For the given number is 4√18 .The Prime factorization would be 4√18 = 2 x 2 x √2 x √3 x √3.
What is prime factorization?Factorization is expressing a mathematical quantity in terms of multiples of smaller units of similar quantities.
For an integer, factorization is the decomposition of that integer in terms of smaller integers which when multiplied with each other give back that considered number.
Those composing integers are called factors of that considered integers.
Prime factorization is when all those factors are prime numbers.
Thus, prime factorization expresses an integer in terms of multiples of prime numbers.
Prime factorization is unique for each integer.
For the given number is 4√18
Prime factorization
4√18 = 2 x 2 x √2 x √3 x √3
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11. Graph.
y - 2 = -2 (x + 2)
Answer:
y=-2x
Step-by-step explanation:
should look like a straight line, that is going up to the left. crossing (0,0) and (1,-2)
what is the rule for 2;13;26;32?
Answer:
sequence
Step-by-step explanation:
HELP NOW PLESAE
WHat is m
An inscribed angle (like angle RTS) is half its intercepted arc.
Angle RTS = 51
Then, we just have a triangle to look at. Remember that the interior angles of a triangle add up to 180.
67 + 51 + x = 180
118 + x = 180
x = 62
Answer: angle RST = 62 degrees
Hope this helps!
Can someone help me I dont know what to do
Step-by-step explanation:
1. find P of semicircle
perimeter of a semicircle = pi×r+d
=3.14×5+10
=25.7
2.find P of rectangle
P=10×4=40cm
3. add P of semicircle and P of rectangle
25.7+40=65.7cm
Tops corporation is organized into two divisions, manufacturing and marketing. both divisions are considered to be profit centers and the two division managers are evaluated in large part on divisional income. the company makes a single product. it is fabricated in manufacturing and then packaged and sold in marketing. there is no intermediate market for the product.
the monthly income statements, in thousands of dollars, for the two divisions follow. production and sales amounted to 10,000 units.
manufacturing marketing
revenues $ 3,000 $ 5,000
variable costs 2,400 3,700
contribution margin $ 600 $ 1,300
fixed costs 500 800
divisional profit $ 100 $ 500
Top company would accept the order as it increases the total profit of the corporation by $90000
How to illustrate the information?As a company as a whole, Tops corporation will accept orders if the contribution margin increases by accepting orders.
a. The contribution margin will be:
= sales price - variable cost of manufacturing department - variable cost of marketing department
= $400 - [$2400*1000/10000units] - $70
= $400 - $240 - $70
= $90
Therefore, the increase in profit will be:
= $90 × 1000
= $90000
Top company would accept the order.
b. The marketing department will accept the order as it increases its profit by $400000-$370000 = 30000.
c. The manufacturing division manager would accept the order as it increases its profit by $60000. This was gotten as:
= (300 × 1000) - (240 × 1000)
= 300000 - 240000
= 60000
The other parts of the question include:
The company has just received an offer to buy 1,000 units of the product this month at a price of $400 per unit. The Marketing Division manager suggests that for the special order only, the transfer price be set at 50 percent of the sales price, or $200 per unit. Instead, assume the transfer price is unchanged from the current transfer price.
Required:
a. Does Tops Corporation want to accept this order?
b. Will the Marketing Division manager be willing to accept this order?
c. Will the Manufacturing Division manager be willing to accept this order?
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Change 36.2% to a fraction.
Answer:
Step-by-step explanation:
Conversion
A % can always be changed into a decimal by dividing by one hundred. In this case
decimal = 36.2/100 = 0.262 \\
Answer: 0.262
Answer:
181/500
Step-by-step explanation:
Angles 1 and 2 are supplementary
Angle 1 = 30°
Answer:
Angle 2 = 150°
Step-by-step explanation:
▪︎ Measures of supplementary angles add up to 180°.
Therefore,
Angle 1 + Angle 2 = 180°
Angle 1 = 30°
30° + Angle 2 = 180°
Angle 2 = 180° - 30° = 150°
Please help with this question I really need help!
Answer:
-6, -6
Step-by-step explanation:
Given :
y = x² + 12x + 36Solving :
This is of the form : a² + 2ab + b²Hence, the factored form is y = (x + 6)²y = (x + 6)(x + 6)x + 6 = 0 ⇒ x = -6x + 6 = 0 ⇒ x = -6The zeros are : -6, -6
What is factorisation?
It is also called Middle Term Splitting
Its a cool thing with which you can solve different orders of polynomials(or any algebraic expressions if you're a pro).
It is writing an expression as a product of 2 or more factors
Answer:
factorization is of writing a number or another mathematical use as a product of several factors, usually smaller of the same kind.
Step-by-step explanation
3 × 5 is a factorization of the integer 15, and is a factorization of the polynomial x² – 4.
Mrs. Gottschalk had 60 feet of ribbon. If each of the 20 students in her class gets an equal length of ribbon, how long will each piece be in inches?
m = − 1 6 , (6, −3) y =
5
6
x + 3
Answer:
6
Step-by-step explanation:
that is because 6 is x and y is -3
For each value of v, determine whether it is a solution to -6(v+4)=-6
Answer:
v = -3
General Formulas and Concepts:
Algebra I
Equality Properties
Multiplication Property of EqualityDivision Property of EqualityAddition Property of EqualitySubtraction Property of EqualityStep-by-step explanation:
Step 1: Define
Identify given.
-6(v + 4) = -6
Step 2: Solve for v
[Division Property of Equality] Divide -6 on both sides:∴ the value of v is equal to -3.
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Topic: Algebra I
in the figure below lines p and q are parallel. what do you notice?
Answer:
Corresponding
Step-by-step explanation:
So, we know that 1&2, 3&4, 5&6, and 7&8 all equal 180 degrees in their pairs. 7&3 are corresponding angles that are less than 90 degrees on their own. We don't know the degrees of each angle, so we can't say their exact angle.
(I know I didn't give the second answer, if you elaborate, maybe I can understand what it's asking better)
Hope this helped!
Answer:
-> Corresponding
-> Are equal
Explanation:
First, we will find where angles 3 and 7 are at. See attached. Since they are in corresponding places on both lines, these angles are corresponding angles.
We know that corresponding angles have the same measurement, so their measures will be equal, or in other words, congruent.
What number goes in the blank?
10, 25, 5, or 0
Answer:
25
Step-by-step explanation:
(x+5)(x+5) = x^2 + 10x + 25
Answer:
25
Step-by-step explanation:
The number that goes in the blank is 25.
The constant must have two factors that multiply to equal the constant and add to equal the coefficient.
The sales tax rate is 10%. If Matt buys a computer keyboard priced at $34, how much tax
will he pay?
Answer:
$3.40
Step-by-step explanation:
10% of $34
= [tex]\frac{10}{100}[/tex] × $34
= 0.1 × $34
=$3.40
Find the amount of sheet metal needed to form a conical funnel of base radius 30 cm and vertical height 50 cm, allowing for a 0.5 cm overlap at the join
The amount of sheet metal needed to form the conical funnel is 5525 cm²
How to determine the amount of sheet?The given parameters are:
Radius, r = 30 cmVertical height, h = 50 cmOverlap = 0.5 cmStart by calculating the slant height (l) of the cone using:
l = √(r² + h²)
This gives
l = √(30² + 50²)
Evaluate
l = 58.31
The lateral surface area of the conical funnel including the overlap is then calculated as:
A = πrl + Overlap * l
This gives
A = 3.142 * 30 * 58.31 + 0.5 * 58.31
Evaluate
A = 5525.4556
Approximate
A = 5525
Hence. the amount of sheet metal needed is 5525 cm²
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The sum of three consecutive intergers is 189 what are the integers
Answer:
62, 63, 64
Step-by-step explanation:
The middle integer of three consecutive integers will be the average of them. That is, it will be their sum, divided by 3.
__
The middle integer is 189/3 = 63.
The three consecutive integers are 62, 63, 64.
_____
Additional comment
If you'd like to write an equation that tells you the same thing, let x represent the middle integer. Then the lower one is x-1, and the upper one is x+1. Their sum is ...
(x-1) +x +(x+1) = 189
3x = 189 . . . . . . . . . . . . simplify
x = 189/3 = 63 . . . . . . . divide by the coefficient of x
(x-1) = 63-1 = 62 . . . . . . find the other two integers
(x+1) = 63+1 = 64
What did you notice about both of your triangles
Answer:
they look similar but one of them is upside down.
In triangle abc, measure of angle a = 90 degrees and line an is an altitude. if ab = 20 in. and ac = 15 in., find bc, bn, nc, an
Answer:
BC = 25 in
AN = 12 in
BN = 16 in
NC = 9 in
Formulas:
Pythagorean Theorem
[tex]c^2 = a^2 + b^2[/tex]
c ... hypotenuse
a ... one leg
b ... another leg
Pythagorean theorem is used in right triangles (triangles in which one angle is 90°).
Area of triangle
[tex]A = \frac{1}{2}bh[/tex]
A ... area of triangle
b ... base (one of the sides of the triangle)
h ... height perpendicular to base
Step-by-step explanation:
Given:
A = 90°
AB = 20 in
AC = 15 in
See attached picture.
1) BC
To find BC we can use Pythagorean theorem, since ABC is a right triangle. We have the lengths of two legs (AB, AC) and we are finding the hypotenuse.
[tex]c^2 = a^2 + b^2\\\text{BC}^2 = \text{AB}^2 + \text{AC}^2\\\text{BC}^2 = 20^2 + 15^2\\\text{BC}^2 = 625\\\sqrt{\text{BC}^2} = \sqrt{625}\\\text{BC} = 25 \text{ in}[/tex]
2) AN
AN is the height corresponding to base BC. To find it we can use formula for the area of the triangle. But first let's find the area of the triangle.
Notice how AB is perpendicular to AC. We can use AB as base and AC as height.
[tex]A = \frac{1}{2}bh\\\\A = \frac{1}{2} \times \text{AB} \times \text{AC}\\\\A = \frac{1}{2} \times 20 \times 15\\\\A = 150 \text{ in}^2[/tex]
Now that we have area, we can use BC as base and AN as height and solve for AN.
[tex]A = \frac{1}{2}bh\\\\A = \frac{1}{2} \times \text{BC} \times \text{AN}\\\\150 = \frac{1}{2} \times 25 \times \text{AN}\\\\\ 300 = 25 \times \text{AN}\\\\12 = \text{AN}\\\\\text{AN} = 12 \text{ in}[/tex]
3) BN
Let's use Pythagorean theorem in right triangle ABN. Hypotenuse is AB.
[tex]c^2 = a^2 + b^2\\\text{AB}^2 = \text{AN}^2 + \text{BN}^2\\20^2 = 12^2 + \text{BN}^2\\400 = 144 + \text{BN}^2\\256 = \text{BN}^2\\\sqrt{256} = \sqrt{\text{BN}^2}\\16 \text{ in} = \text{BN}[/tex]
4) NC
We know the lengths of BC an BN, so we can just subtract.
[tex]\text{NC} = \text{BC} - \text{BN}\\\text{NC} = 25 - 16\\\text{NC} = 9 \text{ in}[/tex]
20. Which formula would you use to calculate the floor space of Firm 3's structure? Explain your choice. (Refer to the Formula table on page 3.) (2 points: 1 point for the formula, 1 point for the explanation)
The formula would you use to calculate the floor space of Firm 3's structure is πr²h.
How to depict the formula?It should be noted that the formula that can be used on this scenario will be:
= πr²h
where,
h = 60
r = 70/2 = 35
The volume will be:
= πr²h
= 3.14 × 35² × 60
= 230790 feet ³
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can someone help me with this? thank you!
Answer:
240cm³
Step-by-step explanation:
To find our answer we will multiply the volume, width, and height.
4 · 20 · 3 = 240. Therefore, 240cm³ is our answer.
Have a good day!
[tex]\qquad\qquad\huge\underline{{\sf Answer}}[/tex]
Let's calculate its volume ~
Volume of a rectangular prism is :
[tex]\qquad \sf \dashrightarrow \:v = l \cdot w\cdot h[/tex]
[tex]\qquad \sf \dashrightarrow \:v = 20 \cdot 4\cdot 3[/tex]
[tex]\qquad \sf \dashrightarrow \:v = 240 \: \: cm {}^{3} [/tex]
Which of the following functions would best model the progression of the points in the scatter plot?
A: a quadratic function
B: a linear function
C: a square root function
D: an exponential function
The function that would best model the progression of points in the given scatter plot is: D. an exponential function.
What is an Exponential Function?If a function is an exponential function, as the x-value increases, the value of y approaches infinity, or as x-value decreases, the value of y approaches 0.
The graph given is a typical example of how an exponential function graph behaves.
Therefore, the best model for the progression of points is: D. an exponential function.
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Jorge is an administrative assistant. He was involved in a serious car accident and broke both wrists. Which of his
insurance plans will provide him with income while he is out of work recovering for six weeks?
A)short-term disability
B)workers' compensation
C)long-term disability insurance
D)medical insurance
Answer:
Medical Insurance
Step-by-step explanation:
Answer:
Medical Insurance
Step-by-step explanation:
serious car accident and broke both wrists.
help 30 points for all ansers
The answers to the problem are:
a) The value of x is : 8
b) ∠ZRB and ∠BTS are not supplementary angles.
c) ∠BST and ∠RSB are complementary angles.
d) ∠ABT is an acute angle
e) SA is not the bisector of the angle ∠ZSY.
Types of AnglesAngles are formed when two lines meet and they are of different types.
acute: this is an angle less than 90°
obtuse: this angle is greater than 90° but less than 180°
reflex: this angle is greater than 180° but less than 360°
Analysis:
∠BRS = 180 - (20X - 22) = 202 - 20X
a) To find x, sum of angles in the triangle = 202-20x + 2x+32 + 5x+10 + 120-10x = 180
364 -23x = 180
23x = 364-180
23x = 184
x = 8
b) ∠ZRB = 20x-22 = 20(8) - 22 = 138°
∠BTS = 2x+32 = 2(8)+32 = 48°
138°+48° = 186° [tex]\neq[/tex] 180°
They are not supplementary
c) ∠BST = 120-10X = 120 - 10(8) = 40°
∠RSB = 5x+10 = 5(8)+10 = 50°
50+40 = 90°. They are complementary
d) ∠ABT = 180 - ∠ABR = 180 - 100 - x = 88°
It is acute since it is less than 90°
e) SA is not an angle bisector, since it dived the angles as 40° and 50° and not equal.
In conclusion, the solution to the questions are:
a) The value of x is : 8
b) ∠ZRB and ∠BTS are not supplementary angles
c) ∠BST and ∠RSB are complementary angles
d) ∠ABT is an acute angle
e) SA is not the bisector of the angle ∠ZSY
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Write an equivalent expression by distributing the "-−" sign outside the parentheses:
8.9r-(-5s-10)
Answer:
8.9r + (5s + 10)
actually the parenthesis aren't necessary...
8.9r + 5s + 10
Step-by-step explanation:
You can change a subtraction to addition if you change the second term to the opposite sign. This problem is like advanced mode of "Add the Opposite"
8.9r - (-5s - 10)
= 8.9r + (+5s + 10)
= 8.9r + (5s + 10)
= 8.9r + 5s + 10
In a unit circle, 0 = 270°. Identify the terminal point and sin 0.
Answer:
terminal point is at (0, -1) and sin 0 = -1
Step-by-step explanation:
In a unit circle the radius of the circle is 1 so
- we know the points where the circle intersects the x-axis and y-axis as a (x , y) coordinates.
(1, 0) where we start on the positive x-axis and where angle is 0°
(0, 1) where we go counterclockwise and where angle is 90°
(-1, 0) where we go continue counterclockwise and where angle is 180°
(0, -1) where we stop in our problem because the angle is 270°
-we also know that x= cos O and y= sin O so the coordinates (x, y) are really
(cos O, sinO)
Given:
0 = 270°
sin 0 = sin 270°
sin 270° = -1
The terminal point is at (0, -1) and sin 0 = -1
What is the volume of the figure?
Answer:
341.25
Step-by-step explanation:
You first split the figure into 2 pieces the triangular prism and the rectangular prism now that we know the dimensions of each figure we can create an expression, we will start with the triangular prism. the expression will be 3/2 x 5/2 x 10.5. Then we solve the rectangular prism. 5 x 5 x 10.5.
Now that we have acquired all the math that we need we can continue to simplify. 3 x 2 x 5/2 was derived from (3 x 5)/2 and we physically drew it out with properties of algebra (a later topic to study) anyways we get 15/2=7.5 and we multiply that by 10.5 giving us 78.75. the triangular prism is easier we just do 25 x 10.5 giving us 262.5. Now that we have succumbed both figures we can combine the to get the volume which is 341.25 (78.75 + 262.5).
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An online clothing store has 4 sweaters for every 5 T-shirts. Which table below represents this relationship?
Answer:
B
Step-by-step explanation:
Do the math
5x1 is 5
4x1 is 4
35÷7 is 5
28÷7 is 4
Hope this helps
Answer:
The second table.
Step-by-step explanation:
4 sweaters for every 5 T-shirts is a ratio of 4/5, which is equal to 0.8. That means that every ratio in the table should also be equal to 0.8 since they are all different versions of 4/5. In the second table, 4/5 = 0.8, 8/10 = 0.8, 28/35 = 0.8, and 32/40 = 0.8, so it is the second table.
Layla owns a small business selling clothing. She knows that in the last week 52 customers paid cash, 20 customers used a debit card, and 11 customers used a credit card. Based on these results, express the probability that the next customer will pay with something other than a credit card as a decimal to the nearest hundredth.
Probability of paYing in credit card
11/830.13P(Not paying in credit card)
1-0.130.87The probability that the next customer will pay with something other than a credit card is 0.87.
What is the probability?Probability refers to a possibility that deals with the occurrence of random events.
The probability of all the events occurring need to be 1.
P(E) = Number of favorable outcomes / total number of outcomes
We are given that Layla owns a small business selling clothing. She knows that in the last week, 52 customers paid cash, 20 customers used a debit card, and 11 customers used a credit card.
Based on these results we have;
Total cards=52+20+11=83
Probability of paying in credit card;
11/83
0.13
Now, P(Not paying in credit card)
1-0.13
0.87
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PLEASE HELP ASWER NEEDED BEFORE 2 HOURS!10. When adding or subtracting mixed numbers, you can use the To help separate the whole numbers from the fractions. Solve the following problems 11. + // 12.1 / +2/3/ 13. 10+ 39/160 14.6 / +9 15.3 1/1 + 4/1/20
Answer:
I was unable to do no. 10 hope others solution can help you