The true statements are:
The greatest common factor of 20 and 30 is 10.
The least common multiple of 20 and 30 is 60.
The common factor is 2.
Consider the numbers 20 and 30,
The factors of 20 are 1, 2, 3, 4, 5, 10, and 20.
The factors of 30 are 1, 2, 3, 5, 6, 10, 15, and 30.
The common factors are 1, 2, 3, 5, 6, 10 and hence the greatest common factors are 10.
And, 2 is a common factor.
The multiples of 20 are 20, 40, 60, 80, 100, ....
The multiples of 30 are 30, 60, 90, 120, ...
Therefore, the least common multiple is 60.
The GCF and LCM of 20 and 30 are 10 and 60 respectively. The common factor is 2.
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you order two tacos and a salad. the salad costs $2.50. you pay 6% sales tax and leave a $3 tip. you pay a total of $13.60. how much does one taco cost?identify an equation that can be used to answer the question.
Answer:
1.25 without the sales tax and tip
Step-by-step explanation:
How to solve for number 3
Answer: m<F = 134
EF = 18in
Step-by-step explanation:
Since both angles FEG and FGE are equal, we could make out that lines EF and FG are equal measures making an isosceles triangle. Therefore we just add up both 23 to get 46 and subtract it by 180 getting 134
the answer for y-3=-3y-43
HELPPPPPP!!! WILL GIVE BRAINLIEST THIS IS HARD PLS HELP!
The code is DHGB.
We are given four puzzles.
1. The equation of the line is : -4x + 2y = 8. The slope of the line is 2. We need to find the parallel line. The slope will be the same. The equation of the parallel line is y = 2x - 5. The code letter is D.
2. The slope of the line is [(3-2)/(0-3)] = -1/3. We need to find the perpendicular line. The slope will be the negative reciprocal. The slope of the perpendicular line is 3. The equation of the perpendicular line is y = 3x - 2. The code letter is H.
3. The slope of the line is [(2-(-2)/(0-(-1)] = 4. We need to find the parallel line. The slope will be the same. The equation of the parallel line is y = 4x - 7. The code letter is G.
4. The equation of the line is : 3x + y = 1. The slope of the line is -3. We need to find the perpendicular line. The slope will be the negative reciprocal. The slope of the perpendicular line is 1/3. The equation of the perpendicular line is y = (1/3)x + 2. The code letter is B.
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What is an equation of the line that passes through the points (2,−6) and (−2,4)?
Answer:
y = - [tex]\frac{5}{2}[/tex] x - 1
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (2, - 6 ) and (x₂, y₂ ) = (- 2, 4 )
m = [tex]\frac{4-(-6)}{-2-2}[/tex] = [tex]\frac{4+6}{-4}[/tex] = [tex]\frac{10}{-4}[/tex] = - [tex]\frac{5}{2}[/tex] , then
y = - [tex]\frac{5}{2}[/tex] x + c ← is the partial equation
to find c substitute either of the 2 points into the partial equation
using (- 2, 4 ) , then
4 = 5 + c ⇒ c = 4 - 5 = - 1
y = - [tex]\frac{5}{2}[/tex] x - 1 ← equation of line
A shop sells cola in three different size bottles.
2 Litre
£1.99
600ml
62p
Which size bottle is the best value for money?
You must show all your working.
1.5 Litre
£1.53
Does this graph show a function? Explain how you know.
O A. Yes; there are no y values that have more than one x-value.
B. No; there are y values that have more than one x-value.
C. Yes; the graph passes the vertical line test.
D. No; the graph fails the vertical line test.
If a vertical line exists moved across the graph and, at any time, touches the graph at only one point, then the graph exists a function. If the vertical line touches the graph at more than one point, then the graph is not a function.
What is meant by vertical line test?The vertical line test is a visual approach for assessing whether a curve in the plane accurately depicts the graph of a function by counting the points on the curve where vertical lines cross it. Consequently, any vertical line in the plane can only ever cross the graph of a function once.
Use the vertical line test to define whether or not a graph represents a function. If a vertical line exists moved across the graph and, at any time, touches the graph at only one point, then the graph exists a function. If the vertical line touches the graph at more than one point, then the graph is not a function.
Therefore, the correct answer is option D. No, the graph fails vertical line test.
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Please help ASAP!!
will give brainliest
The coordinates of the circumcenter of the circle is (3,2)
In geometry, a polygon's circumscribed circle, also known as its circumcircle, is a circle that passes through each of the polygon's vertices.
The center and radius of this circle are its circumcenter and circumradius, respectively.Polygons don't necessarily have circumscribed circles. Due to the fact that its vertices are concyclic, a polygon with one is sometimes referred to as a cyclic polygon or a concyclic polygon. All triangles, all right kites, all regular simple polygons, all isosceles trapezoids, and all rectangles are cyclic shapes.4.The given coordinates are J(6,0) , K(0,0) and L(0,4) .
The coordinates of the circumcenter are (3,2)
5. The given coordinates are J(-6,6) , K(0,0) and L(-4,0) .
The coordinates of circumcenter are (-2,4)
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Please help me solve this
With the explanation
Using proportions, the solution to the given rule of three is as follows:
x = 0.61.
What is a proportion?A proportion is a fraction of a total amount, and equations can be built to find the desired measures in the problem using a rule of three among the proportional amounts, using basic arithmetic operations such as multiplication or division.
The multiplication can be on the line or cross multiplication, depending if the variables are inverse or direct proportional, respectively.
In the context of this problem, the rule of three that represents the relation between the variables is:
1/x = 54/33
Supposing a direct relationship, we apply cross multiplication, hence the solution for x is found as follows:
54x = 33
x = 33/54
x = 0.61.
What is the missing information?This problem is incomplete, hence we are going to suppose that we have to solve for x = alpha considering the drawing as a rule of three.
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A tomato seedling is 6 inches tall and growing 1.5 inches per week. A radish seedling is 8 inches tall and growing 1.4 inches per week. Which system of equations represents the height of the seedlings after x weeks? brainly answer
Answer:
Dude I wish I could help you
A
Step-by-step explanation:
The system of equations that represents the height of the seedling after x weeks is:
y = 6 + 1.5x
y = 8 + 1.4x
What is an equation?Two or more expressions with an equal sign are defined as an equation.
Given that, the tomato seeding is 6 inches tall and growing 1.5 inches per week, and the radish seedling is 8 inches tall and growing 1.4 inches per week.
Let x represent the number of weeks and y represent the total height.
The total height of the tomato seedling after x weeks is:
y = 6 + 1.5x
The total height of the radish seedling after x weeks is:
y = 8 + 1.4x
Hence, the system of equations that represents the height of the seedling after x weeks is:
y = 6 + 1.5x
y = 8 + 1.4x
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4cm/= ? cm/min I am so confused
if we covert 4 cm/second into cm/minute we get answer as 240 centimeters per minute.
What is centimeter?
A centimeter is a unit of measurement that is one tenth of a meter or ten millimeters in the metric system. The length of an object is measured in centimeters, which are metric units of measurement. The abbreviation is cm.
We have given,
4 centimeters per second and we have asked to convert it in centimeters per minute.
We know that 1 minute contains 60 seconds.
It tells us that,
x cm/s = 60x cm/minute
4 cm/s = 60(4) cm/minute
4 cm/s = 240 cm/minute
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Complete Question
Convert 4 cm/s to cm/min
A random sample of students were asked whether they preferred to sweep the floor or to do the dishes, and whether they preferred to hear music or have silence while doing the chore. The results of the survey are summarized in the table. Sweep Dishes Total Music 60 96 Silence 62 104 Total 78. 122 200 What is the probability that a student prefers to do the chore in silence? O A 0.21 OB. 0.31 Ос 0.39 OD. 0.42 E. 0.52
this is:
[tex]P=\frac{\text{silence}}{\text{total}}=\frac{104}{200}=0.52[/tex]answer: E
12% of Cu in a 11.5 g coin
If a coin weighing 11.5 grams, has 12 Percentage of Cu content by mass in it, then the exact quantity of Cu in the coin in grams will be 1.38 grams.
As per the question statement, a coin weighing 12 grams, has 12 % of Cu content by mass in it.
We are required to calculate the exact quantity of Cu present in the coin in grams, from the above mentioned data.
To solve this question, we will simply need to calculate 12% of 11.5, and we will obtain our desired answer, that is,
12% of 11.5 = [(12/100) * 11.5] = (0.12 * 11.5) = 1.38 grams.
Hence, a coin weighing 11.5 grams, having 12 Percentage of Cu content by mass, will have 1.38 grams of Cu inside it.
Percentage: In mathematics, a percentage is a number or a ratio expressed as a fraction of 100 and often denoted using the percent sign, "%", to determine a certain part of one whole.Grams: As per the International System, the gram is a metric unit of mass being equal to one one thousandth of a kilogram.To learn more about Percentage and Grams, click on the link below.
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equation that is perpendicular to 5x +3y=-21 and passes through (-5,1)
The equation of line perpendicular to the line 5x + 3y = -21 will be;
⇒ y = 3x/5 + 4
What is Equation of line?
The equation of line with slope m and passes through the point
(x₁, y₁) is;
⇒ y - y₁ = m (x - x₁).
Given that;
The equation of perpendicular line is,
⇒ 5x + 3y = -21
And, The point on the line will be (-5 , 1)
Now,
The product of the slopes of the perpendicular line will be -1.
Slope of the perpendicular line 5x + 3y = -21 is;
5x + 3y = -21
y = - 5x/3 - 21/3
y = -5x/3 - 7
dy/dx = m₁ = -5/3
So, The slope of line which is perpendicular to the line is;
m₁ m₂ = -1
m₂ = -1/m₁
m₂ = 3/5
So, The equation of line perpendicular to the line 5x + 3y = -21 and passes through the point (-5, 1) is;
⇒ y - y₁ = m (x - x₁).
⇒ y - 1 = 3/5 (x - (-5)).
⇒ y - 1 = 3/5 (x + 5)
⇒ 5 (y - 1) = 3 (x + 5)
⇒ 5y - 5 = 3x + 15
⇒ 5y = 3x + 15 + 5
⇒ 5y = 3x + 20
⇒ y = 3x/5 + 4
Thus, The equation of line perpendicular to the line 5x + 3y = -21 will be;
⇒ y = 3x/5 + 4
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action of Mixed Numbers
Eric rides his bike 4 hours during the week. His little brother rides his bike 12 hours during the week.
How many more hours does Eric ride his bike during the week than his little brother?
Enter your answer as a mixed number in simplest form by filling in the boxes.
Answer:
-8 hours/week
Step-by-step explanation:
Erik = 4 hours/week
Little Brother = 12 hours/week
How many more hours does Eric ride his bike during the week than his little brother?
Erik - Little Brother = (4 hrs/wk - 12 hrs/wk)
Erik rides his bike -8 hours/week more than his little brother.
I need help badly on this one
PLEASE
[tex]\cfrac{x^2-9}{3x^2+8x-3}\div\cfrac{x-3}{x+2}\implies \cfrac{x^2-9}{3x^2+8x-3}\cdot \cfrac{x+2}{x-3}\implies \cfrac{\stackrel{\textit{diff. of squares}}{x^2-3^2}}{(x+3)(3x-1)}\cdot \cfrac{x+2}{x-3} \\\\\\ \cfrac{~~\begin{matrix} (x-3)(x+3) \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}{~~\begin{matrix} (x+3) \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~(3x-1)}\cdot \cfrac{x+2}{~~\begin{matrix} x-3 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~ }\implies \cfrac{x+2}{3x-1}[/tex]
What is the magnitude size of 3.7?
Answer: |3.7| = 3.7 so the answer will be 3.7
Step-by-step explanation:
Natalie is competing in the javelin throw event at her school. in order to qualify for the final round, the mean length of her javelin throws in the first round must be at least 195 feet. she has 1 more throw left in the first round. this list shows the length, in feet, of natalie's first 7 javelin throws. 188, 204, 194, 195, 187, 201, 199 question what is the minimum length, in feet, that natalie must throw the javelin on her next throw in order to qualify for the final round? enter the answer in the box.
The minimum length = 192ft, that Natalie must throw the javelin on her next throw in order to qualify for the final round.
Based on the given conditions,
The length of her javelin throws in the first round must be at least 195 feet.
She has 1 more throw left in the first round.
This list shows the length, in feet, of Natalie's first 7 javelin throws.
= 188, 204, 194, 195, 187, 201, 199
The minimum length is,
= 188 + 204 + 194 + 195 + 187 + 201 + 199
= 1368
Let us assume,
Final length = x
So,
We can write,
( x + 1368 ) / 8 ≥ 195
x + 1368 ≥ 195 * 8
We can multiply the coefficient,
x + 1368 ≥ 1560
x ≥ 1560 - 1368
We can sum or difference the coefficient,
x ≥ 192
This is Inequality function.
Equations and inequalities are mathematical sentences formed by relating two expressions to each other. In an equation, the two expressions are supposed to be equal and shown by the symbol =. Whereas in inequality, the two expressions are not necessarily equal and are indicated by the symbols: >, <, ≤ or ≥.
Therefore,
The minimum length = 192ft, that Natalie must throw the javelin on her next throw in order to qualify for the final round.
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m² x m² x m² x m² can you please help me
Answer:_______
____1 m8
Answer:
m^8
Step-by-step explanation:
you basicly need to add those 2s because m² =m x
Twice a number plus 6 times the
number is 72. Find the number.
Answer:
The number is 9
Explanation:
So, the first thing you have to do is write out the problem. 2x+6x=72
Then, you combine like terms. 8x=72
Then, you have to isolate the variable, so you divide by 8 on both sides. 8x/8=72/8
Then, you have x=9, which is your answer.
Answer:
The number is 9.
Step-by-step explanation:
Framing the expression and solving:
Let the number be 'x'.
Twice a number = 2x
6 times the number = 6 *x = 6x
2x + 6x = 72
Combine the like terms,
8x = 72
Divide both sides by 8,
x = 72 ÷ 8
x = 9
A person can burn 120 calories in 15 minutes of running. Calculate how many
calories the person will burn in 1,5 hours.
Question 5.2 [2 marks]
So, if in 15 minutes, a person can burn 120 calories. In 1 minute, a person can burn 8 calories.
120 ÷ 15
8
15 | 120
120
0
8 CALORIES.NOW, how many calories a person burn in 1.5 hours?
FORMULA (HOURS TO MINUTES)60 × 1.5
60
X 1.5
300
60
90.0
90 MINUTES15 minutes x 8 calories = 120 calories (GIVEN)
90 minutes × 8 calories
90
x 8
720
ANSWER = A person can burn 720 calories in 1.5 hours.how many groups of 3 3/1 are there in 6 1/6
The number of groups of 3 and 1/3 in 6 and 1/6 are 37/20.
We can write the given mixed fraction in the form of an improper fraction form.
Mixed fraction
Mixed fractions are those fractions that are formed by combining a whole number with a fraction.
Improper fraction
A fraction with the numerator value greater than the denominator is known as an improper fraction.
Hence, we can write,
3 and 1/3 = 10/3 and,
6 and 1/6 = 37/6
To find the number of groups of 3 and 1/3 in 6 and 1/6, we will divide 6 and 1/6 by 3 and 1/3
Hence, we can write,
(37/6) ÷ (10/3) = (37/6)*(3/10) = 37/20
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Given m
n, find the value of x and y.
(5x+20) (y-18)
(6x-4)°
The values of x and y are: 24° and 58° respectively.
We know that vertically opposite angles are equal, so:
(5x+20) = (6x-4)
5x-6x = -4-20
-x=-24
x=24
hence x=24°
also, angles on a straight line adds up to 180°, so:
5x+20+y-18=180°
using x=24
5(24)+20+y-18=180°
120+20+y-18=180
140+y-18=180
y+122=180
y=180-122
y=58°
Hence the values of x and y are 24° and 58° respectively.
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Answer correctly for 50 points.
Dont lie or i will report you.
Answer: 36 5/9
Step-by-step explanation:
If f(x) = 4x – 6, then f-1(x) =
Answer:
(x+6)/4
Step-by-step explanation:
We are given the following function:
f(x) = 4x-6
It can also be written as:
y = 4x - 6
Finding the inverse:
We have to exchange y with x, and then isolate y. It becomes:
[tex]x=4y-6[/tex]Isolating y:
[tex]4y=x+6[/tex][tex]y=\frac{x+6}{4}[/tex]The inverse function is:
[tex]f^{-1}(x)=\frac{x+6}{4}[/tex]Collect like terms: 3x(exponent of 2) + 2x + 3x -1
The like terms in the expression are 2x and 3x, and the solution is 3x^2 + 5x - 1
What are expressions?Expressions are mathematical statements that are represented by variables, coefficients and operators
How to collect the like terms?The expression is given as
3x(exponent of 2) + 2x + 3x -1
Rewrite the expression properly
So, we have
3x^2 + 2x + 3x -1
The like terms are the expressions that have the same variables
In this expression, the like terms are 2x and 3x
When evaluated, we have
3x^2 + 5x - 1
Hence, the equivalent expression is 3x^2 + 5x - 1
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Cici likes to collect shoes, but she only has half the number of pairs of shoes that her friend Aubree has. If Cici has 42 pairs of shoes, how many pairs of shoes does Aubree have?
Answer:
84 pairs of shoes
Step-by-step explanation:
Since Cici has pairs of shoes, use this equation to solve for the number of pairs of shoes Aubree has
Can anyone assist me?
please
Make and test a conjecture about the quotient of two negative integersThe quotient of two negative integers is anumber.= =14 =-21 =--21-5
Answer:
The conjecture is;
"The quotient of two negative integers is a positive rational number"
Explanation:
Recall that negative divided by negative is equal to positive;
[tex]\frac{-1}{-1}=1[/tex]for the given question;
[tex]\begin{gathered} \frac{-4}{-5}=\frac{-1\times4}{-1\times5}=1\times\frac{4}{5} \\ \frac{-4}{-5}=\frac{4}{5} \end{gathered}[/tex]secondly;
[tex]\begin{gathered} \frac{-14}{-7}=\frac{14}{7}=2 \\ \frac{-14}{-7}=2 \end{gathered}[/tex]Thirdly;
[tex]\frac{-21}{-5}=\frac{21}{5}[/tex]we can observe that all the quotient of two negative integers solved in the three questions above gave a positive rational number.
Therefore, The conjecture is;
"The quotient of two negative integers is a positive rational number"
Order each step and justification that is needed to solve the equation below. -2x = 28 - 6x Steps Justifications -2r = 28 - 61 Given - 2x + 6r 28 - 61 + 61 Simplification Simplification Division property of equality -41 28 28 4 r = 7 r = - 7 4r = 28 - 4x = 28 Addition property of equally
-2x = 28 - 6x --------------------------> Given
-2x + 6x = 28 - 6x + 6x------------------------------>Addition property of equality
4x = 28 -----------------------------------------> Simplification
4x/4 = 28/4 --------------------------------->Division property of equality
x = 7 --------------------------------------->Simplification
