Answers
Using the attached process, the square roots and cube roots are estimated as follows:
1. √15 = 3.81
2. √44 = 6.6.
3. √81 = 9
4. ∛12 = 2.88.
5. ∛125 = 5
6. ∛320 = 6..8
2)The mistake made by Jan is in the place of 17cm we get 13cm by sing Pythagorean theorem. Therefore, perimeter is 30cm.
3) The error of Joshua is that he miscalculated the third length of the triangle.
From the Pythagorean theorem, we have learned that a²+b²=c²
What is Pythagorean theorem?In mathematics, the Pythagorean Theorem is the fundamental relationship in Euclidean geometry between the three sides of a right triangle. It states that the area of a square whose side is the hypotenuse is equal to the sum of the areas of the squares on the other two sides.
The attachment depicts the procedure we will use.
The first step is to make a list of all the perfect squares from 1 to 100, followed by all the perfect cubes from 1 to 1000.
1 to 100 perfect squares; 4, 9, 16, 25, 36, 49, 64, 81, 100
1 to 1000 perfect cubes; 1, 8, 27, 64, 125, 216, 343, 512, 729, and 1000.
1) √15
The perfect squares that are nearest are 9 and 16.
√9 < √15 < √16
⇒ 3 < √15 < 4
Now, √15 is between 3 and 4.
We can estimate √15 as 3.81
2) √44
The perfect squares that are nearest are 36 and 49.
√36 < √44 < √49
⇒ 6 < √44 < 7
Now,√44 is between 6 and 7.
So, we can estimate √44 as 6.6
3) √81
Because this is a perfect square, the approach used to estimate non-perfect squares does not apply. Thus;√81 = 9
4) ∛12
The perfect cubes that are nearest are 8 and 27
Thus; ∛8 < ∛12 < ∛27
⇒ 2 < ∛12 < 3
Now,√12 is between 2 and 3.
So, we can estimate ∛12 as 2.88.
5) ∛125
Because this is a perfect cube, the approach used to estimate non-perfect squares does not apply. Thus;∛125 = 5
6) ∛320
The perfect cubes that are nearest are 216 and 343
Thus; ∛216 < ∛320 < ∛343
⇒ 6 < ∛320 < 7
Now, ∛320 is between 6 and 7.
So, we can estimate ∛320 as 6..8
2) Perimeter of the triangle=L+L+L
Given, Perimeter=5cm+12cm+17cm
=34cm
The mistake he made wrong is,
By using Pythagorean theorem,
√a²+b²=c²
√5²+12²=c²
√25+144=c²
√169=c²
13=c
Therefore, perimeter of the triangle is 5cm+12cm+13cm=30cm
3) First we calculate the third length of the triangle x.
As the triangle is a right triangle we use Pythagorean theorem.
x²=7²+7²
x²=2(7²)
Squaring on both sides, we get
x=√2(7²)
x=7√2
The other shape in the given figure is square.
Therefore the perimeter P is given by,
P=7+x+x+x+7
So, P=7+7√2+7√2+7√2+7
P=14+21√2
Hence, the error of Joshua is that he miscalculated the third length of the triangle.
From the Pythagorean theorem, we have learned that a²+b²=c².
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Related Questions
What is an equation of the line that passes through the points (4, 4) and (8, 5)?
Answers
Answer:
y=0.25x+3
Step-by-step explanation:
use desmos graphing calculator and put the coordinates into a table
Given L(-6, -7) and M(3, 6), what is the length of LM to the nearest tenth?
LM
Answers
Answer:
LM ≈ 15.8
Step-by-step explanation:
calculate the length d using the distance formula
d = [tex]}\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }[/tex]
with (x₁, y₁ ) = L (- 6, - 7 ) and (x₂, y₂ ) = M (3, 6 )
LM = [tex]\sqrt{(3-(-6))^2+(6-(-7))^2}[/tex]
= [tex]\sqrt{(3+6)^2+(6+7)^2}[/tex]
= [tex]\sqrt{9^2+13^2}[/tex]
= [tex]\sqrt{81+169}[/tex]
= [tex]\sqrt{250}[/tex]
≈ 15.8 ( to the nearest tenth )
Express cos L as a fraction in simplest terms.
15
39
K
36
Answers
The representation of cos L in simplest term is 5/13. It can be obatined by trigonometric ratios.
What are trigonometric ratio?
The ratio of sides of a right angled triangle is known ars trigonometric ratios. There are six trigonometric ratios. Which are as follows:
sin = P/H, cos = B/H, tan = P/B
cosec = H/P, sec = H/B, cot = B/P
Here, P is perpendicular, H is hypotaneous, and B is base. These ratios simplify the calculation.
SInce the angle is not specified hence, consider the given angle is L. Now, L is given angle hence, the base will be 15 and hypotenous will be 39.
Now, consider the trigonometric ratio of cos.
[tex]cosL=\frac{Base}{Hypotenuse}\\[/tex]
Subsitute 15 for base and 39 for hypotenuse in the above expression.
[tex]cosL=\frac{15}{39}\\=\frac{5}{13}[/tex]
Hence, the representation of cos L in simplest term is 5/13. It can be obatined by trigonometric ratios.
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-4x+11y=-32
-9x+4y=11
elimination
Answers
Answer:
x = -3; y = -4
Step-by-step explanation:
We can start by eliminating x, which will give us y:
[tex]9(-4x +11y=-32)\\-4(-9x+4y=11)\\\\-36x+99y=-288\\36x-16y=-44\\\\83y=-332\\y=-4[/tex]
Now we can plug in -4 for y in the first equation to find x:
[tex]-4x+11(-4)=-32\\-4x-44=-32\\-4x=12\\x=-3[/tex]
HELP PLEASE!
The answer choices are
A) 240
B) 270
C) 210
D) 120
Answers
If the rotation is clockwise the angle is 120°.
If the rotation is counterclockwise the angle is 240°
The correct options are A and D.
What is the angle of rotation that maps P to G?
We assume that the rotation is clockwise.
First, we can see that the rotation from P to F is just a rotation of 90°.
(point P as at 9 on a clock and point F is at 12 on a clock).
To go from point F to G, we need to move one of the sections defined by the dashed lines, and we know that each one of these measures 30°, then we need to add another 30° to the angle.
90° + 30° = 120°
Then the angle of rotation to map P to G is 120°.
The correct option is D.
Then if the rotation is counterclockwise, the rotation will be of 240°.
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A company manufactures two types of electric hedge trimmers, one of which is cordless. The cord-type trimmer requires 2 hours to make, and the cordless model requires 10 hours. The company has only 1000 work hours to use in manufacturing each day, and the packaging department can package only 200 trimmers per day.
(a) Write the inequalities that describe the constraints on the number of each type of hedge trimmer produced. (Let x represent the number of cord-type models, and let y represent the number of cordless models.)
Answers
There are commonly used four inequalities:
Less than = <
Greater than = >
Less than and equal = ≤
Greater than and equal = ≥
The inequalities that describe the constraints on the number of each type of hedge trimmer produced are:
x + y ≤ 200
2x + 10y ≤ 1000
What is inequality?It shows a relationship between two numbers or two expressions.
There are commonly used four inequalities:
Less than = <
Greater than = >
Less than and equal = ≤
Greater than and equal = ≥
We have,
Total number of hours = 1000
Total number of trimmers = 200
Let x represent the number of cord-type models,
Let y represent the number of cordless models.
Now,
x + y ≤ 200
2x + 10y ≤ 1000
Thus,
The inequalities that describe the constraints on the number of each type of hedge trimmer produced are:
x + y ≤ 200
2x + 10y ≤ 1000
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When Terri makes fruit salad she uses 4 oranges and 3 cups of grapes for every 2 bananas. If Terry uses five bananas how many oranges and how many cups of grapes will she use? Write and solve a proportion
Answers
Answer:
7.5 cups of grapes
Step-by-step explanation:
4o:3g:2b
With 5b, there's an increase in 2.5 from 2b. (divide 5b/2b)
Since the increase in all the other fruits is proportional by the same amount of 2.5.
This leaves you with 10o:7.5g:5b
kay walks upstairs yo make her legs stronger . Every day at work, she walks up 9 flights of stairs . If there are 13 steps in 1 flight of stairs in 1 flight of stairs , how many steps does kay climb in 5 days at work
Answers
In 5 days at work, kay climbs 585 steps
How to find how many steps kay climbsIf there are 13 steps in 1 flight of stairs then 9 flights of stairs will be
= 13 * 9
= 117 steps
Every day Kay climbs 117 steps in 9 flights in 5 days kay will climb
= 117 * 5
= 585 steps
Kay climbs 585 steps in a 5 days at work
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Determine the domain of the rational function ƒ(a) = 3/a+5
Answers
Answer:
domain { a ∈ R , a ≠ - 5 }
Step-by-step explanation:
the denominator of f(a) cannot equal zero as this would make f(a) undefined. Equating the denominator to zero and solving gives the value that a cannot be.
a + 5 = 0 ( subtract 5 from both sides )
a = - 5 ← excluded value
domain { a ∈ R, a ≠ - 5 }
Graph stuff
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Answers
The quadratic equation y = x² - 8 · x + 18 represents the parabola shown in the figure.
How to derive the quadratic equation behind the graph of the parabola
In this problem we find a representation of a parabola, which is described algebraically by quadratic equations, that is, polynomials of the form:
y = a · x² + b · x + c
Where a, b, c are the coefficients of the polynomial.
We can determine the value of the coefficients from the knowledge of three points set on Cartesian plane. First, select the points from Cartesian plane:
(x₁, y₁) = (0, 18), (x₂, y₂) = (4, 2), (x₃, y₃) = (7, 11)
Second, create a system of linear equations with three variables and three equations by replacing the variables x and y on the quadratic equation:
c = 18
16 · a + 4 · b + c = 2
49 · a + 7 · b + c = 11
Third, solve the system by numerical methods:
(a, b, c) = (1, - 8, 18)
Fourth, write the resulting quadratic equation:
y = x² - 8 · x + 18
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Solve using order of operations
16÷2×6-3
Answers
48 - 3
=46
The Order of Operations, also referred to as PEMDAS, is the rule that defines the sequence in which an expression with multiply operations can be solved.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
In this scenario, we are dividing, multiplying, adding, and subtracting numbers. This being laid out, lets begin.
1. Multiply and divide (left to right).
[tex]16[/tex] ÷ [tex]2 * 6 = 48[/tex]
[tex]=48-3[/tex]
2. Add and subtract (left to right).
[tex]48-3=45[/tex]
Hence, our final solution after using the order of operations would be [tex]45[/tex].
Hope this helps!
Suppose a mutual fund has total assets of $25,500,000 and liabilities of $2,100,000. Currently there are 10,200,000 shares outstanding. Determine the net asset value of the fund? Round to the nearest cent. Show your work
Answers
The net asset value of the given mutual fund will be 2.29.
What is the arithmetic operator?Arithmetic operators are four basic mathematical operations in which summation, subtraction, division, and multiplication involve.,
Division = divide any two numbers or variables called division.
Multiplication = to multiply any two or more numbers or variables called multiplication.
As per the given,
Total assets = $25,500,000
Liabilities = $2,100,000
Total shares = 10,200,000
Net asset = (total assets - total liability)/total shares outstanding
Net assets = (25,500,000 - 2,100,000)/10,200,000
Net assets = 2.29
Hence "The net asset value of the given mutual fund will be 2.29".
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what is the value of the expression 0.307+13.16+0.8
Answers
Answer:
The Answer of the 0.307+13.16+0.8 is 14.267
HELP ME OUT THANKS SO MUCH
Answers
Hope this helps
Answer:
R would equal 12
Step-by-step explanation:
select independent or not independent for each situation
Answers
Answer: the first one
Step-by-step explanation:
À class counted how many banks were in all the nearby cities.
Richmond has________more banks than Dollarville
Answers
Answer:
4
Step-by-step explanation:
Richmond has 7 and Dollarville has 3. 7 - 3 = 4
Select all of the verbal phrases which can be represented by the expression 25.75x + 10
Answers
Answer:
B: 25.75 times a number x, plus 10 | D: the product of 25.75 and x, plus 10
Step-by-step explanation:
B: 25.75 times "x" = 25.75x + 10
D: The product of 25.75 and x = 25.75x + 10
Kathryn invests $1000 in one account and $2200 in an account paying 3 % higher interest. At the end of one year she had earned $130 in interest. At what rates did she invest?
Answers
She invested $1000 at 2% and 2200 at 5% simple interest.
What is simple interest?We know simple interest (SI) is given by SI = (p×r×t)/100, where
p = principle, r = rate in percentage, and t = time in years.
Given, P₁ = 1000, P₂ = 2200, assuming r₁ = x% and r₂ = (x + 3)% and the sum of simple interest obtained from both these investments is $130.
∴ (1000×x×1)/100 + {(2200×(x + 3)×1}/100 = 130.
10x + 22x + 66 = 130.
32x = 64.
x = 2.
So, the rate of interest is 2% and 5%.
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Find the sum of the arithmetic sequence 1, 3, 5, 7, … , 99.
Answers
The sum of the arithmetic sequence 1, 3, 5, 7, … , 99 is 2525
What is Sequence?Sequence is an enumerated collection of objects in which repetitions are allowed and order matters.
Given sequence is 1, 3, 5, 7, … , 99.
It is a arithmetic sequence, the difference between two consecutive terms will be same
d=3-1=2
first term a=1
l=last term =99
We need to find 99 is which term in the sequence
Aₙ = a + ( n - 1 ) d
99=1+(n-1)2
99=1+2n-2
99=2n-1
100=2n
Divide both sides by 2
50=n
Now we need to find the sum of 50 terms
Sₙ=n/2(l+d)
=50/2(99+2)
=25(101)
=2525
Hence, the sum of the arithmetic sequence 1, 3, 5, 7, … , 99 is 2525
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A triangular banner for the basketball championship hangs in the gym. It has an area of 48 square feet. What is the length of the base and height (in ft), if the base is two-thirds of the height?
Answers
From the area of a triangle, the height of the triangle is 12ft
Area of TriangleThe area of a triangle is defined as the total region that is enclosed by the three sides of any particular triangle. Basically, it is equal to half of the base times height, which is given by
A = 1/2 b * h
A = Area of triangleb = baseh = heightIn the given question, the base is two-thirds of the height.
b = 2/3h
Let's substitute the values into the formula
A = 1/2 * 2/3h * h
A = 2/6 * h²
A = 1/3h²
48 = 1/3h²
h² = 48 * 3
h = √144
h = 12ft
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C. Solve the following;
1. Elisse has 20 meters of ribbon. How many 15 cm of ribbon can be cut from it?
2. Mr. JB has a rectangular lot that measures 550 meters by 0.75 km. What is the area of the land in square meter. He is selling the whole lot for 206, 250,000 pesos, how much is the price per square meter?
3. Drinking 8 glasses of water a day is good for your health. If each glass of water is equivalent to 148 mL, how many liters of water you need to consume everyday.
4. Your baby brother has a body temperature of 100°F. What is his body temperature in °C ? Does he has a normal body temperature?
5. Your mother asked you to buy 2.5kg of sugar. Each pack of sugar in the store weighs 250 grams. How many packs of sugar will you buy?
6. The 120 grams powdered milk make 12 cups of milk. How many kilograms of powdered milk can produce 60 cups of milk. How many liters is 60 cups of milk?
7. You have 8 modules to study in a day. Your teacher gave you this schedule for 5 days from Monday to Friday.
Answers
Answer:
133, 412500, 500, 1.184, 37.8, 10, 0.6
Step-by-step explanation:
If we think about how many centimeters are in a meter, we know that
1m = 100cm
Using this, we can see that
20m = 2000cm
Now divide by 15:
2000 ÷ 15 ≈ 133
She can make roughly about 133 ribbons.
To solve the next question, we need to know how many kilometers are in a meter
1km = 0.001m
Let's covert 0.75 into m:
0.75 × 1000 = 750
Now solve for the area:
750 × 550 = 412500
The area of the rectangle is 412500
If he is selling the home for 206,250,000 pesos,
206,250,000 divided by 412500
206,250,000 ÷ 412500 = 500
The price per square meter is 500
If each glass is 148 milliliters, and we need to convert that into liters, we can use the equation:
1L = 1000mL
So converting 148 into liters,
148mL = 0.148L
Now, multiply by 8.
0.148 × 8 = 1.184L
We need to convert 100 Fahrenheit to Celsius.
100 F ≈ 37.8
This is definitely not a normal body temperature.
We can convert grams to kilograms using the equation:
1kg = 1000 g
Converting 2.5kg to g would look like this:
2.5kg = 2500g
250g × 10 = 2500g
We need to buy 10 packs of sugar.
If 120 grams of powdered milk can produce 60 cups of milk, and we need to figure out how many kg can produce the same amount, we use the equation:
1kg = 1000g
Converting 120g to kg would look like this:
120 ÷ 1000 = 0.120
Now, we need to figure out how many times 12 goes into 60.
12 × 5 = 60
Now we multiply 0.120 by 5
0.120 × 5 = 0.6
I hope this helps!
Find X and RDB
X= ______
RDB=______
Answers
Using the secant-secant theorem,
[tex]\frac{13x+7-60}{2}=5x-10 \\ \\ 13x-53=10x-20 \\ \\ 3x-53=-20 \\ \\ 3x=33 \\ \\ \boxed{x=11} \\ \\ m\angle RDB=5(11)-10=\boxed{45^{\circ}}[/tex]
The measure of the angle ∠RDB will be 45°.
What is the angle of the chord?In geometry, a chord of a circle is a straight line segment whose endpoints both lie on the circle. A diameter of a circle is the longest chord, and it passes through the centre of the circle.
Calculate the value of x as below,
( 13x + 7 - 60 ) / 2 = 5x - 10
13x - 53 = 10x - 20
3x - 53 = -20
3x = 33
x = 11
The measure of the angle ∠RDB is,
∠RDB = 5x - 10
∠RDB = ( 5 x 11 ) - 10
∠RDB = 45°
Therefore, the value of an angle ∠RDB will be 45°.
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need help pelase i need it
Answers
Door:80( actual height) 44( height on set)
Table 28( actual height) 15.4 ( height on set)
Stool 18 ( actual height) 9.9 ( height on set)
Step-by-step explanation:
Times the actual height inches by 0.55 and you get your height on set.
Which of the following is a requirement for employees who must wear PPE?
Answers
The option that's a requirement for employees who must wear PPE is C. Participate in PPE training.
What is a personal protective equipment?Personal protective equipment (PPE) is clothing that is comfortable to wear in order to reduce the risk of hazards at work that cause serious illnesses and injuries.
Personal protective equipment (PPE) will be divided into the following categories for this purpose: eye and face protection, hand protection, body protection, respiratory protection, and hearing protection.
Personal protective equipment (PPE) should be used when all other measures to control exposure are ineffective. It only protects the wearer while they are wearing it. PPE offers no protection if it fails.
All personal protective equipment should be designed and built safely, and it should be kept clean and reliable. It should be comfortable for workers to use. Personal protective equipment that does not fit properly can mean the difference between being safe and being dangerously exposed. Employers must provide personal protective equipment to their employees and ensure its proper use when engineering, work practices, and administrative controls are not feasible or provide adequate protection
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Complete question
Which of the following is a requirement for employees who must wear PPE?
a. Speak to the. project manager.
b. Get necessary clothes.
C. Participate in PPE training.
A function's graph is shown below.
If you would like to enlarge the graph or make numbers and letters easier to read, you may click on it to open it in a new window. You may then enlarge that window with your mouse. To further enlarge the image, use your browser's zoom capabilities. On a PC this is usually ctrl shift + (and zooming out is ctrl -). On an Apple computer this is usually apple shift + (and zooming out is apple -).
Use interval notation to answer the following questions.
The domain of this function is ?
The range of this function is ?
Answers
The domain and the range of the function are given as follows:
Domain: (-2,3].Range: [-8, 2).How to obtain the domain and the range of the function?The domain of a function is composed by the set that contains all possible values assumed by the input of the function.
On a graph, the input of the function is given by the values of x, hence the domain of the graphed function is given by the following interval:
(-2,3].
The meaning of the circles on the intervals is of:
Open circle: open interval.Closed circle: closed interval.The range is composed by the set containing all the values assumed by the output of the function.
Hence, on the graph, the range is composed by the values of y of the function, which are given as follows:
[-8, 2).
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help meeeeeeeeeeeeeeee pleaseeeeeeehelp meeeeeeeeeeeeeeee pleaseeeeeeehelp meeeeeeeeeeeeeeee pleaseeeeeeehelp meeeeeeeeeeeeeeee pleaseeeeeeehelp meeeeeeeeeeeeeeee pleaseeeeeeehelp meeeeeeeeeeeeeeee pleaseeeeeee
Answers
Answer: 23.1, 13.35718336 years or 14 rounded
Step-by-step explanation:
[tex]Given:A= 23.1e^{0.0152t}[/tex]
when A = end amount, and t = years after 2000
Part A).
What was the population of the state in 2000. According to our function, this would be when t = 0
[tex]23.1e^{0.0152(0)}\\\\=23.1(1)\\\\=\boxed{23.1}[/tex]
Part B).
When will the population of the state reach 28.3 million?
This would be when A = 28.3
[tex]28.3=23.1e^{0.0152t}\\\\\frac{28.3}{23.1} =\frac{23.1e^{0.0152t}}{23.1} \\\\\frac{28.3}{23.1} =e^{0.0152t}\\\\ln^{\frac{28.3}{23.1} }=ln^{e^{0.0152t}}\\\\ln^{\frac{28.3}{23.1} }=0.0152t\\\\t=\frac{ln^{\frac{28.3}{23.1} }}{0.0152} \\\\\boxed{t=13.35718336 \ \ years}[/tex]
isabel drove 335 miles in 5 hours at the same rate how any miles would she drive in 8 hours
Answers
335/5=67
Therefore, if she was to drive eight hours she would drive 536 miles
Answer=536 miles
A carpenter states that it will take 21.5 hours
to build the deck. If the carpenter charges
$24.00 per hour, how much will the carpenter
be paid?
F
$45.50
G
$129.00
H
$504.00
J $516.00
Answers
Answer:
The carpenter will be paid $516.00
Step-by-step explanation:
1. Multiply
(Since the carpenter is being paid per hour, and the pay is $24.00, and the time it takes to work is 21.5, we can set up this equation):
21.5 x 24.00 = $516.00
May I have Brainliest please? My next rank will be the highest one: A GENIUS! Please help me on this journey to become top of the ranks! I only need 3 more brainliest to become a genius! I would really appreciate it, and it would make my day! Thank you so much, and have a wonderful rest of your day!
Chris bought a guitar for $77.00 and sold it for $126.28. What percent profit did Chris make on the guitar
Answers
Answer:
ten is the fight one
Step-by-step explanation:
True
Answer:
39%
Step-by-step explanation:
126.28 minus 77 is 49.28.
49.28 divided by 126.28 is 0.39 and a bunch of other numbers but round it up and its 0.39. move the decimal to the right two places and youve got 39%
hope this helped!
5. Find the volumes of the following sugar containers. Round to
Domino 1 decimal place.
SUGAR
a. Domino granulated sugar in canister: radius-1.56 inches;
height-6.93 inches
in³
b. Domino sugar cubes in box: length-15.5 cm; width-8.6 cm;
height-3.8 cm.
Domino
SUGAR CUBES
cm³
Answers
The volume of the canister is 36.7 in³. The volume of box is 482.6 cm³
To find the volume of a canister, we can use the formula V = πr²h, where V is the volume, r is the radius, and h is the height.
In this case, the canister has a radius of 1.56 inches and a height of 6.93 inches,
volume of canister = π × (1.56 inches)² × 6.93 inches
volume of canister = 36.7 in³
To find the volume of a box, we can use the formula V = lwh, where V is the volume, l is the length, w is the width, and h is the height.
In this case, the box has a length of 15.5 cm, a width of 8.6 cm, and a height of 3.8 cm
volume of box = 15.5 cm × 8.6 cm × 3.8 cm
volume of box = 482.6 cm³
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