A graph of the system of inequalities is shown in the image and one possible solution is the ordered pair (-4, 24).
How to solve these system of inequalities graphically?In order to solve these system of inequalities graphically, we would assign a variables to the unknown numbers and then translate the word problem into algebraic equation as follows:
Let x represent number of pennies.Let y represent number of nickels.Let T represent total number of coins.Note: 1 quarter is equal to 0.25 dollar, 1 nickel is equal to 0.5 dollar, and 1 dime is equal to 0.1 dollar.
Since Arun has no less than 20 coins worth a maximum of $0.40 combined, an inequality to represent this is given by;
x + y ≥ 20
For a maximum of $0.40 combined, we have:
0.5x + 0.1y ≤ 0.40
From the graph (see attachment), a possible solution is given by the ordered pair (-4, 24).
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The second angle of a triangle is 60 more than the first angle. The third angle is three times the first. Find the three angels
Answer: three angles of the triangle are 24 degrees, 84 degrees, and 72 degrees.
Step-by-step explanation:
Let's call the first angle x.
Then the second angle is x + 60.
And the third angle is 3x.
We know that the sum of the angles in a triangle is always 180 degrees.
We can use this information to set up the following equation:
x + x + 60 + 3x = 180
5x + 60 = 180
5x = 120
x = 24
So the first angle is 24 degrees.
The second angle is 24 + 60 = 84 degrees.
And the third angle is 3x = 3 * 24 = 72 degrees.
Therefore, the three angles of the triangle are 24 degrees, 84 degrees, and 72 degrees.
Arrange the following numbers in ascending order (From the least to the greatest).
(1) +8,+4,0,+2,+3 =
(2) -1,-11,-5,-0,-12
(1) +8,+4,0,+2,+3 = 0 , 2 , 3 , 4 , 8
(2) -1,-11,-5,-0,-12 = -12 , -11 , -5 , -1 , -0
A cylindrical tank is half full of oil.
The cylinder has a base radius of 100cm.
The height of the cylinder is 250cm.
1litre=1000cm3
How many litres of oil are in the tank?
Round your answers to the nearest litre.
A cylindrical tank is half-full of oil. The cylinder has a base radius of 100 cm. The height of the cylinder is 250 cm than the oil present in the tank is 3926.990 lit.
Given :
The cylinder has a base radius of 100 cm.The height of the cylinder is 250 cmThe volume of the half cylinder is given by:
[tex]Volume= \frac{1}{2} (\pi r^{2} ) X h\\\\Volume=\frac{1}{2} X(\pi X(100)^{2} ) X 250[/tex]
[tex]Volume = Volume = 3926990.82 cm^{3}[/tex]
[tex]Volume = 3926.990 lit.[/tex]
So, 3926.990 lit. of oil are present in the cylindrical tank.
Anne donates blood at a rate of 200 mL in 3 minutes. How long will it take Anne to donate 500 mL of blood?
Answer: 7.5 minutes
Step-by-step explanation:
simplify fully (2x-2)/(3x-3)
Answer:
In the exact form, it would be 2/3.
(Hope it works!)
Step-by-step explanation:
Jethro is planting flowers in his garden. He wants the ratio of tulips to roses to be 2 to 1. Jethro wants to plant a total of 33 flowers. How many tulips should he plant?
Answer: 22 tulips
Step-by-step explanation:
2 + 1 = 3
3 goes into 33 11 times, so you multiply each value by 11
2 * 11 = 22 tulips
22 tulips to 11 roses is 2:1 ratio
death valley california has the lowest point in the united states. its elevation is 282 feet below sea level. mount mckinley alaska has the highest point in the united states. it elevation is 20,320 feet above sea level. use integers to describe these two locations in the united states.
By using integers to represent the information, Death Valley will be -282 and Mount Mckinley is 20320.
How to illustrate the Integer?From the information, death valley california has the lowest point in the united states. its elevation is 282 feet below sea level.
Mount mckinley alaska has the highest point in the united states and it's elevation is 20,320 feet above sea level.
It should be noted that by using integers, Death Valley is the lowest point. This will have a negative sign and will be -282. Mount McKinney will be +20320
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The function F(C)=1.8C+32 represents Fahrenheit, F, as a function of the temperature in Celsius, C.
Given that the team temperature in celsius is 92, find the temperature in Fahrenheit.
The value of 92°C to Fahrenheit will be 197.6°F.
How to illustrate the expression?In Mathematics, it is important to note that an expression is simply used to show the relationship between the variables that are provided or the data given regarding an information. in this case, it is vital to note that they have at least two terms which have to be related by through an operator.
Since the function F(C)=1.8C+32 represents Fahrenheit, F, as a function of the temperature in Celsius,.
Therefore, 92°C to Fahrenheit will be:
= (1.8 × 92) + 32
= 197.6°F
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Fill in the table.
Give four consecutive odd integers:
First Integer
X
The simplified sum of the second and forth integers are
Next Integers
The simplified sum of the second and forth integers are; -1 + 5 = 4
How to find the integer?An integer is defined as a whole number that can be positive, negative, or zero. Examples of integers are: -7, 2, 9, 18, 125, and 9803
Now, we are given the consecutive integer sequence as;
x, 1, 3, 5
Now, since the integers are consecutive, then the common difference is the same. Thus;
1 - x = 3 - 1
1 - x = 2
x = 1 - 2
x = -1
Sum of first and fourth term = -1 + 5 = 4
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Which expression is equivalent to (10x)^-3?
Answer:
[tex]\frac{1}{10x^{3} }[/tex] or [tex]\frac{1}{\\1000x^{3} }[/tex]
Step-by-step explanation:
To make the exponent positive, you put it over 1.
What’s the correct answer answer asap
Answer: Slavery
Step-by-step explanation:
PLEASE HELP I NEED THE ANSWERS PLEASE I NEED HELP PLEASE
Felix added 28 to the product of 327 and 14m What is the sum?
Answer:
4,606
Step-by-step explanation:
(327 x 14) +28 Product is the answer in multiplication
4578 + 28
4606
Ten pennies weigh approximately two ounces. How many ounces would you expect a collection of pennies worth $13.40 to weigh?
Answer:
268 ounces
Step-by-step explanation:
13.40 in pennis is 1,340 pennies. If 10 pennies weigh 2 ounces then each penny weighs .2 ounces. So then all you have to do is 1,340×.2 which is 268. So, a bunch of pennies worth $13.40 weigh 268 ounces. :)
Answer:
268 ounces
Step-by-step explanation:
$13.40 = 1340 penny, so, 1340/10*2 is 268
PLEASE HELP ME WITH GEOMETRY
Answer:
Step-by-step explanation:
answer: 50
Okay so we need to find ABC, which is 2x, and we know the angles of a triangle all add up to 180.
To find angle C you must subtract the exterior angle from the total of the line, 180.
C = 180-145
C = 35
So now we have 3 elements, 95, 2x, and 35, and we know they all add up to 180 degrees.
95+35+2x=180
130+2x=180
50=2x
2x is the angle of ABC, so it's 50 degrees
39.
A) adjacent
B) vertical
C) alternate exterior
D) supplementary
40.
A) adjacent
B) supplementary
C) alternate exterior
D) alternate interior
41.
A) vertical
B) supplementary
C) alternate interior
D) complementary
42.
A) adjacent
B) alternate interior
C) vertical
D) alternate exterior
39) a and b here are Adjacent Angles.
40) a and b here are Adjacent Angles.
41) a and b here are Complementary Angles.
42) a and b here are Alternative Interior Angles.
What rules must be met for two angles to be considered Adjacent Angles?The following requirements must be met for two angles to be adjacent.
A common vertex connects two angles.A common arm connects two angles.There are two arms that are unusual.On the other hand, when a transversal connects two coplanar lines, alternate interior angles are generated. They are on the inside of the parallel lines, but on the outside of the transversal.
It is worth noting that Alternate Interior Angles are congruent.
Mathematically, two angles are called complementary IF their measures SUM to 90 degrees.
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Simplify 1.2(0.4-0.9)÷(-6) +3.1
The answer is 16/5=3.2
How to simplify the question?explanation
1.2(0.4-0.9)/(-6) +3.1
simplify the expression:
1.2(0.4-0.9)/-6+3.1
simplified the answer
16/5=3.2
expanded 16/5
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What is the value of X in centimeters
Answer:
x = 22.5
Step-by-step explanation:
Similar figures have proportional side lengths
[tex]\frac{12}{18}[/tex] = [tex]\frac{15}{x}[/tex] [tex]\frac{12}{18}[/tex] = [tex]\frac{2}{3}[/tex]
[tex]\frac{2}{3}[/tex] = [tex]\frac{15}{x}[/tex]
2 x 7.5 = 15, so 3 x 7.5 = 22.5
x = 22.5
The difference of the square of a number and 18 is equal to 3 times that number. Find the positive solution
The positive solution for the number is 6 as the expression will result to a quadratic equation.
What is a quadratic equationA quadratic equation is a second-order polynomial equation in a single variable x in the form ax² + bx + c = 0. with a ≠ 0.
We Shall represent the unknown number with the letter x so that we have:
x² - 18 = 3x
x² - 3x - 18 = 0 {a quadratic equation}
x² + 3x - 6x - 18 = 0 {expand the middle term}
x(x + 3) -6(x + 3) = 0 {factor out x + 3}
(x - 6)(x + 3) = 0
x - 6 = 0 or x + 3 = 0
x = 6 or x = -3
we have two solutions for the quadratic equation and 6 is the positive solution
Therefore, the positive solution for the quadratic equation is 6
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two poles are 80 meters and 60 meters tall. Their bases are located at a distance of 90 meters. A grounding wire needs to connect the top of the poles with each other and the ground. At what point should we connect the wire with the ground if we wanted to use the least amount of wire?
It needs to do that route I guess. But I don't understand the last question well.
Question You and a friend tutor for a total of 12 hours. Use the tape diagram to find how many hours you tutor. You tutor for hours.
The amount of time I spent tutoring from the tape diagram is 4 hours.
How to solve an equationLet x represent one rectangle. Therefore from the tape diagram:
Amount of hours I spent tutoring = x + x = 2x
Amount of hours my friend spent tutoring = x + x + x + x = 4x
Since both me and my friend spent a total of 12 hours, hence:
2x + 4x = 12
6x = 12
Dividing through by 6:
x = 2 hours
Amount of hours I spent tutoring = 2x = 2(2) = 4 hours
The amount of time I tutor is 4 hours.
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Graph the solution to the inequality on the number line.
w-0.9>-2.1
First select the correct ray. Then select the location of the endpoint to plot the inequality on the number line.
The solution set for the inequality given in the task content as required is; w > -1.2.
The graph of the inequality on the number line is as represented in the attached image.
What is the graph of the inequality given; w - 0.9 > -2.1?It follows from the task content that the graph of the inequality w - 0.9 > -2.1 as required is to be determined.
Since the given inequality is; w - 0.9 > -2.1.
The inequality can be solved by first adding 0.9 to both sides of the inequality; Additive property of inequalities;
w - 0.9 + 0.9 > -2.1 + 0.9.
w > -1.2.
On this note, the correct ray is that which points rightwards with an open ring (indicating the > sign).
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The solution of the inequality is graphed in the number line and attached
How to solve the inequalityWhat is inequality in math?Inequality, is a mathematical statement expressing an order relationship between two numbers or algebraic expressions, such as greater than, greater than or equal to, less than, or less than or equal to.
Solid dot and hollow dot in inequality
A region on one side of a line can be used to graphically show an inequality.
For the purpose of indicating that a line is not a part of the region, inequality plots that employ the < or > symbols have a hollow dot
Plotting a solid dot indicates that an inequality that uses the symbol ≤ or ≥ is included in the region.
In the problem, w - 9 > -2.1 will use a hollow dot
w - 0.9 > -2.1
w > -2.1 + 0.9
w > -1.2
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Given: 0.2a +0.06 -0.05
Step 1: 2a +6=5
Step 2: 2a=-1
Step 3: a =-1/2
Answer:
a = -0.05
Step-by-step explanation:
0.2a + 0.06 = -0.05
Step 1: 100 * (0.2a + 0.06 = 0.05)
20a + 6 = 5
Step 2: 20a + 6 - 6 = 5 - 6
20a = -1
Step 3: 20a / 20 = -1/20
a = -0.05
NEED HELP ASAP!
Kurume Abdulla is purchasing a country estate with a selling
price of $1,246,500. His offer of 95% of the asking price is
accepted by the seller. His lender requires a 30% down payment
for estates.
a. What is the purchase price of the estate?
b. What is the amount of the down payment?
c. What is the amount of the mortgage loan?
Answer:
a. The purchase price of the estate is $1,246,500 x 95% = $<<124650095.01=1182975>>1,182,975.
b. The amount of the down payment is $1,182,975 x 30% = $<<118297530.01=354452.5>>354,452.5.
c. The amount of the mortgage loan is $1,182,975 - $354,452.5 = $<<1182975-354452.5=828492.5>>828,492.5.
Step-by-step explanation:
(Score for Question 1: ______ of 3 points)
1. Represent each situation with an inequality.
(a) The sum of a number and 16 is at least -3.
(b) A number increased by -3 is greater than 16.
(c) -3 more than a number is no more than 16.
Answer:
Hello Dear,
Could you send a better explained question?
Thanks!
Please someone help me !!!
the total cost to fill up half of the tank will be $20.25.
What is the arithmetic operation?
The four fundamental operations of arithmetic are addition, subtraction, multiplication, and division of two or more quantities. Included in them is the study of numbers, especially the order of operations, which is important for all other areas of mathematics, including algebra, data management, and geometry. The rules of arithmetic operations are required in order to answer the problem.
For 500 miles the car consumes 60 gallons of gas.
The capacity of the tank is 13.5 gallons.
Filling up half of the tank will require 6.75 gallons of gas.
The cost of a gallon of gas is $3.
So the total cost will be 6.75*3 = $20.25
Hence, the total cost to fill up half of the tank will be $20.25.
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Remove all perfect squares from inside the square root.
[tex]\sqrt180[/tex]
By factor decomposition and algebra properties, the number √180 is equal to 6√5.
How to determine the most simple form of a square root by factor decomposition and algebra properties
In this problem we find an imperfect square root, that is, a square root whose root is an integer. However, we can simplify the expression by means of algebra properties and by redefining the number inside the root operator as a product of integers. Now we proceed to show the complete steps of the procedure:
First, decompose the number inside the root operator by factor decomposition:
√180 = √(2² · 3² · 5)
Second, simplify the resulting expression by algebra properties concerning roots:
√180 = √2² × √3² × √5
√180 = 2 × 3 × √5
√180 = 6√5
Therefore, the number √180 is equivalent by algebra properties and factor decomposition to 6√5.
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i need help with #5 please!!
Answer: [tex]x^{2} +9x+23[/tex]
Step-by-step explanation:
Given equation:
-f(x)+3g(x)
Since the f(x) and g(x) are already given in the problem, all you must do is plug in the values.
[tex]-(-x^{2} -8)+3(3x+5)\\=x^{2} +8+9x+15\\=x^{2} +9x+23[/tex]
For the following two numbers, find two factors of the first number such that their product is the first number and their sum is the second number.
16, 10
Answer
How to enter your answer (opens in new window)
Answer: To find the answer, I first understood that the first number is a product of two factors and the second number is the sum of those two factors.
So, I started by listing out all the factors of the first number which is 16. The factors of 16 are 1, 2, 4, 8, 16.
Then I looked for a pair of factors from the list whose product is 16 and sum is 10.
I found the pair (4, 6) which satisfies the condition.
So, I confirmed that 4 x 6 = 16 and 4 + 6 = 10.
Step-by-step explanation:
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