We would apply the following laws of exponents
(x^y)^z = x^(yz)
a^c * a^d = a^(c + d)
a^c / a^d = a^(c - d)
The given expression is
(4a^2b)^2/(2a^3b^4)^3
By applying the first law above, it becomes
[4^2a^(2*2)b^2]/[2^3a^(3*3)b^(4*3)]
= [16a^4b^2]/[8a^9b^12]
by applying the second and third laws, we have
16/8 * a^(4 - 9) * b^(2 - 12)
= 2a^-5b^-10
Also, x^-1 = 1/x
Thus, the final expression would be
2/a^5b^10
Option C is correct
how are rational munbers written as decimalsfYI:I was listening but I just don't understand
We have 4 rational numbers which we are asked to express in decimal numbers.
To do this, we divide the numerator of each rational number by its denominator, when we do that, we get the following results:
[tex]undefined[/tex]What steps should be followed to solve the following equation for x: -3x - 8 1 point= 4*Add 8 to both sides, then divide by 3Divide by -3, then add 8 to both sidesAdd 8 to both sides, then divide by -3Add 8 to both sides, then add 3 to both sides
1) Evaluating
-3x -8= 4 Adding 8 to both sides
-3x -8 +8=4+8
-3x = 12 Dividing both sides by 3
x=-4
2) Examining the options then
C Add 8 to both sides then divide both sides by 3
Grpah the image of square ABCD after a translation 10 units up.
We have to take the points A, B, C, and D from the original square and move all of them 10 units up as shown in the following diagram:
After translating the points we get the image points A', B', C' and D'.
Finally, connecting the image points we get the image of the square:
If a quadrilateral has exactly 2 lines of symmetry, and both are angle bisectors, then which statement would be true?
The figure must be an isosceles trapezoid because it has 2 congruent base angles.
The figure must be a rectangle because all rectangles have exactly 2 lines of symmetry.
The figure could be a rhombus because the 2 lines of symmetry bisect the angles.
The figure could be a square because the diagonals of a square bisect the right angles.
The third option is correct. That is, the figure could be a rhombus because the 2 lines of symmetry bisect the angles.
What is rhombus?
A rhombus is a quadrilateral that is an equilateral parallelogram and has all of its opposite pairs of sides parallel. Sometimes the word "rhombus" is substituted with "rhomb," and a rhombus is also referred to as a "diamond."
Given: A quadrilateral has exactly 2 lines of symmetry, and both are angle bisectors.
Since the two lines of symmetry in a quadrilateral are angle bisectors, the figure may be a rhombus if the quadrilateral has exactly two lines of symmetry. Figures with four sides and angles are called quadrilaterals. Rectangle is a type of quadrilateral.
Therefore, If a quadrilateral has exactly 2 lines of symmetry, and both are angle bisectors, then the figure could be a rhombus because the 2 lines of symmetry bisect the angles.
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Answer:
third option
Step-by-step explanation:
Below, the two-way table is given for aclass of students.FreshmenSophomoreJuniorsSeniorsTotal46246Male2Female 33TotalIf a student is selected at random, find theprobability the student is a junior given that it'smale. Round to the nearest whole percent.[?]%
Male students. 14
Female students: 16
Total students: 30
Since there are 2 male juniors, the probability of being junior and male is: 6.67%
[tex]\frac{2}{30}\cdot100=6.67[/tex]If we round to the nearest whole porcent: 7%
Please help me with this geometry problem. i don’t understand.
Tangent theorem states that when two tangents intersect out a circle they are said to be equal
Therefore,
Tangent 2x+13 is equal to tangent 4x-8
[tex]\begin{gathered} 4x-8=2x+13_{} \\ by\text{ collecting like terms we will have that,} \\ 4x-2x=13+8 \\ 2x=21 \\ to\text{ find x we will dive both sides by the coefficent of x which is 2} \\ \frac{2x}{2}=\frac{21}{2} \\ x=10\frac{1}{2} \\ x=10.5 \end{gathered}[/tex]Hence,
The value of x =10.5
A teacher bought 28 books for her class. She spent a total of $112.00. What is the price, p, for each book? Let p = price for each book
Evaluate the left hand side to find the value of aa in the equation in simplest form. 4
Given
[tex]\frac{x^{\frac{1}{2}}}{x^{\frac{1}{6}}}[/tex]Solution
Apply exponent rule
[tex]\begin{gathered} x^{\frac{1}{2}-\frac{1}{6}}=x^{\frac{3-1}{6}} \\ \\ \\ x^{\frac{2}{6}}=x^{\frac{1}{3}} \end{gathered}[/tex][tex]a=\frac{1}{3}[/tex]We have
[tex]\frac{x^{\frac{1}{2}}}{x^{\frac{1}{6}}}=x^{\frac{1}{3}}[/tex]Based on the information given in the following graph of a power function, can you determinethe equation of the power function? Why or why not? If you can, find the equation of the powerfunction. If not, describe the equation of the power function as much as you can.
SOLUTIONS
To determine the equation of the power function? Why or why not? If you can, find the equation of the power
[tex]\begin{gathered} (4,2) \\ x=4,y=2 \end{gathered}[/tex]It is easy to get the graph of the exponential function since x - value = 4 and y - value = 2.
An exponential function is defined by the formula f(x) = x^a, where the input variable x occurs as an exponent. The exponential curve depends on the exponential function and it depends on the value of the x.
The general equation of an exponential function is
[tex]y=x^a[/tex][tex]\begin{gathered} y=2,x=4 \\ 2=4^a \\ 4^{\frac{1}{2}}=4^a \\ a=\frac{1}{2} \end{gathered}[/tex][tex]y=x^{\frac{1}{2}}[/tex]At 1:00 AM the temperature was 87º. A cold front came through and at 7:00 PM the temperature was 45°. What is the rate of change in the temperature in degrees per hour?
the rate of change in the temperature per hour is the quotient of the change of temperature divided by the change in hours. Since we have
1:00 AM =1 hr - 87 degrees
7:00 PM=19 hrs - 45 degrees,
then the rate is
[tex]\frac{45-87\text{ }}{19-1}=\frac{-42}{18}=-\frac{7}{3}=-2.33[/tex]Then, the temperature changed -2.33 degrees per hour.
how do you solve y=x-2 and graph it
The equation
y = x - 2
is the equation of a line in the slope-intercept form with a slope of 1 and a y-intercept at (0, -2).
You can graph it by locating two points on the line. One point is (0, -2). The other one can be found with the slope. The slope of 1 means that the next point is 1 unit to the left and 1 unit up, respect the previous point. In this case, the next point is (1, -1). After you locate these two points, draw the line that connects them, as follows
[tex]1144 \times \frac{25}{3699} + 114 \sqrt[1441]{36} - y + x \div 15663 = 2 - \sqrt[44410]{3651} + {2554}^{2} [/tex]first equation. then text
how does equation look in session history???
Which identity/formula was used to simplify from step 2 to step 3?
Solution:
The reciprocal identities of trigonometry include the identities below
[tex]\begin{gathered} \csc \theta=\frac{1}{\sin \theta} \\ \sec \theta=\frac{1}{\cos \theta} \\ \cot \theta=\frac{1}{\tan \theta} \\ \tan \theta=\frac{1}{\cot \theta} \\ \cos \theta=\frac{1}{\sec \theta} \\ \sin \theta=\frac{1}{\csc \theta} \end{gathered}[/tex]The quotient identity include the identities below
[tex]\begin{gathered} \tan \theta=\frac{\sin \theta}{\cos \theta} \\ \cot \theta=\frac{\cos \theta}{\sin \theta} \end{gathered}[/tex]The sum formula of trigonometric identity include
[tex]\begin{gathered} \sin (\alpha+\beta)=\sin \alpha\cos \beta+\cos \alpha\sin \beta \\ \sin (\alpha-\beta)=\sin \alpha\cos \beta-\cos \alpha\sin \beta \\ \cos (\alpha+\beta)=\cos \alpha\cos \beta-\sin \alpha\sin \beta \\ \cos (\alpha-\beta)=\cos \alpha\cos \beta+\sin \alpha\sin \beta \end{gathered}[/tex]The double-angle formula is given below as
Hence,
The final answer is QUOTIENT IDENTITY
What is the slope and y intercept of the line whose equation is y = -4x + 2?b =m=
To find the slope and the intercept of the line
y = -4x + 2
y = mx + b
so in this case the m = -4, because is the coefficient on x rigth over there
and b is going to be the constant term
b = 2
Using only the values given in the table for thefunction, f(x), what is the interval of x-values over whichthe function is increasing?Х-6-5-4-3-2.-101f(x)343-10-11-6-1-2-15O (-6,-3)O (-3,-1)O (-3,0)O (-6, -5)
Given the table:
Х f(x)
-6 34
-5 3
-4 -10
-3 -11
-2. -6
-1 -1
0 -2
1 -15
Let's find the increasing intervals.
A function is increasing over the interval when the values of f(x) increases as the values of x increases.
At the interval:
From x = -3 to x = -1, the values of f(x) increases from -11 to -1.
Therefore, the interval of x-values over which the function is increasing is:
(-3, -1)
ANSWER:
(-3, -1)
What is the accumulated value if the money is compounded semiannually?
Given:
[tex]\begin{gathered} P=20,000 \\ t=6years \\ r=5.5\% \end{gathered}[/tex]Required:
To find the accumulated value.
Explanation:
Consider
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]Here
[tex]\begin{gathered} =20000(1+\frac{0.055}{2})^{2\times6} \\ \\ =20000(1+0.0275)^{12} \\ \\ =27,695.68 \end{gathered}[/tex]Final Answer:
The accumulated value is $27,695.7
What is the image of (−9,−12) after a dilation by a scale factor of 1/3
centered at the origin?
By dilation with a scale factor of 1 / 3 centered at the origin, the image of the resulting point is (- 3, - 4).
How to determine the location of the image of a point by using a dilation formula
In this problem we find the coordinates of a point set on Cartesian plane, whose image is the result of using a dilation centered at the origin, whose definition is introduced below:
P'(x, y) = O(x, y) + k · [P(x, y) - O(x, y)]
Where:
O(x, y) - Center of dilationP(x, y) - Original pointP'(x, y) - Resulting pointk - Scale factorIf we know that O(x, y) = (0, 0), k = 1 / 3 and P(x, y) = (- 9, - 12), then the image of the original point is:
P'(x, y) = (0, 0) + (1 / 3) · [(- 9, - 12) - (0, 0)]
P'(x, y) = (- 3, - 4)
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Locker codes at Lincoln High School consist of 4 digits. No digit can be used more than once. How many locker codes are available at Lincoln High School? A 210 B 3,024 C 5,040 D 10,000
To obtain the number of locker codes available, the following steps are necessary:
Step 1: Create a diagram to represent the slot for each of the digits, as below;
Step 2: State the number ways that each digit can be used to fill any of the spots, as below:
Given that there are the numbers 0,1,2,3,4,5,6,7,8,9 - a total of 10 numbers,
- The first slot can be filled with any of the digits above, and thus can be filled in 10 ways
- The second slot can be filled with any of the remaining 9 numbers after one of them has already been used to fill the first slot. Thus, there are 9 ways the second slot can be filled.
- The same line of reasoning tells us that the third slot will be filled in 8 ways
- Lastly, the fourth slot will be filled in 7 ways
The diagram below gives a better illustration:
Step 3: Multiply the numbers of ways to find the total number of locker codes that are available, as follows:
[tex]10\times9\times8\times7\text{ = 5040}[/tex]Therefore, there are a total of 5040 available locker codes at Lincoln High School
Correct answer = Option C
Select all the correct answers Each of these scatter plots has a line of fit for its data points. Which graphs have a line that is a line of best for the data
There should be as much as many dots above the line and below the line . The line of best fits represent the trend of the data whether positive or negative correlation
The graphs that have a line that is best for the data are
Graph 1
Graph 4
what is the equation in point slope form of the line that passes through the point (5, 0) and has a slope of 1.2?
To see the equation we know that the general equation of a line is:
[tex]y=mx+b[/tex]Where m is the slope. So you know that the slope is 1.2, then you have an equation like this:
[tex]y=1.2x+b[/tex]Since b is just a number we can say that this is also equal to:
[tex]y=1.2(x+c)[/tex]We'll write it this way so it's similar to the options.
Then you know that the line pases through point (5,0). To find the value of constant c we replace the value of x and y from this point (x = 5 and y=0):
[tex]0=1.2(5+c)[/tex]And clear c from this expression
[tex]0=5+c\Rightarrow c=-5[/tex]So the answer is:
[tex]y-0=1.2(x-5)[/tex]Work out the lenght off x
Using the Pythagorean theorem, the length of the side x is √147.
What is the Pythagorean theorem?The Pythagorean theorem, sometimes known as Pythagoras' theorem, is a fundamental relationship between a right triangle's three sides in Euclidean geometry. According to this statement, the areas of the squares on the other two sides add up to the size of the square whose side is the hypotenuse.So, the formula of the Pythagorean theorem:
H² = l² + w², where H is the hypotenuse.Now, substitute the values and calculate as follows:
14² = 7² + x²x² = 14² - 7²x² = 196 - 49x² = 147x = √147Therefore, using the Pythagorean theorem, the length of the side x is √147.
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A bike wheel as a radius of 13 inches. a. About how far does the bike wheel tra in 1 rotation? 5 rotations? 30 rotations? b. Write an equation relating the distance the bike travels in inches, b, to the number of wheel rotations, x. c. About how many rotations does the bike wheel make when the bike travels 1 mile?
The radius of the bike wheel is given as 13 inches. One rotation would be equal to the entire circumference of the bike wheel. Hence;
[tex]undefined[/tex]Find the area of each. 'Use your calculator's value of r. Round your answer to the nearest tenth.
To find the area of a circle given the radius;
[tex]undefined[/tex]solve the equation T = 2x + 3y - z for y.
In order to solve this equation for y, we just need to isolate the variable y in the equation.
So, we have that:
[tex]\begin{gathered} T=2x+3y-z_{} \\ 3y=T-2x+z \\ y=\frac{T-2x+z}{3} \end{gathered}[/tex]So we have that y = (T - 2x + z) / 3
si en un determinado lugar el metro cuadrado de terreno cuesta 250 dolares cuanto vale el lote de 400 metros cuadrados
If a square meter of land costs $250 in a certain place, then 1.6 sq. m. of land can be bought there for $400, calculated using the unitary method.
As per the question statement, the cost of per square meter of land in a certain place is $250,
And we are required to calculate the amount of land that can be bought in the above mentioned place for $400.
To solve this question, we will use the unitary method, that is,
Given, the cost of per square meter of land in a certain place is $250,
Or, in $250, one can buy 1 sq. m. of land in this place,
Or, in $1, one can buy (1/250) sq. m. of land,
And, in $400, one can buy [{(1/250) * 400} = (40/25) = (8/5) = 1.6 sq. m.] of land in that place.
Unitary Method: In Mathematics, the unitary method is a technique for solving a problem by first finding the value of a single unit, and then multiplying this single unit value into the number of concerned units, to obtain our desired resultant.To learn more about Unitary Method, click on the link below.
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Which equation represents a line which is perpendicular to the line y =- +522x - 5y = -302x + 5y = 152y-53 = 10O 5x + 2y 12
Answer:
The equation that represents the perpendicular line is;
[tex]2y-5x=-10[/tex]Explanation:
We want to find the equation of a line perpendicular to the line;
[tex]y=-\frac{2}{5}x+5[/tex]Recall that for two lines to be perpendicular to each other, their slope must be a negative reciprocal of one another.
[tex]m_1.m_2=-1_{}_{}[/tex]so;
[tex]m_2=-\frac{1}{m_1}[/tex]For the given equation, the slope of the given line is;
[tex]m_1=-\frac{2}{5}[/tex]To get the slope of the perpendicular line, let us substitute m1 to the equation above;
[tex]\begin{gathered} m_2=-\frac{1}{m_1} \\ m_2=-\frac{1}{(-\frac{2}{5})_{}} \\ m_2=\frac{5}{2_{}} \end{gathered}[/tex]So, the equation of the perpendicular line would be of the form;
[tex]\begin{gathered} y=m_2x+c \\ y=\frac{5}{2}x+c \\ mu\text{ltiply through by 2} \\ 2y=5x+c \\ 2y-5x=c \end{gathered}[/tex]The equation of the perpendicular line will be of the form;
[tex]2y-5x=c[/tex]Where c is a constant;
From the options, the only equation that is similar to the derived equation is;
[tex]2y-5x=-10[/tex]Therefore, the equation of the perpendicular line is;
[tex]2y-5x=-10[/tex]What is the slope of a line that is perpendicular to the line y = - 1x +5?
○-2
-1/2
1/2
○ 2
The slope of the line that is perpendicular to the line y = - 1x +5 is -1.
What is the slope?The ratio of how much y grows as x grows by a certain amount is known as a line's slope. The slope of a line indicates how steep it is, or how much y rises as x rises. Anywhere along the line, the slope remains constant (the same).
Given:
The equation of the line, y = -x + 5
The slope of the line can be calculated by the intercept form,
so m = -1, Here, m is the slope.
The slope of the perpendicular line will be the opposite
So, M = -1
Therefore, the slope of the line that is perpendicular to the line y = - 1x +5 is -1.
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PLSSSSSS HELPPPP ASAPP i only need everything in measuring segments , congruent segments and segment addition
the answer are:
1. A(X +Y),,B (X+Y) OR d(A,B)
2. If two segments having the same length are congruent segments.This is written as for example: AB is congruent with CD.
AB=CD
3. AC=B, because B is inside points A and C it means that it was the additional point to add and arrive at C.
E-0-16Name a pair of similar triangles.Explain why each pair of triangles is similar.Use the given information to find each missing measure.
The horizontal arrows denote that segments RS and VT are parallel. This means that angleR and angleV are congruent. Similarly, angleS and angleT are congruent. They are denoted in blue and red color, respectively:
Therefore,
[tex]\Delta\text{TUV}\approx\Delta SUR[/tex]by the AA-theorem (angle-angle theorem). That is because:
[tex]\begin{gathered} \angle R=\angle V \\ \angle S=\angle T \\ \angle U=\angle U \end{gathered}[/tex]Now, lets find the missing measure x. Since the above triangles are similar, we have
[tex]\frac{x}{3}=\frac{x+1}{3+9}[/tex]which gives
[tex]\frac{x}{3}=\frac{x+1}{12}[/tex]By multiplying both side by 3, we get
[tex]x=\frac{x+1}{4}[/tex]and by multiplying both side by 4, we have
[tex]4x=x+1[/tex]then, x is given as
[tex]\begin{gathered} 4x-x=1 \\ 3x=1 \end{gathered}[/tex]therefore, we obtain
[tex]x=\frac{1}{3}[/tex]then, the missing side x measures 1/3.
Now, lets find y. In this case, we have
[tex]\frac{y}{3}=\frac{2}{9+3}[/tex]then, it yields
[tex]\frac{y}{3}=\frac{2}{12}[/tex]by multipluying both sides by 3, we have
[tex]\begin{gathered} y=3\cdot\frac{2}{12} \\ y=\frac{2}{4} \\ y=\frac{1}{2} \end{gathered}[/tex]Therefore, the missing side y measures 1/2.
how do you find the length of a side of a triangle when given the length of only one other side?
WE can find the sides if the triangle by apply the Sine rule :
[tex]\frac{a}{\sin A}=\frac{b}{\sin B}=\frac{c}{\sin C}[/tex]where, a,b & c are the sides of triangle
For eg :
Consider an triangle with one side AB = 5
and angles A = 60, angle B = 45 and angle C= 75
So, substitute the value in the expression of Sine
[tex]\begin{gathered} \frac{BC}{\sin A}=\frac{AC}{\sin B}=\frac{AB}{\sin C} \\ \frac{BC}{\sin 60}=\frac{AC}{\sin 45}=\frac{5}{\sin 75} \\ \text{ Substitute the values :} \\ \frac{BC}{\sin60}=\frac{AC}{\sin45}=\frac{5}{\sin75} \\ \frac{BC}{0.866}=\frac{AC}{0.707}=\frac{5}{0.965} \\ \text{ Simplify : }\frac{AC}{0.707}=\frac{5}{0.965} \\ \frac{AC}{0.707}=\frac{5}{0.965} \\ AC=\frac{5}{0.965}\times0.707 \\ AC=3.66 \\ \text{Now, Simplify: }\frac{BC}{0.866}=\frac{5}{0.965} \\ BC=\frac{5}{0.965}\times0.866 \\ BC=4.4 \end{gathered}[/tex]The sides : AB = 5, AC = 3.66 & BC = 4.4