Answers
The solution for given linear inequalities is (-0.5,4.25) from the given graph.
What are linear inequalities?
Inequality represents the mathematical expression in which both sides are not equal. If the relationship makes the non-equal comparison between two expressions or two numbers, then it is known as inequality in Maths. In this case, the equal sign “=” in the expression is replaced by any of the inequality symbols such as greater than symbol (>), less than symbol (<), greater than or equal to symbol (≥), less than or equal to symbol (≤) or not equal to symbol (≠). The different types of inequalities in Maths are polynomial inequality, rational inequality, absolute value inequality.
The symbols ‘<‘ and ‘>’ express the strict inequalities and the symbols ‘≤’ and ‘≥’ denote slack inequalities. A linear inequality seems exactly like a linear equation but there is a change in the symbol that relates two expressions.
e.g. y>x+2
Now,
As we know the solution for the lines which intersect at a certain point is that point or the coordinates of that point i.e. (-0.5,4.25).
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Related Questions
Write each proof. Finish the table.
Answers
The ASA and AAS theorems are used in the proof as explained below for each given statements.
How to Write a Proof?A proof is a logical argument that demonstrates the truth of a mathematical statement.
The proof that can be used to prove each given statements are demonstrated below.
14. Proof for ∆UVY ≅ ∆XVW:
Statement Reason
1. V is the midpoint of YW. 1. Given
2. UY || XW 2. Given
3. YV ≅ WV. 3. Def. of midpoint
4. <UYV ≅ <XWV. 4. Alternate <s theorem
5. <UVY ≅ <XVW 5. Vertical<s theorem
6. ∆UVY ≅ ∆XVW 6. ASA
15. Proof for ∆MSP ≅ ∆RQP:
Statement Reason
1. MS ≅ RQ 1. Given
2. MS || RQ 2. Given
3. <MSP ≅ <RQP. 3. Alternate <s theorem
5. <MPS ≅ <QPR 4. Vertical<s theorem
6. ∆MSP ≅ ∆RQP 6. AAS
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Pls Help fast 50 points
Answers
1. The function for this problem is given as follows: f(x) = x - 3.
2. The numeric value of the function at x = 2 is of f(2) = -1.
How to find the numeric value of a function or of an expression?To find the numeric value of a function or of an expression, we replace each instance of the variable in the function or in the expression by the value at which we want to find the numeric value.
We define the function in this problem as follows:
f(x) = x - 3.
The numeric value at x = 2 is found replacing the lone instance of 2 by 2, hence:
f(2) = 2 - 3
f(2) = -1.
Missing InformationWe attribute the function in this problem as f(x) = x - 3.
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yesterday, you typed 8 pages in 48 minutes. Today, you typed 20 pages in 2 hours. plot the two points where x is the time in minutes and y is the number of pages
Answers
A plot of the two points, where x is the time in minutes and y is the number of pages is shown in the graph attached below.
How to plot the points?First of all, we would convert the value of time in hours to minutes as follows;
Conversion:
60 minutes = 1 hour.
x minutes = 2 hours.
Cross-multiplying, we have:
x minutes = 60 minutes × 2 hours
x minutes = 120 minutes.
In this scenario, the time in minutes would be plotted on the x-axis (x-coordinate) of the graph while the number of pages would be plotted on the y-axis (y-coordinate) of the graph.
Next, we would use an online graphing calculator to plot the points representing the time in minutes and the number of pages on a coordinate axes as shown in the image attached below.
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Write an expression that only uses multiplication and that is equivalent to x reduced by 1/8 of x
Answers
The expression that only uses multiplication and that is equivalent to x reduced by 1/8 of x is: x * (1 - 1/8).
An expression in mathematics is a combination of numbers, variables, and operations that represent a value or set of values.
The expression calculates the reduction of x by 1/8 of x by subtracting 1/8 of x from x, which is x * 1/8. By subtracting this from x, the expression calculates x reduced by 1/8 of x. The expression that only uses multiplication and that is equivalent to x reduced by 1/8 of x is:
x * (1 - 1/8).
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Given the arithmetic series: a +13 + b + 27 + ...
Show that a=6 and b=20
Answers
So here the common difference is
(27-13)/2 = 7
So b = 13+7 = 20
And a = 3-7 = 6
A first aid test has two parts, a theory test and a practical test.
The probability of passing the theory test is 0. 75
The probability of passing only one of the two parts is 0. 36
The two events are independent.
Work out the probability of passing the practical test
Answers
The probability of passing the practical test is 0.25. This is calculated by subtracting the probability of passing the theory test (0.75) from the probability of passing at least one of the two parts (0.36).
0.25
The probability of passing the practical test can be calculated by subtracting the probability of passing the theory test (0.75) from the probability of passing one of the two parts (0.36).
0.36 - 0.75 = 0.25
The probability of passing the practical test is 0.25. This is calculated by subtracting the probability of passing the theory test (0.75) from the probability of passing at least one of the two parts (0.36). The two events of passing the theory test and passing the practical test are independent, so their probabilities can be calculated separately.
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What is the relations between
[tex] \leqslant [/tex]
AXE and
[tex] \leqslant [/tex]
EXD this figure
Answers
The m∠EXD and m∠AXE are the supplementary angles.
The two angles will be linear pairs if the sum is 180° therefore, linear pair of 62° is 118°. The value of x in the figure is 113°
An angle is a geometry in plane geometry that is created by 2 rays or lines that have an identical terminus.
The identical endpoint of the two rays—known as the vertex—is referenced as an angle's sides.
01)
Two angles will be linear pairs if their sum is 180°.
If the first angle is 62° then the second will be 180° - 62° = 118°
Hence "The two angles will be linear pairs if the sum is 180° therefore, linear pair of 62° is 118°".
02)
The angle x is in the same line with supplementary angle 67° so
x = 180 - 67 = 113°.
Hence "The value of x in the figure is 113°".
03)
In the figure, AXD is a straight line, therefore,
m∠EXD + m∠AXE = 180°
Since the sum of two angles is 180° then they are called supplementary angles.
Hence "The m∠EXD and m∠AXE are the supplementary angles".
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What is the distance between the Library and Post Office?
5
5
3
2
In a City
Library
1
Restaurant
O6 units
O 4 units
O 5 units
3 units
Park
Complex
0 1 2 3 4 5 6 7
Museum
Post Office
Answers
Answer: The answer is 5 units
Step-by-step explanation:
If you plot it on a graph and what not it comes out to 5 units, going diagonally.
In a city, the distance between the library and the post office is three units. This may be calculated by counting the gaps between the two points on the grid illustrated above. The Library is in position 1 and the Post Office is in position 4, therefore the distance between them is three units.
What is distance?The amount of space between two locations is defined as distance. It is commonly measured in meters, kilometers, miles, or feet. Distance is used to compute the length of a journey, the time required to go a specific distance, and the speed of an item moving a specific distance. It may also be used to determine the dimensions of an item. In trigonometry, distance is also used to measure angles, such as the angle between two points on a circle. Distance may be present in practically every facet of our daily lives, from city distances to item sizes. Distance is an important term to grasp in both physics and mathematics.
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an indicator of reliability based on the correlations of each item in a measure with every other item is called:
Answers
Inter-Item Reliability is a measure of how consistently different items within a measure are related to each other. It is used to assess the internal consistency of a measure.
An indicator of reliability based on the correlations of each item in a measure with every other item is called: Inter-Item Reliability.
Inter-Item Reliability is a measure of how consistently different items within a measure are related to each other. This is assessed by calculating the correlations between each item and every other item in the measure.
A high level of Inter-Item Reliability indicates that all of the items in a measure are measuring the same construct, providing evidence for the validity and reliability of the measure. Conversely, a low level of Inter-Item Reliability indicates that the items in the measure may not be measuring the same construct, or that the measure may not be reliable or valid.Learn more about Inter-Item Reliability: https://brainly.com/question/13171394
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In ΔRST, r = 79 inches, t = 70 inches and ∠T=58°. Find all possible values of ∠R, to the nearest 10th of a degree
Answers
In ΔRST, the measure of angle R is 73.1°
Let us assume that r represents the opposite side of ∠R, and 't' represents the opposite side of ∠T
i.e., r = side ST and t = side RS
We know that the law of sine for triangle states that the ratio of the side length of a triangle to the sine of the opposite angle, which is the same for all three sides.
i.e., for triangle ABC,
[tex]\frac{sin~A}{a} =\frac{sin~B}{b} =\frac{sin~C}{c}[/tex]
Using sine law for ΔRST,
[tex]\frac{sin~R}{r} = \frac{sin~S}{s} =\frac{sin~T}{t}[/tex]
Consider equation,
[tex]\frac{sin~R}{r} =\frac{sin~T}{t} \\\\\frac{sin~R}{79} = \frac{sin~(58)}{70}[/tex]
79 × 0.8481 = sin(R) × 70
sin(R) = 66.99 / 70
sin(R) = 0.9571
∠R = arcsin(0.9571)
∠R = 73.1°
Thus, measure of angle R = 73.1°
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Finally, Jorge does inventory on the amount of cheese in the restaurant. He starts with Friday. That evening, 12 customers ordered cheeseburgers. Each cheeseburger uses 3/4 of a pound of cheese. The same night, 2 waiters each dropped 1.2 pounds of cheese on the ground and had to throw it away.Jorge wants to know how many pounds of cheese were used that night. He solves an equation and so does his assistant chef, Matty. Who is correct? Jorge: 12x 0.75+ 2x 1.2=13.2. Matty: (12x 0.75) + (2x 1.2 =11.4
Answers
The person who is correct is Matty: (12x 0.75) + (2x 1.2 =11.4 (second option)
Who is correct?The total pound of cheese is the total amount of of cheese used for cheeseburgers and the total amount of cheese wasted.
Total pounds of cheese = total pounds used for cheeseburgers + total cheese wasted
= (pounds of cheese needed for one cheeseburger x number of cheeseburger) + (number of waiters x pounds of cheese dropped)
= (12 x 3/4) + (1.2 x 2)
= 9 + 2.4
= 11.4 pounds
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a six foot man standing 200 feet from a tower observes the angle of elevation to the top of the tower to be 67 degrees. how high is the tower?
Answers
So, the height of the tower is approximately 363.6 feet.
You can use trigonometry to solve this problem.
If we call the height of the tower "h" and the distance between the man and the base of the tower "d", then the angle of elevation is defined as the angle between the line of sight from the observer to the top of the tower and the horizontal line.
We can use the tangent function to relate the angle of elevation to the height and distance.
tan(67) = h/d
We know that the distance between the man and the tower is 200 feet. We can use this information to find the height of the tower.
h = d * tan(67)
h = 200 * tan(67)
The height of the tower is approximately 363.6 feet.
Please note that due to the approximation of the trigonometric functions, the answer may not be exactly as calculated.
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A bookstore had 70 copies of a magazine. Yesterday, it sold 1/5 of them. Today, it sold 5/7 of what remained. How many copies does the bookstore have left?
Answers
Answer: 16
Step-by-step explanation:
1/5 x 70 = 14
70 - 14 = 56
5/7 x 56 = 40
56 - 40 = 16
Answer:
16
Step-by-step explanation:
Yesterday, the bookstore sold 1/5 of the 70 copies, which is 70 * 1/5 = 14 copies.
After selling 14 copies, the bookstore was left with 70 - 14 = 56 copies.
Today, the bookstore sold 5/7 of what remained, which is 5/7 * 56 = 40 copies.
So, the bookstore has 56 - 40 = 16 copies left.
A function is a rule that assigns each _____ exactly one ____.
Answers
Answer:
input, output
Step-by-step explanation:
A function is a rule that assigns each input exactly one output.
Some questions that have you check a list of points, a table of values, a graph or an equation, to figure out if its a function... you check to see if every x only has one y to go with it. This is what the vertical line test does also.
The table shows ordered pairs that belong to quadratic function H. What is the range of H?
Answers
For the quadratic equation -2x²+12x-13, the range is option D: All real numbers less than or equal to 5.
What is a quadratic function?
A polynomial function with one or more variables, where the largest exponent of the variable is two, is referred to as a quadratic function. It is also known as the polynomial of degree 2 since the greatest degree term in a quadratic function is of second degree.
The values for x and h(x) are given in the table.
Real numbers can be said to be all continuous values of quantity, which can be negative or positive values.
The range of h, h(x), in the table given are all real numbers.
The quadratic equation from the points in the table can be deduced as -2x²+12x-13.
The maximum of the graph is at (3,5).
For a parabola ax²+bx+c with Vertex (xv,yv) -
If a<0, then the range is f(x) ≤ yv.
If a>0, then the range is f(x) ≥ yv.
Since, a = -2, then f(x)≤ 5.
Therefore, the range values of h is f(x)≤ 5.
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DESCRIBE A SEQUENCE OF TRANSFORMATIONS THAT WILL MAP ABCD ONTO A’B’C’D’
rotate _____ degrees _____ around E, then ______ over the vertical line k.
Rotate( options )
120.
90
60
180
2 answer options
Counterclockwise
Clockwise
Options answer 3
Translate
Reflect
Rotate
Answers
Rotate 90 clockwise around E, then reflected over the vertical line K
What’s the slope and y intercept for y-5=2(x-5)
Answers
The slope and y intercept for y-5=2(x-5) is 2 and -5 respectively.
What is Linear equation ?
Linear equation can be defined as the equation in which the highest degree is one.
Given
expression
y- 5 = 2(x-5)
y - 5 = 2x - 10
y = 2x+5-10
y = 2x-5
Its in the form of y = mx+c
where m is slope
and c is y intercept.
So,
From the equation ,
we can say that m = 2 that is slope = 2 and y intercept is -5.
Therefore, The slope and y intercept for y-5=2(x-5) is 2 and -5 respectively.
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At a sale this week, a desk is being sold for $272. This is 80% of the original price.
What is the original price?
Answers
Answer:
$340
Step-by-step explanation:
You want to know the original price of a desk priced such that $272 is 80% of its original price.
Original priceWe can write the relation as an equation. If p represents the original price, then we have ...
$272 = 80% × p
p = $272/0.80 = $340 . . . . . . . divide by the coefficient of p
The original price is $340.
<95141404393>
what can go into 28 and 49
Answers
Answer:The factors of 28 and 49 are 1, 2, 4, 7, 14, 28 and 1, 7, 49 respectively
Step-by-step explanation:Some numbers have 28 and 49 as answers
A circle has a circumference of
452.16
452.16452, point, 16 units.
What is the radius of the circle?
Answers
The radius of the circle is approximately =71.96 units
What is circle ?Circles can be defined by their radii and all points on the circumference of a circle are equidistant from the center. Circles are widely used in mathematics, science and engineering for various applications, including modeling and solving problems in geometry.
The formula for the circumference of a circle is 2 * pi * r, where r is the radius.
Given the circumference, we can solve for the radius:
452.16 = 2 * pi * r
r = 452.16 / (2 * pi)
The radius of the circle is approximately 71.96 units.
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A survey asked a random sample students if they estimated they spent more or less than an hour a day on social media.
Answers
According to 43% of eighth graders, they spend more than an hour a day on social media.
What do you meant by Percentage ?A ratio stated as a fraction of 100 is what is meant by the term %. Students were asked in a poll if they thought they spent more or less time per day on social media.more less , 7th 12 14 , 8th 20 ,26 . The number of students who responded "more" must be divided by the total number of 8th graders polled in order to arrive at the %, which must then be multiplied by 100.
This percentage is the proportion of 8th graders who believe they spend more than an hour each day on social media.Twenty of the forty-six students (20+26) responded "more," or roughly 43.48 percent. As a result, 43% of eighth graders claim to spend more than an hour every day on social media.
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A woman wants to measure the height of a nearby tower. She places a 7ft pole in the shadow of the tower so that the shadow of the pole is exactly covered by the shadow of the tower. The total length of the tower's shadow is 182ft, and the pole casts a shadow that is 4.75ft long. How tall is the tower? Round your answer to the nearest .
Answers
The fact that you have called the back is wrong so it will be so.
Priya thinks the answers to these two questions will be different. This month, a website had a 12% decrease in traffic. If there were 250 visitors last month, how many visitors were there this month? This month, another website had a 12% increase in traffic. If there were 250 visitors this month, how many visitors were there last month?
Answers
The number of customers are not exactly same in two cases.
What is percentage?In mathematics →
a percentage is a number or ratio expressed as a fraction of 100.it is often denoted using the percent sign "%".Given is the -
This month, a website had a 12% decrease in traffic. There were 250 visitors last month.This month, another website had a 12% increase in traffic. There were 250 visitors this month.( 1 ) -Number of customers this month -
{x} = 250 - {12% of 250}
{x} = 250 - {12/100 x 250}
{x} = 250 - 12 x 2.5
{x} = 250 - 30
{x} = 220
( 2 ) -Number of customers last month -
250 = {x} + {12% of x}
250 = {x} + (12/100){x}
250 = {x} (1 + 3/25)
250 = {x} (28/25)
{x} = (250 x 25/28)
{x} = 223 {approx.}
Therefore, the number of customers are not exactly same in two cases.
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Michelle bought a car that costs $25,800 and put a down of $8,000 on it. The car loan is for 60 months and has an interest rate of 3.99%. How much will she actually pay for the car? What will her monthly payment be?
Topic: Exponential Growth & Decay Word Problem
Formula: A=P(1+r)^t
Please help this is due at 10:00!!!
Answers
Answer:
$327.73
Step-by-step explanation:
$25,800 - $8,000 = $17,800
The car loan is a total of 60 months (so at 60 her payment will be $0) and the interest rate is 3.99%
Growth formula: A = P(1+r)^t
We're asking for what value at x = 60 would make P(1+r)^60 = 0?
As such, $327.73
Find a value for a that makes each statement true.
1. a ÷ 6 is greater than 1
Type a value in the box below [ ] ÷ 6 > 1
2. a ÷ 6 is equal to 1
Type a value in the box below [ ] ÷ 6 = 1
3. a ÷ 6 is less than 1
Type a value in the box below [ ] ÷ 6 < 1
4. Find a value for a that makes this statement true a ÷ 6 is equal to a whole number
Type the answer in the box below
| |
| |
| |
| |
| |________________________|
Answers
Answer:
1. a > 6
2. a = 6
3. 0 < a < 6
4. a is divisible by 6
Answer:
1. a>6 the answer could be, 7, 8, 9, 10 and it keeps going on.
2. the answer is 6
3. a<6 the answer is anything below 6 so 5, 4, 3, 2, 1, and more.
4. anything that is a multiple of 6 is true. like 6, 12, 18, 24, 30, 36, and it keeps going.
Find the missing variables in the triangle below. Leave your answer in simplest radical form.
Answers
the value of x, y, and z are 2√14, √74, and √252.
What is the right-angle triangle?A triangle is said to be right-angled if one of its angles is exactly 90 degrees. The total of the other two angles is 90 degrees. Perpendicular and the triangle's base are the sides that make up the right angle. The longest of the three sides, the third side is known as the hypotenuse.
Given, the right triangle that has two other right triangles inside it:
From the Pythagorean theorem:
Hyppotaneus ² = height ² + base²
from the Bigger triangle:
H = 14 + 4 = 18
b = y
h = x
Thus,
y² + z² = 18*18
y² + z² = 324.....(1)
from the triangle with a height of 14,
z² = x² + 14²
z² = x² + 196....(2)
From the triangle with the base of 4:
y² = x² + 16...(3)
For equations 2 and 3 substitute the value in equation 1
2x² + 212 = 324
2x² = 112
x² = 56; x = 2√14
Thus,
y² = 56 +16
y² = 74; y = √74
z² = 56 + 196
z² = 252; z = √252
Therefore, the value of x, y, and z are 2√14, √74, and √252.
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You need to buy ome chicken for dinner tonight. You found an ad howing that the tore acro town ha it on ale for $3.09 a pound, which i cheaper than your uual neighborhood tore, which ell it for $3.19 a pound. I it worth the extra drive?
How much chicken will you be buying? 3 pound
How much far are the two tore? My neighborhood tore i 2.3 mile away, and take about 8 minute. The tore acro town i 8.7 mile away, and take about 25 minute.
How kind of mileage doe your car get? It average about 19 mile per gallon in the city.
How many gallon doe your car hold? About 13 gallon
How much i ga? About $3.62/gallon right now.
Answers
Yes, it is worth the extra drive to going the far store for buying the chicken. The difference between the both store worth is about $1.24.
We have to buy some chicken for dinner tonight. We found an ad showing that the store across town has it on sale for $3.09 a pound, which is cheaper than our usual neighborhood store, which sells it for $3.19 a pound.
Let's compare chicken costs: We need 3 pounds of chicken so, we would pay$3.09 ×3 = $19.14 (far store)
$3.19 × 3 = $20.34 (near store)
Let's see at how much it costs to travel in our car:For the neighbourhood store :
Distance = 2.3 mile
Multiply by 2 because we not only have to drive there, but also back home for the round trip: so, total distance = 2.3 miles × 2 = 4.6 miles
As car average is 19 miles per gallon
= 4.6 mile/ 19 miles per gallon
= 0.24 gallon < 13 gallons
Now, costs to travel to each store from the gas used. Cost of gas is $3.62/gallon,
total cost = 0.2421 gallons×$3.62 /gallons = $0.88
Similarly for far store : distance from home to store = 8.7 miles but take double of it we get, 8.7 miles × 2 = 17.4 miles
As car average is 19 miles per gallon
= 17.4 miles /19 miles per gallons
= 0.915 gallons < 13 gallons
The cost of gas for the respective trip = 0.915 gallons × $3.62 /gallons = $3.32
Now, let's add the gas and chicken costs together to get total worth
$19.14 + $3.32 = $22.46 to the far store
$20.34+ $0.88 = $21.22 to the near store
Hence, the worth in travelling far store is greater than neighbourhoid store.
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Complete question:
You need to buy some chicken for dinner tonight. You found an ad showing that the store across town has it on sale for $3.09 a pound, which is cheaper than your usual neighborhood store, which sells it for $3.19 a pound. Is it worth the extra drive? First, determine what information you need to answer this question, then click here to display that info (along with other info).
How much chicken will you be buying? 3 pounds
How far apart are the two stores? My neighborhood store is 2.3 miles away, and takes about 8 minutes. The store across town is 8.7 miles away, and takes about 25 minutes.
How kind of mileage does your car get? It averages about 19 miles per gallon in the city.
How many gallons does your car hold? About 13 gallons
How much is gas? About $3.62/gallon right now.
Yes, it is worth the extra drive to the far store to get the chicken. The value of the two stores varied by around $1.24.
To make chicken for dinner tonight, we must purchase some. We discovered an advertisement indicating that the supermarket across town is selling it for $3.09 per pound, which is less expensive than our typical neighborhood grocery, which charges $3.19 per pound.
Compare the prices of chicken: We would pay for the 3 pounds of chicken that we require.
$3.09 ×3 = $19.14 (far store)
$3.19 × 3 = $20.34 (near store)
Let's look at the expense of driving in our car:
For the local retailer: = 2.3 miles away
Because we need to travel both ways, we must double the distance by two, making the total distance 2.3 miles x 2 = 4.6 miles.
Since the average automobile gets 19 mpg
19 miles per gallon/4.6 miles = 13 gallons x 0.24 gallons
Now, add the cost of gas used to drive to each store. Gas costs $3.62 per gallon.
Total cost = 0.2421 gallons at a cost of $0.88 per gallon.
The same goes for a far store:
the distance from home to the store is 8.7 miles, but if we double that by two, we get 17.4 miles.
Since the average automobile gets 19 mpg = 17.4 miles per gallon /19 miles per mile
13 gallons equals 0.915 gallons.
The gas price for the relevant journey is 0.915 gallons times $3.62 a gallon, or $3.32.
To determine the overall cost,
let's now combine the costs of the chicken and petrol.
$22.46 to the far store from $19.14 plus $3.32
$20.34 plus $0.88 equals $21.22 for the nearby retailer.
Therefore, a far store is more valuable than a nearby store. The difference is $1.24
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PLSSS HELP TURLY KNOW THISSSS
Answers
Answer: 100
Step-by-step explanation:
x/2 = 50
Multiply both sides by 2:
x = 100
Answer:
Easy Peasy, MULTIPLY 2 by 50
ANSWER IS 100Just type 100
Which is a correct solution for the following system of Inequalities
Answers
The answer to the inequality system is y > 2 – x, y < -1
How to find the calculation?Step 1: Formulate each inequality as y = x + b.
(1) x + y > 2
(2) 2x – y > 1
(3) y > 2 - x Each side of the equation had x subtracted (1)
-y > 1 - 2x 2x were taken out of either side of 2.
(4) y < 2x – 1 -1 multiplied each side, then the inequality was turned around.
Graphing the functions as equalities in step two
(5) y = 2 – x
(6) y = 2x - 1
The borders of the inequalities will be formed by the lines. On one side of a line, the condition will be true, but not on the other (see the diagram below).
Step 3: Highlight the graphs' areas where the inequalities exist.
The graph of y > 2 - x is shown by the red line.
Shade the area above the line because y exceeds a value on the high side of the line (red).
The graph of y = 2x - 1 is shown by the blue line.
Shade the area below the line because y is less than a value on the line's low side (blue).
Any location where the colored regions overlap constitutes the solution set for both inequality problems (purple).
4. Check the outcome.
Input a point in the shaded region, such as (2, 2), and confirm that each inequality is true.
(1) x + y > 2 (2) 2x – y >1
2 + 2 > 2 2(2) – 2 > 1
4 > 2 4 – 2 > 1
2 > 1
It verifies.
The answer to the inequality system is
y > 2 – x, y < -1.
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Correct option is A, (1,2) is the correct option for the given system of equations.
System of Equation -Equations occurring simultaneously, system of equations Algebraic equations involving two or more must be solved cooperatively (i.e., the solution must satisfy all the equations in the system).
For a system to have a single solution, the number of equations must equal the number of unknowns.
A set of simultaneous equations, often known as a system of equations or an equation system, is a finite set of equations for which common solutions are sought.
A system of equations is a collection of equations with one or more variables. Systems of equations have solutions that are either the variable mappings that satisfy each component equation or the intersections of all of these equations.
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One month Jane rented movies 3 and video 5 games for a total of 30$. The next month she rented 6 movies and video 2 games for a total of 18$. Find the rental cost for each movie and each video game.
Answers
The rental cost for each movie and each video game are $1.25 and $5.25 respectively
What is an algebraic expression?An algebraic expression can be defined as an expression that is usually composed of terms, variables, constants, factors and coefficients.
These expressions are also made up of some mathematical operations, such as;
DivisionAdditionParenthesesFloor divisionMultiplicationSubtractionFrom the information given;
Let movies be x
Let the video games be y
We have that;
3x + 5y = 30
6x + 2y = 18
Make 'x' the subject from equation 1
x = 30-5y/3
Substitute the value
6(30-5y/3) + 2y = 18
expand the bracket
180 - 30y/3 + 2y = 18
-24y + 180/3 = 18
-24y + 180 = 54
y = $5.25
Then, x = $1.25
Hence, the values are $1.25 and $5.25
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