8x + y = -16
3x + y = -5
The first to take is to subtract the second equation from the first equation
This will eliminate the y-variable leaving you with jus x-variable
That is;
5x = -11
x = -11/5
I need to find the c intercept and write the equation
The C-intercept is the point at which the function crosses the C-axis, then it is at t=0.
As we know two points on the line: (-20, 200) and (30,0), and we found previously the slope m=-4.
We can use the slope-intercept form of the equation of a line to find the C-intercept as follows:
[tex]C=m\cdot t+b[/tex]Where (t,C) is any point on the line, m is the slope and b is the C-intercept.
By replacing the know values we can solve for b:
[tex]\begin{gathered} 0=-4\cdot30+b \\ 0=-120+b \\ \text{Add 120 to both sides} \\ 0+120=-120+b+120 \\ 120=b \end{gathered}[/tex]Therefore,
A real estate agent working in a large city believes that, for three-bedroom houses, the selling price of the house decreases by approximately $2,000 for every mile increase in the distance of the house from the city center. To investigate the belief, the agent obtained a random sample of 20 three-bedroom houses that sold in the last year. The selling price, in thousands of dollars, and the distance from the city center, in miles, for each of the 20 houses are shown in the scatterplot. The table shows computer output from a regression analysis of the data.
(a) Describe the relationship between distance from city center and selling price.
(b) Find the linear regression equation. Interpret the slope and y-intercept in context.
) One house that was 11 miles from city center had a residual of -2.962. What was the actual selling price of the home?
The description of the relationship is a linear relationship, the equation is y = 301.7 - 2.158x and the actual selling price of the home is $275
How to determine the relationship?The given parameter is in the attached figure
Also from the question, we have:
House price decreases by approximately every mile
The above implies that the relationship is an approximately linear relationship
How to find the linear regression equation.From the table, we have
Coefficient constant = 301.7
Coefficient distance = -2.158
This means that
y-intercept = 301.7
Slope = -2.158
So, the equation is
y = y-intercept + slope * x
This gives
y = 301.7 - 2.158x
The interpretation of the slope and y-intercept in context are:
Slope implies that the house price decreases by 2.158 miles, and the y-intercept implies that the initial house price is 301.7
The actual selling price of the homeHere, we have
Residual = -2.962
Miles = 11
This means that
Predicted price = 301.7 - 2.158 * 11
Evaluate
Predicted price = 277.96
So, we have
residual = actual - predicted
This gives
actual = residual + predicted
So, we have
actual = -2.962 + 277.96
Evaluate
actual = 275
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The carnival is in town and has a game where players try to throw darts at a rectangular target. The length of the target is 2 centimeters shorter than twice the width. If the perimeter of the target is 20 centimeters, find the dimensions of the target.
The length of the target is 4cm and the width of the target is 6cm.
What are the dimensions of the target?A rectangle is an object that has four sides and four right angles. The sum of angles in a rectangle is 360 degrees. The perimeter of a rectangle is the distance round the rectangle.
Perimeter = 2( length + width)
Length = w - 2 Width = w20 = 2(w - 2 + w)
20 = 2(2w - 2)
20 / 2 = 2w - 2
10 = 2w - 2
10 + 2 = 2w
12 = 2w
w = 12/2
w = 6
Length = 6 - 2 = 4
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What is the reciprocal of 3 7/8
The reciprocal of 3 7/8 is 8/31.
To find the reciprocal of a number, we invert the fraction by swapping the numerator and denominator.
Let's calculate the reciprocal of 3 7/8.
First, we need to convert the mixed number into an improper fraction. To do this, we multiply the whole number (3) by the denominator (8) and add the numerator (7). This gives us:
3 7/8 = (3 x 8 + 7) / 8 = 31/8
Now, to find the reciprocal, we invert the fraction:
Reciprocal of 31/8 = 8/31
Therefore, the reciprocal of 3 7/8 is 8/31.
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What is the value of x? The value of x is type your answer... 8xº (3x + 35)° (4x + 25)°
please help me solve this
Answer:
a: undefined
b: -15
c: 20
d: 25
Step-by-step explanation:
a: look at x -3 on graph, the left hand limit and right hand limits are different so it's undefined
b: look at x 0 on graph, there is open dot at -15 meaning the limit is there
c: look at x -7 on graph, there is open dot at 20 meaning the limit is there
d: look at x 5 on graph, the y is at 25 meaning the limit is there (it's normal here)
Laura is paid only on commission. She is paid weekly and receives 1.6% of her gross sales. Last week, she had sales of $57000, $23000, $41000, $49000, and $37000. What is Laura's weekly commission?
Answer:
$3,312.00
Step-by-step explanation:
If we add up her sales we get 207,000
We multiply that by .016 to get $3,312.00
If “d = rt” then “t = [?] / [?].” Substitute the correct variable for the question mark in the numerator and denominator.Select one:a. r/db. d/rc. t/dd. .t/r
To solve the equation;
[tex]d=rt[/tex]To solve for t, we shall take the following steps;
[tex]\begin{gathered} d=rt \\ \text{Divide both sides by r;} \\ \frac{d}{r}=\frac{rt}{r} \\ r\text{ cancels out r on the right side of the equation;} \\ \frac{d}{r}=t \\ \text{Therefore;} \\ t=\frac{d}{r} \end{gathered}[/tex]ANSWER:
The correct answer is option (b)
[tex]\frac{d}{r}[/tex]please help me with this problem
answer:
[tex]\frac{-c-d}{d+2c}[/tex]the third one
x/25.75=sin47.5 degrees
The value of x in the equation is 18. 98
What are trigonometric identities?Trigonometric identities are defined as mathematical equations relating to several trigonometric functions, holding true for all the values in the domain of the functions.
The several types of trigonometric identities includes;
sinecosinetangentcotangentsecantcosecantIt is important to note that the trigonometric ratios for major identities are;
sine = opposite/hypotenuse
tangent = opposite/adjacent
cosine = adjacent/hypotenuse
Given the equation;
x/25.75=sin47.5 degrees
Take the following steps to determine the value of 'x'
We have;
cross multiply
x = sin47.5 × 25. 75
Find the value of sin 47. 5 and substitute the value
x = 0. 7373 × 25. 75
multiply through
x = 18. 98
Hence, the value of x is 18. 98
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The complete question:
x/25.75=sin47.5 degrees
Find the value of x
What is an equation of the line that passes through the points (5, 0) and
-2, -3)?
Answer:
Equation of line is given as y = mx + c, where m is the gradient and c is the y-intercept.
Find gradient of the line first.
Formula of gradient is given as y2-y1 ÷ x2-x1 or y1-y2 ÷ x1-x2, where x and y are the coordinates of the points.
Gradient = (-3-0) ÷ (-2-5) = 3/7
Eqn is y = 3/7x + c
Substitute either one of the coordinates into the equation to find c.
0 = 3/7(5) + c
c = -15/7
Hence, the equation of the line is y = 3/7x - 15/7
What is the slope of a line perpendicular to the line whose equation is 3x-6y=144
Answer: 1/2
Step-by-step explanation:
If we have an equaton in a standard form, that is y = mx + b, our slope is m (the coefficient of x). So, let's transform 3x - 6y = 144 into the standard form.
3x - 6y = 144
-6y = - 3x + 144
y = -3/(-6)x - 144/6
y = (1/2)x - 24
As I mentioned above, the slope is the coefficient of x. Here our slope is 1/2.
Identify the Vertex. Let g be a translation 2 units up, followed by a reflection in the x-axis and a vertical stretch by a factor of 4 of the graph of. (Show Work)
The g graph exhibits a four-fold vertical stretch.
The graph of f (x)=[tex]x^{2}[/tex] is translated up to two units, then reflected in the X-axis.
The rule for g.
Identify the vertex
The g graph exhibits a four-fold vertical stretch.
=> g = 4f(x) (x)
an X-axis reflection
=> g = - 4f(x) (x)
(X-axis reflection of (X, Y) is (x , - y)
a conversion two units higher
=> g = -4f(x) + 2
f(x) = x²
=> g = - 4x² + 2
Vertex is at ( 2, 0)
What is a vertical stretch?
When a base graph is multiplied by a particular factor larger than 1, vertical stretch happens. As a consequence, the graph is stretched outward while keeping the input values (or x). We anticipate that the y values in a function's graph will be further away from the x-axis when it is vertically extended.
How to vertically stretch a function?
When given a function’s graph, we can vertically stretch it by pulling the curve outwards based on the given scale factor. Here are some things to remember when we vertically stretch functions:
Ensure that the values for x remain the same, so the base of the curve will not change.
This means that when applying vertical stretches on a base graph, its x-intercepts will remain the same.
Take note of the new critical points, such as the new maximum point of the graph.
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What is the probability of theft occurring in a room if it is left unlocked if 0.75 of dorm rooms are left unlocked, 3% of dorm rooms are affected by theft, and 84.2% of thefts occur in unlocked rooms
The probability that a theft can happen in a room that is left unlocked based on the statistics of dorm rooms affected by theft, is 1.89%
How to find the probability?To find the probability that a room will be subjected to theft if it is left unlocked, the formula is:
= Probability that dorm room is left unlocked x Probability of dorm room being affected by theft x Probability that a theft occurs in a unlocked room
The probability of an unlocked room being robbed is therefore:
= 0.75 x 0.03 x 0.842
= 0.0225 x 0.842
= 0.018945
= 1.89%
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estimate. i need help
Answer:
350'000
Step-by-step explanation:
The real # is 369,852, so 350,000 is closest to all the other options.
In an office building, 88 offices are currently being rented. This represents 80% of the total units. How many offices are there in the building?
There are offices in the building.
Answer:4
Step-by-step explanation:
The length of a rectangle is 21 yards. The width of the rectangle is 5 yards. What isthe area of the rectangle?
To find the area of a rectangle, we can use the following formula
[tex]Aread\text{ of a reactangle = \lparen length\rparen}\times\text{ }(width)[/tex]Therefore, to find the total area we have to multiply his length by his width.
Using the data given in the question, we know that the length is 21 yards and the width is 5 yards. Therefore we find that:
[tex]Area\text{ of the rectangle =}(21\text{ yards\rparen}\times\text{ \lparen5 yards\rparen}=105\text{ yards}^2[/tex]we conclude that the area of the rectangle is 105 yards^2.
Note that the units of the area are square units
Can anyone explain this?
Answer:
Using a class size of 6.
Range = Highest value - Lowest value = 100 - 1 = 99
No. Of class = range/class size = 99/6 = 16.5 ~ 17/classes.
Upper-class limit of class (1) = Lower class limit of class (1) + class size - D
=> 1 + 6 - 1 = 7 - 1 = 6
.: UCL1 = 6
The table is shown below:
The demand equation for a certain product is given by p=120-0.015x, where p is the unit price (in dollars) of the product and x is the number of units produced. The total revenue obtained by producing and selling x units is given by R=xp.
Determine prices p that would yield a revenue of 7110 dollars.
Lowest such price = (Blank) dollars.
Highest such price = (Blank) dollars.
Show your work!
No incorrect answers!
No nonsense answers!
No spam answers!
Thanks!
The prices p that would yield a revenue of 7110 dollars are;
Lowest price = $0.895
Highest price = $119.105
How to solve demand equation?
We are told that the total revenue obtained by producing and selling x units is given by; R = xp.
Now, we are told that the demand equation for a certain product is given by p = 120 - 0.015x.
where;
p is the unit price (in dollars) of the product.
x is the number of units produced.
At a revenue of $7110, we will have;
(120 - 0.015x)x = 7110
120x - 0.015x² = 7110
0.015x² - 120x + 7110 = 0
Using quadratic equation calculator, we have;
x = 59.695 and 7940.305
Thus;
Lowest price = 120 - 0.015(7940.305) = $0.895
Highest price = 120 - 0.015(59.695) = $119.105
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Can someone help me on these three questions? can someone solve and show me how you did it so i can understand
The graph of the function gives the type of function, (continuous or discrete function) the domain and the range as follows;
(A, 2A)
First graph;
Discrete function
Domain; {x| x = -8, -2, 3, 6}
Range; {y| y = 5, 4, -2, 7, }
Second graph
Continuous function
Domain; -4 < x < ∞
Range; 1 ≤ y < 9
(A3.A) 1. The slope of the graph is -1.5
2. The slope of the graph is 1.5
What is a function?A function is an equation defining the relationship between input and output variables
(A, 2A)
A continuous function is one in which a continuous variation in the input values produces a continuous variation in the output. Therefore, a continuous function does not have discontinuity and it has a defined output within the interval in which it is contagious
A discrete function is one that have input values and output only at specified points, such that the function does not have inputs, and therefore, outputs at certain points.
The points in the scatter plot of the first graph are separate and not linked, such that the function is not contagious between any two x–values, which gives;
The function is a discrete function
The domain, which is the set of possible x–values is; {x| x = -8, -2, 3, 6}
The range is {y|y = 5, 4, -2, 7, }
The line joining the points on the second graph, indicates that the graph has values for all input or x–values
Therefore, the function of the graph is a continuous function
The domain is; -4 < x < ∞The range is 1 ≤ y < 9(A3. A) 1. Points on the graph are:
(0, 2), (2, -1)
The slope is given by the equation;
Slope = ∆y ÷ ∆x
Which gives;
Slope = (-1 - 2)/(2 - 0) = -3/2 = -1.52. The given function is; -3•x + 2•y = -6
To find the slope, the function is expressed in the slope and intercept form, y = m•x + c, as follows;
-3•x + 2•y = -6
2•y = 3•x - 6
Therefore;
2•y = 3•x - 6
y = (3•x - 6) = 1.5•x - 3
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K
Solve.
(8v+5)(3v-9) = 0
Given a piece of metal with a mass of 124 grams and a volume of 21 cubic centimeters (cm^3) what is its density? Use the correct formula to obtain your answer. You may work on a separate piece of paper.
13.6 g/cm^3
88 g/cm^3
5.9 g/cm^3
0.21 g/cm^3
We need to know about density to solve this problem. The density of the piece of metal is 5.9 g/[tex]cm^{3}[/tex], so option (c) is the correct answer.
Density is a substance's mass per unit volume. The symbol commonly used for density is ρ. Density can be calculated by dividing the mass by volume. In this question we know that mass of the metal piece is 124 grams and the volume is given to be 21 cubic centimeters. The density can be calculated by dividing the mass by volume of the metal piece.
density =mass/ volume= 124/21=5.90 g/[tex]cm^{3}[/tex]
Therefore the density of the piece of metal is 5.9 g/[tex]cm^{3}[/tex] , so option (c) is the correct answer.
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Help with this problem pls
nswer:
[tex](f\circ g)(x)\text{ = 4x}^2+26x+29[/tex]Explanation:
ere, we want to solve the given composuite function
What we have to do is to replace the x in f(x) with the entirety of g(x)
We have that as:
[tex]\begin{gathered} (f\circ\text{ g\rparen\lparen x\rparen = f\lparen g\lparen x\rparen\rparen} \\ =\text{ f\lparen2x+9\rparen} \end{gathered}[/tex]Now, we replace x in f(x) with 2x+9 as stated
We have that as:
[tex]\begin{gathered} f(2x+9)\text{ = \lparen2x+9\rparen}^2-5(2x+9)\text{ - 7} \\ f(2x+9)\text{ = 4x}^2+36x+81-10x-45-7 \\ f(2x+9)\text{ = 4x}^2+36x-10x+81-45-7 \\ f(2x+9)\text{ = 4x}^2+26x+29 \end{gathered}[/tex]Please help
The second angle of a triangle is 104 more than the first angle. The third angle is two times the first. Find
the three angles.
First angle:
Second angle:
Third angle:
Graph H(x) =|x+5| and t(x)=|2x+5|
The graph of the function H(x) = "x+5" and the graph of the function t(x) = "2x+5" are displayed in the picture that is attached below.
This is further explained below.
What is Graph?Generally, The set of ordered pairings that satisfy the condition [tex]"\displaystyle f(x)=y"[/tex] is the graph of the function f.
These pairings, which are Cartesian coordinates of points in two-dimensional space and hence constitute a subset of this plane, are found under the usual scenario in which both x and f(x) are real values.
In conclusion, The Graph of the function H(x) =|x+5| and t(x)=|2x+5| is given in the image attached below.
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five more than the quotient of nine and three
Answer:
n / 9 + 5 = 3
Step-by-step explanation:
On a blueprint, a guest bedroom has dimensions 3 cm
by 5 cm. If the blueprint is drawn using the scale of
½ cm = 2 ft, what is the actual AREA of the guest
bedroom?
A. 12 square ft
B. 20 square ft
C. 240 square ft
D. 15 square ft
The actual area of the guest bedroom is 240 square ft, if on a blueprint, a guest bedroom has dimensions 3 cm by 5 cm and the blueprint is drawn using the scale of ½ cm = 2 ft.
What is dimension?The minimal amount of coordinates required to specify any point within a mathematical space (or object) is known as the dimension in physics and mathematics. As a result, a line has one dimension (1D), since only one coordinate is required to specify a point on it, such as the point at 5 on a number line.
A surface, like the perimeter of a cylinder or sphere, has two dimensions (2D) because two coordinates are necessary to specify a point on it. For instance, both a latitude and a longitude are necessary to pinpoint a point on the surface of a sphere.
The dimensions are 3cm by 5 cm meaning length = 5cm and breadth = 3cm
Given that ½ cm = 2 ft, that is
1 cm = 4 ft
Using the conversion method
3 cm = 3 × 4
= 12 ft
5 cm = 5 × 4
= 20 ft
Actual area = 20 × 12 ft
= 240 square ft
Thus, the actual area of the guest bedroom is 240 square ft, if on a blueprint, a guest bedroom has dimensions 3 cm by 5 cm and the blueprint is drawn using the scale of ½ cm = 2 ft.
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PLEASE HELP ME WITH THIS
The simplified form of the given expression is x + a - 4
Simplifying an ExpressionFrom the question, we are to simplify the given expression
From the given information, we have that
g(x) = x² - 4x,
Now,
We are to simplify
[tex]\frac{g(x)-g(a)}{x -a}[/tex]
First, we will determine g(a)
From the given function,
g(x) = x² - 4x
∴ g(a) = a² - 4a
Thus,
[tex]\frac{g(x)-g(a)}{x -a}[/tex] becomes
[tex]\frac{x^{2} -4x-(a^{2}-4a)}{x -a}[/tex]
[tex]\frac{x^{2} -4x-a^{2}+4a}{x -a}[/tex]
[tex]\frac{x^{2} -a^{2} -4x+4a }{x -a}[/tex]
Factoring
[tex]\frac{(x+a)(x-a)-4(x-a) }{x -a}[/tex]
Further factorization
[tex]\frac{(x-a)((x+a)-4) }{x -a}[/tex]
Dividing
((x +a) -4)
x + a - 4
Hence,
The simplification gives x + a - 4
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A bag of 9 apples contains 2 rotten apples and 7 good apples. A shopper selects a sample of 4 apples from the bag.
The number of different samples possible when the shopper selects a sample of 4 apples from the bag is 126.
How to calculate the combinations?Combinations are a method of calculating the overall results of an event where the order of the results is irrelevant. From the information, the bag of 9 apples contains 2 rotten apples and 7 good apples. A shopper selects a sample of 4 apples from the bag.
It should be noted that the question has to do with a combination. The number of different samples that are possible will be:
Number of apples = 9
Number to be selected = 4
= ⁹C₄
= 9! / (9 - 4)! 4!
= 9 × 8 × 7 × 6 / 4 × 3 × 2
= 126
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A bag of 9 apples contains 2 rotten apples and 7 good apples. A shopper selects a sample of 4 apples from the bag. How many different samples are possible?
and Relative Change
The value of a car dropped from $23,800 to $22,300 over the last year. Determine the absolute
and relative change in this sitation.
Absolute Change: This car's value decreased by $
Round your answer to the nearest dollar.
Relative Change: This car's value decreased by
Round your answer to the nearest tenth of a percent.
last year.
% last year.
The absolute change or the car's value decreased by $1500.
The relative change: The value of the car decreased by 6.302 %.
The car's value dropped from $23,800 to $22,300 over the last year.
So, the initial price of the car is I = $23,800, and the final value of the car after a year is F = $22,300.
Therefore,
The Absolute change will be:
= I - F
= $23,800 - $22,300
= $1500
Hence, the car's value decreases by $1500.
Now, the relative change is the percentage by which the price decreased over the year.
So,
As the price decreased by $1500.
Let x be the relative change.
Then,
$ 23,800 × x/100 = $1500
238x = 1500
x = 6.302
Hence, the car's value decreased by 6.302% last year.
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