The correct options that gives the required type of equation solution to the system of equations are;
No solution;
2•x + 9 + 3•x + x = 6•x + 5
One solution;
2•x + 9 + 3•x + x = 5•x + 9
Infinitely many solutions;
2•x + 9 + 3•x + x = 6•x + 9
What are the types of solutions to a system of equations?The types of solutions of a system of equations are; no solution, infinitely many solutions, one solution
The given expression is; 2•x + 9 + 3•x + x
The above expression when given as the right hand side of an equation gives;
2•x + 9 + 3•x + x = _x + _No solution;
A situation where the right and left hand side of an equation has no solution is where they form lines that do not meet or intersect.
Two lines do not meet when they are parallel, that is when their slopes are the same and however, their y–intercepts are different
Which gives;
Simplifying the expression on the right into the form, m•x + c, where m represents the slope, gives;
2•x + 9 + 3•x + x = 6•x + 9
An expression that can be written on the left that is parallel but does not intersect with the graph of the expression on the left is therefore; 6•x + 5
The first equation is therefore;
No solution;
2•x + 9 + 3•x + x = 6•x + 5One solution;
When the equation has one solution it means that the straight line graphs of the left and right sides intersect once.
Therefore, the lines are not parallel and therefore, the slopes are different, which gives the expression on the right as follows;
2•x + 9 + 3•x + x = 5•x + 9Infinitely many solutions;
When two equations have infinitely many solutions, we have that the equations meet at infinitely many points, such that the equations are essentially the same, which gives the correct option as follows;
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Natalie is competing in the javelin throw event at her school. in order to qualify for the final round, the mean length of her javelin throws in the first round must be at least 195 feet. she has 1 more throw left in the first round. this list shows the length, in feet, of natalie's first 7 javelin throws. 188, 204, 194, 195, 187, 201, 199 question what is the minimum length, in feet, that natalie must throw the javelin on her next throw in order to qualify for the final round? enter the answer in the box.
The minimum length = 192ft, that Natalie must throw the javelin on her next throw in order to qualify for the final round.
Based on the given conditions,
The length of her javelin throws in the first round must be at least 195 feet.
She has 1 more throw left in the first round.
This list shows the length, in feet, of Natalie's first 7 javelin throws.
= 188, 204, 194, 195, 187, 201, 199
The minimum length is,
= 188 + 204 + 194 + 195 + 187 + 201 + 199
= 1368
Let us assume,
Final length = x
So,
We can write,
( x + 1368 ) / 8 ≥ 195
x + 1368 ≥ 195 * 8
We can multiply the coefficient,
x + 1368 ≥ 1560
x ≥ 1560 - 1368
We can sum or difference the coefficient,
x ≥ 192
This is Inequality function.
Equations and inequalities are mathematical sentences formed by relating two expressions to each other. In an equation, the two expressions are supposed to be equal and shown by the symbol =. Whereas in inequality, the two expressions are not necessarily equal and are indicated by the symbols: >, <, ≤ or ≥.
Therefore,
The minimum length = 192ft, that Natalie must throw the javelin on her next throw in order to qualify for the final round.
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equation that is perpendicular to 5x +3y=-21 and passes through (-5,1)
The equation of line perpendicular to the line 5x + 3y = -21 will be;
⇒ y = 3x/5 + 4
What is Equation of line?
The equation of line with slope m and passes through the point
(x₁, y₁) is;
⇒ y - y₁ = m (x - x₁).
Given that;
The equation of perpendicular line is,
⇒ 5x + 3y = -21
And, The point on the line will be (-5 , 1)
Now,
The product of the slopes of the perpendicular line will be -1.
Slope of the perpendicular line 5x + 3y = -21 is;
5x + 3y = -21
y = - 5x/3 - 21/3
y = -5x/3 - 7
dy/dx = m₁ = -5/3
So, The slope of line which is perpendicular to the line is;
m₁ m₂ = -1
m₂ = -1/m₁
m₂ = 3/5
So, The equation of line perpendicular to the line 5x + 3y = -21 and passes through the point (-5, 1) is;
⇒ y - y₁ = m (x - x₁).
⇒ y - 1 = 3/5 (x - (-5)).
⇒ y - 1 = 3/5 (x + 5)
⇒ 5 (y - 1) = 3 (x + 5)
⇒ 5y - 5 = 3x + 15
⇒ 5y = 3x + 15 + 5
⇒ 5y = 3x + 20
⇒ y = 3x/5 + 4
Thus, The equation of line perpendicular to the line 5x + 3y = -21 will be;
⇒ y = 3x/5 + 4
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how much less than 6 is the sum of 2 3/4 and 2 4/5
Answer: 9/20 or 0.45
Step-by-step explanation:
simplify the expression.
Cary's dad gave her $20.00 to spend on shoes at the mall. Cary spent 85% of the money onone pair of shoes. How much money does Cary's dad get back from his $20.00?
Answer:
$3
Step-by-step explanation:
20 - 20 (85%)
= 20 - 17
= 3
Your friend
needs a trumpet for 1 year. She says she
should buy a trumpet because the cost
to rent one for 1 year is about the same
as the cost to buy one. Do you agree?
Explain.
Based on the cost to rent the trumpet, I agree that the trumpet's buying price is almost the same as the cost to rent the trumpet.
How to find the cost of the trumpet?The trumpet would cost about $575 to be bought if the friend decided to buy it outright.
If they decided to rent the trumpet however, the rental cost of the trumpet would be:
= Initial fee + (Monthly fee x Number of months in year)
The initial fee is $25 and the monthly fee is $45. The total cost to rent the trumpet in a year is:
= 25 + (45 x 12)
= 25 + 540
= $565
The cost of renting is $565 and this is close to the cost of buying which is $575.
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Write the EXPLICIT rule for the arithmetic sequence
-10, -3, 4, 11,...
The difference between the following term is 7 and explicit rule is
[tex]a_{n}=-17+7n[/tex]
What is Explicit rule?Explicit rule is a rule that you can solve without needing the previous term.
How Should Explicit Formula Be Written?The nth term in the series is where the explicit formula can be expressed. The explicit formula of the sequence for the arithmetic progression a, a + d, a + 2d, a + 3d,...a + (n - 1)d is formed by the nth term. An = a + (n - 1)d is the explicit formula for this arithmetic series. The explicit formula can also be calculated for the harmonic and geometric sequences.
Here, [tex]a_{n}=-17+7n[/tex]
put n = 1
[tex]a_{n}[/tex]= =-17+7(1)
= -17+7
=-11 which is the first term
similarly for n = 4
-17+7(4)
= -17+ 28 =11 which is the fourth term.
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What is 4+4 I’m feeling generous “I know what it is I’m not that yak bc I can’t say it but have a nice day :)
Answer:
thx for the points have a nice day too
Step-by-step explanation:
Answer: 8
Step-by-step explanation:
Double 4 and add
or
4x2.
( ik this is a joke ;] )
Find the length and width of the greatest rectangular area that the farmer can enclose with 100 m of fencing. the length is m and the width is m.
Answer:
25 length and 25width
Step-by-step explanation:
we need to find the biggest area with a perimeter of 100 and all sides need to be the same. So you divide 100 by 4 and you get 25 for width and 25 for length
A shop sells cola in three different size bottles.
2 Litre
£1.99
600ml
62p
Which size bottle is the best value for money?
You must show all your working.
1.5 Litre
£1.53
Cici likes to collect shoes, but she only has half the number of pairs of shoes that her friend Aubree has. If Cici has 42 pairs of shoes, how many pairs of shoes does Aubree have?
Answer:
84 pairs of shoes
Step-by-step explanation:
Since Cici has pairs of shoes, use this equation to solve for the number of pairs of shoes Aubree has
Can anyone assist me?
please
How to solve for number 3
Answer: m<F = 134
EF = 18in
Step-by-step explanation:
Since both angles FEG and FGE are equal, we could make out that lines EF and FG are equal measures making an isosceles triangle. Therefore we just add up both 23 to get 46 and subtract it by 180 getting 134
A person can burn 120 calories in 15 minutes of running. Calculate how many
calories the person will burn in 1,5 hours.
Question 5.2 [2 marks]
So, if in 15 minutes, a person can burn 120 calories. In 1 minute, a person can burn 8 calories.
120 ÷ 15
8
15 | 120
120
0
8 CALORIES.NOW, how many calories a person burn in 1.5 hours?
FORMULA (HOURS TO MINUTES)60 × 1.5
60
X 1.5
300
60
90.0
90 MINUTES15 minutes x 8 calories = 120 calories (GIVEN)
90 minutes × 8 calories
90
x 8
720
ANSWER = A person can burn 720 calories in 1.5 hours.A random sample of students were asked whether they preferred to sweep the floor or to do the dishes, and whether they preferred to hear music or have silence while doing the chore. The results of the survey are summarized in the table. Sweep Dishes Total Music 60 96 Silence 62 104 Total 78. 122 200 What is the probability that a student prefers to do the chore in silence? O A 0.21 OB. 0.31 Ос 0.39 OD. 0.42 E. 0.52
this is:
[tex]P=\frac{\text{silence}}{\text{total}}=\frac{104}{200}=0.52[/tex]answer: E
Identify the correct equation of a line that passes through the points \displaystyle \left(-6,-10\right)(−6,−10) and \displaystyle \left(6,-2\right)(6,−2).
The equation of the line that passes through the points ( -6,-10 ) and ( 6,-2 ) is y = (2/3)x - 6.
How to determine the equation of a line from two points?The equation of line is expressed as;
y = mx + b
Where m is slope and b is the y-intercept.
Given the data in the question;
Point 1( -6,-10 )
x₁ = -6y₁ = -10Point 2( 6,-2 )
x₂ = 6y₂ = -2First, we determine the slope "m" of the line.
m = ( y₂ - y₁ ) / ( x₂ - x₁ )
m = ( -2 - (-10) ) / ( 6 - (-6) )
m = ( -2 + 10 ) / ( 6 + 6 )
m = 8 / 12
Slope m = 2/3
Next, we determine the y-intercept "b"
y = mx + b
-10 = (2/3)(-6) + b
-10 = -12/3 + b
-10 = -4 + b
b = -10 + 4
b = -6
Now that the values of slope m and y-intercept b is known, plug these into y = mx + b to determine the equation of the line.
y = mx + b
y = (2/3)x + (-6)
y = (2/3)x - 6
Therefore, the equation of the line is y = (2/3)x - 6.
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(100 POINTS PLEASE HELP ME MY GRADE RELY ON IT)
Last weekend, the movie theatre sold a total of 8,500 movie tickets. Proceeds totaled around 64,600.
There are three ways to buy a movie ticket. Matinee tickets costs $5, student tickets is $6 all day, and regular tickets are $8.50.
Twice as many student tickets were sold than
Matinee. Please write the system of equations.
(SHOULD BE 3 EQUATIONS)
Answer:
x= number of matinee tickets sold = 900
y= number of student tickets sold = 1800
z= number of regular tickets sold = 5800
steps below.
If this helped please mark my answer as the brainliest, thank you!
Answer:
System of equations:
[tex]\begin{cases}m + s + r = 8500\\5m + 6s + 8.5r = 64600\\s = 2m\end{cases}[/tex]
(where m is the number of Matinee tickets sold, s is the number of Student tickets sold and r is the number of Regular tickets sold).
Step-by-step explanation:
Given information:
Total tickets sold = 8,500Total proceeds = $64,600Cost of Matinee ticket = $5Cost of Student ticket = $6Cost of Regular ticket = $8.50Twice as many Student tickets were sold than Matinee tickets.Define the variables:
Let m = number of Matinee tickets sold.Let s = number of Student tickets sold.Let r = number of Regular tickets sold.Equation for the total tickets sold:
m + s + r = 8500Equation for the total proceeds:
5m + 6s + 8.5r = 64600Equation for twice as many Student tickets were sold than Matinee tickets:
s = 2mTherefore, the system of equations is:
[tex]\begin{cases}m + s + r = 8500\\5m + 6s + 8.5r = 64600\\s = 2m\end{cases}[/tex]
Solving the system of equations
To solve the found system of equations, substitute the third equation into the first equation and isolate r:
[tex]\implies m+2m+r=8500[/tex]
[tex]\implies 3m+r=8500[/tex]
[tex]\implies r=8500-3m[/tex]
Substitute the found expression for r and the third equation into the second equation and solve for m:
[tex]\implies 5m+6(2m)+8.5(8500-3m)=64600[/tex]
[tex]\implies 5m+12m+72250-25.5m=64600[/tex]
[tex]\implies 72250-8.5m=64600[/tex]
[tex]\implies 8.5m=7650[/tex]
[tex]\implies m=900[/tex]
Therefore, the total number of Matinee tickets sold was 900.
Substitute the found value of m into the third equation and solve for s:
[tex]\implies s=2(900)[/tex]
[tex]\implies s=1800[/tex]
Therefore, the total number of Student tickets sold was 1800.
Substitute the found value of m into the found equation for r and solve for r:
[tex]\implies r=8500-3(900)[/tex]
[tex]\implies r=8500-2700[/tex]
[tex]\implies r=5800[/tex]
Therefore, the total number of Regular tickets sold was 5800.
12% of Cu in a 11.5 g coin
If a coin weighing 11.5 grams, has 12 Percentage of Cu content by mass in it, then the exact quantity of Cu in the coin in grams will be 1.38 grams.
As per the question statement, a coin weighing 12 grams, has 12 % of Cu content by mass in it.
We are required to calculate the exact quantity of Cu present in the coin in grams, from the above mentioned data.
To solve this question, we will simply need to calculate 12% of 11.5, and we will obtain our desired answer, that is,
12% of 11.5 = [(12/100) * 11.5] = (0.12 * 11.5) = 1.38 grams.
Hence, a coin weighing 11.5 grams, having 12 Percentage of Cu content by mass, will have 1.38 grams of Cu inside it.
Percentage: In mathematics, a percentage is a number or a ratio expressed as a fraction of 100 and often denoted using the percent sign, "%", to determine a certain part of one whole.Grams: As per the International System, the gram is a metric unit of mass being equal to one one thousandth of a kilogram.To learn more about Percentage and Grams, click on the link below.
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Answer correctly for 50 points.
Dont lie or i will report you.
Answer: 36 5/9
Step-by-step explanation:
Jonathan wants to buy a lid for his frying pan. The diameter of the pan is 9 inches. What is the approximate circumference of a lid that will fit his frying choices are A 28.26 in B 56.52in C 14.13in D 254.34in
A 28.26
The approximate circumference of a lid that will fit his frying is 28.26.
Circumference of circle
In geometry, the circumference is the perimeter of a circle or ellipse. That is, the circumference would be the arc length of the circle, as if it were opened up and straightened out to a line segment. More generally, the perimeter is the curve length around any closed figure.
Formula of circumference if a circle is 2[tex]\pi[/tex]r.
Given that the diameter of the pan is 9 inches.
Radius of pan = 4.5 inches
Therefore circumference of pan = 2 × (22/7) × 4.5
= 28.28 inches
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In geometry, the circumference is the perimeter of a circle or ellipse. That is, the circumference would be the arc length of the circle, as if it were opened up and straightened out to a line segment. More generally, the perimeter is the curve length around any closed figure.
Formula of circumference if a circle is 2r.
Given that the diameter of the pan is 9 inches.
Radius of pan = 4.5 inches
Therefore circumference of pan = 2 × (22/7) × 4.5
= 28.28 inches
the answer for y-3=-3y-43
Collect like terms: 3x(exponent of 2) + 2x + 3x -1
The like terms in the expression are 2x and 3x, and the solution is 3x^2 + 5x - 1
What are expressions?Expressions are mathematical statements that are represented by variables, coefficients and operators
How to collect the like terms?The expression is given as
3x(exponent of 2) + 2x + 3x -1
Rewrite the expression properly
So, we have
3x^2 + 2x + 3x -1
The like terms are the expressions that have the same variables
In this expression, the like terms are 2x and 3x
When evaluated, we have
3x^2 + 5x - 1
Hence, the equivalent expression is 3x^2 + 5x - 1
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Carly is saving money babysitting on the weekends. last month, she saved $120. this month, carly saved 30% more than she saved last month. how much did she save this month?
Question: Carly is saving money babysitting on the weekends. last month, she saved $120. this month, carly saved 30% more than she saved last month. how much did she save this month?
Answer: Goodmorning: } It's $156.
Step-by-step explanation: you would change the 30% to a decimal by moving the decimal point two spaces to the right.
this would get you .30 or .3
you would then multiply the $120 by .3
you would get 36
then since she saved 30% MORE you would add the 36 to the 120 and get 156.
Have a nice day !!!
Which equation represents a line which is perpendicular to the line y=2x-4?
Answer:
y = -1/2x - 4
Step-by-step explanation:
The perpendicular line always changes with the negative reciprocal of the slope.
You have 270 ft^2 of carpet. You want to install carpeting in a room that is 20 ft long and 15 ft wide. Do you have enough carpet? Explain how you know. (1pt)
Answer: No, there isn't enough carpet
Explanation:
The room is 20 feet by 15 feet. The floor area is length*width = 20*15 = 300 square feet, which is larger than the 270 sq ft of carpet you have available. Therefore, you don't have enough carpet. The amount needed is 300-270 = 30 sq ft
Answer:
No
Step-by-step explanation:
20 ft*15 ft=300 ft^2
you need to cover 300 ft^2
you only have 270 ft^2
so you can't cover it
Does this graph show a function? Explain how you know.
O A. Yes; there are no y values that have more than one x-value.
B. No; there are y values that have more than one x-value.
C. Yes; the graph passes the vertical line test.
D. No; the graph fails the vertical line test.
If a vertical line exists moved across the graph and, at any time, touches the graph at only one point, then the graph exists a function. If the vertical line touches the graph at more than one point, then the graph is not a function.
What is meant by vertical line test?The vertical line test is a visual approach for assessing whether a curve in the plane accurately depicts the graph of a function by counting the points on the curve where vertical lines cross it. Consequently, any vertical line in the plane can only ever cross the graph of a function once.
Use the vertical line test to define whether or not a graph represents a function. If a vertical line exists moved across the graph and, at any time, touches the graph at only one point, then the graph exists a function. If the vertical line touches the graph at more than one point, then the graph is not a function.
Therefore, the correct answer is option D. No, the graph fails vertical line test.
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6. Trapezoid ABCD with vertices A(-3, 6), B(0, 7),
C(1, 4), and D(-5, 2): (x,y) → (x + 4, y - 1)
A' (
B (
CC.
D’______
The new vertices of the trapezoid after translation:
A'( - 7, 8 ), B'( 7, 2 ), C'( - 1, 0 ), and D'( - 3, 4 ).
Consider the trapezoid ABCD with vertices as:
A( - 3, 6 ), B( 0, 7 ), C( 1, 4 ), and D( - 5, 2 )
When a figure is relocated from one place to another without changing its size, shape, or orientation, a transition known as translation takes place.
For example: ( x, y ) → ( x + 4, y - 1 )
Consider the point ( - 3, 6 ),
Point A when translated 4 units horizontally to the left and 2 units upward will be:
A( - 3, 6 ) → A'( - 3 - 4, 6 + 2 ) = A'( - 7, 8 )
Point B when translated to the right by 7 units and downwards by 5 units will be:
B( 0, 7 ) → B'( 0 + 7, 7 - 5 ) = B'( 7, 2 )
Point C when translated to the left by 2 units and downwards by 4 units will be:
C( 1, 4 ) → C'( 1 - 2, 4 - 4 ) = C'( - 1, 0 )
Point D when translated to the right by 2 units and upwards by 2 units will be:
D( - 5, 2 ) → D'( - 5 + 2, 2 + 2 ) = D'( - 3, 4 )
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2.10 guessing on an exam: in a multiple choice exam, there are 7 questions and 4 choices for each question (a, b, c, d). nancy has not studied for the exam at all and decides to randomly guess the answers. what is the probability that: (please round all answers to four decimal places)
I need help on this question
Yes, The triangles are congruent by SSS i,e option(D)
What are Congruent triangle?
When two corresponding sides and the angle included between them of one triangle match those of two corresponding sides and the angle included between them of another triangle, the two triangles are said to be congruent. Two triangles are said to be congruent if their three sides and three angles, in any orientation, are equal.
By applying the CPCTC (Corresponding Parts of Congruent Triangles are Congruent) theorem, the two sides of the triangle in issue are made equal, hence making the third sides equal.
Therefore, we can say the triangles are congruent by SSS i,e option(D)
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Which is the best estimate of 11-2?
04
06
O22
33
How do I graph the function y = -2/3
The graph for the function y = -2/3 is shown in the image below.
How to Graph the Function of a Horizontal Line?The function of a horizontal line is expressed as y = b, where b is the point on the y-axis where the line intercepts the y-axis.
This means that, the graph of y = b would be a graph that has its line cutting across the y-axis at point b on the y-axis, showing a horizontal line.
Given the function, y = -2/3, this shows that b, which is -2/3, is the value of the y-coordinate where the line intercepts or cuts the y-axis. The graph of this function would be a graph that is horizontal and passes through the point, y = -2/3 on the y-axis.
The graph of y = -2//3 is given in the diagram attached below.
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