we have the inequality
5y – 2x ≤ 9
Remember that
If an ordered pair is a solution to the inequality, then the ordered pair must satisfy the inequality
so
Verify each ordered pair
1) (–3, 1/5)
substitute in the given inequality
5(1/5) – 2(-3)x ≤ 9
1+6 ≤ 9
7 ≤ 9 -----> is true
that means ----> the ordered pair is a solution
2) (5, –17.6)
5(-17.6) – 2(5) ≤ 9
-88-10 ≤ 9 ------> is true
that means ----> the ordered pair is a solution
3) (0, 2)
5(2) – 2(0) ≤ 9
10 ≤ 9 -----> is not true
The ordered pair is not a solution
therefore
The answer is
A. both (–3, 1/5), and (5, –17.6)A candle is 4 inches tall and burns at the rate of 0.6 inch per hour. If the height of the candle after x hours is 1.5 inches, write an equation to represent the situation. Then use this equation to find the expected number of hours in which the candle melted to 1.5 inches.I think the way to start this is x = 1.5 inches but I'm stuck.
Given the following question:
Candle = 4 inches tall
Burns at a rate of 0.6 inches per hour
x = hours
[tex]4-0.6x=1.5[/tex]4 representing the height of the candle
0.6 representing the rate the candle burns
x = the amount of time in hours the candle burns
1.5 = the height of the candle after it burned for x hours
[tex]\begin{gathered} 4-0.6x=1.5 \\ 0.6x=4-1.5 \\ 0.6x=2.5 \\ x=2.5\div0.6 \\ x=4.166 \\ =4.166\text{ hours} \end{gathered}[/tex]not really sure what to do here??
Answer:
[tex]d=-6[/tex]
[tex]a_9=-49[/tex]
Step-by-step explanation:
If the first term of a sequence is [tex]-1[/tex] and the second term is [tex]-7[/tex], then each successive term in the sequence is [tex]6[/tex] less than the previous term. The common difference is [tex]-6[/tex] ( [tex]d=-6[/tex] ).
The formula representing the arithmetic sequence is:
[tex]a_n=-6n+5[/tex]
Therefore, the ninth term in the sequence is:
[tex]a_9=-6(9)+5[/tex]
[tex]a_9=-54+5[/tex]
[tex]a_9=-49[/tex]
sketch the angle then find its reference angle [tex] \frac{13\pi}{4} [/tex]
We need to find the reference angle by sketching the angle:
First, we need to subtract it by 2π, then:
[tex]θ=\frac{13\pi}{4}-2\pi=\frac{5}{4}\pi[/tex]Hence, the reference angle is 5π / 4.
FACTS:In 2010, the glacier was 1000 meters in length; it had retreated 255 meters in 15 years.Questions:1. Calculate the average annual rate of retreat of the glacier
Let's represent the given (length, years) as (x, y)
at time 0 year, the glacier is 1000 meters
at time 15 years, the glacier retreated 255 meters and that's 1000 - 255 = 745
so we have the points (0, 1000) and (15, 745)
Using the slope formula :
[tex]m=\frac{y_2-y_1_{}}{x_2-x_1}[/tex]where m represents the average annual rate of retreat.
[tex]m=\frac{745-1000}{15-0}=\frac{-255}{15}=-17[/tex]The average annual rate of retreat of the glacier is 17 meters per year
What is the image of (-6, -2) after a dilation by a scale factor of 4 centered at theorigin?
The image of (-6, -2) after dilation by a scale of 4 is (-24, -8)
Explanation:The image of (-6, -2) after dilation by a scale of 4 is
(-6*4, -2*4)
= (-24, -8)
How many general tickets should the college sell to maximize revenue
Notice that, since 5000 tickets are reserved for students, there are 13000 available tickets that can be acquired by students or the general public.
Since the cost of a general public ticket is greater than that of a student ticket, we can increase the revenue to its maximum by selling the remaining 13000 tickets to the general public only.
Therefore, the answer is 13,000
What is the volume of the figure below?9 feet14 feet5 feet30ft60ft90ft120ft
The length of rectangular pyramid is l = 5 feet.
The width of rectangular pyramid is w = 4 feet.
The height of rectangular pyramid is h = 9 feet.
The formula for the volume of rectangular pyramid is,
[tex]V=\frac{l\cdot w\cdot h}{3}[/tex]Since there are two rectangular pyramid so net volume of figure is,
[tex]V^{\prime}=\frac{2}{3}\cdot l\cdot w\cdot h[/tex]Substitute the values in the formula to obtain the volume of figure.
[tex]\begin{gathered} V^{\prime}=\frac{2}{3}\cdot5\cdot4\cdot9 \\ =10\cdot4\cdot3 \\ =120 \end{gathered}[/tex]So volume of figure is 120 feet cube.
There are 7 balls numbered I through 7 placed in a bucket What is the probability of reaching into the bucket and randomly drawing two balls numbered 6 and 3 without replacement, in that order? Express your answer as a fraction in lowest terms or a decimal rounded to the nearest millionth.
We have:
- Numbers of balls from 1 to 7 = 7
- Number of balls with number 6 = 1
- Number of ball with number 3 = 1
Then, the probability of ramdomly choosing a 6 is
[tex]p(6)=\frac{1}{7}[/tex]Once we chose a ball, there are 6 balls into the bucket. Then the probability of ramdomly choosing a 3 is
[tex]P(3)=\frac{1}{6}[/tex]Then, the probability of randomly choosing a 6 and 3 in that order, is
[tex]\begin{gathered} P(6\text{and}3)=P(6)\cdot P(3)=\frac{1}{7}\cdot\frac{1}{6} \\ P(6\text{ and 3)=}\frac{1}{7\cdot6} \\ P(6\text{ and 3)=}\frac{1}{42} \end{gathered}[/tex]that is, the probability is 1/42 = 0.023809
instructions for building a polynomial roller coaster in factored form
The polynomial that is used to represent the roller coaster in factored form is y = +a x (x- 500) (x- 1000)
The given conditions are.
The negative intercept at x = 500
the roller coaster passes through the x-axis at x=0 and at x=1000
The polynomial equation is of the form will be
y = a x (x- 500) (x- 1000)
The polynomial will have a root at x=0 , at x=500 and at x = 1000
Polynomials are used in many areas of mathematics and science. For instance, they are employed in calculus, but numerical analysis is used to approximate other functions instead.
Polynomial functions are used in a variety of situations, from basic physics and biology to economics and social science. From straightforward word problems to intricate scientific conundrums, polynomial equations are utilized to represent a wide range of topics.
Polynomials are used in higher mathematics to construct algebraic varieties and polynomial rings, two key concepts in algebra and algebraic geometry with the use of variables.
Therefore the polynomial that is used to represent the roller coaster in factored form is y = a x (x- 500) (x- 1000)
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Roxanne likes to fish. She estimates that 30% of the fish she catches are trout, 20% are bass, and 10% are perch. She designs a simulation.Let 0, 1, and 2 represent trout.Let 3 and 4 represent bass,Let 5 represent perch.Let 6, 7, 8, and 9 represent other fish.The table shows the simulation results. what is the estimated probability that at least one of the next four roxanne catches will be bass?
We have 20 equally probable events in the table. So, each box has probability equal to 1/20.
With this in mind, we must find the numbers 3 and 4 in each box. Then, we can see that there are 12 boxes containing these numbers. Therefore, the probability to catch a bass is
[tex]\begin{gathered} P(\text{bass)}=12\cdot(\frac{1}{20}) \\ P(\text{bass)}=\frac{12}{20} \\ P(\text{bass)}=\frac{3}{5} \end{gathered}[/tex]By converting these result in percentage, we have
[tex]\frac{3}{5}\cdot100=60[/tex]that is, 60% could be bass fish.
Write the equation of a function that has the given characteristics.The graph of y = |x|, shifted 8 units upwardоа y = |x-81y = |x+81y = x| + 8y = |x| - 8
The given function is
[tex]y=|x|[/tex]The transformation is shifted 8 units upwards.
Remember, to move the function upwards we have to sum outside the absolute value bars.
Therefore, the transformed function would be
[tex]y=|x|+8[/tex]Solve this system of equations byusing the elimination method.3x + 3y = 182x + y = 4( [?]. []).
Given the system of equations:
3x + 3y = 18
2x + y = 4
Let's solve the system of equations using the elimination method.
Multiply one equation by a number which makes one variable of each equation opposite.
Multiply equation 2 by -3:
3x + 3y = 18
-3(2x + y) = -3(4)
3x + 3y = 18
-6x - 3y = -12
Add both equations:
3x + 3y = 18
+ -6x - 3y = -12
_________________
-3x = 6
Divide both sides by -3:
[tex]\begin{gathered} \frac{-3x}{-3}=\frac{6}{-3} \\ \\ x=-2 \end{gathered}[/tex]Substitute -2 for x in either of the equations.
Take the second equation:
2x + y = 4
2(-2) + y = 4
-4 + y = 4
Add 4 to both sides:
-4 + 4 + y = 4 + 4
y = 8
Therefore, we have the solutions:
x = -2, y = 8
In point form, we have the solution:
(x, y) ==> (-2, 8)
ANSWER:
(-2, 8)
Driving down a mountain, Bob Dean finds that he descends 3300 feet in elevation by the time he is 4.5 miles (horizontally) away from the high point on the mountain road. Find the sic
descent. (1 mile 5280 feet).
The slope is
(Type an integer or decimal rounded to two decimal places as needed.)
Answer:
[tex]-0.14[/tex]
Step-by-step explanation:
Slope is defined as the change in [tex]y[/tex] divided by the change in [tex]x[/tex].
The change in [tex]y[/tex] is a decrease of 3,300 feet.
The change in [tex]x[/tex] is an increase of 4.5 miles. Converting to feet so that both measurements are in identical units:
[tex]\frac{4.5\text{ mi}}{1}\times\frac{5280\text{ ft}}{1\text{ mi}}=23760\text{ ft}[/tex]
Therefore, the slope is:
[tex]\frac{\Delta{y}}{\Delta{x}}=\frac{-3300}{23760}=-\frac{5}{36}[/tex]
As a decimal rounded to two places:
[tex]-\frac{5}{36}\approx{-0.14}[/tex]
find the mean of the data sets. round answers to the nearest integer. 4. { 24,21,23,22,26,23,24,21} 5. { 3,3,4,3,3,2}
Let's begin by identifying key information given to us:
[tex]24,21,23,22,26,23,24,21[/tex]The mean of the data set is calculated by using the formula:
[tex]\begin{gathered} m=\frac{SumOfTerms}{NumberOfTerms} \\ m=\frac{\Sigma x}{n}=\frac{24+21+23+22+26+23+24+21}{8} \\ m=\frac{184}{8}=23 \\ m=23 \end{gathered}[/tex]Therefore, the mean of the data set is 23
POSSIBLE Match the function rule to the table of values. f(x)=2 х f (x) = (3) f(x) = 32 2 f () = ( 1 ) 28
First, we must evaluate each function at the given values of x.
When x=-2, we have
[tex]\begin{gathered} f(x)=2^x\Rightarrow f(-2)=2^{-2}=\frac{1}{2^2}=\frac{1}{4}=0.25 \\ \end{gathered}[/tex][tex]f(x)=(\frac{1}{3})^x\Rightarrow f(-2)=(\frac{1}{3})^{-2}=\frac{1}{3^{-2}}=3^2=9[/tex][tex]f(x)=3^x\Rightarrow f(-2)=3^{-2}=\frac{1}{3^2}=\frac{1}{9}=0.11[/tex][tex]f(x)=(\frac{1}{2})^x\Rightarrow f(-2)=(\frac{1}{2})^{-2}=\frac{1}{2^{-2}}=2^2=4[/tex]Now, we must compare these result with the tables. Then the solutions are:
What is the volume of the cone? 1 Use the formula 1 = 6 cm 1 1 18 cm 1 1 1 1 A 16-em> or < 50.3 cm B) 32cm or 100.5 CMS 8 cm or
The measure of angle 1 is greater than 97 degrees and at most 115. Graph the possible values of x.
We are given the following:
Angle 1 is greater than 97 degrees and at most 115 degrees
The angle alternate to angle 1 is "(9x +7)"; alternate angles are congruent
Using the information above, we will develop the inequality shown below:
[tex]\begin{gathered} 97^{\circ}10 \\ x>10 \\ \\ \therefore x>10 \end{gathered}[/tex]We will proceed to the second portion of the inequality. We have:
[tex]\begin{gathered} (9x+7)\le115^{\circ} \\ 9x+7\le115 \\ \text{Subtract ''7'' from both sides, we have:} \\ 9x\le115-7 \\ 9x\le108 \\ \text{Divide both sides by ''9'', we have:} \\ \frac{9}{9}x\le\frac{108}{9} \\ x\le12 \\ \\ \therefore x\le12 \end{gathered}[/tex]We will combine both inequalities into one. We have it thus:
[tex]\begin{gathered} x>10 \\ x\le12 \\ \text{Combining the inequalities, we have:} \\ 10We will proceed to plot this inequality on the number line as shown below:You have one type of chocolate that sells for $5.00/lb and another type of chocolate that sells for $7.60/lb. You would like to have 10.4 lbs of a chocolate mixture that sells for $6.50/lb. How much of each chocolate will you need to obtain the desired mixture? You will need BLANK lbs of the cheaper chocolate and BLANK lbs of the expensive chocolate.Please help!! It is urgent.
Answer
You will need 4.4 lbs of the cheaper chocolate and 6 lbs of the expensive chocolate.
Explanation
Let the amount to be made of the type of chocolate (cheaper chocolate) that sells for $5.00/lb be x pounds.
Let the amount to be made of the type of chocolate (expensive chocolate) that sells for $7.60/lb be y pounds.
We would like to make a chocolate mixture that weighs 10.4 lbs. That is,
x + y = 10.4 .......... equation 1
This chocolate mixture is supposed to cost $6.50/lb and weigh 10.4 lbs. Hence, the cost of 10.4 lbs of this chocolate mixture will be
= 6.50 × 10.4 = $67.6
The cost of x pounds of the $5.00/lb = x × 5 = 5x dollars
The cost of y pounds of the $7.60/lb = y × 7.60 = 7.6y dollars
The cost of the two types of chocolate have to amount to $67.6
5x + 7.6y = 67.6 .......... equation 2
Writing the two equations together
x + y = 10.4
5x + 7.6y = 67.6
This simultaneous equation is then solved and the solution obtained is
x = 4.4 pounds and y = 6 pounds.
Hope this Helps!!!
can someone help me with this math problem a write a number line to it
write an inequality: n is at most 40
If a value is at most 40, it means that such value cannot be greater than 40. The values will always take a value that is less tha 40 wih 40 inclusive.
To express this using inequality, we will use the less than or equal to sign in our expression as shown
[tex]n\leq40[/tex]How would you change 65% to a decimal?
In converting percentage to decimals, you need to divide it by 100.
[tex]\frac{65}{100}=0.65[/tex]The answer is 0.65
The functions f and g are defined as follows:f(x)=2x^2-3xg(x)=-5x-1Find f(-3) and g(7)Simplify your answers as much as possible
f(x) = 2x^2 - 3x
f(-3) = 2(-3)^2 - 3(-3)
f(-3) = 2(9) + 9
f(-3) = 18 + 9
f(-3) = 27 This is the first solution
g(x) = -5x - 1
g(7) = -5(7) - 1
g(7) = -35 - 1
g(7) = -36 This is the second solution
f(x) = 3x2 + 4x – 6g(x) = 6x3 – 522 – 2Find (f - g)(x).O A. (f - g)(x) = -6x3 + 8x2 + 4x – 4O B. (f - g)(x) = 623 – 2x² + 4x - 8O C. (f - g)(x) = 6x3 – 8x2 - 4x + 4O D. (f - g)(x) = -6x3 – 2x2 + 4x – 8SUBMIT
We are being asked to subtract one function from another function.
[tex](f-g)(x)=f(x)-g(x)[/tex][tex]\begin{gathered} (f-g)(x)=(3x^2+4x-6)-(6x^3-5x^2-2)=3x^2+4x-6-6x^3+5x^2+2 \\ (f-g)(x)=-6x^3+8x^2+4x-4 \end{gathered}[/tex]Answer: .
Jeff's restaurant sells hamburgers. The amount
charged for a hamburger (h) is based on the cost for a plain hamburger plus an additional charge for each topping (t) as shown in the equation below.
h = 0.60t+5
What does the number 0.60 represent in the equation?
A. the number of toppings
B. the cost of a plain hamburger
C. the additional cost for each topping
D. the cost of a hamburger with 1 topping
Answer:
Step-by-step explanation:
b the cost of the plain burger
Michael monthly salary after tax is 2,675 if Michele pays for rent,food,and other Bill's totaling 2,140 then how much money is left
We are told that Michael has a total of $2675. If he spends $2140, then the total amount left is the difference between the total and the spent amount, that is:
[tex]2645-2140=505[/tex]Therefore, he has $505 left.
Determine the amplitude, period, and phase shift for y=1/3tan (0 +30) and use them to plot the graph of the function.
Given: The function below
[tex]y=\frac{1}{3}tan(\theta+30^0)[/tex]To Determine: The amplitude, the period, and the phase shift
Solution
The graph of the function is as shown below
The general equation of a tangent function is
[tex]f(x)=Atan(Bx+C)+D[/tex]Where
[tex]\begin{gathered} A=Amplitude \\ Period=\frac{\pi}{B} \\ Phase-shift=-\frac{C}{B} \\ Vertical-shift=D \end{gathered}[/tex]Let us compare the general form to the given
[tex]\begin{gathered} y=\frac{1}{3}tan(\theta+30^0) \\ f(x)=Atan(B\theta+C)+D \\ A=\frac{1}{3} \\ B=1 \\ C=30^0 \\ D=0 \end{gathered}[/tex]Therefore
[tex]\begin{gathered} Amplitude=\frac{1}{3} \\ Period=\frac{\pi}{B}=\frac{180^0}{1}=180^0 \\ Phase-shift=-\frac{C}{B}=-\frac{30^0}{1}=-30^0 \end{gathered}[/tex]Hence, the correct option is as shown below
hi! i was wondering how to find the volume of a figure?
Answer: Volume of solid = 700 ft^3
Explanation:
The solid figure can be sectioned into 2 parts; a rectangular prism and a triangular prism.
Considering the rectangular prism, the formula for calculating the volume is
Volume = length x width x height
From the diagram,
length 10
height = 10
width = 5
Volume of rectangular prism = 10 x 10 x 5 = 500
Considering the triangular prism, the formula for calculating the volume is
Volume = base area x length
The base is a triangle
Area of triangle = 1/2 base x height
From the diagram,
base = 10
height = 8
Base area = 1/2 x 10 x 8 = 40
Length = 5
Volume of triangular prism = 40 x 5 = 200
Thus,
Volume of solid = 500 + 200
Volume of solid = 700 ft^3
Write an equation and graph the cosine function with amplitude 3 and period 4 pi.
An equation and graph the cosine function with amplitude 3 and period 4 pi is y is 3cos([tex]\frac{1}{2} x[/tex])
How to write an equation ?
The general form for the cosine function is:
y = A cos(Bx+C)+D
The amplitude is:
|A|
The period is:
P = 2π/B
The phase shift is
ϕ = −C/B
The vertical shift is D
Explanation:
Given:
The amplitude is 3:
|A|=3
The above implies that A could be either positive or negative but we always choose the positive value because the negative value introduces a phase shift:
A=3
Given:
The period is
P = 4π
4π =2π/B
B = 1/2
Nothing is said about the phase shift and the vertical shift, therefore, we shall assume that
C and D are 0.
Substitute these values into the general form:
y = 3cos([tex]\frac{1}{2} x[/tex])
An equation and graph the cosine function with amplitude 3 and period 4 pi is y is 3cos([tex]\frac{1}{2} x[/tex])
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15/2 as a mixed number
We must express the number 15/2 as a mixed number, which is a number consisting of an integer and a proper fraction. To do that, we compute the quotient in the following way:
[tex]\frac{15}{2}=\frac{14+1}{2}=\frac{14}{2}+\frac{1}{2}=7+\frac{1}{2}=7\frac{1}{2}\text{.}[/tex]Answer
The number 15/2 expressed as a mixed number is:
[tex]7\frac{1}{2}\text{.}[/tex]I need help, I’m not sure which one is the answer
Given the triangles are similar, the pair of corresponding sides are proportional.
Then,
[tex]\frac{AB}{ED}=\frac{BC}{EF}[/tex]Knowing that:
AB = 30
ED = 5
BC = 42
EF = x
Substituting the values:
[tex]\begin{gathered} \frac{30}{5}=\frac{42}{x} \\ 6=\frac{42}{x} \end{gathered}[/tex]Multiplying both sides by x and then dividing the sides by 6.
[tex]\begin{gathered} 6*x=\frac{42}{x}*x \\ 6x=42 \\ \frac{6x}{6}=\frac{42}{6} \\ x=7 \end{gathered}[/tex]Answer: x = 7.