[tex]\rightarrow[/tex]Square root of 9 is a whole number that is multiplied by itself to get the original number. The actual value of square root of 9 is 3.
√9 = ±3
[tex]\rightarrow[/tex]If we square +3 or -3, the resulting value will be equal to 9.
[tex]\sf{(+3)^2 = 9}[/tex]
[tex]\sf{(-3)^2 = 9}[/tex]
How to find?:-[tex]\rightarrow[/tex]Number 9 is an odd number and not a prime number. Prime numbers have only two factors, 1 and the number itself. But as we know, 9 have three multiple factors, 1, 3 and 9 itself. Thus, we can write the number 9 in the form of multiple as;
[tex]\sf{1 × 9 = 9}[/tex][tex]\sf{3 × 3 = 9}[/tex][tex]\sf{9 × 1 = 9}[/tex][tex]\rightarrow[/tex]You know that number 9 is a multiple of 3 or when 3 is multiplied by itself, we get the number 9. Therefore, we can write the square root of 9 as;
➾[tex]\sf{\sqrt{9}}[/tex]
➾[tex]\sf{\sqrt{3×3}}[/tex]
➾[tex]\sf{\sqrt{3^2}}[/tex]
[tex]\rightarrow[/tex]The square cancels the square root of a number. Therefore, if we cancel the square root with a square in the above expression, we get,
➾[tex]\sf{\sqrt{9}}[/tex] = ±3
__________________________________
Hope it helps you:)
Solve for x. Leave your answer in simplest radical form. X 4 3
Apply Pythagorean theorem
P²=H²-B²P²=4²-2²P²=16-4P²=12Now
Again apply Pythagorean theorem
x²=12-3²x²=12-9x²=3x=√3Answer:
the final answer for this problem is √3
3/5 of Tom's favorite number is 60. what is tom's favorite number
Answer:
100
Step-by-step explanation:
its saying 60% of his favorite number is 60
because the numbers are the same that means the number must be 100
A ball follows a path described by the function h(x) = -3x^2 +12x +14 where h(x) is the height of the ball after x seconds. After how many seconds will the ball be at its
highest point?
A. 1 second
B. 2 seconds
C. 3 seconds
D. 4 seconds
Answer:
3
Step-by-step explanation:
Abby is going to make 60 Abby is making 60 shortbread biscuits. How much flour
will she need?
Ingredients to make
20 shortbread biscuits
130g butter
60g sugar
180g flour
Step-by-step explanation:
180 grams of flour is needed for 20 short bread biscuits to find how many floor is needed per biscuit we divide
=> 180 ÷ 20=> 9g(per each)since we are find the value of floor per shortbread biscuits we then multiply it by 60
=> 9 × 60=> 540[tex] \therefore [/tex] she needs 540g to make 60 short bread biscuit
~ Done~
What is 12.985 rounded to 2 decimal place?
12.985 rounded to 2 decimal places is 12.99
Answer:
Step-by-step explanation:
Step 1:
Identify the digit in the hundredths place, as it is the 2nd decimal place. The 8 is the digit in the hundredths place.
Step 2:
Look at the digit in the thousandths place and its value is 5 thousandths, so increase the digit in the hundredth's place to 9.
Step 3:
The new number is 12.99 rounded to the 2nd decimal place.
what is 2(9p-1/2) equil to?
Answer:
Step-by-step explanation:
Use distributive property: a*(b - c) = (a*b) -(a*c).
Here, a = 2 ; b = 9p & c = 1/2
[tex]2*(9p - \dfrac{1}{2})=2*9p-2*\dfrac{1}{2}\\\\\\ = 18p - 1[/tex]
9. A quilt pattern will use the block shown in the graph with regular hexagon
ABCDEF that has points A(4,0) and D(-4, 0). What is the area of the hexagon
to the nearest tenth? Show all work. [5 points]
From the given coordinates of point A(4, 0), and D (-4, 0), the area of the hexagon is 33.94 units square.
How can the area of the hexagon be found?The given parameters are;
Shape of the quilt pattern = A regular hexagon
Coordinates of point A = A(4, 0)
Coordinates of point D = D(-4, 0)
Required;
The area of the hexagon
Solution;
The coordinates of the center of the hexagon, P = (0, 0)
A regular hexagon consist of six equilateral triangles.
The length of a side of the triangle = PA
Length of PA = 4 - 0 = 4
Therefore;
Length of a side of the triangle = 4
Height of the triangle = PA × sin(60)
Which gives;
Height of the triangle = 4 × (√3)/2 = 2•√3
Area of one triangle = (4 ÷ 2) × 2•√3 = 4•√2
Area of the 6 triangles is therefore;
A = 6 × 4•√2 = 24•√2
Area of the 6 triangles = Area of the hexagon
Therefore;
Area of the hexagon = 24•√2 = 33.94 square units.Learn more about the area of regular shapes here;
https://brainly.com/question/10572314
HELP WILL GIVE BRAINLIEST!!!!
2. Which of the following equations is FALSE?
BC=20
AC=20
BD= 10
AD= 10
Answer:
letter c the BD= 10
Step-by-step explanation:
Answer:
BD=10
Step-by-step explanation:
1. BAD=BCD=60
Therefore
BA = BC (sides opposite to equal angles are equal)
BA=20
Therefore BC=20
2.BAC+BCA+ABC=180(sum of the interior angles of a triangle is 180)
60+60+ABC=180
ABC=180-120
ABC=60
ABC=BAC=BCA
Therefore ABC is an equilateral triangle
AC=20
4. AC=AD+DC
AD=DC (BD is a perpendicular bisector)
Therefore
AC=2×AD
AC=20
20=2×AD
AD=20÷2
AD=10
Hope this helps!
Give me a real life example of when you would use area. * (your own wording please!!!!)
Answer:
Area is very commonly used in our world we just may not immediately recognize it. Most if not all construction workers use area to figure out how much Sq feet they have to work with. When decorating your home you need to know how much space is in each room. When installing carpet or hardwood you'll need to figure out the area of your room.
Hopefully this helps!
Define the algebraic terms by counting how many terms given on the expression below.
4x + 3n + 5
Answer:
Two terms ( [tex] x [/tex] and [tex] n [/tex])
Step-by-step explanation:
If simplified it gives 3n+4x+5
And cannot be factored
=======================================================
We're given the following expression:
[tex]\bigstar{\boxed{4x+3n+5}[/tex]
Here,
4x is a term
3n is a term
5 is a term
4 is the coefficient of x
x is a variable
3 is the coefficient of n
n is a variable
5 is a constant
Details:-
A coefficient is a number before a variable
A variable is a letter
A constant is a number without any variables next to it
=========================================================
note:-Hope everything is clear; if you need any explanation/clarification, kindly let me know, and I will comment and/or edit my answer :)
10 cm equal to cm can you help me.
Answer:
1000cm
Step-by-step explanation:
there are 100cm in a meter. so we multiply 10 by 100 to get the amount of centimeters in 10 meters which is 1000cm
Answer: There Are 1000 Centimeters(Cm) In 10 Meters(M)
Please help
The Pythagorean theorem states that a² + b² = c² for a right triangle with leg lengths, a and b, and hypotenuse length, c.
The hypotenuse of a right triangle is 5 units long and has the points (3, 0) and (0, 4) as end points. One of the legs has length 3.
Use the Point and Segment tools to draw a right triangle at demonstrates the other leg length is 4.
Answer:
Step-by-step explanation:
Draw the third point at (0, 0). This would make the distance from (3,0) to (0,0) equal to 3, and the distance from (0,4) to (0,0) be 4.
The accompanying diagram show a cross-section of a rectangular pyramid. The cross sectional area is 36in and is 3
inches from the vertex of the pyramid. If the height of the pyramid is Sinches, what is the area of the rectangular base?
The rectangular base area is the space the rectangular base occupies
The area of the rectangular base is 60 square inches
How to determine the area of the rectangular base?The diagram is not given. So, I will apply provide a general solution.
Using the similar shapes concept, the area of the rectangular base can be represented as:
Ratio = Height : Area
This gives
3 : 36 = 5 : Area
Express as fraction
36/3 = Area/5
Evaluate the quotient
12 = Area/5
Multiply both sides by 5
Area = 60
Hence, the area of the rectangular base is 60 square inches
Read more about areas at:
https://brainly.com/question/24487155
Use the open number line to find the difference.
423 – 160 = ____
An open number line is shown. A hop to the left of negative 100 begins at 423. A second hop to the left of negative 50 begins where the first hop ends. A third hop to the left of negative 10 begins where the second hop ends.
A.
363
B.
360
C.
263
D.
260
Two parents were shopping online for
new clothes for their kids. One mom
spent $26.50 on 3 shirts and 1 pair of
pants. Another mom spent $42 on 4 of
the same shirts and 2 of the same pairs
of the same pants. What was the cost
of each shirt and pair of pants?
Answer:
Shirt= $5.50
Pant=$10
Step-by-step explanation:
Let's shirt be 'x' and pant be 'y'
=}. 3x + y = $26.50
4x + 2y = $42
=}. 3x + y = $26.50
2x + y = $21. ( then first term minus
second term )
=}. x = $ 5.50
Now, y = $26.50 - 3x
= $26.50 - 16.50
= $10
Thx I hope it will be helpfulSolve the following inequalities if it is known that function f is increasing on its domain f(4x-3)≥f(2-x^2), Df=(-8,4)
Solve the following inequalities if it is known that function f is decreasing on its domain f(5-x^2)≥f(3x-5), Df=(-∞,4)
The functions f(4x-3)≥f(2-x^2) and f(5-x^2)≥f(3x-5) are quadratic functions
The values of the inequalities are -5 ≤ x ≤ 1 and -5 ≤ x ≤ 2
How to solve the inequalities?Inequality 1: f(4x - 3) ≥ f(2 - x^2), Df = (-8 , 4)
The function increases at (-8,4).
So, we have:
4x - 3 ≥ 2 - x^2
Rewrite as:
x^2 + 4x - 2 - 3 ≥ 0
Evaluate the like terms
x^2 + 4x - 5 ≥ 0
Expand
x^2 + 5x - x - 5 ≥ 0
Factorize the expression
x(x + 5) - 1(x + 5) ≥ 0
Factor out x + 5
(x - 1)(x + 5) ≥ 0
Solve for x
x ≥ 1 or x ≥ -5
Rewrite as:
-5 ≤ x ≤ 1
Inequality 2: f(5 - x^2) ≥ f(3x - 5), Df=(-∞,4)
The function decreases at (-∞,4).
So, we have:
5 - x^2 ≥ 3x - 5
Rewrite as:
x^2 + 3x - 5 - 5 ≤ 0
Evaluate the like terms
x^2 + 3x - 10 ≤ 0
Expand
x^2 + 5x - 2x - 10 ≤ 0
Factorize the expression
x(x + 5) - 2(x + 5) ≤ 0
Factor out x + 5
(x - 2)(x + 5) ≤ 0
Solve for x
x ≤ 2 or x ≤ -5
Rewrite as:
-5 ≤ x ≤ 2
Hence, the values of the inequalities are -5 ≤ x ≤ 1 and -5 ≤ x ≤ 2
Read more about inequalities at:
https://brainly.com/question/11234618
The Brooks family is selecting a furniture set. A furniture set has a bed and a dresser. There are 2 beds and 6 dressers to select from. How many different
furniture sets could they select?
What is I C T computer SCHOOL hi zip am SC 9
Step-by-step explanation:
Different means to minus, so minus 2 from 6. Which gives you the answer 4.
Find the missing side length using the Pythagorean Theorem.
a²+6² = c²
Answer:
18
Step-by-step explanation:
Hello!
In the Pythagorean theorem, the summation of the square of the legs in a right triangle is equal to the square of the hypotenuse.
Let a and b be the legs, and c is the hypotenuse.
a² + b² = c²
In this equation, the hypotenuse is 30, and the measure of one leg is 24.
We can solve this by plugging in the values.
a² + b² = c²24² + b² = 30²576 + b² = 900324 = b²b = 18So the missing side length is 18.
Your company offers three cell phone plans. The details are below:
Plan A allows 450 minutes for $39.99 with .25/minute for each minute over 450.
Plan B allows 900 minutes for $59.99 with .30/minute for each minute over 900.
Plan C allows 1500 minutes for $99.99 with .35/minute for each minute over 1500.
Write a report detailing the following:
An equation or inequality to represent each plan above.
Determine for how many minutes each plan is the best option for two customers. Customer Smith uses roughly 750 minutes per month. Customer Jones uses roughly 1350 minutes per month. Which plan should they choose and why?
Include a detailed explanation of your work, which scenario is better, and why.
Write a summary paragraph for your employees that will be answering and making phone calls.
Answer:
Smith should use 900 minute plan and Jones should use 1500 minute plan
Step-by-step explanation:
There are best answers
1. Equations/Inequalities for Each Plan:
Plan A: Cost = $39.99 + 0.25 * (m - 450), m ≤ 450
Plan B: Cost = $59.99 + 0.30 * (m - 900), m ≤ 900
Plan C: Cost = $99.99 + 0.35 * (m - 1500), m ≤ 1500
2. Best Plan for Customers:
Customer Smith (750 min): Plan B ($59.99)
Customer Jones (1350 min): Plan C ($84.99)
3. For both customers, Plan B offers the best value for 750 minutes, while Plan C is optimal for 1350 minutes due to its lower cost per minute overages.
4. Plan A is the least cost-effective for both. The chosen plans reflect the importance of base minutes and overage charges.
1. Equations/Inequalities for Each Plan:
Let's denote the number of minutes used as "m."
Plan A:
Cost: $39.99 for 450 minutes, then $0.25/minute for each additional minute.
Equation: Cost = $39.99 + 0.25 * (m - 450), if m > 450
Inequality: m ≤ 450
Plan B:
Cost: $59.99 for 900 minutes, then $0.30/minute for each additional minute.
Equation: Cost = $59.99 + 0.30 * (m - 900), if m > 900
Inequality: m ≤ 900
Plan C:
Cost: $99.99 for 1500 minutes, then $0.35/minute for each additional minute.
Equation: Cost = $99.99 + 0.35 * (m - 1500), if m > 1500
Inequality: m ≤ 1500
2. Determine the Best Plan for Customers:
Let's evaluate the cost for both customers using the given plans:
Customer Smith:
Usage: 750 minutes
Plan A: Cost = $39.99 + 0.25 * (750 - 450) = $112.49
Plan B: Cost = $59.99
Plan C: Cost = $99.99
Best Plan: Plan B ($59.99)
Customer Jones:
Usage: 1350 minutes
Plan A: Cost = $39.99 + 0.25 * (1350 - 450) = $297.49
Plan B: Cost = $59.99 + 0.30 * (1350 - 900) = $374.99
Plan C: Cost = $99.99 + 0.35 * (1350 - 1500) = $84.99
Best Plan: Plan C ($84.99)
3. Explanation and Recommendation:
Customer Smith's usage of roughly 750 minutes falls within the range of Plan B's base minutes (900) and is more cost-effective with Plan B. However, for Customer Jones, who uses around 1350 minutes, Plan C offers a lower overall cost due to its higher base minutes (1500). Plan A is the least cost-effective option for both customers due to its lower base minutes and higher per-minute charges.
4. Summary for Employees:
Dear Team,
When assisting customers with choosing a cell phone plan, please consider the following options:
Plan A: $39.99 for 450 minutes, then $0.25/minute.
Plan B: $59.99 for 900 minutes, then $0.30/minute.
Plan C: $99.99 for 1500 minutes, then $0.35/minute.
For customers using around 750 minutes per month, recommend Plan B for its competitive pricing. For customers using around 1350 minutes, advise them to opt for Plan C to optimize cost efficiency. Always ensure to guide customers toward the most suitable plan based on their usage patterns.
Thank you for your dedication to excellent customer service.
Sincerely,
[Your Name]
[Your Position]
To know more about Equations:
https://brainly.com/question/29657983
#SPJ3
Use the quadratic formula to solve the equation: y = x2 - 3x - 1
Group of answer choices
x = 5.6 and -1.3
x = 3.3 and -.3
x = -5.4 and -.4
x = 6.3 and 3.2
Answer:
3.3 and -0.3
Step-by-step explanation:
Using the quadratic formula plug in the a, b, and c values in this equation into the formula and you get 3.3 as a result. Not sure where the 0.3 part came from since it is not the opposite equation, but 3.3 is for sure correct. Work is linked below.
w = 4, x = 5, and y = 6
/ = fraction
8x - (6 + y)
w 3/4 = x²
y² - 0.5w
w/4 + 3(x+y)
Answer:
28, 28, 34, 34
Step-by-step explanation:
8x - (6 + y)
8(5) - (6 + 6)
40-12
28
w ¾ + x²
4(¾) + 5²
3 + 25
28
y² - 0.5w
6² - 0.5(4)
36 - 2
34
w / 4 + 3(x + y)
4 / 4 + 3(5 + 6)
1 + 3(11)
34
which of the points shown below given by the equation y=x
Answer:
I believe its D
Step-by-step explanation: X and Y are both -3
The national cost C in billions of dollars for dental services can be modeled by the linear equation c=2.85n+30.52, where n is the number of years since 1990. What would be the cost in billions of dollars in 2014?
Answer:
c=98.92
Step-by-step explanation:
first I figured out the number of years between 1990 and 2014.I basicly just subtracted 1990 from 2014 then times it by 2.85 the added 30.52
The cost in billions of dollars in 2014 would be 98.92
What is the unitary method?The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.
We are given that national cost C in billions of dollars for dental services can be modeled by the linear equation c=2.85n+30.52, where n is the number of years since 1990.
Then c=2.85n+30.52
Solving then subtracted 1990 from 2014
2014 - 1990
= 24
Now
c = 2.85 (24) +30.52
c = 68.4 +30.52
c = 98.92
Hence, the cost in billions of dollars in 2014 would be 98.92
Learn more about the unitary method, please visit the link given below;
https://brainly.com/question/23423168
#SPJ2
Bernie bought five 30 L buckets of lawn fertilizer. How much fertilizer did he have in all?
Answer:
5 × 30 L = 150 L
______________
A store gives away gift bags during a sale. Of these gift bags, 50% are green, 20% are yellow, and 30% are blue. The average number of items in each green bag is 8. The average number of items in each yellow bag is 5. The average number of items in each blue bag is 8. What is the average number of items in all the gift bags? Enter your answer as a decimal in the box.
Find the missing angles for every point here
In order to find the missing angles, we can see that vertically opposite angles and corresponding angles are equal.
46° + 82° + No. 4 = 180°
No. 4 = 180° - 128° = 52°
Therefore: No. 4 = No. 1 = 52° (vertically opposite angles)
What is angle?In geometry, an angle is actually known to be the figure that is created by two rays that actually meet at an end point that is common to the both rays. It is represented by the symbol: ∠.
So, we can see that:
Line a || Line b and Line c || Line d
46° = 7 (corresponding angles)
So, 46° + 82° + No. 4 = 180°
Thus, No. 4 = 180° - 128° = 52°
Therefore:
No. 4 = No. 1 = 52° (vertically opposite angles)
No. 2 = 180° - 52° = 128° (angles on a straight line)
No. 2 = No. 3 = 128° (vertically opposite angles)
No. 7 = No. 6 = 46° (vertically opposite angles)
No. 8 = 180° - 46° = 134° (angles on a straight line)
No. 8 = No. 5 = 134° (vertically opposite angles).
82° = No. 11 (vertically opposite angles)
No. 9 = 180° - 82° = 98° (angles on a straight line)
No. 9 = No. 10 = 98° (vertically opposite angles)
No. 9 = No. 15 = 98° (alternate angles)
No. 13 = No. 15 = 98° (vertically opposite angles)
No. 12 = No. 14 = 82° (vertically opposite angles)
46°= No. 17 (vertically opposite angles)
No. 18 = 180° - 46° = 134° (angles at a point)
No. 18 = No. 16 = 134° (vertically opposite angles)
No. 19 = 180° - (46° + 82°) = 52° (sum of angles in a triangle)
No. 19 = No. 22 = 52° (vertically opposite angles)
No. 20 = 180° - 52° = 128° (angles on a straight line).
No. 20 = No. 21 = 128° (vertically opposite angles)
No. 25 = No. 2 = 128° (corresponding angles)
No. 25 = No. 24 = 128° (vertically opposite angles)
No. 23 = No. 26° (vertically opposite angles).
So, all the angles are:
1= 52°
2= 128°
3= 128°
4= 52°
5= 134°
6= 46°
7= 46°
8=134°
9= 98°
10= 98°
11= 82°
12= 82°
13= 98°
14= 82°
15= 98°
16= 134°
17= 46°
18= 134°
19= 52°
20= 128°
21= 128°
22= 52°
23= 52°
24= 128°
25= 128°
26= 52°
Learn more about angles on https://brainly.com/question/26167358
PLEASE HELP
The graph below shows a company's profit f(x), in dollars, depending on the price of pens x, in dollars, sold by the company:
Graph of quadratic function f of x having x intercepts at ordered pairs 0, 0 and 6, 0. The vertex is at 3, 120.
Part A: What do the x-intercepts and maximum value of the graph represent?What are the intervals where the function is increasing and decreasing, and what do they represent about the sale and profit?
Part B: What is an approximate average rate of change of the graph from x = 3 to x = 5, and what does this rate represent?
Part C: Describe the constraints of the domain.
Answer:
See below ↓
Step-by-step explanation:
Part A
The x-intercepts represents when the profit of the company is 0 dollars. It means they are making no profit when selling the pens at that pricePart B
y-value when x = 3 ⇒ 120y -value when x = 5 ⇒ 60rate of change = Δy/Δx = -60/2 = -30This rate represents the depreciating profit of the company when increasing the price of a pen from $3 to $5Part C
Domain of the graph is only true for positive values of yDomain ⇒ 0 ≤ x ≤ 6Answer:
Part A
The x-intercepts are when f(x) = 0.
Since x represents the price of pens, and f(x) represents the company's profit, the x-intercepts give the price of the pens when the profit is zero.
⇒ the profit is zero when the price of pens are $0 and $6
The maximum value of the graph (vertex) represents the cost of pens when the profit is at its highest. Therefore, the optimal amount to price the pens to get the maximum profit.
⇒ maximum profit of $120 occurs when the pens are priced at $3
Part B
[tex]\sf average \ rate \ of \ change=\dfrac{change \ in \ y}{change \ in \ x}[/tex]
From inspection of the graph, f(3) = 120 and f(5) ≈ 60
[tex]\sf \implies average \ rate \ of \ change=\dfrac{60-120}{5-3}=-30[/tex]
This means that as the price of the pens increases by $1 (between $3 and $5), the average profit decreases by approximately $30.
Part C
The domain is the set of input values (x-values). As the price of a pen cannot be less than zero, the domain will be x ≥ 0
Unless the company is happy to make a loss, the restricted domain should be 0 ≤ x ≤ 6
length of a rectangle is three times its width. if the length of the rectangle is 64 in, find the width and length
Answer:
Length: 64
Width = 21 1/3
Step-by-step explanation:
Width = Length 64 * 1/3 Width
Width = 21.3333333 or 21 1/3
Answer:
[tex]l=64 in[/tex]
[tex]w=21.3333in[/tex]
Step-by-step explanation:
[tex]l=3w[/tex]
[tex]\frac{64}{3} =21.3333[/tex]
pls help...
What is the mode for the set of data?
Answer:
9
[tex]\rule{70mm}{2pt}[/tex]
Step-by-step explanation:
In statistics, the mode is the value that is repeatedly occurring or you can say that has higher frequency in a given set of numbers or values. For instance in (1, 2, 5, 6, 2, 3) mode is 2 because it has appeared in the given set twice.
As in the given problem, the cross represents the number of a particular number, indicating whether the given number is repeated or not. And if repeated, how many times?
→ 5, 6, 10 = 1 (number of repetition; each)
→ 7, 8 = 2 (number of repetition; each)
→ 9 = 3 (number of repetition)
Therefore, the mode for the given set of data is 9.
Please answer the following questions
An absolute value inequality can be solved using a union or an intersection depending on which sign it is true or false
Answer:
True????????????????????
The statement that "An absolute value inequality can be solved using a union or an intersection depending on which sign it is" is true.
What is Absolute Value Inequality?Absolute value inequalities are kind of inequality expressions which includes the absolute value symbol in the expression.
For example : |x - 5| < 4 is an absolute value inequality.
Given statement is that,
An absolute value inequality can be solved using a union or an intersection depending on which sign it is.
If an absolute value inequality has a sign as "> 0", then the solution contains every real numbers but not values which makes the inequality 0.
in this case, union is used.
Now, if the inequality is "<" or "≤" with a positive number, the we use the intersection.
Hence the given statement is true.
Learn more about Absolute value Inequalities here :3
https://brainly.com/question/30201926
#SPJ2