The probability that a student chosen at random from a class has ginger hair is 5/14.
The probability that they have blonde hair is 9/28.
What is the probability that a student chosen from the class at random has either ginger or blonde hair?
Give your answer as a fraction in its simplest form.
Answer: The probability of a random student to have either ginger or blonde hair is 19/28.
Step-by-step explanation: Before anything is done, let's look and see what information the problem gives us and what we need to find out. We know that there's a 5/14 chance for a student to be ginger, and a 9/28 chance for them to be blonde. We need to find out the combined chance, as we want to know what the chances are for a student to have either hair color.
In order to do this, all we need to find is the sum of both fractions. Because the fractions have different denominators, we need to change one of them to match the other. 14 multiplied by 2 is equal to 28.
If we multiply both the numerator and denominator of 5/14 by 2, we get 10/28. Now, all we have to do is add that to 9/28. When we do that, we get 19/28.
19/28 cannot be simplified, so it is our final answer. Hope this helps!
A wedding menu has 5 starters, 3 mains, and 4 desserts. The list gives the meal options each attendee must choose from. a starter and a main, a main and a dessert, a starter, a main, and a dessert. How many different ways of choosing a meal for this wedding are there
There are 60 different ways of choosing a meal for this wedding.
How many different ways of choosing a meal?There were five distinct main courses available for selection.
There are a total of 15 possible main dish and salad combinations when ordering these 5 distinct main meals together with any one of the 3 available salads.
A total of 60 distinct main dishes, salads, and dessert combinations are conceivable by ordering one of the four potential deserts for each of the 15 various main meals and salad combinations.
60 distinct main dishes might be purchased since.
There are 60 different ways of choosing a meal for this wedding
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What are the x-intercept and the y intercept of the graph of 6x - 3y = 36?
The x-intercept and the y intercept of the graph of 6x - 3y = 36 are x = 6 and y = -12
How to determine the x-intercept and the y intercept of the graph?
From the question, we have the following parameters that can be used in our computation:
6x - 3y = 36
Set y to 0 to determine the x-intercept
So, we have the following representation
6x = 36
Divide by 6
x = 6
Set x to 0 to determine the y-intercept
-3y = 36
Divide by -3
y = -12
hence, the intercepts are x = 6 and y = -12
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Write the equation of the perpendicular bisector’s of the line AB given: A(1,3) & B(-3,5)
Answer:
y = 2x + 1
Step-by-step explanation:
[tex]\frac{5-3}{-3-1}[/tex] = [tex]\frac{2}{-4}[/tex] = [tex]\frac{1}{-2}[/tex]
Perpendicular slopes are the opposite reciprocals . So the slope of the line will be 2
slope (m) = 2
y = 3 You could use either point given. I chose (1,3)
x = 1 From the point given (1,3)
y = mx + b substitute in what you know and solve for b
3 = (2)(1) + b
3 = 2 + b Subtract 2 from both sides
1 = b
The y-intercept is 1.
y = mx + b
y = 2x + 1
carmen has 92 kilograms of clay. she has 5 students in her art class. how much clay does each student get
Answer:
18.4 kg of clay
Step-by-step explanation:
92 kg for 5 students
=> 92 : 5 = 18,4 kg for 1 student
Answer: 18.4 kg
Step-by-step explanation:
DATA :
total mass of clay = 92 kg
total students = 5
how much clay does each student get?
SOLUTION:
assuming that each student got equal amount of clay, we are simply going to divide ⇒92 by 5.
⇒92 ÷ 5
⇒18.4 kg ANSWER
hope that helps...
What is a 123 triangle?
This is a triangle whose three angles are in the ratio 1:2:3 and respectively measure 30° ( π/6), 60° ( π/3), and 90° ( π/2) and the sides are in the ratio 1:√3: 2.
These triangles are also known as special right triangles, such as 30-60-90 triangles, and 45°-45°-90° triangles. Among all right triangles, the 45°–45°–90° degree triangle has the smallest ratio of the hypotenuse to the sum of the legs, √2/2 and the greatest ratio of the altitude from the hypotenuse to the sum of the legs, √2/4.
The 30°-60°-90° triangle is the right triangle whose angles are in an arithmetic progression. The proof of this fact is simple and follows the fact that if α, α + δ, α + 2δ are the angles in the progression then the sum of the angles 3α + 3δ = 180°. By dividing by 3, the angle α + δ must be 60°. The right angle is 90°, and the remaining angle is 30°.
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What is .15 written as a rational number
Answer:
it is a rational number already
Step-by-step explanation:
Tom got a Mr. Potato Head for his birthday. It came with $3$ hairstyles, $2$ sets of eyebrows, $1$ pair of googly eyes, $2$ sets of ears, and $2$ sets of lips, a pair of regular shoes, and a bonus pair of clown shoes. If a complete Mr. Potato Head personality includes eyebrows, eyes, ears, lips, shoes and optionally hair, how many different wacky personalities can Tom come up with? Note that Mr. Potato Head can be bald. Note: You cannot "mix and match". For example, you cannot take the left eyebrow from one pair and the right eyebrow from the other pair.
Answer: Tom can come up with 13 different wacky personalities for Mr Potato Head.
Step-by-step explanation:
Tom can come up with 3 different hairstyles for Mr Potato Head, 2 sets of eyebrows, 1 pair of googly eyes, 2 sets of ears, and 2 sets of lips. He also has 2 pairs of shoes to choose from. If Mr Potato Head can be bald, Tom can also choose to not include a hairstyle.
In total, Tom can come up with 3+2+1+2+2+2+1=13 different combinations of features for Mr Potato Head. Since each combination represents a different personality, Tom can come up with 13 different wacky personalities for Mr Potato Head.
Jesse from Boston goes to his grandpa Isaac in New York by bus at an average speed of 35 mph and it takes him 6 hours. In a while, Jesse and Isaac go back from New York to Boston in Isaac's car at an average speed of 42 mph. How long does Jesse's trip from New York to Boston take?
Answer:
The Average Speed is 48mph
Step-by-step explanation:
I've done this problem before, I wish A+'s upon all that read this answer. take care man!
The time it takes for Jesse to complete his trip from New York to Boston is 5 hours.
How long does Jesse's trip from New York to Boston take?To calculate the time it takes for Jesse's trip from New York to Boston, we need to use the formula: time = distance / speed.
Given that Jesse traveled from Boston to his grandpa Isaac in New York at an average speed of 35 mph, and the trip took him 6 hours, we can determine the distance using the formula: distance = speed × time.
Distance = 35 mph × 6 hours = 210 miles.
Now, for the return trip from New York to Boston, Jesse and Isaac travel at an average speed of 42 mph. To find the time it takes, we divide the distance by the speed:
Time = 210 miles / 42 mph = 5 hours.
Therefore, Jesse's trip from New York to Boston takes 5 hours time.
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please help: find m∠BCD
Answer:
m<BCD=60
Step-by-step explanation:
4x+6=7x-12
3x=18
x=6
4(6)+6
24+6
30
30+30=60
======================================================
Reason:
Use the HL (hypotenuse leg) theorem to prove that triangle BCF is congruent to triangle DCF.
It then leads to the fact that angle BCF is congruent to angle DCF.
Set those angle expressions equal to one another. Solve for x.
angle BCF = angle DCF
4x+6 = 7x-12
4x-7x = -12-6
-3x = -18
x = -18/(-3)
x = 6
Then,
angle BCF = 4x+6 = 4*6+6 = 30angle DCF = 7x-12 = 7*6-12 = 30Both angles are the same measure to confirm the correct x value.
Lastly, add up those angles to get angle BCD.
30+30 = 60 degrees is the final answer.
Which of the following expressions represents 237.45 written in expanded form in terms of the sums of powers to tens
The expanded form in terms of the sums of powers to tens of 237.45 is [tex]2 \times 10^2+3 \times 10^1+7 \times 10^0+4 \times 10^{-1}+5 \times 10^{-2}[/tex]
As per the given data the given decimal number is 237.45.
Here we have to determine the expanded form in terms of the sums of powers to tens.
Expanded Form: In its extended sense, A number is divided up into its place values, then expanded to represent the value of each digit.
Then N can be written in expanded in for terms of 10 is
[tex]$$\Rightarrow N=a \times 10^2+b \times 10^1 + c \times 10^0+d \times 10^{-1}+e \times 10^{-2}$$[/tex]
Let the given number 237.45 is denoted by N.
N = 237.45
First, write the expanded form of a number before the decimal place.
Then using [tex]$\circledast$[/tex], we have
[tex]& N=2 \times 10^2+3 \times 10^1+7 \times 10^0+4 \times \frac{1}{10}+5 \times \frac{1}{10^2} \\[/tex]
[tex]& N=2 \times 10^2+3 \times 10^1+7 \times 10^0+4 \times 10^{-1}+5 \times 10^{-2} \\[/tex]
237.45 = [tex]2 \times 10^2+3 \times 10^1+7 \times 10^0+4 \times 10^{-1}+5 \times 10^{-2}[/tex]
Therefore the expanded form of 237.45 is [tex]2 \times 10^2+3 \times 10^1+7 \times 10^0+4 \times 10^{-1}+5 \times 10^{-2}[/tex].
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Which of the following expressions represents 237.45 written in expanded form in terms of the sums of powers to tens
A. [tex]$2 \times 10^2+3 \times 10^1+7 \times 10^0+4 \times 10^{-1}+5 \times 10^{-2}$[/tex]
B. [tex]$237 \times 100+45 \times 1 / 1000$[/tex]
C. [tex]$2 \times 10^2+3 \times 10^1+7 \times 10^0-4 \times 10^1-5 \times 10^2$[/tex]
D. 200+30+7+0.4+0.05
Thirty people are waiting in line at the cinema. Alex counts 13 people in front of him. Gina counts 21 people between her and Dana. What is the least possible number of people between Dana and Alex
Alex is standing somewhere in between Gina and Dana. Thus, the least possible number of people between Dana and Alex are:
20.
What is the number line called?In advanced mathematics, the number line can be called as a real line or real number line, formally defined as the set R of all real numbers, viewed as a geometric space, namely the Euclidean space of dimension one.
Why is number line important?A number line is useful because it acts as a visual math aid. It can support teachers and parents as they teach children how to count and write numbers. It's also a tool that can help build understanding behind adding, subtracting, multiplying, and dividing numbers.
Let's assume that Gina is standing on first number while Dana on the last. Hence the total number of people in the line are: n= 23.Alex is standing somewhere in between Gina and Dana. Thus, the least possible number of people between Dana and Alex are: (n-2) = 20.
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Fill in the missing information in the table.
Note: The cylinder and cone in each row have the same dimensions.
(I already solved some of them just give me the answers to the parts where I put the zeros, and please hurry)
The missing information, considering the volume of the cone and the cylinder, is given as follows:
Second row: height = 13.3, volume of cylinder = 120π.Third row: Diameter = 12, radius = 6, height = 4, volume of cylinder = 144π.How to obtain the volume of a cone and of a cylinder?The volume of a cylinder of radius r and height h is given as follows:
Vcy = πr²h.
The volume of a cone is one third that of the cylinder, hence:
Vco = πr²h/3.
At the second row, the volume of the cylinder is three times that of the cone, hence:
40π x 3 = 120π.
Considering the volume of the cylinder and the radius, the height is obtained as follows:
πr²h = 120π
9h = 120
h = 120/9
h = 13.3.
For the third row, we have that the base area is of 36π squared units, hence the radius is obtained as follows:
πr² = 36π
r = 6. (as the base is circular).
Hence the diameter is of 12 units, as the length of the diameter is twice that of the radius.
The volume of the cylinder is three times that of the radius, hence:
3 x 48π = 144π
Meaning that the height is then calculated as follows:
πr²h = 144π
36h = 144
h = 144/36
h = 4.
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33
Problem 2
m, p, and z represent the lengths of the three sides of this right triangle.
m
i
Z
Р
Select all the equations that represent the relationship between m, p, and z.
Therefore , the solution of the given problem of equation comes out to bem² + p² =z².
Equation: What is it?The Latin word equ has the meaning of equivalent. Many of the English language's changeable terms, including adequate, temperate, and equality, contain Latin roots in their base words. The Latin root word equ enters our lexicon rather easily because both sides of an equation are, by essence, "equal" to one another.
Here,
Given : a triangle of m,p,z of length of right triangle :
By using Pythagoras theorem :
The relationship comes out to be :
=> m² + p² =z²
Thus , relationship between m , p and z is m² + p² =z² as per Pythagoras theorem.
Therefore , the solution of the given problem of equation comes out to be m² + p² =z².
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8. On a map of scale 1:20 000 the area of a forest is 50 cm². On another map the area of the forest is 8 cm². Find the scale of the second map.
Answer: The scale of a map is a ratio that represents the relationship between distances on the map and distances in the real world. For example, a scale of 1:20 000 means that 1 unit on the map represents 20 000 units in the real world.
In this case, we are given that the area of the forest on the first map is 50 cm² and the area of the forest on the second map is 8 cm². We can use the scale of the first map to find the scale of the second map.
Since the area of the forest on the first map is 50 cm² and the scale is 1:20 000, the area of the forest in the real world is 50 cm² * 20 000 = 1 000 000 cm².
Similarly, since the area of the forest on the second map is 8 cm², the area of the forest in the real world is 8 cm² * x, where x is the scale of the second map.
Setting these two expressions equal to each other, we get:
1 000 000 cm² = 8 cm² * x
Dividing both sides of the equation by 8 cm², we get:
x = 125 000
Therefore, the scale of the second map is 1:125 000.
Step-by-step explanation:
The diameters of the top and bottom of a frustum of a cone are 6cm and
15cm respectively. If the height of the frustum is 30cm, calculate (i) the
curved surface area (ii) the volume of the frustum.
Curved surface area of frustum is 1000.82 cm² and
Volume of frustum is 2756.754 cm³.
What is a conical frustum?Frustum of cone is the part of cone when it is cut by a plane into two parts. The upper part of cone remains same in shape but the bottom part makes a frustum.
Frustum is a Latin word which means ‘piece cut off’. When a solid (generally a cone or a pyramid) is cut in such a manner that base of the solid and the plane cutting the solid are parallel to each other, part of solid which remains between the parallel cutting plane and the base is known as frustum of that solid.
Height of frustum = h = 30 cm
Diameter of top of frustum = 6 cm
Radius of top = R = 6/2 = 3cm
Diameter of bottom of frustum = 15 cm
Radius of bottom = r = 15/2 = 7.5 cm
Slant Height = l = √h²+ (r - R)²
⇒ l = √30² + (7.5 - 3)²
⇒ l = √900 + 20.25 = √920.25 = 30.34 cm
A) Curved surface area of frustum = π(r + R)l
= 3.1416 × (7.5+3) × 30.34
= 3.1416 × (10.5) × 30.34
Curved surface area of frustum = 1000.82 cm²
B) Volume of frustum = (πh/3)(r²+R²+r.R)
= (3.1416 × 30/3)(7.5² + 3² + 7.5×3)
= (31.416) × (56.25 + 9 + 22.5)
= 31.416 × 87.75
Volume of frustum = 2756.754 cm³
Hence, the curved surface area and volume of given conical frustum are 1000.82 cm² and 2756.754 cm³ respectively.
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The sunshine rental company rents cars for $17 per day plus $0. 50 per mile driven. The rent me company rents cars for $20 per day plus $0. 36 per mile driven. When will the two companies be equal in cost?
The two companies will be equal in cost when 21.428 miles are driven.
How do you calculate the cost of rent?
The weekly rental amount is divided by 7 to determine the daily rental rate, then multiplied by 365 (days per year) to determine the yearly rate, and finally divided by 12 to determine the monthly rental amount. For example, a property is advertised as $200 per week, ($200 divided by 7) is $28.57 for the daily rate.
We can set up an equation to represent the cost of renting a car from each company in terms of the number of miles driven, and then solve for the number of miles at which the cost is the same for both companies.
Let x be the number of miles driven.
The cost of renting from Sunshine Rental Company is given by:
Cost1 = 17 + 0.5x
The cost of renting from Rent Me company is given by:
Cost2 = 20 + 0.36x
We can set the two equations equal to each other, and solve for x:
17 + 0.5x = 20 + 0.36x
0.14x = 3
x = 21.428 miles
Hence, the two companies will be equal in cost when 21.428 miles are driven.
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Write the Riemann sum to find the area under the graph of the function f(x) = x4 from x = 5 to x = 7.
Answer:
Refer to the attached image.
Step-by-step explanation:
The circumference of a circle can be represented by the equation C= 2πr. Rewrite
this equation to represent the value of r in terms of C and π. Use your new equation to find the radius of a circle that has a circumference of 54 inches. Leave your answer in terms of pi and solve algebraically
Answer:
see explanation
Step-by-step explanation:
C = 2πr ( r is the radius )
isolate r by dividing both sides by 2π )
[tex]\frac{C}{2\pi }[/tex] = r
given C = 54 , then
r = [tex]\frac{C}{2\pi }[/tex] = [tex]\frac{54}{2\pi }[/tex] = [tex]\frac{27}{\pi }[/tex] inches
What is the inverse of 7 5?
The multiplicative inverse of 7/5 is 5/7 using the formula of multiplicative inverse like (x)^-1 which equals to 1/x.
let's try to learn what is multiplicative inverse.
1/N or [tex]N^-1[/tex] is used to denote a number's multiplicative inverse, such as the number N. From the Latin word "reciprocus," it is also known as reciprocal. Inverse refers to something that is the opposite. The acquired reciprocal of a number is such that its value equals identity 1 when multiplied by the original number. In other terms, it is a technique for producing identity 1 by diluting a number by itself, as in N/N = 1.
One is obtained when a number is multiplied by its own multiplicative inverse.
When a number is multiplied by its original number, the multiplicative inverse of that number, or x^-1, produces a value equal to 1. The multiplicative inverse of 2, for instance, is 2^-1 since it fulfils the formula: 2 x (2^-1) = 2 x (1/2) = 1.It is also known as a number's reciprocal.
Multiplicative inverse of 7/5 is (7/5)^-1 = 1/(7/5) = 5/7.
Given question is incomplete complete question here:
What is the multiplicative inverse of 7/5?
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What is associative property in math?
Answer:
This law simply states that with addition and multiplication of numbers, you can change the grouping of the numbers in the problem and it will not affect the answer. Subtraction and division are NOT associative.
Step-by-step explanation:
PLEASE HELP FAST I WILL GIVE BRAINLIEST, Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used.
Using the properties of integer exponents, match each expression with its equivalent expression.
The 5⁻³ is equivalent to 1/125, - 5⁻³ is equivalent to -1/125, (-5⁻³)⁻¹ is equivalent to -125 and (-5⁻³)⁰ is equivalent to 1
What is Expression?An expression is combination of variables, numbers and operators.
Equivalent expressions are expressions that work the same even though they look different.
5⁻³
This can be written as 1/5³ which is equal to 1/125
-5⁻³
This can be written as -1/5³ which is equal to -1/125
(-5⁻³)⁻¹
We have an exponential property
[tex](x^{a} )^{b} =x^{ab}[/tex]
So (-5⁻³)⁻¹=(-5)³=-125
(-5⁻³)⁻¹ equivalent expression is -125
(-5⁻³)⁰
=(-5)⁰=1
Hence, the 5⁻³ is equivalent to 1/125, - 5⁻³ is equivalent to -1/125, (-5⁻³)⁻¹ is equivalent to -125 and (-5⁻³)⁰ is equivalent to 1
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Serena paid $194.99 for a game system and then bought two equally-priced games. She spent a total of $284.97.
Answer:
Serena paid $194.99 for a game system and then bought two equally-priced games. She spent a total of $284.97.
Step-by-step explanation:
From nose to tail your first dog is 5 feet long. Your first dog is the length of your second dog. How many feet long f is your second dog
According to fraction and ratio, second dog is 3/2 feet long.
In math, what is a fraction?An element of a whole is a fraction. The number is represented mathematically as a quotient, where the numerator and denominator are divided. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction. The numerator of a proper fraction is less than the denominator.
First dog is 5 feet long.
then,
5 feet is equal to 4/5 of the second dog's length.
multiply both sides by 5/4.
5/4 x 5 feet is the second dog's length.
The second dog is 25/4 feet long.
The second dog is 6(1/4) feet long.
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Explain how you decided to divide your wholes into fractional parts and how you decided where your number scale should begin and end. Due 1-2-23
On solving the provided question, we can say that - on doing the fraction we have [tex]\frac{1}{10} ; \frac{1}{100} ; \frac{1}{10000}[/tex]
what is fraction?Any number of equal portions, or fractions, can be used to represent a whole. Fractions in standard English indicate how many units of a certain size there are. 8, 3/4. A whole includes fractions. The ratio of the numerator to the denominator is how numbers are expressed in mathematics. Each of these is an integer in simple fractions. In the numerator or denominator of a complex fraction is a fraction. True fractions have numerators that are less than their denominators. A fraction is a sum that constitutes a portion of a total. By breaking the entire up into smaller bits, you can evaluate it. Half of a full number or item, for instance, is represented as 12.
here we have,
0.1 = 1/10
0.01 = 1/100
0.0001 = 1/10000
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What is the length of leg y of the right triangle?
Answer:
4
Step-by-step explanation:
15) 3x2 - x - 10 When this trinomial is factored completely, one of its factors is A) x 2 B) x - 5 C) 3x 5 D) 3x - 2
When the trinomial 3x² - x - 10 is factored completely, one of its factors is 3x+5.
Solving the given trinomial 3x² - x - 10.
=>3x² - 6x+5x - 10
=>3x(x-2)+5(x-2)
=>(3x+5)(x-2)
The two factors of the given trinomial 3x² - x - 10 is (3x+5) and (x-2), but according to the given options, the correct answer is option C - 3x+5.
Thus, When the trinomial 3x² - x - 10 is factored completely, one of its factors is 3x+5.
Complete question: 3x² - x - 10
When this trinomial is factored completely, one of its factors is
A) x + 2
B) x - 5
C) 3x + 5
D) 3x - 2
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A vending machine has twice as many quarters in it as dollar bills if the quarters and dollar bills have a combined value of $96. 00 how many quarters are in the machine
According to question, we can say that there are 128 quarters in the machine.
What is fraction?Any number of equal portions, or fractions, can be used to represent a whole. Fractions in standard English indicate how many units of a certain size there are. 8, 3/4. A whole includes fractions. The ratio of the numerator to the denominator is how numbers are expressed in mathematics. Each of these is an integer in simple fractions. In the numerator or denominator of a complex fraction is a fraction. True fractions have numerators that are less than their denominators. A fraction is a sum that constitutes a portion of a total. By breaking the entire up into smaller bits, you can evaluate it. Half of a full number or item, for instance, is represented as 12.
N = the number of dollars 2N the number of quaters.....so we have
25(2N) + 1N = 96
1.50N = 96
so, by fraction we have -
N = 96 / 1,50 = 64 dollars
2(64) = 128 quarters
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You have a 5 inch by 7 inch picture that you framed. When you hung the picture, you found that the entire area is 69.56 inches squared. What is the width of the frame?
The width of the frame is 2.4 inches
How to determine the width of the frame?
Let w represent the width of the frame
Then the area of the frame is:
(w + 5)(w + 7) = 69.56
Rewrite it in Standard form of a quadratic equation:
w² + 12w + 35 = 69.56
w² + 12w - 34.56 = 0
Use Quadratic Formula to solve for w:
w = (-b±√(b²-4ac))/(2a)
w = (-12±√(12²-4×1×(- 34.56)))/(2×1)
w = (-12±√(144+138.24))/(2)
w = (-12±16.8)/2
w = -6 ± 8.4
w = -6 + 8.4 or -6-8.4
w = 2.4 or w = -14.4
Since the width cannot be negative.
Thus, w = 2.4 inches
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Consider the parent function f(x) below and graph
On solving the provided question, we can say that - here in graph Between the lowest number, which is 0, and the highest value, which is 5, there is a range. The range is therefore -9=y=5.
What is graphs?
Graphs are visual representations or charts used in mathematics to methodically express data or values. A relationship between two or more objects is frequently represented by a point on a graph. A non-linear data structure called a graph is made up of nodes, or vertices, and edges. Connect the nodes, also known as vertices. This graph comprises a set of vertices V= 1, 2, 3, 5, and a set of edges E= 1, 2, 1, 3, 2, 4, and (2.5), (3.5), (4.5). Statistics graphs (bar charts, pie charts, line charts, etc.) Exponential diagrams. triangle graph, a logarithmic graph
There is a range between the minimum value, which is 0, and the greatest value, which is 5. Thus, the range is -9=y=5.
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