This problem can be seen as the next equation
[tex]\begin{gathered} 4F+2H+1O=T \\ F\text{ = dollars spent on flights} \\ H\text{ = dollars spent at hotels} \\ O\text{ = dollars spent in other stuff} \\ T\text{ = total of points} \end{gathered}[/tex]Since he have charged 9480 dollars in total then we also have the next equation.
[tex]F+H+O=9480[/tex]With the rest of the information, we conclude the next system of equations
[tex]\begin{gathered} 4F+2H+O=14660 \\ F+H+O=9480 \\ F-2H=140 \end{gathered}[/tex]From the first two equations, we can substract them to obtain
[tex]\begin{gathered} 4F+2H+O=14660 \\ - \\ F+H+O=9480 \\ = \\ 3F+H=5180 \end{gathered}[/tex]If we multiply this last equation by 2 and add it to the last equation in the system we have
[tex]\begin{gathered} 6F+2H=10360 \\ + \\ F-2H=140 \\ = \\ 7F\text{ = }10500 \\ \end{gathered}[/tex]So
[tex]\begin{gathered} F=\frac{10500}{7}=1500 \\ H=\frac{1500-140}{2}=680 \\ O=9480-1500-680=7300 \end{gathered}[/tex]Then, he spent 1500 dlls. on flights, 680 dlls. at hotels and 7300 dlls. on others
[tex]\begin{gathered} 4\text{ 2 1 14660 } \\ 1\text{ 1 1 9480} \\ 1\text{ -2 0 140 }\approx \\ 4\text{ 2 1 14660 } \\ 3\text{ 1 0 5180} \\ 1\text{ -2 0 140 }\approx \\ 4\text{ 2 1 14660 } \\ 3\text{ 1 0 5180} \\ 7\text{ 0 0 }10500 \\ \end{gathered}[/tex]Assume that the situation can be expressed as a linear cost function. Find the cost function.Fixed cost is $100; 30 items cost $1000 to produce.The linear cost function is C(x)=___
Given that C(x) is a linear function, it can be expressed as:
[tex]C(x)=a+bx,[/tex]where a, and b are constants.
Now, we are given that there is a fixed cost of 100, therefore, a=100. Now, we know that
[tex]C(30)=1000.[/tex]Therefore:
[tex]1000=100+b(30).[/tex]Solving the above equation for b, we get:
[tex]\begin{gathered} 1000-100=30b, \\ 900=30b, \\ b=\frac{900}{30}, \\ b=30. \end{gathered}[/tex]Answer: [tex]C(x)=100+30x.[/tex]The figure below can be used to prove the Pythagorean Theorem. Use the drop-down menus to complete the proof.
ANSWER :
1. 2ab + c^2
2. (a + b)^2 or (a^2 + 2ab + b^2)
3. 2ab
EXPLANATION :
Recall that the area of a triangle is 1/2 base x height.
and the area of a square is the square of its side.
From the problem, we have 4 congruent triangles.
The area of four triangles is :
[tex]\begin{gathered} A=4\times\frac{1}{2}(ab) \\ A=2ab \end{gathered}[/tex]The area of the square is :
[tex]A=c^2[/tex]Then the total area will be :
[tex]2ab+c^2[/tex]It is equivalent to the area of the whole square in which the side is (a + b)
So that's :
[tex]A=(a+b)^2\quad or\quad(a^2+2ab+b^2)[/tex]Since both expressions are equal, we can equate them :
[tex]\begin{gathered} 2ab+c^2=a^2+2ab+b^2 \\ \text{ Subtracting 2ab from both sides :} \\ 2ab+c^2-2ab=a^2+2ab+b^2-2ab \\ c^2=a^2+b^2 \end{gathered}[/tex]What is 0.2 written as a fraction?
ANSWER
1/5
EXPLANATION
We want to find the value of 0.2 written as a fraction.
To do this, we have that since 2 is directly after the decimal, its place value is tenths, and so we can write that:
[tex]\begin{gathered} \frac{2}{10} \\ \text{write this in lowest terms:} \\ \frac{1}{5} \end{gathered}[/tex]That is the answer.
the ratio of trucks to Cars in the grocery store parking lot is 2 to 3. which statement is ALWAYS true? A: Two out every five vehicles in the parking lot are trucks. B: for every three cars in the parking lot, there are two trucks C: three out of every five vehicles in a parking lot are cars D: for every three trucks in the parking lot there are five cars.
The given ratio of trucks to Cars in the grocery store parking lot is 2 to 3.
We have to check which statements are always true. For that, let's evaluate each statement.
A: Two out every five vehicles in the parking lot are trucks.
The given ratio of trucks to cars is 2:3. That means, the total number of trucks would be 2/5 and cars would be 3/5. Therefore, there would be 2 trucks in five vehicles. Therefore, this statement is true.
B: for every three cars in the parking lot, there are two trucks
As explained in the above scenario, the number of cars would be 3/5 * x and trucks would be 2/5 * x. if x = 5, cars = 3/5 * 5 = 3 and trucks = 2/5 * 5 = 2. Therefore, this statement is true.
C: three out of every five vehicles in a parking lot are cars
Well, the ratio of trucks to cars is 2:3. But, the parking can have other vehicles as well. Therefore, it is not always true that three out of every five vehicles in a parking lot are cars. Therefore, this statement is false.
D: for every three trucks in the parking lot there are five cars.
The given ratio of trucks to cars is 2:3. But this statement makes the ratio 3:5 that is not equal to 2:3. Therefore, this statement is false.
hence, the first two options are correct.
express this number in scientific notation:19 hundred-thousands
we have that
19 hundred-thousands is the same that
19*100*1,000=19*100,000=1
Which expression is equivalent to the given expression? Give a step-by-step guide and explain how you got to your answer, so I can actually learn how to do this.
The Solution:
Given:
Required:
Find an equivalent expression of the given expression.
[tex]\begin{gathered} (2w^{-2})^3(8w^6) \\ \\ 2^3\times8\times w^{-2\times3}\times w^6 \end{gathered}[/tex][tex]\begin{gathered} 8\times8\times w^{-6}\times w^6 \\ \\ 64\times w^{-6+6} \\ 64\times w^0 \\ 64\times1 \\ 64 \end{gathered}[/tex]Answer:
[option B]
what is the one value in the range of this function?
Given the function:
[tex]\mleft\lbrace(^-6,14),(0,4),(3,^-1),(9,^-9)\mright\rbrace[/tex]Since one valid point in the function is (0, 4)
Therefore, the one value in the range of the function is 4
describe the transformation of y=-2(x-2)^2 when compared to the parent function y=x^2
Answer:
Shifted to the right by 2 units
Vertically stretched by a factor of 2
Explanation:
The transformed parabola given is different from the parent function in that is multiplied by 2 and there is 2 subtracted from the x -coordinate.
Subtracting 2 from the x-coordinate shifts the parent function to the right by 2 units.
Multiplying the parent function by 2 stretches it vertical by a factor of 2.
Therefore, when comparing the parent function y = x^2 and its transformed version y = 2 (x-2)^2, the latter can be described as:
The function y = y = 2 (x-2)^2 results when the parent function is
Shifted to the right by 2 units
Vertically stretched by a factor of 2
E su primer día de viaje en bicicleta a campo traviesa,Marco recorrió 120 millas .Planea recorrer 100 millas más cada día. Escribe una expresión algebraica para representar el número total de millas que habrá recorrido después de d dias.
M = distance or total number of miles
d = number of days
M = 120+ 100d
S = 1000 + 30s
S = total amaunt of money
s = number of weeks
Choose the best answer: 8 +9 * 3a. 35b. 51c. 14d. 11
From the order of operations, solve multiplications first and then solve additions:
[tex]8+9\cdot3=8+27=35[/tex]Therefore:
[tex]8+9\cdot3=35[/tex]Which pair of lines are perpendicular? A) y = 4x - 9 and y + 4x = 3 B) y = 3x + 7 and y + 2 = 3(x - 5) C) y = 2x and 2y = x -9 D) y + x = 0 and y = x
First, take into account that the general form of a linear equation is:
y = mx + b
where m is the slope and b the y-intercept.
When two lines are parallel, their slopes are equal.
When two lines are perpendicular, you can verify the following relation between slopes:
m1 = -1/m2
Then:
A)
y = 4x - 9
y + 4x = 3 which is the same as
y = -4x + 3
In this case you can notice that the slopes are not the same and m1 ≠ -1/m2.
Hence, the lines are not neither parallel nor perpendicular.
B)
y = 3x + 7
y + 2 = 3(x-5) which is the same as
y = 3x - 15 - 2
y = 3x - 17
In this case the slopes are the same, then, the lines are parallel
C)
y = 2x
2y = x - 9 which is the same as
y = 1/2 x - 9/2
In this case you can notice that the slopes are not the same and m1 ≠ -1/m2.
Hence, the lines are not neither parallel nor perpendicular.
D)
y + x = 0 which is the same as
y = -x
y = x
In this case you can verify that m1 = -1/m2, then, the line are perpendicular.
write an equation to represent the proportional relationshipnote use x for the independent variable and why for the dependent variable for the questiona factory produces three bottles of sparkling water for every eight bottles of plain water. how many bottles of sparkling water does the company produce when it produces 600 bottles of plain water?
Use the ratio given in the statement to find the equation that represents the proportional relationship:
[tex]\begin{gathered} \frac{8}{3}=\frac{x}{y} \\ 8y=3x \end{gathered}[/tex]Now, replace for the given value and find y. (x represents the number of bottles of plain water and y the number of bottles of sparkling water).
[tex]\begin{gathered} 8y=3\cdot600 \\ y=\frac{1800}{8} \\ y=225 \end{gathered}[/tex]The company produces 225 bottles of sparkling water when it produces 600 bottles of plain water.
EXPONENTIAL AND LOGARITHMIC FUNCTIONSFinding a final amount in a word problem on exponential grow...A car is purchased for $23,000. After each year, the resale value decreases by 30%. What will the resale value be after 5 years?
Resale Price = $3866
Explanations:The resale value of a particular product is given by the formula:
[tex]\begin{gathered} P=P_0\text{ + }(1\text{ - }\frac{r}{100})^t \\ \text{Where P}_0\text{ is the original amount} \\ r\text{ is the depreciation rate} \\ t\text{ is the }time\text{ in years} \\ P\text{ is the resale value} \end{gathered}[/tex][tex]\begin{gathered} P_0=\text{ \$23000} \\ r\text{ = 30\%} \\ t\text{ = 5 years} \end{gathered}[/tex]Substituting these parameters into the equation above:
[tex]\begin{gathered} P\text{ = 23000 }(1\text{ - }\frac{30}{100})^5 \\ P=23000(1-0.3)^5 \\ P=23000(0.7^5) \\ P\text{ = 23000 ( }0.16807) \\ P\text{ = }3865.60999999 \\ P\text{ = 3866} \end{gathered}[/tex]The resale price after 5 years is therefore, P = $3866
I’m trying to complete old assignments and i forgot how to do this one
Cosine of Double Angle
We can use any of these two formulas:
[tex]\begin{gathered} cos(2\theta)=2cos^2(\theta)-1 \\ \\ cos(2\theta)=1-2sin^2(\theta) \end{gathered}[/tex]We are given:
[tex]sin(\theta)=\frac{5}{13}[/tex]So we use the second formula:
[tex]cos(2\theta)=1-2\left(\frac{5}{13}\right)^2[/tex]Operating:
[tex]\begin{gathered} cos(2\theta)=1-2\left(\frac{25}{169}\right) \\ \\ cos(2\theta)=1-\frac{50}{169}=\frac{119}{169} \end{gathered}[/tex]Answer: 119/169
1 log in a 1 8.5. MR-6 Question H. Do the data suggest a linear, quadratic, or an exponential function? Use regression to find a model for the data set
Using a graphing calculator, we determined its behavior
As you can observe in the graph above, the points form a parabola, which belongs to a quadratic expression.
The data suggest a(n) is a quadratic function because the
How does the graph of g(x) -ta's+ 2x-5compare to the graph of the plent function Rx) = ?Ag(x) is shifted 5 units left and 2 units up from f(x).B g(x) is shifted 5 units right and 2 units up from f(x).B g(x) is shifted 5 units left and 2 units down from f(x).B g(x) is shifted 5 units right and 2 units down from f(x).
Given the parent function below
[tex]f(x)=\frac{1}{x}[/tex]The graph of the function above is shown below
Given that the function f(x) has been transformed and the new function is
[tex]g(x)=\frac{1}{x-5}+2[/tex]The transformation above can be described as
g(x) is shifted 5 units to the right and 2 units up from f(x)
The final answer is Option
Which statement is not true about the pattern shown? 2/3 k 12 24 8 16 12' 24 1) Each fraction is equivalent to 3 1) Each fraction is equal to the previous fraction in the pattern multiplied byz. 1) Each fraction is greater than the previous fraction. The next fraction in the pattern is 32 48
We need to evaluate the fractions below:
[tex]\frac{2}{3},\frac{4}{6},\frac{8}{12},\frac{16}{24},\ldots[/tex]All these fractions have the same value, they're equivalent to "2/3". On each step there is a product of 2 on the numerator and 2 on the denominator, therefore they're related by the factor of "2/2". If we multiply the last term by the factor we get:
[tex]\frac{16}{24}\cdot\frac{2}{2}=\frac{32}{48}[/tex]The only one statement that is false is: "Each fraction is greater than the previous fraction". They all have the same value, so the correct option is the third.
Two lines are represented by the equations - y = 63 +10 and y = mr. For which value of m the lines be parallel? --12 -3 o 3 12
First you must know that for two lines to be parallel to each other, they must have the same slope.
The standard eqF
Question..Which statements is not true of dot plotAnswer choices :The data must be sorted before the graph can can be made.You need to know know the extreme values to write the number line The total number of mraks tells you the size of the data set. An outliner will show as a gap inthe data.
Answer:
The data must be sorted before the graph can be made.
Explanation:
A dot plot is can be made as a number line with dots above each number. The number of dots above each number represents the number of times that the number appears in the data.
Therefore, we will need to know the extreme values to write the number line, the total number of marks or dots will tell the size of the data and if there are outliers, there will be a gap in the graph.
So, the statement that is not true is:
The data must be sorted before the graph can be made.
The width of a rectangle is 2x + 4, and the length of therectangle is 8x + 16. Determine the ratio of the width to thelength.Enter your answer as a fraction in the form a/b.
Given the parameters of the rectangle:
length = (8x + 16)
width = (2x + 4)
The ratio of the width to the length of the rectangle is evaluated as
[tex]\begin{gathered} \frac{\text{width}}{length}\text{ = }\frac{(2x\text{ + 4)}}{(8x\text{ + 16)}} \\ \text{factorize the denominator} \\ \Rightarrow\frac{(2x\text{ + 4)}}{4(2x\text{ + 4)}} \\ =\frac{1}{4} \end{gathered}[/tex]Hence, the ratio of the width to the length is
[tex]\frac{1}{4}[/tex]
75% of what number is 187.5?
Answer: 140.63
Explanation
The proportion of 75% is:
[tex]\frac{75\%}{100\%}=0.75[/tex]Finally, multiplying the proportion times the quantity:
[tex]187.5\cdot0.75=140.63[/tex]Find the density of a metal cone with a height of 20 centimeters and a radius of 5 centimeters. The mass is 2500 grams. Round to the nearest hundredth.
We are asked to find the density of the metal cone.
The density of a body is given by:
[tex]density(\rho_{})=\frac{Mass}{\text{Volume}}(gcm^{-3})_{}[/tex]We have been given the Mass of the body as 2500 grams
All we need to find is the volume in order to find the density of the metal
The metal is a cone. The volume of a cone is given by:
[tex]\begin{gathered} \text{Volume}=\frac{1}{3}\times\pi\times r^2\times h \\ \\ r=\text{radius}=5\operatorname{cm} \\ h=height=20\operatorname{cm} \end{gathered}[/tex]Now we can find the volume of the metallic cone:
[tex]\text{Volume}=\frac{1}{3}\times\pi\times5^2\times20=523.599\operatorname{cm}^3[/tex]We have been given the mass of the cone and we just finished calculating the volume of the metal, therefore, we can find the density of the metal as:
[tex]\begin{gathered} density(\rho)=\frac{Mass}{Volume} \\ \\ \therefore\rho=\frac{2500}{523.599}\text{gcm}^{-3} \\ \\ \rho=4.7746\text{gcm}^{-3}\approx4.78\text{gcm}^{-3} \end{gathered}[/tex]Therefore, the final answer is: 4.78g/cubic
Each drop contains 0.14mL. After 6 drop how much liquid has been dropped?
The total amount of liquid dropped is 0.84 mL
Here, we want to calculate the total amount of liquid dropped
From the question, we are given the amount of each drop
So the total amount of 6 drops will be 6 multiplied by the amount of each drop
Mathematically, that would be;
[tex]0.14\text{ mL }\times\text{ 6 = 0.84 mL}[/tex]The price of Quiktrip stock dropped a total of $372.33 over a 7 day period. The stock dropped the same amount each day. What amount did they lose each day?
Stella, this is the solution:
• Average amount the stock dropped each day = 372.33/7
,• Average amount the stock dropped each day = $ 53.19
Without using technology, describe the end behavior of f(x) = 3x32 + 8x2 − 22x + 43.
In order to find the end behavior of a polynomial we simply must observe the higher exponential behavior. Since it is so much higher than the others terms it will indicate the end behavior of the total function.
In the case:
[tex]f(x)=3x^{32}+8x^2-22x+43.[/tex]It is enough to analyze the end behavior of 3x³² in order to find the end behavior of the whole polynomial.
When x tends to infinityWhen x tends to infinity
x ⇒ ∞
then
3x³² grows and grows (infinitely!)
3x³² ⇒ ∞
When x tends to minus infinityWhen x tends to minus infinity
x ⇒ -∞
x takes negative numbers however x³² is always positive, because it has an even exponent, then
when x ⇒ -∞
then
3x³² grows and grows (infinitely too)
3x³² ⇒ ∞
Answer- as x ⇒ -∞, 3x³² ⇒ ∞ and as x ⇒ ∞, 3x³² ⇒ ∞
simplify the expression. 1.4z^2 + 5.4 + 6z - 2.1 - 3z. + z^2 =
1.4z² + 5.4 + 6z - 2.1 - 3z + z² =
Combining similar terms:
= (1.4z² + z²) + (6z - 3z) + (5.4 - 2.1) =
= 2.4z² + 3z + 3.3
Find the slope of a line crossing through the following points (3,9) and (4,5)
Given two points on a line,
[tex]\begin{gathered} (x_1,y_1) \\ \mleft(x_2,y_2\mright) \end{gathered}[/tex]The slope of the line is:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Since we have points (3, 9) and (4, 5), we have:
[tex]m=\frac{5-9}{4-3}=\frac{-4}{1}=-4[/tex]So, the slope is -4.
The total cost (in dollars) of producing x a golf clubs per day is given by the formula C(x) = 550 + 130x - 0.9x^2(A) Find the marginal cost at a production level of r golf clubs.C'(x) =(B) Find the marginal cost of producing 55 golf clubs.Marginal cost for 55 clubs
We have a cost function that express the cost of producing x golf clubs per day:
[tex]C(x)=550+130x-0.9x^2[/tex]A) We have to to find the marginal cost. The marginal cost at a certain level of production x represents the cost of producing one more unit.
It can be calculated as the first derivative of the cost function:
[tex]\begin{gathered} C^{\prime}(x)=550(0)+130(1)-0.9(2x) \\ C^{\prime}(x)=130-1.8x \end{gathered}[/tex]B) In this case, we have to calculate the marginal cost when the level of production is 55 golf clubs (x = 55):
[tex]\begin{gathered} C^{\prime}(55)=130-1.8(55) \\ C^{\prime}(55)=130-99 \\ C^{\prime}(55)=31 \end{gathered}[/tex]Answer:
A) C'(x) = 130 - 1.8x
B) C'(55) = 31
how do i graph this equation ?Is this relation a function ?Is the graph discrete or continuous?
Graph of a function
A typical function can be expressed as
y = f(x)
which means we can give x any value and we obtain a value for y
It's said that y depends on x
The equation given in the question has the form
x = -3
Note there is no y in the equation, which means the value of y is unknown, only the value of x is certain.
In other words, when x = -3, y can have any value, and no other value of x can be used
The graph of the function is shown below
The graph is shown as a red line
for a relation to be a function, each value of x must have one and only one value of y
the relation is not a function because the only value of x has many values of y
Please solve this, also, pls ignore the part that's scratched/ crossed out :)
The standard form is given by:
[tex]\begin{gathered} y=Ax^2+Bx+C \\ or \\ x=Ay^2+By+C \end{gathered}[/tex]Therefore:
[tex]x=\frac{y^2}{2}-y+\frac{5}{2}[/tex]The vertex is the point V(h,k) which is given by:
[tex]\begin{gathered} k=\frac{-b}{2a} \\ h=y(k) \\ ---- \\ k=-\frac{-1}{2(\frac{1}{2})}=1 \end{gathered}[/tex][tex]y(1)=\frac{1^2}{2}+-1+\frac{5}{2}=2=h[/tex]Therefore, the vertex is:
[tex]V=(2,1)[/tex]the focus is:
[tex](3,1)[/tex]And the directrix is:
[tex]x=1[/tex]