Answer:
parallel
Step-by-step explanation:
same slope
Ruby and her children went into a movie theater and she bought $42 worth of bags of popcorn and drinks. Each bag of popcorn costs $6 and each drink costs $4. She bought a total of 8 bags of popcorn and drinks altogether. Determine the number of bags of popcorn and the number of drinks that Ruby bought.
Answer:
5 bags of popcorn
3 drinks
Step-by-step explanation:
Let's set up a system of equations!
Let p equal the number of bags of popcorn and d be the number of drinks.
We know Ruby bought 8 total, so we know [tex]p + d = 8[/tex]. We also know that she spent $42 total, so we can multiply their respective costs by the number to set up another equation: [tex]6p+4d=42[/tex]. We have our system of equations now!
Let's use substitution to solve this. From the first equation, subtracting p from both sides gives us that [tex]d=8-p[/tex]. We can plug this into our second equation to solve for p. Plugging in this for d gives us [tex]6p+4(8-p)=42[/tex]. Multiplying through and then combining like terms results in [tex]32+2p=42[/tex]. We then can subtract 32 from both sides and divide us by 2, which gives us that p = 5.
Now we solve for d! We can plug in the value of p into the equation [tex]p+d=8[/tex], to get that d = 3. To check our work, we can plug these values into the other equation, which gives us [tex]6*5 + 4*3 = 42[/tex]. This is true, so our values are correct!
Thank you! Feel free to contact me with any questions about my answer. I hope this helps!
six countries in a certain region sent a total of 75 representatives to an international congress, and no two countries sent the same number of representatives. of the six countries, if country a sent the second greatest number of representatives, did country a send at least 10 representatives?
One of the six countries sent 41 representatives to the congress.
What, in the simplest words, is the Congress?
The Congress is our country's legislative body, which drafts our laws. The United States Senate and the United States House of Representatives are the two branches of Congress.
Each state has two U.S. Senators and a minimum of one U.S. Representative; the number of U.S. Representatives that can be elected depends on the number of citizens in the state.
(1) One of the six countries sent 41 representatives to the congress
(2) Country A sent fewer than 12 representatives to the congress
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which graph represents the solution to this system of inequalities? y < -x - 3 y > 2x - 4
The intersection region of every solution in the system of inequalities is the system's solution. Inequality y≤x2 should be graphed first. y=x2 serves as the related equation.
Which point is a solution to the system of inequalities?Get y alone on one side of a two-variable linear inequality (like x and y) before graphing it. Once the inequality sign has been replaced with an equality sign, take into consideration the relevant equation that results. This equation's graph is a straight line.Create a comparable graph for every systemic inequality. The intersection region of every solution in the system of inequalities is the system's solution.Example
Graph the inequalities and solve the system:
y≤x−2y>−3x+5
Inequality yx2 should be graphed first. y=x2 serves as the related equation.
The border line is solid due to the inequality's, which is not a rigid one.
The inequality yx2 should be substituted in for a point that is not on the line, such as (0,0).
0≤0−20≤−2
It's untrue. The point (0,0) is therefore not part of the solution. Subtract from the line's lower half.
To do the same for the second inequality's related equation, y>3x+5, which has a rigorous inequality, draw a dashed line. The half that does not contain the point (0,0) should be shaded because it does not satisfy the inequality at that location.
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A ladder is leaning against a building forming a 25-degree angle with the building. If the ladder is 8 feet away from the building, how long is the ladder?
A: About 15 ft.
B: About 7.5 ft.
C: About 9 ft.
D: About 3 ft.
Answer: About 15 feet.
Step-by-step explanation: To solve this problem, we can use the Pythagorean theorem. The ladder forms the hypotenuse of a right triangle with the building and the ground, with the angle at the building forming the right angle. If the ladder is 8 feet away from the building, then the length of the ladder is the same as the length of the other leg of the triangle.
We can use trigonometry to find the length of this leg. In a right triangle, the tangent of an angle is equal to the length of the opposite side divided by the length of the adjacent side. In this case, the adjacent side is the length of the ladder and the opposite side is 8 feet, so we can write the following equation:
tan(25 degrees) = opposite side / adjacent side
tan(25 degrees) = 8 feet / adjacent side
To find the length of the adjacent side (the ladder), we can divide both sides of the equation by the tangent of 25 degrees:
adjacent side = 8 feet / tan(25 degrees)
According to my calculations, the length of the ladder is about 15 feet, so the correct answer is A: About 15 ft.
Mariya is solving the quadratic equation by completing the square.
4x2-20x+3=0
4x2-20x=-3
A(x2-5x)=-3
What is the value of A?
Answer:
A = 4
Step-by-step explanation:
4x2-20x=-3 and A(x2-5x)=-3
Hence:
4x2-20x = A(x2-5x)
4x^2 - 20x = A(x^2 - 5x)
Divide both sides by (x^2 - 5x) to isolate A:
(4x^2 - 20x)/(x^2 - 5x) = (x^2 - 5x) * A/(x^2 - 5x)
A = (4x^2 - 20x)/(x^2 - 5x)
A = (4x(x - 5)) / (x(x - 5)) ==> factor each polynomial
A = (4x) / (x) * (x - 5)/(x - 5)
A = (4x) / (x) * 1 ==> (x-5)/(x-5) = 1
A = (4x) / (x)
A = 4x/x ==> simplify
A = 4
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Find the area of the following parallelogram:
3cm,5cm, and 4.5
What is the area of the parallelogram?
Please show your work.
Step-by-step explanation:
Area of parallelogram = base • height
Where,
Base = 4.5 cm
Height = 5 cm.
Area = 4.5 cm • 3 cm
Area = 13.5 cm²
Have a nice day :)
Solve each system by elimination: 4x-7y=10 3x+2y=-7
Using the elimination method, the solution to the system of equations is as follows:
x = 19 / 13 and y = - 74 / 13
How to solve system of equation?System of equations can be solved using different methods such as the elimination method, substitution method, and graphical method.
Let's use the elimination method to solve the system of equations as follows:
The elimination method is the process of eliminating one of the variables in the system of equations using the addition or subtraction methods in conjunction with the multiplication or division of coefficients of the variables.
Therefore,
4x - 7y = 10
3x + 2y = -7
multiply equation(ii) by 3.5
4x - 7y = 10
10.5x - 7y = 24.5
subtract equation(i) from equation(ii)
6.5x = 14.5
x = 14.5 / 6.5
x = 145 / 65
x = 19 / 13
Let's find y
3(19 / 13) + 2y = -7
57 / 13 + 2y = -7
2y = - 7 - 57 / 13
2y = -91 - 57 / 13
2y = - 148 / 13
cross multiply
26y = - 148
y = - 148 / 26
y = - 74 / 13
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b) Since Barrow is looking for a good batter for his team, do you think that the batting average or the
slugging average is more indicative of a good batter? Answer the question and explain your
reasoning in 2-3 sentences.
Slugging average is more indicative of a good batter rather than batting average.
Define slugging average.The total number of bases a player accumulates per at-bat is represented by slugging percentage. In contrast to on-base percentage, which takes walks and hit-by-pitch pitches into account, slugging percentage simply considers hits. Slugging average is distinct from batting average in that not every hit is worth the same amount.
Given
Since Barrow is looking for a good batter for his team
In my point of view, Slugging average is more indicative of a good batter.
The slugging percentage is a player's average number of bases per at-bat. Slugging percentage, unlike on-base percentage, solely accounts for hits and excludes walks and hit-by-pitch pitches from its computation. In contrast to batting average, slugging percentage does not reward every hit equally.
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Select the correct text.
A spherical ball for a machine was made with a radius of 2 centimeters.
If the ball has a mass of 278.1 grams, which material was used to make the ball?
Copper-8.3 g/cm³
Brass -8.6 g/cm³ Iron - 7.8 g/cm³
The mass of the ball is 278.1 g, the material used to make the ball must be brass which having density of 8.6 g/cm³.
How to find mass of the ball ?To determine the material used to make the ball, we need to first calculate the volume of the ball.
The volume of a sphere with radius r is given by:
V = (4/3) * π * r^3
Plugging in the given values, we get:
V = (4/3) * π * (2 cm)^3
= (4/3) * π * 8 cm^3
= (4/3) * 8π cm^3
= 32π cm^3
We can then use the density of each material (given in g/cm³) to calculate the mass of the ball if it were made of that material:
Copper: 8.3 g/cm³ * 32π cm³ = 266.4 g
Brass: 8.6 g/cm³ * 32π cm³ = 275.2 g
Iron: 7.8 g/cm³ * 32π cm³ = 250.4 g
Since the mass of the ball is 278.1 g, the material used to make the ball must be brass.
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un camion lleva 2 646 kilos de naranja en 147 cajas. ¿ cuantos kilos pesa cada caja?
por faaaa ayuda....
18 Kilos
Step-by-step explanation:
2646 /147 = 18
please answer the problem in the image :)
question: "The lengths of the three sides of a triangle (in centimeters) are consecutive odd integers. If the perimeter is 45 centimeters, find the value of the shortest of the three side lengths."
The value of the shortest of the three sides of the triangle is 13 cm.
How to find the length of a triangle?A triangle is a polygon with threes sides. The perimeter of a triangle is the sum of the whole three sides.
The lengths of the three sides of a triangle (in centimetres) are consecutive odd integers. The perimeter is 45 cm.
The shortest side of the three sides can be calculated as follows:
let
the first side = x
second side = x + 2
third side = x + 4
Hence,
perimeter = x + x + 2 + x + 4
45 = 3x + 6
45 - 6 = 3x
3x = 39
divide both sides by 3
x = 39 / 3
x = 13
Therefore,
shortest side = 13 cm
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If CD represents 100%, what is the length of a line segment that is 25%? Explain.
Answer: (1/4)CD
Step-by-step explanation:
CD is 100% when the line segment is 25% of it or 1/4 of it! Then the line segment is (1/4)CD.
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RST and WXY are similar triangles. RS = 2, WX = 5, ST = x + 1, and XY = 3x-1
Solve for x. HELP PLEASE ANYONE
Answer: x=7
Step-by-step explanation:
2/5=x+1/3x-1
find the LCD
15x-5
multiply 2/5 by 3x-1
multiply x+1/3x-1 by 5
6x-2=5x+5
x=7
How do I graph the line that has a slope of 1/10 and includes the point (0, 5)???
Answer:
Step-by-step explanation:
A 10% slope is one that rises by 1 unit for every 10 units travelled horizontally (10 %). For example, a roof with a 10% slope that is 20 m across will be 2 m high. This is the same as a gradient of 1/10, and an angle of 5.71° is formed between the line and the x-axis.
Shelly wants to tell her friend how large of a sale a
local store is having, but she forgets the discount
amount. All Shelly knows is that she bought a
shirt for $6 that normally costs $10. Shelly can
tell her friend that the store has decreased prices
by how much?
EXPERT NEEDED!! please help me with these! much appreciated
The value of a is -4 from the given system of linear equations.
The system of given equations are ax+12y=-6 and 2x-6y=4.
What is a linear system of equations?A system of linear equations consists of two or more equations made up of two or more variables such that all equations in the system are considered simultaneously. The solution to a system of linear equations in two variables is any ordered pair that satisfies each equation independently.
Here, ax+12y=-6 -------(I) and 2x-6y=4 -------(II)
Given, no solution for the system
So, (a1/a2) = (b1/b2) ≠ (c1/c2)
Now, a/2 = 12/(-6)
a=-4
Hence, the value of a is -4 from the given system of linear equations.
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For a ride on a rental scooter, Kevin paid a $2 fee to start the scooter plus 12 cents per minute of the ride. The total bill for Kevin's ride was $19.64. For how
many minutes did Kevin ride the scooter?
minutes
Answer:
1 minute, Because per minute is $2, 12 cents
A large tree casts a shadow that is 51 feet long. A 6-foot-tall person standing next to the tree casts a shadow that is 4.5 feet long. How tall is the tree?
Answer:
68 feet tall
Step-by-step explanation:
Imagine the shadows for both the tree and the person are set up like right triangles. The length of their shadows are the bases of the triangles, while the actual heights of the tree and person are the heights of the triangle. We can set up proportions since "height of the person" divided by " their shadow's length" should equal "height of tree" divided by "tree shadow length".
Set up a proportion of the person's high height relative to their shadow's length (which is 6/4.5). Set this equation equal to the tree's proportion (which is x/51).
Solve for x.
[tex]\frac{6}{4.5} = \frac{x}{51}\\Isolate x by multiply 51 to both sides\\\\(306/4.5)=x\\68=x[/tex]
The proportion is solved and the height of the tree is A = 68 feet
What is Proportion?The proportion formula is used to depict if two ratios or fractions are equal. The proportion formula can be given as a: b::c : d = a/b = c/d where a and d are the extreme terms and b and c are the mean terms.
The proportional equation is given as y ∝ x
And , y = kx where k is the proportionality constant
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Given data ,
Let the proportion be represented as A
Now , the value of A is
Now , we can set up the following proportion:
Height of tree / length of tree's shadow = height of person / length of person's shadow
On simplifying , we get
A / 51 = 6 / 4.5
Now we can solve for A by cross-multiplying and simplifying:
A = 51 x 6 / 4.5
A = 68 feet
Therefore, the tree is 68 feet tall
Hence , the proportion is solved
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( x + 4 ) ( 2 x + 9 )
Simplifying the algebraic expression [tex]( x + 4 ) ( 2 x + 9 )[/tex] will give an answer [tex]2x^{2}+17x+36[/tex].
The technique of writing an algebraic expression in the most effective and compact form without altering the original expression's value is known as simplification.
The procedure involves gathering related phrases, which calls for adding or removing terms from an expression.
According to the distributive property of algebraic expressions, each term in an expression's sum or difference must be multiplied by a number outside of the parenthesis. A number is used as the value outside of the parenthesis with the total or difference.
Here the algebraic expression is:
[tex]( x + 4 ) ( 2 x + 9 )[/tex]
Use the distributive property to simplify the expression,
⇒ [tex]( x + 4 ) ( 2 x + 9 )[/tex]
⇒ [tex](x)(2x)+(x)(9)+(4)(2x)+(4)(9)[/tex]
⇒ [tex]2x^{2} +9x+8x+36[/tex]
⇒ [tex]2x^{2} +17x+36[/tex]
Therefore, the solution will be [tex]2x^{2} +17x+36[/tex] when the algebraic expression is simplified.
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Draw the graph for y=2x-3 for -2<=x<=3
The coordinates in a graph indicate the location of a point with respect to the x-axis and y-axis.
The coordinates in a graph show the relationship between the information plotted on the given x-axis and y-axis.
The graph is shown below.
What are coordinates in a graph?The coordinates in a graph indicate the location of a point with respect to the x-axis and y-axis.
The coordinates in a graph show the relationship between the information plotted on the given x-axis and y-axis.
We have,
y = 2x - 3 for -2 ≤ x ≤ 3.
The x values are between -2 and 3
For x = -2,
y = 2 x (-2) - 3 = -4 - 3 = -7
For x = 3,
y = 2 x 3 - 3 = 6 - 3 = 3
Now,
The graph is shown below.
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Write 1.3 days in hours and minutes.
In 1 day, there are 24 hours.
In 1 hour, there are 60 minutes.
Solving the QuestionTo convert 1.3 days into hours, multiply by 24:
[tex]1.3*24=31.2[/tex]
Therefore, 1.3 days is equivalent to 31.2 hours.
To convert 31.2 hours into minutes, multiply by 60:
[tex]31.2*60=1872[/tex]
Therefore, 31.2 hours is equivalent to 1872 minutes.
Answer1.3 days
31.2 hours
1872 minutes
Perimeter: ___meters
Answer:
300
Step-by-step explanation:
the way to find perimeter is to add the numbers that are on the outside of the shape.
Answer: 300m
Step-by-step explanation: To find the Perimeter of the triangle or any shape, you need to add the length of the outside!
In this case, it is 104, 58, 138. Add all of them together you get 300m
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A basketball coach recorded how many shots each of the 30 players at tryouts made in a set of 6
attempts. Here are the results:
The median would lie in the mean of the 15th and the 16th position.
What is median?The middle value in a sorted, ascending or descending list of numbers is known as the median, and it has the potential to describe a data collection more accurately than the average does. It reflects the midway of the data since it is the point above and below which half (50%) of the observed data falls.
The mean (average), mode, and standard deviation are some other descriptive statistics that are frequently contrasted with the median.
Given, the total number of basketball players present (n) = 30
Total number of attempts made = 6
Since there are even number of players present, 30, the location of the median would be n/2 and n/2 + 1 positions.
For 30, the positions would be
= 30/2 and 30/2 + 1
= 15 and 16th position
Hence, the median would lie in the mean of the 15th and the 16th position.
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rate?
2) James Bond took 4.5 minutes to complete a Grand Prix circuit when driving at an average speed.
97 mph. How long would it take to complete one circuit driving at a speed of 112 mph.
Answer: 30 meters
Step-by-step explanation:
A boy is standing on an elevator which is traveling downward with a constant velocity of 30 meters per second.
What is the minimum temperature?
STEM AND LEAF
I will appreciate your help cause my grade is going down :(
7) The minimum temperature is 31⁰F. So, the answer is option B.
What is stem and leaf plot?The frequency of various types of values can be easily observed using a stem and leaf plot, also known as a stem and leaf diagram. This graph displays numerical data that is arranged in chronological order. There is a stem and a leaf for each piece of data.
Each first or second digit of the data value is divided into a stem, and the last digit is represented by a leaf, in a stem and leaf plot, which is represented by a particular table. The stem and leaf plot key is the "|" symbol that is used to indicate the values of the stem and the leaf. In the case of 46, the stem is 4 and the leaf is 6.
7) The minimum value in the stem is 3
And the minimum value in the leaf is 1
So, according to the given key 4|3=43°F
Here | denotes the key symbol.
So, in this solution the minimum value of stem is 3 and the minimum value of leaf is 1
Therefore, it must be 3|1
Hence, from the given key
This can be written as 31⁰F
Therefore, the answer is option B.
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Given: Triangle ABC i iocele with A a the vertex angle and egment AD biect egment BC, Prove: Segment AD biect angle BAC
Proof that the bisector of an isosceles triangle also bisects the angle.
Is bisector a midpoint?A line segment's midpoint is the point on the segment where it divides into two congruent parts. a right-angled segment bisector that crosses the segment. A line (or portion of a line) that cuts through the middle is known as a segment bisector.
Is the bisector always 90?When two lines cross at right angles or 90 degrees, they are said to be perpendicular to one another. A line that splits a line into two equally sized halves is known as a bisector. A line segment's perpendicular bisector implies that it intersects the segment at a 90-degree angle and splits it into two equal halves.
Let ABC be the isosceles triangle with AB=AC, B=C, and BAD=CAD as the vertical angle bisectors.
As a result, the triangles satisfy the ASA criterion.
⟹BD=DC
Thus, the base is divided by the vertical angel's bisector.
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When Alvin woke up in the morning, it was –
9°F. By the afternoon, the temperature had risen to –
2°F.
There is a 7°F difference in temperature between the morning and the afternoon.
What causes the temperature change?A body's level of heat might alter as a result of a temperature shift.To calculate the difference, subtract the final temperature from the initial temperature.Change in temperature now equals -2-(-9) = -2+9=7.As a result, there is a 7°F difference in temperature from morning to afternoon.Alvin awoke in the morning to a temperature of -9°F. The afternoon saw a rise in temperature to -2°F.We need to figure out why the temperature changed from the morning to the afternoon.To learn more about change in temperature refer to:
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The sum of two numbers is 33. One number is 2 times as large as the other. What are the numbers?
Find the range of the function f(x)=x^2- 6x if the domain is (-7,-2, 1)
The range of the function will be;
⇒ Range = (91, 16, - 5)
What is Domain?The set of all inputs of the function is called Domain of set.
Given that;
The function is,
⇒ f (x) = x² - 6x
And, The domain = (- 7, - 2, 1)
Now,
Since, The function is,
⇒ f (x) = x² - 6x
We know that;
The range of the function gives the value of y.
Here, The domain (x) = (- 7, - 2, 1)
Put x = - 7;
⇒ f (-7 ) = (-7)² - 6 × - 7
= 49 + 42
= 91
Put x = - 2;
⇒ f (- 2) = (-2)² - 6 × - 2
= 4 + 12
= 16
Put x = 1;
⇒ f (1) = (1)² - 6 × 1
= 1 - 6
= - 5
Thus, The range = (91, 16, - 5)
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If a statistic used to estimate a parameter is such that the mean of its sampling distribution is equal to the true value of the parameter being estimated, what is the statistic said to be?.
The statistic said to be Unbiased Estimator If a statistic used to estimate a parameter is such that the mean of its sampling distribution is equal to the true value of the parameter being estimated.
What is statistic?The study of statistics focuses on gathering, organizing, organizing, analyzing, interpreting, and presenting data. It is customary to start with a statistical population or a statistical model to be researched when applying statistics to a scientific, industrial, or social problem. Statistics are numerical representations of sample characteristics. One population parameter is the average income in the United States. On the other hand, a sample statistic is the average income for a sample taken from the United States. Although both figures correspond to the mean income, only one is a statistic.
Here,
The reported statistic is Independent Estimator If the mean of the sampling distribution for a statistic used to estimate a parameter matches the actual value of the parameter being estimated.
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