The room floor has a rectangular dimensions with an area of 48 square metres and it will take 32 metres of the carpet to cover the floor completely without wastage.
How to calculate for the required metre of carpetThe floor has rectangular dimensions 8 m by 6 m such that:
area of the floor = 8 m × 6 m
area of the floor = 48 m²
Since the carpet roll is 1.5 metres wide;
48 m²/ 1.5 m = 32 m
Therefore, it will take 32 meters of the carpet to cover the rectangular floor with 8m by 6m dimensions completely without wastage.
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19. (i)
(ii)
Express 1050 as the product of its prime
factors.
Find two numbers, both greater than 40, that
have a highest common factor of 21 and
lowest common multiple of 1050.
(i) 1050 as the product of its prime factors is 1050 = 2 x 3 x 5² x 7.
(ii) The two numbers having a highest common factor of 21 and
lowest common multiple of 1050 are (760,1160).
What is a prime factor?
A natural number other than 1 whose only factors are 1 and itself is said to have a prime factor. In actuality, the first few prime numbers are 2, 3, 5, 7, 11, and so forth. Now, we may also apply the so-called prime factorization, which actually involves using factor trees, for numbers.
To get the prime factors of 1050, start dividing the number by its primes -
1050 ÷ 525 = 2
525 ÷ 175 = 3
175 ÷ 35 = 5
35 ÷ 7 = 5
7 ÷ 1 = 7
So here the prime factorisation of 1050 -
= 2 x 3 x 5 x 5 x 7
= 2 x 3 x 5² x 7
Therefore, the prime factors are 2, 3, 5, and 7.
Now, it is given that HCF of numbers = 21
LCM of numbers = 1050
Calculate the two numbers by using the following procedure -
Let the two numbers be 40x and 40y respectively.
Product of numbers = LCM × HCF
Now, the equation will be -
40x × 40y = 1050 × 21
40(x × y) = (1050 × 21)
xy = 22050/40
xy = 551.25 ≈ 551
So, the co-primes with product 551 are (1,551) and (19,29).
So, the prime numbers are (40×1,40×551) and (40×19,40×29).
Therefore, the most suitable pair is (40×19,40×29) = (760,1160).
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Which property is used in the following calculation?
2(5⋅33)
(2⋅5)⋅33
10(33)
330
A Associative Property of Multiplication
B Identity Property of Multiplication
C Distributive Property
D Commutative Property of Multiplication
E None of these
The property used here is the associative property of Multiplication.
What is the Associative Property?According to the Associative property, when 3 or more numbers are added or multiplied, the result (sum or the product) remains the same even if the numbers are grouped in a different way. Here, grouping is done with the help of brackets. This can be expressed as, a × (b × c) = (a × b) × c and a + (b + c) = (a + b) + c.
Given here: 2(5⋅33)=(2⋅5)⋅33
=10(33)
=330
Clearly the property a × (b × c) = (a × b) × c is used here
Hence, The property used here is the associative property of Multiplication.
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Which unit rate corresponds to the proportional relationship shown in the graph?
Drag and drop the answer into the box to match the graph with its unit rate.
The unit rate for the graph given is 5/4 cm s⁻¹.
What are algebraic expressions?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 a graph as shown in the image.
Unit rate is defined as the rate at which {y} changes per unit change in {x}. Mathematically -
{r} = Δy/Δx
{r} = (y₂ - y₁)/(x₂ - x₁)
We can write the unit rate as -
r = (10 - 0)/(8 - 0)
r = 10/8
r = 5/4
Therefore, the unit rate for the graph given is 5/4 cm s⁻¹.
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100 POINTS AND BRAINLIEST!!
Answer:
Step-by-step explanation:
4. A = 1/2(2+6)3 = 12
5. m∠a = 50 because the 2 horizontal lines are parallel
m∠b = 180 - 110 = 70 because consecutive angles in a parallelogram are supplementary
Answer:
4. A = 1/2(2+6)3 = 12
5. m∠a = 50
m∠b = 180 - 110 = 70
Adam sovled 12 math problems in 42 minutes. If he continues at this pace how many minutes will it take him to solve 20 math problems
The number of minutes it will take Adam to solve 20 math problems is 70 minutes.
How to solve ratio problems?Number of math problems Adam solve in 42 minutes = 12
Number of minutes it will take Adam to solve 20 math problem = x
Number of math problem : Time taken
12 : 42 = 20 : x
12/42 = 20/x
12 × x = 20 × 42
12x = 840
divide both sides by 12
x = 840/12
x = 70 minutes
Hence, it will take Adam 70 minutes to solve 20 math problems.
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A baker makes 6 loaves of bread using 7 pounds of dough.
If each loaf is the same weight, how many pounds is one loaf
of bread?
A. 6/7 pound
B. 1 pound
C. 7/6 pound
D. 13 pounds
find the length of the side b if given side c is 1949 ft and a is .8 miles for the given triangle. (1 mile = 5280 feet)
The length of the given side must be less than 44189 feet as the sum of the length of the other two sides is always greater than the third side.
What is a triangle?A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. A triangle with vertices A, B, and C is denoted \triangle ABC.
Given here: Length of the triangle c=1949 ft. a=8 miles
Thus a in feet = 8×5280
=42240 ft
Thus the length of the third side must be less than the sum of the other two sides a and c
or b<42240+1949
b<44189
Hence, The length of the given side must be less than 44189 feet as the sum of the length of the other two sides is always greater than the third side.
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Please provide with the diagram for more exact value for b.
Quick please, If f(x) = 2x + 3 and g(x) = 5 - f(x), what is g(3)?
if f(x) = 2x + 3 and g(x) = 5 - f(x) then g(3) value is 2.
What is a function?A relation is a function if it has only One y-value for each x-value.
Given that function f(x) = 2x + 3 and
g(x) = 5 - f(x),
We need to find the g(3).
g(x)=5-2x+3
g(x)=8-2x
Now to find g(3) we have to replace x by 3
g(3)=8-2(3)
=8-6
=2
Hence, if f(x) = 2x + 3 and g(x) = 5 - f(x) then g(3) value is 2.
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Determine the intervals on which the function is (a) increasing; (b) decreasing; (c) constant.
For a given function, y = F(x), the function is known as an increasing function if the value of y increases as the value of x increases, and the function is known as a decreasing function if the value of y decreases as the value of x increases.
How can you tell whether a function is neither growing nor shrinking?If f'(x)>0 or f'(x)0, then f is increasing in that interval; if f'(x)=0, then f is neither increasing nor decreasing in that interval.
You must first take the derivative, then make it equal to 0, and then determine which zero values the function is positive between in order to determine when a function is rising. In order to determine when the function is positive and, thus, rising, test values on all sides of these.
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the cycling team raises money to buy a bike that cost 5,643 the team collects the same amount of money each week for 33 weeks to pay for the bike.
How much money did they make each week?
Answer:
$171 each week
Step-by-step explanation:
5643/33 = 171
A big dump truck delivers gravel to a construction site. The dump truck has a rectangular bed that is 3 meters wide and 4 meters long. The truck bed is filled with gravel to a height of 2 meters. What is the volume of gravel in truck bed?
The volume of gravel in truck bed given its width, height and length is 24 cubic meters
What is the volume of gravel in truck bed?The truck bed has the shape of a cuboid
Volume of a cuboid = Length × width × height
Width of the dump truck= 3 meters
Length of the dump truck= 4 meters
Height of the dump truck= 2 meters
Volume of a cuboid = Length × width × height
= 4 × 3 × 2
= 24 cubic meters
Hence, the gravel in the dump truck has the volume 24 cubic meters
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In preparation for a party, Tori is putting desserts onto platters. The chocolate cake is cut into 24 pieces and the cheesecake is cut into 42 pieces. If she wants to prepare identical platters without having any cake left over, what is the greatest number of platters she can prepare?
If in preparation for a party, Tori is putting desserts onto platters and the chocolate cake is cut into 24 pieces and the cheesecake is cut into 42 pieces. the greatest number of platters she can prepare is 6.
How to find the greatest number of platters?Given data:
Chocolate cake = 24 pieces
Cheesecake = 42 pieces
So,
The greatest common divisor (GCF) of 24 and 42 is 6
So,
24 pieces / 6 = 4
42 pieces /6 =7
Based on this he can take 4 chocolate cakes and 7 cheesecake while the greatest number of platters she can prepare is 6.
Therefore 6 is the greatest number of platters she can prepare.
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A fifth grader takes a standardized achievement test (mean = 120, standard deviation = 8) and scores a 128. What is the child's percentile rank?
The child's percentile rank is 84.13%.
How do you determine the percentile?To determine the percentile rank of a score, you need to know the mean and standard deviation of the test, as well as the score in question. In this case, the mean is 120 and the standard deviation is 8.
To convert the child's score of 128 to a percentile rank, you would first convert it to a z-score using the formula (score - mean) / standard deviation = z-score.
In this case:
(128 - 120) / 8 = 1
This z-score of 1 represents the number of standard deviations above the mean the child's score is. To convert this z-score to a percentile rank, you can use a table of the standard normal distribution, which shows the proportion of values that are less than or equal to a given z-score.
A z-score of 1 corresponds to a percentile rank of 84.13%
So, the fifth grader who scored 128 on a standardized achievement test has a percentile rank of 84.13%. This means that 84.13% of students scored lower than the child on this test.
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Which equation does not belong with the other three?
Responses
y=3^x
y is equal to 3 to the x th power
f\left(x\right)=2\left(4\right)^x
f of x is equal to 2 times 4 to the x the power
f\left(x\right)=\left(-3\right)^x
f of x is equal to negative 3 to the x the power
y=5\left(3\right)^x
y is equal to 5 times 3 to the x the power
Question 2
Why did you select this equation?
Because it is the only equation that ___ an exponential function.
The exponential function f(x) = 2(4)ˣ doesn't belong to the other three.
What is an exponential function?
A mathematical function is an exponential function. The word, unless expressly stated differently, refers typically to the positive-valued function of a real variable. However, it can be extended to complex numbers or adapted to other mathematical objects like matrices or Lie algebras.
Here, we have
Given:
y = 3ˣ,
f(x) = 2(4)ˣ
f(x) = (-3)ˣ
y = 5(3)ˣ
We have to determine which equation does not belong with the other three.
We concluded that
All equations are multiples of 3 but f(x) = 2(4)ˣ is not a multiple of 3.
Hence, the exponential function f(x) = 2(4)ˣ doesn't belong to the other three.
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21.5.3 Test
Question 11 of 25
Which is a correct expansion of (4x+1)(2x² - 2)?
A. 4x 2x² + 4x
(1) + 1 • 2x²+1 • (-2)
B. 4x 2x² + 4x
(-2) +1.4x+1• (-2)
C. 4x2x² + 4x (-2) +1.2x²+1 (-2)
SUBMIT
The answer to the phrase 3+52 expanded is 28.When an expression is expanded, it is reduced to its most basic form.
Which is a correct expansion ?We must multiply out the brackets in order to extend and simplify an expression. The resulting phrase is then made simpler by grouping like terms together.
It is possible to get rid of brackets by expanding them, often known as multiplying out.
Factorization is being done in reverse.Increasing each term inside a bracket by the expression outside the bracket is referred to as expanding it.
3+5^2
= 3 + 5²
= 3 + (5 × 5)
= 3 + 25
= 28
In response to the expression's expansion, 3+52 is 28.
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Option C) The Polynomial is (4x +1)(2x² - 2)
The expansion will be 4x*2x² - 4x*2 + 2x² - 2
What is Expansion of a polynomials ?If no variable is included in parentheses and all terms that are similar have been merged, a polynomial is expanded. Multiply the components of a polynomial (typically by applying the distributive property), or carry out the corresponding operations, to extend it.
A polynomial is an equation made up of coefficients and indeterminates that uses only the addition, subtraction, multiplication, and powers of positive-integer variables. x² + 4x + 7 is an illustration of a polynomial with a single indeterminate x.
When a polynomial with coefficients in a specific field or in integers is factored, its coefficients are expressed as the product of irreducible factors with coefficients in the same field.
The Polynomial is (4x +1)(2x² - 2)
The expansion will be 4x*2x² - 4x*2 + 2x² - 2
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The graph shows the absolute value parent function. 5 5. -5. Which statement is true? 5 A. (0, 1) is the x- and y-intercept of the function. B. (1, 1) is the x- and y-intercept of the function. C. (0,0) is the x- and y-intercept of the function. k
The function of the absolute value is always positive the correct answer would be option (B).
What is a graph?
A graph can be defined as a pictorial representation or a diagram that represents data or values.
What is absolute value?
Absolute value is defined as the magnitude or size of a number, no negatives are allowed. The distance a number is from 0 on the number line is known as the absolute value of the number.
For example, |5| is 5 because it is 5 units away from 0. Also, |-5| is also 5 because -5 is 5 units from 0.
We have to determine the statement best describes the function.
We have been given that the graph represents the absolute value parent function.
Since the parent function's graph with an absolute value that is always positive.
Therefore, the graph of the absolute value parent function would be always positive.
Hence, the correct answer would be option (B)
Which fractions are equal to 0.6
1 over 6,60 over 100,1 over 60,6 over 10
Landon is deciding between two landscaping companies for his place of business.
Company A charges $30 per hour and a $175 equipment fee. Company B charges $45
per hour and a $100 equipment fee. Let A represent the amount Company A would
charge for t hours of landscaping, and let B represent the amount Company B would
charge for t hours of landscaping. Write an equation for each situation, in terms of t,
and determine the interval of hours, t, for which Company A is cheaper than
Company B.
A =
B =
Company A is cheaper than Company B when t
Note: The interval will only apply for valid values of t in the domain.
Answer: A = 30t + 175 and B = 45t + 100
hope this helps!
Step-by-step explanation:
To determine when Company A is cheaper than Company B, we need to find when A < B. We can set the two equations equal to each other and solve for t:
30t + 175 < 45t + 100
-15t < -75
t > 5
So, Company A is cheaper than Company B for any value of t greater than 5 hours. The interval for which Company A is cheaper is (5, ∞).
3. For which value of x is the figure a rhombus?
Ox=6
Ox= 7.5
Ox = 12
Ox = 18.75
(2x +39)⁰
(6x-9)°
Therefore, in the rhombus figure whose vertices are Ox=6, x is equal to 12.Equation is (2x + 39)0 and (6x-9)° and the values of Ox are 7.5, 12, 18, and 18.75.
what is quadrilateral ?Having four edges and four corners, a quadrilateral is a four-sided polygon in geometry. The phrase is a contraction of the Latin terms quadri and latus (meaning "side"). Having four sides, four vertices, and four corners, a rectangle is a two-dimensional form. Essentially, there are two types of concave and convex. Convex quadrilaterals can also be divided into a number of subclasses, such as trapezoids, parallelograms, rectangles, squares, and rhombuses. A rectangle is a form that exists in two dimensions and has four straight sides. The various shapes of quadrilaterals include parallelograms, trapezoids, rectangles, kites, squares, and rhombuses.
given
2x+39 = 6x-9
2x = 6x - 48
-4x = -48
x = -48 / -4
x = 12
Therefore, in the rhombus figure whose vertices are Ox=6, x is equal to 12.Equation is (2x + 39)0 and (6x-9)° and the values of Ox are 7.5, 12, 18, and 18.75.
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Please help me with this
Answer:
what do u have to do like what the question
When looking for the range of a graph, which values are you looking for?
A. x-values
B. y-values
When looking for the range of a graph, y-values are looked for.
What is the range?
A function's range can be used to describe one of two related ideas: The function's codomain a representation of the action A binary relation f between two sets X and Y is a function if there is exactly one y in Y such that f connects x to y for every x in X.
Here,
We have to determine when looking for the range of a graph, which values are looking for.
The domain is all x-values or inputs of a function and the range is all y-values or outputs of a function. When looking at a graph, the domain is all the values of the graph from left to right. The range is all the values of the graph from down to up.
Hence, when looking for the range of a graph, y-values are looked for.
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The product of 7 and the cube of a number.
The product of 7 and the cube of a number, N is 7N³
How to find the product of 7 and the cube of a number?
Word problems are sentences describing a 'real-life' situation where a problem needs to be solved by way of a mathematical calculation.
In order to determine the product of 7 and the cube of a number. We need to represent the number with a letter.
Let N represent the number.
Thus, we can then write that the product of 7 and the cube of a number, N is:
7 × N³ = 7N³
Note: product means multiplication
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pls help help pls this is due today i would appraciate help
The teacher wrote two numbers on the board. Eric added the numbers and got
58. Olivia subtracted the second number from the first number and got 28. What
is the first number the teacher wrote on the board?
Answer:
Let x be the first number that the teacher wrote on the board and y be the second number. From the problem, we know that:
x + y = 58 (from Eric's calculation)
x - y = 28 (from Olivia's calculation)
To find the value of x, we can add the equations together:
x + y = 58
x - y = 28
2x = 86
x = 43
So the first number that the teacher wrote on the board is 43.
linear or exponential function
The way the y-values alter when the x-values rise by a certain amount is different for linear and exponential relationships: The y-values in a linear connection differ equally. The ratios of the y-values are equal in an exponential relationship.
What is Exponential vs. linear growth Function?The way the y-values change when the xx-values rise by a certain amount is different for linear and exponential relationships:
The y-values have equal differences in a connection that is linear.
The y-values have identical ratios in an exponential relationship.
Vertical growth
Think at how this table illustrates the relationship:
x 12 15 18 21
y -2 5 12 19
Here, the xx-values grow by a constant difference of 3 units,
x +3 +3 +3
12 15 18 21
and the yy-values increase by a constant difference of 7.
y +7 +7 +7
-2 5 12 19
Because each y-value is 7 77 more than the one before it, this connection can be characterized as linear.
Exponential growth is a second example.
Think at how this table illustrates the relationship:
x 0 1 2 3
y 1 3 9 27
x +1 +1 +1
0 1 2 3
and a 3 constant factor is applied to the y-values.
y *3 *3 *3
1 3 9 27
Since each y-value is 3 times more than the one before it, this connection is exponential.
The Complete Question.
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A container of coffee is 1/6 full. The container contains 2/3 pound of coffee
a. Write a division expression that represents the capacity of the container.
b. Write a related multiplication expression that represents the capacity of
the container.
c. Find the capacity of the container.
Answer:
Step-by-step explanation:3/10
Pavel and Sarah are knitting hats to sell. Pavel spends
£20 on wool and Sarah spends £80. They sell all the hats for a total of
£1000. Is it fair that they get £500 each? Explain your answer.
What is the ratio if I have 6 black tea bags to 4 green tea bags if there are 60 tea bags
Answer: which tea bag is 60?
Step-by-step explanation:
Answer: ratio of black tea bags = 36, green bags = 24
Step-by-step explanation: first you add the ratio 6 and 4, which will give you ten, then you divide them consecutively by 10 and multiply by 60. this will give you 6/10 [tex]*[/tex] 60 = 36 and 4/10 [tex]*[/tex] 60 = 24.
I hpoe i have satisfied you with my answer
After rolling the two dice 10 times amit Oe simultaneously, Jerome recorded that 20% of the time, he rolled pairs that included at least one six. Based on his results, if Jerome were to roll the die 65 more times, how many pairs could he predict will contain at least one six?
12 pairs could he predict will contain at least one six using empirical probability formula.
What kind of probability exists between the number of times an event's outcome occurred and the total number of trials that were conducted?The empirical probability formula generates a ratio between the total number of times the desired occurrence was attempted to and the number of times it actually occurred. As an illustration, consider the case where I rolled the dice three times and each time I got 12, giving the result a statistical probability of 12/12 or 100%.
Probability is a form of ratio where we measure the likelihood of a given occurrence in comparison to all other possible outcomes.
Explanation:
12/10 * 10 = 6/5 * 10
= 12.
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How would I write terms 2,3,4 of an arithmetic sequence where a1=-7 and the common difference is 12?
Therefore , the solution of the given problem of arithmetic mean comes out to be a2=5 ,a3 = 17 and a4 = 29.
The definition of arithmetic mean.The sum of all values in a list multiplied by the total no. all items in the list yields the arithmetic average, often known as the group's means. The growth in arithmetic follows a similar pattern. The following equation + 7 + 9 equals 21, but 21 multiplied by 3 (there's several currently three numbers) equals 7, proving that the mean of the numbers 5, 7, while 9 is 4, and the median of the real numbers 5, 8, and 9 is 3.
Here,
Given : a1 = -7
and common difference d = 12
Thus,
For a2 = a + d = -7 + 12 = 5
a3 = a+2d = -7 + 24 = 17
and a4 = a + 3d = -7 + 36 = 29.
Therefore , the solution of the given problem of arithmetic mean comes out to be a2=5 ,a3 = 17 and a4 = 29.
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