Answer:
y= -1/8x+3.5
Step-by-step explanation:
Plot your points and draw a line thru them. Find the slope: -1/8. Find the y-int: 3.5.
y = mx+b where x and y are variables, m is the slope and b is the y-int
y=-1/8x+3.5
Hope that helps
please help with this problem.no explanation needed, I am just looking for an answer
we have that
the answer is BreakfastThe temperature in Fairbanks was -27 degrees F. Phoenix was 100 degrees F warmer than Fairbanks. What was the temperature in Phoenix?
Step 1: Given data
Fairbanks temperature - -27 degrees
Phoenic temperature is 100 warmer than Fairbanks temperature
Step 2: Find the temperature of Phoenix.
Since the temperature of Phoenix is 100 warmer than that of Fairbank, then you will add 100 to the temperature of Fairbank.
Step 3: Final answer
The temperature of Fairbank = -27 + 100
= 73 degrees
13. Name the legs.
a. AB & BC
b. AC & BC
c: BC & AC
Legs are mentioned below.
Define triangles.A triangle is a polygon with three vertices and three sides. The angles of the triangle are formed by the connection of the three sides end to end at a point. The triangle's three angles add up to 180 degrees in total. A triangle's side is one of its legs. The term "leg" for a right triangle typically refers to a side other than the one across from the right angle (which is termed the hypotenuse). The word catheti also refers to legs.
Given,
a) AB and BC
AB = height
BC = base
b) AC and BC
AC = hypotenuse
c) BC and AC
BC = Base
AC = hypotenuse
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Annot a traperakthe of this Be sure to include the correct unit in your answer
To find the area of the trapezoid, we will use the formula below:
[tex]A=\frac{a+b}{2}h[/tex]where a and b are the base and h is the height.
From the diagram given, a=7 , b=17 and h = 5.
Substitute the values into the formula and evaluate.
That is;
[tex]A=\frac{7+17}{2}\times5[/tex][tex]=\frac{24}{2}\times5[/tex][tex]=12\times5[/tex][tex]=60[/tex]Hence, the area of the trapezoid is 60 yd².
+Find the number to add to x2 + 14x to make it a perfect square trinomial. Write that trinomial as the square of a binomial.O add 49; (x + 7)?o add 196; (x + 14)2o add 28: (x + 14)2O add 14; (x + 7)?
A binomial square have the following form:
[tex](x+a)^2=x^2+2ax+a^2[/tex]So, from the coefficient of the second term, we can get the value a and with the value a we can calculate a² for the value of the third term, that is, the value we need to add to make it a perfect square.
We have the expression:
[tex]x^2+14x[/tex]By comparing the second terms, we see that:
[tex]\begin{gathered} 14=2a \\ 2a=14 \\ a=\frac{14}{2} \\ a=7 \end{gathered}[/tex]Since we have a, we can calculate a²:
[tex]a^2=7^2=49[/tex]So, this means the number we need to add is 49 and, since a is 7, the trinomial can be rewritten as:
[tex]x^2+14x+49=(x+7)^2[/tex]So, add 49 and the square binomial is:
[tex](x+7)^2[/tex]. Imagine that you wanted to test the effects of driving at different speeds on the gas mileage of your car. To find out, you drove a distance of 100 miles at many different rates of speed. During your first trip. you drove at exactly 55 miles per hour and calculated that your gas mileage was 20 miles per gallon. During your next trips, you either decreased or increased your rate of speed. Study the graph below from your trips and see if you can identify a control as well as the independent and dependent variables. Explain which axes the dependent and independent variables should be on. Also, what can you conclude from this experiment? How might your car get better gas mileage?
We are asked to study a graph of car performance and give details about the dependent and independent variables. Here is the graph in question:
Our control point is: the info given: 55 miles per gallon gave 20 mi/gallon gas usage. We see clearly that point on the graph, located at (55, 20) on the red line.
Therefore, the gas performance, is the quantity we are studying and it is the "DEPENDENT" variable. As such, it should be graphed on the veritical axis as it is on the graph provided.
The INDEPENDENT variable is the speed we are trying (in the first case the 55 mph (miles per hour) . This variable is what is plotted on the horiontal axis.
Given the shape of the graph: we see it as a line decreasing as we go at higher speeds, the better performance (more miles per gallon) will be obtained as we reduce the speed (going towards 45 miles per hour or even less). Notice that at the beginning of the horizontal axis (for about a 35 mph speed) we see the maximum height of the line at around 27 miles per gallon. So to answer the last question: We could get better gas mileage if we reduce the travelling speed at 35 miles per hour.
use the first five terms of the exponential series of e^x and a calculator to approximate e^0.2 to the nearest hundredth
Solution:
Using the Maclaurin series;
[tex]e^x=1+x+\frac{x^2}{2!}+\frac{x^3}{3!}+\frac{x^4}{4!}+\frac{x^5}{5!}+...[/tex]Thus;
[tex]\begin{gathered} x=0.2; \\ \\ e^{0.2}=1+(0.2)+\frac{(0.2)^2}{2!}+\frac{(0.2)^3}{3!}+\frac{(0.2)^4}{4!} \\ \\ e^{0.2}\approx1.22 \\ \end{gathered}[/tex]ANSWER: 1.22
suppose that the function V = 40x to the 2nd -500× + 5000 describes the value of a car from 1960 to 2012. What year did the car have the least value? (x = 0 is 1960)
We have the next function
[tex]V=40x^2-500x+5000[/tex]In 1960, x=0
[tex]V=5000[/tex]In 1965, x=5
[tex]V=3500[/tex]In 1966, x=6
[tex]V=3440[/tex]In 1967, x=7
[tex]V=3460[/tex]In 1968, x=8
[tex]V=3560[/tex]As we can see the year with the least value is 1966
What is the equation of the line that passes through the point (5,-5) and has a slope of -1/2
Answer: y= -1/2x - 2.5
Step-by-step explanation:
Slope: y= mx+ b
m being the slope
b being the y intercept
You're given the slope, so you substitute m for -1/2
y=mx+b
y = -1/2x + b
You have the coordinates (5, -5) which you can substitute (the line passes through that point.)
-5 = -1/2(5) + b
-5 = -2.5 + b
+2.5 +2.5
-2.5= b
y= -1/2x + 2.5
Check:
-5 = -1/2(5) - 2.5
-5 = -2.5 - 2.5
-5 = -5
Large drinks cost $2.75 each and medium drinks cost $2.15 each. A restaurant sold 52 drinks yesterday and took in a total of $131.60. How many medium drinks did they sell?
To solve this type of question we need to form 2 equations of 2 variables and solve them to find the 2 variables
Let x is the number of the large drinks and y is the number of the medium drinks
Since the restaurant sold 52 drinks, then
[tex]x+y=52\rightarrow(1)[/tex]Since the cost of the large drink is $2.75 each, then
The cost of the large drinks is 2.75(x)
Since the cost of the medium drink is $2.15 each, then
The cost of the medium drinks is 2.15(y)
Since the total cost of them is $131.60, then
Add 2.75(x) and 2.15(y) and equate the sum by 131.60
[tex]\begin{gathered} 2.75(x)+2.15(y)=131.60 \\ 2.75x+2.15y=131.60\rightarrow(2) \end{gathered}[/tex]Now we have a system of equations to solve it
Multiply equation (1) by -2.75 to make x equal in values of the two equations and different in signs to eliminate it
[tex]\begin{gathered} (-2.75)x+(-2.75)y=(-2.75)(52) \\ -2.75x-2.75y=-143\rightarrow(3) \end{gathered}[/tex]Add equations (2) and (3)
[tex]\begin{gathered} 2.75x+2.15y+(-2.75x)+(-2.75y)=131.60+(-143) \\ (2.75x-2.75x)+(2.15y-2.75y)=131.6-143 \\ 0-0.6y=-11.4 \\ -0.6y=-11.4 \end{gathered}[/tex]Divide both sides by -0.6
[tex]\begin{gathered} \frac{-0.6y}{-0.6}=\frac{-11.4}{-0.6} \\ y=19 \end{gathered}[/tex]They sold 19 medium drinks yesterday
A recipe book shows measurement conversions for pints to cups. It shows that 1.5 pints equals 3 cups and 2.5 pints equals 5 cups.
Write an equation that shows the proportional relationship between pints and cups where p represents pints and n represents cups.
p equals 3 over 1.5 times n
n equals 1.5 over 3 times p
p = 0.5n
n = 0.5p
The equation that t shows the proportional relationship between pints and cups is p = 3 over 1.5 times n
What is the equation?The mathematical operation that would be used to determine the equation is division. Division is the process of grouping a number into equal parts using another number. The sign used to denote division is ÷. Division is one of the basic mathematical operations.
In order to determine the proportional relationship, divide the measurement for cups by the measurement for pints.
p = 3 / 1.5n
p = 2n
p = 5 / 2.5
p = 2
This means that one pint represents two cups.
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When I was 2 my sister was twice my ag Now I'm 40, how old is my sister...
Answer:
Let you be "x"
and your sister be "y"
when you are 2 your sister is twice your
x=2 y=4
so your sister is 2 year older than you
now you're 40 so your sister would be
Step-by-step explanation:
When I was 2 my sister was twice my ag Now I'm 40 then my sister age is 80.
\
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Given,
When I was 2 years my sister was twice of my age.
Let us consider the ages by using a equation like this
x/y------>X represents my age/ y represents my sister age
x/y ----->2/4=40/a
a is the age of sister when i was 40.
Now let us solve 2/4=40/a
One by two equal to forty by a.
Apply cross multiplication
2a=160
Divide both sides by 2
a=80
Hence, if I'm 40, my sister is 80 years old.
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A right triangle with vertices P(-3,9) Q(-3,5) R(-7,5) is reflected on the y-axis then the image is rotated 180 degrees about the origin. What are new coordinates of the right triangle?
We could start by drawing the triangle we are given. However, it would be better to draw the triangle after the y-axis reflection. To calculate the y-axis reflection, we first think as follows
We see that the reflected point is at the same height as the original point. This means that the y coordinate should remain the same. So, the only thing that changed is the x coordinate. This suggests that, to calculate the reflection about the y-axis, we simply multiply by -1 the first coordinate. So, after the reflection we get the points
P'(-3*(-1),9)=(3,9)
Q'(-3*(-1),5)=(3,5)
R'(-7*(-1),5) =(7,5)
Now, if we plot this points we get
So, if we rotate this 180° we would get the following
So the new points after rotating 180°, would be
P''(-3,-9)
Q''(-3,-5)
R''(-7,-5)
Carol earns a 13% commission on the sales she makes. Complete the table by determining the amount of commission she earned each week.
The commission on $950 = 13/100 x 950 = $ 123.5
The commission on $2200 = 13/100 x 2200 = $286
The commission on $3000 = 13/100 x 3000 = $390
The commission on $2600 = 13/100 x 2600 = $338
Each commission = 13/100 x the amount in question
In 1990, the profit of the Gamna company was $10,007,911. each year after 1990, profits fell by $37,104 on average. construct a linear model for this scenario and use it to solve for the profits in the year 2020.
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data
initial profit = $10,007,911
profits fell per year = $37,104
linear model = ?
profits (2020) = ?
Step 02:
linear model:
x = years
y = 10007911 - 37104 x
Step 03:
profits (2020):
x = 30
y = 10007911 - 37104 (30)
y = 8894791
The answer is:
linear model: y = 10007911 - 37104 x
profits (2020): $8,894,791
a rectangle is drawn so that the width is 1 foot shorter than the length. the area of a rectangle is 30 square feet. find the length of the rectangle.___feet
If the width (W) of the rectangle is 1 ft shorter than its length (L), then we can write the following equatiion:
W = L - 1
now since we know the formula for the area of a rectangle:
Area = length x width
Area = L * W
30 = L * (L - 1)
where we have substituted the width W using the expression in terms of the length in the first equation we wrote.
then we multiply as indicated:
30 = L^2 - L
and write all terms on one side of the equal sign:
L^2 - L - 30 = 0
we try solving this quadratic equation by grouping:
L^2 - 6 L + 5 L - 30 = 0
L (L - 6) + 5 (L - 6) = 0
(L - 6) * (L + 5) =0
then there are two possible solutions to make that product equal to zero:
L = 6
or
L= -5
We pick the POSITIVE answer since we are looking for a length
therefore the length of the rectangle is 6 feet.
Type a "6" in the blank of your question.
Solve: (2,1); m=undefined. Answer has to be in slope intercept form, so y=mx+b. SHOW ALL WORK SO I CAN HAVE A BETTER UNDERSTANDING :)
The equation of the line is x = 2
How to determine the line equation?The slope of the line is given as
Slope = Undefined
This can be rewritten as
m = Undefined
The point on the line is also given as
(x, y) = (2, 1)
For a line with an undefined slope, it means that:
The line is a vertical line
The equations of all vertical lines are represented as
x = x₁
In this case,
(x₁, y₁) = (2, 1)
Remove the y-coordinate
x₁ = 2
Substitute x₁ = 2 in the equation x = x₁
So, we have
x = 2
Hence, the line has an equation of x = 2
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The Scooter Company manufactures and sells electric scooters. Each scooter cost $200 to produce, and the company has a fixed cost of $1,500. The Scooter Company earns a total revenue that can be determined by the function R(x) = 400x − 2x2, where x represents each electric scooter sold. Which of the following functions represents the Scooter Company's total profit?
The total profit of the company is represented by the equation -2x^2-600x-1500
Cost of each scooter = $200
Fixed cost of each scooter = $1500
An algebraic equation of the second degree in x is a quadratic equation. The quadratic equation is written as ax2 + bx + c = 0, where x is the variable, a and b are the coefficients, and c is the constant term. The coefficient of x2 must be a non-zero term (a 0) in order for an equation to meet the definition of a quadratic equation.
Function of revenue R(x) = 400x -2x^2
Let x represent each electric scooter sold
The total cost of the scooter = Fixed cost + variable cost number of scooters sold
= 1500 + 200x
Profit = Revenue - Cost
= 400x - 2x^2 - 1500 + 200x
= 600x - 2x^2 -1500
-2x^2 - 600x -1500
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I need the answer ASAP
Answer:
I'm pretty sure it's the last on but I could be wrong
Step-by-step explanation:
Miguel and Arjun performed different operations on 12 and 2. Miguel divided 12 by 2: 12 ÷ 2 = x x = 6 Arjun multiplied 12 by 2: 12 × 2 = y y = 24 Which statements are true about Miguel’s and Arjun’s work? Check all that apply. Both operations resulted in the same answer. The product of 12 and 2 is represented by y. The difference between 12 and 2 is represented by x. Miguel found the quotient of 12 and 2. Arjun found the sum of 12 and 2.
What transformations have been made from the parent graph f(x) = log x to get f(x) = log(x - 2)? OA. 2 units in the x direction B. -2 units in the x direction C.-2 units in the y direction D. 2 units in the y direction Reset Selection Next
Given:
The function f(x) = log(x) and f(x) = log(x - 2).
Required:
What transformtaion have been made from parent function?
Explanation:
The graph of the function,
The graph of f(x) = log(x - 2) shifted to 2 units in the x - direction.
Answer:
Option A is correct.
Match each equation with an equivalent equation. Some of the answer choices are not used.
3x+5=4x+8
3(x+5)=4x+8
3x+4x=8-5
The equivalent equations in the given choices are : 3x+5=4x+8 and 3x+4x=8-5.
What are equivalent equations?
Algebraic equations with equivalent solutions or roots are called equivalent equations. An analogous equation is one that is created by adding or removing the identical quantity or expression from both sides of a given equation. An equation is equivalent if both sides are multiplied or divided by the same non-zero value.
The equations that are equivalent are :
3x+5=4x+8 and 3x+4x=8-5
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Please help me with this Homework .
$2000 are invested in a bank account at an interest rate of 10 percent per year.
Find the amount in the bank after 9 years if interest is compounded annually.
Answer:
1,800 im not sure tho
Step-by-step explanation:
A 5-ounce bottle of glue costs $2.85. What is the unit price?
Answer:
$0.57 per ounce
Step-by-step explanation:
2.85/5 = 0.57
Answer:
Step-by-step explanation:
First, set up an equation: $2.85/5 oz.
Next, divide both the numerator and denominator by 5. NOTE: do them one at a time.
2.85/5=$0.57
5/5=1
So, the unit rate is $0.57/oz.
Find the constant of proportionality, then write an equation relating x and yy is directly proportional to x, and y = 81 when x = 9
When x=9, y=81.
To find the proportionality constant take the ratio of y/x.
[tex]\begin{gathered} \frac{y}{x}=\frac{81}{9} \\ =9 \end{gathered}[/tex]Thus, the proportionality constant is 9.
The relation between y and x can be determined as,
[tex]\begin{gathered} \frac{y}{x}=constant \\ \frac{y}{x}=9 \\ y=9x \end{gathered}[/tex]Thus, the required relationship between x and y is y=9x.
What is the slope of the line passing through the points (-3, 4) and (4, -1)?
The slope of the line passing through the given points is equal to -5/7.
What is a slope?A slope is also known as gradient and it's typically used to describe both the direction, ratio, and steepness of the function of a straight line based on its coordinates or points.
How to calculate the slope of a line?Mathematically, the slope of any straight line can be calculated by using this formula;
[tex]Slope = \frac{Change\;in\;y\;axis}{Change\;in\;x\;axis}\\\\Slope = \frac{y_2\;-\;y_1}{x_2\;-\;x_1}[/tex]
Substituting the given points into the formula, we have;
Slope = (-1 - 4)/(4 - (-3))
Slope = -5/(4 + 3)
Slope = -5/7
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2)Point C is reflected across a b such that in maps and to point D. Point C and D are then connected to form CD. Which of the following must be true? A)CD bisects ABB)AB=CD C)CD is parallel to ABD) CD is perpendicular to AB
Point C is reflected across a line AB such that it maps to point D.
Points C and D are then connected to form a line CD.
Let us draw a figure to better understand the problem
As you can see from the above figure,
We have reflected the point C across the line AB and the reflected point is mapped to point D.
Then we connected the point C to point D using the red color to form line CD.
The line CD is perpendicular to line AB.
All other options depend on the exact scenario which means they may or may not be true.
But we can be sure about option D that it must always be true.
Therefore, option D is the correct answer.
A plane travels 20 degrees east of south what is its compass heading?
If x = 10, y = 5, and z = 11, what is the tangent ratio for g½2/110/115/11
Recall that by definition, in a right triangle:
[tex]tan\theta=\frac{oppposite\text{ leg}}{adjacent\text{ leg}}.[/tex]In the given triangle, if we consider angle g, we get:
[tex]tan(g)=\frac{x}{y}.[/tex]Substituting x=10, and y=5, we get:
[tex]tan(g)=\frac{10}{5}=\frac{2}{1}.[/tex]Answer: [tex]\frac{2}{1}.[/tex]In which set(s) of numbers would you find the number49integerO rational numberOreal numberO natural numberwhole numberO irrational number
Rational numbers, Real numbers, Natural numbers, whole number
Explanation:[tex]49\text{ can also be written as }\frac{49}{1}[/tex]Rational numbers can be written as a fraction. 49 can be written as a fraction
Real numbers consists of natural numbers, whole umbers, integers and rational numbers.
Since it is already a rational number, then it is also a real number
Natural numbers are counting numbers from 1 to positive infinity. 49 is between 1 to positive infinity.
Hence, it is a natural number
whole numbers start from 0 to positive infinity. 49 is between 0 to positive infinity.
Hence, it is a whole number
Irrational numbers cannot be written in the form of fraction. SInce 49 can be written as fraction, it is not an irrational number
Hence, the set(s) of numbers would you find the number 49 are Rational numbers, Real numbers, Natural numbers, whole number
