3x + 3y = 6 (eq. 1)
9x - 5y = -24 (eq. 2)
Multiplying equation 1 by 3,
3(3x + 3y) = 3*6
3(3x) + 3(3y) = 18
9x + 9y = 18 (eq. 3)
Subtracting equation 2 to equation 3,
9x + 9y = 18
-
9x - 5y = -24
---------------------
14y = 42
y = 42/14
y = 3
Replacing this result into equation 1,
3x + 3(3) = 6
3x + 9 = 6
3x = 6 - 9
3x = -3
x = -3/3
x = -1
Find the minimum value if f(x) = xe^x over [-2,0]
Given function:
[tex]f(x)=xe^x[/tex]The minimum value of the function can be found by setting the first derivative of the function to zero.
[tex]f^{\prime}(x)=xe^x+e^x[/tex][tex]\begin{gathered} xe^x+e^x\text{ = 0} \\ e^x(x\text{ + 1) = 0} \end{gathered}[/tex]Solving for x:
[tex]\begin{gathered} x\text{ + 1 = 0} \\ x\text{ = -1} \end{gathered}[/tex][tex]\begin{gathered} e^x\text{ = 0} \\ \text{Does not exist} \end{gathered}[/tex]Substituting the value of x into the original function:
[tex]\begin{gathered} f(x=1)=-1\times e^{^{-1}}_{} \\ =\text{ -}0.368 \end{gathered}[/tex]Hence, the minimum value in the given range is (-1, -0.368)
Anna has four more nickels than dimes in her pocket for a totalof $1.25. Which equation could be used to determine the numberof dimes, x, in her pocket?A$0.05(x + 4) + $0.10x = $1.25B $0.05(4x) + $0.10x + $1.25C$0.05x + $0.10(x + 4) = $1.25D$0.05x + $0.10(4x) = $1.251 point
Let 'x' be the amount of nickels Anna has, and 'y' the amount of dimes.
If she has '4 more nickels than dimes' this is:
[tex]y=x+4[/tex]And the total amount is $1.25, that can be written as:
[tex]0.05\cdot x+0.10\cdot y=1.25[/tex]If we replace the equivalence between y and x here we get:
[tex]0.05x+0.10(x+4)=1.25[/tex]The correct answer is option C
true or false? if a line is horizontal, there is no x-intercept
The Solution:
Given that a line is horizontal.
We are asked to determine whether it is true or false that the line has no x-intercept.
Clearly, horizontal lines do not hintercept with x-axis.
Therefore, there is certainly no x-intercept.
Thus, the correct answer is [TRUE]
What statements are true regarding undefine terms in geometry A point has no length or width. A point indicates a location in a coordinate plane. A plane has one dimension, length A line has a define begging and end A plane consists of an infinite set of lines. A line consists of an infinite set of points
Explanation:
Question:
What statements are true regarding undefine terms in geometry
A point has no length or width.
This is true because a point cannot have a dimension
A plane consists of an infinite set of lines.
This is not true because from the definition of a plane, it must have an infinite set of lines or points.
A plane has one dimension, length
This statement is not true because a line is a one dimensional object and as such can only have one dimension which is its' length.
A point indicates a location in a coordinate plane.
This statement is true because any point located on a plane must have an ordered pair of an x and y coordinate
A line has a define begging and end
This is not true because A distance along a line must have no beginning or end.
A line consists of an infinite set of points
This is not true becaue a plane consists of an infinite set of points
Hence,
The final answers are
A point indicates a location in a coordinate plane.
A point has no length or width.
I need help with Number 5 please tell me what to put in the box
The price of a pair of tires is $130.56. We want to know the price of ten tires. Ten tires, is the same as five pairs of tires, then, since we know the price of a pair the price of five pairs will be just five times the price of the pair.
The price of five pairs is:
[tex]5\times130.56=652.80[/tex]$652.80.
Use the given graph to create the equation for the rational function. The function is written in factored form to help you see how the given information shapes our equation.vert asymp at x=-3 opposite end behavior, vert asymp at x=2 same end behavior, bounce off x axis at x=1, y int at -1/2The numerator is: Answer (x-Answer)^2 The denominator is: (x+Answer )(x-Answer )(x-Answer )
Solution
The function is written in factored form
Using vertical asymptote at x = 3 opposite end behaviour
vert asymp at x=2 same end behavior, bounce off x axis at x=1, y int at -1/2
[tex]\begin{gathered} y=\frac{A(x-1)^2}{(x+3)(x-2)^2} \\ -\frac{1}{2}=\frac{A(0-1)^2}{(0+3)(0-2)^2} \\ -\frac{1}{2}=\frac{A}{12} \\ 2A=-12 \\ A=-\frac{12}{2} \\ A=-6 \end{gathered}[/tex][tex]y=\frac{-6(x-1)^2}{(x+3)(x-2)^2}[/tex]Therefore the numerator is : -6(x-1)²
The denominator is : (x+3)(x-2)²
Given f(x)=x^3+kx+5f(x)=x
3
+kx+5, and x+1x+1 is a factor of f(x)f(x), then what is the value of kk?
The value of k associated to the cubic equation f(x) = x³ + k · x + 5 is equal to - 6.
What is the value of k of a cubic equation?
In this question we have a cubic equation of the form f(x) = x³ + k · x + 5 and we need to determine the value of k such that the binomial x + 1 is a factor of f(x). A value of x is a factor of the polynomial if and only if the following expression is observed:
f(x) = 0, for x = a
If we know that x = 1 and f(1) = 0, then the value of k is:
1³ + k · 1 + 5 = 0
k + 6 = 0
k = - 6
The cubic equation has a value of k equal to - 6.
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Determine whether each linear relationship is a direct variation. If so, state the constant of proportionality. (Example 4) 4. Pictures, x 3 4 5 6 51 Minutes, 185 235 285 335 Profit, y 24 32 40 48 Cost, y 60 100 140 180 7. 6. Game, X 2 5 20 5 15 10 Year, x Polnts, y 4 1 5 6 7 25 50 12.5 37.5 Helght, y
table 4 . Direct Variation, constant of proportionality =8
Table 5: No. There is not a direct variation, for the growth is not at a constant factor.
1) To state whether there is a direct variation, we need to examine each row to stat how it increases or decreases
2) So for table 4
x y
3 24
4 32
5 40
6 48
For this, we can write a linear function y=8x
Yes. Direct Variation. Constant of proportionality 8
Table 5
x y
185 60
235 100
285 140
335 180
No. There is not a direct variation, for the growth is not at a constant factor.
Table 6
x y
5 12.5
10 25
15 37.5
20 50
We can set a linear function for that y=5/2 x
Yes. Direct Variation. Constant of proportionality 5/2 (2.5)
Table 7
x y
2 4
3 5
4 6
5 7
There is not a direct variation, for the growth is not at a constant factor.
Three consecutive even integers of which the largest is 2n
Integers are whole numbers. They are either positive or negative
Even numbers are numbers that are completely divisible by 2 without a remainder.
Even numbers could be 2, 4, 6, 8, 10. the list goes on
If 2n is the largest even integer in the given sequence, then the lesser consecutive even integers would be
2n - 2
2n - 2 - 2 = 2n - 4
Three consecutive even integers of which the largest is 2n are
2n - 4, 2n - 2, 2n
The figure below shows a circular lawn.Its diameter is 72 ft.72 ftftft?2(a) Use the calculator to find the area and circumference of the lawn.Use 3.14 for T in your calculations, and do not round your answers,Make sure to include the correct units.?AreaCircumference: 0(b) The lawn will be surrounded by tape.Which measure would be used in finding the amount of tape needed?Circumference AreaCheck2021 McGraw. Educatio ARON
We are given a circle with a diameter of 72 ft. We are asked to determine its area. To do that we will use the following formula:
[tex]A=\frac{\pi D^2}{4}[/tex]Where "D" is the diameter. Replacing the values:
[tex]A=\frac{(3.14)(72ft)^2}{4}[/tex]Solving the operations:
[tex]A=4069.44ft^2[/tex]Now we are asked to determine the circumference of the circle, to do that we use the following formula:
[tex]C=\pi D[/tex]Replacing the values:
[tex]C=(3.14)(72ft)[/tex]Solving the operations:
[tex]C=226.08ft[/tex]Since the circumference is the measure of the longitude of the circle, if it were to be surrounded by tape this is the measure we would have to use.
An engineer has designed a value that will regulate water pressure on an automobile engine. The valve was tested on 120 engines and the mean pressure was 4.6 pounds/square inch. Assume the variance is known to be 0.64. If The valve was designed to produce a mean pressure of 4.4 pounds/square inch, is there sufficient evidence at the 0.1 level that the Valve performs above the specifications? State the null and alternative hypothesis for the above scenario
The valve was designed to produce a mean pressure of 4.4, this means that our null hypothesis has to be:
[tex]H_0:\mu=4.4[/tex]Since we want to determine if there is sufficient evidence that the valve is aboce the specifications, this means that we want to determine if the mean is greater than 4.4, that is, the alternartive hypothesis is:
[tex]H_a:\mu>4.4[/tex]In a survey of 52 pet owners, 26 said they own a dog, and 14 said they own a cat. 13 said they own botha dog and a cat? How many owned a dog but not a cat?
From the given data we know that
[tex]26[/tex]owners own a dog, but out of those,
[tex]13[/tex]own both a cat and a dog.
Therefore, the number of pet owners that own only a dog is
[tex]26-13.[/tex]Answer:
[tex]13.[/tex]Find the reference angle for 342°. 1) 35°2) 5°3) 18°4) 162°
For an angle a in the fourth quadrant, the reference angle is given by:
360º - a
The angles in the fourth quadrant are those between 270º and 360º. So, 342º is in the fourth quadrant, and its reference angle is:
360º - 342º = 18º
Therefore, the third option is correct.
how can u do 3725 x 28
Which equation accurately represents this statement? Select three options. Negative 3 less than 4.9 times a number, x, is the same as 12.8. Negative 3 minus 4.9 x = 12.8 4.9 x minus (negative 3) = 12.8 3 + 4.9 x = 12.8 (4.9 minus 3) x = 12.8 12.8 = 4.9 x + 3
The required three options accurately represent the statement are options b, c, and e.
The equation is the relationship between variables and represented as y = ax + b is an example of a polynomial equation.
Here,
According to the question,
A negative 3 less than 4.9 times a number, x, is the same as 12.8.
12.8 = 4.9x -(-3)
which matched with options b, c, and e.
Thus, the required three options that accurately represent the statement are options b, c, and e.
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Hi, can you help me to find (if passible) the complement andsupplement of the angle 3pi/ 4.
Two angles are called complementary if their measures add to 90 degrees, and called supplementary if their measures add to 180 degrees.
In radians this are
[tex]\begin{gathered} \frac{\pi}{2}\text{ for }90\degree \\ \pi\text{ for }180\degree \end{gathered}[/tex]To find the complement of 3π/4, subtract it by π/2
[tex]\frac{\pi}{2}-\frac{3\pi}{4}=-\frac{\pi}{4}[/tex]To find the supplement of 3π/4, subtract it by π.
[tex]undefined[/tex]Solve the following equation by factoring.x? - 15x = 0Rewrite the equation in a completely factored form.
PLS HELP ASAP!!!!!!!!!!!!!!!!
Answer: n = 42
Step-by-step explanation:
3 (42 - 6)= 126 - 18
= 108
2(42+12) = 84+24
= 108
In overall, the second equation is not greater than the first equation
A recipe for chocolate cupcakes makes 24 cupcakes that are 350 calories each. Instead you decideto make mini-cupcakes, and the same recipe yields 40 mini-cupcakes. If you eat four mini-cupcakes,how many calories will you eat?Enter a whole number wiha no units.
The recipe yields:
[tex]24\cdot350=8400[/tex]8400 calories in total.
Those 8400 calories are equally divided into 40 mini-cupcakes. Then, each mini-cupcake has
[tex]\frac{8400}{40}=210[/tex]210 calories for each mini-cupcake.
Therefore, 4 mini-cupcakes contain:
[tex]210\cdot4=840[/tex]The answer is 840 calories
please help me understand how to solve for the domain!
Given:
f(x) = x^2 + 4x + 4 and g(x) = x^2 - 2x - 8.
we are to find the domain of (f/g) (x)
before we find the domain of the function, its best we know what a domain is.
The Domain of a function is the set of all possible inputs for the function. it can also be seen as the set of input or arguement values for which the function is real and defined.
recall that we have x + 2 as our the simplest form
x - 4
so the domain we wil be looking for is x + 2
x - 4
so we have to take t denominator of the above and compare to zero
x - 4 = 0
x = 4
so this is undefined
the function domain
x < 4 or x > 4
so the domain is:
(- infinity, 4) U (4, infinity)
The correct option is A.
Write the mixed number as an improper fraction. 2 8/9
Raina, Kevin, and Eric have a total of $66 in their wallets. Kevin has 3 times what Eric has. Raina has $9 less than Eric. How much does each have?
In order to determine the amount of money Rain, Kevin and Eric have, write the given situation as an algebraic equation.
If x is the money of Raina, y the money of Kevin and z the money of Eric, you have, based on the given problem, the following equations:
x + y + z = 66 All of them have a total of $66
y = 3z Kevin has 3 times what Eric has
x = z - 9 Raina has $9 less than Eric
Replace the expressions for x and y into the first equation and solve for z, as follow:
(z - 9) + (3z) + z = 66
z - 9 + 3z + z = 66
3z = 66 + 9
3z = 75
z = 75/3
z = 25
Next, replace the previous value of z into the expressions for x and y:
y = 3(25)
y = 75
x = 25 - 9
x = 16
Hence, the amount of money each of them has is:
Raina: $16
Kevin: $75
Eric: $75
Brenda had $23 to spend on two notebooks. After buying them she had $19. How much did each notebook cost
Red Ribbon Week starts Friday. If the average smoker pays $8.25 for packof cigarettes and smokes 1.5 P(packs per day). Using the equationC=8.25PT, determine how much does that smoker spend on cigaretteseach day? Each week? Each 30 day month? Each 365 day year? (T is theamount of time in days)
You have the next equation:
[tex]c=8,25PT[/tex]Data: P=1.5
How much does that smoker spend on cigarettes:
Each day: As T is amunt of time in days, to find how much that smoker spend on cigarettes in one day you: Sustitute the T by 1 in the equation:
T=1day
[tex]c=8,25(1.5)(1)[/tex][tex]c=12.375[/tex]Each day the smoker spends $12.375Each week: A week have 7 days
T=7days
[tex]c=8,25(1.5)(7)[/tex][tex]c=86.625[/tex]Each week the smoker spends $86.625Each 30 day month:
T=30 days
[tex]c=8.25(1.5)(30)[/tex][tex]c=371.25[/tex]Each 30 day month the smoker spends $371.25Each 365 day year:
T=365 days
[tex]c=8.25(1.5)(365)[/tex][tex]c=4516.875[/tex]Each 365 day year the smoker spends $4516.875
Hi! I need some help with this question!I am pretty sure my answer is correct , but I just need to check in overall and review the question!Thank you!
we know that
A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form y=kx
Verify each table
Remember that
In a proportional relationship, the linear equation passes through the origin (0,0)
we have that
Am B and C passes through the origin
so
I will check table D
we have the points
(10,30) and (15,45)
Find the slope
m=(45-30)/(15-10)
m=15/5
m=3
Find the equation in slope intercept form
y=mx+b
we have
m=3
point (10,30)
substitute
30=3(10)+b
b=0
y=3x
Verify with this equation for the other points
For x=100
y=3(100)=300 ----> is ok
For x=200
y=3(200)=600 ----> is ok
that means
table D is proportional
Verify table C
we have
(0,0) and (1,3)
m=(3-0)/(1-0)
m=3
Find the equation in slope intercept form
y=mx+b
we have
m=3
point (0,0)
y=3x
Verify the other points
For x=2
y=2(3)=6
6 is not equal to 9
that means
table C is not proportiona
answer is C
For the function f(x) = √x/2, find f-1(x).
1. replace f(x) with y:
[tex]\begin{gathered} y=\frac{\sqrt[]{x}}{2} \\ \end{gathered}[/tex]2. Replace every x with a y and replace every y with an x:
[tex]\begin{gathered} x=\frac{\sqrt[]{y}}{2} \\ \end{gathered}[/tex]3. Solve for y:
[tex]y=4x^2=(2x)^2[/tex]4. replace y with f-1(x):
[tex]f^{-1}(x)=(2x)^2[/tex]Solve for the area of a parallelogram that has a base of 1/2 in and a height of 8 in.
The area of a parallelogram is given by the equation:
[tex]A=b\times h[/tex]Where b is the base of the parallelogram and h is the height.
In this case, b=1/2 in and h=8in, then:
[tex]\begin{gathered} A=(\frac{1}{2}in)(8in) \\ =4in^2 \end{gathered}[/tex]Therefore, the area of the described parallelogram, is:
[tex]4in^2[/tex]-8.2d + 28.1 = 3.6d is the solution Positive or Negative?
The given expression : -8.2d + 28.1 = 3.6d
Simplify the expression for the d :
-8.2d + 28.1 = 3.6d
Subtract 3.6d on both side of the equation
-8.2d -3.6d + 28.1 = 3.6d -3/6d
-11.8d + 28.1 = 0
Subtract 28.1 on both side :
-11.8d + 28.1 - 28.1 = -28.1
-11.8d = -28.1
Multiply both side by ( -1)
(-1) ( -11.8d) = (-1)(-28.1)
11.8d = 28.1
Divide both side by 11.8
11.8d/11.8 = 28.1/11.8
d = 2.38
Answer : d = 2.38
after swimming 80 ft below the surface of the water a whale swims of 40 ft using a number line to help you create an equation that shows the location of the well and relation to the water surface
We have a whale that swims 80 ft below the surface and then goes up 40 ft.
We can describe her trajectory from surface (y=0) to 80 ft below (y=-80) and then 40 ft up (y=-80+40=-40).
The correct interpretation is Option D: the equation is -80+40=-40. The whale is 40 ft below the surface.
match the angle measurements in radians with equilateral measurements less than or equal to 360°
The first thing we have to know is that pi= 180º
[tex]\begin{gathered} \frac{23\pi}{4}=\frac{23(180º)}{4}=1035 \\ \end{gathered}[/tex]From this value of 1035 we must subtract 360 for each turn of the circumference until it gives us a value less than 360
[tex]\begin{gathered} 1035-360=675 \\ 675-360=315º \end{gathered}[/tex]So the first answer would be
[tex]\frac{23\pi}{4}\to315º[/tex]Using the same methodology the following angles would give
[tex]\begin{gathered} \frac{18\pi}{5}_{}\to288º \\ \frac{22\pi}{9}\to80º \\ \frac{19\pi}{3}_{}\to60º \end{gathered}[/tex]