The expression in its simplest form cannot be simplified or factorized any further.
From the options given, answer option A, which is
[tex]2x^2\sqrt[]{7y}[/tex]Cannot be factored any further.
This expression is in its simplest form.
The others, that is options B, C and D can be simplified further.
The answer is option A
The table below shows the relationship between the number of water bottles at a park that are thrown away and the number of water bottles at the park that are recycled for each of five months. Which statement correctly descrīdes the relationship between the number of water bottles that are thrown away and the number of water bottles that are recycled at the park each month? Water Bottles at a Park Water Bottles Water Bottles Thrown Away Recycled 40 12 15 24 80 110 A. The relationship is proportional. For every 3 bottles that are thrown away each month, 10 bottles are recycled. B. The relationship is proportional. For every 10 bottles that are thrown away each month, 3 bottles are recycled. c. The relationship is not proportional. The number of water bottles that are thrown away increases more from month to month than the number of water bottles that are recycled. D. The relationship is not proportional. The difference between the number of bottles that are thrown away and the number of bottles that are recycled is not the same for each month.
EXPLANATION
As we can see in the picture, there is a proportional relationship between the bottles that are thrown away each month and those recycled.
Considering two ordered pairs as for instance, (x_1,y_1)= (40,12) and (x_2,y_2)= (50,15) give us the appropiate rate.
[tex]\text{rate}=\frac{y_2-y_1}{x_1-x_1}[/tex]The rate is as follows:
[tex]rate=\frac{(15-12)}{(50-40)}=\frac{3}{10}\frac{bottles\text{ recycled}}{\text{bottles thrown away}}[/tex]In conclusion, for each 10 bottles thrown away, there are 3 bottles recycled.
The answer is the option B.
what number is part of the solution set to the inequality below?m-20> 12 _
What's the common difference of the sequence -5, -2, 1,4,7, ...?
To find the common diference we substract each of the number by the previous one:
[tex]\begin{gathered} -2-(-5)=3 \\ 1-(-2)=3 \\ 4-1=3 \\ 7-4=3 \end{gathered}[/tex]Therefore the common difference is 3 and the answer is B.
Given that the measure of ∠x is 120°, and the measure of ∠y is 60°, find the measure of ∠z.
The measure of ∠x is 120°, and the measure of ∠y is 60°, find the measure of , ∠z = 0°
What about the triangle angle?A triangle's internal angles always add up to 180°, although its exterior angles are equal to the sum of the two interior angles that are not next to it. Another method for calculating a triangle's exterior angle is to subtract the angle of the vertex of interest from 180°.
Given that,
For triangle,
∠x is 120°
∠y is 60°
now , ∠z = [180° - (120°+60°)]
∠z = 0°
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Which measure is the best estimate of the area of the banner in square meters?
Answer:
6 square meters.
Explanation:
The banner is made up of two congruent triangles and two congruent trapezoids.
The banner forms a triangle with base:
[tex]\begin{gathered} 1\frac{3}{4}+1+1+1\frac{3}{4} \\ =5.5\text{meters} \end{gathered}[/tex]The height of the triangle = 2 meters.
Therefore, the area of the banner:
[tex]\begin{gathered} A=\frac{1}{2}bh \\ =\frac{1}{2}\times5.5\times2 \\ =5.5m^2 \end{gathered}[/tex]The measure that is the best estimate of the area of the banner is 6 square meters.
The temperature in Phoenix, Arizona is 97 degrees. The temperature on Antarctica can be -3 degrees.How far apart are the temperatures of these two cities?
Answer:
100 degrees
Explanation:
Given that:
The temperature in Phoenix, Arizona = 97 degrees.
The temperature on Antarctica = -3 degrees.
To determine how far apart the temperature of the two cities are, we find the difference in temperature.
[tex]\begin{gathered} \text{Difference }=97^0-(-3^0) \\ =97^0+3^0 \\ =100^0 \end{gathered}[/tex]The temperature in the two cities is 100 degrees apart.
State all integer values of x in the interval (1 less than or equal to x less than or equal to 8 ) that satisfy the following inequality:
-3x+9 > 1
The inequality is -3x+9>1. The inequality value of x is greater then 8/3.
Given that,
The inequality is -3x+9>1
We have to find the x value.
Inequalities specify the relationship between two values that are not equal. Equal does not imply inequality. When two values are not equal, we typically use the "not equal symbol ()".But several inequalities are utilized to compare the numbers, whether it is less than or higher than.
Take the inequality is greater then symbol,
-3x+9>1
-3x>1-9
-3x>-8
x>-8/-3
x>8/3
Therefore, the inequality value of x is greater then 8/3.
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what algebra property is this equation: (4y+1)x0=0
Answer:
It would be called the algebraic property of 0.
Step-by-step explanation:
3. The 9 boys in Mr. Ackerman's class went
outside for recess. They wore their gloves.
Isaiah and Michael each lost a glove while
outside. How many gloves did the boys bring
back into the classroom?
Answer:
14.
Step-by-step explanation:
Multiply 9x2 = 18
do 18-4 = 14
boom answer
Answer: 16
Step-by-step explanation:
9 boys in Mr. Ackerman's class
And gloves is plural so it means each boy has 2 gloves/
9 x 2 = 18
Then, 2 boys lost one glove..... glove is singular and there are 2 boys.
This means 2 gloves are missing
18 - 2 = 16
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Graph each equation rewrite in slope-intercept form first if necessary.Y=-1/3x+4
To graph the linear equation, follow the steps below.
Step 01: Find one point of the line.
To do it, choose a x-value and find its corresponding y-value.
Let's choose x = 0.
Substituting x in the equation to find y:
[tex]\begin{gathered} y=-\frac{1}{3}x+4 \\ y=-\frac{1}{3}*0+4 \\ y=0+4 \\ y=4 \end{gathered}[/tex]First point: (0, 4).
Step 02: Find another point of the line.
Let's choose x = 3.
Substituting x in the equation to find y:
[tex]\begin{gathered} y=-\frac{1}{3}*3+4 \\ y=-\frac{1}{3}*3+4 \\ y=-\frac{3}{3}+4 \\ y=-1+4 \\ y=3 \end{gathered}[/tex]Second point: (3, 3).
Step 03: Plot the two points and connect them to draw the graph.
The graph is shown below:
X is a normally distributed random variable with mean 71 and standard deviation 9.
What is the probability that X is between 60 and 82?
Write your answer as a decimal rounded to the nearest thousandth.
Since the standard deviation is 10 and the first given score is 40, the 40 is 2 standard deviations below the mean.
On the other hand, 80 is 2 standard deviations above the mean.
Thus, we subtract the probability below the z-score which is 2, 0.97725, and the probability below the z-score which is -2, 0.02275.
[tex]\begin{gathered} P(X)=0.97725-0.02275 \\ P(X)=0.9545 \end{gathered}[/tex]We may obtain the values using the z-score table.
Therefore, the approximate value of the probability is 0.955.
What is the slope of the line passing through the points (2,
-5) and (4, 1)?
Answer: 3
Step-by-step explanation:
We can use the slope formula to calculate the slope of the line passing through these two points.
[tex]\displaystyle \frac{y_{2} -y_{1} }{x_{2} -x_{1} }=\frac{1--5}{4-2} =\frac{1+5}{4-2} =\frac{6}{2} =3[/tex]
Write 60% as afraction in lowest terms.
60% as a fraction is 3/5
To solve this, first we need to conver the percentage to decimal:
[tex]undefined[/tex]Which is the graph of g(x) = (0.5)^x+3 -4?
The graph of the function g(x) = (0.5)ˣ +3 -4 is shown (refer the graph attached below.)
What do we mean by the graph of the functions?The collection of all points in the plane with the form (x, f(x)) that make up a function f's graph. We could also say that the graph of f is the graph of y = f. (x). As a result, the graph of an equation is a particular instance of the graph of a function. To determine if a graph represents a function, use the vertical line test. The graph is a function if a vertical line drawn across it is moved and only ever touches it at one point. The graph is not a function if the vertical line touches it at more than one location.So, the graph of the function g(x) = (0.5)ˣ +3 -4 will be:
(Refer to the graph attached below.)Therefore, the graph of the function g(x) = (0.5)ˣ +3 -4 is shown.
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The correct question is given below:
What is the graph of g(x) = (0.5)^x+3 -4?
Consider the following quadratic equation:35x2 = 13x + 12Step 1 of 2: Using the standard form ax² + bx + c = 0 of the given quadratic equation, factor theleft hand side of the equation into two linear factors.AnswerKeypadKeyboard Shortcuts= 0
Given: The quadratic equation below
[tex]35x^2=13x+12[/tex]To Determine: The two linear factors of the given equation using standard form of a quadratic equation
The standard form of a quadratic equation is given as
[tex]ax^2+bx+c=0[/tex]Re-write the given equation in the standard form as shown below
[tex]\begin{gathered} 35x^2=13x+12 \\ 35x^2-13x-12=0 \end{gathered}[/tex]Factor the left hand side as shown below
[tex]35x^2-28x+15x-12=0[/tex][tex]\begin{gathered} 7x(5x-4)+3(5x-4)=0 \\ (5x-4)(7x+3)=0 \\ \text{Therefore} \\ 35x^2-13x-12=0,in\text{ factored form is} \\ (5x-4)(7x+3)=0 \end{gathered}[/tex]Hence, the two linear factors of the given equation is
(5x -4)(7x + 3) = 0
Find the area of the shaded region. Round your answer to one decimal place, if necessary. Note: The figure is not drawn to scale.
Area is the quantity that expresses the extent of a region on the plane or on a curved surface. the area of shaded region is 15.728 inches square.
What is Area?Area is the quantity that expresses the extent of a region on the plane or on a curved surface
The diameter of circle is 5, d=5
and the length of side of the equilateral triangle is 3.
to find the area of shaded region we need to find the area of circle and then we have to remove the area of triangle.
π(d/2)²-1/2×a²×sin60⁰
3.14(5/2)²-1/2×3²×√3/2
3.14×2.5²-1/2×9×√3/2
3.14×6.25 -1/2×9×0.866
3.14×6.25-7.794/2
3.14×6.25-3.897
19.625-3.897
15.728
Hence area of shaded region is 15.728 inches square.
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What is the range of the function? ƒ(x) =3/x+4 +1
Enter your answer, in interval notation, by filling in the boxes. Use the drop-down menu at the upper left of keyboard options as
necessary.
Answer:
(-∝;1)∪(1;+∞).
Step-by-step explanation:
for more details see the attached graph.
need a bit of help. Show work
Answer:
1) yes
2) yes
Step-by-step explanation:
I know #1 is parallel because from the slope-intercept form shown, the slopes of line a and line b are the same, meaning it is parallel.
I known #2 is perpendicular because from the slope-intercept form shown, the slopes of line a and line b are the negative reciprocal of eachother.
Find the 11th term in this sequence. *10 poin1) -2, 4. -8, 16, ...Find a11
Given the terms
-2, 4, -8, 16
The first term = -2
The second term is 4
The third term is -8
The fourth term is 16
We can observe that this is a geometric sequence
So to get the 11th term, we will first get the formula
Step 1: Get the common ratio (r)
[tex]\text{common ratio=}\frac{\sec ond\text{ term}}{first\text{ term}}=\frac{third\text{ term}}{\sec ond\text{ term}}[/tex][tex]r=\frac{4}{-2}=\frac{-8}{4}=-2[/tex]Step 2: Get the formula for the nth term
The formula is given by
[tex]T=r^n[/tex][tex]T=(-2)^n[/tex]where T is the nth term
n is the number of terms
Step 3: Find the 11th term
[tex]T_{11}=(-2)^{11}[/tex][tex]T_{11}=-2048[/tex]The 11th term is -2048
I Need help with this question.
How do you rewrite -8 - 4 = -12 in two different ways?
Answer:
Step-by-step explanation:
-4 - 8 = -12
-4 + 12 = 8
Let f(x)= sqrt x. Find (g)x, the function that is f(x) shifted up 2 units and left 5 units
The function f(x) becomes [tex]g(x)=\sqrt{x+5} +2[/tex] after shifting up 2 units and left 5 units.
How is a function vertically and horizontally shifted?Vertical shift: A new function g(x)=f(x)+k, where k is a constant, is a vertical shift of the function f(x), given a function f(x). The output values are all altered by k units. The graph will shift to the right if k is positive. If k is negative, the graph will shift downward.
Horizontal shift: A new function g(x)=f(x-h), where h is a constant, is a horizontal shift of the original function f, where f is a function. Graph shifts to the right if h is positive. If h is negative, the graph will shift to the left.
It is given that [tex]f(x)=\sqrt{x}[/tex].
The graph is shifted up 2 units first.
So, the function becomes [tex]\sqrt{x} +2[/tex]
Now the function is shifted 5 units to the left.
So, the new function. [tex]g(x)=\sqrt{x+5} +2[/tex]
So, the function f(x) becomes [tex]g(x)=\sqrt{x+5} +2[/tex] after shifting up 2 units and left 5 units.
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9zxaA14ePolynomialThe parallelogram shown below is transformed. Identify the type of transformation thatoccurred, then write the algebraic rule that describes the transformation. Use a table like theone shown to help you.(5) = ?Copy the text below into the answer space and then replace the _ with your answer.Expression23-(1-1)Op 1 OpType of Transformation:Algebraic Representation: *Get reald67850.0 mLITGGPre-ImageImageWhathappensto x?Whathappensto y?E'HX3FHIG'GEH'9.Enter your answer
Given the parallelogram and its image
For the point E'
Pre image is E = (2 , 5 )
Image is E' = ( -2 , -5 )
What happen to x? is multiplicative inverse ( multiplied by -1)
What happen to y? is multiplicative inverse ( multiplied by -1)
For the row of F' ;
Pre - image is F = (4 , 8 )
Image is F' = ( -4 , -8 )
What happen to x? is multiplicative inverse ( multiplied by -1)
What happen to y? is multiplicative inverse ( multiplied by -1)
For the row of G' :
Pre - image is G = ( 6 , 5 )
Image is G' = ( -6 , -5 )
What happen to x? is multiplicative inverse ( multiplied by -1)
What happen to y? is multiplicative inverse ( multiplied by -1)
For the row of H' :
Pre - image is H = ( 4 , 2 )
Image is H' = ( -4 , -2 )
What happen to x? is multiplicative inverse ( multiplied by -1)
What happen to y? is multiplicative inverse ( multiplied by -1)
so,
As shown, Type of Transformation: is reflection over the point ( 0 , 0 )
Or can be written reflection Through the origin
Algebraic Representation: ( -x , -y )
the rule of translation
(x , y ) → ( -x , -y)
Which value is equivalent to 62 +42 +24? o 28 O 68 o 96 0
Answer:
128
Explanation:
Given the expression
62 + 42 + 24
Adding the values up will give;
= 62 + (66)
= 128
Hence the equivalent value is 128
A group of people were asked if they had run a red light in the last year. 478 responded "yes", and 200 responded "no".Find the probability that if a person is chosen at random, they have run a red light in the last year.
ANSWER
[tex]P=0.705[/tex]EXPLANATION
The probability that if a person has run a red light in the last year can be found by dividing the number of people that have run a red light in the last year by the total number of people in the group.
The total number of people in the group is:
[tex]\begin{gathered} 478+200 \\ \Rightarrow678 \end{gathered}[/tex]Therefore, the probability is:
[tex]\begin{gathered} P=\frac{478}{678} \\ P=0.705 \end{gathered}[/tex]Which of the following are solutions to the system graphed below?
The solution to the system of inequalities is the shaded area shown in the graph. This also includes the bounding lines of the shaded area since they are all solid lines.
To find the answer, we will check the coordinates provided in the options to see which falls within the shaded portion.
On observation, we can see that the following coordinates fall within the shaded area:
[tex]\begin{gathered} (-5,5) \\ (-4,1) \end{gathered}[/tex]The correct options are OPTION 3 and OPTION 4.
PHS AND FUNCTIONSg local maxima and minima of a function given the graph
A local minimum, also called a relative minimum, is a minimum within some neighborhood that need not be (but maybe) a global minimum
(a) The function h(x) has two local minimums. The values at which h has a local minimum is :
[tex]\text{0, 4}[/tex](b) The local minimum values of h:
[tex]=\text{ -2}[/tex]Which statement must be true if ARST = AXYZ?
OA LT = LX
OB. RS=XY
OC. RT = XY
OD. ZS = LX
RS = XY ,Because ΔRST & ΔXYZ are congruent .option c is correct .
What does the word "congruent" signify in mathematics?
If one of the geometric figures can be superimposed on the other so that their entire surface coincides, then the two are said to be congruent, or to be in the relation of congruence.SSS (three sides the same), RHS (right-angled triangle, hypotenuse, and a side the same), ASA or AAS (two angles and a side the same), and SAS are examples of similar triangle shapes (side-angle-side, two sides and the included angle the same).Are cogent means equivalent?
If and only if the measurements of two angles are equivalent, they are congruent. If and only if the two segments have equal measurements, they are congruent. A pair of triangles are identical if and only if their corresponding angles and sides are identical.In ΔRST & ΔXYZ are congruent so, ΔRST ≅ ΔXYZ
RS = XY Because ΔRST ≅ ΔXYZ .
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When 91 is divided by 1 1/9 the quotient is closest to what whole number?
Justify your answer.
When 91 is divided by 1 1/9 the quotient is closest to 81.
What is a quotient?
When we divide a number by the dividend the result of the division is known as quotient.
We are given a number as 91
We have to divide 91 by 1 1/9
We get, [tex]\frac{91}{\frac{10}{9} }[/tex]
On simplifying the above equation we get,
[tex]\frac{91}{10}[/tex]·[tex]9[/tex]
[tex]=\frac{819}{10}[/tex]
=81.9
This can be rounded off as this value is close to 82.
Hence when 91 is divided by 1 1/9 the quotient is closest to 82.
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A rectangle has a height of 3x and a width of 2x-3Express the area or the entire triangle
Answer
6x² - 9x
Explanation
Given:
Height = 3x
Width = 2x - 3
The area of a rectangle = Length x Width
From the figure, length = height = 3x
Area = 3x(2x - 3)
In expanded form, we shall open the parenthesis
Area = (6x² - 9x) squared unit
Please solve no.13 (i) from here only solve (i) please
The exchange rate (US$1 = S$x) means that for every S$ she will receive 1 US dollar. Therefore, one can write the equation:
[tex]\begin{gathered} y=x\begin{cases}x=S \\ y=US\end{cases} \\ y=2000\lbrack US\rbrack \end{gathered}[/tex]