Answers
Answer:
f(x) = 10400·(1/4)^x; table values: x = -1, f(x) = 162.5g(x) = 1.8·2.4^xIncorrect for b < 1.Step-by-step explanation:
You want to write exponential functions through the given points.
1. TableThe exponential function ...
f(x) = a·b^x
will have the values ...
f(0) = af(1) = ab ⇒ b = f(1)/f(0)Using these relations we can write the function from the table values:
f(x) = 10400·(2600/10400)^x
f(x) = 10400·(1/4)^x
Then your table is ...
[tex]\begin{array}{|c|c|c|c|c|c|c|}\cline{1-7}\vphantom{\dfrac{b}{g}}x&-1&0&1&3&4&6\\\cline{1-7}\vphantom{\dfrac{b}{g}}f(x)&41600&10400&2600&162.5&40.625&2.5390625\\\cline{1-7}\end{array}[/tex]
2. PointsUsing the given points in the exponential function form, we have ...
4.32 = a·b^1
59.71968 = a·b^4
Dividing the second equation by the first, we find ...
59.71968/4.32 = b^3 ⇒ b = 2.4
Using this in the first equation, we get ...
4.32 = a·2.4 ⇒ a = 1.8
The equation of the function is ...
g(x) = 1.8·2.4^x
3. IncreasingThe exponential function ...
y = a·b^x . . . . . . a > 0, b > 0
will be increasing when the growth factor (b) is greater than 1. When 'b' is less than 1, the function will be decreasing.
Sarah's belief is incorrect.
Answer:
[tex]\textsf{1.} \quad f(x)=10400(0.25)^x[/tex]
(-1, 41600) and (3, 162.5)
[tex]\textsf{2.} \quad g(x)=1.8(2.4)^x[/tex]
3. Sarah is incorrect.
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{9 cm}\underline{General form of an Exponential Function}\\\\$f(x)=ab^x$\\\\where:\\\phantom{ww}$\bullet$ $a$ is the initial value ($y$-intercept). \\ \phantom{ww}$\bullet$ $b$ is the base (growth/decay factor) in decimal form.\\\end{minipage}}[/tex]
Question 1The y-intercept is when x = 0.
Therefore, from inspection of the given table, the y-intercept is 10400:
[tex]\implies a=10400[/tex]
Substitute point (1, 2600) and a = 10400 into the exponential function and solve for b:
[tex]\implies 2600=10400b^1[/tex]
[tex]\implies 2600=10400b[/tex]
[tex]\implies b=\dfrac{2600}{10400}[/tex]
[tex]\implies b=0.25[/tex]
Therefore, the equation of the function is:
[tex]\boxed{f(x)=10400(0.25)^x}[/tex]
Find the value of x when f(x) = 41600:
[tex]\begin{aligned} f(x)&=41600\\\implies 10400(0.25)^x&=41600\\(0.25)^x &=\dfrac{41600}{10400}\\(0.25)^x &=4\\\ln (0.25)^x &=\ln 4\\x \ln (0.25)&=\ln 4\\x&=\dfrac{\ln 4}{\ln (0.25)}\\x&=-1\end{aligned}[/tex]
Find the value of f(x) when x = 3:
[tex]\begin{aligned}x=3 \implies f(3) & =10400(0.25)^3\\& =10400(0.015625)\\& = 162.5\end{aligned}[/tex]
Therefore, the completed table is:
[tex]\begin{array}{|c|c|c|c|c|c|c|}\cline{1-7} \vphantom{\dfrac12}x & -1 & 0 & 1 & 3 & 4 & 6\\\cline{1-7} \vphantom{\dfrac12}f(x) &41600 &10400 &2600 &162.5 &40.625 & 2.5390625\\\cline{1-7} \end{array}[/tex]
Question 2Given points:
(1, 4.32)(4, 59.71968)Substitute the given points into the exponential formula g(x) = abˣ
[tex]\implies ab=4.32[/tex]
[tex]\implies ab^4=59.71968[/tex]
To find b, divide the equations:
[tex]\implies \dfrac{ab^4}{ab}=\dfrac{59.71968}{4.32}[/tex]
[tex]\implies b^3=13.824[/tex]
[tex]\implies b=\sqrt[3]{13.824}[/tex]
[tex]\implies b=2.4[/tex]
Substitute one of the points and the found value of b into the equation and solve for a:
[tex]\implies 2.4a=4.32[/tex]
[tex]\implies a=\dfrac{4.32}{2.4}[/tex]
[tex]\implies a=1.8[/tex]
Therefore, the equation of the function is:
[tex]\boxed{g(x)=1.8(2.4)^x}[/tex]
Question 3Sarah is incorrect. For an exponential function in the form a · bˣ:
If a > 0 and b > 1 then it is an increasing function.If a > 0 and 0 < b < 1 then it is a decreasing function.Related Questions
Can someone help me simplify 4(3x^2y^4)3 / (2x^3y^5) ^4??? Actually answer, give explanation. How did you arrive to the answer??
Answers
The simplified form of the given expression, 4(3x^2y^4)3 / (2x^3y^5) ^4, is 27/x⁶y⁸
Simplifying an expressionFrom the question, we are to simplify the given expression
From the given information,
The expression is
4(3x^2y^4)3 / (2x^3y^5) ^4
First, we will write the given expression properly
The given expression written properly is
4(3x²y⁴)³ / (2x³y⁵)⁴
Simplifying the expression
4(3x²y⁴)³ / (2x³y⁵)⁴
4 × (3x²y⁴)³ / (2x³y⁵)⁴
4 × (3)³(x²)³(y⁴)³ / (2)⁴(x³)⁴(y⁵)⁴
4 × (3)³ × (x²)³ × (y⁴)³ / (2)⁴ × (x³)⁴ × (y⁵)⁴
4 × 27 × x⁶ × y¹² / 16 × x¹² × y²⁰
108 × x⁶ × y¹² / 16 × x¹² × y²⁰
This can be further expressed as
108/16 × x⁶/x¹² × y¹²/y²⁰
27/4 × 1/x⁶ × 1/y⁸
= 27/x⁶y⁸
Hence, the simplified expression is 27/x⁶y⁸
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Anna, Sandra, and Jessy take Graduate Management Admission Council’s GMAT examinations. Their scores on the GMAT are roughly normally distributed with a mean of 527 and a standard deviation of 90. What is the probability that Anna obtains the highest grade?
Answers
First, we need to convert Anna's score to a standard score by subtracting the mean and dividing by the standard deviation. Let's say Anna scored a 580 on the GMAT. The standard score is then (580 - 527) / 90 = 0.7.
Then, we need to find the probability that Anna's score is higher than both Sandra's and Jessy's scores. Because the scores are independent, we can simply multiply the probabilities that Anna's score is higher than each of Sandra's and Jessy's scores.
To find the probability that Anna's score is higher than Sandra's score, we need to find the area under the standard normal curve to the right of Anna's standard score. Using a standard normal table or a calculator, we can find that this probability is 0.7448.
To find the probability that Anna's score is higher than Jessy's score, we again need to find the area under the standard normal curve to the right of Anna's standard score. This probability is also 0.7448.
The probability that Anna obtains the highest grade is then 0.7448 * 0.7448 = 0.5534, or about 55.34%. This means there is about a 55.34% chance that Anna will obtain the highest grade among the three students.
If tan(x) = 0.4, find tan(x+kπ), where k∈Z
a. -0.4
b. -0.4k
c. 0
d. 0.4
e. answer not possible
(please answer with explanation)(80 pts)
Answers
tan(x + kπ) = 0.4 where k∈Z
What do you mean by trignometry?
Trigonometry is one of the important branches in the history of mathematics that studies the relationship between the sides and angles of right triangles.
Trigonometric ratios of triangles are also called trigonometric functions. Sine, cosine, and tangent are three important trigonometric functions, abbreviated sin, cos, and tan
It is given that tan(x) = 0.4
Also, tan(x + kπ) = tanx where k∈Z
Therefore, tan(x + kπ) = 0.4 where k∈Z
Hence, option D is correct.
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True or false If the sample size is at least 30, we use the z-critical value
Answers
Z-tests are closely related to t-tests, but t-tests are best performed when the data consists of a small sample size, i.e., less than 30. The given statement is true.
Does critical value depend on sample size?
The sample size and the crucial value that the researcher employed must be connected. The variations in critical values between the t-distribution and the normal-shaped sampling distribution, however, are minimal for sample sizes bigger than 30.
Z-tests and t-tests are closely related, but t-tests work best with small sample sizes of data, or those with fewer than 30 participants. Additionally, whereas z-tests assume that the standard deviation is known, t-tests assume that it is unknown.
You must use the t-distribution table when working problems when the population standard deviation (σ) is not known and the sample size is small (n<30). General Correct Rule: If σ is not known, then using t-distribution is correct.
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Find the volume of the figure below. Round your answer to the nearest tenta
A. 5870.8 ft³
B. 6575.3 ft³
C. 4559.3 f³
D. 5017.8 ft
12 ft
11 ft
Answers
(Evaluate a function for a given domain and a domain value for a given range.)
If f(x)=3-5x, then find the value of each of the following. Show your work/thinking.
a) f(2)
b) f(-4)
c) f(0)
can you please explain
Answers
Answer:
a) 3-5*2=-7
b)3-5*-4=23
c)3-5*0=3
Step-by-step explanation:
you would plug each of them into the equation because they give you x so
a) 3-5*2=-7 x=2
b) 3-5*-4=23 x=-4
c) 3-5*0=3 x=0
30-60-90 triangle with a measure of 10 (longer leg) find the hypotenuse and shorter leg
Answers
For given 30-60-90 triangle, the measure of the shorter leg = 5.78 units and hypotenuse = 11.55 units
In this question we have been given 30-60-90 triangle with a measure of 10 (longer leg)
We need to find the hypotenuse and shorter leg.
We know that longer leg of 30-60-90 triangle is opposite to angle 60
Consider the sine of angle 60
sin(60) = 10/hypotenuse
(√3)/2 = 10/hypotenuse
hypotenuse = 10 * (2/√3)
hypotenuse = 11.55 units
By Pythagoras theorem,
hypotenuse² = (longer leg)² + (shorter leg)²
11.55² = 10² + (shorter leg)²
(shorter leg)² = 11.55² - 10²
shorter leg = √(33.4025)
shorter leg = 5.78 units
Therefore, shorter leg = 5.78 units and hypotenuse = 11.55 units
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A 16 foot long ladder is placed against a 12 foot high wall, reaching the top exactly. (Round your answer to the nearest hundredth if necessary.)
7th/8th math quick it is a test
pwese quick
Answers
The distance of the foot of the ladder from the wall is 10.58m, the distance can find using pythagoras theorem states that in a right-angled triangle.
What is Pythagoras Theorem?A right triangle's three sides are related in Euclidean geometry by the Pythagorean theorem, also known as Pythagoras' theorem. According to this statement, the areas of the squares on the other two sides add up to the area of the square whose side is the hypotenuse.
Learn how to apply the Pythagorean theorem to find the distance between two points using the distance formula. The Pythagorean theorem can be rewritten as d=√((x_2-x_1)²+(y_2-y_1)²) to calculate the separation between any two points.
Let AC be the ladder and A be the window.
Given: AC=15m, AB=12m, CB=am
In right angled triangle ACB,
(Hypotenuse) ² =(Base)² +[Perpendicular)² [By Pythagoras theorem]
⇒(AC)² =(CB)² +(AB)²
⇒(16)² =(a)² +(12)²
⇒256 = a² + 144
⇒ a = √112 = 10.58cm.
The distance of the foot of the ladder from the wall is 9m.
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A sales representative can take one of 3 different routes from City Upper C to City Upper D and any one of 6 different routes from City Upper D to City Upper G. How many different routes can she take from City Upper C to City Upper G, going through City Upper D?
Answers
The number of different routes she can take from City Upper C to City Upper G is 18
How to determine the number of different routes can she take from City Upper C to City Upper G?From the question, we have the following parameters that can be used in our computation:
Routes from City Upper C to City Upper D = 3 routes
Routes from City Upper D to City Upper G = 6 routes
The number of different routes she can take is calculated as
Routes = Routes from City Upper C to City Upper D x Routes from City Upper D to City Upper G
Substitute the known values in the above equation, so, we have the following representation
Routes = 3 * 6
Evaluate
Routes = 18
Hence, the number of routes is 18
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An ounce of gold costs $1310 and an ounce of silver costs $20. Find all possible weights of
silver and gold that make an alloy (combination of metals) that costs less than $900.
s = number of ounces of silver
g = number of ounces of gold
Find the inequality for this question
Answers
By using linear inequation it can be calculated that-
The shaded region right of the y axis and above the x axis gives all possible solution.
The required linear inequation is
1310g + 20s < 900
What is linear inequation?
Inequation shows the comparision between two algebraic expressions by connecting the two algebraic expressions by >, <, ≥, ≤
A one degree inequation is known as linear inequation
Let the alloy has g ounces of gold and s ounces of silver
An ounce of gold costs $1310 and an ounce of silver costs $20.
Cost of the alloy should be less than $900
The required linear inequation is
1310g + 20s < 900
The graph has been attached
The shaded region right of the y axis and above the x axis gives all possible solution.
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Brielle uses 2/3 cup of nuts for every 2 cups of oatmeal to make granola bars. What fraction of a cup of nuts does Brielle use for 1 cup of oatmeal?
Answers
Brielle uses 1/3 of a cup of nuts for 1 cup of oatmeal.
What is unitary method?
The unitary method is a process of finding the value of a single unit, and based on this value finding the required solution.
According to the given question:
Brielle uses 2/3 cup of nuts for every 2 cups of oatmeal to make granola bars.
To find the fraction cup of nuts required for 1 cup of oatmeal, using unitary method
2 cups ----- 2/3 cup of nuts
1 cup ------- [tex]\frac{2/3}{2}[/tex] cup of nuts = 1/3 cup of nuts
Therefore Brielle uses 1/3 of a cup of nuts for 1 cup of oatmeal.
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In December, Mr. Dillon opened a checking account and made deposits of $1530, $896, $571, and $472. He also wrote checks for $32, $918, $825, $661, and $224. What was his balance at the end of the month?
Answers
Mr. Dillon balance at the end of month is $809.
What is checking account?In a financial institution, a checking account is a deposit account that permits both deposits and withdrawals.
What is deposit?Money kept or held in any bank account is referred to as a deposit.
What is withdrawal?A withdrawal entails taking money out of a trust, pension, savings plan, or bank account.
As Mr. Dillon opened a checking account, so balance is $0 in starting.
When he deposits $1530, $896, $571, $472
Total deposit= $1530+$896+$571+$472
= $ 3,469
Check is a kind of withdrawal.
He wrote check of $32 , $981 , $825 , $661 , $224
Total withdrawal= $32+$981,$825+$661+$224
= $2,660
Balance= Total deposit - Total withdrawal
= $3,469 - $2,660
= $809
Therefore, balance is $ 809.
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Sammy is playing a board game. He rolls two number cubes, each numbered 1-6. If he rolls a sum of 2 he wins $50; otherwise he loses $5. How much should Sammy expect to win or lose on average per roll?
Answers
he is supposed to lose an average of 1.36$ per roll
Answer:
Sammy loses $3.47 on average
Step-by-step explanation:
When you roll two number cubes, the number of possible combinations is 36 ( 6 * 6 ).
The only way to get a sum of two is rolling snake eyes (two ones), which means there's only one combination that gets this sum.
The chances of winning is 1/36 whilst the chance of losing is 35/36
$50*(1/36) - $5(35/36) = $1.39 - $4.86 = -$3.47
which means Sammy loses $3.47 on average
Write an equation in slope-intercept form of the line that passes of the line that passes through the given points and is parallel to the graph of the given equation. (2,-2) ; y= -x-2
Answers
The equation of the line that passes through the point (2, -2) and is parallel to the graph of y = -x - 2 is y = -x - 4.
What is the system of linear equations?
A system of linear equations is a group of one or more linear equations that can be solved by using a simultaneous equation or elimination method. Therefore, by using the substitution method and writing the solution of the system in terms of coordinate point (x, y) = (-1, 1).
To write the equation of a line in slope-intercept form (y = mx + b), we need to find the slope of the line (m) and the y-intercept (b).
To find the slope of the line, we can use the slope formula:
m = (y2 - y1)/(x2 - x1)
The equation y = -x - 2 is in slope-intercept form, so the slope of the line is -1.
The y-intercept is the point where the line intersects the y-axis. This point is (0, b), where b is the y-intercept.
Since the given line passes through the point (2, -2), we can substitute these values into the slope-intercept form of the equation to find the y-intercept:
-2 = -1 * 2 + b
Solving for b gives us:
b = -4
Therefore, the equation of the line that passes through the point (2, -2) and is parallel to the graph of y = -x - 2 is y = -x - 4.
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help meeeeeeeeeee pleaseeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee
Answers
Answer:
2.0 acres
Step-by-step explanation:
C(x) = 270 ln(x+1) + 1900 = 2200
270 ln(x+1) = 300
ln(x+1) = 10/9
x+1 = e^(10/9)
x = e^(10/9) - 1 = 2.0377
[tex]x+\frac{8x}{x-7} =\frac{56}{x-7}[/tex]
Answers
The equation has two solutions, on is extraneous and x = 7, and the real solution is x = -8.
How to solve the equation?Here we have the following equation:
x + 8x/(x - 7) = 56/(x - 7)
This is the original equation, notice that if x = 7, we will have a zero on the denominators, and we can't divide by zero, thus, x can't be equal to 7.
Now let's multiply all the equation by (x - 7)
(x - 7)*x + 8x = 56
Now we have a quadratic equation:
x^2 - 7x + 8x - 56 = 0
x^2 + x - 65 = 0
Using the quadratic formula we will get the two solutions:
[tex]x = \frac{-1 \pm \sqrt{1^2 - 4*1*-56} }{2*1} \\\\x = \frac{-1 \pm15}{2*1}[/tex]
Then the two solutions are:
x = (-1 + 15)/2 = 7 (this one is an extraneous solution, we can discard this one)
x = (-1 - 15)/2 = -8
This is our solution.
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Need answer asap don’t know
Answers
The length of the JU would be 60 units.
What is the Basic Proportionality Theorem?
The basic Proportionality Theorem (can be abbreviated as BPT) states that, if a line is parallel to a side of a triangle that intersects the other sides into two distinct points, then the line divides those sides in proportion.
In the given figure side TU is parallel to side LK
If JK = 64 and JU = -4 + 4x
then UK = JK - JU
= 64 - (-4 + 4x)
=68 - 4x
Similarly,if JL = 72 and JT = 27
then TL = JL - JT
= 72 - 27
= 45
Now by using the property of the basic proportionality theorem, we can write
[tex]\frac{JT}{TL} =\frac{JU}{UK}\\\\ \frac{27}{45} =\frac{-4+4x}{68 - 4x}\\\\\frac{3}{5} = \frac{-4+4x}{68 - 4x}\\\\3(68-4x) = 5(-4+4x)\\\\204 - 12x=-20+2x\\\\204+20=14x\\\\x=\frac{224}{14}\\\\x=16[/tex]
Now we can calculate the length of JU = -4 + 4x
= -4 + 4(16)
= -4 + 64 = 60
Hence, the length of the JU would be 60 units.
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TRIGONOMETRY HELP!!
Answers
The measure of the arc length of the sector will be 1.047 units. Then the correct option is A.
What is the arc length of the sector?Let r is the radius of the sector and θ be the angle subtended by the sector at the center. Then the arc length of the sector of the circle will be
Arc = (θ/2π) 2πr
The radius of the sector is 1 unit and the central angle is π/3. Then the measure of the arc length of the sector will be given as,
Arc = [(π/3)/2π] 2π(1)
Simplify the equation, then we have
Arc = [(π/3)/2π] 2π(1)
Arc = (1/6) × 2π
Arc = π/3
Arc = 1.047 units
The proportion of the circular segment length of the area will be 1.047 units. Then, at that point, the right choice is A.
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Please help! I really don't understand this, and if I could get the answer along with a really simple way to solve next questions like this it would be rlly helpful !!!!!!!
A fruit company packages its fruit into two types of boxes: large and small. This morning, the company made two deliveries. The table below shows the number of boxes in each delivery and the total weight (in kilograms).
1st delivery 2nd delivery
number of large boxes 3 9
number of small boxes 5 7
total weight (in kilograms) 116 238
Let x be the weight (in kilograms) of each large box.
Let y be the weight (in kilograms) of each small box.
(a) Write a system of equations that could be used to find the weight (in kilograms) of each type of box.
[ ]x + [ ]y = [ ]
[ ]x + [ ]y = [ ]
(b) How much does each type of box weigh (in kilograms)?
Weight of each large box: [ ] kilograms
Weight of each small box: [ ] kilograms
I know how to solve part a of the problem, at least. But part b is so difficult for me to understand, and I don't get it at all.
Answers
(a) The system of equations that could be used to find the weight (in kilograms) of each type of box is
3x + 5y = 116
9x + 7y = 238
(b)
Weight of each large box: 15.75 kilograms
Weight of each small box: 13.75 kilograms
What is a system of equations?
A finite set of equations for which common solutions are sought is referred to in mathematics as a set of simultaneous equations, often known as a system of equations or an equation system.
Given that, the weight of 3 large boxes and 5 small boxes is 116 kilograms.
The weight of 9 large boxes and 7 small boxes is 238 kilograms.
Let x be the weight (in kilograms) of each large box.
Then the weight of 3 large boxes is 3x kilograms.
Then the weight of 9 large boxes is 9x kilograms.
Let y be the weight (in kilograms) of each small box.
Then the weight of 5 large boxes is 5y kilograms.
Then the weight of 7 large boxes is 7y kilograms.
The weight of 3 large boxes and 5 small boxes is 3x + 5y kilograms.
The weight of 9 large boxes and 7 small boxes is 9x + 7y kilograms.
Therefore,
3x + 5y = 116 .....(i)
9x + 7y = 238 .....(ii)
Solve equation by using elimination method:
Multiplying equation(i) by 3 and subtract equation (ii) from it:
9x + 15y = 348
9x + 7y = 238
(-) (-) (-)
_____________
8y = 110
y = 13.75
Putting y = 13.75 in equation (i)
3x + 5×(13.75) = 116
3x = 47.25
x = 15.75
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Please help!!!!
What is AC?
Answers
Answer:
Step-by-step explanation:
I think its 40
The triangle is isosceles so the left and right side are equal in length.
you would equal 4x+4=6x-14 and solve, getting 18=2x the 9=x
A parking garage bases its prices on the number of hours that a vehicle parks in the garage.
The first two hours cost $2 per hour, between two hours and six hours cost $2 per hour, and all hours after that cost $1.
b
The first two hours cost $2 per hour, between two and four hours cost $1 per hour, and all hours after that cost $0.50.
c
The first two hours cost $4, between two hours and six hours cost $2 per hour, and all hours after that cost $1.
d
The first two hours cost $4, between two hours and six hours cost $1 per hour, and all hours after that cost $0.50.
Answers
Answer:
c The first two hours cost $4, between two hours and six hours cost $2 per hour, and all hours after that cost $1.
Step-by-step explanation:
You want an interpretation of the graph that is a constant 4 up to x=2, has a slope of 2 for 2 ≤ x < 6, and a slope of 1 for x ≥ 6. The vertical axis is labeled dollars, and the horizontal axis is labeled hours.
Graph interpretationThe constant value of y = 4 for x < 2 means the cost of parking is $4 for the first two hours.
The slope of 2 from x=2 to x=6 means the cost of parking is $2 per hour between 2 and 6 hours.
The slope of 2 for x ≥ 6 means the cost of parking is $1 per hour for more than 6 hours.
The description of c applies.
__
Additional comment
The slope, or "unit rate", is the ratio of "rise" to "run". It can be simpler to choose a "run" of 1 and look at the corresponding "rise".
From x=2 to x=3, the cost rises from $4 to $6, a rise of 2 for the run of 1. That is why we say the slope is 2, or the "unit rate" in dollars per hour is $2 per hour.
Line q passes through the points (3,5) and (-2,4).
10. Give a second pair of coordinates on the line parallel to q that passes through (0,1).
11. Give a second pair of coordinates on the line perpendicular to q that passes through (3,5).
Answers
The second pair of coordinates on the line parallel to q that passes through (0,1) is (1,-4/5) and that of (3,5) is (1,7).
How to solve equation of a line?The general form of the equation of a line is y=mx+c
where
m=slope
c is a constant
The equation of the line is
m= [tex]\frac{y-y_{1} }{x-x_{1} }[/tex]
M=[tex]\frac{5-4}{3+2}[/tex]
m=1/5
From the slope formula
m = -1/5
X₎=0
y₎=1
substitute these in the formula for slope
[tex]\frac{-1}{5} =\frac{y-1}{x-0}[/tex]
x=5y-5
x-5y=5
Now, with the above-derived equation, we need to find the other co-ordinate as these coordinates will satisfy this equation.
when x=1,
x-5y=5
1-5y=5
-5y=5-1
y=[tex]\frac{-4}{5}[/tex]
The other coordinate is (1,-4/5)
11. In the second line (3,5)
Using the slope formula
m=[tex]\frac{Y_{2}-Y_{1} }{X_{2}-X_{1} }[/tex]
[tex]\frac{-1}{5} =\frac{y-5}{x-3}[/tex]
x-3=-y+2
x+y=5+3
x+y=8
Also, with the above-derived equation, we need to find the other co-ordinate as these coordinates will satisfy this equation.
when x=1,
x+y=8
1+y=8
y=8-1
y=7
Therefore the second coordinate is (1,7)
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Maria is going to purchase cranberry juice and lemon-lime soda for a new fruit punch recipe. The recipe calls for 3.5 times as many bottles of lemon-lime soda as cranberry juice. If she has $17.40, what is the most bottles of cranberry juice she can buy if cranberry juice costs $3.80 per bottle and lemon-lime soda costs $1.40 per bottle?
Answers
Answer:
Maria can buy at most 2 bottles of cranberry juice and 7 lemon-lime soda bottles.
Step-by-step explanation:
Setting up the SolutionFor this problem, we can set up an algebraic expression to represent the price, and this will help us solve the problem.
So firstly, let's assign the number of cranberry juice bottles to the variable "C". We could technically represent this as the variable name "cranberry juice bottles", but "C" is a bit more easier to write when writing an algebraic expression while still making it easy to distinguish. Let's also assign the number of lemon-lime soda to the variable "L".
Now let's find a way to express the price of each. The price of buying a certain amount of items, can generally be expressed as: [tex](\text{items bought})*(\text{item price})[/tex], since you have to pay the item price for each item bought, also known as, multiplication.
Since we know that the price of a cranberry juice bottle is $3.80 then that means the total amount used towards cranberry juice can be expressed as: [tex]3.80C[/tex]. We're just multiplying the number of cranberry juice bottles times the price. Likewise, we can represent the total amount used towards lemon-lime soda as: [tex]1.40L[/tex]. The same logic is being applied here.
Now if we add both of these, we get the total amount that will be spent which is: [tex]3.80C + 1.40L = T[/tex], and in this case I just set it equal to "T" which just represents the total spent.
Now there's two more things to do. Generally we can't really solve two-variable equations and we want to express one variable in terms of the other, so that we can rewrite the equation as a one-variable equation.
There is one piece of information given that allows us to do this. "The recipe calls for 3.5 times as many bottles of lemon-lime soda as cranberry". So we can represent the numbers of lemon-lime soda bottles as 3.5 times the amount of cranberry juice bottles. We can express it as: [tex]L=3.5C[/tex]
So now let's plug this into the equation, instead of "L". This gives us: [tex]3.80C + 1.40(3.5C) = T[/tex]
let's multiply the 1.40 by the 3
[tex]3.80C + 4.9C= T[/tex]
now let's add up the values.
[tex]8.7C=T[/tex]
Now lastly, this represents the total amount that is going to be spent. Since Maria only has $17.40, we want this total to be less than or equal to 17.40 (assuming there is no sales tax, but this was never given). this gives us our final expression we will be using: [tex]8.7C\le 17.40[/tex]
Solving the ProblemFrom here solving the problem is actually pretty easy. Think of the inequality as a linear equation, we can still apply the same (for the most part) algebraic manipulations we apply to linear equations. We just divide both sides by 8.7 to isolate the C
[tex]\frac{8.7C}{8.7}\le\frac{17.40}{8.7}\\\\C\le 2[/tex]
So Maria can buy a maximum of 2 bottles of cranberry juice. From this we can actually determine the number of lemon-lime soda bottles.
So we know that:
[tex]C=2[/tex]
From this we can determine what L is, since remember the equation we set up earlier?
[tex]L = 3.5C[/tex]
Let's just plug C into the equation, and we get:
[tex]L=3.5(2)[/tex]
Multiply
[tex]L=7[/tex]
So Maria can buy at most 2 bottles of cranberry juice and 7 lemon-lime soda bottles.
please help‼️
Write the vertex form for the quadratic function f, whose vertex is (4, 9) and has leading coefficient
a=2.
Answers
Answer:
y=2(x-4)^2+9
Step-by-step explanation:
Vertex form: y=a(x-h)^2+k
The vertex represents the h and k variables.
Is ( − 3, 2) a solution of 7 x + 9 y > − 3
Answers
Answer:
No
Step-by-step explanation:
x > -9y-3/7 (Solve for X)
_____________________________________________________
y > -7x/9 - 1/3 (Solve for Y)
_____________________________________________________
Therefore, (-3, 2) is not a solution.
A horse eats 10 kg of hay each day. she is for equal sized meals each day how many grams are in each meal ?
Answers
Answer:
For the problem with the horse: 10,000 grams
For the problem with the hiker labeled 11: 2 feet
I hope these answers are of use to you!
Step-by-step explanation:
Okay, for the horse problem I understood that it was a horse eating exactly 10 kg per day. If she does, then you just convert 10 kilograms to grams. To do this, you multiply the amount of kilograms by 1,000, since that is how it works.
10 x 1,000 = 10,000 grams.
For the problem labeled 11 with the hiker, you divide 120 ft by 60 since there are 60 seconds in a minute.
120 divided by 60 = 2 feet
Please see attached problem
Answers
The sum of a number and six is four less than six times the number
Answers
4 - 6x is linear equation .
What in mathematics is a linear equation?
A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept.
Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.
What makes an equation linear?
A linear equation's graph almost always takes the shape of a straight line.
Definition of a Linear Equation: Each term in a linear equation has an exponent of 1, and when this algebraic equation is graphed, it always produces a straight line. It is called a "linear equation" for this reason.
let the number be =x
4 - 6x
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if 2x - 4y = 0 is written as a directly proportional function, where y is a function of x, then what is k?
a. 2
b. 1/2
c. 4
d. 1
Answers
Answer:
b
Step-by-step explanation:
4y = 2x
y = 2/4 x
y = 1/2 x where y = kx then k = 1/2
The rectangular floor of a classroom is 34 feet in length and 22 feet in width. A scale drawing of the floor has a length of 17 inches. What is the perimeter, in inches, of the floor in the scale drawing?
Answers
The perimeter of the scale floor is 56 inches.
What is Perimeter?The perimeter of a shape is defined as the total distance around the shape. It is the length of the outline or boundary of any two-dimensional geometric shape.
To solve, we can set up fractions:
34/17 = 22/x
Cross multiply and you get:
34x = 374
Divide each side by 34:
x = 11
Since we are trying to find the perimeter of the floor, you can use this equation:
2w + 2l = p
Substitute to solve:
2 ( width = 11 )
2 ( length = 17 )
2 ( 17 ) + 2 ( 11 ) = p
34 + 22 = p
p = 56
Hence, the perimeter is 56inches
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