This shows that the greatest common factor is 8, Hence Venita's error is that she incorrectly determined the GCF.
Greatest common factorGiven the following expression
32ab - 8
Find the factors of each terms
32ab = 8 * 4. * a * b
8 = 8 * 1
Since 8 is common to both factors, hence
32ab - 8 = 8(4ab -1)
This shows that the greatest common factor is 8, Hence Venita's error is that she incorrectly determined the GCF.
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In how many ways can $9$ friends sit at a circular table if two of them, Anna and Bob, insist on having exactly two people seated between them? (As usual, two seatings are considered the same if one is a rotation of the other.)
There are 10,080 different ways in which the friends can seat on the circular table.
In how many ways the friends can seat?
There are 9 friends, such that two of them need to be separated by exactly two people.
Because the table is circular, we can consider the first position as the position where Bob is.
Now let's count the number of options for each of the other 8 positions. (counting to the left).
The next two positions have 7 and 6 options respectively (as these can be taken by any of the other 7 friends)
For the next seat, we could seat Anna or one of the remaining 5 friends.
Let's assume we seat Anna there, then for each of the next positions, we will have, respectively, 5, 4, 3, 2, 1 options.
The total number of combinations is given by the product between the numbers of options, so we have:
C = 7*6*5*4*3*2*1
But we also need to consider the case where Anna is on the first position (and Bob on the third), so we just need to add a factor equal to 2.
C = 2*(7*6*5*4*3*2*1) = 10,080
There are 10,080 different ways in which the friends can seat on the circular table.
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what is the 10th term for sequence 4; 8; 13; 19; 26
Answer:
40
Step-by-step explanation:
If a study determines the difference in average salary for subpopulations of mechanical engineers and civil engineers is NOT significant, then the subpopulations of mechanical and civil engineers are ________ different salaries.
Both are not earning different salaries.
If a study determines the difference in average salary for subpopulations of mechanical engineers and civil engineers is NOT significant, then the subpopulations of mechanical and civil engineers are not earning different salaries.
Study determines that there is not any significant study so thats why both are not earning.
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For which value of x is the expression y
=
a. 1
b. -1
C. 5
d. -5
3x-3
x-5
- undefined?
1
Step-by-step explanation:
when we put 1 in the equation the nominator becomes zero and it becomes undefined
Hii!
___________________________________________________________
[tex]\stackrel\star\rightsquigarrow\circ\boldsymbol{\underbrace{Answer:}}}\circ\leftharpoonup[/tex]
The value of x should be 5! ^^
[tex]\stackrel\star{\rightsquigarrow\circ\boldsymbol{\underbrace{Explanation:}}}\circ\leftharpoonup[/tex]
[tex]\boxed{\\\begin{minipage}{7cm} For\,an\,expression \\ \boldsymbol{to\,be\,und efined,} \\ \,its\,denominator\,should\,be\,zero \end{minipage}}}[/tex]
Remember this! ^^
Now let's consider this:
Which value of x will make the denominator equal to 0?
Is it 1? If we stick 1 in, we will not obtain 0.
[tex]\twoheadrightarrow\sf y=\cfrac{3\cdot1-3}{1-5}[/tex]
[tex]\bullet[/tex] Simplify this
[tex]\twoheadrightarrow\sf y=\cfrac{3-3}{-4}[/tex]
---
We will obtain 0 in the numerator, but not in the denominator; if the numerator is 0, then the fraction, or fractional expression, is 0.
Let's try 5. 5-5 is equal to 0, so this sounds promising! ^^
[tex]\twoheadrightarrow\sf y=\cfrac{3\cdot5-3}{5-5}[/tex]
[tex]\bullet[/tex] Look what we obtain when we simplify
Don't we obtain 15-3/0?
Like I said above, if an expression has 0 as its denominator, it's undefined.
--
Hope that this helped! Best wishes.
[tex]\textsl{Reach far. Aim high. Dream big.}[/tex]
--
THE LENGTH OF A PAINTING OF A TREE IS 2/9 OF THE LENGTH OF THE ACTUAL TREE. IF THE LENGTH OF THE PAINTING OF THE TREE IS 16 INCHES, WHAT IS THE LENGTH IN INCHES OF THE ACTUAL TREE
The length of the actual tree will be 72 inches.
Fraction is the portion of a total amount where the above part of the fraction is the denominator and the bottom part of the fraction is called the numerator.
The equation whose highest degree of the variable is 1 is called a linear equation.
Here given that the length of a painting of the tree is 2/9 of the actual length of the tree.
So mathematically the length of a painting= (2/9)*the length of actual tree
Let the length of the actual tree is x
then from above it is clear that the length of a painting of the tree= (2/9)x
Given the length of the painting is 16 inches.
So the linear equation will be (2/9)x= 16
⇒ x= 16/(2/9)
⇒x= 16*9/2
⇒x=72 inches
Therefore the length of the actual tree will be 72 inches.
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Write and solve an inequality that means a number plus six is less than or equal to twenty-four.
Answer:
Inequality: x + 6 ≤ 24
Solution: x ≤ 18
Step-by-step explanation:
Plus: "+" → to add something to something else
Less than or equal to: "≤" → the expression on the left side of the inequality sign is smaller than the expression on the right side of the sign.
Let x be the unknown number.
A number plus 6 is less than or equal to twenty-four:
x + 6 ≤ 24
To solve the found inequality, subtract 6 from both sides:
⇒ x + 6 - 6 ≤ 24 - 6
⇒ x ≤ 18
Therefore, the solution to the inequality is x ≤ 18. The unknown number x can be any real number equal to or less than 18.
No be n
n+6≤24Solve
n≤24-6n≤18Solution set
(-oo,18]Use the moving and additivity principles to explain and she weighs why the next triangle has an area of 1/2 (b*h) Square units for the given choices of B and H. One! If it naturally with the expression b*(1/2h) and the other should fit naturally with the expression 1/2(b*h)
Answer: The given triangles have an area [tex]1/2[/tex] × [tex]base[/tex] × [tex]height[/tex]
Step-by-step explanation:
The moving principle states that if you move a shape rigidly without stretching it the area does not change whereas the additivity principle states that if you combine different shapes without overlapping them then the area is the cumulative sum of each of the figures.
Since both, the principle will give out the same answers. the arrangement for the expression can be manipulated also.
For the first triangle applying the moving principle gives,
Area [tex]=[/tex] [tex]b[/tex] × [tex](\frac{1}{2}[/tex] · [tex]h)[/tex]
For the second triangle applying the additivity principle,
Area [tex]=\frac{1}{2}[/tex] ([tex]b[/tex] · [tex]h[/tex])
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Graph the equation.
Y= - 3/2x
Answer:
Step-by-step explanation:
Part B
Assume the statement is true for n=k. Prove that it must be true for n=k+1, therefore proving it true for all natural
numbers, n.
Hint: Since the total number of dots increases by n each time, prove that d (k) + (k+1)=d (k+ 1).
The inductive step is assuming that the statement is true for some n = k , where k is one of the values we want to prove the statement for, it shows that it is also true for n = k+1.
How to carry out Mathematical Induction?Suppose we have the statement 3n > 4n for all positive integers n.
Now, the statement above is false when n = 1 , since 3 is less than 4. However, it will be true for all other positive integers.
In that case, we can still prove this statement by induction for all integers n ≥ 2 .
Thus, the inductive step is assuming that the statement is true for some n = k , where k is one of the values we want to prove the statement for, it shows that it is also true for n = k+1.
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If the volume of the pyramid is 192 yd³; and the area of the base is 64 yd², what is the height measured in yards?
Answer:
177
Step-by-step explanation:
Which is true regarding the graphed function f(x)?
• f(O) = 3
• f(5) = - 1
• f(3) = 2
O f(2) = -2
Answer:
f(5) = -1
Step-by-step explanation:
The points on the graph are (0,4), (1,3),(2,2), (3,1), (4,0), (5,-1).
The answers are in the form:
f(x) = y
That is, the number in the parenthesis is the x and the number by itself on the right is the y. The only one that is a point on the line is f(5) = -1, which is the point (5,-1)
24. This week, Cristina eamed P594.65 from selling burgers for 35 days. How much he will earn in 5 days?
A. P84.95
B. P94.95
C. P104.95
D. P114.95
25. You have four quizzes in your math subject in a quarter. You got 88.75 for the first quiz, 85.5, 90.5, and 87.25 in the second, third and fourth quizzes, respectively. What is your average in the four quizzes this quarter?
A. 86.5
B. 88
C. 89.5
D. 90 26. Amberich put P580.00 into a savings account for one year. The rate of interest on the account was 6.5%. How much was the interest for one year in pesos and centavos?
A. P67.70
B. P37.70
C. P57.70
D. P17.70
24. This week , Cristina eamed P594.65 from selling burgers for 35 days . How much he will earn in 5 days ?
A. P84.95
B. P94.95
C. P104.95
D. P114.95
25. You have four quizzes in your math subject in a quarter . You got 88.75 for the first quiz , 85.5 , 90.5 , and 87.25 in the second , third and fourth quizzes , respectively . What is your average in the four quizzes this quarter ?
A. 86.5
B. 88
C. 89.5
D. 90
26. Amberich put P580.00 into a savings account for one year . The rate of interest on the account was 6.5 % . How much was the interest for one year in pesos and centavos ?
A. P67.70
B. P37.70
C. P57.70
D. P17.70
Question 24 :
P594.65 : 35 days
P594.65/7 : 35/7 days
P84.95 : 5 days
⇒ A. P84.95
Question 25 :
88.75 + 85.5 + 90.5 + 87.25 / 4
352/4
88
⇒ B. 88
Question 26 :
I = P × r × t
I = 580.00 × 0.065 × 1
I = P37.70
⇒ B. P37.70
If f(n)= n²-n, then f(-4) is
O-20
12
-12
20
Answer:
20
Step-by-step explanation:
Plug in -4 for n:
(-4)^2 - (-4) = 16 + 4 = 20
7
2
3
Mark this and return
f(x)
The functions f(x) and g(x) are graphed.
3
-6-5-4-3-2-1₁-
"AssessmentViewer(Ant
N
5
-2+
-3-
6
g(x)
7
2 3 4 5 6 x
8
Which represents where f(x) = g(x)?
Of(2)= g(2) and f(0) = g(0)
f(2)= g(0) and f(0) = g(4)
Of(2)= g(0) and f(4) = g(2)
Of(2)= g(4) and f(1) = g(1)
Save and Exit
Answer: Option 1
Step-by-step explanation:
The graphs intersect at x=0 and x=2, meaning f(2)=g(2) and f(0)=g(0).
The functions have the intersecting points at x = 2 and x = 0 and the relation is f ( 0 ) = g ( 0 ) and f ( 2 ) = g ( 2 )
What is a function rule?The function rule is the relationship between the input or domain and the output or range. A relation is a function if and only if there exists one value in the range for every domain value.
A function is a relation from a set of inputs to a set of possible outputs where each input is related to exactly one output.
Given data ,
Let the first function be represented as f ( x )
Let the second function be represented as g ( x )
Now , the function f ( x ) is a parabolic function and g ( x ) is a linear function
And , the intersecting points of both f ( x ) and g ( x ) are
x = 2 and x = 0
So , both the functions f(x) and g(x) intersect at two points, one at x = 2 at the x-axis in the graph and one at y = 4 at y-axis of the graph
Therefore , f ( 0 ) = g ( 0 ) and f ( 2 ) = g ( 2 )
Hence , the functions are solved
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The function f(x)=5(x−1) is shown on the coordinate plane.
Select from the drop-down menus to correctly describe the end behavior of f(x).
As x decreases without bound, the graph of f(x) ______
1. approaches y=0
2. increases without bond
3. decreases without bond
As x increases without bound, the graph of f(x) ______
1. approaches y=0
2. increases without bond
3. decreases without bond
As x decreases without bound, the graph of f(x) approaches y = 0
As x increases without bound, the graph of f(x) increases without bound
What is Function?An expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
Given:
f(x)=5^(x−1)
When x -> -∞
[tex]lim_{ x- > -\infty.[/tex] f(x)= 5 ^(x-1) = 0
When x -> ∞
[tex]lim_{ x- > \infty.[/tex] f(x)= 5 ^(x-1) = ∞
Hence,
As x decreases without bound, the graph of f(x) approaches y = 0
As x increases without bound, the graph of f(x) increases without bound
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Use the graph of the function to find its domain and range. Write the domain and range in interval notation
Answer:
Step-by-step explanation:
This is part A to one of my questions to help answer the second one, the second question is posted if anyone can help
Answer:
Step-by-step explanation:
Part A: Since 400 is being multiplied 1.06^t, for it to be equal to 399 the value 1.06^t must be less than 1. The lowest value for t given the domain restriction is 0 which would only result in 1 which will given the initial amount of 400. t would need to be less than 0 for 1.06^t to start going below the value 1 but since there is a domain restriction since t represents time, that value cannot go below 400 to reach 399.
A carpet installer charges a flat rate of $40 + $1.50 per square foot for labor so the total cost for the labor depends on the amount of carpet installed the relationship between the total cost for labor and the amount of corporate installed is the domain of the relation is the range of the relation is
The domain of the linear function is (1.5, ∞) and the range of the linear function will be (40, ∞).
What are domain and range?The domain means all the possible values of x and the range means all the possible values of y.
A carpet installer charges a flat rate of $40 and $1.50 per square foot for labor.
So the total cost for the labor depends on the amount of carpet installed, the relationship between the total cost for labor and the amount of corporate installed.
Then the domain of the relation is the range of the relation will be
Let y be the total amount and x be the number of square foot.
y = 1.5x + 40
Then the domain of the linear function is (1.5, ∞) and the range of the linear function will be (40, ∞).
The graph is given below.
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evaluate-4x + 2y - z if x = - 2, y = 3, and z = -4
Answer:
-4(-2)+2(3)-(-4)
8+6+4
16 is the answers
Step-by-step explanation:
please mark me as brainlest
Timothy is an hourly employee and he can work maximum of 40 hours in a week. If the weekly salary depends on the number of hours (h) worked, what will be the domain of the function in this context?
a. h < 40, h ∈ Z
b. h ≥ 0, h ∈ R
c. 0 ≤ h ≤ 40, h ∈ R
d. h ≤ 40, h ∈ R
Answer:
C
Step-by-step explanation:
0 ≤ h ≤ 40, h ∈ R
Hope this helps :)
Help, Help, Brainliest available to the best Answer!
Find the Variance
Considering the given data-set, it's mean and the formula, the variance is of 870 lbs².
What is the variance of a data-set?The variance of a data-set is given by the sum of the differences squared between each observation and the mean, divided by the number of values.
The mean is the sum of all observations divided by the number of observations, hence:
M = (145 + 175 + 180 + 205 + 120)/5 = 165.
And the variance, in lbs squared, is given by:
V = [(145-165)² + (175-165)² + (180-165)² + (205-165)² + (120-165)²]/5 = 870.
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Express cos A as a fraction in simplest terms.
Answer:
See below
Step-by-step explanation:
Here is one way
cos^2 + sin^2 = 1
cos^2 = 1 - sin^2
For angle A cos^2 = 1 - (10/26)^2
cos ^2 = 1 - 100/676
= 576/676
cos A = 24/26 = 12/13
Another way would be to use the Pythagorean theorem to find length of AB .... then cos A = length AB / 26
which terms could have the greatest common factor of 5m2n2? select two:
m5n5
5m4n3
10m4n
15m2n2
24m3n4
Answer:
5m4n3 and 15m2n2
Step-by-step explanation:
you just have to find the 2 that each are divisible by 5m2n2, which are 5m4n3 and 15m2n2.
5. Identify the sign of the leading coefficient and describe the end behaviour. Using this
information, decide if each function is cubic or quartic.
The sign of the leading coefficient can be found using the graph of a polynomial function.
What is polynomial?Polynomial is the combination of variables and constants systematically with "n" number of power in ascending or descending order.
[tex]\rm a_1x+a_2x^2+a_3x^3+a_4x^4..........a_nx^n[/tex]
We have given the graph of polynomial functions:
In the first graph:
The leading coefficient is positive.
x → ∞, f(x) → ∞
x → -∞, f(x) → -∞
Degree of a function = 3
In the second graph:
The leading coefficient is negative.
x → ∞, f(x) → -∞
x → -∞, f(x) → -∞
Degree of a function = 4
In the third graph:
The leading coefficient is positive.
x → ∞, f(x) → ∞
x → -∞, f(x) → ∞
Degree of a function = 4
In the fourth graph:
The leading coefficient is negative.
x → ∞, f(x) → -∞
x → -∞, f(x) → ∞
Degree of a function = 3
Thus, the sign of the leading coefficient can be found using the graph of a polynomial function.
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(x) = x + 0.14x, then find the value of T(290).
A. 300.45
B. 351.2
C. 325.8
D. 330.6
Answer:
D. 330.6
Step-by-step explanation:
To evaluate the function for a specific value of x, put that value where x is in the function definition, and do the arithmetic.
__
T(x) = x +0.14x . . . . . given function definition
T(290) = 290 +0.14×290 = 290 +40.6 . . . . substitute 290 for x
T(290) = 330.6
The value of T(290) will be 330.6.The relation between them is shown as T(x) is dependent and x is the independent variable. Option D s correct.
What is a function?A connection between independent variables and the dependent variable is defined by the function.
Functions help to represent graphs and equations. A function is represented by the two variables one is dependent and another one is an independent function.
Given relation;
T(x) = x +0.14x
Substitute the value of x we get;
T(290) = 290 +0.14×290
T(290) = 330.6
Hence, option D s correct.
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distance between (-5,1) and (0,-4)?
Answer:
7.07106781187
Which expression is equivalent to (1−sinβ)(1+sinβ)/cos2β for all values of β for which (1−sinβ)(1+sinβ)/cos2β is defined?
Select the correct answer below:
tan2β
tanβ+secβ
tanβ
sec2β
1
Work Shown:
[tex]\frac{(1-\sin(\beta))(1+\sin(\beta))}{\cos^2(\beta)}\\\\\frac{1-\sin^2(\beta)}{\cos^2(\beta)}\\\\\frac{\cos^2(\beta)}{\cos^2(\beta)}\\\\1\\\\[/tex]
Therefore, [tex]\frac{(1-\sin(\beta))(1+\sin(\beta))}{\cos^2(\beta)}=1\\\\[/tex] is an identity for all values of β for which the original expression is defined. I used the difference of squares rule for the 2nd step. Then I applied the pythagorean trig identity for the 3rd step.
The interior angle of a regular polvgon is 9 times the size of its exterior angle
Work out how many sides the polygon has
==================================================
Work Shown:
x = exterior angle
9x = interior angle
interior + exterior = 180
9x+x = 180
10x = 180
x = 180/10
x = 18
n = number of sides
n = 360/x
n = 360/18
n = 20
There are 20 sides to the regular polygon.
Side notes:
The formula to determine n only works for regular polygons.A polygon with 20 sides is known as an icosagon.Any pair of adjacent interior and exterior angles are supplementary. They add to 180 degrees.if p = (-1,-1) find the image of p under the following rotation. 90 degrees counterclockwise about the origin
Answer:
( 1, - 1 )
Step-by-step explanation:
how to evaluate 16/81 1/2
An expression is defined as a set of numbers, variables, and mathematical operations. The value of (16/81)^(1/2) is 4/9.
What is an Expression?In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.
The value of the given expression (16/81)^(1/2) can be calculated as shown below,
[tex](\dfrac{16}{81})^{\frac12}\\\\=\sqrt{\dfrac{16}{81}}\\\\= \dfrac49[/tex]
Hence, the value of (16/81)^(1/2) is 4/9.
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Answer:
★The square root of 16/81 = 4/9.
