The equation in slope-intercept form of a line that has a slope of −1/2
and passes through the point (−2, 7) is y = (-1/2)x + 6.
Given:
slope-intercept form of a line that has a slope of −1/2 and passes through the point (−2, 7).
slope m = -1/2
substitute m and (-2,7) in standard form y = mx + c
7 = -1/2*-2 + c
7 = 2/2 + c
7 = 1 +c
c = 7 - 1
c = 6
substitute c and m value
y = mx+c
y = (-1/2)x + 6
Therefore The equation in slope-intercept form of a line that has a slope of −1/2 and passes through the point (−2, 7) is y = (-1/2)x + 6.
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Jim was playing a game in which he gained and lost points. First, helost four points. Next, he lost nine points. Write the total change to hisscore as an integer.
Let the total game played be x
The first game he played he lost 4 points
Mathematically,
Total game = lost game + gained game
x = 4 + gained game
gained game = x - 4
next game he lost 9 points again
out of the total x game he had already lost 4 and now losing 9 points
The remaining game after losing 4 will be x-4
x - 4 = lost game
the new lost game is 9 points
x - 4 = 9
isolating x
you have x = 9+4
x = 13
Choose the correct answer(s) below. Select all that apply.N A. ZHDEB. ZGFDC. ZHDFD. ZBDCE. ZGDFF. There are no angles adjacent and congruent to ZBDG
OK
These angles are
HDE and GFD
Letter A
Letter B
Letter C
Write logaa=4x in exponential form and find x to evaluate logaa for any a>0, a≠1.
Given:
[tex]\log _aa=4x[/tex]To find the exponential form of the above, all we need to do is to raise the base a to the power of 4x.
That is;
[tex]a^{4x}=a[/tex]To find the value of x, we need to raise the power of the right - hand side so that we can equate the exponent
That is;
[tex]a^{4x}=a^1[/tex]4x = 1
Divide both-side by 4
[tex]x=\frac{1}{4}[/tex][tex]\text{Log}_aa=4(\frac{1}{4})[/tex][tex]\text{Log}_aa=1[/tex]
the function g is a transformation of f. The grab below shows us as a solid blue line and g as a dotted red line. what is the formula of gA) g(x) =(x/2+1)²-3B) g(x) =(2x+1)²-3C) g(x) =(x/2-1)²-3D) g(x) =(x/2+1)²+3
First we notice that the vertex of the parabola is shift one unit to the left and three units down. To begin we need to remember the following rules:
Suppose c>0. To obtain the graph of
y=f(x)+c, shift the graph of f(x) a distance c units upwards.
y=f(x)-c, shift the graph of f(x) a distance c units downward.
y=f(x-c), shift the graph of f(x) a distance c units to the right.
y=f(x+c), shift the graph of f(x) a distance c units to the left.
Once we have this rules and knowing that the vertex move like we mentioned before we have that the new function should be of the form:
[tex]f(x+1)-3[/tex]From the graph we also notice that the function g is stretch by a factor of two, remembering the rule for stretching graphs:
If c>1 then the function y=f(x/c), stretch the graph of f(x) horizontally by a factor of c.
With this we conclude that the function g has to be of the form:
[tex]f(\frac{x}{2}+1)-3[/tex]Finally, we notice that the function f is:
[tex]f(x)=x^2[/tex]Threfore,
[tex]g(x)=(\frac{x}{2}+1)^2-3[/tex]then the answer is A.
HAve a nice day !
2. Consider the linear expression.
3.2a - 1 - 4 1/3a + 7 - a
(a) What are the like terms in the expression?
(b) Simplify the linear expression.
Please type ALL the steps down.
a. The like terms are: 3.2a, -4⅓a, and -a; and -1 and 7.
b. The linear expression is simplified as: -2.1a + 6.
How to Simplify a Linear Expression?To simplify a linear expression, the like terms in the expression are combined together. Like terms in a linear expression are terms that have the same variables or variables with the same powers. Constant terms are also like terms. These like terms are combined together to simplify any given expression.
a. Given the linear expression, 3.2a - 1 - 4⅓a + 7 - a, the following are the like terms that exist in the expression:
3.2a, -4⅓a, and -a are like terms because they have the same variable.
-1 and 7 are like terms, because they are constants.
b. To simplify the linear expression, 3.2a - 1 - 4⅓a + 7 - a, combine the like terms together:
3.2a - 4⅓a - a - 1 + 7
3.2a - 4.3a - a - 1 + 7
-2.1a + 6
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Using the slope formula, find the slope of the line through the given points.(-3,-7) and (8,-7)
the slope of the line is 0
ExplanationThe slope of a line is a measure of its steepness of a line , The vertical change between two points is called the rise, and the horizontal change is called the run. The slope equals the rise divided by the run:
[tex]\begin{gathered} slope=\frac{rise}{run}=\frac{change\text{ in y}}{change\text{ in x}}=\frac{y_2-y_1}{x_2-x_1} \\ where \\ P1(x_1,y_1\text{ \rparen and P2\lparen x}_2,y_2)\text{ are 2 points from the line} \end{gathered}[/tex]so
Step 1
given
[tex]\begin{gathered} P1=(-3,-7) \\ P2=(8,-7) \end{gathered}[/tex]replace in the formula
[tex]\begin{gathered} slope=\frac{y_{2}-y_{1}}{x_{2}-x_{1}} \\ slope=\frac{-7-(-7)}{8-(-3)}=\frac{-7+7}{11}=\frac{0}{11}=0 \end{gathered}[/tex]hence, the slope of the line is 0
I hope this helps you
A- what is R(300) interpret this result B- what is the revenue from the sale of 2,000 hats write in functional notation3 part question
Okay, here we have this:
Considering the provided information, and the given function we are going to calculate R(300) and then we will interpret the result, so we obtain the following:
[tex]\begin{gathered} R(x)=17x \\ R(300)=17\cdot300 \\ R(300)=5100 \end{gathered}[/tex]Considering that x corresponds to the number of hats sold, then it means that if 300 hats are sold, the total revenue will be equal to $5100.
Given the parent graph f(x)=e^x, which of the following functions has a graph that has been translated 3 to the left and reflected over the x-axis?following functions given to pick from are g(x)=−e^x+3g of x is equal to negative e raised to the x plus 3 powerg(x)=e^−(x+3)g of x is equal to e raised to the negative open paren x plus 3 close paren powerg(x)=e^3−xg of x is equal to e raised to the 3 minus x powerg(x)=−e^3−x
Given the parent function:
[tex]f(x)=e^x[/tex]Let's determine the function that has a graph which has been translated 3 units to the left and reflected over the x-axis.
To find the function, apply the transformation rules for functions.
• After a translation 3 units to the left, we have:
[tex]g(x)=e^{x+3}[/tex]• Followed by a reflection over the x-axis:
[tex]g(x)=-e^{x+3}[/tex]Therefore, the function that has a graph which has been translated 3 units to the left and reflected over the x-axis is:
[tex]g(x)=-e^{x+3}[/tex]32. What is the rate of change of y with the respect to x for 24x - 4y = 50
The equation for the graph is given as
[tex]24x-4y=50[/tex]Let us rearrange the equation into its Slope-Intercept form given as
[tex]y=mx+c[/tex]Where
m = rate of change
c = y-intercept
Therefore, we will have
[tex]-4y=-24x+50[/tex]Divide all terms by -4 to make y a standalone variable:
[tex]\begin{gathered} \frac{-4y}{-4}=\frac{-24x}{-4}+\frac{50}{(-4)} \\ y=6x-\frac{25}{2} \end{gathered}[/tex]Comparing with the Slope-Intercept equation, the rate of change is given as 6.
Which of the following expressions is equivalent to -5(-2x - 3)? If you get stuck, use boxes like the ones we used tohelp organize our class work.(А) 3х - 3B 10x - 3C 10x + 15D10x - 15
We want to find the expression equivalent to -5(-2x - 3), we would have to expand the expression;
[tex]\begin{gathered} -5(-2x-3) \\ -5(-2x)-5(-3) \\ =10x+15 \end{gathered}[/tex]Therefore, the answer is 10x+15, Option C
Which Platonic solid has twenty faces that are equilateral triangles?A. HexahedronB. OctahedronC. IcosahedronD. Dodecahedron
STEP - BY - STEP EXPLANATION
What to find?
The platonic solid that has twenty faces that are equilateral triangles.
Given:
Platonic solid.
Let's check each option.
A hexahedron is a polyhedron with 6 faces.
So this is not an option.
An octahedron is a polyhedron with 8 faces.
This option is also ruled out.
A Dodecahedron is a polyhedron with 12 faces.
This is also not an option.
An Icosahedron is a polyhedron whose faces are 20 equilateral triangles.
Hence Icosahedron is the correct option.
ANSWER
C. Icosahedron
Find 3 ratios that are equivalent to the given ratio 6:13
In order to find equivalent ratios, we can multiply the numerator and denominator by the same value.
For example, let's multiply by 2, by 3 and by 4:
[tex]\begin{gathered} 6:13\\ \\ =6\cdot2:13\cdot2\\ \\ =12:26\\ \\ \\ \\ 6:13\\ \\ =6\cdot3:13\cdot3\\ \\ =18:39\\ \\ \\ \\ 6:13\\ \\ =6\cdot4:13\cdot4\\ \\ =24:52 \end{gathered}[/tex]Therefore the equivalent ratios are 12:26, 18:39 and 24:52..
jamial walked 210 miles he has walked 70%of the way how many more miles does he have left
Given that: jamial walked 210 miles he has walked 70%of the way
So 70% of the total walked he covered
[tex]210\times\frac{70}{100}=147\text{ miles}[/tex]He covered 147 miles
The remaining distance he have to be cover :
[tex]210-147=63\text{ miles}[/tex]can somebody please help me with my homework math by the way
Here, we want to subtract the mixed fraction from the whole number
To do this, we need to express the mixed fraction as an improper fraction
To do this, we will multiply the numerator by the whole number and add the numerator
We have this as;
[tex]5\frac{3}{4}\text{ = }\frac{(5\times4)+3}{4}\text{ = }\frac{20+3}{4}\text{ = }\frac{23}{4}[/tex]We can now perform the subtraction as follows;
[tex]17-\frac{23}{4}\text{ = }\frac{4(17)-23}{4}\text{ = }\frac{68-23}{4}\text{ = }\frac{45}{4}[/tex]To properly write the answer, we have to express 45/4 as a mixed fraction
What we have to do here is to divide 45 by 4, then place the quotient at the front, then, the remainder as the numerator
We have this as;
[tex]\frac{45}{4}\text{ = 11}\frac{1}{4}[/tex]special right triangle find the value of the variables answer must be in simplest radical form
Here, we have a special right triangle.
Let's solve for the variables, x and y.
Given:
common side = x
Hypotenuse of the larger triangle = 8
Let's find x using trigonometric ratio.
We have:
[tex]\begin{gathered} \sin \theta=\frac{opposite}{hypotenuse} \\ \\ \sin 30=\frac{x}{8} \\ \\ x=8\sin 30 \\ \\ x=8(0.5) \\ \\ x=4 \end{gathered}[/tex]To solve for y, we have:
[tex]\begin{gathered} \tan \theta=\frac{opposite}{adjacent} \\ \\ \tan 60=\frac{x}{y} \\ \\ \tan 60=\frac{4}{y} \\ \\ \text{Multiply both sid}es\text{ by y:} \\ y\tan 60=\frac{4}{y}\ast y \\ \\ y\tan 60=4 \\ \\ \text{Divide both sides by tan60} \\ \\ \frac{y\tan 60}{\tan 60}=\frac{4}{\tan60} \\ \\ \\ y=\frac{4}{\tan 60} \end{gathered}[/tex]Solving further:
[tex]\begin{gathered} y=\frac{4}{\sqrt[]{3}} \\ \\ \end{gathered}[/tex]Multiply both numerator and denominator by √3:
[tex]\begin{gathered} y=\frac{4}{\sqrt[]{3}}\ast\frac{\sqrt[]{3}}{\sqrt[]{3}} \\ \\ y=\frac{4\sqrt[]{3}}{3} \end{gathered}[/tex]ANSWER:
[tex]\begin{gathered} x=4 \\ \\ y=\frac{4\sqrt[]{3}}{3} \end{gathered}[/tex]Janie is performing a construction. Her work is shown below.If she connects points D and H, she will create
Looking at the diagram, If she connects points D and H, she will create angle HDG.
We can see that angle HDG is equal to angle ABC. Therefore,
angle HDG is guaranteed to be congruent to anngle ABC
A triangle has side lengths of 6, 8, and 10Is it a right triangle?
To be a right triangle it must comply with the following:
[tex]a^2+b^2=c^2[/tex]Where:
a = 6
b = 8
c = 10
So:
[tex]\begin{gathered} 6^2+8^2=10^2 \\ 36+64=100 \\ 100=100 \end{gathered}[/tex]This means that it is a right triangle.
Answer: Yes, It is a right triangle
What is the volume of a sphere with a diameter of 7.5 cm, rounded to the nearesttenth of a cubic centimeter?
Read the proof. Statement Reason 1. given Given: AE1 EC; BD 1 DC 1. AEI EC;BD IDC Prove: AAEC - ABDC A 2. ZAEC is a rt. 2; ZBDC 2. definition of is a rt. 2 perpendicular 3. ZAEC • ZBDC 3. all right angles are congruent 4. ? 4. reflexive property 5. AAEC - ABDC 5. AA similarity theorem. What is the missing statement in step 4? B D O ZACE = ZBCD O ZEAB DBC O ZEAC LEAC O ZCBD ZDBC
Answer:
(a) ∠ACE≅∠BCD
Step-by-step explanation:
You want to know the missing statement in the proof that goes with reason "Reflexive Property."
ProofYou are proving two triangles are similar by showing two corresponding angles are congruent. Corresponding angles in the two triangles are ...
EAC and DBCAEC and BDCACE and BCDThe proof already shows AEC is congruent to BDC in statement 3.
Reflexive propertyThe reflexive property says an angle is congruent to itself. Looking at the list of corresponding angles, the only angle that corresponds to itself is angle C, which can be named ∠ACE or ∠BCD.
The appropriate choice is ...
∠ACE≅∠BCD . . . . Reflexive property
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The missing statement in step 4 should be:ZACE = ZBCD
This statement is missing from the proof and should be included to establish the congruence between the angles in the two triangles.Let's go through the proof step by step and explain each statement and reason.
Given:
AE = EC; BD = DC
AEI = EC; BD = DC
Reason: Given
ZAEC is a right angle; ZBDC is a right angle
Reason: Definition of a right angle. This statement indicates that angle ZAEC and angle ZBDC are both right angles.
ZAEC ≅ ZBDC
Reason: All right angles are congruent. This statement asserts that angle ZAEC and angle ZBDC are congruent (have the same measure) because they are both right angles.
[Missing Statement]
Reason: Reflexive property. This statement is missing in the proof and should be included. The reflexive property states that any angle is congruent to itself. In this case, it implies that angle ZAEC is congruent to angle ZAEC.
AAEC ≅ ABDC
Reason: AA similarity theorem. This statement indicates that triangle AAEC is congruent to triangle ABDC. The AA similarity theorem states that if two pairs of corresponding angles in two triangles are congruent, then the triangles are similar.
So, to complete the proof, the missing statement in step 4 should be:
ZACE = ZBCD
Reason: Reflexive property. This statement establishes that angle ZACE is congruent to angle ZBCD, based on the reflexive property.
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write an equation to find the area of each figure. Then determine the area of the composite figure. When pi is used, the area will be an approximation.
ANSWER:
The area of the composite figure is 34 m^2
STEP-BY-STEP EXPLANATION:
To calculate the area of the complete figure, you have to separate the figure in two ways, just like this:
Figure A is a square and we calculate the area like this:
[tex]\begin{gathered} A_A=l^2 \\ A_A=4^2=16 \end{gathered}[/tex]Figure B is a trapezoid and we calculate the area like this:
[tex]\begin{gathered} A_B=\frac{b_1+b_2_{}}{2}\cdot h \\ A_B=\frac{4+8}{2}\cdot3 \\ A_B=18 \end{gathered}[/tex]Now the total area is the sum of both parts:
[tex]\begin{gathered} A_T=A_A+A_B \\ A_T=16+18 \\ A_T=34 \end{gathered}[/tex]Each person in a group of students was identified by year and asked when he or she preferredtaking classes: in the morning, afternoon, or evening, The results are shown in the table. Findthe probability that the student preferred afternoon classes given he or she is a junior. Roundto the nearest thousandth. When Do You Prefer to Take Classes?
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data
Junior
Morning 17
Afternoon 20
Evening 3
Step 02:
Junior
probability afternoon = junior afternoon / total junior afternoon
total junior afternoon = 17 + 20 + 3 = 40
probability afternoon = 20 / (17 + 20 + 3) = 0.5
The answer is:
probability afternoon = 0.5
identify the form of line of the following equation 4x+5y=6
To make the graph of the equation, we need to solve for y
[tex]\begin{gathered} 4x+5y=6 \\ 5y=-4x+6 \\ y=-\frac{4}{5}x+\frac{6}{5} \end{gathered}[/tex]Then, the slope of the line is -4/5, this means that the line decreases 4 units when we move 5 units to the right. Also, the y-intercept, that is, the point where the line crosses the y axis, is 6/5
Please do this fast and quick I need to sleep
Given:
distance from sea level to top of hill = initial heeight = 73.5 meters
velocity = 9.8 m/s
[tex]\begin{gathered} For\text{ vertical movement:} \\ Final\text{ height = acceleration\lparen t}^2)\text{ + velocity\lparen t\rparen+ initial height} \\ Since\text{ it is reaching sea level, final height = 0} \\ acceleration\text{ = -9.8 m/s}^2 \\ \\ 0\text{ = -}\frac{1}{2}(9.8)t^2\text{ + 9.8t + 73.5m} \end{gathered}[/tex][tex]\begin{gathered} 0\text{ = -4.9t}^2\text{ + 9.8t + 73.5} \\ 4.9t^2\text{ - 9.8t - 73.5 = 0 \lparen quadratic equation\rparen} \\ \\ \text{Using formula method to find the value of t:} \\ t\text{ = }\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \\ t\text{ = }\frac{-(-9.8)\pm\sqrt{(-9.8)^2-4(4.9)(-73.5)}}{2(4.9)} \\ \text{ t = }\frac{-(-9.8)\pm\sqrt{1536.64}}{9.8} \\ t\text{ = }\frac{9.8\pm39.2}{9.8} \end{gathered}[/tex][tex]\begin{gathered} t\text{ = }\frac{9.8+39.2}{9.8}\text{ ot }\frac{9.8\text{ - 39.2}}{9.8} \\ \\ t\text{ = 5 or -3} \end{gathered}[/tex]Since we can't have t to be negative, t = 5
The cannonball will reach the sea level at 5 seconds
How many square feet of outdoor carpet are needed for this hole
The area of a rectangle is:
[tex]Ar=l\cdot h[/tex]Where:
Ar = area of the rectangle
l = lenght
w = width
And the area of a triangle is:
[tex]At=\frac{1}{2}\cdot b\cdot h[/tex]Where:
At = area of the triangle
b = base
h = height
To solve this problem divide the figure into triangles and rectangles, according to the figure below.
And the square feed (A) needed will be:
A = A1 - A2 + A3 + A4 + A5
Step 01: Calculate A1.
Figure 1 is a rectangle with sides 5 and 6 ft.
[tex]\begin{gathered} A1=5\cdot6 \\ A1=30ft^2 \end{gathered}[/tex]Step 02: Calculate A2.
Figure2 is a rectangle with sides 2 and 3 ft.
[tex]\begin{gathered} A2=2\cdot6 \\ A2=6ft^2 \end{gathered}[/tex]Step 03: Calculate A3.
Figure 3 is a triangle with base 4 (12 - 6 - 2 = 4) and height 3 ft.
[tex]\begin{gathered} A3=\frac{4\cdot3}{2} \\ A3=\frac{12}{2} \\ A3=6ft^2 \end{gathered}[/tex]Step 04: Calculate A4.
Figure 4 is a rectangle with sides 4 (12 - 6 - 2 = 4) and 2 (5 - 3 = 2) ft.
[tex]\begin{gathered} A4=4\cdot2 \\ A4=8ft^2 \end{gathered}[/tex]Step 05: Calculate A5.
Figure 5 is a rectangle with sides 2 and 5 ft.
[tex]\begin{gathered} A4=2\cdot5 \\ A4=10ft^2 \end{gathered}[/tex]Step 06: Find the area of the figure.
A = A1 - A2 + A3 + A4 + A5.
[tex]\begin{gathered} A=30-6+6+8+10 \\ A=48ft^2 \end{gathered}[/tex]Answer: 48 ft² is needed for this hole.
Hello, I need help on how to read attached graph based on the questions.Thank you
As can be seen in the above graph:
(a) g(x) > 0 in the interval: (-4, -2) U (0, 2)
(b) g(x) < 0 in the interval: (-2, 0)
(c) g(x) = 0 at the next x-values: -4, -2, 0, 2
Graphically, the derivative of a function evaluated at a point is seen as the slope of the tangent line that passes through that point of the function.
Then, if the slope is positive, the derivative is positive, if the slope is zero (a horizontal line), the derivative is zero, and if the slope is negative, the derivative is negative.
In the next graph, we can see some of these slopes:
Therefore, the intervals where g'(x) is positive, negative or zero are:
(d) g'(x) > 0 in the interval: (-4, -3) U (-1, 1)
(e) g'(x) < 0 in the interval: (-3, -1) U (1, 2)
(f) g'(x) = 0 at the next x-values: -3, -1, 1
The grade a student makes on a test varies directly with the amount of time the student spends studying. Suppose a student spends 5 hours studying and makes a grade of 89 on the test. What is an equation that relates the grade earned on a test, g, with the amount of time spent studying, t. in hours?
It is given that,
A student spends 5 hours studying and makes a grade of 89 on the test.
To write an equation that relates the grade earned on a test in t hours.
Let us take,
For 5 hours, the grade is 89
For 1 hour, the grade will be,
[tex]\frac{89}{5}=17.8[/tex]Then for t hours, the general equation will be,
[tex]g=17.8t[/tex]Hence, the answer is g=17.8t.
A straw is placed in a rectangular box that is 6 inches by 4 inches by 8 inches, as shown. If the straw fits exactly in the box diagonally from the bottom left corner to the top right back corner, how long is the straw? Leave your answer in simplest radical form.
Explanation
you can solve this by using the distance between 2 points formula
[tex]D_{ab}=\sqrt[]{(x-x_1)^2+(y-y_1)^2+(z-z_1)^2}[/tex]then
Step 1
Let
P1(0,0,0)
P2(6,4,8)
now , replace
[tex]\begin{gathered} D_{ab}=\sqrt[]{(x-x_1)^2+(y-y_1)^2+(z-z_1)^2} \\ D_{ab}=\sqrt[]{(6-0)^2+(4-0)^2+(8-0)^2} \\ D_{ab}=\sqrt[]{(6)^2+(4)^2+(8)^2} \\ D_{ab}=\sqrt[]{36^{}+16+64} \\ D_{ab}=\sqrt[]{116} \\ D_{ab}=\sqrt[]{4\cdot29} \\ D_{ab}=2\sqrt[]{29} \end{gathered}[/tex]I hope this helps you
Please help me on my hw I need help on #2
Given:
The number is,
[tex]5.232323\ldots\text{.}[/tex]To express the given number into fraction . it means in the form,
[tex]\frac{a}{b}[/tex]We can express the given number into geometric series as,
[tex]\begin{gathered} 5.232323\ldots=5+\frac{23}{100}+\frac{23}{10000}+\frac{23}{100000}+\text{.}\ldots\ldots \\ =5+\frac{23}{100}+23(\frac{1}{100})^2+23(\frac{1}{100})^3+\text{.}\ldots\ldots\text{.}\mathrm{}(1) \\ \frac{23}{100}+23(\frac{1}{100})^2+23(\frac{1}{100})^3+\text{.}\ldots=-23+\sum ^{\infty}_{n\mathop=1}23(\frac{1}{100})^{n-1} \\ =-23+\frac{23}{1-\frac{1}{100}} \\ =-23+\frac{23(100)}{99} \\ =-23+\frac{2300}{99} \\ =\frac{-2277+2300}{99} \\ =\frac{23}{99} \end{gathered}[/tex]Now, equation (1) becomes,
[tex]5+\frac{23}{99}=\frac{518}{99}[/tex]Answer:
[tex]\frac{518}{99}[/tex]3^9/3^6= answer in exponential form
To express this fraction in exponential form we have to remember the following property:
[tex]\frac{a^m^{}}{a^n}=a^{m-n}[/tex]Applying it to our problem we have:
[tex]\begin{gathered} \frac{3^9}{3^6}=3^{9-6} \\ =3^3 \end{gathered}[/tex]So the exponential form of our fraction is
[tex]3^3[/tex]n were to share the juice equally, how much would each child get?
Please let me know what is the amount of juice to be shared equally among n people.
Please share an image of the problem so I can see the values in question.
What is the amount of juice to be shared?
Whatever that value is, you divide it by the number of children present.
Another problem seems to be show which number is smaller and which one is larger between the following:
[tex]1\text{ }\frac{2}{3}\text{ and 3}[/tex]So, we proceed to write the mixed number as an improper fraction:
[tex]1\text{ }\frac{2}{3}=1+\frac{2}{3}=\frac{3}{3}+\frac{2}{3}=\text{ }\frac{5}{3}[/tex]and on the other hand, the number 3 can be written as 9/3 (nine thirds)
Therefore, since the mixed number is 5/3 and 3 is 9/3, we see clearly that 5/3 is smaller than 9/3 : One shows 5 of the "thirds" while the other one involves 9 of the "thirds".
Now it seems that you want to add the mixed number plus the 3. so, since they already are expressed with the same DENOMINATOR, we can easily add them:
[tex]1\frac{2}{3}+3=\frac{5}{3}+\frac{9}{3}=\frac{14}{3}=4\text{ }\frac{2}{3}[/tex]