Answer:
a) rational
b) irrational
Step-by-step explanation:
a) 36 = 6²
So sqrt(36) = 6
b) 72 = 2 × 36
sqrt(72) = sqrt(2) × sqrt(36)
Since 2 is not a perfect square, sqrt(72) is irrational
Final answer:
√36 is a rational number because 36 is a perfect square, which results in a whole number when square rooted. However, √78 is an irrational number as it is not a perfect square and cannot be simplified to a fraction of two integers.
Explanation:
We are tasked with determining whether each given root, √36 and √78, is a rational or irrational number. First, we observe that √36 is the square root of 36. Since 36 is a perfect square (6 x 6), √36 equals 6, which is a rational number because it can be expressed as the quotient of two integers (6/1).
On the other hand, √78 is not a perfect square; its square root cannot be simplified to a whole number or a simple fraction of two integers. Therefore, √78 is an irrational number because it cannot be written exactly as a simple fraction or repeating or terminating decimal.
FGHI is a parallelogram. Find the measure of angle I.
*show your work please*
Answer:
I = 130
Step-by-step explanation:
The sum of all four angles in a four-sided closed shape will ALWAYS be equivalent to 360 degrees. Also, the opposite angles of a parallelogram will ALWAYS be equivalent. This means F = H.
To begin, the measure of F, y + 7, and the measure of H, 3y - 79, are equal. This equation looks like: y + 7 = 3y - 79
Now subtract y from both sides: 7 = 2y - 79
Add 79 to both sides: 86 = 2y
And divide both sides by 2: 43 = y
Now that you have the value of y, plug 43 into y and solve for both equations:
43 + 7 = 3(43) - 79
50 = 129 - 79
50 = 50
So now we know that the measure of angles F and H are 50. 50 + 50 is 100.
Since we know that the sum of all four sides must be equivalent to 360. subtract 100 from 360 to get the sum of the measures of angles I and G:
360 - 100 = 260
So now 260 must equal I + G. Since I and G must be equivalent, just divide 260 by 2 and you have your answer: 260/2 = 130
The following data points represent the number of
alligators in each body of water near Tom's house.
8,5, 12, 15
Find the mean absolute deviation (MAD) of the data
set.
alligators
Answer:
3.5 alligators
Step-by-step explanation:
i did khan academy
Answer:
3.5
Step-by-step explanation:
I just answered it :) it was correct btw
Find the sum of the integers from 1 to 99 (inclusive).
Show ALL working.
A cook has 223 cups of flour. A recipe calls for 234 cups of flour. Does the cook have enough flour? If not, how much more flour is needed?
Answer: 11 more cups of flour is needed.
Step-by-step explanation: 234 - 223 = 11
We find that the cook needs 11 more cups of flour to meet the recipe's requirement of 234 cups, as they only have 223 cups.
To determine whether the cook has enough flour to follow a recipe requiring 234 cups, a simple subtraction operation is performed. The cook starts with 223 cups of flour. The amount needed subtracts the amount available: 234 cups (needed) - 223 cups (available) = 11 cups. So, the cook requires 11 more cups of flour to have enough for the recipe.
Two numbers have a sum of 1 and a product of -12. Use the quadratic equation n^2+n-12=0 to determine the 2 numbers
Answer:
4 and -3
Step-by-step explanation:
4-3=1
4(-3)=-12
The two numbers that have a sum of 1 and a product of -12 is -4 & 3
Solving quadratic equationsFrom the question, we are determine the two unknown numbers by solving the quadratic equation
The given quadratic equation is
n² + n -12 = 0
The quadratic equation can be solved as follows
n² + n -12 = 0
By factorizing
n² +4n -3n -12 = 0
n(n+4) -3(n+4) = 0
(n+4)(n-3) = 0
Then,
n+4 = 0 OR n -3 = 0
∴ n = -4 OR n = 3
Hence, the two numbers that have a sum of 1 and a product of -12 are -4 & 3
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Typically seven out of every 100 babies bom in the River Creek hospital have a birth defect, most of
them minor defects
A. What typical percentage of the babies have birth defects?
b. What typical percentage of the babies do not have birth defects?
c. About how many babies with birth defects would you expect to find in a group of 500 babies
Answer: I believe that the answer is either C or A
Step-by-step explanation:
Typically, 7% of babies born in the River Creek hospital have birth defects, which means 93% of babies do not. In a group of 500 babies, about 35 are expected to have birth defects.
Explanation:A. The typical percentage of babies having birth defects is 7%, because 7 out of every 100 is the equivalent of 7% when expressed as a percentage.
B. To find the percentage of babies that do not have birth defects is therefore 100%-7% = 93%, because the percentage of babies that have defects and those that do not should add up to 100%.
C. If you were to expect about 7% of babies to have a birth defect in a group of 500 babies, you would calculate it as: 500 x 0.07 = 35 babies. So, you would typically expect to find about 35 babies with birth defects in a group of 500 babies.
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which data set is exponential? please help!
Answer:
I think it's B.
Step-by-step explanation:
Answer:
I believe that the answer is A but it could be B
This is a picture of a cube and the net for the cube.
What is the surface area of the cube?
Answer:
[tex]486\ in^2[/tex]
Step-by-step explanation:
we know that
The surface area of the cube is equal to the area of its six square faces
so
[tex]SA=6b^2[/tex]
where
b is the length side of the cube
we have
[tex]b=9\ in[/tex]
substitute
[tex]SA=6(9)^2=486\ in^2[/tex]
Answer:
486
Step-by-step explanation:
Two angles are said to be congruent if:
O
A. they have the same angle measure.
O
B. they share a side.
O
C. the sum of their measures is 180°
Given: x + 2y = -6. Solve for x.
Answer:
x= −6−2y
Step-by-step explanation:
Subtract 2y from both sides of the equation x= −6−2y
Answer:-6-2y
Step-by-step explanation:
X+2y=-6
subtract 2y from both sides
X+2y-2y=-6-2y
X=-6-2y
Jada and diego baked a large batch of cookies.
They selected 1/4 of the cookies for there teachers
They threw away one burnt one
They delivered 2/3 of the remaining cookies to to a nursing home
They gave 3 cookies to neighborhood kids
They wrapped up the 2/3 of the remaining cookies for there friends
After this they had 15 cookies left. How many did they have to start with and how did u do it?? Please help
Started with 54 cookies, considering fractions, removals, and distributions, ending with 15 cookies.
let's break it down:
1. **Initial Batch**: They started with an unknown number of cookies, denoted as [tex]\( x \).[/tex]
2. **Cookies for Teachers**: They took [tex]\( \frac{1}{4} \) of the cookies for their teachers, leaving \( \frac{3}{4}x \)[/tex] cookies.
3. **Burnt Cookie**: They discarded one burnt cookie, resulting in [tex]\( \frac{3}{4}x - 1 \) cookies.[/tex]
4. **Cookies for Nursing Home**: They gave [tex]\( \frac{2}{3} \) of the remaining cookies to the nursing home, keeping \( \frac{1}{3} \) of \( \frac{3}{4}x - 1 \) cookies.[/tex]
5. **Cookies for Neighborhood Kids**: They gave 3 cookies to the neighborhood kids, resulting in [tex]\( \frac{1}{3}x - 3 \) cookies.[/tex]
6. **Cookies for Friends**: They wrapped up [tex]\( \frac{2}{3} \) of the remaining cookies for their friends, keeping \( \frac{1}{3} \) of \( \frac{1}{3}x - 3 \) cookies.[/tex]
7. **Final Count**: They were left with 15 cookies, so [tex]\( \frac{1}{3}x - 3 = 15 \).[/tex]
[tex]\[ \frac{1}{3}x - 3 = 15 \]\[ \frac{1}{3}x = 15 + 3 \]\[ \frac{1}{3}x = 18 \]\[ x = 18 \times 3 \]\[ x = 54 \][/tex]
So, they initially had 54 cookies.
Use the diagram to fi d the missing lenght of the pool (please i need the help)
Answer:
D) 50ft
Step-by-step explanation:
(18×x) + (32×18) + [(48-18-18)×(32-11)]
= 1728
18x + 576 + (12×21) = 1728
18x = 1728 - 828
18x = 900
x = 50
Solve for n.
17.1 = 5.7 x n
Answer:
n = 3
Step-by-step explanation:
Equation: 17.1 = 5.7 * n
Divide both sides by 5.7 to get n by itself.
Step 1: Divide both sides by 5.7
17.1 = 5.7 * n
17.1 / 5.7 = 5.7 * n / 5.7
divide divide
3 = n
Answer: n = 3
We are given the following equation and want to solve for the unknown variable, n:
[tex]17.1=5.7 \times n[/tex]
To solve for an unknown variable, we want to isolate the variable by doing operations to both sides of the equation:
This includes adding, subtracting, multiplying, and dividing both sides by the same valueFor this equation, we'll divide both sides by 5.7 to isolate the unknown variable n
[tex]17.1 \boxed{\div 5.7} = 5.7 \times n \boxed{\div 5.7}[/tex]
After dividing both sides by 5.7 and simplifying, we get:
[tex]3=n[/tex]
The next step is a bit tedious, but in math, you usually want to have the variable on the LEFT side of the equation after isolation.
After reversing the equation accordingly, we have:
[tex]\boxed{n=3}[/tex]
We have a value for n, which is 3.
Let me know if you need any clarifications, thanks!
~ Padoru
Which product is grater than 63. it's I ready work
Answer:
Step-by-step explanation:
bruh
Answer:
I need more information
Which of the following lines is perpendicular
to the equation given below?
y=-2x+8
The equation of the line perpendicular to y = -2x + 8 is y = 1/2x + 8.
A line is perpendicular to another line if their slopes are negative reciprocals of each other. The slope of the line y = -2x + 8 is -2, so the slope of a line perpendicular to it would be 1/2.
Of the above choices, only line (C) has a slope of 1/2. Therefore, the equation of the line perpendicular to y = -2x + 8 is y = 1/2x + b, where b is the y-intercept.
To find the value of b, we can substitute a point on the line y = -2x + 8 into the equation y = 1/2x + b. For example, the point (0, 8) lies on the line y = -2x + 8. Substituting this point into the equation y = 1/2x + b, we get:
8 = 1/2 * 0 + b
b = 8
Therefore, the equation of the line perpendicular to y = -2x + 8 is y = 1/2x + 8.
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Two cylindrical cans are mathematically similar.
The larger can has a capacity of 1 litre and the smaller can has a capacity of 440 ml.
Calculate the diameter, d, of the 440 ml can.
Answer:
The diameter of the smaller can is ≅ 9.14 cm
Correct statement and question:
Two cylindrical cans are mathematically similar.
The larger can has a capacity of 1 liter and a diameter of 12 cm and the smaller can has a capacity of 440 ml.
Calculate the diameter, d, of the 440 ml can.
Source:
Previous question that can be found at brainly
Step-by-step explanation:
Let's recall that:
A. The formula of the volume of a cylinder is π*r²*h, where:
r is the radius of the cylinder (half of the length of the diameter) and h, represents the height of the cylinder.
B. 1 liter = 1,000 milliliters = 1,000 cubic centimeters
Therefore, we can find the height of the larger can, this way:
V = π*r²*h
Replacing with the value we know:
d = 12 ⇒ r = 6
1,000 = 3.1416 * 6² * h
1,000 = 113.0976h
h = 1,000/113.0976
h = 8.84 cm (rounding to the next hundredth)
Now we can find the ratio of the radius to the height of the larger can to find the measures of the smaller can, this way because the cylinders are mathematically similar:
Ratio = Radius/Height
Ratio = 6/8.84
Ratio = 0.6787
It means the radius of the smaller can is 0.6787 multiplied by the value of the height of the smaller can. Let x represent the height h of the smaller can, we can write this equation to solve for x:
V = π*r²*h
Replacing with the values we know:
height = x
radius = 0.6787x
440 = π * (0.6787x)² * x
440 = 3.1416 * 0.4606x² * x
440 = 1.4471x³
x³ = 440/1.4471
x³ = 304.06
∛x = ∛304.06
x = 6.73 ⇒ height of the smaller can = 6.73 cm and radius of the smaller can = 6.73 * 0.6787 = 4.57
If radius = 4.57 cm ⇒ diameter = 2 * 4.57 = 9.14 cm
The diameter of the smaller can is ≅ 9.14 cm
The diameter of the 440 ml can is approximately 9.12 cm.
To determine the diameter of the smaller can, we use the fact that the two cans are mathematically similar. This means that their dimensions have a constant ratio, known as the scale factor.
The capacity of the larger can is 1 liter (1000 ml), and the capacity of the smaller can is 440 ml.
The scale factor for volumes is given by:
Scale Factor (Volume) = (Volume of smaller can) / (Volume of larger can) = 440 ml / 1000 ml = 0.44
Since the cans are similar, the scale factor for the linear dimensions (such as diameter) is the cube root of the volume scale factor:
Scale Factor (Diameter) = ∛(Scale Factor (Volume)) = ∛(0.44)
Using a calculator, we find:
∛(0.44) ≈ 0.76
Now, we multiply the diameter of the larger can by this scale factor to find the diameter of the smaller can:
Diameter of the smaller can = Diameter of the larger can × Scale Factor (Diameter) = 12 cm × 0.76 ≈ 9.12 cm
Therefore, the diameter of the 440 ml can is approximately 9.12 cm.
Complete question:
Two cylindrical cans are mathematically similar.
The larger can have a capacity of 1 liter and the smaller can have a capacity of 440 ml.
Calculate the diameter, d, of the 440 ml can if the diameter of the larger can is 12 cm.
Find the surface area of the triangular prism.
Answer: Area is 168ft^2
Step-by-step explanation:
Find the area of the circle. 26m. Round to the nearest tenth.
Answer:
Step-by-step explanation:
A=[tex]\pi r^{2}[/tex]
A=3.14*26*26
A=2122.64
A=2122.6[tex]m^{2}[/tex]
The calculated area is 530.66 [tex]m^2[/tex], which rounds to 530.7 [tex]m^2[/tex].
To find the area of a circle with a given diameter, you first need to find the radius, which is half of the diameter. Since the diameter provided in the question is 26 meters, the radius would be 13 meters. The formula to calculate the area (A) is A = π[tex]r^2[/tex], where (pi) is approximately 3.14 and r is the radius of the circle.
Using the aforementioned radius of 13 meters, the area can be calculated as follows:
A = 3.14 x [tex](13 m)^2[/tex]= 3.14 x 169 = 530.66 [tex]m^2[/tex]
When rounded to the nearest tenth, the area of the circle is 530.7 [tex]m^2[/tex].
What is the exact volume of the cylinder? 3in, 6in
18in
36in
54in
63in
Answer:
54π in³
Step-by-step explanation:
The volume (V) of a cylinder is calculated as
V= πr²h ( r is the radius and h the height )
Here r = 3 and h = 6, thus
V = π × 3² × 6 = π × 9 × 6 = 54π in³
The diagram shows are square with perimeter 40cm
Work out the percentage of the area inside the square that is shaded
To find the percentage of the shaded area inside the square, we need to determine the area of the shaded region and calculate the percentage relative to the total area of the square. Without more information or measurements, we can't determine the exact size of the shaded area or the percentage.
Explanation:To find the percentage of the area inside the square that is shaded, we need to determine the area of the shaded region and then calculate the percentage. Given the perimeter of the square is 40cm, we can find the length of each side by dividing the perimeter by 4, which gives us 10cm. The area of the square is found by squaring the length of one side, so the area is 10cm x 10cm = 100cm². To find the shaded area, we need to subtract the area of the square from the total area. Assuming the shaded region is a smaller square with side length x, the area of the shaded region is x². So the shaded area is 100cm² - x².
To calculate the percentage, we divide the shaded area by the total area of the square and multiply by 100. So the percentage of the area inside the square that is shaded is (100cm² - x²) / 100cm² * 100.
It's important to note that we don't have enough information to determine the exact size of the shaded area or calculate the percentage without more details or measurements of the shaded region.
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On average, Ainsley and her friends could complete 44 sit-ups in one minute. The number of sit ups done by each of her friends is listed below. How many did Ainsley complete? *
47, 46, 38, 45, 41
Answer:
i think ainsley completed 45
Step-by-step explanation:
Answer:
45
Step-by-step explanation:
A light bulb consumes 960 watt hours per day. How many watt hours does it consume in 3 days and 18 hours
Answer:
3600
Step-by-step explanation:
960*3=2880
To find how many per hour: 960/24= 40
40*18=720
720+2880=3600
Answer:
3600 watts
Step-by-step explanation:
960 multiplied by 3 , then divide 18 by 24. Multiply 0.75 by 960, and then add 2880 and 720.
Rectangle A’B’C’D’ is the image of rectangle ABCD after dilation. What is the scale factor of the dilation?
Answer:
The scale factor of the dilation is 3
Step-by-step explanation:
we know that
A dilation is a non rigid transformation that produce similar figures
so
Rectangle ABCD and rectangle A'B'C'D' are similar
Remember that
If two figures are similar, then the ratio of its corresponding sides is proportional
Let
z ----> the scale factor
[tex]z=\frac{D'C'}{DC}[/tex]
we have
[tex]D'C'=12-3=9\ units[/tex] ----> difference of x-coordinates
[tex]DC=4-1=3\ units[/tex] ---> difference of x-coordinates
substitute
[tex]z=\frac{9}{3}=3[/tex]
The scale factor is greater than 1
so
The dilation is a enlargement
You have a large beach ball that has a radius of 15 inches. What is the volume of the ball? Use 3.14 for pi.
Answer:
Therefore,
[tex]\textrm{Volume of Ball}=14130\ inches^{3}[/tex]
Step-by-step explanation:
Given:
Spherical Shape Ball
[tex]Radius =15\ inches[/tex]
pi = 3.14
To Find:
Volume of Ball= ?
Solution:
Formula for Volume of Sphere is given by
[tex]\textrm{Volume of Sphere}=\dfrac{4}{3}\pi (Radius)^{3}[/tex]
Substituting the given values we get
[tex]\textrm{Volume of Ball}=\dfrac{4}{3}\times 3.14\times 15^{3}=14130\ inches^{3}[/tex]
Therefore,
[tex]\textrm{Volume of Ball}=14130\ inches^{3}[/tex]
please help me again
Answer:
60
Step-by-step explanation:
Step 1: Solve for x
x + 3x + 2x = 180
6x / 6 = 180 / 6
x = 30
Step 2: Find the measure of angle C
Angle C = 2x
Angle C = 2(30)
Angle C = 60 degrees
Answer: 60
Use percent to find the new amount. You may round to the
nearest whole number when necessary.
56 increased by 25%
Good morning
Answer:
70Step-by-step explanation:
56 increased by 25% = 56+25%
= 56 + 56×(25÷100)
=70
________________________________
:)
The quadratic equation x^{2}-6x=12 is rewritten in the form (x+p)^2=q, where q is a constant. What is the value of p ?
Answer:
p = - 3
Step-by-step explanation:
Given
x² - 6x = 12
To obtain the required form use the method of completing the square
add ( half the coefficient of the x- term )² to both sides, thus
x² + 2(- 3)x + 9 = 12 + 9
(x - 3)² = 21
Thus p = - 3
Given the quadratic functions expressed as;
x² - 6x = 12
The value of p given the quadratic expression is -3
Complete the square at the left hand side of the equation.
Add the square of the half of coefficient of x to both sides.
coefficient of x = -6
Half of coefficient of x = -6/2 = -3
Square of the result = (-3)² = 9
Add 9 to both sides of the equation
x² - 6x + 9 = 12 + 9
Factoring the left hand side
(x-3)² = 21
Comparing the result with (x+p)² = q
The value of p wil be -3
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The ratio of the weight of an object on planet earth to the weight of the same object on planet B is 100 to 3 if an elephant weighs 4800 pounds on planet a find the elephants way down planet b
Answer:
144 pounds
Step-by-step explanation:
Weight of object Earth: Weight of Object Planet B
100:3 = 4800:b
100/3=4800/b
100b=14400
b=144
Therefore, 144 pounds
The weight of an elephant on planet B can be calculated using the weight ratio of 100 (on Earth) to 3 (on planet B). By setting up a proportion and solving for the unknown weight, we find that the elephant weighs 144 pounds on planet B.
Since the ratio is 100 to 3, we can set up a proportion to find the elephant's weight on planet B.
First, represent the known weight ratio between Earth and planet B: 100 (earth weight) to 3 (planet B weight).
Then, set up the proportion using the weight of the elephant on Earth (4,800 pounds) and let x represent the unknown weight on planet B:
100/3 = 4800/x
To solve for x, cross-multiply and divide:
100x = 4800 * 3
Finally, divide both sides by 100 to find x:
x = (4800 * 3) / 100
x = 144 pounds
Therefore, the elephant would weigh 144 pounds on planet B.
a penny has a diameter of 0.75 inches. Find the circumference of a penny
Answer:
The penny has a circuferance of 2.356194
Step-by-step explanation:
To get this I used the formula for circumference c = πd or c = 2π x r²
And you just plug in 0.75 for d and multiply it by 5 to get you answer
PLEASE VOTE BRAINLIESTThe circumference of the penny is approximately 2.36 inches.
What is the circumference of the penny?A circle is simply a closed 2-dimensional curved shape with no corners or edges.
The circumference of a circle is expressed mathematically as;
Circumference = 2πr or dπ
Where r is the radius, d is the diameter, and π is constant pi.
Given the parameter:
Diameter of the penny d = 0.75 inches
Circumference =?
To find the circumference of the penny, we can use the formula for the circumference of a circle.
Circumference = dπ
Plug in the diameter values:
Circumference = 0.75 × π
Circumference = 0.75π in or 2.36 in.
Therefore, the circumference is approximately 2.36 inches.
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P( 4) =
13 and Q( 4) = 8, evaluate P( 4) Q(4).