The measurement of the largest square tiles she can use is 6 feet.
Finding all common factors between two numbers and choosing the biggest one yields the highest common factor (HCF). For instance, the numbers 8 and 12 share the elements 1, 2, and 4. Four is the greatest common factor.
Steps for calculating HCF:
Step 1: Write each integer as the sum of its prime factors in step one.
Step 2: List the shared factors between the two numbers.
Step 3: The HCF is the sum of all the common prime factors ( use the lower power of each common factor)
Given,
Measurement of the rectangular floor:
length = 150 feet
breadth = 132 feet
The measurement of the largest square can be calculated by finding the HCF of 132 and 150.
132 = 2*2*3*11
150 = 2*3*5*5
So, HCF (132, 150) = 2*3 = 6.
Hence, the measurement of the largest square tiles she can use is 6 feet.
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(3x³ - 8x² + 16x - 1) ÷ (x − 1) answer ?
Answer:
[tex]= \frac{-125x^3-1}{x-1}[/tex]
Sydney picked 28 raspberries and 35 blueberries to make two desserts.
She needs 4 raspberries for each raspberry tart and 5 blueberries for each
blueberry tart. She wants to know how many desserts she will be able to
make with the berries.
-4x = -60 on a graph
The graph of the equation -4x = -60 is shown below.
How to Graph the Equation of a vertical Line?A vertical line is expressed as the equation, x = b. Here, the variable "b" is the point on the x-axis where the line intercepts the horizontal axis.
Thus, to plot the graph for a vertical line with the equation, x = b, we would simply draw a vertical line that crosses the x-axis at point b.
Given the equation, -4x = -60, rewrite the equation in the form x = b, to determine the value of b:
-4x/-4 = -60/-4 [division property of equality]
x = 15
This means that the graph of the equation, -4x = -60, would be a graph that has a vertical line that crosses the x-axis at 15.
the graph is shown below.
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Please help me with this (will give more credit for the best answer)
Answer:
1. 5ft
2. 2ft
3. 2ft
4. 1ft
Step-by-step explanation:
Which of the following statements is true about congruent angles?
Answer: Congruent angles are the angles that have equal measure. So all the angles that have equal measure will be called congruent angles. They are seen everywhere, for example, in equilateral triangles, isosceles triangles, or when a transversal intersects two parallel lines.
Step-by-step explanation:
Find the value of X
complete the slope-intercept form of an equation that represents the relationship in the table
Answer:
y = 3x -4
Step-by-step explanation:
You want the slope intercept equation representing the relationship between x and y, given (x, y) = (1, -1) and (4, 8).
SlopeThe slope can be found using the formula ...
m = (y2 -y1)/(x2 -x1)
m = (8 -(-1))/(4 -1) = 9/3 = 3
InterceptThe y-intercept can be found using the equation ...
b = y1 -m(x1)
b = -1 -3(1) = -4
Slope-intercept equationThe slope-intercept equation of a line has the form ...
y = mx + b
Using the above values of m and b, this becomes ...
y = 3x -4
__
Additional comment
Attached is a graph showing the points and the line the equation represents.
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Vince is cutting a rectangular piece of pegboard to use in his garage for organization. The width of the pegboard is 8 inches less than half the length. The perimeter of the pegboard is 224 inches. What is the length of the pegboard?
The length of the rectangular pegboard is 80 inches
What is a rectangle?A rectangle is a polygon with four sides in which two opposite sides are parallel and equal
How to find the length of the rectangular pegboard?Since Vince is cutting a rectangular piece of pegboard to use in his garage for organization. The width of the pegboard is 8 inches less than half the length. The perimeter of the pegboard is 224 inches.
Let
L = length of pegboard and W = width of pegboard.Since the width of the pegboard is 8 inches less than half the length, we have that
W = L/2 - 8
Also, since the pegboard is a rectangle, its perimeter, P = 2(L + W)
Now, its perimeter P = 224 inches.
So, 2(L + W) = 224
L + W = 112
Now, substituting the width, W into the equation, we have
L + W = 112
L + L/2 - 8 = 112
L + L/2 = 112 + 8
L + L/2 = 120
3L/2 = 120
L = 120 × 2/3
L = 240/3
L = 80 inches
So, the length of the pegboard is 80 inches
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a list of 1111 positive integers has a mean of 1010, a median of 99 and a unique mode of 88 what is the largest possible value of an integer in the list?
The largest possible value in the list is 35.
What is mean, median and mode?
Adding the numbers together and dividing the result by the total number of numbers in the list yields the arithmetic mean. An average is most frequently used to refer to this. The middle value in a list that is arranged from smallest to greatest is called the median. The value that appears the most frequently on the list is the mode.
Given: There is a list of 11 positive integers.
Has a mean of 10, a median of 9 and a unique mode of 8.
Since the mode (8) is less than the median (9), the mode can only appear (at most) 5 times since the mode is the 6th number in the list (assuming the list has been sorted in ascending order).
If so, the first five numbers can be 8, the following four numbers can be 9, and the next greatest number can be 10, which means the largest number must be 110 - (8 x 5 + 4 x 9 + 10) = 110 - 86 = 24.
The largest number must be 110 - 77 = 33 if the mode repeats just twice, in which case we can let the first ten numbers be 1, 2, 3, 8, 8, 9, 10, 11, and 13, totaling 77.
The biggest number in this scenario is 110 - 75 = 35 if the mode repeats itself three times. Alternatively, we can let the first ten numbers be 1, 1, 8, 8, 8, 9, 10, 10, and 11 totaling 75.
Therefore, the largest possible value of an integer in the list is, 35.
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4x+4≤9x+8
please help
Answer:
x ≥ - [tex]\frac{4}{5}[/tex]
Step-by-step explanation:
4x + 4 ≤ 9x + 8 ( subtract 5x from both sides )
4 ≤ 5x + 8 ( subtract 8 from both sides )
- 4 ≤ 5x ( divide both sides by 5 )
- [tex]\frac{4}{5}[/tex] ≤ x , then
x ≥ - [tex]\frac{4}{5}[/tex]
Answer:
4x + 4 ≤ 9x + 8 Subtract 4x from both sides
4 ≤ 5x + 8 Subtract 8 from both sides
-4 ≤ 5x Divide both sides by 5
≤ x
x ≥
Step-by-step explanation:
which property is used in the problem below, the commutative property or the associative property??
(4 x 2) x 3 = (2 x 4) x 3
A ball is dropped from a tall building. the formula in the box relates the distance in meters {d} fallen to the time in seconds, {t}. d=4.9t if the ball falls for a total of 1.2 seconds before hitting the ground, approximately how tall is the building?
The building is 5.88 units tall.
It is given that the ball is dropped from a tall building.
The formula in the box relates the distance in meters "d" fallen to the time in seconds "t".
The formula is given below :
d = 4.9*t
The ball falls for a total of 1.2 seconds before hitting the ground.
The ball will travel a distance in the time interval from when the ball is dropped until it hits the ground.
The time for which the ball travels the distance is 1.2 seconds.
The distance travelled by the ball is :
d = 4.9*t
d = 4.9*1.2
d = 5.88
Hence, the ball travels a distance of 5.88 after it is dropped from the top of the building and before hitting the ground.
The height of the building is equal to the distance calculated.
The height of the building is 5.88.
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can someone help me really quick please
The value of p is $ 6.75.
It is given in the figure that the price of 6 apples in the grocery store is $ 4.50.
We have to find the value of p which is the price of 9 apples.
By unitary method, we can write,
Price of 1 apple = 4.5/6 = 3/4 = $ 0.75.
Hence,
Price of 9 apples = 0.75*9 = 6.75 dollars
Hence, the value of p is $ 6.75.
Unitary method
The unitary method is generally a way of finding out the solution of a problem by initially finding out the value of a single unit, and then finding out the essential value by multiplying the single unit value.
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Peter says,
"If you subtract 18 from my number and multiply the difference by -6, the result is -84."
What is Peter's number?
I already made the equation, I just am struggling solving it
-6(x-18)=-84
Answer:
x = 32
Step-by-step explanation:
-6(x-18) = -84
Divide both sides by -6
x - 18 = 14
Add 18 to both sides
x = 32
f(x) = 3x + 10
g(x) = x - 2
Find f(g(5))
Answer: 19
Step-by-step explanation:
[tex]g(5)=5-2=3\\\\\impies f(g(5))=f(3)\\\\=3(3)+10=19[/tex]
How far does a rider travel in one complete rotation around the Ferris wheel?
Use 3.14 as an approximation for Pi and round the second answer below to the nearest whole number.
If the diameter of the Ferris wheel is 80 meters, then a rider will travel 251.2 meters in one complete rotation around the Ferris wheel.
The diameter of the Ferris wheel = 80 meters
The radius of the Ferris wheel = Diameter / 2
= 80/2
= 40 meters
The Total distance travelled by the rider in one revolution = The circumference of the wheel
The circumference of the wheel = 2πr
Where r is the radius of the wheel
Substitute the values in the equation
The circumference of the wheel = 2×3.14×40
= 251.2 meters
Hence, if the diameter of the Ferris wheel is 80 meters, then a rider will travel 251.2 meters in one complete rotation around the Ferris wheel
The complete question is :
If the diameter of the Ferris wheel is 80 meters, how far does a rider travel in one complete rotation around the Ferris wheel?
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the population of a city will quadruple in 15 years. if its current population is 6,000, using the given rate of change, what will its approximate population be 7 years from now
Answer:
11200
Step-by-step explanation:
can anyone please solve this 3 dimensional equation?
The solution for the system of equations of three variables is:
x = 4
y = -1
z = -3
Or (4, -1, -3) written as a point.
How to solve the system of equations?
Here we have a system of equations on 3 variables, the system is:
3x + 2y + z = 7
5x + 5y +4z = 3
3x + 2y + 3z = 1
Notice that the "x" and "y" coefficients in the first and last equation are the same ones, so we can take the difference between these to get:
(3x + 2y + 3z ) - (3x + 2y + z ) = 1 - 7
2z = -6
z = -6/2 = -3
So the value of z is -3.
Replacing that in the first and second equation we get:
3x + 2y - 3 = 7
5x + 5y + 4*(-3) = 3
Now we can simplify these:
3x + 2y = 10
5x + 5y = 15
We can divide the second one by 5 to get:
(5x + 5y)/5 = 15/5
x + y = 3
Isolating x, we get:
x = 3 - y
Now we replace that in the other equation:
3*(3 - y) + 2y = 10
9 - y = 10
9 - 10 = y
-1 = y
Now we know the value of y, finally with:
x = 3 - y
We can get the value of x:
x = 3 - (-1) = 4
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a particular community in the mid west experiences on average 3.9 tornadoes every year. what's the probability that the next tornado comes after 7 months have passed? give your answer in decimal form with three significant digits.
0.8973 is the probability that the next tornado will occur within the next seven months.
Applying the rule of three, we can infer that since the average number of tornadoes in a year is 3.9, the average number of tornadoes in a nine-month period is 3.9*7/12 = 2.275. It is reasonable to believe that the distribution of tornadoes over time is Poisson. Let's refer to X as the number of tornadoes in a seven-month period. X has a Poisson distribution with a parameter of 2.27.
The probability of X being greater than or equal to 1 is equivalent to the likelihood that the next tornado will occur within the next seven months.. However P(X≥1) = 1-P(X=0), and
[tex]p(X=0) = (e^{2.275} * 2.275^{0}) / 0![/tex] = 0.1027
Thus, the probability that the next tornado comes within the next 7 months is 1-0.1027 = 0.8973.
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For her science fair project, Madelyn is growing crystals with sugar water. She wants to know if the size of the container has an effect on crystal growth. To start, Madelyn pours a sugar-water mixture into a small bowl. Then she pours triple the amount of the mixture into a large bucket. She decides to add red coloring so the crystals are more visible. Madelyn adds the same amount of red coloring to both containers. Which container's sugar water mixture is a darker shade of red?
The container whose sugar water mixture is a darker shade of red is: A. the small bowl's mixture is a darker shade of red.
What is a ratio?A ratio can be defined as a mathematical expression that's used to denote the proportion of two (2) or more quantities with respect to one another and the total quantities.
In this scenario, the ratio of the sugar water mixture in the small bowl (S) to the sugar water mixture in the large bucket (L) can be represented by this mathematical expression:
S:L = 1:3
Also, when red coloring is added to both containers, we have:
S:L = 1r:3r
In this context, we can reasonably and logically deduce that the mixture in the small bowl would have a darker shade of red because it is less diluted in comparison with the sugar water mixture in the large bucket.
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Complete Question:
For her science fair project, Madelyn is growing crystals with sugar water. She wants to know if the size of the container has an effect on crystal growth. To start, Madelyn pours a sugar water mixture into a small bowl. Then she pours triple the amount of the mixture into a large bucket. She decides to add red coloring so the crystals are more visible. Madelyn adds the same amount of red coloring to both containers. Which container's sugar water mixture is a darker shade of red?
answer choices
The small bowl's mixture is a darker shade of red.
The large bucket's mixture is a darker shade of red.
Neither. The mixtures are the same shade of red.
a lake is stuck with 1,550 young carp. the number of the original fish alive after t years is given by the function P (t)= 1550e^-0.4t, when will there be 440 of the original fish left from to the nearest tenth
so the time needed is 3.1 years
Someone please help!
Answer:
Step-by-step explanation:
1. b. (2,14)
2. a. (-1,4)
3. c. (-2,2)
Answer: 1. b
2. a
3. c
Step-by-step explanation:
We will change the second equation to y form, then we get:
2x - y = - 6
- y = -2x - 6
y = 2x + 6
Then we plug in each point to see whether it fixes the equations.
a) 1. y = 3x + 8
4 ?= 3(-1) + 8
4 ?= -3 + 8
4 x 5
a) 2. y = 2x + 6
4 ?= 2(-1) + 6
4 ?= -2 + 6
4 = 4
Point a is a solution of the second equation, but not a solution for the first equation.
b) 1. y = 3x + 8
14 ?= 3(2) + 8
14 ?= 6 + 8
14 = 14
b) 2. y = 2x + 6
14 ?= 2(2) + 6
14 ?= 4 + 6
14 x 10
Point b only fits the first equation, but does not fix (not a solution) of the second equation.
c) 1. y = 3x + 8
2 ?= 3(-2) + 8
2 ?= -6 + 8
2 = 2
c) 2. y = 2x + 6
2 ?= 2(-2) + 6
2 ?= - 4 + 6
2 = 2
Point c fits both the first equations and the second equations.
A bicycle company has designed and built a new model of sports bicycle. They have determined that the profit for the sale of the bicycles can be modeled by the function ��(��) =− 2�� , where x is the price of each bicycle. Which of the 2+ 920�� + 84, 000 following is a sale price for the bicycles that will allow the company to achieve a profit of $189,800?
Answer:120 dollars
Step-by-step explanation:
1/2 - 9/4x = -2/3 solve for x and simplify your answer as much as possible
Answer: 14/27
Step-by-step explanation:
solve the following proportionx 2— = —32 8x=
We have to solve for x:
Multiply both sides of the proportion by 32:
[tex]\frac{x}{32}(32)=\frac{2}{8}(32)[/tex][tex]x=\frac{64}{8}[/tex]Simplify:
[tex]x=8[/tex]PLEASE HELP QUICKLY
What is the center of the hyperbola?
(y+3)^2/9 − (x−2)^2/2 = 1
Enter your answer by filling in the boxes.
The hyperbola has a center of (2, -3)
How to calculate the center of the hyperbola?The equation of the hyperbola is given as
(y + 3)²/9 − (x − 2)²/2 = 1
A hyperbola is generally represented as
(y - k)²/a² − (x − h)²/b² = 1
Where the coordinates of the center of the hyperbola is
Center = (h, k)
Next, we compare (y - k)²/a² − (x − h)²/b² = 1 and (y + 3)²/9 − (x − 2)²/2 = 1
From the comparison, we have
(h, k) = (2, -3)
This means that the center is (2, -3)
Hence, the coordinates of the center is (2, -3)
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find mean propertion between 5 and 125
select all the angles that are congruent to <6
The angles that are congruent to angle 6 in the given diagram are:
∠2, ∠3, and ∠5.
What are Congruent Angles?Interior angles that lie opposite to each other along a transversal that cut across the parallel lines they are found on are said to be congruent angles based on the alternate interior angles theorem.
Also, vertical angles have angle measure that are the same, that is, they are congruent as well, so also are corresponding angles.
In the image given, angles 3 and 6 are alternate interior angles. Therefore, they are congruent.
∠5 is congruent to ∠6 because they are vertical angles.
∠2 is congruent to ∠6 because they are corresponding angles.
The angles that are congruent to angle 6 are: angles 3, 5, and 2.
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(08.07) 10 8 6 + 4 3 -2 2 2 -8 -10 -12 - 14 + -16 Which of the following functions best represents the graph? (4 points) Of(x) = x3 + x2 - 9x - 9 f(x) = x3 + 4x2 - X-4 Of(x) = x3 + 3x2 – 3x - 9 Of(x) = x3 + 2x2 - 4x - 8
Given data:
The given graph of the polynomial.
The value of the given polynomial is zero, at x=-3, -1, and 3.
Substitute -3 for x in the expression of the first polynomial.
[tex]\begin{gathered} f(-3)=(-3)^3+(-3)^2-9(-3)-9 \\ =-27+9+27-9 \\ =0 \end{gathered}[/tex]Substitute -1 for x in the expression of the first polynomial.
[tex]\begin{gathered} f(-1)=(-1)^3+(-1)^2-9(-1)-9 \\ =-1+1+9-9 \\ =0 \end{gathered}[/tex]Substitute 3 for x in the expression of the first polynomial.
[tex]\begin{gathered} f(3)=(3)^3+(3)^2-9(3)-9 \\ =27+9-27-9 \\ =0 \end{gathered}[/tex]As all the points are satisfied for the first option.
TThus, the first option is correct.
Evelyn needs to order some new supplies for the restaurant where she works. The restaurant needs at least 769 glasses. There are currently 205 glasses. If each set on sale contains 12 glasses, write and solve an inequality which can be used to determine xx, the number of sets of glasses Evelyn could buy for the restaurant to have enough glasses.
Answer: 769 bottles ≤ 12x + 205, or 564 bottles ≤ 12x
Step-by-step explanation:
➜ They need at least 769 bottles, so our inequality will use either ≤ or ≥ depending on how we set it up.
➜ They currently have 205 bottles, so we will use addition to show there are some glasses currently owned
➜ If each set contains 12 glasses, we will multiply x, the number of sets bought, by 12
With these details, we will write an inequality.
769 bottles ≤ 12x + 205
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