Here is a simple example of set-builder notation set builder notation it says " the set of all x's, such that X is greater than 0".
Mr. Martin is giving a math test next period. The test, which is worth 100 points, has 29 problems. Each problem is worth either 5 points or 2 points. Write a system of equations that can be used to find how many problems of each point value are on the test.
Let x be the number of questions worth 5 points and let y be the number of questions worth 2 points.
Answer:
There are 14 problems worth 5 points and 15 problems worth 2 points.
Step-by-step explanation:
x - the number of 5 points worth problems
y - the number of 2 points worth problems
The test has 29 problems.
x+y=29x+y=29
The test is worth 100 points.
5x+2y=100
The system of equations:
x+y=29
5x+2y=100
The solution:
x+y=29 ∣×(−2)
5x+2y=100
Substract −2x−2y=−58 from 5x+2y=100
−2x−2y=−58
5x+2y=100
------------------
3x=42
3x/3 = 42/3
x=14
x+y=29
14+y=29
14+y-14 = 29 - 14
y=15
There are 14 problems worth 5 points and 15 problems worth 2 points.
7) In the given figure, PQR is an equilateral triangle with coordinates of Q and
R as (-2, 0) and (2, 0) respectively. Find the coordinates of the vertex P.
The coordinates of the vertex P is calculated as (0,2√3).
What is defined as the distance formula?The distances among two points as a characteristic of their coordinates are given by an algebraic expression (like coordinate system).
The Pythagorean theorem is used to derive distance formulae for points in rectangular coordinates in 2- and three-dimensional Euclidean space.Because it has a starting and ending point, a line segment can be graphed in both two-dimensional and three-dimensional coordinate planes.Because of the two-dimensional coordinate plane, the starting and stopping points can also be marked as two-dimensional coordinates (x₁, y₁) and (x₂, y₂), culminating in the distance formula as: d = √(x₂ - x₁)² + (y₂ - y₁)².Now, according to the given question;
The coordinates of the points Q and R is given as;
Q and R as (-2, 0) and (2, 0).
Now, as the all three points P,Q and R forms the equilateral triangle. Then, the distance of each side or the distance between two consecutive points are equal.
Calculate the distances between the points;
Distance between Q and R;QR = √(2 + 2)² + (0 - 0)²
QR = 4
Distance between Q and P;Let the coordinated of P be (x, y);
Then,
QP = √(x + 2)² + (y + 0)²
QP = QR = 4
4 = √(x + 2)² + (y)² ........(equation 1)
Distance between R and P;RP = √(x - 2)² + (y + 0)²
RP = QR = 4
4 = √(x - 2)² + (y)² ........(equation 2)
Equating equation 1 and 2.
√(x + 2)² + (y)² = √(x - 2)² + (y)²
Squaring both side;
(x + 2)² + (y)² = (x - 2)² + (y)²
x² + 4 - 4x + y² = x² + 4 - 4x + y²
Simplifying the equation;
x = 0.
Put the value of x in equation 1;
4 = √(x + 2)² + (y)²
y = 2√3.
Therefore, the coordinates of the point P are found to be (0, 2√3).
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Write 7 times 100,000 + 6times 10,000+ 2times 1,000+ 5 times 100 + 8 times 1 in standered form
M is the midpoint of segment JK. The coordinate of J are (-4, 7) and the coordinates of M are (2, 5). Find the coordinates of K.
The coordinates of K are (8,3).
There is a line segment JK with M as its midpoint. This means the length of JM = length of MK.
Also the coordinates of J is (-4,7) and the coordinates for M are (2,5).
As M is the midpoint, the x-distance and y-distance between (-4,7) and (2,5) are same as that between (2,5) and K.
x- distance between (-4,7) and (2,5) = 2- (-4) = 6
So x- coordinate of K = 2+6 = 8
y-distance between (-4,7) and (2,5) = 5-7 = -2
So y-coordinate of K = 5+(-2) = 3
Hence the coordinates of K are (8,3).
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What is the inequality that matches the graph?
Answer:
x ≥ 1
Step-by-step explanation:
The number line shows that the dot is closed which means that the number it is on, is one of the solutions that works for the inequality. So x stands for/means that any number greater than 1 or equal to 1 is a solution.
For the function h defined as h(x) = nx² + 28, n is a constant and h(3) = 1. What is the value of h(-6) ?
Answer:
Step-by-step explanation:
Step One
The first step is to find the value of n.
h(x) = n(x) + 28
h(3) = 1
That means that 1 is on the left and wherever there is an x on the right, it will have a value of 3
Step Two
Substitute values
1 = n(3) + 28
Step 3
Solve
1 = 3*n + 28 Subtract 28 from both sides
1 + - 28 = 3n Combine
-27 = 3n Divide both sides by 3
-27/3 = 3n/3
- 9 = n
Step 4
Let x = - 6 on the right side of the original equation.
h(-6) = 3*-6 + 28
h(-6) = -18 + 28
Answer
h(-6) = 10
a hot cup of tea is placed on a counter and left to cool. the temperature of the tea, in degrees fahrenheit (correct to the nearest degree), x minutes after the cup is placed on the counter is modeled by a continuous function t(x) for 0
Since T is continuous for [tex]0\leq x \le 10[/tex], [tex]\lim_{x \to 4} T(x)=T(4)[/tex] From the table:
[tex]\lim_{x \to 4} T(x)=172^{0}[/tex]
By continuous function, what do you mean?A continuous function in mathematics is one that causes the value of the function to continuously vary as the input changes over time. This indicates that there aren't any discontinuities or sudden changes in value. In other words, a function is continuous if and only if its graph is devoid of any gaps or breaks. It is simple to predict where it won't be continuous for many functions. Where we have operations like division by zero or logarithms of zero, functions won't be continuous. Examples of continuous functions over the set of all real numbers are polynomial functions, exponential functions, and the sin and cosine graphs.
For the final answer the table is to be checked and all the values are written.
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Marsha pays $30 each month for a car wash membership. Which of the following represents the total amount subtracted from her account after 8 months of having the membership?
|−30| − 8 = $22
−8|30| = −$240
8|−30| = $240
|−30| − |8| = $22
Marsha pay $30 each month for a car wash membership.
In one month Marsha pay $30
In eight month Marsha pay 8*$30 = $240
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Answer:
A. |-30| - 8 = $22
Step-by-step explanation:
You are told to subtract 30 and 8, and the 30 is represented as |-30| - 8 = $22
(if this is incorrect am sorry ;-;)
25 points plus brainliest
Answer:
I believe it's B
4x - 5y = 16
Step-by-step explanation:
First you divide the whole term by -1 to get rid of negative in front of equation and then you add the c term (-16) to both sides to get the final answer.
I hope you get this right.
marcy drew a scale drawing of a petting zoo. the goat pen, which is 9 meters wide in real life, is 15 centimeters wide in the drawing. what is the scale of the drawing?
Answer:
1 cm = 0.6 m.
Step-by-step explanation:
15 cm to 9 meters
= 15 cm to 900 cm
so 1cm = 900/15 cm
1cm = 60cm
1 cm = 0.6 m.
If x = 45, y = 63, and the measure of AC = 4 units, what is the difference in length between segments AB and AD? Round your answer to the nearest hundredth. (1 point)
A
Hence , the difference in length between segments AB and AD is 1.17 units .
Trigonometric functions are referred to as Circular Functions will be merely outlined because the functions of associate angle of a triangle. It means the connection between the angles and sides of a triangle area unit given by these trig functions. the essential pure mathematics functions area unit circular function, cosine, tangent, cotangent, secant and trigonometric functionThe angles of circular function, cosine, and tangent area unit the first classification of functions of trig. and also the 3 functions that area unit cotan, secant and trigonometric function will be derived from the first functions. Basically, the opposite 3 functions area unit usually used as compared to the first pure mathematics functions.
The diagram of the given question is given below .
Applying sin rule in triangle ABC , we get
sin(x°) = AC/AB
sin(45°) = 4 / AB
1 /√2 = 4 / AB
AB = 4√2
AB ≈ 5.657
Similarly, apply sin rule in triangle ACD, we get
sin(y°) = AC /CD
sin(63°) = 4 / CD
AD = 4.489
Now distinction in lengths of AB and AD = 5.657 - 4.489
= 1.168
≈ 1.17
Therefore, distinction within the lengths of AB and AD are going to be 1.17 units.
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entering 60.00 into the price field entering 3.00 into the price of leather field entering 38.00 into the price of sneakers field
The required total of price area, leather field, and sneakers field is evaluated with the help of arithmetic operations as 102.
Given that,
Joining 60.00 into the price, area joining 3.00 into the price of the leather field entering 38.00 into the price of sneakers field,
The sum of the components is to be determined.
In mathematics, it deals with a number of procedures according to the statements. There are four primary arithmetic operators, addition, subtraction, multiplication, and division,
Here,
Joining 60.00 into the price area,
Joining 3.00 into the price of the leather field.
entering 38.00 into the price of sneakers field,
The sum = 60.00 + 3.00 + 38.00
The sum = 102
Thus, the required total of entries is evaluated with the help of arithmetic operations as 102.
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What is the next fraction in this sequence?Simplify your answer.
1/2, 4/7, 9/14, 5/7,....
Answer:
Step-by-step explanation:
[tex]\displaystyle\\\frac{1}{2},\ \ \frac{4}{7},\ \ \frac{9}{14},\ \ \frac{5}{7} ,\ \ ... \\\\\frac{1*7}{2*7} ,\ \ \frac{4*2}{7*2} ,\ \ \frac{9}{14}, \ \ \frac{5*2}{7*2} ,\ \ ...\\\\\frac{7}{14},\ \ \frac{8}{14} , \ \ \frac{9}{14},\ \ \frac{10}{14},\ \ \frac{11}{14},\ \ ...,\ \ \frac{6+n}{14} , \ \ n=1,\ 2,\ 3,\ ...[/tex]
4. Juan has 28 paperback books that measure
re 1 1/4 inches each, how many books will fit on one
shelf if each shelf measures 30 inches?
Answer:
24 books can fit on 1 shelf.
Step-by-step explanation:
Question: Juan has 28 paperback books that measure 1 and 1/4 inches each. How many books will fit on one shelf if each shelf measures 30 inches?
Step-by-step:
We know that each book is 1 and 1/4 inches each. It might be easier to convert the fraction into a decimal.
1/4 inches is 1 divided by 4 which equals to 0.25 inches
1 inch + 0.25 inches = 1.25 inches
so, 1 and 1/4 inches = 1.25 inches
To find out how many books fit on a shelf, we need to find: length of 1 bookshelf divided by length of 1 book
We know that one bookshelf is 30 inches and 1 book is 1.25 inches
so, 30/1.25 or 30 divided by 1.25 = 24
Therefore, 24 books can fit on 1 shelf.
the product of 5 minus 6 has a result of 24
The expression for the phrase is 5 * (x - 6) = 24
How to write an expression for the phrase?The phrase is given as:
the product of 5 minus 6 has a result of 24
Products means *
So, we have
5 * (x minus 6) has a result of 24
x minus 6 means x - 6
So, we have
5 * (x - 6) has a result of 24
has a result of 24 means = 24
So, we have
5 * (x - 6) = 24
Hence, the expression for the phrase is 5 * (x - 6) = 24
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A sequence is ____ while a series is ______. A series is definite if_________, it is infinite if ________.
Answer: A sequence is a enumerated collection of objects in which repetitions are allowed/order matters while a series is a infinite series. A series is definite if its based on the concept of sequences.
A series could be finite or infinite because its mainly often represented in compact form which is also known as a sigma notation(∑)to indicate the summation involved. infinite series is the sum of an infinite sequence.
Step-by-step explanation:
Write in point slope form an equation of the line through the pair of points.
(9,8) and (6,1)
________________________________________________
What is an equation of the line in point-slope form? Show your work.
A.) y - 8 = -7/3(x - 9)
B.) x - 8 = 7/3(y - 9)
C.) y = -7/3x - 13
D.) y - 8 = 7/3(x-9)
Answer:
d) y - 8 = 7/3(x - 9)
Explanation:
[tex]\sf point-slope\:form :[/tex]
[tex]\sf y - y_1 = m(x - x_1) \ \ where \ (x_1, y_1), \ (x_2, y_2) \ are \ points \ and \ m \ the \ slope[/tex]
Find the slope:
[tex]\sf slope: \dfrac{y_2 - y_1}{x_2- x_1} \ \ where \ (x_1 , \ y_1), ( x_2 , \ y_2) \ are \ points[/tex]
[tex]\sf \rightarrow slope\ (m) : \dfrac{1-8}{6-9} = \dfrac{-7}{-3} = \dfrac{7}{3}[/tex]
Find the equation:
in point slope form:
[tex]\sf y - 8 = \dfrac{7}{3} (x - 9)[/tex]
[tex]\sf y = \dfrac{7}{3} x - 21+8[/tex]
in slope intercept form
[tex]\sf y = \dfrac{7}{3} x -13[/tex]
solve the equation for x if 2 to the power x = 8
Answer:
x=3Step-by-step explanation:
solve the equation for x if 2 to the power x = 8
2^x = 8
log(2x)=log(8)
x*log(2)=log(8)
x=((log(8))/((log(2))
x=3
----------------------------
check
2^3 = 8
2 * 2 * 2 = 8
8 = 8
the answer is good
Help needed! This shouldn't be too difficult...
Answer:
2.62 x 10^16
Step-by-step explanation:
Step-by-step explanation:
Let look at the numerator:
(3.1 x 10^6)(6.97 x 10^4)
= (3.1 x 6.97) x 10^(6+4)
= 21.607 x 10^10
So 21.607 x 10^10
_______________
8.245 x 10^-6
= (21.607/8.245) x 10^(10 - -6)
= 2.62 x 10^(10 + 6)
= 2.62 x 10^16
I hope this helps
Answer:2.62061855 x 10^16
Step-by-step explanation:
Draw a scaled copy of this polygon that has a perimeter of 30 units. what is the scale factor? explain how you know. help please
The scale factor is 3.
calculate scalar factor for given data?[tex]scale factor =\frac{scaled\ measure}{actual\ measure}[/tex]
∵ If sides of a polygon are changed by a scale factor 'a' then its perimeter is also changed by the same scale factor,
[tex]scale factor =\frac{scaled\ perimeter}{actual\ perimeter}[/tex]
The actual perimeter of the polygon = 10 unit,
Also, the scaled perimeter = 30 units
Hence,
[tex]scaled factor = \frac{30}{10} =3[/tex]
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PLEASE HELP BRANILY NEED THIS ASAP
Answer:
A. $7.46
Step-by-step explanation:
184.54 - 5.50 = 179.04
179.04 / 24 = 7.46
The answer WITHOUT SUBTRACTING THE DELIVERY FEE is: $7.69 (B).
If you're supposed to subtract the delivery fee, then the answer is $7.46 (A).
----------------------------------
Hope this helps!
Have a great day and God bless! :)
a whole number larger than 2 leaves a remainder of 2 when divided by each of the numbers 3, 4, 5 and 6.
A whole number larger than 2 leaves a remainder of 2 when divided by each of the numbers 3, 4, 5, and 6 is 62.
What are whole numbers?Whole numbers are numbers without fractions and consist of positive integers and zero. It is represented by the symbol "W," and the numbers are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9,...............Zero in its entirety represents nothing or a null value.To find the whole number:
LCM of 3, 4, 5, and 6 = 3 × 2 × 2 × 5 = 60Add the remainder 2 in 60: 60 + 2 = 62So, the whole number is 62.Therefore, a whole number larger than 2 leaves a remainder of 2 when divided by each of the numbers 3, 4, 5, and 6 is 62.
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On wednesday, a local hamburger shop sold a combined total of hamburgers and cheeseburgers. the number of cheeseburgers sold was three times the number of hamburgers sold. how many hamburgers were sold on wednesday?
The number of hamburgers sold on Wednesday is 141 and the number of cheeseburgers sold on Wednesday is 423
Although a part of your question is missing, you might be referring to this full question: On Wednesday, a local hamburger shop sold a combined total of 564 hamburgers and cheeseburgers. The number of cheeseburgers sold was three times the number of hamburgers sold. How many hamburgers were sold on Wednesday?
Total number of burgers sold on Wednesday = 564
Let the number of hamburgers sold on Wednesday be x
Let the number of cheeseburgers sold on Wednesday be y
Formulating the equation we get:
x + y = 564-----(1)
It is also given that, the number of cheeseburgers sold was three times the number of hamburgers. So,
y = 3x
Substituting y = 3x in equation (1) we get
x + 3x =564
4x = 564
x = 141
Putting x = 141 in equation (1) we get
y = 423
So, the number of hamburgers sold is 141 and the number of cheeseburgers sold is 423
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PLEASE ANSWER,,,, 30 POINTS,,,, BRAINLYIEST !!!! ||||||||||||| The dot plot below shows the number of different types of trees in Seth's garden:
A straight line is shown with 4 equidistant marks. The first mark is labeled Redbud, the second mark is labeled Magnolia, the third mark is labeled Snowbell, and the fourth mark is labeled Maple. The first mark has 1 dot, the second mark has 5 dots, the third mark has 2 dots, and the fourth mark has 3 dots. Below the line is written Number of Trees
Which table shows the data displayed in the dot plot?
A). Garden Trees Number
Redbud 0
Magnolia 4
Snowbell 1
Maple 2
B). Garden Trees Number
Redbud 1
Magnolia 5
Snowbell 2
Maple 3
C). Garden Trees Number
Redbud 1
Magnolia 6
Snowbell 7
Maple 10
D). Garden Trees Number
Redbud 3
Magnolia 2
Snowbell 5
Maple 1
Answer: B
Step-by-step explanation:
Only makes sense its the same as the question I might be wrong
An uncle wills $3000 to his two nieces and one nephew. The older niece is to receive twice what the younger niece receives, and the nephew is to receive an amount equal to the sum of the nieces' amounts. How much will each person receive?
Answer:
See Explanation
Step-by-step explanation:
So, the uncle has $3000.
The Oldest Niece gets double what the Younger Niece gets half her amount. The nephew gets the total of these 2 combined.
The Youngest Niece gets $500.
500x2=1000
The Oldest Niece gets $1000.
1000+500=1500
The Nephew gets $1500.
1500+1000+500=3000
Order the square root of 70, negative 8.2 repeating, twenty five thirds, and negative eight and four sevenths from least to greatest.
negative eight and four sevenths, negative 8.2 repeating, square root of 70, twenty five thirds
negative eight and four sevenths, negative 8.2 repeating, twenty five thirds, square root of 70
negative 8.2 repeating, negative eight and four sevenths, twenty five thirds, square root of 70
negative 8.2 repeating, negative eight and four sevenths, square root of 70, twenty five thirds
The order from least to greatest is -8.222 <-7.43 < 8.333 < 8.366
The numbers given are:
The square root of 70 =√70 = 8.366
Negative 8.2 repeating = -8.222
Twenty five thirds = 25/3 = 8.333
Negative eight and Four sevenths = -8 and 4/7 = (-52)/7 = -7.43
So from least to greatest,
-8.222 <-7.43 < 8.333 < 8.366
That is, Negative 8.2 repeating < Negative eight and Four sevenths < Twenty five thirds < The square root of 70
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Your friend and your cousin discuss measuring with a ruler. Your friend says that you must always line up objects at the zero on a ruler. Your cousin says it does not matter. Who is correct, and why?
friend; A measurement always starts with a value of zero.
friend; A ruler does not match numbers one to one unless the measurement starts at zero.
cousin; you can choose any number for the start of the object and any number for the end.
cousin; The distance is the absolute value of the difference of the numbers lined up with the beginning and the end of the object.
The correct option is the last one:
"Cousin; The distance is the absolute value of the difference of the numbers lined up with the beginning and the end of the object."
Who is correct, your friend or your cousin?
Now, remember that a rule is equivalent to a number line.
Now, suppose that you are measuring an element with a length of 16 centimeters.
If you measure it by lining up one of the ends of the element with the zero, then the other end will be at the line number 16.
And if you line it up from a different number, let's say 3cm, then the other end of the object (which still measures 16cm) will be at 19cm.
In both cases, to find the measure of the object that you are measuring with the ruler, you need to find the difference between the two numbers on the ruler that line up with the object ends.
If you line up with the zero, you need to subtract zero, so the measure is easier:
16cm - 0cm = 16cm
If you line up with other number, like the 3 in this case, you need to perform the subtraction:
19cm - 3cm = 16cm
In both cases, we will get the same measure. So your cousin is correct, and the correct option is the last one:
Cousin; The distance is the absolute value of the difference of the numbers lined up with the beginning and the end of the object.
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A car valued at $20,000 depreciates at a rateof 2% during the first 5 years, then at a rateof 2.5% every year after that. What will thecar’s value be after 10 years?)
Answer:
$15928.81
Step-by-step explanation:
hope this works
2000 x (0.98)^5 = ans
ans x (0.975)^5 = 15928.81442 which rounds to $15928.81
Question Progress
Homework Progress
24 / 63 Marks
a) Work out the value of (15)*× (√3)?
x
b) Work out the value of (19) × (√30) ?
x
1 14
豐
54%
Answer:
(a) 15
(b) 270
Step-by-step explanation:
Part (a)Given expression:
[tex]\left(\sqrt{5}\right)^2 \times \left(\sqrt{3}\right)^2[/tex]
[tex]\textsf{Apply the exponent rule}:\quad \left(\sqrt[n]{a}\right)^n=a,\quad \textsf{$n$ is odd or $a \geq 0$}[/tex]
[tex]\implies 5 \times 3[/tex]
Multiply the numbers:
[tex]\implies 15[/tex]
Part (b)Given expression:
[tex]\left(\sqrt[3]{9} \right)^3 \times \left(\sqrt{30}\right)^2[/tex]
[tex]\textsf{Apply the exponent rule}:\quad \left(\sqrt[n]{a}\right)^n=a,\quad \textsf{$n$ is odd or $a \geq 0$}[/tex]
[tex]\implies 9 \times 30[/tex]
Multiply the numbers:
[tex]\implies 270[/tex]
Now we have to,
→ work out the value for the following.
We know that,
→ square ( ²) and square root (√) gets cancelled each other.
→ cube ( ³) and cube root (³√) gets cancelled each other.
a) (√5)² × (√3)² = ?
→ (√5)² × (√3)²
→ 5 × 3 = 15
Thus, the answer is 15.
b) (³√9)³ × (√30)² = ?
→ (³√9)³ × (√30)²
→ 9 × 30 = 270
Thus, the answer is 270.
ALMN is an isosceles triangle with LM = LN, LM LN, LM = 3x - 2, LN = 2x+1, and MN = 5x - 2. Find the length of MN.
Answer:
x = 3
Step-by-step explanation: