A. The equations for the amounts of money Lyle and Shaun have in their accounts are represented as:
f(x) = 20x + 100
g(x) = 10x + 500
B. When f(x) = g(x), x = 40.
How to Write the Equation of a System?A linear equation can be written in slope-intercept form y = mx + b. Here, the value of m is the unit rate or slope, while the value of b is its y-intercept or initial value.
Part A:
Equation for Lyle:
y-intercept / initial value (b) = $100
Slope / unit rate (m) = $20
To write the equation, substitute m = 20 and b = 100 into f(x) = mx + b:
f(x) = 20x + 100.
Equation for Lyle:
y-intercept / initial value (b) = $500
Slope / unit rate (m) = $10
To write the equation, substitute m = 10 and b = 500 into g(x) = mx + b:
g(x) = 10x + 500.
Part B: To solve the system, we would do the following:
20x + 100 = 10x + 500
20x - 10x = -100 + 500
10x = 400
x = 400/10
x = 40
Learn more about system of linear equations on:
https://brainly.com/question/14323743
#SPJ1
what statistical test would perform to test your hypothesis: average time to deliver goods, once the order is placed over phone, is more than 30 minutes in the population. group of answer choices t-test linear regression z-test anova
To test the given hypothesis : average time to deliver goods, once the order is placed over phone, is more than 30 minutes in the population, the T-test or T statistical test should be performed.
A parametric statistical test makes assumptions about the population parameters and data distributions. T-tests, z-tests, linear regression, and anova tests are examples of these tests, which assume data from a normal distribution.
Z-test:-When the variances are known and the sample size is large, a z-test is used to determine whether two population means differ. The parameters used are the population mean and standard deviation. The Z-test is used to confirm that the sample drawn is from the same population.T-test:-The t-test compares the means of two samples. When the population parameters (mean and standard deviation) are unknown, a t-test is used.ANOVA Test:-ANOVA is a statistical technique used to determine whether the means of two or more groups differ significantly from one another. ANOVA compares the means of different samples to determine the impact of one or more factors. If we use a t-test instead of an ANOVA test, the results will be inaccurate because there are more than two samples.Linear Regression model :-A linear relationship exists between the response variable and the predictor variables in linear regression. It can be used to predict the value of one continuous variable based on the value of another.As we all know, a statistical test known as a t-test is used to compare the means of two groups. It is frequently used in hypothesis testing to determine whether a procedure or treatment truly affects the population of interest or whether two groups differ.
Thus,The T-test or T statistical test should be performed to test the given hypothesis.
To learn more about T-test refer here
https://brainly.com/question/28486320
#SPJ4
How do you find the domain and range of a graph equation and table?
The domain of a graph is made up of all the input values displayed on the x-axis since the term "domain" refers to the set of potential input values. The y-axis on a graph indicates the available expected output, or range of graph.
In the given question, we have to explain how we can find the domain and range of a graph equation and table.
The domain and range are typically listed in a table's left and right columns, respectively. In a relation or function, the domain can alternatively be thought of as the input values (x), and the range as the output values (y).
Graphs can be used as another tool for determining the domain and range of functions. The domain of a graph is made up of all the input values displayed on the x-axis since the term "domain" refers to the set of potential input values. The y-axis on a graph indicates the available expected output, or range.
To learn more about domain and range link is here
brainly.com/question/28135761
#SPJ4
Please help, answers only!
Answer:
y = -2x+2
Find slope
find x intercept
y=mx+b
Is it 1 is a perfect square?
No, 1 is not a perfect square. A perfect square is a number that is the result of multiplying an integer by itself.
A perfect square is a number that is the result of multiplying an integer by itself. Therefore, 1 does not meet this criteria.A perfect square is a number that is the result of multiplying an integer by itself.
For example, 4 is a perfect square because it can be expressed as 2 x 2. Similarly, 9 is a perfect square because it can be expressed as 3 x 3. However, 1 does not meet this criteria as it is not the result of multiplying an integer by itself.
Learn more about square here
https://brainly.com/question/22970240
#SPJ4
Select the values that make the inequality -w <-8 true.
Then write an equivalent inequality, in terms of w.
(Numbers written in order from least to greatest going across.)
-13
-8
-3
07
8.1
O-9
-7.9
O
7.9
9
-8.1
0 -7
03
8
13
The values that make the inequality -w<-8 true are 8.1, 9, 13.
The equivalent inequality is w > 8.
What is the order from least to greatest?
There are two ways to arrange a set of integers in mathematics. It implies that there are two possible orderings for the numbers: ascending and descending. Ascending order refers to the arrangement of numbers in which the smallest number comes before the largest. The numbers are listed in this fashion in ascending order. It is ideal for the first number to be less than the second.
Descending order refers to arranging the integers from largest to least value. The numbers are in decreasing order in this manner. It is ideal for the first number to be higher than the second.
Given inequality is -w < -8.
Now putting w = -13, -8, -3, 07, 8.1, O-9, -7.9, O, 7.9, 9, -8.1, 0 -7, 03, 8, 13 in the given inequality.
-(-13) < -8 → 13 < -8 (false)
-(-8) < -8 → 8< -8 (false)
-(-3) < -8 → 3 < -8 (false)
-7 < -8 (false)
-(8.1) < -8 (true)
-(0-9) < -8 → 9 < -8 (false)
-(-7.9) < -8 → 7.9 < -8 (false)
-9 < -8 (true)
-(0-7) < -8 → 7 < -8 (false)
-(03) < -8 → 3 < -8 (false)
-8 < -8 (false)
-13 < -8 (true)
Rewrite the given inequality:
Multiply -1 on both sides:
(-1) × (-w) > (-1) × (-8)
w > 8
To learn more about inequality, click on below link:
https://brainly.com/question/20124187
#SPJ1
What is the slope of the line through − 7 − 2 and − 6 7?
The slope of the line through − 7 − 2 and − 6 7 is 9. A line's steepness can be determined by looking at its slope.
Where y and x denote the first and second values, respectively, and y and x2 denote the third and fourth values, respectively, and m is the slope
I by itself would result in m in our scenario.
m= y2 - y/x2 - x
Since x and y are random positions, I will state that the first point, X, is at (-7, -2) and the second point, Y, is at (-6, 7). Therefore, we will enter the values below in their place:
m= [7 -(-2)]/ (-6) -( -7)]
m= 9/1
m = 9
The slope of the equation would be nine.
For more information on slope kindly visit to
https://brainly.com/question/16941905
#SPJ4
Two positive numbers have a sum of 8 and a product of 13. Algebraically determine the value of the larger of the two numbers to the nearest hundredth
The values of a and b are 6.83 and 1.17 respectively rounded to the nearest hundredth.
What is a numerical expression?A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.
Let the numbers be a and b.
Given, (a + b) = 8..(i) and ab = 8.
Now,
(a + b)² = a² + 2ab + b².
64 = a² + b² + 16.
a² + b² = 48.
Now,
(a - b)² = a² + b² - 2ab.
(a - b)² = 48 - 16.
(a - b)² = 32.
(a - b) = 5.66...(ii)
Adding (i) and (ii) we get 2a = 13.66 ⇒ a = 6.83 and b = 8 - 6.83 ⇒ b = 1.17.
learn more about numerical expressions here :
https://brainly.com/question/29199574
#SPJ1
9 ft, 20ft, and 14ft. Repreent the ide of a triangle. Determine if the triangle i a right triangle
It is not a right triangle.
What is pythagorus theorem?
The relationship between the three sides of a right-angled triangle is explained by the Pythagoras theorem, commonly known as the Pythagorean theorem. The Pythagoras theorem states that the square of a triangle's hypotenuse is equal to the sum of its other two sides' squares. Let's study more about the Pythagoras theorem, its equations, and derivations before moving on to instances with solutions using squares and triangles.
given sides 9ft,20ft and 14ft.
if a triangle is a right triangle then it should be follow the pythagorus theorem
[tex]h^{2} =p^{2} + b^{2}[/tex]
where h is hypotenuse, p is perpendicular side and b is base side.
[tex]20^{2} =9^{2} +14^{2} \\400=81+196\\400\neq 277[/tex]
hence it is not a right triangle
To know more about pythagorus theorem checkout https://brainly.com/question/14604966
#SPJ4
How do you sketch a graph of a function?
The graph of a function can be sketched by plotting points.
First and foremost, it is to be determined if the function is odd/even or periodic. Next, we find the x and y intercepts. To sketch a graph of a function, one can start by plotting a few points that lie on the graph using the coordinates given by the function. For example, if the function is y = x², then points (0, 0), (1, 1), and (2, 4) can be plotted by substituting the values of x into the function to find the corresponding values of y.
Subsequent to this, one can connect the points with a smooth curve to form the graph of function. If the function is a straight line, the graph will be a straight line. If the function is quadratic, the graph will be a parabola. The graph may take on a more complicated shape for more complex functions.
Read more about the graph of a function on:
https://brainly.com/question/26857518
#SPJ4
A system of a linear equation is said tk be consistent if it had at least one solution ? true false​
A system of a linear equation is said tk be consistent if it had at least one solution is true
In a linear equation, the largest power of the variable is always equal to 1. It's also known as a one-degree equation. Typically, Ax + B = 0 is used to represent a linear equation with one variable. The variables x, A, and B in this case serve as constants and coefficients, respectively. The typical form of a linear equation with two variables is Ax + By = C. Here, x and y are the variables, A and B are the coefficients, and C is the constant. If there is at least one solution, a set of linear equations is considered to be consistent. This means that when all equations in the system are solved, at least one set of values for the variables can be found which satisfy all equations simultaneously. So, the statement is true.
Learn more about linear equation here
https://brainly.com/question/11897796
#SPJ4
Solve k−7≤0. Graph the solution pls help me find the solution.
the graph will contain all the plane which is less than or equal to 7
What is inequality?
Inequalities are mathematical expressions where neither side is equal. In inequality, as opposed to equations, we compare two values. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign in between. Sometimes it can be about a "not equal to" relationship, where one thing is more than the other or less than. In mathematics, an inequality is a relationship that results in a non-equal comparison between two numbers or other mathematical expressions.
The given inequality is k−7≤0
k ≤ 7
Hence the graph will contain all the plane which is less than or equal to 7.
Learn more about inequality here:
brainly.com/question/14098842
#SPJ1
What is the slope of the line that passes through the points (- 2.5 and 1 4?
The slope of the line that passes through the points (-2,5) and (1,4) is -1/3.
The slope of a line can be defined as the measure of the steepness of that particular line. If we were to define it mathematically, we would define it as the change in y-intercepts divided by the change in x-intercepts.
We know that the formula for finding the slope of a line is -
= m = y₂-y₁/x₂-x₁ (i)
The given values are = x₁ = -2 ; x₂= 1 ; y₁= 5 ; y₂= 4
We use the given values and (i) to find -
= m = 4-5 / 1-(-2)
= m = -1/3
Hence, the slope of this line is -1/3.
Learn more about the slope of a line on
https://brainly.com/question/16180119?referrer=searchResults
#SPJ4
2 9 14 36 40 Which number is a multiple of 12?
Answer:
36
Step-by-step explanation:
because 12×3=36, hope that helps.
Select that integer that matches the following situation:
I go for a hike in Colorado. The top of the mountain is , feet above sea level.
Question 4 options:
A: 144
B: 14,000
C: -14
D: -14,000
PLEASE GIVE ME A CORRECT AND ACTUAL ANSWER PLS
Find the equation of the axis of symmetry of the following parabola algebraically
y=−3x^2+18
The equation of the axis of symmetry of y=−3x^2+18 parabola algebraically is x = 0.
we use for that the fact that the x position of the vertex of a parabola of the general form: [tex]y = ax^{2} + bx + c[/tex], is given by:
[tex]x_{vertex}[/tex] = [tex]\frac{-b}{2a}[/tex]
which in our case becomes:
[tex]x_{vertex}[/tex] = [tex]\frac{-0}{-6}[/tex]
[tex]x_{vertex}[/tex] = 0
Parabola:
A parabola is a curve whose equation has a point on it that is equally spaced from both a fixed point and a fixed line. The parabola's fixed line and fixed point are together referred to as the directrix and focus, respectively. It's also crucial to remember that the fixed point is not located on the fixed line. A parabola is a locus of any point that is equally distant from a given point (focus) and a certain line (directrix). An essential curve of the coordinate geometry's conic sections is the parabola.To know more about Parabola:
https://brainly.com/question/15696613
#SPJ1
What is parallel and perpendicular slope?
when two non-vertical lines are in the same plane and have the same slope, they are said to be parallel lines. whereas the non-vertical lines are in the same plane and intersect at an angle of 90, they are said to be perpendicular.
A parallel lines is when two lines have the same slope, meaning they will never intersect. This is represented by the same "rise over run" ratio in the equation of the line. The perpendicular lines is when two lines have a slope that is the opposite reciprocal of each other. This means that the lines will intersect at a 90-degree angle and can be represented by the equation y = -1/m * x + b, where m is the slope of one of the lines. Both of these concepts are important for understanding the basics of linear equations, as well as for determining the lines of best fit in graphs.
To know more about parallel lines refer to the link brainly.com/question/16701300
#SPJ4
a coin-operated soft drink machine was designed to discharge, on average, 7 oz of beverage per cup. in a test of the machine, 10 cupfuls of beverage were drawn from the machine and measured. the average and sd of the ten measurements were 7.1 oz and 0.12 oz, respectively. assume that the histogram of beverage discharge from this machine roughly follows a normal curve. does this machine discharge more than 7.0 oz or does the difference represent chance variation?
The machine discharge more than 7.0 oz or does the difference represent chance variation is 0.0274
What is meant by variation?
In math, variance refers any difference between the individuals in a species or groups of organisms of any species.
Here we have given that a coin-operated soft drink machine was designed to discharge, on average, 7 oz of beverage per cup. in a test of the machine, 10 cupful's of beverage were drawn from the machine and measured. the average and SD of the ten measurements were 7.1 oz and 0.12 oz, respectively. assume that the histogram of beverage discharge from this machine roughly follows a normal curve.
And we need to find machine discharge more than 7.0 oz or does the difference represent chance variation.
By using the Applet, to find the exact p-value we first need to find P(Z≥2.63) where Z is a t9 random variable.
=> P(Z≥2.63)=0.0137
=> 2×P(Z≥2.63)=0.0274
=> P-value=0.0274
So, the p-value associated with the test is 0.0274
To know more about variance here.
https://brainly.com/question/28107529
#SPJ4
Please D: I'm so dum
Answer:
6: H
3: A
Step-by-step explanation:
6: We only want a pound of fertilizer, if we have 7.8 pounds then we would have to divide by the cost in order to get only the cost of one. 67.86 ÷ 7.8 = 8.70
3: 3/4 is less than one hour. We only want one hour. We divide the 18 miles by 3, which is 6 but since it's a little less than an hour, it must be lower. The only option less than 6 is 4.5
Describe the end behavior of the function -2x^3-13x^2+8x+52
Answer:
Step-by-step explanation:
lim x -> +oo -2x³ - 13x² + 8x + 52
x³ (-2 -13/x + 8/x² + 52/x³)
+oo³ (-2 - 13/+oo + 8/+oo² + 52/oo³)
+oo(-2 + 0 + 0 + 0)
-oo
lim x -> -oo -2x³ - 13x² + 8x + 52
x³ (-2 -13/x + 8/x² + 52/x³)
-oo³ (-2 - 13/-oo + 8/-oo² + 52/-oo³)
-oo(-2 + 0 + 0 + 0)
+oo
Manny took home a couple of his friends after soccer practice. He originally had 7 gallons of gas in his car. He used 1.08 gallons of gas to take one friend home and three fifths gallons to take the other friend home. How much gas did he have left in his car after taking both friends home?
1.07 gallons
5.32 gallons
5.86 gallons
5.92 gallons
Answer: b.5.32
Step-by-step explanation:
What are the 5 steps of solving a linear equation in two variables strategy?
A system of two-variable linear equations can be solved using one of five strategies. Here is a description of those techniques:
Graphical MethodSubstitution MethodCross Multiplication MethodElimination MethodDeterminant MethodGiven,
Linear equation in two variables;
The equations with one, zero, or an infinite number of solutions are known as linear equations with two variables since each of the variables has an exponent order of one. A linear equation with two variables has the conventional form axe + by + c = 0, where x and y are the variables.
The answers can also be expressed as ordered pairs, such as (x, y). Two straight lines, which could be intersecting, parallel, or coincident, are included in the graphic representation of the system of linear equations in two variables.
Here,
A system of linear equations in two variables can be solved using one of five techniques. These techniques are described below:
Graphical MethodSubstitution MethodCross Multiplication MethodElimination MethodDeterminant MethodLearn more about solving linear equations here;
https://brainly.com/question/29545212
#SPJ4
Please help me!!!!! Ill rate 5/5 and thank your profile
The last box 2/37.5 = 4/75 = 0.8/15 have same proportional relationship.
what is proportional relationship?
When two variables are correlated in a manner that their ratios are equal, this is known as a proportional relationship. In a proportional connection, one variable is always a constant value multiplied by the other, which is another way to think of them. The "constant of proportionality" is the term used to describe that constant.
Given x and y will have a proportional relationship if the ratio of x to y will be equal for all given values.
9/8 ≠ 12/8
16/28 = 4/7 ≠6/10.5
12/32= 3/8 ≠8/20
1.5/8 = 3/16 ≠4/18
2/37.5 = 4/75 = 0.8/15
Hence the last box have same proportional relationship.
Learn more about proportional relationship, by the following link.
brainly.com/question/12242745
#SPJ1
Please help this is due in a few Brainliest will be rewarded!!!!!
Step-by-step explanation:
the middle one has to be the same for both part ratios.
the best here is to bring the ratio element of B in the first part ratio to 10. we need to double the B element there
for that (as a ratio is a fraction) we also have to adapt the A element in the same way.
so, we get
4×2 : 5×2 : 9 =
= 8 : 10 : 9
and that is also shown in the graphic.
Answer:
X:Y:Z= 8:10:9
Step-by-step explanation:
Let x be the number of students in class A
Let y be the number of students in class B
Let z be the number of students in class C
x:y = 4:5
y:z= 10: 9
x:y:z = ?
Find the LCM of the y terms (5 and 10 ) which is 10
Divide 10 by the first y term (5) = 2
Divide 10 by the second y term(10) = 1
X: y = (4 x 2) :(5 x 2)= 8:10
y:z =(10 x 1) : (9:1)= 10:9
x:y:z= 8:10:9
What is the equation of a line that passes through 1/3 and 2 0?
The equation of a line that passes through (1/3, 2) is y = 6x – 4 with slope.
1. To solve for the equation of the line, we need to use the point-slope form.
2. The point-slope form is y-y1=m(x-x1).
3. We are given the point (1/3, 2). We can plug this into the equation as x1=1/3 and y1=2.
4. To find the slope (m), we need to calculate the rise over run. We can use the point (1/3, 2) and another point to calculate the slope.
5. Let's choose the point (0,0). The rise is 2 and the run is 1/3. So the slope (m) is 6.
6. Now we can plug our values into the point-slope form and solve for y.
7. y-2=6(x-1/3).
8. We can simplify this equation by subtracting 2 from both sides.
9. y=6x-4.
10. This is the equation of the line that passes through (1/3, 2).
Learn more about slope here
https://brainly.com/question/3605446
#SPJ4
< Quadrilateral L' is the image of quadrilateral L under a dilation. What is the center of the dilation? ( pls help i need it asap )
The center of the dilation from the quadrilateral WXYZ to quadrilateral W'X'Y'Z' is point A.
What is a dilation?Dilation is the process of resizing or transforming an object. It is a transformation that makes the objects smaller or larger with the help of the given scale factor. The new figure obtained after dilation is called the image and the original image is called the pre-image.
Given that, quadrilateral L' is the image of quadrilateral L under a dilation.
The origin is often used as the center of dilation.
Connect all the points from quadrilateral WXYZ and quadrilateral W'X'Y'Z' to point A.
Therefore, the center of the dilation is point A.
To learn more about the dilation visit:
https://brainly.com/question/13176891.
#SPJ1
Find the area of the figure below, formed from a triangle and a parallelogram.
8 mm
3 mm
5 mm
4 mm
5 mm
5 mm
O 44 square millimeters
O 32 square millimeters
O 34 square millimeters
O22 square millimeters
The correct option for the area of the figure formed by a triangle and a parallelogram is 32 square millimeters.
How to evaluate for the area of the figureTo get the area of the figure, we solve for the area of the triangle and that of the parallelogram, and then add our results together.
area of a triangle is half the product of its base and height
area of parallelogram is the base multiplied by its height
the triangle has base = 8mm and height = 3mm
so
area of the triangle = (8mm × 3mm)/2
area of the triangle = 24mm²/2
area of the triangle = 12mm²
the parallelogram has base = 5mm and height = 4mm
so
area of the parallelogram = 5mm × 4mm
area of the parallelogram = 20mm²
Therefore, the area of the figure which is the sum of the area of the triangle and the area of the parallelogram is;
12mm + 20mm² = 32mm² or 32 square millimeters
Know more about area here: https://brainly.com/question/12416394
#SPJ1
Given AB=CB and DB bisects ABC
Prove A=C
∠A = ∠C by congruent parts of congruent sides
What is CPCT ?Corresponding parts of congruent triangles is referred to as CPCT. According to the CPCT theorem, if two or more triangles are taken that are congruent to one another, then the corresponding angles and sides of the triangles are likewise congruent to one another.
According to the given Information
Given
AB = CB
DB bisects ∠ABC
∠ABD = ∠CBD
Proof
In Δ ABD and Δ CBD
AB = CB ( given )
∠ABD = ∠CBD ( given )
BD = BD ( Common Side )
So
Δ ABD ≅ Δ CBD ( SAS congruence )
∠A = ∠C ( CPCT )
Congruent Parts of Congruent Sides
Hence
∠A = ∠C by congruent parts of congruent sides
To know more about Congruent Triangles
https://brainly.com/question/22062407
#SPJ1
Find the midpoint of the line segment with the given endpoint. (-3,-5),(4,5)
Answer:
[tex]\left(\frac{1}{2}, 0 \right)[/tex]
Step-by-step explanation:
Using the midpoint formula,
[tex]\left(\frac{-3+4}{2}, \frac{-5+5}{2} \right)=\left(\frac{1}{2}, 0 \right)[/tex]
Which expression is equivalent to this polynomial? 9x2 + 7
Answer:
2+7=9 so 9x9=81
Step-by-step explanation:
Sean is building a rectangular garden that is 10 feet by 6 feet what should the length of the diagonals
The length of the diagonal is 11.7 feet in the rectangular garden.
The two shorter sides of the rectangle have lengths of 10 feet and 6 feet, and the hypotenuse is the diagonal of the rectangle.
So, we can use the Pythagorean theorem to find the length of the diagonal as follows:
a² + b² = c²
where a and b are the lengths of the shorter sides of the rectangle (10 feet and 6 feet), and c is the length of the diagonal.
Substituting the values for a, b, and c, we get:
10² + 6² = c²
100 + 36 = c²
136 = c²
c = √136
c = 11.7
Therefore, the length of the diagonal is 11.7 feet in the rectangular garden.
Learn more about Pythagoras's theorem here:
brainly.com/question/343682
#SPJ1