The simplified expression for -27z^3-9z^4+18z^6, using the greatest common factor, is given as follows:
9z³(-3 - z + 2z³).
How to factor an expression by GCF?To find a symbolic expression by the greatest common factor, we have to:
Find the greatest common factor of the numeric coefficients.Find the greatest common factor of the exponents.Then we multiply these GCFs.
For this problem, the numeric coefficients are given as follows:
27, 9 and 18, hence the GCF is of 9.
The exponents are given as follows:
z³, z^4 and z^6, hence the GCF is of z³, which is the expression with the lowest exponent.
Then the GCF of the expression is given as follows:
9z³.
To simplify the expression, each term of the expression is divided by 9z³, hence the factored expression is:
9z³(-3 - z + 2z³).
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Features of the function f(x)=-log3x+6
The following are the properties of the given logarithmic function f(x) = -log3x+6:
The function's domain is (0, ∞).
The function's range is (-∞, ∞) i.e. the set of all real numbers.
At x = 0, the component shows the presence of a vertical asymptote.
The constant reflects the x-axis logarithm.
What are the properties of logarithms?There are four basic properties of logarithms:
logₐ(xy) = logₐx + logₐy.
logₐ(x/y) = logₐx - logₐy.
logₐ(xⁿ) = n logₐx.
logₐx = logₓa / logₓb.
We have been given that the function f(x) = -log3x+6
As per the above function,
The function's domain is (0, ∞).
The function's range is (-∞, ∞) i.e. the set of all real numbers.
At x = 0, the component shows the presence of a vertical asymptote.
The constant reflects the x-axis logarithm.
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A diver is standing on a diving board 5 1/4 feet above sea level.
He jumps off and dives into the water for a total of 15 1/2 feet.
How far below sea level is the diver?
Answer:
Step-by-step explanation:
5 1/4 feet above sea level minus 15 1/2 will equal the distance the diver is below sea level.
5 1/4 - 15 1/2 = 10 1/4 feet below sea level
The following figure is made of a square and a rectangle.
What is the perimeter of the figure?
Consequently, the combined perimeter of the square and rectangle in the previous diagram is 36 cm.
What is the perimeter of the quadrilateral?We combine each side's value.
For instance, the typical solution is to multiply the length by two and the width by two, then add the results to determine the perimeter if the quadrilateral is a square, rectangle, parallelogram, or any other shape with two equal opposite sides and angles.
In the given diagram, we can infer that
the diagram is a combination of a square and a rectangle
so for the rectangle:
the perimeter is =2(l+b)
=2(8+5)
=26 cm
so for the square :
the perimeter is =2(side +side):
=2(5+5)
=20cm
to get the total perimeter ,we will add both the perimeters but subtract one side (5cm) because it is common in both the quadrilaterals twice:
so we get:
20+26-10=36cm
Therefore, the perimeter of the preceding diagram of a square and a rectangle combined is 36cm.
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question in screenshot
The value of tan33° is 11/20.
What is a right triangle?A triangle with an angle measure of 90° is called a right triangle.
Given that, tan(x) = (length of the opposite side)/ (length of an adjacent side)
Therefore, for the given triangle, it follows:
tan33° = 11/20
Hence, the value of tan33° is 11/20.
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Suppose you have a population with mean 25 and standard deviation 20. You take samples of size 100 and consider the distribution of the means of those samples. What is the mean of the sample means?.
The mean of the sample means of the given data is 40
The provided sample size is 100, with a standard deviation 20and mean of the as 25.
Mean of the population, μ = 25
The standard deviation of the population, σ = 20.
Size of the sample, n = 100
Let X be the mean of the sample means,
The formula for the sample mean is
X = μ
where μ, as we know is the mean of the population
By substituting the value in the above equation, we get
X = 40
Therefore, we get the mean of the sample means is 40
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Augustina has 2 posters with length x inches. One poster has a width of x+3 inches, and the other has a width of x+7 inches. Write an expression to represent the area of wall that the posters will cover.
Answer:
20 inches
Step-by-step explanation:
7x2=14
3x2=6
14+6=20
A student needs to select a statistical question to research for a project. Which of the following questions should the student select? A How many days have I been absent from school this year? B How many students in the school were absent on November 1st of this school year? C How many days have each of the students in my class been absent this month? D How many students in my class were absent last Wednesday? PLSS HELP OH GOD I WANT TO PAST
When the student needs to select a statistical question to research for a project, the question that he should select is D. How many students in my class were absent last Wednesday?
How to illustrate the information?Any question that may be answered statistically is one for which data collection is possible and for which there will be some degree of data variability. Because there is no variability in the data used to answer the question, questions that can only be answered with a single data point are not statistical questions.
To do research for a project, a student must choose a statistical question. In this case, it should be noted that it's important to select a question that's specific. This was illustrated by option D.
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Abc has vertices a(-2, "-1)" b(1,2 and c(2,-4) if a'b'c' is a dilation of abc with a scaled factor of 2.5 and center of dilation (0, 0), give the coordinates of the vertices of a'b'c
The new coordinates of the vertices a'b'c' are (-5, -2.5), (2.5, 5) and (5, -10) respectively of the triangle.
What is defined as the scale factor?Scaling (or dilation) is the process of making something bigger or smaller. As a result, if we scale this same coordinates points, we multiply the points by the scale factor to really get new coordinates points that are greater or less than the original points.For the given question;
The vertices of the triangle has the coordinates of a, b and c;
a = (-2, -1)b = (1, 2) c = (2, -4)The dilation of the abc is factored with the scale factor of 2.5.
Thus, to find the new coordinates of a'b'c' multiply each value with 2.5.
a' = 2.5×(-2, -1) = (-5, -2.5)b' = 2.5×(1, 2) = (2.5, 5)c' = 2.5× (2, -4) = (5, -10)Thus, the new coordinates of the vertices a'b'c' are (-5, -2.5), (2.5, 5) and (5, -10) respectively.
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Consider the relation
The domain of the relation is 2, 5, 3, 6 and 7.
How to find the domain of a relation?The domain of the relation can be found as follows;
The domain of a function is the set of all possible inputs for the function.
The domain are usually the independent variable of a function.
The domain are associated with the x values.
Hence, the domain of the relation is as follows:
domain = {2, 5, 3, 6 , 7}
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The temperature during a very cold day is recorded every 2 hours for 12 hours. The data are given in the table below. What type of polynomial would best model these data?
cubic
linear
quartic
quadratic
Answer: A. Cubic
Step-by-step explanation:
What is the special angle pair relationship between the two
Answer: same side interior angles
Step-by-step explanation:
Please Help I don’t want to fail this test my grade is low!
What is the slope?
Simplify your answer and write it as a proper fraction, improper fraction, or integer.
Answer:
1/3
Step-by-step explanation:
the is slope of this graph is 1_3
Answer:
1/3
Plssssss mark as brainliest
Step-by-step explanation:
To find the slope of a graph you need to look for 2 pairs of accurate xand y values
First value which is accurate is:
x = 1 and y= 4
Second pair which is accurate is :
x = 7 and y = 6
Gradient = rise/run = y2-y1/x2-x1
im taking y2 as 6, x2 as 7, y1 as 4 and x1 as1
6-4/7-1
=2/6
=1/3
Round 64.87 to the nearest tenth.
Answer:
64.9
Step-by-step explanation:
Since 7 is equal to or above 5 it will add +1 to the 8
Answer:
64.87 rounded to the nearest tenth is 64.9 since it is past 5 :)
Step-by-step explanation:
there are 6 boys and 14 girls in a class what is the percentage
Answer:
percentage of boys:
6/20x100
=30%
percentage of girls:
14/20x100
=70%
Answer:
Step-by-step explanation:
70%
Please help me do the Q1. 5 ii)
The most appropriate choice for trigonometric function will be given by
Greatest value = 2, least value = -3
What are trigonometric functions?
Trigonometric functions are those functions which shows the relationship between side and angle of a right angled triangle.
There are six trigonometric functions-
[tex]sin\theta, cos\theta, tan\theta, cot\theta, sec\theta, cosec\theta[/tex]
[tex]sin\theta=\frac{perpendicular}{hypoteunse}\\ \\cos\theta=\frac{base}{hypoteunse}\\\\tan\theta=\frac{perpendicular}{base}\\\\cot\theta=\frac{base}{perpendicular}\\\\sec\theta=\frac{hypotenuse}{base}\\\\cosec\theta=\frac{hypotenuse}{perpendicular}[/tex]
Here,
5 ii)
[tex]2 sin^{2} x - 3cos^{2}x \\2(1-cos^2x)-3cos^2x\\2 - 2cos^2x -3cos^2x\\2 - 5cos^2x\\[/tex]
Now,
[tex]0\leq cos^{2}x \leq 1\\ -1 \leq -cos^2x\leq 0\\-5\leq -5cos^2x\leq 0\\-5+2\leq 2-5cos^2x\leq 0+2\\-3\leq 2-5cos^2x\leq 2[/tex]
Greatest value = 2, least value = -3
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Twice a number increased by twenty is at least eighty-five. Select all possible values of the number.
Answer:
2x+20≥84
2x≥64
x≥32
Step-by-step explanation:
Line of Symmetry
Draw the line of Symmetry for each shape. Write how many
17% of 56
…………………………….
Answer: 9.52
Step-by-step explanation: I looked it up but you would do 17 divided by 56 and get a decimal and then move the decimal point over 2 spaces to the right and then you have your answer.
Hope it helped
in scientific notation 8599000000 = 8.559 x 10^z what is the value of x
Answer:
z = 9
Step-by-step explanation:
X is not a valve is it a multiplication sign. I believe that you are looking for the value of z.
To find the value of z you simply have to count how many times you moved the decimal point. In this case you move the decimal point 9 times. Since you move it to the left z is positive. Z=9
There are 4 identical triangles, each with an area of 4 square units. When put together, they form a square. What is the side length of the square?
William works at a nearby electronics store. He makes a commission of 6\%6%6, percent on everything he sells. If he sells a computer for \$764.00$764.00dollar sign, 764, point, 00, how much money does William make in commission?
\$\
Based on the commission percentage that William makes when he sells goods at the electronics store, the amount that William made in commission from the computer is $ 45. 84.
How to find the money made from commission?Commission made on goods and services are a percentage that is paid to sales people when they make a certain number of sales. The commission is based on the amount that the good or service in question is sold for.
The commission to William here can be found by the formula:
= Percentage made for commission on everything sold x Amount that the computer sold for
Solving for the commission to William gives:
= 6 % x 764
= 0. 06 x 764
= $ 45.84
In conclusion, the commission that William made from the sale of the computer which was valued at $ 764 is $ 45.84.
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Answer:
45. 84
Step-by-step explanation:
Based on the commission percentage that William makes when he sells goods at the electronics store, the amount that William made in commission from the computer is $ 45. 84.How to find the money made from commission?Commission made on goods and services are a percentage that is paid to sales people when they make a certain number of sales. The commission is based on the amount that the good or service in question is sold for. The commission to William here can be found by the formula:= Percentage made for commission on everything sold x Amount that the computer sold for Solving for the commission to William gives:= 6 % x 764 = 0. 06 x 764= $ 45.84
I NEED HELP WITH THIS PLEASE
Answer: 4. 27x + 18 8. 4x - 5
Step-by-step explanation: should be right
Write the quadratic equation that has roots [tex]\frac{(-1-\sqrt{2})}{3}[/tex] and [tex]\frac{(-1+\sqrt{2})}{3}[/tex] if its coefficient with [tex]x^{2}[/tex] is equal to 9.
The quadratic equation is [tex]9x^2-2/3x-\frac{1+2\sqrt{2}}{3}[/tex]
Quadratic Equation:
A quadratic function is a function of degree two.
The general form of the quadratic equation is as follows:
x² + (sum of roots)x + Product of roots.
Given,
Here we have the roots,
[tex]\frac{-1-\sqrt{2} }{3} ,\frac{-1+\sqrt{2} }{3}[/tex]
And the coefficient with x² is equal to 9.
Through the given details we have to find the quadratic equation.
To find the equation we have to identify the sum of roots and the product of roots.
So, the sum of roots is,
[tex]= > \frac{-1-\sqrt{2} }{3} +\frac{-1+\sqrt{2} }{3}[/tex]
[tex]= > \frac{-1 }{3} +\frac{-1 }{3}\\= > \frac{-2}{3}[/tex]
Now the product of roots is,
[tex]= > \frac{-1-\sqrt{2} }{3} \times\frac{-1+\sqrt{2} }{3}[/tex]
[tex]= > \frac{1-\sqrt{2}-\sqrt{2}-2 }{3}=\frac{-1-2\sqrt{2} }{3}[/tex]
So, the quadratic equation is,
[tex]= > 9x^2-2/3x-\frac{1+2\sqrt{2}}{3}[/tex]
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A rectangular garden is 5 ft longer than it is wide. Its area is 300 ft2. What are its dimensions?
Answer:
width=x
length=5x
area= 300ft2
area=lxb
300=5x(x)
300=5x^2
x^2=60
x=7.74
7.74(5)=38.7
dimensions are 38.7ft by 7.74 ft
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Step-by-step explanation:
the area of a rectangle is
length × width = 300 ft²
length = width + 5
(width + 5) × width = 300
width² + 5×width = 300
width² + 5×width - 300 = 0
the general solution to such a quadratic equation is
width = (-b ± sqrt(b² - 4ac))/(2a)
in our case
a = 1
b = 5
c = -300
width = (-5 ± sqrt(5² - 4×1×-300))/(2×1) =
= (-5 ± sqrt(25 + 1200))/2 =
= (-5 ± sqrt(1225))/2 = (-5 ± 35)/2
width1 = (-5 + 35)/2 = 30/2 = 15 ft
width2 = (-5 - 35)/2 = -40/2 = -20 ft
negative lengths for an actual object don't make sense, so width = 15 ft is our solution.
length = width + 5 = 15 + 5 = 20 ft
The height h in feet that a pole vaulter can reach can be estimated using
the formula h = 20, where v is the velocity of the athlete in feet per second.
If the height for a women's pole vault is about 9.8 feet, about how fast was
the holder running? How far will the pole vaulter run in 2 seconds?
Using the numeric value of functions, it is found that the pole vaulter will run 50 feet farther in 2 seconds.
How to find the numeric value of a function/expression?To find the numeric value of a function, we replace each instance of the variable by the desired value.
The formula for the velocity is given as;
v=8√h
where h is the height.
we have the height is of h = 9.8,
hence:
v = 8√(9.8) = 25 feet per second.
The holder was running at the rate of 25 feet per second.
Then, within two seconds, the distance is given as;
d = 25 x 2 = 50 feet.
Hence, The pole vaulter will run 50 feet farther in 2 seconds.
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What is the volume of a cuboid with 10cm 8cm and 6cm
Answer:
480 cm³
Step-by-step explanation:
volume = width × heigh × length
volume = 10 cm × 8 cm × 6 cm
volume = 480 cm³
Hope it Help~
Mrs. Williams made her homemade chicken soup she made 6 3⁄4 cups of soup each servings was 1 1⁄8 cup how many servings are there trying to explain to her how to do it not just give her the answer that it's 6
Answer:
Mrs. Williams made her homemade chicken soup. She made 6 3/4 cups of soup. Each serving size was 1 1/8 cup. = 6
Step-by-step explanation:
this picture below shows how to solve the problem step by step hope this really helps !
if you know this your smartest person in the world
what is the ratio for 1/3 kilograms to 2/3 foot
0.5kg per foot
Answer:
Step-by-step explanation:
ee piles of rocks. the mean weight of the rocks in a is 40 pounds, the mean weight of the rocks in b is 50 pounds, the mean weight of the rocks in the combined piles a and b is 43 pounds, and the mean weight of the rocks in the combined piles a and c is 44 pounds. what is the greatest possible integer value for the mean in pounds of the
The greatest possible integer value for the mean is calculated as 59.
What is defined as the consistent solution?A system is said to be consistent if it has at least one solution. A consistent system is independent if it has exactly one solution. It is dependent if a consistent system has had an infinite number of solutions.Assume that the three piles contain A,B,C rocks, that mean of pile C is x, and the mean of a combination of B and C is y. We will maximize y if the following conditions are met:
40A + 50B = 43(A+B)
40A + xC = 44(A+C)
50B + xC = y(B+C)
that can be reorganized as follows:
7B = 3A
(x - 44)C = 4A
(x - y)C = (y - 50)B
Let's see if y=59 is possible. If so, it's already the solution. Otherwise, there will be an inconsistency. As a result, the third equation is as follows:
(x - 59)C = 9B.
So, 15C = (x-44)C - (x-59)C = 4A - 9B
45C = 4(3A) - 27B = 28B - 27B,
105C = 28A-9(7B) = A
Thus,
A = 105C, B = 45C, Put the values
x = 4(105) + 44 = 464, That gives consistent solution.
Therefore, the value of y is found to be 59, the greatest possible integer value for the mean.
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