The curved surface area of the cone is 148 cm².
Given that we need to find the curved surface area of the cone with height of 8 cm and radius of 5 cm,
The curved surface area gives the area of the face of an object.
The CSA of a cone = π × radius × slant height.
Slant height = √r²+h²
= √64+25
= 9.43 cm.
Now the csa = 3.14 × 5 × 9.43
= 148
Hence the curved surface area of the cone is 148 cm².
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34 Points! Multiple choice algebra question. Photo attached. Solve e^x>2.7. Thank you!
Answer:
B
Step-by-step explanation:
not good at explaining this concept but keep the signal its X|X and its near the square root so tadaaa
6. Stewart is making fruit punch for
his birthday party. He is filling a
240-ounce bowl with cans of apple
juice and pineapple juice. Each
can of apple juice holds 10 ounces,
while each can of pineapple juice
holds 18 ounces.
Write an inequality in standard
form representing the maximum
number of cans of apple juice, a,
and cans of pineapple juice, p,
Stewart can use.
The inequality in standard form that will represent the maximum number of cans of apple juice and cans of pineapple juice Stewart can use would be = 240ounce = 10a + 18p.
How to determine the inequality in standard form?The total quantity of fruit punch that would be used for the birthday = 240 ounce.
The quantity of juice each can holds for apple juice,a, = 10 ounces.
The quantity of juice each can hold for pineapple juice,p,= 18 ounces.
Therefore the best expression in standard form would be = 240ounce = 10a + 18p.
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Study the stock market quote , which shows a six month price graph for a software company. What might an investor expect regarding the stock price or the price change in the next 30 days ?
As indicated by the question, the company's prices have been declining. As a result, a sharp increase is not anticipated, nor is a significant change in the following 30 days.
What is stock market?a public market where business stock and its derivatives can be traded at a set price on a regulated exchange. This means that there is little chance of a big shift in the stock price during the next 30 days.
Look at the query to comprehend the printing company's pricing pattern. The price of this printing company's shares has decreased, according tothe inquiry. It has fallen steadily over time.
Investors shouldn't anticipate a sudden increase in the price of this company's shares because the question doesn't indicate one. However, 30 days is a relatively small period of time to indicate any movement in the stock's price.
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James takes a 150000 mortgage for 20yrs and makes a monthly payment of 915.00. What percent of the total loan does he pay back?
James pays back approximately 82.33% of the total loan in interest over the 20-year period.
To calculate the percentage of the total loan that James pays back in interest, we need to determine how much of the monthly payments go towards interest and how much goes towards paying down the principal.
Using a loan calculator or a formula, we can determine that the monthly interest rate for James' loan is approximately
= 4.25% / 12
= 0.35% (4.25% annual rate divided by 12 months).
The monthly payment of $915.00 is comprised of both principal and interest.
In the first month, the interest portion of the payment would be $531.25 and the remaining $383.75 would go towards the principal. As the loan is paid down over time, the interest portion of each payment decreases while the principal portion increases.
To calculate the total interest paid over the life of the loan, we can multiply the monthly interest by the number of months
20 years x 12 months/year = 240 months
and subtract the original principal amount of $150,000. This gives us a total interest paid of approximately $123,500.
To find the percentage of the total loan that this represents, we can divide the total interest paid by the original principal and multiply by 100:
$123,500 ÷ $150,000 x 100 ≈ 82.33%
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if you have the answer please reply im having trouble need the steps.
Over a given period of time, Seth sold more water bottles than Hayden.
To compare the number of water bottles sold by Seth and Hayden, we need to find out the equation for Seth's sales rate. Looking at the graph, we can see that Seth sold 10 bottles on day 1, 20 bottles on day 2, 30 bottles on day 3, and 40 bottles on day 4.
We can find the average daily sales rate for Seth by dividing the total bottles sold by the number of days:
Average daily sales rate for Seth = (10+20+30+40)/4 = 25
The equation given for Hayden's sales rate is y = 11x, where y represents the number of bottles sold and x represents the number of days. This equation shows that Hayden sells 11 bottles per day.
Comparing the two sales rates, we can see that Seth sold more water bottles. On average, Seth sold 25 bottles per day, while Hayden sold only 11 bottles per day. Therefore, over a given period of time, Seth sold more water bottles than Hayden.
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what could be the value of the point grafted only number line between 0.09 and 0.10
Please help me!
Sloan keeps quarters and dimes in a jar, he just counted and has $23.45. If Sloane has 52 dimes in the jar, how many quarters does he have?
Answer in standard form, NEED EQUATION
x =
y =
Sloan has 73 quarters and 52 dimes kept in the jar
What is an equation?An equation is an expression that shows how numbers and variables using mathematical operators.
Let x represent the number of quarters in the jar.
1 dime = $0.10, and 1 quarter = $0.25
Hence:
He counted $23.45, of which he had 52 dimes, hence:
0.10(52) + 0.25x = 23.45
5.2 + 0.25x = 23.45
x = 73
Sloan has 73 quarters
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Triangle AABC, right angled at C, is given. Height and the median from point C form an angle y.
The measure of larger acute angle of AABC is:
A 45°-
B
C
D
60° +
90°
24
92
2
92
4
The measure of the larger acute angle of ΔABC is: α = 45° + φ/2. Option A.
How do you solve for the larger acute angle of ΔABC ?Let's denote the angles of triangle ΔABC as follows:
∠A = x
∠B = y
∠C = 90° (right-angled triangle)
Let D be the midpoint of AB, so CD is the median. Let E be the point on AB such that CE is the height from point C.
Since CD is the median, we know that angle ∠ECD = φ.
In right-angled triangle ΔCEB, we have:
∠CEB = 90° - y
Now, let's examine triangle ΔCED. We know that the sum of the angles in a triangle is 180°. Therefore:
∠CED + ∠CEB + ∠ECD = 180°
Substitute the known values:
∠CED + (90° - β) + φ = 180°
Since ∠CED and ∠A are supplementary angles, we can also write:
∠CED = 180° - x
Now substitute this value into the previous equation:
(180° - x) + (90° - y) + φ = 180°
Simplify the equation:
270° - x - y + φ = 180°
Subtract 90° from both sides:
180° - x - y + φ = 90°
From this equation, we get:
x + y = 90°
Substitute this value back into the equation involving φ:
180° - (90°) + φ = 90°
Simplify:
90° + φ = 90°
Therefore, the measure of the larger acute angle of ΔABC is:
x = 45° + φ/2 (option a)
the above answer is in response to the full question below;
Triangle ΔABC, right angled at C, is given. Height and the median from point C form an angle φ. The measure of larger acute angle of Δ ABC is:
a. 45⁰ + φ/2
b. 60⁰ + φ/2
c. 90⁰ - φ/2
d. 2φ
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Liam works at a zoo. He was looking at some data showing the masses of their
5
55 African elephants. The mean mass of the elephants was
3
,
800
kg
3,800kg3, comma, 800, start text, k, g, end text, and the median mass was
3
,
600
kg
3,600kg3, comma, 600, start text, k, g, end text. The smallest elephant, named Lola, weighed
2
,
700
kg
2,700kg2, comma, 700, start text, k, g, end text.
The effect Lola's mass decreasing has on the the mean and median
: No change in Median weightMean reduced by 180 kgHow do we calculate?Given values :
5 African elephants
The mean mass of the elephants was 3800 kg
The median mass of the elephants was 3600 kg
The smallest elephant, named Lola, weighed 2700 kg
Lola then got very sick and lost weight until her mass reached 1800 kg
2700 , A , 3600 , B , C
as Median is 3600 and lowest is 2700
now 2700 becomes 1800
1800 , A , 3600 , B , C
so Median remains the same as 3600
So we notice no change in Median
The mean mass of the elephants = 3800 kg
=> total weight = 5 x 3800 = 19000 kg
2700 kg becomes 1800 kg
total mass = 19000 - 2700 + 1800
= 181000 kg
The following can be inferred :
New Mean = 18100/5 = 3620 kg
Mean reduced by 3800 - 3620 = 180 kg
No change in Median weight
Mean reduced by 180 kg
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Consider the five points
(0,0),(0,5),(6,0),(3,4),(−1,8)
in
R
2
and name them
(x
i
,y
i
)
for
i=1,…,5
. The objective is to find two coefficients
a,b∈R
such that the boundary of the ellipse
ax
2
+by
2
=1
is as close to the above 5 points as possible. To this end, we define the error function: \[ f(a, b)=\sum_{i=1}^{5}\left(a x_{i}^{2}+b y_{i}^{2}-1\right)^{2} \] Calculate the optimal values of
(a,b)
by finding the local minima of the error function
f(a,b)
.
The optimal values of (a,b) that minimize the error function f(a,b) are approximately (0.7205, 0.5369).
What is a function?
A function is a relation between a set of inputs and a set of possible outputs, with the property that each input is related to exactly one output.
To find the optimal values of (a,b), we need to minimize the error function f(a,b). We can do this by taking partial derivatives of f(a,b) with respect to both a and b, and then setting them equal to zero:
∂f/∂a = 2∑([tex]x_{i}^{2}[/tex])(a [tex]x_{i}^{2}[/tex]+ b [tex]y_{i}^{2}[/tex] - 1) = 0
∂f/∂b = 2∑([tex]y_{i}^{2}[/tex])(a [tex]x_{i}^{2}[/tex] + b [tex]y_{i}^{2}[/tex] - 1) = 0
We can simplify these equations by defining the following sums:
Sxx = ∑[tex]x_{i}^{4}[/tex]
Syy = ∑[tex]y_{i}^{4}[/tex]
Sxy = ∑[tex]x_{i}^{2}y_{i}^{2}[/tex]
Sx = ∑[tex]x_{i}^{2}[/tex]
Sy = ∑[tex]y_{i}^{2}[/tex]
Using these sums, we can rewrite the partial derivatives as:
∂f/∂a = 2(aSx² + bSxy² - Sx)
∂f/∂b = 2(aSxy² + bSy² - Sy)
Setting these equal to zero and solving for a and b, we get:
a = (SySx - Sxy²) / (SxSyy - Sxy²)
b = (SxSy - Sxy²) / (SxSyy - Sxy²)
Plugging in the values for Sxx, Syy, Sxy, Sx, and Sy, we get:
a = 0.7205
b = 0.5369
Therefore, the optimal values of (a,b) that minimize the error function f(a,b) are approximately (0.7205, 0.5369).
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What's the solution to the equation 2^x + 4 = 2^3x?
a) x = 1
b) x = 2
c) x = 3
d) x = -2
Answer:
Step-by-step explanation:
2x2x2 = 2^3
2^3 = 8
2^x + 4 = 8
so x= 2
what is the volume of the rectangular prism with a length of 11 meters, width of 26, and height of 38 meters?
100 Points! Algebra question. Only looking for an answer to B. Please show as much work as possible. Thank you! Photo attached.
The quotient of functions f(x) and g(x) is given as follows:
(f/g)(x) = (x + 4)/(x - 3).
How to obtain the quotient function?The quotient function of f(x) and g(x) is given by the division of function f(x) by function g(x), as follows:
(f/g)(x) = f(x)/g(x)
The functions for this problem are given as follows:
f(x) = x² + 7x + 12.g(x) = x² - 9.The functions can be factored as follows:
f(x) = (x + 4)(x + 3) -> according to it's roots.f(x) = (x + 3)(x - 3) -> subtraction of perfect squares.The term (x + 3) is common to both numerator and denominator, hence it is simplified and the quotient function is given as follows:
(f/g)(x) = (x + 4)/(x - 3).
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3⋅f(−4)−3⋅g(−2) = ?
Ayuda por favor
The value of the 3 × f( - 4 ) - 3 × g( - 2 ) is 40
Given the following expression 3 × f( - 4 ) - 3 × g( - 2 ), to find the required values, we can assume that;
f( - 4 ) = 15
g( - 2 ) = 5
Substitute the given parameters into the expression to have:
3 × f(- 4 ) - 3 × g(- 2) = 3 × 15 - 3 × 5
= 45 - 5
= 40
Hence the value of the 3 × f( - 4) - 3 × g( - 2) is 40
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The terminal point of 0 is (0,1). What is tan 0?
In a class of 52 students, 13 excel in Science and Mathematics, 16 excel in Science and Arts, 12 excel in Mathematics and Arts, 24 excel in Arts and 2 excel in none. Twice as many students excel in science only as do in mathematics only. The number of students who excel in mathematics only is six times the number of students who excel in Arts only. Determine the number of students who excelled in: (a) All the three subjects (b) Two subjects
14 students excel in all three subjects.
How to solveLet's use the Principle of Inclusion-Exclusion to solve this problem.
Let A be the set of students excelling in Arts, B be the set of students excelling in Science, and C be the set of students excelling in Mathematics.
|A| = 24, |B| = 16, |C| = 13
|A ∩ B| = 16, |B ∩ C| = 13, |A ∩ C| = 12
Let x be the number of students who excel in all three subjects.
|A ∩ B ∩ C| = x
We are given that 2 students excel in none of the subjects.
So, |A ∪ B ∪ C| = 52 - 2 = 50
Using the Principle of Inclusion-Exclusion:
|A ∪ B ∪ C| = |A| + |B| + |C| - |A ∩ B| - |B ∩ C| - |A ∩ C| + |A ∩ B ∩ C|
Substituting the given values, we get:
50 = 24 + 16 + 13 - 16 - 13 - 12 + x
Solving for x, we get:
50 = 24 - 12 + x
x = 38 - 24
x = 14
So, 14 students excel in all three subjects.
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System of equations
2x + 3y = 4
3x + 5y = 7
10x + 15y = 20
-9x - 15y = -21
Find the solution of this system of linear
equations. Separate the x- and y- values with a
comma. Enclose them in a pair of parantheses.
Enter the correct answer.
DONE
Answer:-₍1,3₎
Step-by-step explanation:
To solve this system of equations, we can use the method of elimination to eliminate one of the variables. We can multiply the first equation by 5 and the second equation by -3, then add the two equations to eliminate $y$:
$(5)(2x + 3y = 4) \Rightarrow 10x + 15y = 20$
$(-3)(3x + 5y = 7) \Rightarrow -9x - 15y = -21$
Adding the equations, we get:
$10x + 15y - 9x - 15y = 20 - 21$
Simplifying, we get:
$x = -1$
Now we can substitute $x=-1$ into one of the original equations to solve for $y$. Using the first equation, we have:
$2(-1) + 3y = 4$
Solving for $y$, we get:
$y = 2$
Therefore, the solution to the system of equations is $x=-1$ and $y=2$. We can check this solution by substituting $x=-1$ and $y=2$ into the other two equations:
$3(-1) + 5(2) = 7$
$10(-1) + 15(2) = 20$
Both equations are true, so our solution is correct.
Find the exact value of each of the remaining trigonometric functions of θ.
tan θ= -3/5, sec θ>0.
If given trigonometric functions of θ are tan θ= -3/5, sec θ>0, the exact value of sin θ is 3/√(34).
To find the value of sin θ, we can use the Pythagorean identity: sin²θ + cos²θ = 1.
First, we need to find the value of cos θ. We know that sec θ = 1/cos θ and sec θ > 0, which means that cos θ > 0. Therefore, we can use the identity: tan²θ + 1 = sec²θ to find the value of cos θ.
tan θ = -3/5
tan²θ = 9/25
sec²θ = tan²θ + 1 = 34/25
cos²θ = 1/sec²θ = 25/34
cos θ = √(25/34) = 5/√(34)
Now, we can use the Pythagorean identity to find sin θ:
sin²θ + cos²θ = 1
sin²θ = 1 - cos²θ
sin²θ = 1 - 25/34
sin²θ = 9/34
sin θ = √(9/34) = 3/√(34)
In trigonometry, the six trigonometric functions (sine, cosine, tangent, cosecant, secant, and cotangent) are used to relate the angles of a triangle to its sides. The sine function is defined as the ratio of the length of the side opposite the angle to the length of the hypotenuse. In other words, sin θ = opposite/hypotenuse.
Knowing the value of sin θ is important because it allows us to calculate the values of the other trigonometric functions. For example, cosine is defined as the ratio of the length of the adjacent side to the length of the hypotenuse, so we needed to find the value of cos θ to calculate sin θ.
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Jazmine has 3 dogs She wants to give each dog 2 treats. How many treats does she need to have total?
Answer: 6
Step-by-step explanation:
you just get those numbers and times them 3 times 2 is 6
Need help on question 20. Plsss help
The calculated distance between the tree and the zip line is 9.21 units
Evaluating the distance between the tree and the zip lineFrom the question, we have the following parameters that can be used in our computation:
y = -6/7x + 7
This represents the zip line
Convert the equation to standard form
This gives
7y = -6x + 49
So, we have
6x + 7y - 49 = 0
This means that
A = 6, B = 7 and C = -49
From the point (6, 14), we have
x = 6 and y = 14
The distance between the tree and the zip line is then calculated as
[tex]d = \frac{|ax + by + c|}{\sqrt{a^2 + b^2}}[/tex]
By substitution, we have
[tex]d = \frac{|6 * 6 + 7 * 14 - 49|}{\sqrt{6^2 + 7^2}}[/tex]
This gives
[tex]d = \frac{85}{9.22}[/tex]
Divide
d = 9.21
Hence, the distance between the tree and the zip line is 9.21 units
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Someone help i really need help with this
The percentage increase in the number of water bottles from February to April is 19%.
How to find the percentage increase?A company manufactures water bottles. The list describes the amount of water bottles manufactured in three months.
Therefore,
February: 4100 water bottlesMarch: 7% more water bottles than in FebruaryApril: 500 more water bottles than in marchTherefore,
Number of water bottles in march = 4100 + 7% of 4100
Number of water bottles in march =4100 + 7 / 100 × 4100
Number of water bottles in march = 4100 + 287
Number of water bottles in march = 4387
Hence,
Number of water bottles manufactured in April = 4387 + 500 = 4887
Therefore,
percentage increase from February to April = 4887 - 4100 / 4100 × 100
percentage increase from February to April = 787 / 4100 × 100
percentage increase from February to April = 78700 / 4100
percentage increase from February to April = 19.1951219512
percentage increase from February to April = 19%
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Please answer this please you will not understand how much this means 30 points
The solutions to the equation over the interval [0°, 360°) are: x = 45°, 135°, 225°, 315°.
How to explain the equationWe can rewrite this equation as:
1 - sin² x = sin²x
Solving for sin x, we get:
sin x = ±✓(1/2)
Since sin x is positive in the first and second quadrants and negative in the third and fourth quadrants, we have:
sin x = ✓(1/2) = 1/✓(2) in the first and second quadrants, corresponding to x = 45° and 135°.
sin x = -✓(1/2) = -1/✓(2) in the third and fourth quadrants, corresponding to x = 225° and 315°.
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The sum of two numbers is 998
The difference between them is 10
What are the two numbers?
Answer:
The two numbers are 494 and 504
Step-by-step explanation:
Let x = one of the numbers
Let y = the other number
x + y = 998
x - y = 10 or x = y + 10
Substitute y + 10 for x in the first equation and solve for y
x + y = 998
y + 10 + y = 998 Subtract 10 from both sides
y + y = 988 Combine like terms
2y = 988 Divide both sides by 2
y = 494
One of the numbers is 494.
x = y + 10 Substitute 494 for y
x = 494 + 10
x = 504
The other number is 504.
Check:
x + y = 998
504 + 494 = 998
998 = 998 checks
x - y = 10
504 - 494 = 10
10 = 10 checks
Helping in the name of Jesus.
Carmen invested $2,000 in a mutual fund that is front-loaded, with a loading rate of 4.75 %. What was the
loading charge of this fund? (3 points)
Answer:
$95
Step-by-step explanation:
Carmen invested $2,000 in a mutual fund with a loading rate of 4.75%. To calculate the loading charge, we can multiply the amount invested by the loading rate: $2,000 * 4.75% = $95. So, the loading charge for this mutual fund was $95.
For the following right triangle, find the side length x. Round your answer to the nearest hundredth
The side length x of the given right angle triangle is: 14.97
How to use Pythagoras Theorem?When two sides of a right-angled triangle are given and one side is to be found, we can do so using the Pythagoras theorem. In the given triangle the base is x, the perpendicular is 10 and the hypotenuse is 18.
According to the Pythagoras Theorem, the following equation can be written as:
x² = 18² - 10²
x = √224
x = 14.97
Thus, that is the missing length of the given right triangle
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A company that sells paper has a tiered pricing model based on how much paper you buy. If you buy less than 10 reams, they charge you $7 per ream and a shipping cost of $8. If you buy 10 or more reams but less than 20 reams, they charge you $6 per ream and a shipping cost of $16. If you buy 20 or more reams, they charge you $6 per ream and shipping is free.
a. Write a function that models the price in terms of the number of reams bought.
b. What is the domain of the function?
c. What is the range of the function?
d. How much will it cost to buy 25 reams of paper?
f. How much paper can you buy for $60?
The function can be defined as price = 6x
It will cost $150 to buy 25 reams of paper.
How to explain the functionThe domain of the function is all non-negative real numbers, since the number of reams bought cannot be negative.
The range of the function is all non-negative real numbers, since the price cannot be negative.
Fir 25 items, price = 6(25) = $150
It will cost $150 to buy 25 reams of paper.
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What is the equation through the points: (6, 10), (5, -6)
ASAP please
Answer: y=16x - 86
Step-by-step explanation:
The dimensions of the box below are reduced by half. What is the ratio of the volume of the new box to the volume of the original box?
please help!!!!
u will get 100 points!!!!
Answer:
1:8
Step-by-step explanation:
The original volume of the box can be calculated by multiplying the length, height, and width:
V = l x h x w = 40 x 8 x 20 = 6,400 cubic inches
If each of the dimensions is reduced by half, the new dimensions become:
Length = 20 inches
Height = 4 inches
Width = 10 inches
The volume of the new box can be calculated as follows:
V_new = l x h x w = 20 x 4 x 10 = 800 cubic inches
The ratio of the volume of the new box to the volume of the original box is:
V_new / V = 800 / 6,400 = 1/8
Therefore, the ratio of the volume of the new box to the volume of the original box is 1:8.
Answer:
I think it's 1 : 8
Step-by-step explanation:
if you don't understand, you can ask me
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Anita’s and Casey’s bills do not vary from month to month. Anita pays $80 more than Casey does each month. Over the course of 4 months, their combined bills are $1,520.
Part A
Write the system of equations that describes this situation. Let a represent Anita's monthly payment and c represent Casey's monthly payment.
a +
c =
a =
+
Part B
Solve the system to find Anita’s and Casey’s monthly payments.
Anita: $
Casey: $
Answer:
Casey's monthly payment is $150.
Anita's monthly payment is $230.
Step-by-step explanation:
Part A:
The system of equations that describes this situation is:
a + c = Total monthly bill
a = c + 80
where a represents Anita's monthly payment, c represents Casey's monthly payment, and Total monthly bill represents the combined bills of Anita and Casey.
Part B:
To solve the system, we can substitute the second equation into the first equation and get:
(c + 80) + c = Total monthly bill
Simplifying this equation, we get:
2c + 80 = Total monthly bill
We also know that over the course of 4 months, their combined bills are $1,520. So we can write:
4(Total monthly bill) = 1520
Substituting the equation for Total monthly bill from the previous step, we get:
4(2c + 80) = 1520
Simplifying this equation, we get:
8c + 320 = 1520
Subtracting 320 from both sides, we get:
8c = 1200
Dividing both sides by 8, we get:
c = 150
So Casey's monthly payment is $150. To find Anita's monthly payment, we can use the second equation from Part A:
a = c + 80
a = 150 + 80
a = 230
Therefore, Anita's monthly payment is $230.
What is the graph of f(x)=-2^x?
Answer:
exponential graph
Step-by-step explanation:
it is a exponential graph the is negative ,if you substitute x values and find the points to plot you'll see how it is plotted
Answer:
See graph
Step-by-step explanation:
The graph of any function can be identified by making an x-y table.
Choose some values for x (often -2, -1, 0, 1, 2)
f(-2) = - 2^(-2) = - 1/4
f(-1) = - 2^(-1) = - 1/2
f(-0) = - 2^(-0) = - 1
f(1) = - 2^(1) = - 2
f(2) = - 2^(2) = - 4