f(x) is a linear function whose slope is equal to -1 and y-intercept is equal to -7.
What is f(x)?
Here we have f(x) defined as:
f(x) = -x - 7
Now, we define a general linear function as:
g(x) = m*x + b
Where m is the slope and b is the y-intercept.
Now, we can rewrite f(x) as:
f(x) = (-1)*x + (-7)
So f(x) is a linear function with a slope of -1 and a y-intercept of -7.
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. Ashton picked 6 pounds of pecans. He wants to share the pecans equally among 5 of his neighbors. How many pounds of pecans each neighbor get? A 5/11 pound B 5/6 pounds C 1 1/2 pounds D 2 1/5
Explanation:
Ashton wants to divide 6 pounds of pecans between 5 neighbors. We have to divide 6 by 5 and write it as a mixed number, because we'll get an improper fraction:
[tex]\frac{6}{5}=\frac{5+1}{5}=\frac{5}{5}+\frac{1}{5}=1+\frac{1}{5}\rightarrow1\frac{1}{5}[/tex]Answer:
The correct option is C 1 1/5 pounds
Line r has an equation of y + 3 = -(x + 2). Line s includes the point (-10, -8) and is
parallel to line r. What is the equation of line s?
Write the equation in slope-intercept form. Write the numbers in the equation as simplified
proper fractions, improper fractions, or integers.
Answer:
y = - x - 18
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
the equation of a line in point- slope form is
y - b = m (x - a)
m is the slope and (a, b ) a point on the line
y + 3 = - (x + 2) ← is in point- slope form
with slope m = - 1
• Parallel lines have equal slopes , then
y = - x + c ← is the partial equation
to find c substitute (- 10, - 8 ) into the partial equation
- 8 = 10 + c ⇒ c = - 8 - 10 = - 18
y = - x - 18 ← equation of line s
The equation in slope-intercept form is y=-x-18.
What is the equation of a line?The general equation of a straight line is y=mx+c, where m is the gradient, and y = c is the value where the line cuts the y-axis. This number c is called the intercept on the y-axis.
Given that, Line r has an equation of y + 3 = -(x + 2).
y+3=-x+2
y=-x+2-3
y=-x-1
Here, slope m=-1
Line s includes the point (-10, -8) and is parallel to line r.
The slope of a line parallel to given line is m1=m2
Substitute m=-1 and (x, y)=(-10, -8) in y=mx+c, we get
-8=-1(-10)+c
c=-18
So, the equation is y=-x-18
Therefore, the equation in slope-intercept form is y=-x-18.
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Given the following sequence of numbers find the recursive formula, and the appropriate sequence formula,(arithmetic or geometric) and find the next three numbers in the sequence.8. 3, 9, 15, 21, 27,9. 5, 9, 13, 17, 21,10. -243, 81, -27, 9,11. Using the sequence find the n for the following terms 6, 1, 4,-9...... -254
see explanation below
Explanation:8) 3, 9, 15, 21, 27
The common difference = 15-9 = 9-3
The common difference = d = 6
Hence, it is an arithmetric sequence
The recursive formula:
[tex]\begin{gathered} a_{n+1}=a_n+\text{ 6} \\ \text{OR} \\ a_n=a_{n-1}+\text{ d} \\ a_n=a_{n-1}+6 \end{gathered}[/tex]The appropriate formula:
[tex]\begin{gathered} a_n=a_1+\text{ (n-1)d} \\ \text{where a}_1\text{ = }3\text{ } \\ a_n=3_{}+\text{ (n-1)d} \end{gathered}[/tex]The next three numbers in the sequence:
[tex]\begin{gathered} \text{The last term in the sequence given was 6th term. } \\ \text{The next }3\text{ terms will be: 7th, 8th and 9th term} \end{gathered}[/tex][tex]\begin{gathered} a_7\text{ = 3 + (7-1)}\times6 \\ =\text{ 3+ (6)(6) = 3 + 36} \\ 7th\text{ term = }a_7=39 \end{gathered}[/tex][tex]\begin{gathered} a_8\text{ = 3 + (8-1)}\times6 \\ =\text{ 3+ (7)(6) = 3 + 4}2 \\ 8th\text{ term = }a_8\text{ =}45 \end{gathered}[/tex][tex]\begin{gathered} a_9\text{ = 3 + (9-1)}\times6 \\ a_9\text{ = }3\text{ + 8(6) = 3 + 48} \\ 9th\text{ term = }51 \\ \end{gathered}[/tex]SOMEONE HELP ME WITH THIS
Answer:
A = 44
Step-by-step explanation:
11 x 8 = 88
88 / 2 = 44
1. At Pages Aplenty book store, the more books you buy, the more books you get! With the special deal, a customer gets 2 free books for every 7 purchased books. Larry purchased 21 books.
(x means multiplication)
21/7=3, so he gets the deal 3 times. 2x3=6, so he gets 6 bonus books, leading to a total of 27 books.
the sum of 3 and twice a number is 33
hello
to solve this question, we should let the unknown number be represented by x
[tex]\begin{gathered} x+2x=33 \\ 3x=33 \\ \text{divide both sides by the coefficient of x} \\ \frac{3x}{3}=\frac{33}{3} \\ x=11 \end{gathered}[/tex]the first number (x) is equal to 11, we can find the other number.
[tex]2x=2\times11=22[/tex]from the calculations above, the numbers are 11 and 22
2. How does scale factor change the area?
A. by the scale factor
B. by the scale factor cubed
C. by the scale factor squared
The area will change if the scale factor length is increased or reduced.
Option A is the correct answer.
What is the scale factor?
This refers to the extent to which a shape is increased or reduced. It is used in drawings of shapes eg rectangles, squares, circles, etc.
What is area?
This refers to the total space occupied by a particular shape or object. it is measured in square meters,m².
The area of an object can change, if the scale factor is increased or reduced by a particular amount.
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1) When we solve systems of linear equations, we are finding the valuesfor x and y that are true for both equations in a system. What does thissolution indicate on a graph?
Answer
The solution of this system of equations is usually the point where the lines meet each other. The solution is at the point of intersection of the lines.
The value for x is the x-coordinate of this point of intersection and the value for y is the y-coordinate of this point of intersection.
Explanation
The graph of a system of equations show straight lines that correspond to each of the equations.
The solution of this system of equations is usually the point where the lines meet each other. The solution is at the point of intersection of the lines.
The value for x is the x-coordinate of this point of intersection and the value for y is the y-coordinate of this point of intersection.
Hope this Helps!!!
Answer:
The solution of this system of equations is usually the point where the lines meet each other. The solution is at the point of intersection of the lines.
The value for x is the x-coordinate of this point of intersection and the value for y is the y-coordinate of this point of intersection
Step-by-step explanation
The graph of a system of equations show straight lines that correspond to each of the equations. The solution of this system of equations is usually the point where the lines meet each other. The solution is at the point of intersection of the lines. The value for x is the x-coordinate of this point of intersection and the value for y is the y-coordinate of this point of intersection
14/25 as a decimal
with solution please, ty!
Answer:0.56
Step-by-step explanation:
You simply divide 14 by 25
so 14÷25 or 14/25
put that in a calculator and it comes out to 0.56
Answer:0.56
Step-by-step explanation:
if you make the 25 into 100 which is x4 and 14x4= 56
so it will be 56/100 which is 0.56
helpppp. find the quotient 2^3 divided by 5^2
8/25
2/5
25/8
Answer:
8/25
Step-by-step explanation:
2x2x2=8
5x5=25
= 8/25
what is the slope y=5x-3
Answer:
The slope is 5.
Explanation:
In the slope-intercept form of an equation
[tex]y=mx+b[/tex]m is the slope, and b is the y-intercept of the equation.
Now in our case,
[tex]\begin{gathered} m=5 \\ b=-3 \end{gathered}[/tex]therefore, the slope is 5 and the y-intercept is -3.
Using the Pythagorean theorem fill in the table assume a and b are the lengths of the legs and c is the hypotenuse
The other side of the triangle by using Pythagoras theorem is 15 cm.
Given that,
The triangle has an hypothesis 25cm, adjacent is 20 cm and opposite is x cm.
We have to find the other side by using Pythagorean theorem.
The hypotenuse of a triangle, which has a straight angle of 90 degrees, has a square that, according to the Pythagoras theorem, equals the sum of the squares of the other two sides.
c²=a²+b²
25²=20²+x²
625=400+x²
x²=625-400
x²=225
Square root on both sides.
x=√225
x=15.
Therefore, The other side of the triangle by using Pythagoras theorem is 15 cm.
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Help please!!!
It’s about ratios
Answer:
B
Step-by-step explanation:
Proportional means that the values should be equal to each other:
15/21= 0.714...
20/25= 0.8
20/24=0.833...
15/18= 0.833...
16/20=0.8
20/24=0.8333...
5/6=0.8333...
6/5=1.2
Hope this helps!
Choose the correct equation type for each system. ry = 3x - 2 |3x-y=4 Consistent S-y = -x +5 12y = -4x + 20 y = -x + 4 [x=-y-6 > y = 4x + 2 y = 6x - 10 (y=2x+1 y = -2x + 3 =+3 - 2x + 5y = 0 y = x
Let's solve each system to check if it is a consistent or inconsisent system of equations:
a.
[tex]\begin{gathered} \begin{cases}y=3x-2 \\ 3x-y=4\end{cases} \\ \text{ Substituting the value of y from the first equation in the second:} \\ 3x-(3x-2)=4 \\ 3x-3x+2=4 \\ 2=4 \end{gathered}[/tex]This system has no solution, therefore it is a inconsistent system.
b.
[tex]\begin{gathered} \begin{cases}\frac{1}{2}y=-x+5 \\ 2y=-4x+20\end{cases} \\ \text{Multiplying the first equation by 4:} \\ 2y=-4x+20 \end{gathered}[/tex]Both equations represent the same line, so the system has infinite solutions, therefore it is a consistent dependent system.
c.
[tex]\begin{gathered} \begin{cases}y=-x+4 \\ x=-y-6\end{cases} \\ \text{ Applying the value of y from the first equation in the second one:} \\ x=-(-x+4)-6 \\ x=x-4-6 \\ 0=-10 \end{gathered}[/tex]This system has no solution, therefore it is a inconsistent system.
d.
[tex]\begin{gathered} \begin{cases}y=4x+2 \\ y=6x-10\end{cases} \\ \text{Comparing the y values:} \\ 4x+2=6x-10 \\ 6x-4x=2+10 \\ 2x=12 \\ x=6 \\ \\ y=4\cdot6+2=24+2=26 \end{gathered}[/tex]This system has one solution, therefore it is a consistent independent system.
e.
[tex]\begin{gathered} \begin{cases}y=2x+1 \\ y=-2x+3\end{cases} \\ \text{Comparing the y values:} \\ 2x+1=-2x+3 \\ 2x+2x=3-1 \\ 4x=2 \\ x=\frac{1}{2} \\ \\ y=2\cdot\frac{1}{2}+1=1+1=2 \end{gathered}[/tex]This system has one solution, therefore it is a consistent independent system.
f.
[tex]\begin{gathered} \begin{cases}-2x+5y=0 \\ y=\frac{2}{5}x\end{cases} \\ \text{ Applying the value of y from the second equation in the first one:} \\ -2x+5\cdot(\frac{2}{5}x)=0 \\ -2x+2x=0 \\ 0=0 \end{gathered}[/tex]This system has infinite solutions (the equations represent the same line), therefore it is a consistent dependent system.
A friend plans to use 80 feet of fencing to surround three sides of a rectangular vegetable garden. The fourth side of the vegetable garden is bordered by a wall.
a. Write a function that models the area A of the vegetable garden in square feet when the length of the fence parallel to the wall is x feet.
b. For what lengths x is the area of the vegetable garden greater than 350 square feet?
c. For what lengths x is the area of the vegetable garden greater than 750 square feet?
d. Is it possible for the fence to enclose an area greater than 900 square feet? Explain.
a. A function that models the area A is A(x)=
The function that models the area of the rectangular field is given by
A(x) = 1 / 2 ( 80x -x² ) .
a) The length of the side parallel to the wall is given as x feet.
Total length of the fence = 80 feet.
fence required for each side = 80-x feet
length of each side = 1/2 (80-x)
Area of the rectangular garden
= 1/2(80-x)·x
= 1 / 2 ( 80x - x² )
Therefore the area written in function form is A(x) = 1 / 2 ( 80x -x² ) .
b) Now we have to find the length of x for which the area is greater than 350 square feet.
1 / 2 ( 80x -x² ) > 350
or, ( 80x -x² ) > 700
or, (x-10)(x-70)<0
or, 10 < x < 70
So for x greater than 10 and less than 70 feet the rea is greater than350 square feet.
c) Now we have to find the length of x for which the area is greater than 700 square feet.
1 / 2 ( 80x -x² ) > 700
or, ( 80x -x² ) > 1400
Hence solving we get:
25.68 < x < 54.14 feet.
So for x greater than 25.68 and less than 54.14 feet the area is greater than 700 square feet.
d) Now we have to find the length of x for which the area is greater than 900 square feet.
A(x) = 1 / 2 ( 80x -x² )
or, A'(x) = 1 / 2 (80-2x) (differentiate with respect to x)
or, A'(x) = 40 - x
Now at A'(x) =0 , we get x = 40
Now for A(40) the area is the greatest.
A(40) = 800.
Hence the maximum area that can be covered by the fence is 800 square feet. Therefore we can say that the area greater than 900 is not possible.
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A small business sells sno-cones at the southern end of the amusement park. They had to pay the amusement park $8,500 for the space to sell the sno-cones, and it costs the business $0.80 in supplies for each sno-cone they sell.
If the small business can afford to pay less than $30,000 in expenses for the summer, what is the maximum number of sno-cones they can afford to sell?
Answer:
Step-by-step explanation:
In the summer time your friend wants to have a snow cone stand at a local grocery store parking lot. You want to make sure he actually makes money. The grocery store charges $300 per month. All products are calculated to be 25 cents per customer. Your plans are to sell each cone for $1.25. a. Write a mathematical expression representing the cost of operation for a month. b. Write a mathematical expression representing sales. c. Create an equation that will represent overall profit of the operation for a month. d. Simplify the equation into slope intercept form and standard form. What is the slope and explain its meaning in the context of selling snow cones? What is the intercept and what is its meaning? e. Describe the method of graphing the slope intercept form and also the standard form of the equation. f. What is the domain and range of the equation? Is the relation a function, why? g. How many snow cones do you need to sell to break even in the first month? h. How much is the profit if you sell 425, 550 or 700 snow cones in the first month of business? . Thomas and Jenny went to a bakery to pick up some cookies for dessert. Thomas bought 3 pumpkin cookies and 2 raisin cookies. Jenny bought 2 pumpkin cookies and 4 raisin cookies. Thomas consumed 870 calories and Jenny consumed 750 calories. a. Write a system of equations to represent this situation. b. Solve each equation for y and graph to find the solution. How many calories are the pumpkin and raisin cookies? c. Solve the same equations using substitution and the elimination methods. Compare all of your answers. Perform the following to demonstrate you can work with geometric sequences: a. Write 5 numbers that are an example of a geometric sequence. b. Show the value of the common ratio. c. Write an equation that would give you the value of the 23rd term in the sequence d. Find the sum of the first 10 terms of the sequence. Show your work or explain you answer.
what type of variables do we need to investigate correlation? select one: a. one numeric and one categorical variable b. two categorical variables c. you can investigate correlation between any variables d. two numeric variables
When examining the linear relationship between two numerical variables, correlation is used.
It calculates how powerful statistics are. The direction and strength of relationships between variables are studied and measured through correlation, which quantifies co-variation rather than causality. As a result, we must never assume that correlation implies a cause-and-effect relationship.
For instance, when two variables X and Y are found to change in one direction, the other variable's value is discovered to change either in the same direction (i.e., a positive change) or in the opposite direction. This relationship is known as a correlation (i.e. negative change).
On graph paper, a straight line can be used to depict how the two variables move with respect to one another if a correlation exists because it is linear.
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please HELP!!! GUYS
the homework is due tom
Answer:
A(-4.5;2) B(0;-3.5).......
8th grade mathWhich quadrant is the answer to this system of equations in?A. Quadrant 1B. Quadrant 2 C. Quadrant 3D. Quadrant 4
Given the figure, we can deduce the following information:
1. The lines intersect at point (-2,-2).
To determine which quadrant is the answer to the given system of equations, we note the quadrants as shown below:
Based on the given graph, we can notice that the lines intersect at point (-2,-2) which is located at Quadrant 3.
Therefore, the answer is C. Quadrant 3.
Calculate the area??
Answer:
120cm²
Step-by-step explanation:
the figure is formed by a rectangle and two isosceles triangles, the measures of the rectangle are: 12cm and 5cm, the base of the triangles is 12cm and the height is (13 - 5) : 2 = 4cm
Rectangle Area = b × h
12 × 5 = 60cm²
Triangle Area = 1/2 b × h
1/2 12 × 5 = 30cm²
just sum the single Areas
60 + 30 + 30 =
120cm²
Solve the proportion [tex]\frac{1.7x10^8}{12} = \frac{5.1x10^4}{x}[/tex]
The value of unknown variable [x] is x = 36 x 10⁻⁴
What is the general equation of a Straight line? How it represents a proportional relationship?
The general equation of a straight line is -
[y] = [m]x + [c]
where -
[m] is slope of line which tells the unit rate of change of [y] with respect to [x].
[c] is the y - intercept i.e. the point where the graph cuts the [y] axis.
y = mx also represents direct proportionality. We can write [m] as -
m = y/x
OR
y₁/x₁ = y₂/x₂
We have a proportional relationship of the form -
y₁/x₁ = y₂/x₂
We can write it as -
x = (5.1 x 10⁴ x 12)/(1.7 x 10⁸)
x = 36 x 10⁻⁴
Therefore, the value of unknown variable [x] is x = 36 x 10⁻⁴
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The product of 14 and x is equal to 28 more than x.
The value of x is given by 28/13.
Given the product of 14 and x is = 14*x = 14x
According to question, the product is equal to 28 more than x. So,
14x = 28+x
14x-x = 28
13x = 28
x = 28/13
Hence the value of x is 28/13.
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2(3+x)=18 what does x equal
We need to solve the following equation:
[tex]\begin{gathered} 2(3+x)=18 \\ \end{gathered}[/tex]In order to do that, we have to isolate the "x" variable on the left side.
[tex]\begin{gathered} 2\cdot3+2\cdot x=18 \\ 6+2\cdot x=18 \\ 2\cdot x=18-6 \\ 2\cdot x=12 \\ x=\frac{12}{2} \\ x=6 \end{gathered}[/tex]The value of x is 6.
A dentist kept a record of the number of new cavities his patients had per year for the last 10 years. The scatterplot below shows the average number of new cavities per year for patients in the 4-to 32-year age range. Which of the following best describes the trend line of the data shown in the scatterplot? O a horizontal line a line with a negative slope, a line with a positive slope,no trend line
Equation of a line two-points form
The line passes through (1, -2) and (-2, -2)
Answer:
y = - 2
Step-by-step explanation:
the equation of a line passing through points with the same y- coordinates is
y = c ( where c is the value of the y- coordinate )
the line passes through (1, - 2 ) and (- 2, - 2 ) both with y- coordinate - 2, so
y = - 2 ← equation of line
The following table represents the highest educational attainment of all adultresidents in a certain town. If a resident who has a master's degree is chosen atrandom, what is the probability that they are aged 40 or over? Round your answer tothe nearest thousandth.
The answer is: 0.0362
The total number of Master's degree holders = 2848 (from the question)
In order to choose people 40 and above from this Master's degree holder subset,
You choose:
People 40-49 AND People 50 and over.
Number of people 40-49 = 475
Number of people 50 and over = 699
But we also need to take into consideration, the probability of picking a person 40-49 years old OR 50 and over
total Number of people 40 - 49 are 3518
The total Number of people 50 and above are 6518
Thus, we can write the probability as:
[tex]\begin{gathered} P(\text{choosing 40-49)=}\frac{475}{3518} \\ P(\text{choosing 50 and above)=}\frac{699}{6518} \\ P(choo\sin g\text{ Master's degre}e)=\frac{2848}{19076} \\ \\ \text{Thus, for choosing 40-49 AND Master's degre}e\colon \\ P(\text{choosing 40-49 AND Master's degr}ee)=\frac{475}{3518}\times\frac{2848}{19076}=0.0202 \\ \\ \text{For choosing 50 and above AND Master's degre}e\colon \\ P(\text{choosing 50 and above AND Master's degree)=}\frac{699}{6518}\times\frac{2848}{19076}=0.016 \\ \\ \text{Thus choosing Master's degree holder, 40 or over:} \\ P(\text{choosing 40-49 AND Master's degr}ee)+ \\ P(\text{choosing 50 and above AND Master's degree)} \\ =0.0202+0.016=0.0362 \end{gathered}[/tex]The final answer is: 0.0362
What is the height, x, of the equilateral triangle shown?
an equilateral triangle with the angles labeled as 60 degrees and a side length of 10 inches, the height labeled as x
The equilateral triangle's height, (x), is 7√3 inches.
What are Equilateral triangles?An equilateral triangle in geometry is a triangle with equal-length sides on all three sides. In the well-known Euclidean geometry, an equilateral triangle is also equiangular, meaning that each of its three internal angles is 60 degrees and congruent with the others.So, the equilateral triangle's side length is 14 inches.
As a result, we may use the Pythagoras theorem to determine the triangle's height.
c² = a² + b²Now, substitute the values and calculate as follows:'
c² = a² + b²14² - 7² = b²b² = 196 - 49b² = 147b = 7√3Therefore, the equilateral triangle's height, (x), is 7√3 inches.
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Complete question:
What is the height, x, of the equilateral triangle?
An equilateral triangle with angles labeled as 60 degrees and a side length of 14 inches, the height labeled as x
Which of these is the absolute value parent function?O A. f(x) = 5x - 11B. f(x) = 13x1c. f(x) = \x{ + 2OD. f(x) = |x|
Concept
The parent function of absolute functions is y = |x|, and it passes through the origin.
So a parent absolute function is a function that have not been transformed.
So the absolute value parent function is f(x) = |x|
Final answer
f(x) = |x|
The area of a quadrant of a circle is 8 cm². Find the radius and perimeter.
The radius of the circle will be 3.19.
The perimeter of the circle will be 20.03.
What is Circle?
The circle is a closed two dimensional figure , in which the set of all points is equidistance from the center.
Given that;
The area of a quadrant of a circle is 8 cm².
Now,
Since, We know that;
The area of a quadrant of a circle = πr² / 4
So, We can formulate;
⇒ πr² / 4 = 8
Solve for r as;
⇒ 3.14 x r² = 8 x 4
⇒ r² = 32/3.14
⇒ r² = 10.19
⇒ r = √10.19
⇒ r = 3.19
Since, The perimeter of the circle = 2πr
Substitute all the values, we get;
The perimeter of the circle = 2πr
The perimeter of the circle = 2 x 3.14 x 3.19
= 20.03
Thus, The radius of the circle will be 3.19.
The perimeter of the circle will be 20.03.
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help meeeeeeeeeeeeeee pleaseeeeeee
Answer: Width = 4.7 meters, Length = 6.7 meters
Step-by-step explanation:
Let the width be [tex]w[/tex]. It follows that the length is [tex]w+2[/tex].
[tex]w(w+2)=32\\\\w^2+ 2w-32=0\\\\w=\frac{-2 \pm \sqrt{2^2 -4(1)(-32)}}{2(1)}\\\\w \approx 4.7 \text{ } (w > 0)\\\\\implies w+2 \approx 6.7[/tex]