
Answer:
the answer is
Step-by-step explanation:
Q/R= G/F
= QF=GR
divide both sides by Q
Q and Q are off so
therefore F= GR/Q
I need help is -2x=3/8 a literal equation?
The equation -2x=3/8 is not a literal equation.
What is a literal equation?A literal equation can be defined as an equation which primarily of letters.
It is an equation made up of several variables or letters.
Examples of literal equations are;
V = dts = ut + 1/2 at^2Area = πr²D = m/ vWe can see from the examples shown that the equations or formulas have several variables or letters that could be written in terms of other variables.
Given the equation;
-2x=3/8
We can see that there is only one variable to be worked out and hence, is not a literal equation.
Thus, the equation -2x=3/8 is not a literal equation.
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Isabel sold t-shirts at a festival and made profit of $71. She made $4 for each t-shirt she sold. Her total expenses were $25. How many t-shirts did she sell?
Answer:24
Step-by-step explanation:
71 + 25=96
96 divided by 4 equals 24
you have to add her profit and her expenses to see how much she needed to sell
Arianna buys computer games from an online store. each game she orders costs $22 and shipping for her total is $9. arianna can spend no more than $75. how many computer games can arianna buy?
There are 3 computer games she can brought at $75.
Unitary method
Unitary method is defined as the process of finding the value of a unit and then the value of a required number of units.
Given,
Arianna buys computer games from an online store.
Each game she orders costs $22 and shipping for her total is $9.
Arianna can spend no more than $75.
Here we need to find how many computer games did Arianna Brought.
Let x be the number of computer games she brought.
We know that,
Cost for one game = $22
Shipping cost = $9.
She spent = $75.
So, it can be written as,
=> 22x + 9 = 75
=> 22x = 75 - 9
=> 22x = 66
=> x = 66/22
=> x = 3.
So, she can brought 3 computer games at $75.
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which of the following is equivalent to 3^4 ? Which of the following is equivalent to 3^ 4 ?
12
81
7
64
81 is equivalent to 3^4
What Is the Power of a Number?
The power of a number stands for how many multiples of the number there are. The power of a number is represented by something called an exponent
When a number is "raised to the second power," it means that the number is multiplied together twice, for example. When a number is "raised to the fifth power," it means that it is multiplied together five times.
we have to solve 3^4
here 3 raised to the fourth power
then 3 is multiplied together 4 times
3*3*3*3
81
Hence ,81 is equivalent tp 3^4
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helppppppppppppppppppppppp
Answer:
see explanation
Step-by-step explanation:
the 2 expressions are difference of squares and factor in general as
a² - b² = (a + b)(a - b)
Then
4w² - 36
= (2w)² - 6²
= (2w + 6)(2w - 6)
and
25[tex]x^{4}[/tex] - 64y²
= (5x²)² - (8y)²
= (5x² + 8y)(5x² - 8y)
Write an equation of ine that passes through (5,-2) and (7,6) in slope intercept form
The equation of the line i slope intercept form is y = 4x - 22.
What is slope ?Slope is the amount a point moves in y axis upon the amount a point move in x axis.We can also say that slope is rise over run.
According to the given question we have to an equation of line that passes through (5,-2) and (7,6) in slope intercept form.
We know equation of a line in slope intercept form is y = mx + b.
Two points are given (5,-2) = (x₁,y₁) and (7,6) = (x₂,y₂) and we know slope (m) = (y₂ - y₁)/(x₂ - x₁).
∴ slope (m) = { 6 - (-2) }/( 7 - 5)
slope (m) = 8/2
slope (m) = 4.
Now the equation can be written as
y = 4x + b.
Putting any of the given pair of points for x and y in y = mx + b.
6 = 4(7) + b
6 = 28 + b
b = - 22.
∴ The required equation is y = 4x - 22.
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What’s the GCF of 42, 70, 84
Answer: 14
Step-by-step explanation:
First. take the prime factorization of all three numbers:
42: 21*2 ==> 3*7*2
70: 35*2 ==> 5*7*2
84: 42*2 ==> 21*2*2 ==> 3*7*2*2
Notice any common factors? That's the GCF.
GCF: 7*2=14
GCF: 14
Answer:
14
Step-by-step explanation:
The greatest number that divides 42, 70, and 84 exactly is their greatest common factor.
Factors of 42 = 1, 2, 3, 6, 7, 14, 21, 42
Factors of 70 = 1, 2, 5, 7, 10, 14, 35, 70
Factors of 84 = 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84
The GCF of 42, 70, and 84 is 14.
The greatest number that divides 42, 70, and 84 is 14.
What is GCF?
The biggest positive integer that divides evenly into all the numbers with no remainder is the greatest common factor (GCF, GCD, or HCF) of a set of whole numbers. For instance, the GCF is equal to 6 for the set of numbers 18, 30, and 42.
How do I get the GCF of something?
The greatest common factor among numbers can be discovered in a number of ways.
Factoring:
List each number's factors in order to calculate the GCF by factoring. The factors that evenly divide into the number with no remainder are known as whole numbers. The GCF is the largest number that appears on each list of common factors for each number.
Example: Find the GCF of 18 and 27
The factors of 18 are 1, 2, 3, 6, 9, 18.
The factors of 27 are 1, 3, 9, 27.
The common factors of 18 and 27 are 1, 3 and 9.
The greatest common factor of 18 and 27 is 9.
Prime Factorization:
List all of each number's prime factors to determine the GCF by prime factorization. List the prime factors that each of the original numbers has in common. Include the most instances of each prime factor that each original number has in common. To find the GCF, multiply these by one another.
You'll observe that the prime factorization approach may be simpler than straight factoring as numbers grow larger.
Example: Find the GCF (18, 27)
The prime factorization of 18 is 2 x 3 x 3 = 18.
The prime factorization of 27 is 3 x 3 x 3 = 27.
The occurrences of common prime factors of 18 and 27 are 3 and 3.
So the greatest common factor of 18 and 27 is 3 x 3 = 9.
There is another method but it focuses on more complex numbers.
Hope this helps!
a sporting event coordinator has 200 mini foam fingers she gives 2 foam fingers to each student in attendance. there are 26 left. how many students are in attendance?
thank u <3
The total number of students which are there in the sporting events are 87.
The total number of mini foam fingers which the sporting event coordinator has is 200. Since he gives 2 foam fingers to each student present in the event therefore each student has 1 pair of mini foam fingers.
So, in total there are 200/2 = 100 pairs of mini foam fingers.
The total number of mini foam fingers left after distribution is equal to 26.
So total pairs of mini foam fingers left = 26/2 = 13
Therefore, the number of students which are present in attendance is given by:
Total pairs of foam fingers - total pairs of foam fingers left
=> 100-13 = 87
Therefore, total number of students in attendance are 87.
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I went to a toy shop and bought a toy car which costs $16.80, but there was a 20% discount. how much did I pay?
Step-by-step explanation:
16.80 - 20% of 16.80 = 13.44
you paid 13.44$
Answer:
=13.44
Step-by-step explanation:
0.20×16.80=3.36
16.80-3.36=13.44
Help please
15 points
need by the end of today
Answer:
16. G
17. C
Step-by-step explanation:
Sort the following numbers into the correct category:
If you do this I will do the following: Like, Friend you, (if you want me to.) give you the brainiest, (when two people answers then I will be able to pick the best one.) and I believe that is all! Please do this and if you do not do it correctly like I wanted it and yes, I do want it to be actually “CORRECT.” So please help me complete this.And once you have done this I will say, “Thank you for your help!” :)
Answer:
sqrt of 49 is simplified as 7 so its a rational that can be put in all the rows
Step-by-step explanation:
Rational numbers: -1.3, 2.7777.., 25/2 also known as 12.5, O
Integers: sqrt of 49 also known as 7, 0
Whole numbers: sqrt of 49 also known as 7, 0
Natural numbers: sqrt of 49 also known as 7, 0
Irrational numbers: sqrt of 2, Pi,
HELP ME PLEASE TY
Abraham needs one-half of a point to get an A– in Math. What rational number can be used to represent the number of points needed for Abraham to get an A–?(1 point)
In order for Abraham to receive an A, he will need to earn a total of 1.5 points, which is the rational number that may be used to represent that amount.
Explain the concept of rational numbers.?It is important to keep in mind that a number is considered rational if it can be expressed in the form of a fraction.
It is possible when decimals and numbers have worked effectively.
In light of the fact that Abraham must get a grade of A– in mathematics in order to achieve an A, the rational number that can be used to symbolize the number of points that Abraham must earn in order to get an A will be the number 1.5.
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You sold your car for $1,000 which had cost $1,450. How much did you lose expressed as a %?.
Answer:
45%
Step-by-step explanation:
1,450 - 1,000 = 450
the 450 becomes 0.45
to make 0.45 a percent, we multiply it by 100
0.45 x 100 = 45
45%
Nitrogen dioxide gas and nitrogen trioxide gas combine to produce dinitrogen pentoxide gas.
Write a balanced chemical equation for this reaction.
A balanced chemical equation for this reaction is given as
NO2(g)+NO3(g)→N2O5(g)
This is further explained below.
What is a chemical equation?Generally, A chemical reaction occurs that takes place when two or more molecules contact with the appropriate orientation and sufficient force to generate a new product.
This process is referred to as a chemical reaction. During this procedure, atomic bonds are both broken and formed in the course of the operation.
Synthesis, decomposition, from another, and double displacement reactions are the four primary categories of chemical reactions. Synthesis is the process of creating new molecules from existing ones.
In conclusion, A balanced chemical equation for this reaction is given as
NO2(g)+NO3(g)→N2O5(g)
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Find the distance between A(7,-7) and B(13,0). Write your answer as a radical and as a decimal rounded to the nearest tenth.
The distance between A(7,-7) and B(13,0) is 9.2 units
Distance between two pointsThe formula for calculating the distance between two point is expressed as;
D = √(x₋₂-x₁)²+(y₂-y₁)²
Given the coordinate points A(7,-7) and B(13,0).
Substitute
AB = √(13-7)²+(0-7)²
AB = = √(6)²+(-7)²
AB = √36+ 49
AB = √85
AB = 9.2 units
Hence the distance between A(7,-7) and B(13,0) is 9.2 units
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If Z is the Circumcenter of TUV, find each missing measure
Answer is
VY = 17
UZ =21
WV = 14.7
TV = 29.4
TU = 38
SOLVING STEPS
WV = [tex]x^{2}[/tex]+[tex]15^{2}[/tex] = [tex]21^{2}[/tex]
⇒[tex]x^{2}[/tex] + 225 = 441
⇒ [tex]x^{2}[/tex] = 441-225
⇒ [tex]x^{2}[/tex] = 216
⇒ x = [tex]\sqrt{216}[/tex]
VY = 17
UZ =21
WV = 14.7
TV = 29.4
TU = 38
The circumcentre of a triangle is defined as the point where the perpendicular bisectors of the sides of that particular triangle intersect. In other words, the point of concurrency of the bisector of the sides of a triangle is called the circumcentre.
Method to Calculate the Circumcentre of a Triangle
Steps to find the circumcentre of a triangle are:
Calculate the midpoint of given coordinates, i.e. midpoints of AB, AC, and BC
how to calculate the slope of the particular line :
By using the midpoint and the slope, find out the equation of the line (y-y1) = m (x-x1)
Find out the equation of the other line in a similar manner
Solve two bisector equations by finding out the intersection point
Calculated intersection point will be the circumcentre of the given triangle
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1. Jake reads the following problem: If the original scale factor for a scale drawing of a square swimming pool is 1/90, and the length of the original drawing is measured to be 8 inches, what is the length on the new scale drawing if the scale factor of the new scale drawing length to actual length is 1/144? He works out the problem: 8 inches ÷ 1/90 = 720 inches 720 inches× 1/144 = 5 inches Is he correct? Explain why or why not.
Yes Jake is correct we the scales are accurately represented.
How to calculate the value?From the information, the original scale factor for a scale drawing of a square swimming pool is 1/90, and the length of the original drawing is measured to be 8 inches.
Therefore, the original length will be:
= 8 ÷ 1/90
= 8 × 90
= 720 inches
Therefore, Jack is correct.
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calculate these values
a= _____
b= _____
The values of a and b of the given matrix multiplication is gotten as; a = 2 and b = 3
How to multiply Matrices?
To multiply matrix, we follow patterns depending on the type of matrix. Thus, from the given matrix, we can say that;
(1 * -1) + (0 * -1) + (1 * 3) = a
-1 + 0 + 3 = a
a = 2
Similarly;
(1 * -1) + (0 * 2) + (1 * 4) = b
-1 + 0 + 4 = b
b = 3
Thus, the values of a and b of the given matrix multiplication is gotten as; a = 2 and b = 3
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meaning of primary school
Answer:
primary school is a primary school
Answer:the meaning of primary school is elementary school basically grades Kinder-5th grade
Step-by-step explanation:
−|−5⋅(−7)| simplified
The answer to this question is:
−|−5⋅(−7)| = −35
The non-negative quantity of a real number x, regardless of its sign, is its absolute value (or modulus), | x |. For instance, the number 5 has a value of 5 and an absolute value of 5.
So, here first we have to solve the expression written inside the modulus and then the remaining part.
−| −5⋅(−7) | = −| −5*(−7) |
= −| 35 |
The absolute value of | 35 | is non-negative value of 35
| 35 | = 35
So, −| −5⋅(−7) | = −| 35 | = −35
Therefore, −|−5⋅(−7)| = −35
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