Composite numbers are whole numbers that contain more than two elements.. Examples of composite numbers include 36 and 42. These numbers are divisible by more than just 1 and themselves. 36 is divisible by 1, 2, 3, 4, 6, 9, 12, and 18. 42 is divisible by 1, 2, 3, 6, 7, 14, and 21.
Example 1: To find the factors of 36
Step 1: Start by dividing 36 by 2, which gives us 18.
Step 2: Divide 18 by 2, which gives us 9.
Step 3: Divide 9 by 3, which gives us 3.
Step 4: Divide 3 by 3 which gives us 1.
Step 5: The factors of 36 are 1, 2, 3, 4, 6, 9, 12, and 18.
Example 2: To find the factors of 42
Step 1: Start by dividing 42 by 2, which gives us 21.
Step 2: Divide 21 by 3, which gives us 7.
Step 3: Divide 7 by 7 which gives us 1.
Step 4: The factors of 42 are 1, 2, 3, 6, 7, 14, and 21.
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Exercise 1(a)
Write the first
six term of a A.P which
a=5, d=4
Answer:
5, 9, 13, 17, 21, 25
Step-by-step explanation:
Given a₁ = 5 and d = 4
Add d = 4 to the previous term, that is
a₁ = 5
a₂ = a₁ + 4 = 5 + 4 = 9
a₃ = a₂ + 4 = 9 + 4 = 13
a₄ = a₃ + 4 = 13 + 4 = 17
a₅ = a₄ + 4 = 17 + 4 = 21
a₆ = a₅ + 4 = 21 + 4 = 25
Find the slope of a line that passes through the given two points using ratio method
The slope formula, or the ratio of the change in the y values to the change in the x values, is m=(y2-y1)/(x2-x1).
What is slope ?A line's steepness and direction are measured by the line's slope.
Without actually using a compass, determining the slope of lines in a coordinate plane can assist in forecasting whether the lines are parallel, perpendicular, or none at all.
A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes.
The y coordinate's net change is y, and the x coordinate's net change is x.
Hence, The slope formula, or the ratio of the change in the y values to the change in the x values, is m=(y2-y1)/(x2-x1).
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Choose the system of linear equations that represents the mapping diagrams.
Answer:
A
Step-by-step explanation:
If you substitute each x value from the input boxes into the equations, you can find your answer.
The first input value is 1, and the output value is 12, so plug those into the first equation in the answer options.
y = 4x + 8
(12) = 4(1) + 8
12 = 4 + 8
12 = 12
Because the simplified equation ended in a true equality statement, that pair works with the equation.
The next x value is 3 and the y value is 20:
y = 4x + 8
(20) = 4(3) + 8
20 = 12 + 8
20 = 20
Again, it ends in true equality statement, so it also works with the equation.
(28) = 4(5) + 8 = 28 so that one works as well.
Then check the second equation with the second set of input and output values.
(2) = -7(-1) - 5 = 2
The first x and y values of that system work.
(9) = -7(-2) - 5 = 9
The second one works as well.
(16) = -7(-3) - 5 = 16
The last one is equal as well.
So the equations in A, or the first option, work with all of the inputs and outputs.
c.) Find the Surface Area of the Regular Pyramid. Surface Area: Volume: 24 yds 20 yds
How do you find the 3rd side of a triangle?
The third side of a triangle, the following formula can be used c² = a² + b² - 2abcos(C)
To calculate the third side of a triangle, first find the lengths of the other two sides and the angle opposite the third side. Then plug these values into the formula above and solve for c.
Where c is the third side of the triangle, a and b are the other two sides, and C is the angle between them.
For example, for a triangle with two sides of length 4 and 6, and an angle between them of 75 degrees, the formula would look like this:
c² = 42 + 62 - 2(4)(6)cos(75)
Solving for c yields a third side length of 8.4.
To solve for c, first square the two side lengths: 42 = 16 and 62 = 36. Then, multiply the two side lengths together and multiply by the cosine of the angle between them: 2(4)(6)cos(75) = 43.9. Finally, add the two squared values together and subtract the result of the multiplication: 16 + 36 - 43.9 = 8.1. Then, take the square root of this result to get the length of the third side: √8.1 = 8.4.
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The number of girls in chorus is 5 more than 3 times the number of boys. If
there are 29 girls in the school chorus, how many boys are in chorus?
Answer:
Way too many
Step-by-step explanation:
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HELP I NEED HELP ASAP HELP I NEED HELP ASAP HELP I NEED HELP ASAP HELP I NEED HELP ASAP
Answer:
B
Step-by-step explanation:
pls help!!! asap!! will give brainliest NO LINKS
Answer:
it's -63
good luck if you want explanation comment
Answer: 63
Step-by-step explanation:
All triangles' angles added up should be 180 degrees, so 70+47=117 and 180-117=63.
180 = a+b+c
180 = 47 + 70 + c
180 - 47 - 70 = c
or,
180 - (47+70) = c
A set of data has the trend line modeled by the equation Y =1.5x + 11. What value of X corresponds to y =56?
Answer:
x = 30
Step-by-step explanation:
Plug in 56 in place of y, then solve for x.
56 = 1.5x + 11
Subtract 11.
45 = 1.5x
Divide both sides by 1.5.
45/1.5 = x
30 = x
Answer:202
Step-by-step explanation:
I did it
Carol has three times as many 10-dollar bill as 5-dallar bills. She has a total of $350. How many 5-dollar bills dose Carol have?
Answer:
30
Step-by-step explanation:
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The store sells boxes of adhesive
bandages. The boxes have: 12, 15, 18, 20, 25, 36, 40, 45,
50, 64, 75, or 100 bandages per box.
Which boxes have bandages that can be separated
into 2 first-aid kits with no leftover bandages?
Which boxes have bandages that can be separated into
5 first-aid kits with no leftover bandages?
Which boxes have bandages that can be separated into
10 first-aid kits with no leftover bandages?
Therefore, there are 12 bandages in 2 boxes, which is the answer to the unitary method presented problem.
What is a unitary method?The term "unitary" refers to a single or separate unit or variable . As a result, this strategy's objective is to establish values in terms of a single unit. For instance, if a car travels 44 kilometres on two litres of gas, the unitary technique can be used to determine how many kilometers it will drive on one.
Here,
Given: Each box of bandages has three packs, with two bandages in each pack.
Now, determine how many bandages there are in two boxes.
Therefore, we solve using the unitary method:
One pack contains two bandages.
In 3 packs, there are therefore = 2*2 = 6 bandages.
One box contains three packs as stated.
Consequently, we multiply 2 by 6 to obtain the bandages in 2 boxes:
=> 2 * 6 = 12
Therefore, there are 12 bandages in 2 boxes, which is the answer to the unitary method's presented problem.
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For positive acute angles A and B, it is known that tan A = 12/35 and sin B = 9/41. Find the value of cos(A - B) in the simplest form
The simplest form of the value of the trigonometric identity cos(A-B) is
1508/1517.
What is are the trigonometric identities?
Trigonometric Identities are equality conditions that apply to all values of the equation's variables and which require trigonometry functions.
There are numerous unique trigonometric identities that involve both the side length and angle of a triangle. Only the right-angle triangle is valid for the trigonometric identities to work.
cos(A-B) = cosA cosB + sinA sinB
Given,
tan A = 12 / 35
So sin A = 12 / [tex]\sqrt{12^2 + 35^2}[/tex] = 12 / 37
cos A = 35 / 37
Now,
sin B = 9/41
cos B = [tex]\sqrt{1 - sin^{2} B }[/tex] = [tex]\sqrt{1 - (\frac{9}{41} )^{2} }[/tex] = 40/41
Now substituting the above values in the cosine formula
cos(A-B) = cosA cosB + sinA sinB
= (35/37) (40/41) + (12/37) (9/41)
= 1508/1517 = 0.994
Therefore the simplest form of cos(A-B) is 1508/1517.
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Given the following system of equations, solve for 'x' and 'y.
2x - 15y = 139
-3x + 16 y = -176
Answer:
X=32, y=-5
Step-by-step explanation:
Directions: The Johnson family is redesigning their backyard this spring. They want to include a sandbox area,
a swing set area, a patio area, a pool area and a grill area. Their plans for the yard layout in feet is shown in the
figure below. Use the figure and your knowledge of polynomials, perimeter, and area to solve the following:
1) The formula for area is,
⇒ Area of rectangle = Length × Width
And, The formula for perimeter is,
⇒ Perimeter = 2 (Length + width)
2) An expression for the length of the south side of the yard is,
⇒ Length = (5x + 2) + (x² - 9) + (x² - 7x + 12)
3) The simply expression for the length of the south side of the yard is,
⇒ Length = 2x² - 2x + 5
4) An expression for the perimeter of the pool area is,
⇒ Perimeter = 2 ( (x² + 10) + (8x + 8) )
5) 5) The simply expression for the perimeter of the pool area is,
⇒ Perimeter = 2x² + 16x + 36
What is mean by Rectangle?A rectangle is a two dimension figure with 4 sides, 4 corners and 4 right angles. The opposite sides of the rectangle are equal and parallel to each other.
Given that;
The Johnson family is redesigning their backyard this spring. They want to include a sandbox area, a swing set area, a patio area, a pool area and a grill area.
Now,
1) The formula for area is,
⇒ Area of rectangle = Length × Width
And, The formula for perimeter is,
⇒ Perimeter = 2 (Length + width)
2) An expression for the length of the south side of the yard is,
⇒ Length = (5x + 2) + (x² - 9) + (x² - 7x + 12)
3) The simply expression for the length of the south side of the yard is,
⇒ Length = (5x + 2) + (x² - 9) + (x² - 7x + 12)
= 5x + 2 + x² - 9 + x² - 7x + 12
= 2x² - 2x + 5
4) An expression for the perimeter of the pool area is,
⇒ Perimeter = 2 ( (x² + 10) + (8x + 8) )
5) The simply expression for the perimeter of the pool area is,
⇒ Perimeter = 2 ( (x² + 10) + (8x + 8) )
= 2 (x² + 10 + 8x + 8)
= 2 (x² + 8x + 18)
= 2x² + 16x + 36
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A) A sequence is defined using this term-to-term rule.
Un+1 = 2un+ 20
If uy = 8, find u2
b) Another sequence is defined using this term-to-term rule,
unty = ku,+r
where k and rare constants.
Given that u, = 37, uz = 188 and ug = 943, find the value of k and
the value of r.
The Value of the two constants K and R are 5 and 3 respectively.
a) To find u2, you can substitute u1 = 8 into the term-to-term rule to get:
u2 = 2u1 + 20 = 2(8) + 20 = 36
So u2 = 36.
b) To find the values of k and r, you can use the given values of u1, u2, and u3 to set up a system of equations. Using the term-to-term rule:
u2 = ku1 + ru3 = ku2 + rSubstituting in the given values:
u2 = 188 = k(37) + ru3 = 943 = k(188) + rSolving for r and k, we get:
k = 5 and r = 3.
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Determine the domain of the following graph
Answer:
Step-by-step explanation:
1) The domain is related to the behaviour of the x
the graph started when x is -11 and finish when x is 1
so
D : [-11 ; 1]
or -11 ≤x ≤ 1
the range is related to the behavior of y
the graph start when y is -7 and finish when y = 0
Range : [-7;0]
or -7≤ y ≤ 0
One of the legs of a right triangle measures 8 cm and its hypotenuse measures 10 cm. Find the measure of the other leg. If necessary, round to the nearest tenth.
Answer:
6
Step-by-step explanation:
delta math
The required measure of the other leg will be 6 cm in the given right triangle.
What is Pythagoras's theorem?Pythagoras's theorem states that in a right-angled triangle, the square of one side is equal to the sum of the squares of the other two sides.
We have been given that one of the legs of a right triangle measures 8 cm and its hypotenuse measures 10 cm.
Let the measure of the other leg would be x cm.
According to Pythagoras's theorem,
⇒ c² = a² + b² ....(i)
As per the given question, we have
c = 10cm, a = 8 cm and b = x
Substitute the values in the above formula, and solve for x
⇒ 10² = 8² + x²
⇒ 100 = 64 + x²
⇒ x² = 100 - 64
⇒ x² = 36
⇒ x² = 6²
⇒ x = 6
Therefore, the required measure of the other leg will be 6 cm in the given right triangle.
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TRANSLATE EACH PHRASE INTO AN ALGEBRAIC EXPRESSION
1) 4 times a number,increased by 11.
2) 8 times the sum of a number and 7.
3) 1 less than twice a number.
4) the sum of a number and 3 times that number.
5) 12 more than 5 times a number.
6) 16 increased by 1 more than a number.
7) 20 decreased by 5 less than a number.
8) 6 less than a number increased by 15.
Answer:
Step-by-step explanation:
Let the number be x then,
1) 4 * x + 11
2) 8 * (x + 7)
3) 2x - 1
4) x+ 3x
5) 5x + 12
6) 16 + 1 + x = 17 + x
7) 20 - ( x - 5) = 20 - x + 5 = 25 - x
8) x - 6 + 15 = x +9
Identify like terms
24a - 12b + 4 - 8a
Answer:
The like terms in this expression are 24a and -8a, and -12b and 12b.
Step-by-step explanation:
The like terms 24a and -8a can be combined by adding the coefficients and the variables, which gives us 24a - 8a = 16a.
The like terms -12b and 12b can be combined by adding the coefficients and the variables, which gives us -12b + 12b = 0.
So the like terms in this expression are 24a, -8a, and -12b, 12b.
a rectangular picture frame has dimensions of 2 feet by 3 feet.
I dont know
I would just pick c
b) Sita had 50 sweets. She ate 10 sweets and gave 8 sweets to her brother. If she divided the rest of them among her 8 friends equally, how many sweets would each friend get
Answer:
4 sweets per friend
Step-by-step explanation:
so first you want to minus 10 sweets since she ate 10 leaving her with 40 sweets. then she gives 8 sweets to her brother leaving her with 32 sweets left. If you divide the remaining sweets ( 32 ) by 8 you get 4 sweets per friend
find the mean,median and mode for x,2x,3x,4x,5x
Answer:
Mean: 3x
Median: 3x
Mode: None
Step-by-step explanation:
The mean is the sum of all the numbers divided by how many there are.
x + 2x + 3x + 4x + 5x = 15x and 15x/5 = 3x. So the mean is 3x.
The median is the number in the middle when the values are in order from least to greatest. The median is 3x.
The mode is the number that appears most often in the data set. In this case, the mode is none because no number appears more than the other numbers.
An app for your cell phone cost 4.99 but it is discounted 55% off on your birthday if tax is still charged at a rate of 1% what would be the final cost of the app?
find the output, g, when the input, r is 3
g= -5 + 13
The output of function g(r) = -5x + 13 when r is 3 is -2.
What is a function?A function is a relationship between inputs where each input is related to exactly one output.
Example:
f(x) = 2x + 1
f(1) = 2 + 1 = 3
f(2) = 2 x 2 + 1 = 4 + 1 = 5
The outputs of the functions are 3 and 5
The inputs of the function are 1 and 2.
We have,
g(r) = -5r + 13
Input r = 3
g(3)
= -5 x 3 + 13
= -15 + 13
= - 2
Thus,
The output is -2.
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What is the sum of the greatest common factor of $3$ and $6$ and the least common multiple of $3$ and $6$?
The sum of the greatest common factor (HCF) and least common multiple (LCM) of 3 and 6 is 9.
Highest common factor (HCF) and Least common multiple(LCM)The H.C.F. defines the highest common factor present in between given two or more numbers, while L.C.M. defines the least common multiple number which is exactly divisible by two or more numbers.
factors of 3 are 1 and 3
factors of 6 are 1, 2, 3, and 6
3 = 1 × 3
6 = 2 × 3
LCM = 2 × 3
LCM = 6
HCF = 3
sum of HCF and LCM of 3 and 6 = 3 + 6
sum of HCF and LCM of 3 and 6 = 9
Therefore, 9 is the sum of the greatest common factor HCF least common multiple LCM of 3 and 6.
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Can someone please help me with this :(
Answer:
1=B
Step-by-step explanation:
¿Cuántos decimetros hoy en un metro?
PLEASE ANWSER!!!
PICTURE
Answer:
The 4th would be 0.25
Step-by-step explanation:
what is the volume of a cylinder in cubic feet with a height of 12 feet in a base diameter of 12 feet
Answer:
1357.17 cubic feet
Step-by-step explanation:
The volume of a cylinder is
[tex]\pi {r}^{2} h[/tex]
We know the height is 12, and the radius is simply half our diameter, which in this case is
[tex] \frac{12}{2} = 6[/tex]
plug these two numbers into our formula and we have found our volume.
Which bag of potatoes is the better deal?
Answer:
5 kg.
Step-by-step explanation:
2 kg for $0.96 is more expensive than 5 kg for $1.95