Slope m is positive when
x₁≥ -2
y₁ ≥ -5
Define slope.Slope, usually referred to as rise over run, is the "steepness" of the line. By dividing the difference in y values between two points by the difference in x values, we may determine slope. The ratio of the increase in elevation between two points to the run in elevation between those same two points is referred to as the slope. A line that is moving up will have a positive slope, and a line that is moving down will have a negative slope, if you view the line from left to right.
Given,
Point (-2. -5)
Slope = [tex]\frac{y_{1}-(-5) }{x_{1}-(-2) }[/tex]
Slope = [tex]\frac{y_{1}+5 }{x_{1}+2 }[/tex]
Slope m is positive when
x₁≥ -2
y₁ ≥ -5
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Under his cell phone plan, Angel pays a flat cost of $35 per month and $5 per gigabyte. He wants to keep his bill under $50 per month. Write and solve an inequality which can be used to determine x, the number of gigabytes Angel can use while staying within his budget.
Answer:
4 gigabytes
Step-by-step explanation:
$55-$35 =$20
Under $55 = less than (<) $55
According to given question we have,
$35 + $5 × g < 55
35 + 5g < 55
compare like terms and simplify we get,
5g < 55 - 35
5g < 20
g < 20/5
g < 4 gigabytes
Inequality: 5x + 35 <50
Answer: x < 3
Calculate rates (backwards)
If pipe costs $30, at $6 / m, how many metres would you get?
Answer:
5 m
Step-by-step explanation:
$30 divided by $6 a m
30/6=5 m
Cheyenne is playing a board game. Her score was −175 at the start of her turn, and at the end of her turn her score was −325. What was the change in Cheyenne’s score from the start of her turn to the end of her turn? How did you determine your answer?
Enter the correct answers in the boxes.
points
I subtracted
from
.
Answer: -150
Step-by-step explanation:
To find the change in the score we need to find the difference between the two scores. To do this easily, we can add 175 to -325.
-325 + 175 = -150
By doing this we get the difference and the answer to the question.
Answer: -150
Step-by-step explanation: I subtracted from -325.
I need some help... I am very confused.
The base of the triangle shown is 12 millimeters
What is an equation?An equation is an expression that can be used to show the relationship between numbers and variables.
Given that:
A is the area of the triangleb is the base of the triangleh is the heightb = 2A/h
For the triangle, A = 36 mm², h = 6 mm
Substituting:
b = 2(36)/6
Simplifying gives:
b = 12 mm
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After a 5-hour flight from Newark, Harry arrived in
Denver at 2:30 pm. If the time in Newark is 2 hours
later than the time in Denver, what was the time in
Newark when Harry began the flight?
E. 10:30 am
F. 11:30 am
G. 12:30 pm
H. 3:30 pm
We need to know how to solve different time zone problems to solve this problem. The time in Newark when Harry began the flight is 11:30 am, option (F) is the correct answer.
In this question we have two cities Newark and Denver that have a time difference of 2 hours. Newark is 2hrs later than the time in Denver. The flight from Newark to Denver takes 5 hrs. Harry arrived at 2:30 pm, we need to find out at what time the flight left Newark. If we subtract 5 hrs from 2:30 pm we get 9:30 am, so when the flight left Newark it was 9:30 am in Denver, since the time in Newark is 2 hrs later than Denver, so it was 11:30 am in Newark.
Therefore the time when the flight left Newark is 11:30 am, option (F) is the correct answer.
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The prime factor tree for 6 is shown
below.
Complete the prime factor tree for 15 and
use it to help you find the lowest common
multiple (LCM) of 6 and 15.
2
6
3
15
Answer: 3
Step-by-step explanation:
6 - 2, 3
15- 3, 5
The unit cost, in dollars, to produce bins of cat food is $18 and the fixed cost is $30000. The price-demandfunction, in dollars per bin, is p(x) = 568 - 2xFind the cost function.C(x) =Find the revenue function.R(x) = Find the profit function.P(x) = 568 – 2xAt what quantity is the smallest break-even point?
The smallest breakeven point attains at 75.
A formula or equation that describes the behavior of specific sources of income when it is plotted on a graph is called a revenue function.
The cost function calculates the lowest cost of producing a specific level of output at some fixed factor prices.
A relationship that demonstrates the difference that results from subtracting the cost function from the revenue function is called a profit function.
Here, the Price/Demand Function is presented as
P(x) = 568 - 2x
Which means that when there is a demand for x units of cat food, the price will be set at 568 - x for each unit.
Let's now consider the revenue resulting from this demand, or x units.
Revenue = Demand * Price per unit
R(x) = x * (568-2x)
= 568x – 〖2x〗^2
Now let us Evaluate the Cost Function
Cost = Variable cost + Fixed Cost
Variable cost = cost per unit * number of units
= 18*x
= 318
Fixed Cost = 30000 as given in the problem.
Hence
Cost Function C(x) = 18x + 30000
Now let’s find the Profit Function
Profit = Revenue - Cost
P(x) = R(x) - C(x)
568x - 〖2x〗^2 – (18x + 30000)
568x -〖 2x〗^2 – 18x + 30000
-〖 2x〗^2 + 550x - 30000
Finding the quantity at which we reach break-even point is the next step.
At break-even point, we understand this Profit = 0
Hence P(x) = 0
-〖 2x〗^2 - 550x + 30000 = 0
Dividing both sides by -2 we get
X2 – 275x + 15000 = 0
Now we have to find the factors of 15000 whose sum is 275.
Now we have to solve the above quadratic equation using splitting the middle term method.
X2 – 275x + 15000 = 0
X2 – 200x - 75x + 15000 =0
X(x-200) - 75 (x-200) = 0
(x-75) (x-200) = 0
Either (x - 75) = 0 or (x-200) = 0, therefore
(x-75) = 0 = x =75
(x-200) = 0 x =200
Smallest of which is 75.
As a result, 75 units are required to reach the break-even point.
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URGENT!! ILL GIVE
BRAINLIEST! AND 100 POINTS
A package of 6 pairs of insulated socks cost 49.74 What is the unit price of the pairs of socks?
Grace works as a salesperson at an electronics store and sells phones and phone accessories, and makes a fixed commission for each phone sale and a different fixed commission for each accessory sale. Yesterday Grace sold 18 phones and 21 accessories and made a total commission of $204. Today she sold 6 phones and 14 accessories and made a total commission of $82. Determine the price of each phone and the price of each accessory.
What's the commission for each phone and the commission for each accessory?
The commission for each phone exists $2 and the commission for each accessory exists $9.
How to find the price of each phone and the price of each accessory?Given: Commission on 18 phones and 21 accessories = $204
commission on 6 phones and 14 accessories = $82.
Let the commission of each phone be P and the accessory be A.
From the given information, we get
18P + 21A = 204
6P + 7 A = 68 -----(1)
6P + 14 A = 82 ------(2)
By substitution of (1) in equation (2),
⇒ 68 - 7A + 14A = 82
simplifying both of the above equations we get
⇒ 7A = 14
⇒ A = 2
The value of A = 2.
Commission of each accessory = $2
To estimate the commission on each phone:
6P + 7 x 2 = 68
⇒ 6P = 54
⇒ P = 9
Commission of each phone = $9
Therefore, the required answers are 2 and 9.
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Dana has 12 jelly beans that she wants to divide among 3 friends. Select the three statements that describe how Dana should divide the jelly beans.
Answer:
Step-by-step explanation: 12/3 is 4
He following cards are dealt to three people at random, so that everyone gets the same number of cards. what is the probability that everyone gets a red card?
The probability that everyone will get a red card is 0.5.
What probability exactly is?Probability is a branch of mathematics that deals with numerical representations of the probability that an event will happen or that a statement is true.The probability of an event is a number between 0 and 1, with 0 roughly denoting impossibility and 1 denoting certainty.The probability is the likelihood that something will happen, to put it simply.The likelihood or likelihood of various outcomes can be discussed when we don't know how an event will turn out.The study of events that fit into a probability distribution is known as statistics.So, the probability that everyone gets a red card:
Probability formula: P(E) = Favourable events/Total number of eventsAs cards are distributed to 3 people, divide both favorable events and total events by 3.Then,
P(E) = Favourable events/Total number of eventsP(E) = (26/3)/(52/3)P(E) = 26/3 × 3/52P(E) = 26/52P(E) = 0.5Therefore, the probability that everyone will get a red card is 0.5.
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Samuel wants to save enough money to buy a new couch, but isn’t sure which bank’s savings account he should sign up for. Wells Fargo has a yearly interest rate of 6%. Chase has an interest rate of 0.5% compounded monthly. If Samuel deposits $3000 at the beginning of the year and makes no additional deposits or withdrawals, which bank would have the higher balance after one year?
wells Fargo would have a higher balance after one year
Step-by-step explanation:
wells Fargo would have a higher balance after one year
The residents of a city voted on whether to raise property taxes. The ratio of yes votes to no votes was 5 to 4. If there were 2348 no votes, what was the total
number of votes?
Answer:
2935
Step-by-step explanation:
if you divide the total of no votes (2348) to 4 you will get 587
587 x the number of yes votes (5)
would be 2935
Use the following variables for #'s
(3-5):
f= -6 g= 7 h=9
4) 5-f
The value of the expression 5 - f is 11.
An expression, often known as a mathematical expression, is a finite collection of symbols that are well-formed in accordance with context-dependent principles.
A variable is a symbol and placeholder for any mathematical object. In particular, a variable may represent a vector, a number, a function, a matrix, the argument of a function, a set, or an element of a set.
We have the value of the following variables,
f = - 6,
g = 7 and,
h = 9
Now consider the expression 5 - f,
Substituting the value of f in the expression we get,
5 - f = 5 - ( - 6 )
5 - f = 5 + 6
5 - f = 11
Therefore, the value of 5 - f is 11.
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4) At Rory’s school, students must join one after school club. Based on the data in Graph #2, which club attracted about 30% of students?
x
A. yearbook
B. art
C. drama
D. hiking
E. running
F. science
The hiking club attracted about 30% of the students as per the given graph. which is the correct answer would be option (D).
What is a graph?A graph can be defined as a pictorial representation or a diagram that represents data or values.
At Rory’s school, students must join one after-school club. Based on the data in the given graph,
According to the given graph
We can see that hiking and science clubs together attracted about 50% of students.
Here as a comparison to hiking and science clubs, we found that the hiking club is more attractive than the science club which is approximant about 30% of the students.
Therefore, the hiking club attracted about 30% of the students.
Hence, the correct answer would be an option (D).
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i need help with the first question in this picture
Initial price of the TV = $899
discount in % = 25 % = 0.25
First, we will find the amount discounted:
[tex]\begin{gathered} Amount\text{ discounted = }25\text{ \% }\times\text{ 899} \\ Amount\text{ discounted = }0.25\text{ }\times\text{ 899} \\ Amount\text{ discounted = \$224.75} \end{gathered}[/tex]sales price after the discount was removed:
[tex]\begin{gathered} sales\text{ price = }initial\text{ price - amount discounted} \\ sales\text{ price = 899 - 224.75} \\ sales\text{ price before }Tax\text{ = \$674.25} \end{gathered}[/tex][tex]\begin{gathered} \text{Sales tax = 8.125 \% = 0.08125} \\ \text{Tax = sales price before tax }\times\text{ sales tax} \\ \text{Tax = 674.25 }\times\text{ 0.08125} \\ \text{Tax = \$}54.78 \end{gathered}[/tex][tex]\begin{gathered} \text{Sales price with tax = sales price before tax + Tax} \\ \text{Sales price with tax = 674.25 + 54.78} \\ \text{Sales price with tax = \$729.03} \end{gathered}[/tex]6.
Select all the conditions for which it is possible to construct a triangle.
A. A triangle with angle measures 60 degrees, 80 degrees, and 40 degrees
B. A triangle with side lengths 4 cm, 5 cm, and 9 cm
C. A triangle with side lengths 4 cm, 4 cm, and 7 cm
D. A triangle with side lengths 5 cm and 12 cm and a 90 degree angle.
E. A triangle with 2 right angles.
Help idmeadiitly
3. Write an equation where the left side is your power of 10 times n and the right side is the result of multiplying 0.1515... by that power. (2 points)
(10)n = 10(0.11515).
4. Write the original equation, n = 0.1515... underneath your equation from question 3. Then subtract the equations. Show your work. (2 points)
ill give 100 points answer fast and brainlist
The required equation in which case the left side is the power of 10 times n and the right side is the result of multiplying 0.1515 by 10 is; (10)n = 10(0.1515).
The resulting equation from the subtraction is therefore; 9n = 9 (0.1515).
What is the result of the subtraction of both equations?3. It follows from the task content that the equation represented by the statement; "the left side is your power of 10 times n and the right side is the result of multiplying 0.1515".
Hence, the algebraic expression which represents the situation is; (10)n = 10(0.1515).
4. Also, by subtracting the equation n = 0.1515 from the equation above; we have;
(10)n = 10(0.1515).
-
n = 0.1515
Therefore, the resulting equation from the subtraction is;
(10n - n) = 10(0.1515) - 0.1515
9n = 9 (0.1515).
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Two angles form a linear pair. The measure of one angle is z and the measure of the other angle is 2.4 times z plus 10°. Find the measure of each angle.
Two angles form a linear pair.
so, the sum of the angles are 180
the measure of the angles are z and (2.4 * z + 10)
so,
z + (2.4 * z + 10) = 180
solve for z
so,
z + 2.4 * z + 10 = 180
3.4 z = 180 - 10
3.4 * z = 170
divide both sides by 3.4
so, z = 170/3.4 = 50
so, the angles are 50 and 130
- 1/4 x (- 4/3) as a fracction
Answer: the answer is x/3
Step-by-step explanation:
When you write the equivalent algebraic expression f8 for f² f6, why do you add the exponents?
The equivalent algebraic expression f⁸ for f² f⁶ is because product of power law states to add the exponents.
What is algebraic expression?In mathematics, an expression that incorporates variables, constants, and algebraic operations is known as an algebraic expression (addition, subtraction, etc.).
Algebraic expression types:
Number ExpressionExpression of a BinomialExpression of a Polynomiallet,
RHS = f² f⁶
RHS = f²⁺⁶
RHS = f⁸ = LHS
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Identify the reason that would be used to justify step 2 in the proof below.
Converse of the Consecutive Interior Angle Theorem
Corresponding Angles Postulate
Alternate Exterior Angle Theorem
Vertical Angles Theorem
The reason that would be used to justify step 2 in the proof below is: Corresponding Angles Postulate (Option B).
What is A corresponding Angle Postulate?Congruence and likeness tests in geometry require comparing corresponding sides and angles of polygons. In these tests, each side and angle of one polygon are matched with a side or angle of the second polygon, with care taken to maintain the order of adjacency.
A mathematical proof is an inductive explanation for a mathematical assertion that demonstrates that the provided assumptions logically ensure the conclusion.
There are several methods for demonstrating anything. There are three of them:
direct proof, proof by contradiction, and proof by induction. We'll go through each of these proofs and when and how they're utilized.Learn more about Corresponding Angles:
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Carla has already written 10 pages of a novel. She plans to write 15 additional pages per month until she is finished. Write and solve a linear equation to find the total number of pages written at 5 months.
(show as much details upon answering)
Answer:
linear equations;15m+10=w
15 pages written for every month for 5 months plus the 10 pages she has already written is equal to the total number of pages written in 5 months m=number months written in this case it is 5 months.
w=number of pages written in 5 months 15(5)+10=w
75+10=w
85 Pages written=w
will have written 85 Pages in 5 months
Classify the TriangleThe answer choices are : equilateral, scalene or isosceles
The three sides and three angles of the given triangle are given to be equal.
An equilateral triangle has three sides of equal length and three equal angles.
So, the given triangle is equilateral.
Wendy has a negative balance in her checking account. Her balance is -$13.
If Wendy deposits $60, then buys 4 notebooks for 2 dollars each, how much money would Wendy have in her account after the purchases?
Find the equation of the straight line passing through the point (3, 3)
which is perpendicular to the line
y=-}x-4
Answer:y=1/2x-41/2
Step-by-step explanation: First we have to find the slope of the line that's given, y - 4 = 2(x+2). The slope is 2 (if we multiply 2*x we would get 2x and the 2 is the slope).
Two lines are perpendicular if their slopes are negative reciprocals. So if the first line has a slope of 2, a perpendicular line would have a slope of -1/2
Now we have to find the equation for the line with slope of -1/2 that passes through the point (3,3). If we use the point-intercept form we can write it as:
y = mx + b
Since the slope is -1/2 and we know that when x = 3, y = 3 (since the line passes through that point) we can substitute the values and solve for b
y = mx+b
3 = -1/2 *3 + b
3 = -3/2 + b
3 = -11/2 + b
41/2 = b
Now we can write the equation as
y = -1/2x + 41/2
kelly sold 35 books at £1.40 each. 28 bracelets at £1.50 each. some badges at 80p each. She got a total of £115. Work out how many badges Kelly sold
Answer:
the answer is 30 !! :)
Step-by-step explanation:
115-(35*1.40)-(28*1.50)= 24
24/.8 = 30
∆GET ≅ ∆ABS. AB= 10, BS=13, AS=18, and GT=4x-8, what is the value of 'x'?
The value of x for GT is 6.5 .
What is the congruence of triangles?
If all three corresponding sides and all three corresponding angles are equal in size, two triangles are said to be congruent. Slide, twist, flip, and turn these triangles to create an identical appearance. They are in alignment with one another when moved.
Given, ΔGET ≅ ΔABS
Following the statement that corresponding sides of congruent triangles are congruent, we have:
GE = AB, ET = BS and GT = AS -(i)
AB = 10, BS = 13, AS = 18, GT = 4x - 8 -(ii)
Comparing (i) and (ii) we have, 4x - 8 = 18 ⇒ 4x = 26 ⇒ x = 26/4 = 6.5
Thus, the value of x for GT is 6.5 .
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A 25-foot ladder is leaning against the side of a building and is positioned such that the base of the ladder is 15 feet from the base of the building. How far above the ground is the point where the ladder touches the building?
Let us use a diagram to demonstrate the event .
From the diagram we are asked to find the value h. The value h can be found using pythagora's theorem.
[tex]\begin{gathered} h^2=25^2-15^2 \\ h^2=625-225 \\ h^2=400 \\ \text{square root both sides} \\ h=\sqrt[]{400} \\ h=20\text{ ft} \end{gathered}[/tex]