How many solutions can be found for the system of linear equations represented on the graph?
Responses
A infinitely many solutionsinfinitely many solutions
B two solutionstwo solutions
C one solutionone solution
D no solution
Answers
Answer:
the answer is b
Step-by-step explanation:
Related Questions
5. Write the following expression: the product of 10 and 4, taken to the fourth power, minus the quantity of 25 divided by 5.
Answers
We can write the given statement as an expression as -
(10 × 4)⁴ - (25/5)
What are algebraic expressions?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.Given is the mathematical statement as -
" the product of 10 and 4, taken to the fourth power, minus the quantity of 25 divided by 5 ".
We can write the expression as -
(10 × 4)⁴ - (25/5)
Therefore, we can write the given statement as an expression as -
(10 × 4)⁴ - (25/5)
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I Need help quick! Tyyy!
Answers
The required answer of given parts are 1) 4500 ft² 2) 2700 ft² 3) $1485.
What is right angled triangle?A triangle is said to be right-angled if one of its angles is exactly 90 degrees. The sum 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.
According to question:1) Area of design = area of rectangle + 2(area of triangle)
Area of design = (60×30) + 60×45
Area of design = 1800 + 2700
Area of design = 4500 ft²
2) Area covered by grass = 2(area of triangle)
Area covered by grass = = 60×45
Area covered by grass = 2700 ft²
3) installment of grass is $0.55 per ft².
So,
For 2700 ft²
= 2700 ft²(0.55)
= $1485
Thus, required answers are 1) 4500 ft² 2) 2700 ft² 3) $1485.
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Researchers created a new fertilizer. They conducted an experiment to compare the new fertilizer to the old fertilizer. They divided tomato plants into two groups. They applied the new fertilizer to one group and the old fertilizer to another group. The variable is the number of tomatoes per plant on a randomly selected day.
Which one of the following statements is valid?
A. The new formula of fertilizer works better. Plants with the new fertilizer had more tomatoes.
B. The old formula of fertilizer was better because the plant with the most tomatoes was treated with the old fertilizer.
C. The average number of tomatoes per plant with the old fertilizer is higher than the average amount of tomatoes per plant with the new fertilizer.
D. We can make no conclusions from this data about which fertilizer is better because the two groups have a different number of plants
Answers
The plant that produced the most tomatoes was treated with the old fertilizer, thus it was better. So statement B is correct.
A line plot is one type of graph that helps us to represent the data along the number line. This plot is also referred to as a dot plot. In this plot, we show the data as a check or point above a number line. Each point or check in this plot represents the frequency of each value.
The given plot about fertilizers is a line plot. In this plot, 1 dot over 2 in the old fertilizer treatment means about 2 plants have one tomato.
By comparing the line plot for both the new fertilizer and old fertilizer, we will be able to say that there are more tomatoes produced when the old fertilizer is used than the new fertilizer.
Nearly 65 tomatoes were produced when old fertilizer is used but only 58 tomatoes were produced when new fertilizer is used. Therefore, statement B is correct.
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The price of an item has been reduced by 35% . The original price was $60. What is the price of the item now?
Answers
===================================================
Explanation:
The price drops by 35%, so it keeps the remaining 65% (since 100-35 = 65)
65% of $60 = 0.65*60 = 39 dollars
-------
A slightly longer method:
35% of 60 = 0.35*60 = 21
You save $21 and the final price is 60-21 = 39 dollars
Three rectangular prisms are shown below. Prism A is a rectangular prism with a height of six inches, length of three inches, and a width of two inches. Prism B is a rectangular prism with a height of three inches, length of five inches, and a width of two inches. Prism C is a rectangular prism with a height of two inches, length of seven inches, and a width of two inches. Which statement is true? (4 points) a The volume of Prism A is less than the volume of Prism C. b Prism B has the greatest volume. c Prism B has a greater volume than Prism C. d Prism B and Prism C have the same volume.
Answers
The true statement is, c.) Prism B has a greater volume than Prism C.
What is volume?In mathematics, volume is the space taken by an object. Volume is a measure of three-dimensional space. It is often quantified numerically using SI derived units or by various imperial or US customary units. The definition of length is interrelated with volume.
here, we have,
Prism A is a rectangular prism with a height of six inches, length of three inches, and a width of two inches.
Prism B is a rectangular prism with a height of three inches, length of five inches, and a width of two inches.
Prism C is a rectangular prism with a height of two inches, length of seven inches, and a width of two inches.
now,
volume of prism=V = B*H
where, B is the area of base.
so, by calculating we get,
V-prism A= 36 inch^3
V-prism B= 30inch^3
V-prism C=28 inch^3
Hence, c.) Prism B has a greater volume than Prism C.
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Answer:
C
Step-by-step explanation:
4. The two trapezoids below are similar. What
is the length of segment EF?
24 am
A
D
30 cm
B
C
G.
7.5 cm
X
E
H
Help please
Answers
The length of the segment EF for the given trapezoids is 6 cm.
How do trapezoids work?Quadrilaterals called trapezoids have two parallel and two non-parallel sides. It also goes by the name Trapezium. A trapezoid is a closed, four-sided shape.
An opposing set of sides are parallel. The four angles of a trapezium add up to 360 degrees, and their diagonals cut each other in half. It has four odd-numbered sides. Thus, the opposing sides of an isosceles trapezium are congruent, as well as the diagonals.
Trapezoids ABCD and EFGH are similar,
Hence, corresponding sides ratio are equal:
Thus, AB/EF = DC/HG
24/x = 30/7.5
30x = 180
x = 180/30
x= 6
Hence, the length of the segment EF is 6 cm.
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Fiona wants to earn at least $100 this week. She makes $11 an hour babysitting. Choose the inequality that shows the number of hours Fiona needs to babysit in order to reach her goal.
h≥11
h>9
h>8
h≥9
Answers
The inequality that shows the number of hours Fiona needs to babysit in order to reach her goal is h>9.
What is inequality?
The idea of inequality, which is the state of not being equal, especially in terms of status, rights, and opportunities1, is at the core of social justice theories. However, because it frequently has diverse meanings to different people, it is prone to misunderstanding in public discourse.
Given that,
Fiona wants to earn at least [tex]\$[/tex]100
She makes [tex]\$[/tex]11/hour
in order to reach her goal = 100/11 = [tex]\$[/tex]9.09 .
The inequality that shows the number of hours Fiona needs to babysit in order to reach her goal is h>9.
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Which of the following is an equation of the line through 11,3 and7,9
Answers
The linear equation for the coordinate points given is obtained as y = -3/2x + 19.5.
What is a linear equation?
A linear equation is one that has a degree of 1 as its maximum value. No variable in a linear equation, thus, has an exponent greater than 1. A linear equation's graph will always be a straight line.
The coordinate points for the lines are (11,3) and (7,9).
The slope-intercept form of an equation/function is - y = mx + b
To find the slope m use the formula -
(y2 - y1)/(x2 - x1)
Substituting the values in the equation -
[9 - 3]/[7 - 11]
(6)/(-4)
3/-2
So, the slope point is obtained as m = 3/-2.
The equation becomes - y = -3/2x + b
To find the value of b substitute the values of x and y in the equation -
3 = -3/2(11) + b
3 = -33/2 + b
b = 3 + 33/2
b = (6 + 33)/2
b = 39/2
b = 19.5
So, the value for b is 19.5.
Now, the equation becomes -
y = -3/2x + 19.5
The graph for the equation is plotted.
Therefore, the equation is obtained as y = -3/2x + 19.5.
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4. Please Help ASAP!
Use this balanced reaction to show that you can write the equation that makes chemical sense.
Explain how your symbols were derived in paragraph form..
Answers
The simulation provides information about the concept of balancing a chemical equation through visual representation and interactive tasks.
What is your understanding about given chemical reaction?The user is able to balance the equation by adjusting the coefficients of the reactants and products to ensure that the number of atoms of each element is conserved on both sides.It did not have to research outside the simulation for information about balancing a chemical equation. The simulation provides enough information to understand the concept.The simulation can be used to check learning by allowing the user to practice balancing different chemical equations and receive feedback on their work. This helps to reinforce the understanding of the concept and identify any areas where further improvement is needed.In the balanced reaction CO2 + H2O -> C2H6 + O2, the coefficients were derived by ensuring that the number of atoms of each element was conserved on both sides of the equation. This means that the same number of carbon, hydrogen, and oxygen atoms are present in the reactants and products. To balance the equation, the coefficients were adjusted until this condition was met.To show the molecular representations of a balanced reaction, the molecular structures of the reactants and products can be drawn, showing the individual atoms and their connections. In the case of the reaction CO2 + H2O -> C2H6 + O2, the molecular structure of CO2 is a linear arrangement of two oxygen atoms bonded to a carbon atom. The molecular structure of H2O is a bent arrangement of two hydrogen atoms bonded to an oxygen atom. The molecular structure of C2H6 is a hexagonal arrangement of six hydrogen atoms bonded to a carbon atom. The molecular structure of O2 is a linear arrangement of two oxygen atoms bonded to each other. These representations were derived by following the basic principles of chemical bonding and considering the arrangement of atoms in the molecules.
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The points plotted on the coordinate grid represent the rule y = x + 4. Which table also represents this rule?
Answers
Answer:
See below
Step-by-step explanation:
No table was given but it should look something like
x y
-3 1
-2 2
-1 3
0 4
1 5
2 6
3 7
Whatever number you select for x add 4 to it and that will give you your y value
C is the circumcenter of isosceles triangle ABD with vertex angle ∠ABD. Does the following proof correctly justify that triangles ABE and DBE are congruent? It is given that triangle ABD is an isosceles triangle, so segments AB and DB are congruent by the definition of isosceles triangle. It is given that C is the circumcenter of triangle ABD, making segment BE a median. By the definition of perpendicular, angles AEB and DEB are 90°, so triangles ABE and DEB are right triangles. Triangles ABE and DEB share side BE making it congruent to itself by the reflexive property. Triangles ABE and DBE are congruent by HL
Answers
The incenter is where a triangle's angle bisectors meet. Since C is the incenter, segment BC should be the angle bisector. So, there is an error in line 3; segment AB and BC are congruent.
Any triangle with any 2 sides that are the same length is defined as an isosceles triangle. An isosceles triangle has two equal-sized angles that are opposite from one other and have equal sides.
If all three angles of the three triangles are acute, the circumcenter of an isosceles triangle sits inside the triangle. The circumcircle's chords are the sides of the triangle. In this case, the circumcenter is outside of the triangle since one of the angles is 90 degrees.
The circumcenter of a triangle ABC is the location where the perpendicular bisectors of its sides cross.
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The complete question is given below:
A table shows miles and hours for today and yesterday. The number of miles is 15 for today and m for yesterday. The number of hours is 2.5 for today and 4 for yesterday.
Answers
The distance covered on the yesterday was 24 miles.
What is proportion?Proportion is a mathematical comparison between two numbers. According to proportion, if two sets of given numbers are increasing or decreasing in the same ratio, then the ratios are said to be directly proportional to each other.
Given that, The number of miles is 15 for today and m for yesterday. The number of hours is 2.5 for today and 4 for yesterday, the rate is same for both the days, therefore, this will represent a proportion,
Therefore, establishing the proportion,
15 / 2.5 = m / 4
15 × 4 / 2.5 = m
m = 24
Since, we got the value of m is 24 miles.
Hence, the distance covered on the yesterday was 24 miles.
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graph the quadrilateral with the given vertices in a coordinates plane then show that the quadrilateral is a parallelogram E(-3,0),F(-3,4),G(3,-1),H(3,-5)
Answers
If one set of the opposite sides of a quadrilateral is equal and parallel, the shape is referred to as a parallelogram.
Is quadrilateral is a parallelogram?A quadrilateral is a parallelogram if each pair of opposite angles in it is equal. The quadrilateral ABCD is a figure in which A = C and B = D. We are aware that a quadrilateral's angles add up to 360 degrees. ABCD is therefore a parallelogram.
A quadrilateral is a parallelogram if one pair of its opposite sides is both equal and parallel. A quadrilateral becomes a parallelogram if its diagonals cut each other in half.
The opposite sides of a parallelogram are equal to one another. A parallelogram's diagonals are consistently equal. The diagonals do not cross each other in a parallelogram. The diagonals in a parallelogram are always at right angles to one another.
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Mateo has 8 liters of punch for a party. Each glass holds 1/5
liter of punch.
How many glasses can Mateo fill with punch?
amswer in simplest from fraction
Answers
Mateo can fill 40 glasses with punch and this can be calculated as :
8 liters = 8 x (5/1) = 40 liters
By solving the above equation following will be obtained.
Therefore, Mateo can fill 40 glasses with punch.
Mathematics, where the numerator and denominator are divided. Each is an integer in a simple fraction. Whether it is in the numerator or denominator, a complex fraction contains a fraction. The numerator and denominator of a correct fraction are opposite each other.
If numerator value is less than the denominator value, it is a proper fraction.If a numerator value is greater than denominator value, then it is called an improper fraction.
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In a school containing 360 children, 198 are girls. What percent of all the students are girls? What percent of the children are boys? The number of girls is what percent of the number of boys?
Answers
3/5=?/10=33/?
Complete the empty places
Answers
The values in the empty places are 0.6 and 3.3 respectively.
What is division and multiplication?Multiplication is the process of adding a number repeatedly. When m is multiplied by n, m is being added to itself n times in total. The multiplication sign is "." A way to divide or distribute a number into equal parts is by division. The two key arithmetic operations in mathematics are multiplication and division. Similar to addition and subtraction, the processes of multiplication and division are intimately tied to one another. All real numbers are subjected to these processes.
The value of 3/5 can be calculated by dividing the numerator and the denominator.
3/5 = 0.6
The given expression is:
10 = 33/ x
Isolate the value of x:
10x = 33
x = 33/10
x =3.3
Hence, the values in the empty places are 0.6 and 3.3 respectively.
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to own and operate a home printer it costs $100 for the printer and additional $0.05 per page for ink
let p represent the number of pages let t represent the total costs
A,write an equation to represent each printing scenario Y=mx+b
Answers
The equation that represents each printing scenario will be t = 0.05p + 100.
What is a linear equation?A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.
The linear equation is given as,
y = mx + c
Where m is the slope of the line and c is the y-intercept of the line.
Owning and operating a home printer costs $100 for the printer and an additional $0.05 per page for ink.
Let 'p' represent the number of pages and 't' represent the total costs. Then the equation is given as,
t = 0.05p + 100
The equation that represents each printing scenario will be t = 0.05p + 100.
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Earth is about 9. 27 x 107 miles from the Sun. Venus is about 6. 68 x 107 miles
from the Sun. About how much farther from the Sun is Earth than Venus?
Answers
Earth is 2.59 x 10⁷ miles farther from the Sun than Venus.
Let us assume that d₁ represents the distance between the earth and the sun.
d₂ represents the distance between the earth and the Venus.
The distance between the earth and the sun is 9.27 x 10⁷ miles.
d₁ = 9.27 x 10⁷ miles
And the distance between the Sun and the Venus is about 6. 68 x 10⁷ miles.
⇒ d₂ = 6. 68 x 10⁷
To find : by how much farther from the Sun is Earth than Venus
We need to find the absolute difference between d₁ and d₂
Let d be the absolute difference between d₁ and d₂
d = |d₁ - d₂|
d = | (9.27 x 10⁷) - (6. 68 x 10⁷ )|
d = |(9.27 - 6.68) x 10⁷ |
d = 2.59 x 10⁷ miles
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Ten people were chosen at random and surveyed. The survey asked participants for the number of hours they watched TV per day and their ages. Letting X represent the number of hours the participant watched TV per day and Y represent the participant's age, the surveyor calculated the correlation coefficient between X and Y to be 0.19. Interpret the correlation coefficient calculated by choosing the statement below which correctly describes the association between X and Y. A. weak positive association B.weak negative association C. strong positive association D. strong negative association
Answers
Answer:
The correlation coefficient of 0.29 indicates that the correlation is a weak positive correlation. Thus option (D) is the correct answer.
What is correlation?
"Correlation is a statistical tool that studies the relationship between two variables. Data sets have a positive correlation when they increase together, and a negative correlation when one set increases as the other decreases".
For the given situation,
Correlation coefficient = 0.29
Positive correlation: the two variables change in the same direction.
Negative correlation: the two variables change in opposite directions.
No correlation: there is no association or relevant relationship between the two variables.
The correlation coefficient lies between 0 to 0.3 indicating that the correlation is a weak positive correlation.
Hence we can conclude that option (D) weak positive correlation is the correct answer.
incoming calls to a customer service center are classified as complaints (73% of calls) or requests for information (27% of calls). of the complaints, 40% deal with computer equipment that does not respond and 57% deal with incomplete software installation; in the remaining 3% of complaints, the user has improperly followed the installation instructions. the requests for information are evenly divided on technical questions (50%) and requests to purchase more products (50%). round your answers to four decimal places (e.g. 0.9876). (a) what is the probability that an incoming call to the customer service center will be from a customer who has not followed installation instructions properly? enter your answer in accordance to the item a) of the question statement (b) find the probability that an incoming call is a request for purchasing more products. enter your answer in accordance to the item b) of the question statement statistical tables and charts
Answers
The probability of that an incoming call to the service centre is 0.0219. And the probability that an incoming call is a request for purchasing more products is 0.135.
Probability of an event gives the possibility of an event which is never greater than 1 and the probability of impossible event is 0 and the probability of sure event is 1.
Probability = number of favourable cases/ total number of outcomes
a) The probability that an incoming call to the customer service = Probability of incoming calls to the service centre * probability of remaining number of calls in the centre = 0.73* 0.03 = 0.0219.
b) the probability that an incoming call is a request for purchasing more products = Probability of request of calls in the service centre * probability of request of purchase. = 0.5 * 0.27 = 0.135.
Hence, the probability that incoming call to the service is 0.0219 and of the request of purchase is 0.135.
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what is (-5x+3)-(-7x7)
Answers
Answer: (-5x+3) - (-7x7) = -5x + 3 - (-7x7) = -5x + 3 + 7x7 = 2x7
The expression (-5x+3) - (-7x7) is the result of subtracting two algebraic expressions. When subtracting algebraic expressions, we need to distribute the negative sign to each term before combining like terms.
The first step is to distribute the negative sign to each term in the second expression, (-7x7). This gives us:
(-5x+3) - (-7x7) = -5x+3 + 7x7
Now we can combine the like terms, x7, to get the simplified expression:
-5x+3 + 7x7 = 2x7
So the final answer is 2x7.
Step-by-step explanation:
† 7x7 = 2×7
The expression (-5x+3) - (-7x7) is the result of subtracting two algebraic expressions. When subtracting algebraic expressions, we need to distribute the negative sign to each term before combining like terms.
The first step is to distribute the negative sign to each term in the second expression, (-7x7).
This gives us:
(-5×+3) -(-7×7) = -5×+3 + 7×7
Now we can combine the like terms, ×7, to get the simplified expression:
-5x+3 + 7×7 = 2x7
So the final answer is 2x7.
The baker made a batch of chocolate chip, oatmeal raisin, and sugar cookies. If P(chocolate chip) = 68%, interpret the likelihood of randomly selecting a chocolate chip cookie from the batch.
Likely
Unlikely
Equally likely and unlikely
This value is not possible to represent probability of a chance event.
Answers
Answer:
Likely
Step-by-step explanation:
68% is more than 2/3, so the event is likely to occur.
Answer: Likely
The table shows the costs of movie tickets and large bags of popcorn for two groups of people.
a. Can you determine how much each ticket costs? Explain.
b. A third group buys 5 tickets and 4 large bags of popcorn for $82. How much more does a ticket cost than a large bag of popcorn?
Answers
According to the unitary method,
(a) Ticket cost for 5 people is $28.75
(b) The cost for ticket is $28.75 and the cost for popcorn is $53.25
In math the term called unitary method is defined as a basic concept to find the value of a single unit and then using that value to find the value of multiple units.
Here we have know that each person in a group buys a movie ticket, a drink, and a popcorn.
And the cost for each of the product is listed as Ticket is $5.75, Drink is $2.00 and Popcorn is $3.25.
Then the cost of 5 people is calculated as,
=> 5.75 x 5
=> 28.75
And the third group buys 5 tickets and 4 large bags of popcorn for $82.
Then the cost of the ticket is calculated as,
=> 82 - 28.75
=> 53.25
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I need help with this problem. Please show work and tell me if its one solution or all or none.
2x-y=9
2x+y=11
Answers
Answer:
x = 5, y = 1
Step-by-step explanation:
2x - y = 9
2x + y = 11 subtract equation 2 from equation 1
0 - 2y = -2
y = -2/-2 = 1 substitute into equation 1 or 2 to solve for x
2x - 1 = 9
2x = 10
x = 10/2 = 5
Can someone please help me? I need help ASAP
I need to show work btw
Answers
Answer:
Step-by-step explanation:
yes the triangle can be formed
Calculate the angular momentum of a ballet dancer who is spinning at 1.5 rev/sec. Model the dancer as a cylinder (I = MR 2) with a mass of 62 kg, a height of 1.6 m and a radius of 0.16 m.
Answers
The angular momentum of an object can be calculated using the formula L = Iω, where L is the angular momentum, I is the moment of inertia, and ω is the angular velocity.
In the case of the ballet dancer, we are told that they are spinning at 1.5 rev/sec, and that they can be modeled as a cylinder with a moment of inertia of 22 MR^2, a mass of 62 kg, a height of 1.6 m, and a radius of 0.16 m.
We can calculate the moment of inertia of the cylinder using the formula I = (1/2) MR^2, where M is the mass and R is the radius.
Plugging in the values we have, I = (1/2)(62 kg)(0.16 m)^2 = 3.072 kg-m^2
We can then calculate the angular momentum of the dancer by plugging in the values we have into the formula L = Iω,
L = (3.072 kg-m^2)(1.5 rev/sec) = 4.608 kg-m^2/s
So the angular momentum of a ballet dancer who is spinning at 1.5 rev/sec, modeled as a cylinder with a moment of inertia of 22 MR^2, a mass of 62 kg, a height of 1.6 m and a radius of 0.16 m is 4.608 kg-m^2/s.
10. Hamal has a new part-time job bagging groceries after school. The 2 po equation y = 10x + 50 shows the relationship between his hours of work (x) and the amount of money in his bank account (y). How much money did he have in his bank account before he started working?*
Answers
If the relationship between his hours of work (x) and the amount of money in his bank account (y) is represented by equation "y = 10x + 50" , then the money did he have in his bank account before he started working is $50 .
The equation y = 10x + 50 shows the relationship between Hamal's hours of work (x) and the amount of money in his bank account (y).
When x = 0, the equation becomes y = 10(0) + 50, which simplifies to y = 50. So when Hamal has not worked any hours, he has $50 in his bank account.
In other words, the y-intercept of the equation is 50, which represent the amount of money Hamal had in his bank account before he started working.
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Two Javan Rhinoceroses share a zoo exhibit. The younger one weighs tons, while the older one weighs 2,400 pounds. Which one weighs more?Explain
Answers
Answer:
if younger one weighs 1 ton, then older one is heavier
Step-by-step explanation:
1 ton = 2000lbs
- 5x15x + 12x - 4x I don’t know how to solve this
Answers
Answer:
Step-by-step explanation:
Multiply the numbers:
-5x*15x + 12x - 4x.
Which should get you: -75xx + 12x - 4x
Then combine exponents : -75xx + 12x - 4 = -75x^2 + 12x - 4x
Combine like terms: -75x^2 + 8x
Then find common factor with is -1
Lastly, rewrite in factored form : -1(75x^2 + 8x) = -1(75x - 8)x
noah spent 150$ to buy movie tickets for 15 students and 3 adults. Adult tickets cost $4 more than student tickets Use A as the price for an adult price and S for the price of student tickets.
Answers
The amounts of each ticket that were purchased are given as follows:
Adult: $11.67.Student: $7.67.How to obtain the amounts?The amounts are obtained using a system of equations, for which the variables are given as follows:
Variable a: number of adult tickets.Variable s: number of student tickets.Noah spent $150 to buy movie tickets for 15 students and 3 adults, hence:
3a + 15s = 150
a + 5s = 50
a = 50 - 5s
Adult tickets cost $4 more than student tickets, hence:
a = 4 + s.
The solution for s is then obtained as follows:
50 - 5s = 4 + s
6s = 46
s = 46/6
s = $7.67.
Then the price of an adult ticket is of:
7.67 + 4 = $11.67.
Missing InformationThe problem asks for the amounts of each ticket that were purchased.
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