1. The table of values showing the amount Kevin owes his friend after t weeks is as follows:
Table of Values:Week Amount Owed
0 $90
1 $85
2 $80
3 $75
4 $70
...
18 $0 ($5 - $5)
2. The equation representing the amount (L) Kelvin owes his friend after t weeks is L = 90 - 5t.
What is an equation?An equation is a mathematical statement showing that two mathematical expressions using the equation symbol (=) are equal or equivalent.
Equations establish the numerical relationship existing between two or more mathematical expressions, numbers, values, or variables.
Week Amount Owed
0 $90
1 $85 ($90 - $5)
2 $80 ($85 - $5)
3 $75 ($80 - $5)
4 $70 ($75 - $5)
The total amount borrowed = $90
The amount of repayment = $5
The repayment period = weekly
Equation:Let the balance after t weeks of payment = L
L = 90 - 5t
In eighteen weeks, Kevin will complete the repayment of the loan.
Check:
If t = 18
L = 90 - 5t
L = 90 - 5(18)
L = 90 - 90
L = 0
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HELP ME PLEASEEEEEEE
Answer:
A
Step-by-step explanation:
Using the table, the last point has coordinates (120, 190).
Answer:
A
Step-by-step explanation:
the 5th point has the coordinates (129, 190).
120 followers : that is 2 units to the right of 100 on the followers axis.
now we go up to 190 of posts per month.
what point do we find there ? A
What are the next four multiples of 1/7
What are the next four multiples of 1/7 ?
so, it will be :
[tex]\begin{gathered} 2\cdot\frac{1}{7}=\frac{2}{7} \\ \\ 3\cdot\frac{1}{7}=\frac{3}{7} \\ \\ 4\cdot\frac{1}{7}=\frac{4}{7} \\ \\ 5\cdot\frac{1}{7}=\frac{5}{7} \end{gathered}[/tex]2.1 A new field is to be turned into a soccer ground. It is covered in weeds and volunteers are needed to clear it. It was estimated that it would take 2 men 12 days to weed. The following table was drawn up: No. of Volunteers 3 5 6 No. of days 12 4 2.1.1 Complete the table above. (6) 2.1.2 Is the relationship represented direct or indirect proportion? Give a reason for your answer. (3) 2.1.3 Give the names of the two variables given above and indicate which is independent and which is dependent? (4) 2.1.4 If the field must be complete in 1 day, how many volunteers will be needed? (2) 2.1.5 Draw a graph on the set of axes provided below to represent the data given (5) above. Number of days to weed a field. 12 11 10 9 No. 00 N of 6 5 days 1 3 2 1 0 0 1 2 3 5 6 7 8 DO 9 11 12
For 2 Volunteers hours= 12 days
For 3 = X days = 10 days
For 4= 8 days
For 5 = 6 days
from 12 to 4 there are 8
And from 6 to 2, there are 4
Then divide 8/4= 2
Part B) Is an INVERSE relationship, because more volunteers, means less time
Part C) Independent variable is , number of volunteers
Dependent variable is time to clear soccer field
Part D) How many volunteers in 1 day ?
= 12+2= 14 volunteers
A street light is at the top of a 17ft tall pole. A woman 6ft tall walks away from the pole with a speed of 4ft/sec along a straight path. How fast is the tip of her shadow moving when she is 45ft from the base of the pole?
A woman 6 ft tall walks away from a 17 ft tall pole with a street light on top of it.
Graphically:
From the diagram, we can say that:
[tex]\frac{x}{6}=\frac{y}{11}\ldots(1)[/tex]The laws of motion of the woman and the shadow with respect to the base of the pole are:
[tex]\begin{gathered} y(t)=y_0+v_y\cdot t \\ x(t)=x_0+v_x\cdot t \end{gathered}[/tex]Where x0 and y0 are the initial positions, vx and vy are the shadow speed and the speed of the woman, respectively. We know that vy = 4 ft/s, so if we say that the starting point for the woman was 11 feet away from the pole, then using equation (1):
[tex]\begin{gathered} y_0=11 \\ \frac{x_0}{6}=\frac{y_0}{11}\Rightarrow x_0=6 \end{gathered}[/tex]Then, the laws of motion are:
[tex]\begin{gathered} y(t)=11+4\cdot t \\ x(t)=6+v_x\cdot t \end{gathered}[/tex]We now calculate the instant of time when y = 45 ft. Using the law of motion of the woman:
[tex]\begin{gathered} 45=11+4\cdot t \\ 34=4\cdot t \\ t=8.5\text{ sec} \end{gathered}[/tex]Again, using the equation (1):
[tex]\begin{gathered} \frac{x(8.5)}{6}=\frac{y(8.5)}{11} \\ x(8.5)=\frac{6\cdot45}{11} \\ 6+v_x\cdot8.5=\frac{270}{11} \\ 8.5v_x=\frac{204}{11} \\ v_x=\frac{24}{11}\text{ ft/sec} \end{gathered}[/tex]AyA(-5,6)B (3,6)D(-5,-1)C(3,-1)-20-laFind the area of the rectangle ABCD.B. 72 square unitsA. 40 square unitsC. 56 square unitsD. 36 square units
Given:
Given a rectangle with coordinates A(-5, 6), B(3, 6), C(3, -1) and D(-5, -1).
Required: Area of rectangle ABCD
Explanation:
First, find the length and width of the rectangle.
[tex]\begin{gathered} \text{ Length, }DC=\sqrt{(-5-3)^2+(-1-(-1))^2} \\ =\sqrt{(-8)^2+0^2} \\ =8 \\ \text{ Width, }BC=\sqrt{(3-3)^2+(6-(-1))^2} \\ =\sqrt{0^2+7^2} \\ =7 \end{gathered}[/tex]The are of the rectangle is
[tex]\begin{gathered} A=\text{Length}\times\text{Width} \\ =8\times7 \\ =56 \end{gathered}[/tex]Option C is correct.
Final Answer: Rectangle ABCD has area 56 square units.
Restrict the domain of the function so that the function is a one-to-one function and has an inverse. Find the inverse function, State the domain and ranges of the function and its inverse. Explain your results.
Section 1/3 (From our Algebra 2 textbook) Solve the system of linear equations in two variables by elimination or substitution. 33. 3x + y =7 - 2x - y =9
Answer:
The solution to the given system of linear equation is;
[tex]\begin{gathered} x=16 \\ y=-41 \end{gathered}[/tex]Explanation:
Given the linear system of equation;
[tex]\begin{gathered} 3x+y=7\text{ ---------------1} \\ -2x-y=9\text{ --------------2} \end{gathered}[/tex]We want to solve the simultaneous equation by elimination.
We need to eliminate either x or y. from the given equation, we can see that by adding equation 1 and 2 together we can eiminate y;
So, let's add equation 1 and 2 together;
[tex]\begin{gathered} 3x-2x+y-y=7+9 \\ x=16 \end{gathered}[/tex]Since we have the value of x, we can use it to get y by substituting into equation 1;
[tex]\begin{gathered} 3x+y=7 \\ 3(16)+y=7 \\ 48+y=7 \\ y=7-48 \\ y=-41 \end{gathered}[/tex]Therefore, the solution to the given system of linear equation is;
[tex]\begin{gathered} x=16 \\ y=-41 \end{gathered}[/tex]Which type of angles are described in the second question?
In the first case:
The angle is an acute angle. It measures more than zero but less than 90 degrees.
Second case:
The angle is an obtuse angle. It measures more than 90 degrees but less than 180 degrees.
Third case:
The angle is a right angle. It measures exactly 90 degrees.
Fourth case:
The angle is a straight angle. It measures exactly 180 degrees.
Mcm de 2,5,10,25 grupo de valores
i don't know the answer
The denominator of a fraction is three more than the numerator
Let it be x the numerator. Then we have:
• x + 3: Denominator.
,• x + 9: Numerator increased by nine.
,• (x + 3) + 9: Denominator increased by nine.
Since the simplified result of the fraction is 13/14, we can write and solve for x the following equation.
[tex]\begin{gathered} \frac{x+9}{(x+3)+9}=\frac{13}{14} \\ \frac{x+9}{x+3+9}=\frac{13}{14} \\ \frac{x+9}{x+12}=\frac{13}{14} \\ \text{ Apply cross product} \\ (x+9)\cdot14=13\cdot(x+12) \\ \text{ Apply distributive property} \\ 14\cdot x+9\cdot14=13\cdot x+13\cdot12 \\ 14x+126=13x+156 \\ \text{ Subtract 126 from both sides } \\ 14x=13x+156-126 \\ 14x=13x+30 \\ \text{ Subtract 13x from both sides} \\ 14x-13x=13x+30-13x \\ x=30 \end{gathered}[/tex]Now, we replace the value of x into the left expression from the equation we just solved.
[tex]\begin{gathered} \text{ Original fraction }=\frac{x+9}{(x+3)+9} \\ \text{ Original fraction }=\frac{30+9}{30+3+9} \\ \text{ Original fraction }=\frac{39}{42} \end{gathered}[/tex]Therefore, the original fraction is 39/42.
Catherine drives to school each day and lives 5 miles away. After school, she drives to Kroger , which is 2 additional miles away from her house. Then she heads home and studies for a test before having dinner. Sketch a graph showing Catherine's distance from her home throughout the day.
The total distance covered by catherine is 10 miles as the problem says, " Catherine drives to school each day and lives 5 miles away. After school, she drives to Kroger , which is 2 additional miles away from her house. Then she heads home and studies for a test before having dinner".
What is distance?Distance is defined as an object's total movement without regard for direction. Distance can be defined as how much ground an object has covered regardless of its starting or ending point. The magnitude or size of displacement between two positions is defined as distance. The distance between two points differs from the distance traveled between them. The total length of the path traveled between two points is referred to as the distance traveled. Travel distance is not a vector. Distance refers to "how much ground an object has covered" while moving, whereas displacement refers to how far an object is out of place. Displacement is a Vector quantity, whereas distance is a Scalar quantity.
Here,
The total distance from home to school=5 miles
She goes to kroger that is 2 miles from her home,
so, 5-2=3 miles
So she travels 3 miles back from school.
Then she goes 2 miles from kroger to home.
5+3+2=10 miles
According to the problem, Catherine's total distance traveled is 10 miles "Catherine lives 5 miles away and drives to school every day. She drives to Kroger after school, which is two miles away from her house. She then returns home to study for a test before eating dinner ".
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What is the equation in slope -intercept form , of the line that is parallel to the guven line and passes through the point (0, 12
Answer:
A. y=-5+12
Step-by-step explanation:
It asks for slope intercept form which is y=mx+b. This matches the first option but not the last.
First you can rewrite the given equation (10x+2y=-2) in slope intercept form. That will give you y=-5x=1. (in the slope intercept form the number in front of the X is ur slope and the last number is ur Y intercept).
The question says that ur line is parallel to the given equation line. This means that they have the same slope. In your rewritten equation, y=-5x=1, the slope is -5 because it is in front of the X. A is the only option with -5 in the slope position.
All options are eliminated now but in case u want to know, when it tells you that the line passes through (0,12) that means the X intercept is 12. Because 0 is the x axis, and 12 is the Y. Y intercept just means the point where your line touches the Y axis.
Y intercept goes at the end and that also matches your first equation.
The equation for the motion of an object with constant acceleration is d=vt+0.5at2where d is distance traveled in ft, v is starting velocity in ft/s, a is acceleration inft/s2, and t is time in seconds. A racecar begins with a velocity of 200 ft/s andaccelerates at 100 ft/s2.8Write an expression for the distance the car travels after t seconds.
Replacing the values in the equation, we have:
D(t) = (200 ft/s)*t + 0.5*(100 ft/s2)*t^2
D(t) = (200 ft/s)*t + (50 ft/s2)*t^2 (Multiplying)
The answer is:
D(t) = (200)*t + (50)*t^2 (Distance in ft)
What does -(-82) mean and my teacher said evaluate too
Answer:
82
Step-by-step explanation:
it means minus of minus 82. minus times minus equals to plus so the given number is a positive number.
What is the perpendicular slope to your line? I got the Slope along with the slope-intercept. but I keep getting 0.33333 (etc) for the perpendicular and i dont know if it right tells me to show all my work
The perpendicular slope of the given line is -1/3.
What is a perpendicular?In elementary geometry, two geometric objects are perpendicular if they intersect at right angles.The squareness condition can be represented graphically using the squareness symbol ⟂.Can be defined between two lines, between a line and a plane, and between two planes.Two perpendicular lines make a right angle.The word "perpendicular" means "right angle".This is because when two straight lines intersect, they form a right angle.Vertical lines can point in any direction.
Slope formula = y₂-y₁ / x₂₋x₁Now, insert values in the formula and calculate as follows:
Slope = y₂-y₁ / x₂₋x₁Slope = -1 -3 / 4 - (-8)Slope = -4/12 = -1/3Therefore, the perpendicular slope of the given line is -1/3.
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PLEASE HELP ASAP! I am struggling fr rn
Answer:
1. -8
2. -4
3. 17
Step-by-step explanation:
To solve these questions, all you need to do is plug in the number into the function.
1. (2)² - 4(2) - 4
= 4 - 8 - 4
= -8
2. (4)² - 4(4) - 4
= 16 - 16 - 4
= -4
3. (-3)² - 4(-3) - 4
= 9 + 12 - 4
= 17
2 cubed x what x 5 = 120
please i really need help
Answer:
2x3x5=120
Step-by-step explanation:
Answer:
30 is the missing number.
Step-by-step explanation:
The equation is,
→ 2³ × x × 5 = 120
Then the value of x will be,
→ 2³ × x × 5 = 120
→ 8 × x × 5 = 120
→ x × 40 = 120
→ x = 120/40
→ [ x = 30 ]
Hence, the value of x is 30.
Solve: -8 + | 1 + 9x | ≤ 2
Answer:
-11/9 and 1
Step-by-step explanation:
Simplify the expression: 2-5-(2/3
6
1
12
5-(²/3 + 10)
Answer:
you can get back to you on that date is
Step-by-step explanation:
yay I will get back to you on that date is the family
If you would like to make $2283 in 9 years, how much would you have to deposit in an account that pays simple interest of 5%
To solve this question, we would use the formula of simple interest.
[tex]\begin{gathered} S\mathrm{}I=\text{PRT} \\ s\mathrm{}i=\text{simple interest} \\ p=\text{ principal} \\ r=\text{rate} \\ t=\text{time} \end{gathered}[/tex]So the given data are
[tex]\begin{gathered} p=\text{?} \\ s\mathrm{}i=2283 \\ t=9 \\ r=5\text{ \%=0.05} \end{gathered}[/tex]We would need to find the principal
[tex]\begin{gathered} 2283=p\times0.05\times9 \\ 2283=0.45p \end{gathered}[/tex]Divide both sides by the coefficient of p
[tex]\begin{gathered} \frac{2283}{0.45}=\frac{0.45p}{0.45} \\ p=5073.33 \end{gathered}[/tex]In order to make an interest of 2283 in 9 years, you would have to save $5073.33 now
Estimate the answers to the following calculations by rounding each number to a 1 decimal place and then adding them together. 12.55 and 1.74 = 30.38 and 5.49 = 19.16 and 11.42 =
Answer:1.7
Step-by-step explanation:
One Decimal Place Rule #1: If the last digit in 1.74 is less than 5, then remove the last digit.
One Decimal Place Rule #2: If the last digit in 1.74 is 5 or more and the second to the last digit in 1.74 is less than 9, then remove the last digit and add 1 to the second to the last digit.
One Decimal Place Rule #3: If the last digit in 1.74 is 5 or more and the second to the last digit in 1.74 is 9, then remove the last digit, make the second to last digit 0, and add 1 to the number to the left of the decimal place.When rounding 1.74 to one decimal place we use
One Decimal Place Rule #1. Therefore, the answer to "What is 1.74 rounded to 1 decimal place?" is:
The estimated answers by rounding each number to a 1 decimal place and then adding them together are 14.3, 35.9, 30.6, respectively.
Here are the estimated answers to the following calculations:
12.55 and 1.74 rounded to 1 decimal place are 12.6 and 1.7. The sum is 14.3.
30.38 and 5.49 rounded to 1 decimal place are 30.4 and 5.5. The sum is 35.9.
19.16 and 11.42 rounded to 1 decimal place are 19.2 and 11.4. The sum is 30.6.
The sum of all three calculations is 14.3 + 35.9 + 30.6 = 80.8.
To estimate the answers, we simply rounded each number to 1 decimal place. This means that we lost some precision, but the overall accuracy of the estimates is still good. For example, the actual sum of 12.55 and 1.74 is 14.29, which is very close to our estimate of 14.3.
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Given that 1+i is a root of the equation
x³ + 2x² + λx + μ = 0,
(a) find the values of the real constants λ and μ,
(b) find all the other roots of the equation.
[10]
(a) The values of the real constants λ and μ are -6 and 8, respectively.
(b) The roots of the equation are (1 + i), (1 - i), and -4.
We are given an equation. The equation is cubic in nature. It means the equation has three roots. The equation is given below.
x³ + 2x² + λx + μ = 0
One of the roots of the equation is given to us. The known root is "1 + i". The given root is a complex root. We know that complex roots occur in conjugate pairs. So, another root of the equation is "1 - i". Let the third root be represented by the variable "a". We can form the factors as given below.
[x - (1 + i)][x - (1 - i)](x - a) = 0
[x² - x(1 - i) - x(1 + i) + (1 + i)(1 - i)](x - a) = 0
[x² - x + ix - x - ix + (1² - i²)](x - a) = 0
[x² - 2x + (1 + 1)](x - a) = 0
(x² - 2x + 2)(x - a) = 0
x³ - ax² - 2x² + 2ax + 2x - 2a = 0
x³ - (a + 2)x² + (2a + 2)x - 2a = 0
This equation must be the same as the given equation. Now we will compare the coefficients of different powers of "x".
First, we compare the coefficient of x².
2 = -(a + 2)
a + 2 = -2
a = -4
Now, we compare the coefficient of x.
λ = 2a + 2
λ = 2*(-4) + 2
λ = -8 + 2
λ = -6
Now we compare the constant terms.
μ = -2a
μ = -2*(-4)
μ = 8
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Not equivalent to 3x -6
The equivalent equation for 3x - 6 is 3(x - 2).
What is equation?Equation: A statement that two variable or integer expressions are equal. In essence, equations are questions, and the motivation for the development of mathematics has been the systematic search for the answers to these questions.
Given equation:
3x - 6
Take 3 as common from both the term,
= 3(x - 2)
Therefore, the equivalent equation for 3x - 6 is 3(x - 2).
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Write the quadratic equation in Standard From whose graph has the following: x-intercepts: 2, 5 passes through the point (4, -2) Group of answer choices
The equation of the quadratic equation is y = x² - 7x + 10.
What is x-intercept of a graph?
The points where a line crosses x- axis and y- axis are known as the x-intercept and the y-intercept, respectively.
Given that the x-intercepts of the graph are 2 and 5.
If a and b x-intercepts of a graph, then the equation of the graph is y = A(x -a)(x - b).
Assume the equation of the quadratic equation will be y = A(x -2)(x - 5).
The graph is passes through the point (4, -2).
Putting x = 4 and y = -2 in the equation y = A(x -2)(x - 5)
-2 = A(4 -2)(4 - 5)
-2 = -2A
A = 1
The equation of the quadratic equation is y = (x -2)(x - 5)
y = x² - 7x + 10.
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A town doubles its size every 17 years. If the population is currently 3,070, what will the
population be in 68 years?
Answer: 49120 would be your answer!
multiply by 2 four times.
QUICK ANSWERS PLEASE!37. What common angle do AACF and ABCG share?BСAFGA. ZCB. ZFC. ZAD. ZB
Explanation
as we can see in the picture, after drawing the angles, we can observe the common angles is
[tex]A)\angle C[/tex]I hope this helps you
A restaurant leaves comment cards on all of its tables to learn about customer satisfaction. Each comment card is a brief survey that customers can fill out if they choose to.
To learn about customer satisfaction, a restaurant places comment cards on each table. Each comment card contains a brief survey that customers can complete if they want to participate in the voluntary response sample.
What is meant by voluntary sample?Voluntary sampling occurs when researchers seek willing subjects for their study. You can solicit volunteers in person, online, through open postings, and a variety of other methods. When using voluntary sampling, a researcher frequently neglects to manage sample makeup.A voluntary response sample is a sample made up of volunteers. When compared to a random sample, these types of samples are almost always biased.A voluntary response sample is made up of people who freely chose to participate in the sample group. Those who want to participate in a voluntary response sample usually do so because they are interested in the survey's topic.
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The radius of a circle is 3 centimeters. What is the circumference?Give the exact answer in simplest form. ___ centimeters (pi, fraction)
ANSWER
[tex]18\frac{6}{7}[/tex]SOLUTION:
The formula for circumference is 2 * pi * r
the value of pi can be estimated as 3.14 or 22/7
Using the formula
[tex]\begin{gathered} 2\text{ }\times\text{(}\frac{22}{7}\text{)}\times3 \\ \frac{132}{7} \\ 18\frac{6}{7} \end{gathered}[/tex]A clerk sold three pieces of one type of ribbon to different customers. One piece was 8 3/8 yards long, another was 6 4/5 yards long, and the third was 15 3/4 yards long. What was the total length of that type of ribbon sold?
EXPLANATION
If one piece was 8 3/8 yards long, another 6 4/5 and the another 15 3/4 we need to compute the total length as shown as follows:
The total length was:
[tex]\text{Total length=8}\frac{3}{8}+6\frac{4}{5}+15\frac{3}{4}=30\frac{37}{40}=\frac{1237}{40}=30.92\text{ yards long}[/tex]Need help solving! I got 4x+17 with a remainder of 42 not sure if it is correct!
Given:
[tex]\frac{4x^2+5x-9}{x-3}[/tex]Using synthetic division we get,
Hence, the answer is,
[tex]4x+17+\frac{42}{x-3}[/tex]