The exact value of sin 4π/3 using both double and half angle identities is: -¹/₂√3
How to use Trigonometric Identities?Trigonometric Identities are defined as the equalities that involve trigonometry functions and holds true for all the values of variables given in the equation. There are various distinct trigonometric identities involving the side length as well as the angle of a triangle.
Using the trigonometric identity: sin 2A = 2sin A cos A
Thus:
sin 2(2π/3) = 2 sin (2π/3) cos (2π/3)
From trigonometric tables, we have:
= 2((√3)/2 * -1/2)
= -¹/₂√3
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Use the fraction bar interactive to find the difference: One-third minus StartFraction 5 over 6 EndFraction
Answer:
-1/2
Step-by-step explanation:
Answer:
common denominator
6
1/3 - 5/6 difference
-1/2
Step-by-step explanation:
hope I wasn't to late
have a good day guys
:)
Subtract three hundred sixty-five thousandths from one and nine-tenths...
Answer:
1.535
Step-by-step explanation:
"one and nine-tenths" is 1.9
We SAY one point nine, but the official way to say the number is one and nine tenths. The one is a whole one. The "and" is the where the decimal point goes and the first place to the right of the decimal is the tenths place.
"three hundred sixty five thousandths" is 0.365
The second decimal place is the hundredths place, just fyi but its not in this problem. The third decimal place is the thousandths place.
1.9 - 0.365 is your question.
if you are allowed to use a calculator, just punch that in. If you are not allowed to use a calculator, then be sure to line up the decimal point when you subtract. Put 1.900 on top and subtract 0.365 and line up the decimal!
Answer:
1.535
Step-by-step explanation:
hope this helps
conti. 7-10 thanks a lot!
unhelpful answers will be deleted.
Answers:
10. b. \(\displaystyle 13\)
9. b. \(\displaystyle 20\)
8. a. \(\displaystyle 33\)
7. a. \(\displaystyle 25°\)
Step-by-step explanations:
10. Both segments are considered congruent, so turn both expressions into an equation:
\(\displaystyle 3x - 5 = x + 7 \hookrightarrow \frac{-12}{-2} = \frac{-2x}{-2} \\ \\ 6 = x\)
Plug this back into the equation to get \(\displaystyle 13\)on both sides.
9. All edges in a square obtain congruent right angles and edges, so set \(\displaystyle 45\)equivalent to the given expression:
\(\displaystyle 45 = 2x + 5 \hookrightarrow \frac{40}{2} = \frac{2x}{2} \\ \\ \boxed{20 = x}\)
8. Both angles are considered supplementary, so turn both expressions into an equation and set it to one hundred eighty degrees:
\(\displaystyle 180 = (4x - 15)° + (x + 30)° \hookrightarrow 180° = (15 + 5x)° \hookrightarrow \frac{165}{5} = \frac{5x}{5} \\ \\ \boxed{33 = x}\)
7. In this rectangle, segment EO is a segment bisectour, making these angles Complementary Angles. Therefore, set an equation up to find its complement:
\(\displaystyle 90° = 65° + m\angle{VOE} \\ \\ \boxed{25° = m\angle{VOE}}\)
I am joyous to assist you at any time.
Does the image reflect over the x or y axis ?
Answer:
x- axis, I'm pretty sure
Step-by-step explanation:
Answer: The x axes
Step-by-step explanation:
If the perimeter of the pre-image is 41.49 units, what is the perimeter of
the image? Explain your reasoning.
The perimeter of the image is 13.83 units.
The pre-image and the image are missing and so i have attached them.From the attached image, we can see that the pre image is the triangle with coordinates as; X(3, 18), Y(18, 18), Z(18, 9).While the image is the triangle with coordinates of X’(1, 6), Y’(6, 6) and Z’(6, 3).From the coordinates given, we can see that there is a dilation because each of the coordinates have similar scale factors with which they were dilated. For example;X(3, 18) → X’(1, 6)
Y(18, 18) → Y’(6, 6)
Z(18, 9) → Z’(6, 3)
What is clear is that there is a common scale factor of 1/3.Thus, if the pre - image has a perimeter of 41.49, then the perimeter of the image will be; 1/3 × 41.49 = 13.83 units
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Find the area of the sector
Find the area of the full circle:
Area = pi x r^2
Area = 3.14 x 17^2
Area = 907.46 square units
A full circle is 360 degrees. The sector is 120degrees.
Multiply the area of the circle by the sector degrees/ full circle degrees
907.46 x 120/360 = 302.486 square units round off as needed.
Answer:
289/3\(\pi\) m² or 302.6400923... m²
Step-by-step explanation:
These type of questions are very simple, you just have to know how to approach them properly. I'll give you the general structure using this as an example for your understanding.
The general structure goes like this:
Find the area of the entire circleUsing the angle, find out how much of the circle is covered by the sector.Multiply answer from Step 2 from the area to figure out the area of the sector.Area of a circle is \(\pi r^{2}\), so \(\pi\)×17² = 289\(\pi\) m²
The angle is 120° out of 360°, think of a sector as the percentage of the area of the circle.
120/360 = 1/3
1/3 × 289\(\pi\) = 289/3\(\pi\) m² or 302.6400923... m²
find the coordinate vector of a =[ 2 3 4 5] with respect to the basis = [e22, e21, e12, e11 ] of m22.
The coordinate vector of vector a = [2, 3, 4, 5] with respect to the basis B = [e22, e21, e12, e11] of M22 is [3, 4, 5, 2].
To find the coordinate vector, we need to express vector a as a linear combination of the basis vectors. The given basis B represents the standard basis for a 2x2 matrix.
Let's break down the process step by step:
Start with the basis vectors: e22, e21, e12, e11.
Express vector a as a linear combination of the basis vectors:
a = 2 * e22 + 3 * e21 + 4 * e12 + 5 * e11
The coefficients in front of each basis vector represent the coordinates of a with respect to the basis B.
Therefore, the coordinate vector of a with respect to B is [2, 3, 4, 5].
However, it's important to note that the given basis B is not the standard basis for a 2x2 matrix. The standard basis for a 2x2 matrix consists of the following vectors: e11 = [1, 0, 0, 0], e12 = [0, 1, 0, 0], e21 = [0, 0, 1, 0], e22 = [0, 0, 0, 1].
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8X - 17 +5X - 3 = 71
Answer: x=7
Step-by-step explanation:
got it right on edg
Answer:
x = 7
Step-by-step explanation:
8x - 17 + 5x - 3 = +71
13x - 20 = +71
+ 20 = +20
13x = 91
13x/13 = 91/13
x = 7
PLEASE HELP ME TO GET UNGROUNDED AND A BETTER GRADE ASAP
LOTS OF LOVE!
Answer:
e=32, f=79, d=69
Step-by-step explanation:
32 and e are vertical angles, so they share the same value. Same with 69 and d. 69+e+f=180, so process of elimination gives you your answer. Lmk if you need any more help or a better explanation, hope you get ungrounded !
Answer:
f = 79 , e = 32 , d = 69
Step-by-step explanation:
32 + 69 + f = 180
101 + f = 180
f = 79
----------------------------------------------------
69 + 79 + e = 180
148 + e = 180
e = 32
If x and y are integers and x = 50y + 69, which of the following must be odd? O xy O x+y O x+2y 3x - 1 O 3x+1
Since 50 is an even number, we know that x will be even if y is even (50 times an even number is still even) and odd if y is odd (50 times an odd number is odd). Therefore, the only answer choice that must be odd is x+y.
Given that x and y are integers and x = 50y + 69, let's determine which of the following expressions must be odd.
1. xy: Since x is odd (50y + 69), when it is multiplied by any integer y, the result will always be odd. Therefore, xy must be odd.
2. x + y: If x is odd, adding it to an even integer (y) would result in an odd number. However, adding it to an odd integer (y) would result in an even number. Therefore, x + y does not necessarily have to be odd. xy: We can't determine if this is odd or even without knowing the values of x and y.
- x+y: This expression is always odd. To see why, consider two cases:
If x and y are both odd, then x+y is even+odd=odd.
If x and y are both even, then x+y is even+even=even.
If one of x and y is odd and the other is even, then x + y is odd + even =odd.
3. x+2y: We can't determine if this is odd or even without knowing the values of x and y.
3x-1: This expression will be odd if x is odd (3 times an odd number is odd) and even if x is even (3 times an even number is even).
3x+1: This expression will be odd if x is even (3 times an even number plus 1 is odd) and even if x is odd (3 times an odd number plus 1 is even).
x + 2y: Since x is odd and 2y is always even, their sum must be odd. Therefore, x + 2 y must be odd.
4. 3x - 1: This expression is odd, since 3x will always be odd (as x is odd) and subtracting 1 from an odd number results in an even number. Therefore, 3x - 1 does not necessarily have to be odd.
5. 3x + 1: This expression is odd, since 3x will always be odd (as x is odd) and adding 1 to an odd number results in an even number. Therefore, 3x + 1 must be odd.
In conclusion, the expressions that must be odd are xy, x + 2y, and 3x + 1.
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Question
Simplify −3−80−−√6. The simplified expression is $$
The simplified expression of −3−80−−√6 is approximately equal to -87.378.
To simplify the expression −3−80−−√6, we'll break it down into steps:
1: Simplify −√6
To simplify the square root of 6, we find the square root of 6, which is approximately 2.449. Therefore, −√6 can be simplified as -2.449.
2: Evaluate 80−−√6
We substitute the value of −√6 (-2.449) into the expression 80−−√6:
80−−√6 = 80−(-2.449) = 80+2.449 = 82.449
3: Simplify −3−82.449
Now, we substitute the value of 82.449 into the expression −3−82.449:
−3−82.449 = -3 - 82.449 = -85.449
Therefore, the simplified expression of −3−80−−√6 is approximately equal to -87.378.
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Give the domain and range of the given relation, then determine if the relation is a function.
{(−3,−2), (5,1), (0,−4), (−1,−2), (−2,3), (1,−6)}
Domain:
Range:
Answer:
Domain: {-3, 5, 0, -1, -2, 1}
Range: {-6, -4, -2, 1, 3}
The relation is a function.
Step-by-step explanation:
The domain of this relation is the set of all x-values from the ordered pairs, which are:
Domain: {-3, 5, 0, -1, -2, 1}
The range of the relation is the set of all y-values from the ordered pairs, which are:
Range: {-6, -4, -2, 1, 3}
To determine if the relation is a function, we need to check if there are any repeated x-values with different y-values. If there are no such cases, then the relation is a function.
Looking at the domain and range, we can see that each x-value has only one corresponding y-value, so there are no repeated x-values with different y-values. Therefore, the relation is a function...
In case ya'll was wondering about this question, this is basically solutions, no solutions, or infinitely
Jane buys several shirts for $27.50 each, and a pair of shorts for $19. Yuki shops at a different store and buys the same number of shirts for $24 each, plus a pair of shorts for $33. Is there a situation in which they pay the same amount for their purchases. Explain.
Answer:
Step-by-step explanation:
Beginning the e-commerce development process with a mobile presence rather than a desktop website is referred to as which of the following?
1. A) RWD 2. B) AWD 3. C) mobile rst design 4. D) RESS
Beginning the e-commerce development process with a mobile presence rather than a desktop website is referred to as Mobile First Design.Mobile First Design is a strategy for designing responsive websites that prioritize mobile devices over desktop computers. This means that when designing a site, the mobile experience comes first, followed by the tablet and desktop experiences.
Mobile First Design has become a popular design strategy due to the increasing use of mobile devices to access the internet. It acknowledges the fact that mobile devices have smaller screens, slower internet connections, and limited processing power, which means that websites must be designed to work well on these devices
Mobile First Design includes a variety of design strategies to optimize sites for mobile devices, including responsive design, adaptive design, and progressive enhancement. Responsive design involves using flexible grids, images, and media queries to create a website that responds to the screen size of the device it's viewed on.Adaptive design uses a combination of flexible and fixed elements to create a website that adapts to different screen sizes.
Progressive enhancement involves designing a website with basic functionality that works well on any device, and then adding additional features for more capable devices as they become available.
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if the slope of a line is k, and the line passes through the points (0, k 3) and (-3 , 0), what is the value of k
Answer:
1
Step-by-step explanation:
assuming your points are (0,3) and (-3,0) you would "rise" 3 and "run" 3 to get from one point to the next on a graph, making your rise over run (aka slope) 3/3 which is equal to 1.
A car dealership increased the price of a certain car by 11%. The original price was $42,200.
(a) Fill in the blank to write the new price in terms of the original price.
Write your answer as a decimal.
New price - Original price
(b) Use your answer in part (a) to determine the new price.
So, with percentages the easiest way is to multiply the 42200 by 0.11. After that you get (4642.00) < Answer to A so you add 42200 to 4642 to get the new price. That should bring you to (46842.0) < Answer to B
How many seconds are in 13 weeks?
Answer:
1,123,200 seconds
Step-by-step explanation:
86400 seconds in a day
86400*13= 1,123,200 seconds
What is the value of the function y=2x-3 when x = −1?
0-5
0 -1
O2
O 3
Answer:
-5
Step-by-step explanation:
2(-1) - 3
-2 - 3
-5
In a triangle, the ratio of the measures of the sides is 4: 7: 10 , and its longest side is 40 centimeters. Find the perimeter of the triangle in centimeters.
F 37 cm
G 43 cm
H 84 cm
J 168 cm
The perimeter of the triangle is 40 centimeters, which corresponds to answer choice G, 43 cm, option opt G is correct.
To find the perimeter of the triangle, we need to add the lengths of all three sides.
Given that the ratio of the side lengths is 4:7:10,
and the longest side is 40 centimeters,
we can set up the equation:
4x + 7x + 10x
= 40
Combining like terms,
we have:
21x = 40
Dividing both sides by 21,
we find:
x = 40/21
Now, we can find the lengths of the three sides by multiplying x with the respective ratios:
Side 1:
4x = 4 * (40/21)
= 160/21
Side 2:
7x = 7 * (40/21)
= 280/21
Side 3:
10x
= 10 * (40/21)
= 400/21
Adding all three sides together,
we get:
(160/21) + (280/21) + (400/21)
= 840/21
= 40
The perimeter of the triangle is 40 centimeters, which corresponds to answer choice G, 43 cm,option opt G is correct.
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The perimeter of the triangle is 84 centimeters, which corresponds to option H.
To find the perimeter of the triangle, we need to determine the lengths of all three sides.
Given that the ratio of the measures of the sides is 4:7:10, we can represent the lengths of the sides as 4x, 7x, and 10x, where x is a constant.
We are also given that the longest side of the triangle is 40 centimeters, which corresponds to the side with a length of 10x.
To find the value of x, we can set up the following equation:
10x = 40
Dividing both sides of the equation by 10, we get:
x = 4
Now that we have the value of x, we can determine the lengths of the other two sides:
The length of the first side is 4x, which is 4 * 4 = 16 centimeters.
The length of the second side is 7x, which is 7 * 4 = 28 centimeters.
To find the perimeter of the triangle, we add up the lengths of all three sides:
16 + 28 + 40 = 84 centimeters.
Therefore, the perimeter of the triangle is 84 centimeters, which corresponds to option H.
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Decide whether the data table represents a linear function or an exponential function
Answer:
A
Step-by-step explanation:
Answer is a because the common difference is -9
Answer:
the data represent a linear function because there is a common difference of -9
Step-by-step explanation:
f(x) = (4x/9) -8
Find
f-¹(-10)
Answer:
Step-by-step explanation:
f x = (4x/9)
so it will be x into 4x = 9/f
so 4x square = 9/f
What is 3.116372 rounded to the nearest hundred thousandths place?
Answer:
3.11637
Step-by-step explanation
I got it right ayyy :p
Isaiah invested
$
1300
$1300 in an account that pays 5% interest compounded annually. assuming no deposits or withdrawals are made, find how much money isaiah would have in the account 5 years after his initial investment. round to the nearest tenth (if necessary).
Answer:
Isaiah will have a final amount of $1659.17.
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
BracketsParenthesisExponentsMultiplicationDivisionAdditionSubtractionLeft to RightAlgebra I
Compounded Interest Rate Formula:
\(\displaystyle A = P \bigg( 1 + \frac{r}{n} \bigg) ^{nt}\)
Step-by-step explanation:
Step 1: Define
Identify given variables.
P = $1300
r = 0.05
n = 1
t = 5
Step 2: Find Gain
[Compounded Interest Rate Formula] Substitute in variables:∴ Isaiah would make approximately $359.18 and have a final amount of $1659.17.
___
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___
Topic: Algebra I
Assume that △GHI = △LMN. Which of the following congruence statements are correct? Check all that apply.
A. ∠N = ∠I
B. GH = LM
C. ∠M= ∠H
D. IG = LM
E. IH = NM
F. ∠L = ∠I
Answer:
A. ∠N = ∠I
B. GH = LM
C. ∠M= ∠H
E. IH = NM
Step-by-step explanation:
The given statement "△GHI = △LMN" means that triangle GHI is congruent to triangle LMN. Congruent triangles have the same size and shape. Therefore, corresponding sides and angles of the triangles will be equal.
To determine which congruence statements are correct, we need to identify the corresponding sides and angles of the triangles. The corresponding sides and angles are those that are in the same position in each triangle. For example, side GH corresponds to side LM, angle N corresponds to angle I, and so on.
Using this information, we can check each statement:
A. ∠N = ∠I: This statement is true because ∠N and ∠I are corresponding angles in the congruent triangles.
B. GH = LM: This statement is true because GH and LM are corresponding sides in the congruent triangles.
C. ∠M= ∠H: This statement is true because ∠M and ∠H are corresponding angles in the congruent triangles.
D. IG = LM: This statement is false because IG and LM are not corresponding sides in the congruent triangles.
E. IH = NM: This statement is false because IH and NM are not corresponding sides in the congruent triangles.
F. ∠L = ∠I: This statement is false because ∠L and ∠I are not corresponding angles in the congruent triangles.
Therefore, the correct congruence statements are A, B, and C.
As the project progresses, the actual finish times (AFs) of completed activities will determine
the earliest start and earliest finish times for the remaining activities in the network diagram, as well as the total slack.
As the project progresses, the actual finish times (AFs) of completed activities play a crucial role in determining various aspects of the project schedule.
The AFs are used to calculate the earliest start and earliest finish times for the remaining activities in the network diagram. These calculations are based on the dependencies between activities and the actual durations of completed activities.
By considering the AFs, the project team can determine the earliest possible start and finish times for the remaining activities, taking into account the sequence of activities and any imposed constraints. This information helps in managing the project schedule and identifying any potential delays or critical paths.
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On its municipal website, the city of Tulsa states that the rate it charges per 5 CCF of residential water is $21.62. How do the residential water rates of other U.S. public utilities compare to Tulsa's rate? The data shown below ($) contains the rate per 5 CCF of residential water for 42 randomly selected U.S. cities.10.38 9.08 11.7 6.4 12.32 14.43 15.4610.02 14.4 16.08 17.5 19.08 17.88 12.7516.7 17.25 15.54 14.7 18.81 17.89 14.818.32 15.95 26.75 22.22 22.66 20.88 23.3518.95 23.6 19.16 23.65 27.7 26.95 27.0426.89 24.58 37.76 26.41 38.91 29.36 41.55(a)Formulate hypotheses that can be used to determine whether the population mean rate per 5 CCF of residential water charged by U.S. public utilities differs from the $21.62 rate charged by Tulsa. (Enter != for ≠ as needed.)H0:Ha:(b)What is the test statistic for your hypothesis test in part (a)? (Round your answer to three decimal places.)What is the p-value for your hypothesis test in part (a)? (Round your answer to four decimal places.)(c)At α = 0.05, can your null hypothesis be rejected? What is your conclusion?Do not reject H0. The mean rate per 5 CCF of residential water throughout the United States differs significantly from the rate per 5 CCF of residential water in Tulsa.Reject H0. The mean rate per 5 CCF of residential water throughout the United States does not differ significantly from the rate per 5 CCF of residential water in Tulsa.Do not reject H0. The mean rate per 5 CCF of residential water throughout the United States does not differ significantly from the rate per 5 CCF of residential water in Tulsa.Reject H0. The mean rate per 5 CCF of residential water throughout the United States differs significantly from the rate per 5 CCF of residential water in Tulsa.(d)Repeat the preceding hypothesis test using the critical value approach.State the null and alternative hypotheses. (Enter != for ≠ as needed.)H0:Ha:Find the value of the test statistic. (Round your answer to three decimal places.)State the critical values for the rejection rule. Useα = 0.05.(Round your answers to three decimal places. If the test is one-tailed, enter NONE for the unused tail.)test statistic≤test statistic≥State your conclusion.Do not reject H0. The mean rate per 5 CCF of residential water throughout the United States differs significantly from the rate per 5 CCF of residential water in Tulsa.Reject H0. The mean rate per 5 CCF of residential water throughout the United States does not differ significantly from the rate per 5 CCF of residential water in Tulsa.Do not reject H0. The mean rate per 5 CCF of residential water throughout the United States does not differ significantly from the rate per 5 CCF of residential water in Tulsa.Reject H0. The mean rate per 5 CCF of residential water throughout the United States differs significantly from the rate per 5 CCF of residential water in Tulsa.
The null hypothesis for the data will be 21.62 and the alternate hypothesis is 2.02 for the p-value for the data is 0.2253 .
The charge at which anything happens is referred to as the velocity at which it happens.
The required details for mean rate :
(a) H0: µ = 21.62
Ha: µ ≠ 21.62
(b) t = -1.231
p-value = 0.2253
(c) Stop rejecting H0 right now. No longer significantly different from the domestic water tariff in Tulsa, the suggested household water charge per five CCF for the entire USA.
(d) H0: µ = 21.62
Ha: µ ≠ 21.62
t = -1.231
check statistic ≥ 2.020
Don't dismiss H0 any longer. The suggested five CCF residential water charge for the entirety of the USA is no longer significantly different from the five CCF residential water tariff in Tulsa.
The P-value is higher at 0.05, the level of significance. The impact in this instance is negligible. The attempt to reject the null hypothesis failed.
The conclusion is that there is insufficient statistical support to determine whether other American cities have a different mortality rate than Tulsa.
The crucial values for t at this level of significance are t=2.019.
Given that the statistic t = -1.15 is inside the acceptance range in this case, the null hypothesis is not disproved.
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ANSWER FAST 15 points
Which set of line segments could create a right triangle? (4 points)
5, 6, 11
5, 9, 10
5, 13, 18
5, 12, 13
Answer:
5 12 13 equals a right triangle
Answer:
5 12 13
Step-by-step explanation:
Numbers that describe diversity in a distribution are referred to as measures of 1) variability. 2) central tendency. 3) standard deviation. 4) association.
Measures of variability describe diversity in a distribution.
Measures of variability describe the spread or dispersion of values in a distribution. They provide information about how spread out or clustered the data points are. Common measures of variability include the range, variance, and standard deviation.
Measures of central tendency, on the other hand, describe the center or average of a distribution. They provide information about the typical or central value around which the data points are located. Common measures of central tendency include the mean, median, and mode.
Standard deviation is a specific measure of variability that quantifies the average amount by which data points in a distribution deviate from the mean. Association refers to the relationship or connection between two or more variables in a dataset, often analyzed using correlation or regression analysis. It is not a measure of diversity in a distribution.
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Which function has a range limited to only negative numbers?
Answer:
F(x)=-x^2
Step-by-step explanation:
The one example of function with range of only negative number is:
F(x)=-x^2
Why this? We know for every x, x^2 is positive. So -x^2 will be negative.
Jimmy has $88 in his piggy bank. He is saving his
allowance of $15 per week and putting it in his piggy
bank as well. The amount of money in the piggy bank,
y dollars, is a function of the number of weeks saved, x.
a.) Write an algebraic equation for this function.
b.) Construct a table for x and y values for the function above.
Use values for x from 0 to 5.
c.) If Jimmy wants to buy a new video game system for $250, how
many weeks allowance will he need to save?
(This isn't a mutiple choice question)
Answer:
88/15=5.86666666667
Step-by-step explanation:
5.86666666667 because it is