4. Martin was asked to solve the following system of equations. Hegraphed the two equations below, and decided that the answer was"infinitely many solutions". Do you agree with Martin? Why or why not? Ifyou disagree, what should the answer be?*y=-x-3y=-***+3
Answers
Types of solutions in a system of equations:
Based on this image, we can see that when they are parallel lines (same slope), there is no solution because the lines never touch.
The type of solution Martin was describing is when the lines are the same (letter b in the image) and it looks like one line when graphed.
Answer: We disagree with Martin because the lines never touch, meaning that the system has no solutions.
Related Questions
1. Alice made the conjecture below.(a + b)2 = a + b2OWhich values of a and b are not counterexamples to the conjecture?a = 1, b = 1a = 0, b = 1aa = -1, b = 1a = -1, b = 2
Answers
the expression is
(a+b)^2=a+b^2
substitute a=1 and b=1
(1+1)^2 = 1+1^2
4=2
that is not possible. so these are the values of a and b that is not counterpart example to the conjecture.
now substitute a=0, b=1
(0+1)^2 = 0+1^2
1=1
so this is true for the above expression.
now for a=-1, b=1
(-1+1)^2 = -1+1^2
0=0
this is true.
now for a=-1, b=2
(-1+2)^2 = -1+2^2
1=3
that is not possible
so a=1, b=1 and a=1,b=2 is the values that not counterpart example to the conjecture.
express the fuction graphed on the axes below as a piecewise function
Answers
Concept
Find the equation of line for the second line.
x1 = -2 y1 = 1
x2 = -4 y2 = 2
Next, apply equation of a line formula
[tex]\begin{gathered} \frac{y-y_1}{x-x_1\text{ }}\text{ = }\frac{y_2-y_1}{x_2-x_1} \\ \frac{y\text{ - 1}}{x\text{ + 2}}\text{ = }\frac{2\text{ - 1}}{-4\text{ + 2}} \\ \frac{y\text{ - 1}}{x\text{ + 2}}\text{ = }\frac{1}{-2} \\ -2(y\text{ - 1) = 1(x + 2)} \\ -2y\text{ + 2 = x + 2} \\ -2y\text{ = x} \\ y\text{ = }\frac{-1}{2}x \end{gathered}[/tex]Final answer
The graphed as a piecewise function is given below
determine whether the equation is linear to x. 5-3x=0
Answers
By definition a linear equation is an equation in which the highest power of any variable in the equation is always 1. In this case we have the equation:
[tex]5-3x=0[/tex]We notice that this equation only has one variable, x, and that its power is 1. Therefore, the equation is linear.
May I please get help with this math problem. I am so lost and confused
Answers
We are given three angles and we are asked to determine if the angles are the angles of a triangle. To do that we need to have into account that the measure of the angles of a triangle always adds up to 180, therefore, if we add up the angles and the result is 180, then these angles can be angles measures of a triangle. If the result is different from 180 the angles can't be the angle measures of a triangle. Taking the first set of three angles we get:
[tex]58+34+42=134[/tex]Since the result is different from 180 then these angles can't be the angle measure of a triangle.
The same procedure is used to determine the other sets of angles.
Consider the following expression:-27 x (-18)By the laws of signs, this is equivalent to27 x 18 this is equivalent to:27 x 18= 486we can conclude thatthe correct answer is:486I feel like that’s wrong, it’s not algebra can anyone help
Answers
The answer is actually CORRECT.
The correct procedure is when two negatives multiply each other, the answer is always a positive.
Therefore;
[tex]\begin{gathered} -27\times(-18)=27\times18 \\ 27\times18=486 \end{gathered}[/tex]We can conclude that the correct answer is 486
A factory makes car batteries. The probability that a battery is defective is1/6 If 400 batteries are tested, about how many are expected to be defective?A. 40 B. 25C. 16D. 375
Answers
Since there are 400 batteries are tested
Since the probability of the defective batteries is 1/6
The number of defective batteries =
[tex]\frac{1}{16}\times400=25[/tex]The answer is B
linear equation in deletion method2x + y − 3z = 13x − y − 4z = 75x + 2y − 6z = 5
Answers
The given system is:
[tex]\begin{gathered} 2x+y-3z=1\ldots(i) \\ 3x-y-4z=7\ldots(ii) \\ 5x+2y-6z=5\ldots(iii) \end{gathered}[/tex]Add (i) and (ii) to get:
[tex]\begin{gathered} 2x+y-3z=1 \\ + \\ 3x-y-4z=7 \\ 5x-7z=8\ldots(iv) \end{gathered}[/tex]Multiply (ii) by 2 to get:
[tex]6x-2y-8z=14\ldots(v)[/tex]Add (iii) and (v) to get:
[tex]\begin{gathered} 6x-2y-8z=14 \\ + \\ 5x+2y-6z=5 \\ 11x-14z=19\ldots(vi) \end{gathered}[/tex]Multiply (iv) by 2 to get:
[tex]10x-14z=16\ldots(vii)[/tex]Subtract (vii) from (vi) to get:
[tex]\begin{gathered} 11x-14z=19 \\ - \\ 10x-14z=16 \\ x=3 \end{gathered}[/tex]Put x=3 in (iv) to get:
[tex]\begin{gathered} 5\times3-7z=8 \\ -7z=8-15 \\ -7z=-7 \\ z=1 \end{gathered}[/tex]Put x=3 and z=1 in (i) to get:
[tex]\begin{gathered} 2(3)+y-3(1)=1 \\ 6+y-3=1 \\ y+3=1 \\ y=-2 \end{gathered}[/tex]So the values are x=3,y=-2 and z=1.
Find the slope of the line that passes through (9, 9) and (6, 7)
Answers
The slope of the line passing through the coordinates (9, 9) and (6, 7) is 2/3.
What is the slope of the line with the given coordinates?Slope is simply expressed as change in y over the change in x.
Slope m = ( y₂ - y₁ )/( x₂ - x₁ )
Given the data in the question;
Point 1( 9, 9 )
x₁ = 9y₁ = 9Point 2( 6, 7 )
x₂ = 6y₂ = 7To determine the slope, plug the given x and y values into the slope formula and simplify.
Slope m = ( y₂ - y₁ )/( x₂ - x₁ )
Slope m = ( 7 - 9 )/( 6 - 9 )
Slope m = ( -2 )/( -3 )
Slope m = ( 2 )/( 3 )
Slope m = 2/3
Therefore, the slope of the line is 2/3.
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The slope of the required line is 2/3 which passes through points (9, 9) and (6, 7).
What is the slope of the line?The slope is simply expressed as an inclination of the line in the coordinate system.
Slope m = (y₂ - y₁) / (x₂ - x₁)
Given that the line that passes through two points (9, 9) and (6, 7)
Let x₁ = 9, y₁ = 9 and x₂ = 6, y₂ = 7
The slope of the required line is
m = (y₂ - y₁ )/( x₂ - x₁ )
Substitute the values in the formula to get the slope of the line,
m = ( 7 - 9 )/( 6 - 9 )
m = ( -2 )/( -3 )
m = ( 2 )/( 3 )
m = 2/3
Therefore, the slope of the line would be 2/3.
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7+[9÷(9x1 to the second power)]
Answers
The value of the expression 7+[9÷(9x1 to the second power)] is 64/9
What is a fraction?A fraction can be described as the part of a whole set or element.
There are several types of fractions, which includes;
Simple fractionsComplex fractionsMixed fractionsProper fractionsImproper fractionsSome examples of these fractions are given as;
Simple fractions: 1/5, 1/6
Mixed fractions: 2 1/8, 3 1/4
Proper fractions: 2/3, 4/5
Improper fractions; 4/1, 6/3
Given the expression;
7+[9÷(9x1 to the second power)]
This is expressed as;
7 + ( 9 ÷ (9)^2
Find the square
7 + ( 9 ÷ 81)
find the ratio
7 + 1/9
Find the common multiple
63 + 1 /9
64/9
Hence, the value is 64/9
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Triangle ABC lies on the coordinate plane with vertices located at A(7,6), B(-3,5), and C(-4,9). The triangle is transformed using the rule (x,y) -> (2x,y-3) to create triangle A'B'C'. Select all possible answers for the vertices of triangle A'B'C'. Question 1 options: (14,3) (9,3) (-6,10) (-8,6) (-6,2)
Answers
All of the possible answers for the vertices of triangle A'B'C' after using this translation rule (x, y) → (2x, y - 3) include the following:
A. (14, 3)
D. (-8, 6)
What is a translation?In Geometry, a translation can be defined as a type of transformation which moves every point of a geometric figure or object in the same direction, as well as for the same distance.
Next, we would transform triangle ABC by using this translation rule (x, y) → (2x, y - 3) to create the vertices of triangle A'B'C' as follows:
(x, y) → (2x, y - 3)
Coordinate A = (7, 6) → Coordinate A' (2(7), 6 - 3) = (14, 3)
Coordinate B = (-3, 5) → Coordinate B' = (2(-2), 5 - 3) = (-4, 2)
Coordinate C = (-4, 9) → Coordinate C' = (2(-4), 9 - 3) = (-8, 6)
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Solve for x: 4 open parentheses 2 x minus 1 close parentheses plus 8 minus 14 x equals negative 8 x plus 4 plus 2 x The solution is X = _________
Answers
Answer:
x = 1
Step-by-step explanation:
4(2x-1)+8-14= -8x+ 4+ 2x
Compare A and B in three ways, where A = 51527 is the number of deaths due to a deadly disease in the United States in 2005 and B = 17241 is the number of deaths due to the same disease in the United States in 2009. a. Find the ratio of A to B. b. Find the ratio of B to A. c. Complete the sentence: A is ____ percent of B.
Answers
ANSWER
Ratio of A to B = 2.99 (to 2 decimal places)
Ratio of B to A = 0.33 (to 2 decimal places)
A is 299% of B (to nearest integer)
STEP BY STEP EXPLANATION
for ratio of A to B:
[tex]\begin{gathered} \frac{A}{B}\text{ = }\frac{51527}{17241}\text{ = }2.98863 \\ \text{ = 2.99 (to 2 decimal places)} \end{gathered}[/tex]for ratio of B to A:
[tex]\begin{gathered} \frac{B}{A}\text{ = }\frac{17241}{51527}\text{ = 0.33460 } \\ \text{ = 0.33 (to 2 decimal places)} \end{gathered}[/tex]A is x % of B:
[tex]\begin{gathered} A\text{ = }\frac{x}{100}\times B \\ x\text{ = }\frac{100\text{ }\times A}{B} \\ x\text{ = }\frac{100\text{ }\times\text{ 51527}}{17241}\text{ = 298.86} \\ x\text{ = 299\% (to nearest integer)} \end{gathered}[/tex]Hence, the ratio of A to B = 2.99 (to 2 decimal places), B to A = 0.33 (to 2 decimal places) and A is 299% of B (to nearest integer).
The revenue for a small company is given by the quadratic function r(t) = 5tsquared + 5t + 630 where t is the number of years since 1988 and r(t) is in thousands of dollars. If this trend continues, find the year after 1998 in which the company’s revenue will be $730 thousand. Round to the nearest whole year.
Answers
for:
[tex]\begin{gathered} r(t)=730 \\ 5t^2+5t+630=730 \\ so\colon \\ 5t^2+5t-100=0 \end{gathered}[/tex]Divide both sides by 5:
[tex]t^2+t-20=0[/tex]Factor:
The factors of -20 which sum to 1, are -4 and 5 so:
[tex](t-4)(t+5)=0[/tex]So:
[tex]\begin{gathered} t=4 \\ or \\ t=-5 \end{gathered}[/tex]Since a negative year wouldn't make any sense:
[tex]t=4[/tex]Therefore, the company revenue will be $730 for the year:
[tex]1998+t=1998+4=2002[/tex]Answer:
2002
x+3y=6 2x+6y=-18 solve
Answers
The system of equation x + 3y = 6 and 2x + 6y = -18 has no solution.
What is the solution to the given system of equation?Given the system of equation in the question;
x + 3y = 6
2x + 6y = -18
To find the solution to the system of equation, first solve for x in the first equation.
x + 3y = 6
Subtract 3y from both sides
x + 3y - 3y = 6 - 3y
x = 6 - 3y
Now, replace all occurrence of x in the second equation with 6 - 3y and solve for y
2x + 6y = -18
2( 6 - 3y ) + 6y = -18
Apply distributive property to remove the parenthesis
12 - 6y + 6y = -18
-6y and +6y cancels out
12 = -18
Since 12 equal -18 is not true, there is no solution to the system of equation.
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PLEASE HELP
OFFERING 10 POINTS
Answers
Answer: AAS
Step-by-step explanation:
Two sides are congruent, two angles are congruent, and vertical angles are congruent
The function f(x) is graphed below. what is true about the graph on the interval from x = y to x = ∞?* it is positive and increasing* it is positive and decreasing * it is negative and increasing* it is negative and decreasing
Answers
Looking at the graph, we will the following:
The portion ab is increasing
The portion bc is decreasing
The portion cd is decreasing
The portion de is increasing
The portion ef is increasing
The portion fg is decreasing
The portion beyond g is increasing
In the interval x = y to x = ∞, we will observe that the graph is positive & increasing
Hence, the first option is correct (it is positive and increasing)
helppppppppppp!!!!!!!!!!! pleaseeee
Answers
Answer:
Domain: [3, ∞)
Range: [1, ∞)
Step-by-step explanation:
The domain represents the x-axis
The point starts at 3 and points to what can assume to be infinity
Since the dot is close it is included.
In interval notation:
[3, ∞)
The range represents the y-axis
The point starts at 1 and goes to infinity
The dot is included so we use a bracket
Interval notation
[1, ∞)
I hope this helps!
Suppose Yolanda places $9000 in an account that pays 8% interest compounded each year. Assume that no withdrawals are made from the account. Follow the instructions below. Do not do any rounding. (a) Find the amount in the account at the end of 1 year. $ (b) Find the amount in the account at the end of 2 years. $0 X S
Answers
Compound interest - The amount in the account at the end of 1st year is $9720 and The amount in the account at the end of 2nd years is $10497.6
What is compound interest?
The interest earned on savings that is calculated using both the initial principal and the interest accrued over time is known as compound interest. It is thought that Italy in the 17th century is where the concept of "interest on interest" or compound interest first appeared. It will accelerate the growth of a sum more quickly than simple interest, which is only calculated on the principal sum. Money multiplies more quickly thanks to compounding, and the more compounding periods there are, the higher the compound interest will be.
We are given that the principal amount is $9000
An the interest is 8%
Hence after 1 year the amount will be
[tex]A=9000(1+0.08)\\A=9000(1.08)\\A=9720\\[/tex]
After 1 year the amount becomes $9720
Now After 2 years we will get interest on $9720
Hence the amount after 2 years will be
[tex]B=9720(1+0.08)\\B=9720(1.08)\\B=10497.6[/tex]
Therefore the amount after 2 years is $10497.6
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Escriba la razón del primer número al segundo: 32 a 44 simplifique si es posible.
Answers
Write the ratio of the first number to the second.
[tex]\begin{gathered} 32\colon44 \\ \text{Ratio}=\frac{32}{44} \\ \text{Ratio}=\frac{8}{11} \\ \text{The ratio therefore is 8}\colon11 \end{gathered}[/tex]Please assist me. I have no idea how to start this equation
Answers
Part a
Remember that the linear equation in slope-intercept form is
y=mx+b
where
m is the slope or unit rate
b is the y-intercept or initial value
In this problem
the equation is of the form
C=m(n)+b
where
m=8.50
b=350
therefore
C=8.50n+350Part b
A reasonable domain for n (number of cups)
Remember that the number of cups cannot be a negative number
so
the domain is the interval [0, infinite)
but a reasonable domain could be [0, 500]
Find out the range
For n=0 -----> C=350
For n=500 ----> C=8.50(500)+350=2,100 ZAR
the range is the interval [350,2,100]
Part c
calculate the cost
For n=100 cups ----> C=8.50(100)+350=1,200 ZAR
For n=200 cups ----> C=8.50(200)+350=2,050 ZAR
For n=400 cups ---> C=8.50(400)+350=3,750 ZAR
Part d
Average cost
Divide the total cost by the number of cups
For 100 cups ------> 1,200/100=12 ZAR per cup
For 200 cups ----> 2,050/200=10.25 ZAR per cup
For 400 cups ----> 3,750/400=9.38 ZAR per cup
Part e
it is better to order more cups, to reduce the initial ZAR 350 cost.
Part f
In this problem we have the ordered pairs
(200, 2150) and (400, 3750)
Find out the slope m
m=(3750-2150)/(400-200)
m=8 ZAR per cup
Find out the linear equation
C=mn+b
we have
m=8
point (200,2150)
substitute and solve for b
2150=8(200)+b
b=2150-1600
b=550
therefore
The linear equation is
C=8n+550Part g
A reasonable domain could be [0, 600]
Find out the range
For n=0 ------> C=550
For n=600 ----> C=8(600)+550=5,350
The range is the interval [550,5350]
Part h
The gradient is the same as the slope
so
slope=8
that means ----> the cost of each cup is 8 ZAR
Part i
For n=600
C=8(600)+550=5,350 ZAR
Part j
we have the inequality
8n+550 < 8.50n+350
Solve for x
550-350 < 8.50n-8n
200 < 0.50n
400 < n
Rewrite
n > 400
For orders more than 400 cups is more effective to order from Cupomatic
Verify
For n=401
C=8n+550=8(401)+550=3,758 ZAR
C=8.50n+350=8.5(401)+350=3,758.5 ZAR
the cost is less in CUPOMATIC, is ok
the answer is
For orders more than 400 cups is more effective to order from CupomaticThree commercials are played in a row between songs on the radio. The three commercials fill exactly 3 minutes of time. If the first commercial uses 1 – minutes, and the second uses 3 minute, how long is the third commercial? The third commercial is minutes long.
Answers
3 commercials
3 minutes
3 = 1st commercial + 2nd commercial + 3rd commercial
3 = 1 1/5 + 3/4 + 3rd commercial
3rd commercial = 3 - 6/5 - 3/4
= 60/20 - 24/20 - 15/20
= 21/20
The third commercial last = 21/20 or 1 1/20.
Herb Garrett has an 80% methyl alcohol solution. He wishes to make a gallon of windshield washer solution by mixing his methyl alcohol solution with water. If 128 ounces or a gallon of windshield washer fluid contain 6% methyl alcohol, how much of the 80% methyl alcohol solution and how much water must be mixed? Express your answer in ounces.
Answers
First, calculate the total volume of alcohol in the gallon of windshield washer solution by calculating what is 6% of a gallon equal to. Since a gallon is equal to 128 ounces, then:
[tex]undefined[/tex]Construct a scatterplot and identify the mathematical model that best fits the data. Assume that the model is to be used only for the scope of the given data and consider only linear, quadratic, logarithmic, exponential, and power models. Use a calculator or computer to obtain the regression equation of the model that best fits the data. You may need to fit several models and compare the values of R2.Average sunset times are taken for six months across the summer. Giving the months April through September values 1 through 6, find the regression equation of the best model.y = –0.357x2 + 2.17x + 17.87y = 21.24 e0.983xy = 21.20 – 0.343xy = 20.62x–0.029
Answers
We will have the following:
From the options given we graph each possible solution with the data, that is:
In order:
From this, we can see that the function that best fits the data is:
[tex]y=-0.357x^2+2.17x+17.87[/tex]the number of people with the flu during the epidemic is a function,f, of the number of days,d, since the epidemic began. The equation began. The equation f(d)= 50*(3/2)^d defines f.How quickly is the flu spreading? or what is the exponential growth factor?
Answers
We have that the general exponential formula is:
[tex]f(x)=a\cdot b^x[/tex]In this case, we have:
[tex]f(d)=50\cdot(\frac{3}{2})^d[/tex]the term b on the exponential formula is also known as the growth factor. Therefore, in this case the growth factor is b=3/2
A salad recipe requires 3 cups of spinach and 1/2 cup of pecans. At this rate, what amount of pecans should be used with 2 cups of spinach?
Answers
We need 3 cups of spinach for each 1/2 cup of pecans.
Then we have:
[tex]\begin{gathered} \frac{2\text{ cups of spinach}}{3\text{ cups of spinach}}=\frac{x\text{ cups of pecans}}{\frac{1}{2}\text{ cups of pecans}} \\ \frac{x}{\frac{1}{2}}=\frac{2}{3} \\ x=\frac{1}{2}\cdot\frac{2}{3} \\ x=\frac{1}{3} \end{gathered}[/tex]Answer: It will be needed 1/3 cup of pecans
A package of 5 pairs of insulated socks costs 27.95$. What is the unit price of the pairs of ?
Answers
Answer:
$5.59
Step-by-step explanation:
You want the unit price of a pair of socks, given that 5 pairs cost $27.95.
Unit priceThe unit price is found by dividing the price by the number of units.
$27.95/5 = $5.59
The unit price of a pair of socks is $5.59.
How many rays are in the next two terms in the sequence?
Answers
The sequnce is
2, 3, 5, 9, ....
this sequence follows the next formula:
[tex]a_n=2^{n-1}+1[/tex]where an is the nth term.
[tex]\begin{gathered} a_1=2^{1-1}+1=1 \\ a_2=2^{2-1}+1=3 \\ a_3=2^{3-1}+1=5 \\ a_4=2^{4-1}+1=9 \\ a_5=2^{5-1}+1=17 \\ a_6=2^{6-1}+1=33 \end{gathered}[/tex]The next two terms are 17 and 33
which property justifies the equation 0.5 (8.4 -1.6) equals 0.5 (8.4) -0.5 (1.6)?
Answers
Given the following expression:
[tex]\text{0}.5(8.4-1.6)=0.5(8.4)-0.5(1.6)[/tex]Remember that we have the following general rule:
[tex]a(b+c)=a\cdot b+a\cdot c[/tex]this rule is called the distributive property, which is used on our given expression.
10.1.3The hour hand of a clock moves from 5 to 9 o'clock. Through how many degrees does it move?
Answers
Step 1: Lets calculate angle on each hour hand
since the wall clock takes the shape of a cirle
Therefore,
The total angles in a walk clock is 360°
Angle on each hour hand is
There are 12 hour hands on the clock ,
Therefore,
[tex]\begin{gathered} \text{Angle on each hour hand is =}\frac{360^0}{hands\text{ on the clock}}^{} \\ \text{Angle on each hour hand =}\frac{360^0}{12}=30^0 \end{gathered}[/tex]Since the hour hand moved from 5 o'clock to 9 o'clock
It has moved a distance of (9 - 5)= 4 hands on the clock
If each hand on the clock=30°
Therefore,
The angle in degrees moved through 4 hour hands on the clock will be calculated as,
[tex]\begin{gathered} \text{Angle moved = angle on each hand}\times no\text{ of hands moved} \\ \text{Angle moved=30}^0\times4=120^0 \end{gathered}[/tex]The hour hand of the clock moved from 5 o'clock to 9 o'clock through an angle of 120°
PLEASE HURRY AND HELP I NEED THIS TODAY
Solve k over negative 1.6 is greater than negative 5.3 for k.
k > −8.48
k < −6.9
k > −6.9
k < 8.48
Answers
Answer: [tex]k < 8.48[/tex]
Step-by-step explanation:
[tex]\frac{k}{-1.6} > -5.3\\\\k < (-5.3)(-1.6)\\\\k < 8.48[/tex]