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The graph is given by:
Related Questions
Given the exponential equation:, find a common base and solve for x.
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EXPLANATION:
Given;
We are given the exponential equation shown below;
[tex](\frac{125}{8})^{4x-1}=(\frac{4^2}{25^2})^{x+1}[/tex]Required;
We are required to
(i) Find a common base
(ii) Solve for x
Step by step solution;
To solve this problem we shall start with the following steps;
[tex][(\frac{5}{2})^3]^{4x-1}=[(\frac{2}{5})^4]^{x+1}[/tex]For the left side of the equation, we can refine by applying the rule of exponents;
[tex]\begin{gathered} Flip\text{ the left side of the equation:} \\ (\frac{2}{5})^{-3} \end{gathered}[/tex]Therefore, we now have;
[tex][(\frac{2}{5})^{-3}]^{4x-1}=[(\frac{2}{5})^4]^{x+1}[/tex][tex](\frac{2}{5})^{-12x+3}=(\frac{2}{5})^{4x+4}[/tex]We now have a common base and that means;
[tex]\begin{gathered} If: \\ a^x=a^y \\ Then: \\ x=y \end{gathered}[/tex]Therefore;
[tex]-12x+3=4x+4[/tex][tex]-12x-4x=4-3[/tex][tex]-16x=1[/tex]Divide both sides by -16;
[tex]x=-\frac{1}{16}[/tex]ANSWER:
[tex]x=-\frac{1}{16}[/tex]WCompare Function ValuesGiven the functions f(2) = 2:24 and g(x) = 11 - 2", which of the followingstatements is true?O f(3) > g(3)O f(3) < 9(3)Submit AnswerO f(3) = g(3)
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Notice that
[tex]\begin{gathered} f(3)=2\cdot(3)^4=162 \\ g(3)=11\cdot2^3=88 \end{gathered}[/tex]Notice that
[tex]\begin{gathered} f(6)=6^2=36 \\ g(6)=2^6=64 \\ \end{gathered}[/tex]Then, f(6) < g(6)
Type the correct answer in each box. Use numerals instead of words In the figure, lines BD and QS are parallel
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..Given: Two parallel lines BD and QS and a transversal AT
To Determine: The measure of CRQ and CRS
Solution
From the image given, angle DCR and CRQ are alternate angles
Also angle DCR and angle CRS are each pair of the same interior angles
Please note that alternates angles are equal and each pair of same-side interior angles are supplementary
Apply the theorem above
[tex]\begin{gathered} \angle CRQ=\angle DCR(alternate-angles) \\ \angle CRQ=77^0 \end{gathered}[/tex]Also
[tex]\begin{gathered} \angle DCR+\angle CRS=180^0(same-ineterior-angles) \\ 77^0+\angle CRS=180^0 \\ \angle CRS=180^0-77^0 \\ \angle CRS=103^0 \end{gathered}[/tex]Hence:
∠CRQ = 77⁰
∠CRS = 103⁰
can you please help me
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The formula for the area of a circle is:
[tex]A=\pi\cdot r^2[/tex]also the diameter can be written in function of the radius
[tex]D=2\cdot r[/tex]from this equation we can find the radius
[tex]r=\frac{D}{2}[/tex]this transforms the formula for the area into
[tex]\begin{gathered} A=\pi\cdot(\frac{D}{2})^2 \\ A=\frac{\pi}{4}\cdot D^2 \end{gathered}[/tex]since the diameter is equal to 26cm, then the area will be
[tex]\begin{gathered} A=\frac{\pi}{4}\cdot676cm^2 \\ A=169\pi(cm^2)\approx530.93cm^2 \end{gathered}[/tex]The owners of a recreation area are filling a small pond with water. Let W be the total amount of water in the pond (in liters). Let T be the total number of minutes that water has been added. Suppose that w= 35T +300 gives W as a function of T during the next 70 minutes.Identify the correct description of the values in both the domain and range of the function. Then, for each, choose the most appropriate set of values.
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Given:
[tex]W=35T+300[/tex]To find:
The domain and the range when t = 70 minutes.
Explanation:
When t = 70, we get
[tex]\begin{gathered} W=35(70)+300 \\ W=2750l \end{gathered}[/tex]The ordered pair of the solution is,
[tex](70,2750)[/tex]As the domain is the set of all input values, so the domain will be,
[tex][0,70][/tex]As the range is the set of all output values, so the range will be,
[tex][300,2750][/tex]Final answer:
The domain is,
[tex][0,70][/tex]The range is,
[tex][300,2750][/tex]which of the following expressions is equal to 5^6/5^2?
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Simplify the expression 5^6/5^2.
[tex]\begin{gathered} \frac{5^6}{5^2}=5^6\cdot5^{-2} \\ =5^{6-2} \\ =5^4 \\ =5\cdot5\cdot5\cdot5 \\ =625 \end{gathered}[/tex]Solve for a if the line through the two given points has the given slope.(a, 6) and (0, 1), m = 1a=
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Given:
Two points are,
[tex](a,6),(0,1)[/tex]The slope is,
[tex]m=1[/tex]To find:
The value of a.
Explanation:
Using the slope-intercept form of a line equation,
[tex]y=mx+c[/tex]Substituting y-intercept c = 1 and slope m = 1 we get,
[tex]y=(1)x+1[/tex]Then substituting the first point we get,
[tex]\begin{gathered} 6=a+1 \\ a=6-1 \\ a=5 \end{gathered}[/tex]The value of a is 5.
Final answer:
The value of a is 5.
For the following situation, (a) write an equation in the form y=mx+b, (b) find and interpret the ordered pair associated with the equation for x=5, and (c) answer the question.A health club membership costs $80, plus $48 per month. Let x represent the number of months and y represent the cost in dollars. How much does the first year’s membership cost?
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Based on the question, a health club membership costs $80, plus $48 per month. This can be written as $80 + $48 per month = health membership cost.
If x = month and y = cost, then we can rewrite the equation as:
[tex]\begin{gathered} 80+48x=y \\ or \\ y=48x+80 \end{gathered}[/tex]a. This is our equation in the form of y = mx + b. (y = 48x + 80).
b. If the number of months is 5 or x = 5, we can solve for the total cost of membership by replacing "x" with "5" in the equation.
[tex]\begin{gathered} y=48x+80 \\ y=48(5)+80 \\ y=240+80 \\ y=320 \end{gathered}[/tex]The ordered pair is (5, 320).
This ordered pair indicates that the cost for 5-month membership is $320.
c. Since there are 12 months in 1 year, replace "x" in the equation with 12 and then, solve.
[tex]\begin{gathered} y=48x+80 \\ y=48(12)+80 \\ y=576+80 \\ y=656 \end{gathered}[/tex]Therefore, the first year's membership cost is $656.
hi I'm having trouble on solving systems and graphing them
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The system of equations is
0 = 2y + 6 - x (1)
0 = 4y + 3x - 8 (2)
To solve it graphically we must find 2 points on each line
So let us choose values of x and find their corresponding values of y
Let x = 2
Substitute it in equation (1)
0 = 2y + 6 - (2)
Add the like terms on the right side
0 = 2y + (6 - 2)
0 = 2y + 4
Subtract 4 from both sides
0 - 4 = 2y + 4 - 4
-4 = 2y
Divide both sides by 2
-2 = y
The 1st point is (2, -2)
Let x = 4
Substitute it in the equation to find y
0 = 2y + 6 - (4)
0 = 2y + (6 - 4)
0 = 2y + 2
Subtract both sides by 2
0 - 2 = 2y + 2 - 2
-2 = 2y
Divide both sides by 2 to find y
-1 = y
The 2nd point is (4, -1)
Now you can plot these to points and join them to draw the 1st line
We will do the same with equation (2)
Let x = 4
Substitute it in the equation (2)
0 = 4y + 3(4) - 8
0 = 4y + 12 - 8
Add the like terms in the right side
0 = 4y + (12 - 8)
0 = 4y + 4
Subtract 4 from both sides
0 - 4 = 4y + 4 - 4
-4 = 4y
Divide both sides by 4
-1 = y
The 1st point on the second line is (4, -1)
Let x = -4
0 = 4y + 3(-4) - 8
0 = 4y -12 - 8
0 = 4y + (-12 - 8)
0 = 4y - 20
Add 20 to both sides
0 + 20 = 4y - 20 + 20
20 = 4y
Divide both sides by 4
5 = y
The 2nd point on the second line is (-4, 5)
Plot the two points and join them to form the second line
As you see the two lines have point (4, -1),
then the two lines will intersect at this point
The solution of the system is (4, -1)
In the diagram, A CAT ~ADOG. Find the value of I.С161810215DT248.3I =
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we where given two sides of the triangle without the third side
lets take the given sides to a and b
then let the third side be c which is also x
let a = 16
b = 10
c = x
using pythagoras theorem
x^2 = a^2 - b^2
x^2 = 16^2 - 10^2
x^2 = 256 - 100
x^2 = 156
therefore,
x = the square root of 156
x = 12
Solve for k in 2 - (k+4) = 3a.) What is the variable?b.) What is happing to the variable? (list the operations from the first thing to the last thing)c.) What is the inverse (opposite) of the last thing that happened to the variable. (Make a list of the steps to solve)
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We have the equation 2-(k+4)=3.
The variable is k, because is the only unknown number. Solving for k:
[tex]\begin{gathered} 2-(k+4)=3 \\ 2=3+(k+4)=3+4+k=7+k \\ 2-7=k \\ -5=k \end{gathered}[/tex]The variable has the following operations:
• Add 4
,• Multiply by (-1)
,• Add 2
The inverse of the last thing is Subtract 2, subtract is the opposite of add.
The vertex of parabola that opens downwards is at (0,4)
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The true statement is that the points of intersection are of equal distance from the y-axis.
What is parabola?A parabola is a U-shaped plane curve where any point is at an equal distance from a fixed point (known as the focus) and from a fixed straight line which is known as the directrix.
Given that the vertex of a parabola that opens downward is at (0, 4).
The vertex of a second parabola is at (0, -4).
Therefore, the points of intersection are the distance from the y-axis.
This is because the symmetry axis of both parabolas is x = 0, thus the intersection points must be at same distance from x- axis and y-axis.
Learn more about this parabola here:
brainly.com/question/8158213
#SPJ1
The complete question is;
The vertex of a parabola that opens downward is at (0, 4). The vertex of a second parabola is at (0, –4). If the parabolas intersect at two points, which statement must be true?
The second parabola opens downward.
The second parabola opens upward.
The points of intersection are on the x-axis.
The points of intersection are of equal distance from the y-axis.
You stand 40 feet from a tree. The anlge of elevation from the ground tothe top of the tree is 47 degrees. How tall is the tree? (round to the nearesttenth)0 42.9 feet0 27.3 feet29.3 feetO 40 feet
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The first step is to draw the picture.
We want to find the opposite side.
We know the adjacent side
The trig function with opposite and adjacent is tangent
tan 47 = opp / adjacent
tan 47 = opp/40
40 * tan 47 = opp side
42.8947484 = opp side
Rounding to the nearest tenth
42.9 ft
ED has a midpoint at C.If CD=6+x and CE = 2x +1, what is the length of ED?5112210
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Answer: Length of ED = 22
Since according to the question and the diagram drawn above, C is the midpoint of ED;
ED = 2CE = 2CD
CE = CD
6 + x = 2x + 1
6 - 1 = 2x - x
x = 5
CD = 6 + x = 6 + 5
CD = 11
CE = 2x + 1
CE = 2(5) + 1 = 10 + 1
CE = 11
Also note from the line drawn that ED = CE + CD
Therefore, ED = 11 + 11
ED = 22
Help Please! Will give brainliest and 45 points!
What is 12/10 as a fraction? What is 132/100 as a fraction? What is 546/100 as a fraction? What is 123/10 as a fraction? What is 872/100 as a fraction?
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What is 12/10?
6/5 or 1 1/5 or 1.2
________________
What is 132/100?
33/25 or 1 8/25 or 1.32
________________
What is 546/100?
273/50 or 5 23/50 or 5.46
________________
What is 123/10?
123/10 or 12 3/10 or 12.3
________________
What is 872/100?
218/25 or 8 18/25 or 8.72
Answer:
12/10 = 1.2132/100 = 1.32 546/100 = 5.46123/10 = 12.3 872/100 = 8.72Step-by-step explanation:
1) 12/10 as a decimal is?
→ 12/10
→ 6/5 = 1.2
2) 132/100 as a decimal is?
→ 132/100
→ 1.32
3) 546/100 as a decimal is?
→ 546/100
→ 5.46
4) 123/10 as a decimal is?
→ 123/10
→ 12.3
5) 872/100 as a decimal is?
→ 872/100
→ 8.72
Hence, these are the answers.
question provided in photo only need help with system b
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Consistent dependent
Infinitely many solutions
Explanation:The given system of equations is:
[tex]\begin{gathered} y=-\frac{3}{2}x\ldots\ldots\ldots....\ldots\ldots\ldots\text{.}(1) \\ 3x+2y=0\ldots\ldots\ldots\ldots.......\ldots(2) \end{gathered}[/tex]A system of equations is consistent if it has at least one solution.
A system of equations is dependent if it has infinite number of solutions.
Considering the graph of the lines drawn in the question, the two lines are perfectly drawn on each other, which means that there are infinite numbers of solutions.
Therefore, the system of equations is consistent dependent.
This means that the system has infinitely many solutions. mber
A certain state uses the following progressivetax rate for calculating individual income tax:Income ProgressiveRange ($)Tax Rate0 - 20002%2001 - 9000 5%9001 and up5.4%Calculate the state income tax owed on a $60,000per year salarytax = $[?]your answer to the nearest whole dollar amount.
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Answer:
$3240
Explanation:
If the tax rate for $9001 and up is 5.4%, we can calculate the state income tax when the income is $60,000. So,
$60,000 x 5.4% = $60,000 x 5.4/100 = $3240
Therefore, the tax will be:
$3240
State the null and alternative hypotheses for the claimThe average score of high school basketball games is less than 88.
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Together 2 people earn $28000. One earned $2000 more than the other. How much is the smaller income?
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Let x be the smaller income and y be the bigger income.
So, if both earn together $28,000, then:
[tex]x+y=28000[/tex]If one earns $2000 more than the other, we can say the the bigger minus the smaller is equal to 2000, that is:
[tex]y-x=2000[/tex]Now, we can solve the second equation for y and input it into the first equation:
[tex]\begin{gathered} y-x=2000 \\ y=x+2000 \end{gathered}[/tex][tex]\begin{gathered} x+y=28000 \\ x+x+2000=28000 \\ 2x=28000-2000 \\ 2x=26000 \\ x=\frac{26000}{2} \\ x=13000 \end{gathered}[/tex]Thus, the smalle income is $13,000, alternative D.
is 16.5 a rational or irrational number
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a rational number can be expressed by a fraction, if you cant is am irrational number
so
16.5 can by expressed like
[tex]\frac{165}{10}[/tex]so is a rational number, you can simplify the fraction
[tex]\frac{165}{10}\longrightarrow\frac{33}{2}[/tex]Thr sum of 2 numbers is 97.The greater number is three less then four times the lesser number.Find the numbers
need answer soon PLEASE!!!!
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Answer:
Greater number: 77 Lesser number: 20
Step-by-step explanation:
Sooo
20 × 4 is 80
80 - 3 = 77
77 + 20 = 97
Answer:
77 & 20
Step-by-step explanation:
x+y=97
x=4y-3
4y-3+y=97
5y=97+3
5y=100
5 5
y=20
x=4y-3
x=4(20)-3
x=80-3
x=77
don't forget to follow , rate & like
2 points6. Which system of questions can be used to find the number of smallboxes, x, and the number of large boxes, y, on the pallet?*Small boxes and large boxes are stacked together on a pallet.The total number of boxes is 10.• The small boxes weigh 5 pound each.The large boxes weigh 12 pounds each.The total weight of the boxes is 78 pounds.O a. x + y = 7 and 5x + 12y = 10b. x + y = 10 and 5x + 12y = 10Ο Ο Ο ΟC. X + y = 10 and 5x + 12y = 78O d. x + y = 78 and 5x + 12y = 78
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Let x be the number of small boxes and y be the number of large boxes. Then, for the first statement, we can write
[tex]x+y=10[/tex]For the second statement, we can write
[tex]5x+12y=78[/tex]Then, the answer is option C.
amir drove from Jerusalém to the lowest on place on Earth , the dead Sea His altitude relative to sea level as a function of time is graphed what was amir's altitude at the begining of the drive?
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Explanation
Step 1
define
given: ∠D ≅ ∠C and ∠CAB ≅ ∠DBA. Prove ΔABC ≅ ΔBAD
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To prove that
[tex]\Delta ABC\cong\Delta BAD[/tex]We have to prove that they share at least 2 angles.
1.
[tex]\angle D\cong\angle C[/tex]This is a given fact.
2.
Notice that
[tex]\Delta ADE\cong\Delta\text{BEC}[/tex]Since they already share two angles: DEA and CEB (They are vertically opposite)
This way, we can conclude that:
[tex]\angle DAE\cong\angle\text{CBE}[/tex]In other words, the two angles on top of A and B are equal.
Therefore, we can conclude that
[tex]\angle DAB\cong\angle CBA[/tex]And since ΔABC and ΔBAD share two of their angles, we can conclude that they also share their third and that:
[tex]\Delta ABC\cong\Delta BAD[/tex]Q.E.D
real exponential equation the base B must be positive. graph the equation using basis that are less than one or greater than one to determine any differences. what differences are there if any?
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Let's graph the following functions.
[tex]\begin{gathered} f(x)=2^x \\ g(x)=(\frac{1}{2})^x \end{gathered}[/tex]The image below shows the graph.
According to the graph, the difference between the function is that f(x) is increasing and g(x) is decreasing, this behavior is caused by the base of the powers, the base 1/2 (between 0 and 1) gives a decreasing exponential function, and the base 2 (greater than 1) gives an increasing exponential function.
Hence, C is the right answer.Can you help me with this assignment
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The question provides one endpoint and then the midpoint. The midpoint on the coordinate grid is (0, -7) and one endpoint is (-2,-6).
The formula for calculting the midpoint is given as follows;
[tex]\begin{gathered} M=\frac{x1+x2}{2},\frac{y1+y2}{2} \\ Take\text{ the x coordinates and y coordinates one after the other,} \\ 0,7=\frac{-2+x2}{2},\frac{-6+y2}{2} \\ \text{The x coordinates and the midpoint coordinate are} \\ 0=\frac{-2+x2}{2} \\ \text{Cross multiply and you have;} \\ 0=-2+x2 \\ 2=x2 \\ \text{The y coordinates and the midpoint coordinates are;} \\ 7=\frac{-6+y2}{2} \\ \text{Cross multiply and you have;} \\ 14=-6+y2 \\ 14+6=y2 \\ 20=y2 \\ \text{Therefore, the coordinates for the other midpoint is derived as;} \\ (2,20) \end{gathered}[/tex]Therefore, the coordinates of B is calculated as (2, 20)
Write a piecewise function describing your weekly pay P, in terms of the number of hours worked, h.
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SOLUTION
the wage for less that 40 hours of work is
[tex]12h[/tex]The wage for more than 40 hours is:
[tex]1.5\times12=18h[/tex]Therefore the piecewise function is
[tex]\begin{cases}12h{,0\lt h\le40} \\ 18h{,h\gt40}\end{cases}[/tex]
Select all prime numbers 2,4,6,7,9,5
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The Solution:
Given the set of numbers below:
[tex]2,4,6,7,9,5[/tex]We are asked to select all the prime numbers in the set.
A prime number is a number that can only be divided by 1 and itself. That is, it is a number that has only two factors.
So, the prime numbers in the set are:
[tex]2,7,5[/tex]Since these numbers only have two factors each.
Therefore, the correct answer is {2,7,5}
Answer:
The prime numbers would be 2, 5, and 7.
Step-by-step explanation:
Prime numbers are numbers that can only be multiplied by 1 and itself.
Here is a list of the common factors of each number:
2: 1, 2
4: 1, 2, 4
6: 1, 2, 3, 6
7: 1, 7
9: 1, 3, 9
5: 1, 5
So, our prime numbers are 2, 5, and 7.
May I have Brainliest please? My next rank will be the highest one: A GENIUS! Please help me on this journey to become top of the ranks! I would really appreciate it, and it would make my day! Thank you so much, and have a wonderful rest of your day!
For the equation −2 + 3 = 6 a. Find y when x is 3b. Find x when y is 4
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Given equation,
[tex]-2x+3y=6[/tex](a) Find y when x is 3.
[tex]\begin{gathered} -2\times(3)+3y=6 \\ -6+3y=6 \\ 3y=12 \\ y=4 \end{gathered}[/tex](b) Find x when y is 4.
[tex]\begin{gathered} -2x+3y=6 \\ -2x+3\times4=6 \\ -2x+12=6 \\ -2x=-6 \end{gathered}[/tex]Thus, the value of x is
[tex]\begin{gathered} 2x=6 \\ x=3 \end{gathered}[/tex]What’s the answer to which expression is larger 5^3 or 4^4
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5^3 = 5 x 5 x 5 = 125
4^4 = 4 x 4 x 4 x 4 = 256
256 > 125
4^4 is larger than 5^3