The factored form of 6 + 27 is 3(2 + 9) using GCF.
What is GCF?The greatest common factor, which is the product of two or more numbers, is the biggest number (GCF). A natural number is created by dividing them by the biggest number (factor). There are a few factors that both share once all the number's components have been identified. The greatest common factor is the one with the largest number among the common factors. The highest common factor is another name for the GCF (HCF)
The given expression is:
6 + 27
Take the factors of the individual numbers:
6 = 1, 2, 3, 6
27 = 1, 3, 9, 17
Take the common factor from both the numbers, in this case it is 3.
Now, factor out the number from the given expression:
6 + 27
3(2 + 9)
Hence, the factored form of 6 + 27 is 3(2 + 9) using GCF.
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Please help with the question below
The area of the given image design is; 15 in²
How to find the area of a triangle?The formula to find the area of a triangle is;
Area = ¹/₂(base * height)
Let us divide the image into two triangles and as such;
Area of biggest triangle = ¹/₂(14 * 15)
= 85 in²
We will now deduct the rectangle that was removed by finding its' area to get;
Area of rectangle = length * width
= 10 * 7 = 70 in²
Thus;
Area of image = 85 - 70
Area of image = 15 in²
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X
1
2
3
4
5
f(x)
3
9
15
21
27
Linear, exponential, quadratic or neither??
From the data points given, the linear equation is obtained as y = 6x - 3.
What is a linear equation?
A linear equation is one that has a degree of 1 as its maximum value. No variable in a linear equation, thus, has an exponent greater than 1. A linear equation's graph will always be a straight line.
The data points given are -
X = 1, 2, 3, 4, 5
f(x) = 3, 9, 15, 21, 27
The slope of the line is given as m.
The slope can be deduced using the formula -
(y2 - y1) / (x2 - x1)
m = (9 - 3) / (2 - 1)
m = 6/1
m = 6
The slope-intercept form of a equation is y = mx + b
Substitute the values of x, y and m in the equation -
3 = 6(1) + b
3 = 6 + b
b = 3 - 6
b = -3
So, the equation becomes -
y = 6x - 3
This equation forms a straight line in the graph.
Therefore, y = 6x - 3 is a linear equation.
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A manufacturer of bolts has a quality-control policy that requires it to destroy any bolts that are more than 2 standard deviations from the mean. The quality-control engineer knows that the bolts coming off the assembly line have mean length of 10 cm with a standard deviation of 0. 05 cm. For what lengths will a bolt be destroyed?
The bolts that are destroyed due to being more than 2 standard deviations from the mean will have a length of 10 cm ± 0.15 cm.
This means that any bolts that are shorter than 9.85 cm or longer than 10.15 cm will be destroyed. Any bolts that fall within this range will pass the quality-control check and will not be destroyed.
The manufacturer should also have a policy in place to ensure that bolts that are found to be too short or too long are discarded and not put into circulation. This will help maintain the quality of the bolts that are produced.
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Triangle BCD has vertices B(-8,3), C(-4, 6), and D(2, 0). If the triangle is reflected across the x-axis and dilated by a scale factor of 0. 5 with respect to the origin, what are the coordinates of the vertices of triangle B"C"D"?
If the vertices of the triangle BCD with vertices B(-8,3), C(-4, 6), and D(2, 0) , and if they are reflected across x axis and dilated by a scale factor of 0.5 then the coordinates of B"C"D" are B''(-4 , -1.5) , C"(-2 , 3) and D"(1 , 0) .
If the point (x,y) is reflected across the x axis , then the reflected points are (x,-y) .
the vertices of the triangle BCD are : B(-8,3), C(-4, 6), and D(2, 0) ;
So , the reflected vertices are : B'(-8,-3) , C'(-4,-6) and D'(2,0) ;
if the point (x,y) is dilated by a scale factor of "k" , then the dilated vertices are written as : (kx , ky) .
the dilation factors is = 0.5 ;
So , the vertices B'(-8,-3) , C'(-4,-6) and D'(2,0) after dilation will be written as :
⇒ B''(-8×0.5 , -3×0.5) , C"(-4×0.5 , 6×0.5) and D"(2×0.5 , 0) ;
After simplifying further ,
we have ;
⇒ B''(-4 , -1.5) , C"(-2 , 3) and D"(1 , 0) ;
Therefore , the coordinates of the triangle B"C"D" are B''(-4,-1.5) , C"(-2,3) and D"(1,0) .
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(50 POINTS!!) I will give brainliest to the correct answer.
An isosceles triangle has an angle that measures 100°. What measures are possible for the other two angles? Choose all that apply.
70°
40°
30°
80°
Answer:
d) 80°
Step-by-step explanation:
For isosceles triangle,
→ The other two angles are equal.
The given angle,
→ <A = 100°
Formula we use,
→ <A + <B + <C = 180°
Forming the equation,
→ 100° + x + x = 180°
Now the value of x will be,
→ 100° + x + x = 180°
→ 100° + 2x = 180°
→ 2x = 180° - 100°
→ 2x = 80°
→ x = 80°/2
→ [ x = 40° ]
Adding values of both angles,
→ x + x = 2x
→ 2 × 40° = 80°
Hence, option (d) is correct.
PROBLEMS (1) A book and 3 pens together cost $90.00. If the pen cost $10 less than the book, calculate the price of each pen,
The cost of each pen is $25. This can be solved using unitary method.
Unitary method: what is it?In the unitary technique, the value of a single unit is determined first, and then the value of the required number of units is determined.
When employing ratio and proportion to solve a problem, it is essential to comprehend the units and values.
To make things simpler, always place the known facts on the left and the things that need to be calculated on the right. The number of apples in the aforementioned situation is known, but it is unclear how much the fruit is worth on the market.
It should be stressed that the unitary technique applies the notions of ratio and proportion to problems.
Let the cost of each pen be x .
then according to the question, the cost of book will be x-10
now
90 = 3x + x - 10
x = 25
hence the cost of the book is x - 10 = 15
and the cost of each pen is 25
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a convex polyhedron $p$ has 26 vertices, 60 edges, and 36 faces, 24 of which are triangular, and 12 of which are quadrilaterals. a space diagonal is a line segment connecting two non-adjacent vertices that do not belong to the same face. how many space diagonals does $p$ have?
A convex polyhedron have 241 space diagonals.
As we know that the every pair of vertices of the convex polyhedron determines either an edge, a face diagonal or a space diagonal.
Here, we have 26 vertices.
so, the total line segments determined by the vertices:
²⁶C₂
= 26! / 2! × (26 - 2)!
= 325
Out of 325 line segments, 60 are edges (Given).
We know that each triangular face has zero face diagonals and each quadrilateral face has two face diagonals.
So there are 2 × 12 = 24 face diagonals.
This means, 325 - 60 - 24 = 241 line segments segments must be the space diagonals.
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Arthur is purchasing ingredients to prepare hotdogs for his school's food fair.
Hotdog buns come in packs of 6 while the sausages come in packs of 10.
What is the least number of packs of each item he should buy to get an equal number of buns
and sausages?
Step-by-step explanation:
To have an equal number of buns and sausages, Arthur needs to find the least common multiple (LCM) of 6 and 10.
The LCM of 6 and 10 is 30.
Therefore, he should buy at least 30 packs of buns and 30 packs of sausages to get an equal number of buns and sausages.
That way, he would have 30/6 = 5 packs of buns and 30/10 = 3 packs of sausages.
Two linear equations are represented by using the tables below. A 2-column table with 4 rows is titled Equation A. Column 1 is labeled x with entries negative 5, negative 2, 0, 1. Column 2 is labeled y with entries negative 4, negative 1, 1, 2. A 2-column table with 4 rows is titled Equation B. Column 1 is labeled x with entries negative 6, negative 3, 3, 6. Column 2 is labeled y with entries negative 4, negative 2, 2, 4. The data points for equation A are plotted on the coordinate plane below and are connected by using a straight line. On a coordinate plane, a line goes through points (negative 5, negative 4), (negative 2, negative 1), (0, 1), (1, 2). What is the solution to the system of equations?
Answer:
I need more information
Step-by-step explanation:
The solution to the system of equations cannot be determined from the information provided. The tables provide a set of x and y values for each equation, but they do not provide enough information to determine the equations themselves. In order to find the solution, we would need to know the form of the equations and be able to solve them simultaneously. The information provided is just a set of points that are plotted on a coordinate plane that is connected by using a straight line, but it is not enough to find the solution of the system of equations.
Find the domain of y=−9x−26/x+3.
All Real Numbers except x = 9
All Real Numbers except x = -9
All Real Numbers except x = 3
All Real Numbers except x = -3
The domain of the function will be All Real Numbers except x = -9. The correct option is B.
What are a range and domain?The range of values that we are permitted to enter into our function is known as the domain of a function. The x values for a function like f make up this set (x). A function's range is the set of values it can take as input. After we enter an x value, the function outputs this set of values.
Given that the function is y=−9x−26/x+3. As the domain is defined as all the input values going into the function. The domain will be all the real numbers except -9. Because the function is undefined on -9.
The graph of the function is attached with the answer below.
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3
5
of the pupils in Year 9 say their favourite colour is red.
There are 80 pupils in Year 9.
How many students said red is their favourite colour?
We will apply the percentage method to find that 48 students said red is their favourite colour.
Probability is a constituent part of computation that deals with the occurrence of a random event. The value is defined from zero to one. Probability is familiarised to predict how likely events are to happen. Probability is the degree to which something is possible to happen.
Total number of pupils in class 9 = 80
We need to calculate the number of students choosing red as their favourite colour.
We are given that 80 pupils are there in year 9.
Out of these, 3/5 of the pupils say that their favourite colour is red.
Let n be the number of pupils who say red is their favourite colour.
∴ n = (3/5) × 80
∴ n = 48
--The given question is incorrect; the correct question is
"3/5 of the pupils in a year 9 class say their favourite colour is red. There are 80 pupils in Year 9. How many students said red is their favourite colour?"--
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The coefficients of the terms on the right side of a _____ equation are the numbers in Pascal's Triangle.
The coefficients of the terms on the right side of a binomial equation are the numbers in Pascal's Triangle.
Pascal’s Triangle is a method to know the binomial coefficients of terms of binomial expression (x + y)n, where n can be any positive integer and x, and y are real numbers. Pascal's Triangle is represented in a triangular form, it is kind of a number pattern in the form of a triangular arrangement. It begins with 1 on the top and with 1 running down on the two sides of the triangle. In the pascal triangle, each new number is between two numbers and below them and its value is the sum of two numbers above. This triangle is used in different types of probability conditions. Here each row represents the coefficient of expansion of (x + y)ⁿ.
Properties of Pascal’s Triangle:
Each number in Pascal’s Triangle is the sum of two numbers above it.Numbers in a row are symmetric in nature.Each number represents a binomial coefficient.Numbers on the left and right sides of the triangle are always 1.the nth row contains (n+1) numbers in it.Therefore, the coefficients of the terms on the right side of a binomial equation are the numbers in Pascal's Triangle.
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3.
Which is cheaper: 115 plums for $276.00 at Shop ZYX or 198 plums for $633.60 at Shop PWR?
3a What is the cost of a single plum at Shop ZYX?
3b
3c
Enter your next step here
() ba
dollars
The cheaper plan is given as follows:
Shop ZYX.
The cost of a single plum at Shop ZYX is given as follows:
$2.4.
How to obtain the cheaper plan?To obtain the cheaper plan, we must obtain the cost of a single plum for each shop.
The cost of a single plum for each shop is obtained using a proportion, with the division of the total cost by the number of plums.
Hence the cost per plum in each shop is given as follows:
Shop ZYX: 276/115 = $2.4.Shop PWR: 633.6/198 = $3.2.More can be learned about proportions at https://brainly.com/question/24372153
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evaluate (8+t power of 3)-6
Answer:
t³+2Step-by-step explanation:
(8+t³)-68+ t³-6t³ +(8 - 6)t³+2- Hope this helps!
Segment GM is an altitude of AAGE.
Based on the information in the diagram, what is the length of A-F?
A. O 19.7
B. O 18.4
C. O 17.0
D. O 14.1
The segment lengths in the diagram are given as follows:
GE = 13.AM = 2.083.AG = 5.42.What are the segment lengths?Using the Pythagorean Theorem, the length of segment GE is given as follows:
(GE)² = 5² + 12²
(GE)² = 169
GE = 13.
Applying the geometric mean theorem, the length AM is obtained as follows:
(GM)² = ME x AM
25 = 12 AM
AM = 2.083.
Then, applying the Pythagorean Theorem, the length AG is found as follows:
(AG)² = 2.083² + 5²
AG = 5.42.
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Height (cm) in weights (kg) are measured for 100 randomly selected adult males and weight range from Heights of 132 193cm and weights of 4250 kg let the predictor variable X be the first variable given the hundred paired measurements yield mean equals 168. 42 CM y mean equals 81. 58 kg mg are equal 0. 141 P value equals 0. 162 + y equals -101 + 1. 09 x find the best predicted value of y way to give an adult male who is unearned 6872 tall
The best predicted weight for an adult male who is 185 cm tall is approximately 164.65 kg.
A linear pattern with no other non-linear patterns or outliers is indicated by a scatter plot.
To find the best predicted value of weight (y) for an adult male who is 185 cm tall, you can use the equation:
y = -101 + (1.09 * x)
where x is the height in centimeters.
Substituting 185 for x, we get:
y = -101 + (1.09 * 185) = 164.65 kg
So the best predicted weight for an adult male who is 185 cm tall is approximately 164.65 kg.
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Find P(blue and odd).
The probability of getting blue and an odd number will be 1/10.
How to calculate the probability?Probability simply means the chance that a particular thing or event will happen. It is the occurence of likely events. It is simply the area of mathematics that deals with the numerical estimates of the chance that an event will occur or that a particular statement is true.
The probability of getting blue is 2/10 and the probability of getting odd number is 5/10.
Therefore, the probability of getting blue and an odd number will be:
= 2/10 × 5/10
= 1/10.
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is 3/11 and 17/6 Proportional
The ratios 3/11 and 17/6 is not proportional.
What is Proportion?Proportions are defined as the concept where two or more ratios are set to be equal to each other.
Suppose we have two ratio p : q and r : s. If both these ratios are proportional, then we can write it as p: q : : r : s.
This is same as p : q = r : s or p/q = r/s
The given ratios are 3/11 and 17/6.
For two ratios a/b and c/d to be proportional, a/b must be equal to c/d.
If 3/11 and 17/6 are proportional,
3/11 must be equal to 17/6.
Or doing the cross multiplication,
3 × 6 must be equal to 11 × 17.
18 must be equal to 187.
But 18 ≠ 187
So the ratios are not proportional.
Hence 3/11 and 17/6 are not proportional.
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Which lines best approximate the directrices of the ellipse? Round to the nearest tenth. X = −4. 6 and x = 4. 6 x = −3. 5 and x = 3. 5 y = −4. 6 and y = 4. 6 y = −3. 5 and y = 3. 5
The lines best approximate the directrices of the ellipse y = 10.6 or y = -6.6
The term called directrices of the ellipse is defined as a line parallel to the latus rectum of ellipse and is perpendicular to the major axis of the ellipse.
Here we know that first of all here the known form is an ellipse with a vertical major axis so it would have to be
=> d = a²/c
Here d refers the distance between the center and the directrix.
When we take the value of a= 8, b=3, then we get the value of C as,
=> c² = a²- b²
Apply the value on it, then we get
=> c ² = 64-9
Then the value of is about 7.4
Then the value of d is calculated as,
=> d = 64/7.4 = 8.6
So the value of y is defined as,
=> 2 + 8.6 = 10.6
Or if it falls the negative direction, then we get
=> y = 2 - 8.6 = -6.6
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In triangle MNO, Angle M is congruent to angle O. NO = 12 and OM=14. Find MN
The length of MN is 14 units.
What is isosceles triangle?A type of triangle known as an isosceles triangle has any two sides that are both the same length. The theorem that describes the isosceles triangle states that "if the two sides of a triangle are congruent, then the angle opposite to them are also congruent." This means that the two angles of an isosceles triangle opposite to equal sides are equal in measure. For example, in the triangle ΔABC, if sides AB and AC are equal, then ABC is an isosceles triangle where ∠B = ∠C.
Given;
ΔMNO,
∠M = ∠N
Also, NO=12 and OM=14
The angles are equal then triangle is isosceles and for given triangles the two sides are equal;
Sides opposite to angles are;
NO and MO
MO = NO = 14 units
Therefore, the length of third side of triangle MNO is 14 units.
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Represent the following sentence as an algebraic expression, where "a number" is the letter x.
\text{A number is subtracted from 3.}
A number is subtracted from 3.
The required algebraic expression is x-3
What is an Algebraic Expression?An algebraic expression in mathematics is an expression which is made up of variables and constants, along with algebraic operations (addition, subtraction, etc.). Expressions are made up of terms.
Given here: The statement "A number subtracted from 3 "
Thus translating the given text we get the following:
Let the number be x
And we have have to subtract 3 from x
Thus the algebraic expression is given by x-3
Hence, The required algebraic expression is x-3
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in a candy factory, the nutty chocolate bars contain 18.0 % (by mass) cashews. if 11.3 kg of cashews were used one day, how many pounds of nutty chocolate bars were made?
Answer:
62.8 kg or 128.43 lbs
Step-by-step explanation:
if 18 percent of all the chocolate bars is is cashews at 11.3 kgs, the chocolate makes up the other 82 percent so theres a total of 62.78 kgs of candy total and you can use the eqaution for 1kg equal 2.205 lbs to find a total of 138.43 lbs of total chocolate bars
Pierre added a 14 inch layer of yogurt to a granola bar that is 1116 inches thick. Which statements are true about finding the total thickness? Select three options.
Using the arithmetic operation of addition the total thickness of granola bar and yogurt collectively is 1130 inches.
What is arithmetic operation?
A subject of mathematics known as arithmetic operations deals with the study and use of numbers in all other branches of mathematics. Basic operations including addition, subtraction, multiplication, and division are included.
The thickness of granola bar is = 1116 inches
The thickness of layer of yogurt is = 14 inches
To find the total thickness use the formula -
Total Thickness = Thickness of granola bar + Thickness of yogurt
The arithmetic operation of addition is used to find the total thickness.
Substitute the values into the equation -
Total Thickness = 1116 + 14
Total Thickness = 1130
Therefore, the total thickness is obtained as 1130 inches.
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Solve for x using logarithms.
[tex]3^{2-3x} = 4^{2x+1}[/tex]
Answer:
[tex]\large\boxed{\sf 0.133 }[/tex]
Step-by-step explanation:
The given equation to us is ,
[tex]\longrightarrow 3^{2-3x}= 4^{2x+1} \\[/tex]
Take log to base 10 on both sides,
[tex]\longrightarrow \log_{10} 3^{2-3x}= \log_{10} 4^{2x+1} \\[/tex]
Now recall that, [tex] \log a^m = m\ log \ a [/tex]
[tex]\longrightarrow (2-3x) \log_{10} 3 = (2x+1)(\log_{10} 4)\\[/tex]
We can write it as ,
[tex]\longrightarrow (2-3x) \log_{10}3=(2x+1)\log_{10}2^2 \\[/tex]
Again using the property mentioned above,
[tex]\longrightarrow (2-3x)\log_{10}3 = 2(2x+1)\log_{10} 2 \\[/tex]
[tex]\longrightarrow (2-3x)\log_{10}3 = (4x+2)\log_{10} 2 \\[/tex]
Now we know that ,
log 3 = 0.477log 2 = 0.301On substituting the values, we have ,
[tex]\longrightarrow (2-3x)0.477 = (4x+2)0.301 \\[/tex]
simplify by opening the brackets,
[tex]\longrightarrow 0.954 - 1.431x = 1.204x + 0.602 \\[/tex]
[tex]\longrightarrow 1.204x + 1.431x = 0.954 - 0.602 \\[/tex]
[tex]\longrightarrow 2.635x = 0.352 \\[/tex]
[tex]\longrightarrow x =\dfrac{0.352}{2.635} \\[/tex]
[tex]\longrightarrow \underline{\underline{ x = 0.133 }} \\[/tex]
and we are done!
Grade 5 mathematics
8➗0.4=
Hi There! Your Answer would be 20. Why you might ask? allow me to tell you the reason!
you first make a "House" Around the Dividend, the biggest number goes outside of the box, then you just do basic division until you get a zero!
We would be left with 20.
If this helped you make me brainliest
Keep Learning; Keep Asking!
5) A 345ml tin of paint costs £4.80
A 250ml tin of paint costs £3.35
Which tin is better value for money?
The tin with 250ml is better value for money. The solution has been obtained using the unitary method.
What is a unitary method?
The unitary method is used to calculate the value of a single unit from a given multiple, to put it simply. With the unitary method, you first determine the value of a single unit before determining the value of the necessary quantity of units.
We are given two tins.
First : 345ml tin of paint costing £4.80
Second: 250ml tin of paint costing £3.35
Now, using the unitary method, we get
First tin
For 350ml, cost is £4.80
So, for 1ml, cost will be
£4.80/350 = £0.014
Second tin
For 250ml, cost is £3.35
So, for 1ml, cost will be
£3.35/250 = £0.013
Hence, the tin with 250ml is better value for money.
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f(x)=(1/5)x+12 find inverse
The inverse equation of the function is y = 5x - 12
How to determine the inverse equationFrom the question, we have the following parameters that can be used in our computation:
f(x) = 1/5x + 12
Express as an equation
So, we have
y = 1/5x + 12
Swap x and y
This gives
x = 1/5y + 12
Next, we make y the subject
1/5y = x - 12
This gives
y = 5x - 12
Hence, the inverse is y = 5y - 12
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How to find proportional parts in triangles and parallel lines?
The proportional parts in triangles and parallel lines can be found by similarity and ratios.
The ratio of any related side lengths is always the same when two triangles are similar. The scale factor can be used to identify the triangle's proportionate components. The longer side of one triangle is twice as long as the comparable side in the other. In contrast, the alternate interior angles are identical when two parallel lines are cut by a transverse line. Additionally, the matching angle pairs are all equal. Trigonometry can be used to determine the length of the opposite side of a pair of parallel lines if we know the length of one side and the matching angle.
One can use similarity ratios to determine the proportional components of triangles and parallel lines. Comparable geometries have equivalent sides that are in proportion. To get the missing side length, one can arrange ratios of corresponding sides and utilise cross-multiplication. Further, similar triangles can also be employed. When two triangles are comparable, their corresponding sides and angles are proportionate and equal.
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A new car is purchased for $23,000 and over time its value depreciates by one half every 3 years. How long, to the nearest tenth of a year, would it take for the value of the car to be $7,800 (25 PTS)
It take for the value of the car is 4.7 years.
Now, According to the question:
A new car is purchased for $23,000
and, over time its value depreciates by one half every 3 years.
It take for the value of the car to be $7,800.
According to the statement :
The equation will be :
y = 23,000 × [tex](\frac{1}{2} )^n[/tex]
7,800 = 23,000 × [tex](\frac{1}{2} )^n[/tex]
By simplification, we get:
n = 1.56
Over time its value depreciates by one half every 3 years.
So, 1.56 × 3 = 4.68 ≈ 4.7 years.
Hence, It take for the value of the car is 4.7 years.
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Which inequality matches the graph? -2x + 3y > 7 02x-3y
the inequality model. 5x-6y <0 is attached below.
What is inequality?
Inequalities are mathematical expressions where neither side is equal. In inequality, as opposed to equations, we compare two values. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign in between. Sometimes it can be about a "not equal to" relationship, where one thing is more than the other or less. In mathematics, an inequality is a relationship that results in a non-equal comparison between two numbers or other mathematical expressions.
2x + 3y > 7x-3y
5x-6y <0
So we have to plot this inequality.
Hence, the inequality model. 5x-6y <0 is attached below.
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