The general equation is:
[tex]\frac{b^{2k}\cdot b^{3k}}{b^{4k}}=b^k[/tex]In the firs case, b = 5 and k = 1.
[tex]\begin{gathered} \frac{5^{2\cdot1}+5^{3\cdot1}}{5^{4\cdot1}}=5^1 \\ \frac{5^2+5^3}{5^4}=5^{} \end{gathered}[/tex]In the second case, b = 9 and k = 2.
[tex]\begin{gathered} \frac{9^{2\cdot2}+9^{3\cdot2}}{9^{4\cdot2}}=9^2 \\ \frac{9^4+9^6}{9^8}=9^2 \end{gathered}[/tex]In the third case, b = 2 and k = 3.
[tex]\begin{gathered} \frac{2^{2\cdot3}+2^{3\cdot3}}{2^{4\cdot3}}=2^3 \\ \frac{2^6+2^9}{2^{12}}=2^3 \end{gathered}[/tex]In the fourth case, b = 3 and k = 4.
[tex]\begin{gathered} \frac{3^{2\cdot4}+3^{3\cdot4}}{3^{4\cdot4}}=3^4 \\ \frac{3^8+3^{12}}{3^{16}}=3^4 \end{gathered}[/tex]Choose two pairs of alternate interrior angles.
D. <7 & <12
<6 & <9
A packing machine wastes 0.17 liters of fruit punch for every case of 36 juice boxes that it fills.
If each juice box contains 0.12 liters, how many liters of fruit punch is packaged per liter of fruit punch wasted?
Round your answer to the nearest tenth.
The quantity of liters of fruit punch that is packaged per liter of fruit punch after waste would be = 4.15 liters.
What is a packaging machine?A packaging machine is defined as the industrial equipment that is used package finished product of food and food products such as juice.
For every case of 36 juice boxes = 0.17 liter of wastes juice
The quantity of juice per box = 0.12 liter
This means that the 36 juice boxes = 36 × 0.12 = 4.32 liters
The quantity of juice that is packaged after the wastes has been removed would be;
= 4.32 - 0.17
= 4.15 liters
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The dimensions and number of animals are given for different corrals
Suppose that the corrals are rectangular in shape. The formula of the area of a rectangle is
[tex]\begin{gathered} A=lw \\ l\to\text{ length} \\ w\to\text{ width} \end{gathered}[/tex]Therefore, the areas of the four different corrals are
[tex]\begin{gathered} A_1=50\cdot40=2000 \\ A_2=60\cdot35=2100 \\ A_3=55\cdot45=2475 \\ A_4=65\cdot40=2600 \end{gathered}[/tex]Then, divide each area by its corresponding population,
[tex]\begin{gathered} \frac{A_1}{110}=18.1818\ldots<20 \\ \frac{A_2}{115}=18.2608\ldots<20 \\ \frac{A_3}{125}=19.8<20 \\ \frac{A_4}{110}=20=20 \end{gathered}[/tex]Therefore, the only corral that meets the requirement is corral 4, the answer is option D.
According to Descartes's rule of sign, how many possible positive and negative roots are there for the equation 0=−4x6−3x5+2x2−4x+1?Drag the choices to the boxes to correctly complete the table.
According to Descartes’ Rule of Signs, if we let
[tex]f(x)=a_nx^n+a_{n-1}x^{n-1}+\cdot\cdot\cdot+a_1x+a_0[/tex]be a polynomial function with real coefficients:
then,
the number of positive real zeros is either equal to the number of sign changes of f(x) or is less than the number of sign changes by an even integer.
the number of negative real zeros is either equal to the number of sign changes of f(-x) or is less than the number of sign changes by an even integer.
In this case,
[tex]f(x)=-4x^6-3x^5+2x^2-4x+1[/tex]We will now check the number of sign changes of f(x)
There are 3 sign changes.
Therefore, f(x) has 3 or 1 positive real roots
Next we find f(-x),
[tex]\begin{gathered} f(-x)=-4(-x)^6-3(-x)^5+2(-x)^2-4(-x)+1 \\ \text{hence,} \\ f(-x)=-4x^6+3x^5+2x^2+4x+1 \end{gathered}[/tex]We will now check the number of sign changes of f(-x)
There are 1 sign changes.
Therefore, f(x) has 1 negative real root
Number of possible positive roots: 1 or 3
Number of possible negative roots: 1 only
name the property illustrated by each statement if a=4.75 and 4.75 = b, then a=b
Answer:
Symmetric Property
Step-by-step explanation:
Mary has a tall vase in the shape of a rectangular prism. The vase has a length of 2 1/2 inches, a width of 2 1/2 inches and a height of 12 inches. If Mary fills the vase 1/2 full of water, how much water is in the vase?
Answer:
.eirjjejrjrjejejejejej
Solve m (a – 5) = 12 for the variable a.
I7 < x + 13 And what it looks like on a number line
ok
7 < x + 13
7 - 13 < x
-6 < x
Which proportion describes the relationship between corresponding sides of the triangles?
Answer: C. WX/RS = 3/6
Explanation:
In the triangle WXY the vertical side is WX, and the horizontal side is XY.
In the triangle RST the vertical side is RS, and the horizontal side is ST.
Since both triangles are similar, this means that their angles have the same measurements, and that there is a propotion or relationship between their sides.
The corresponding sides in this triangle are the following:
WX is a corresponding side with RS
XY is a corresponding side with ST
WY is a corresponding side with RT
Out of the options that we have, the only one that relates two corresponding sides is:
[tex]C\mathrm{}\frac{WX}{RS}=\frac{3}{6}[/tex]This is because as we pointed out, WX ans RS are correponding sides.
Also from the image we see that WX = 3 and RS = 6 wich is correctly placed in option C. Thus C represents the proportion between the two corresponding sides.
Answer: C. WX/RS = 3/6
1/4 + 3/16
What’s the answer
Answer:
[tex] \frac{7}{16} [/tex]
Step-by-step explanation:
1/4 is equal to 4/16
4/16 + 3/16 = 7/16
Answer:
[tex]\frac{7}{16}[/tex]
Step-by-step
1/4 + 3/16
16+4 ·/4·3
16 + 12/ 4 · 6
28/4· 16
= 7/16
Check PictureThe graph of the rational function f(x) is shown below. Using the graph, determine which of the following local and end behaviors are correct.
Solution
For the rational function given, we are to determine the local an end behaviors.
[tex]\begin{gathered} As\text{ }x\rightarrow-3^-,f(x)\rightarrow\infty \\ As\text{ }x\operatorname{\rightarrow}-3^+,f(x)\operatorname{\rightarrow}\infty \\ As\text{ }x\operatorname{\rightarrow}-\infty,f(x)\operatorname{\rightarrow}-1 \\ As\text{ }x\rightarrow\infty,f(x)\rightarrow-1 \end{gathered}[/tex]These are the correct local and end behaviors
The graph of an equation drawn through which two points would best represent therelationship between the number of miles and the cost of the trip?
(10,5) and (250, 120)
1) Since we don't have the exact points, all we can do is a visual approximation of the line that best fits in.
2) So let's draw a line, like this on that graph also known as the eye-ball method. We are going to make it half, or almost half of it for each side.
3)Hence, examining the options we pick (10,5) and (250,120) as the best options that could represent the relationship between the number of miles ad the cost of that trip.
Since the line represents an average cost, and those points are approximately the same distance from the line.
Write the numbers that will fill in the eighth row of Pascal’s triangle.
To answer this question, we're going to use some important properties of the Pascal's triangle.
1) If we number the rows starting at zero, then the kth row has k + 1 elements.
2) If we number the elements on the kth row starting with zero, then the mth element of row k is given by
[tex]\begin{pmatrix}{k} \\ {m}\end{pmatrix}=\frac{k!}{m!(k-m)!}[/tex]Using those two properties, we can answer our question.
We want to know the numbers that will fill in the eighth row, this means our k = 8.
From the first property, we know that we have 9 elements on this row, and they are given by
[tex]\begin{pmatrix}{8} \\ {m}\end{pmatrix}=\frac{8!}{m!(8-m)!},m=0,1,2,\ldots,8[/tex]Plugging each m value on this equation, we have
[tex]\begin{gathered} \begin{pmatrix}{8} \\ {0}\end{pmatrix}=\frac{8!}{0!(8-0)!}=\frac{8!}{8!}=1 \\ \begin{pmatrix}{8} \\ {1}\end{pmatrix}=\frac{8!}{1!(8-1)!}=\frac{8!}{7!}=8 \\ \begin{pmatrix}{8} \\ {2}\end{pmatrix}=\frac{8!}{2!(8-2)!}=\frac{8\cdot7}{2}=28 \\ \begin{pmatrix}{8} \\ {3}\end{pmatrix}=56 \\ \begin{pmatrix}{8} \\ {4}\end{pmatrix}=70 \\ \begin{pmatrix}{8} \\ {5}\end{pmatrix}=56 \\ \begin{pmatrix}{8} \\ {6}\end{pmatrix}=28 \\ \begin{pmatrix}{8} \\ {7}\end{pmatrix}=8 \\ \begin{pmatrix}{8} \\ {8}\end{pmatrix}=1 \end{gathered}[/tex]And those are the values on the eighth row.
Neve has 12 full boxes of jars of slime and 7 loose jars of slime. If Neve has a total of 187 jars of slime, which equation can be used to find the number of jars in each box?
Answer:
15 jars in each box
Step-by-step explanation:
linear equation:
12*N + 7
Now we know that Neve has 187 jars in total, then we can write:
12*N + 7 = 187
We want to find the value of N, which is the number of jars in each box, so we need to solve the linear equation:
12*N + 7 = 187
12*N = 187 - 7
12*N = 180
N = 180/12 = 15
Izzy is calculating the amount of time it takes a rocket to get to the moon. The moon is around 239,000 miles from Earth. How many hours would it take a rocket that can travel at 500miles per minute to travel to the moon? Round to the nearest hour8 hours20 hours478 hours28,680 hours
8 hours
Explanation
Step 1
Let
distance = 239000 miles
speed = 500 miles per minute
time( hours) = t
Step 2
to find the time, use
[tex]\begin{gathered} \text{distance= speed }\cdot\text{ time } \\ \text{time}=\frac{dis\tan ce}{\text{speed}} \end{gathered}[/tex]replace
[tex]\begin{gathered} \text{time}=\frac{239000\text{ miles}}{500\frac{miles}{m\in\text{ute}}} \\ \text{time}=478\text{ minutes} \end{gathered}[/tex]Hence, time = 478
Step 2
convert the minutes into hours
if 1 hour = 60 minutes
then, x=hurs for 478 minutes
[tex]\begin{gathered} 1\rightarrow60 \\ x\rightarrow478 \\ \text{the ratio is the same, so} \\ \frac{1}{60}=\frac{x}{478} \end{gathered}[/tex]Now, solve for x
[tex]\begin{gathered} \frac{1}{60}=\frac{x}{478} \\ 1\cdot478=60\cdot x \\ x=\frac{478}{60} \\ x=7.96\text{ hours } \end{gathered}[/tex]Step 3
Round to the nearest hour
[tex]7.96\rightarrow8[/tex]8 hours
Factor completely; simplify if possible.
t² + 12t + 36 =
Hi guys I need your help :)
Answer:
I'm pretty sure its already simplified because it's t2 t and number
13/10÷2/10 please help me solve this i need explanation.
When we are doing divisions with fractions, the best thing to do is also write the division as a fraction like this:
[tex]\begin{gathered} \frac{13}{10}\frac{\cdot}{\cdot}\frac{2}{10} \\ \Rightarrow\frac{\frac{13}{10}}{\frac{2}{10}} \end{gathered}[/tex]Now, we multiply 13x2 and put it in the numerator, and 10x2 in the denominator:
[tex]\frac{\frac{13}{10}}{\frac{2}{10}}=\frac{13\cdot10}{2\cdot10}[/tex]Then we solve and simplify if needed:
[tex]\frac{13\cdot10}{2\cdot10}=\frac{130}{20}=\frac{13}{2}[/tex]therefore, the answer is 13/2
1. AMNO with M(-5,2), NO. 4), and O(4.5): (-6, -2) /1 a. What kind of transformation is this? /3 b. What are the vertices of the image after the transformation?
Answer:
a. Translation
b. M'(-11, 0)
N'(-6, 2)
O'(-2, 3)
Explanation:
<-6, -2> indicates that the triangle MNO will be translated 6 units left and 2 units down, so <-6, -2> is a translation.
On the other hand, to know the new vertices, we need to apply the following rule:
(x, y) ----> (x - 6, y - 2)
So, the vertices of the image after the transformation are:
M(-5, 2) ----> (-5 - 6, 2 - 2) = M'(-11, 0)
N(0, 4) ----> (0 - 6, 4 - 2) = N'(-6, 2)
O(4, 5) ----> (4 -6, 5 - 2) = O'(-2, 3)
Therefore, the answers are:
a. Translation
b. M'(-11, 0)
N'(-6, 2)
O'(-2, 3)
3. How do these values relate to Max and Mary's ages?
The numbers of the intersections of the two lines represent the solution for the problem
for this, the point is (5,3) since they are the corresponding ages of them
divide (x3−8x2+2)÷(x−3)
Answer: -37
Step-by-step explanation:
standard: -13 -[tex]\frac{37}{x-3}[/tex]
quotient: -13
Remainder: -37
Answer:
[tex]x^{2} + \frac{-5x^{2} + 2}{x - 3}[/tex]
Step-by-step explanation:
Attached on file below.
10 divided by 98 long division please
Answer:
Step-by-step explanation:
0 0
____________
9 8 | 1 0
- 0
______
1 0
- 0
______
1 0
Darius was walking from one class to the other during the passing period when he realized his shoes were untied. He stopped to tie his shoes and then glanced at the clock. The clock read 11:52 AM. He had to get to his classroom by 11:55 or he would be counted tardy to class. His class is 30 feet away. How fast will Darius have to move to make it to class on time?
Darius has to move at a speed of 1.67 feet per second to make it to class on time.
What is a unit rate?It is the quantity of an amount of something at a rate of one of another quantity.
In 2 hours, a man can walk for 6 miles
In 1 hour, a man will walk for 3 miles.
We have,
From 11:52 am to 11:55 am, 30 feet of distance has to be covered.
The distance:
= 11:55 - 11:52
= 3 minutes
This means,
In 3 minutes, 30 feet need to be covered
30 feet = 3 minutes
Dividing 3 into both sides.
10 feet = 1 minute.
1 minute = 60 seconds
10 feet = 60 seconds
Dividing 60 into both sides.
10/6 feet = 1 second
5/3 feet = 1 second
1.67 feet = 1 second
The speed is 1.67 feet per second.
Thus,
Darius has to move at a speed of 1.67 feet per second to make it to class on time.
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Pls help me lol I dhdhrhdhs
Answer:
........................C...................................
2y + 2x = 14 solve for y
Answer:
y = -x + 7
Step-by-step explanation:
Answer:
y = 7 - x
Step-by-step explanation:
move all the terms to the right side of the equation then solve for the variable y
hope this helped
have a good day ^^
What is the value of y when x is 4/5 ?
According to the direct variation model, the value of the variable y is the mixed number [tex]3 \frac {1}{5}[/tex]. (Correct choice: C)
What is the value of a variable according to a direct variation model?If a variable y varies directly with the variable x, then we can derive the following relationship to find the missing value:
y₁ / x₁ = y₂ / x₂
Where:
x₁, x₂ - Value of the variable x.y₁, y₂ - Value of the variable y.If we know that x₁ = 3 / 5, y₁ = [tex]2 \frac{2}{5}[/tex] and x₂ = 4 / 5, then the value of y₂ is:
y₁ = 2 + 2 / 5 = 12 / 5
y₂ = (y₁ / x₁) · x₂
y₂ = [(12 / 5) / (3 / 5)] · (4 / 5)
y₂ = (12 / 3) · (4 / 5)
y₂ = 4 · (4 / 5)
y₂ = 16 / 5
y₂ = 15 / 5 + 1 / 5
y₂ = 3 + 1 / 5
y₂ = [tex]3 \frac{1}{5}[/tex]
The value of the missing variable is the mixed number [tex]3 \frac{1}{5}[/tex].
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can you please solve this practice problem for me I really need assistance.find the y-intercept.
Given the graph in the attached image.
we want to find the y-intercept b.
The y intercept b is the point at which the line graph intercept the y axis.
For the given graph the line touches the y axis at;
[tex]y=450[/tex]So, the y-intercept is;
[tex]b=450[/tex]what is 6 feet 4 inches in decimal form
Answer:
6.333
Step-by-step explanation:
During an experiment, the current in a circuit was measured 8 times and recorded as shown below. Calculate the standard deviation of the current to two decimal places.
Standard Deviation for given set of data is 0.25634797778466.
What is standard deviation?
Standard deviation is a measurement of how evenly distributed a set of numbers is. Since the variance is the squared average of the squared deviations from the mean, it represents the square root of the variance.For instance: To determine the standard deviation, sum all of the numbers inside this data set, divide by the total number of numbers, and the result is the standard deviation.Given that,
Sample size :12.3,11.9,12.5,12.1,12.6,11.9,12.2,12.1
Count, N: 8
Sum, submission x: 97.6
Mean, x: 12.2
Variance, s2: 0.065714285714286
s^2 = Σ(xi - x)^2/N - 1
= (12.3 - 12.2)2 + ... + (12.1 - 12.2)^2/8 - 1
= 0.46/7
= 0.065714285714286
s = √0.065714285714286
= 0.25634797778466
Standard Deviation for given set of data is 0.25634797778466.
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11) Solve the system by the addition method.
5x + 15y = -80
0.1x = -4.1 -0.3y
"5x + 15y = -80" + "0.1x = -4.1 -0.3y" using the addition method given equation "5.1x + 15.3y = -12.1".
What is the addition method of equations?A mathematical statement that has an "equal to" symbol between two expressions with equal values is called an equation. As in 3x + 5 = 15, for instance. Equations come in a variety of forms, including linear, quadratic, cubic, and others. Using the Addition Method to Solve Two-Variable Equation Systems The addition method, also known as the elimination method, is a third approach to solving systems of linear equations. In this method, the sum is zero by adding two terms with the same variable but opposite coefficients.So, "5x + 15y = -80" + "0.1x = -4.1 -0.3y" using addition method:
Change 0.1x = -4.1 -0.3y to: 0.1x + 0.3y = -4.1Now, "5x + 15y = -80" + "0.1x = -4.1 -0.3y" (refer to the image attached below for calculation)The resulting equation is: 5.1x + 15.3y = -12.1
Therefore, "5x + 15y = -80" + "0.1x = -4.1 -0.3y" using the addition method given equation "5.1x + 15.3y = -12.1".
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Solve the system by graphing and determine the number of solutions it has. (Hint: to graph find the y-intercept and slope of the line.)-4x + y = 5-2y = -8x + 4
Given the system of equations:
-4x + y = 5
-2y = -8x + 4
To solve the system of equations by graphing, apply the slope-intercept form:
y = mx + b
Where m is the slope and b is the y-intercept.
Rewrite each equation to slope-intercept form
Equation 1:
-4x + y = 5
Add 4x to both sides:
-4x + 4x + y = 4x + 5
y = 4x + 5
Equation 2:
-2y = -8x + 4
Divide all terms by -2:
[tex]\begin{gathered} \frac{-2y}{-2}=\frac{-8x}{-2}+\frac{4}{-2} \\ \\ y=4x-2 \end{gathered}[/tex]We have the equations in slope intercept form:
y = 4x + 5
y = 4x - 2
From the slope intercept form of both equatios, we can see both equations have the same slope.
Slope = 4
Since they have the same slope, they are parallel lines.
The solution will be the points of intersections, but parallel lines do not intersect.
Therefore, we can say the system has no solution.
We have the graph below:
From the graph above, both lines do not intersect. Therefore, there is no solution.
ANSWER:
No solution
