The equation q^2=36 has two solutions because both a positive and a negative number squared can result in a positive number. The solutions are q=6 and q=-6, illustrating the concept of integer powers and square roots.
Explanation:To solve the equation q squared equals 36 (q2 = 36), we look for the number that, when multiplied by itself, gives the product of 36. In mathematics, finding a value that satisfies this condition involves taking the square root of both sides of the equation. Thus, we have two potential solutions since both positive and negative values can be squared to yield a positive result.
The square root of 36 is 6, so our equation gives us two possible solutions: q = 6 or q = -6. This demonstrates the concept of integer powers, where for instance, raising 4 to the power of 3 (43) means multiplying 4 by itself three times. When dealing with the square root, we are essentially doing the opposite: we are asking what number multiplied by itself gives us the original number under the square power.
what does n÷6 is??????
you plan to leave a 15% tip and your dinner bill is $45(tax included). How much total should you leave
i need help
Fundraising your school raised 125% of its fundraising goal the school raised $6750.what was the goal
A tortoise travels 11 feet in one hour. In each subsequent hour, the tortoise travels one-third the distance it traveled in the previous hour. How far does this tortoise travel in 6 hours?
The distance that a tortoise will cover in 6 hours is:
16.47735 feet.
Step-by-step explanation:It is given that :
A tortoise travels 11 feet in one hour.
In each subsequent hour, the tortoise travels one-third the distance it traveled in the previous hour.
This means that in 2 hours it travels a total of:[tex]11+\dfrac{1}{3}\times 11\ feet[/tex]
which is equal to:
[tex]11\times \dfrac{4}{3}\ feet=\dfrac{44}{3}\ feet[/tex]
in the 3 hours it will travel a total of:[tex]=11+\dfrac{1}{3}\times 11+\dfrac{1}{3^2}\times 11\ feet[/tex]
In 4 hours it will travel a total of:[tex]=11+\dfrac{1}{3}\times 11+\dfrac{1}{3^2}\times 11+\dfrac{1}{3^3}\times 11\ feet[/tex]
In 5 hours it will travel a total of:[tex]=11+\dfrac{1}{3}\times 11+\dfrac{1}{3^2}\times 11+\dfrac{1}{3^3}\times 11+\dfrac{1}{3^4}\times 11\ feet[/tex]
In 6 hours it will travel a total of:[tex]=11+\dfrac{1}{3}\times 11+\dfrac{1}{3^2}\times 11+\dfrac{1}{3^3}\times 11+\dfrac{1}{3^4}\times 11+\dfrac{1}{3^5}\times 11\ feet=16.47735\ feet[/tex]
Hence, the answer is:
16.47735 feet
Why was the country of Australia created
How much sugar is there in 100g of 15% sugar syrup?
In 100g of 15% sugar syrup, there is 15g of sugar.
Sugar SyrupSugar syrup is a thick viscous liquid that mostly contains water and dissolved sugar in it. therefore, a 20% sugar syrup means having a 20:80 ratio of sugar and water in a unit of sugar syrup.
Given to us,100g of sugar syrup 15% sugar,
Now, 15% of sugar means having a 15:85 ratio of sugar and water in 100g of sugar syrup. Let the sugar in 100g of sugar syrup be x. so, the water in the syrup is (100-x), therefore,
[tex]\bold{\dfrac{15}{85} = \dfrac{sugar}{water}}[/tex]
Substituing the values we get,
[tex]\dfrac{15}{85} = \dfrac{x}{100-x}\\\\15\times(100-x) = 85x\\1500 - 15x = 85x\\1500 = 85x +15x\\1500 = 100 x\\\\x = \dfrac{1500}{100}\\\\x = 15[/tex]
Hence, In 100g of 15% sugar syrup, there is 15g of sugar.
Learn more about sugar syrup:
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PLEASE HELP!!!!!!
Of all students, calculate the relative frequency for males who carpool.
0.204
9
33
0.088
Answer:
It's 0.088.
Step-by-step explanation:
So the males who carpool is 9 right? Well relative frequency is the frequency divided by the total. So we must divide 9 by 102.
9÷102 = 0.088
Kristen and Sam notice that the means of their scores for the first marking period were the same. Kristen commented that the standard deviation of her scores was 8.4 while the standard deviation of Sam's was 4.8. Which statement must be true?
In week 3 the two athletes concentrate on biking. Minh's goal is to bike 125 1/2 miles. At the end of the week he found that he actually biked 125 1/6 miles. PJ's Goal was to bike 120 1/4 miles. At the end of the week he found that he actually biked 120 miles. Which athlete was closer to making their goal? Explain
A quadratic equation is shown below: 10x2 − 3x − 1 = 0 Part A: Describe the solution(s) to the equation by just determining the radicand. Show your work. (5 points) Part B: Solve 16x2 − 2x − 5 = 0 by using an appropriate method. Show the steps of your work, and explain why you chose the method used. (5 points)
A) Consider the equation [tex]10x^2-3x-1=0[/tex]
We have to describe the solutions to this equation.
We will determine the radicand = [tex]b^2-4ac[/tex]
= [tex](-3)^2 - 4(10)(-1) = 9+ 40 = 49[/tex] which is greater than zero,
Therefore, the given equation ha real roots.
B) Consider the equation [tex]16x^2-2x-5=0[/tex]
We will use middle splitting term method to solve this equation.
[tex]16x^2+8x-10x-5 =0[/tex]
[tex]8x(2x+1) -5(2x+1)=0[/tex]
[tex](2x+1)(8x-5)=0[/tex]
So, [tex]2x+1=0[/tex]
[tex]x = \frac{-1}{2}[/tex] and [tex]x = \frac{5}{8}[/tex]
I chose this method, because this is more easier and takes less time.
If jeremy gives his horse 12 gallons of water each day. How many one quart pails of water is that
Need help with this question: Write the equation of the parabola with focus (5,2) and directrix x=1
Caitlin creates an architectural blueprint of a rectangular dining room. The area of the actual dining room is 900 times as large as the area of the dining room on the blueprint. The length of the dining room on the blueprint is 4 inches. What is the length of the actual dining room?
Steven earns extra money babysitting. He charges $31.00 for 4 hours and $54.25 for 7 hours.
Enter an equation to represent the relationship. Let x represent the number of hours Steven babysits and y represent the amount he charges.
The equation is y =
PLEASE HELP WILL GIVE BRANLIEST!!!!!!!!!
please help me write the equation for the problem below
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A chess club has 500 members but is losing 30 members each year. A computer club has 150 members and is gaining 20 members per year. Wrote and solve an equation to find the number of years it will take for the two clubs to have the same number of members.
Find the volume of the triangular prism. Round to the nearest cubic unit.
•288 cm^3
•144 cm^3
•576 cm^3
•71 cm^3
Answer:
114 cm∧3
Step-by-step explanation:
V= area of base x height
1) calculate the area of the base with formula: 1/2 bh
B=1/2 (8) (6)=24 then Multiply to get the area: Bh
2) (24) (6)= 144cm∧3
hope this helps.
4 times x plus 2 is at most 10
which expression represents the perimeter of the model shown below? PLEASE HELP
Matt has a rectangular garden that is 10 ft wide and 24 Ft long . He wants to build a fence from one corner to the opposite corner . How many feet of fence does Matt need ???
The length of the fence Matt needs is 26 ft.
Explanation:To find the length of the fence, we can use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
In this case, the width of the garden is one side of the right triangle, the length of the garden is the other side, and the fence is the hypotenuse.
So, we can calculate the length of the fence as follows:
Length of the fence = √((Width)^2 + (Length)^2)
Substituting the given values, we get:
Length of the fence = √((10 ft)^2 + (24 ft)^2)
Length of the fence = √(100 ft^2 + 576 ft^2)
Length of the fence = √676 ft^2
Length of the fence = 26 ft
Final answer:
To calculate the length of fence needed for Matt's garden, the Pythagorean theorem is used, resulting in needing a fence that is 26 feet long.
Explanation:
Calculating the Fence Length Across a Rectangular Garden
Matt has a rectangular garden with dimensions of 10 feet in width and 24 feet in length. To find the length of the fence that Matt needs to build from one corner of the garden to the opposite corner, we will use the Pythagorean theorem, since the corners of the garden and the fence form a right triangle.
The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b). The formula is c² = a² + b².
For Matt's garden, the length is 'a' = 24 ft and the width is 'b' = 10 ft. Plugging these values into the formula, we get:
c² = 24² + 10²
c² = 576 + 100
c² = 676
We then take the square root of both sides to solve for 'c':
c = √676
c = 26 ft
Therefore, Matt needs 26 feet of fence to reach from one corner of the garden to the opposite corner.
Morgan bought a pair of shoes at a sale of 25%. If the amount she paid was $1000, find the marked price.
The marked price of the shoes that Morgan bought at a 25% discount for $1000 is $1333.33. The calculation was done by dividing the discounted price by (1 minus the discount percentage in decimal form).
The question involves finding the marked price of an item given the discounted price and the discount percentage. Morgan paid $1000 for a pair of shoes after getting a 25% discount. To find the original marked price, we can use the formula:
Discounted Price = Marked Price × (1 - Discount Percentage)
Here, the Discounted Price is $1000, and the Discount Percentage is 25%, which is equivalent to 0.25 in decimal form.
By rearranging the formula to solve for the Marked Price, we get:
Marked Price = Discounted Price ÷ (1 - Discount Percentage)
Now we can calculate:
Marked Price = $1000 ÷ (1 - 0.25) = $1000 ÷ 0.75 = $1333.33
Therefore, the marked price of the shoes was $1333.33.
Find the missing angle
20 POINT FOR ONE QUESTIONS PLEASE HELP THANK YOU!!! I WILL MARK BRAINLIEST
1. What is the value of z?
Find the area of the trapezoid to the nearest tenth.
What is 0.24 ̅ (4 is repeating) expressed as a fraction in simplest form?
Show your work please
Here, we need to find express 0.2444... as a fraction in simplest form.
Let the fraction be expressed as x
Now,
x = 0.2444....
Since, x is recurring in 1 decimal places, we multiply it by 10.
10x = 2.4444....
From left hand-side, x is subtracted and from 0.24444... from right hand side
10x - x = 2.4444.... - 0.24444....
So now,
9x = 2.2
x = [tex] \frac{2.2}{9} [/tex]
x = [tex] \frac{22}{90} [/tex]
x = [tex] \frac{11}{45} [/tex]
Thus, fraction as simplest form = [tex] \frac{11}{45} [/tex]
enter the missing value into the box to complete the ratio comparing 500 meters to 3 kilometers
How many liters equal 1258 cm3
The 1258 cm³ is equal to 1.258 liters.
To convert 1258 cm³ to liters, you can use the fact that 1 liter is equal to 1000 cm³. Therefore, the conversion from cubic centimeters to liters is straightforward.
Identify the given volume: 1258 cm³.
Know the conversion factor: 1 liter = 1000 cm³.
Perform the conversion:
[tex]1258 \ cm^3 \times \left( \frac{1 \ liter}{1000 \ cm^3} \right) = 1.258 \ liters[/tex]
what type of figure is quadrilateral fxyh
Answer: Quadrilateral fxyh is a trapezoid
Step-by-step explanation: Hi, the correct answer is trapezoid.
A trapezoid is a Quadrilateral ( a polygon with four sides) with a pair of opposite sides parallel. These parallel sides are called the bases of the trapezoid, and the other non-parallel sides are known as the "legs" of the trapezoid.
Feel free to ask for more if it´s necessary or if you did not understand something.
According to the table, what is the mode of the average high temperatures for states listed in the chart? A) no mode B) 55° F C) 81° F D) 88° F
please explain how to do this type of math I need help ;-;
Answer:no mode
Step-by-step explanation:
Which sign makes the statement true 16/25 or 64%
a bag contains 20 pink marbles and 12 yellow marbles. you choose a marble at random. what is the probability of selecting a pink marble?