Find (if possible) conditions on a and b such that the following system has no solution, onesolution and infinitely many solutions.2 – 2y = 1ac + by = 5.
Answers
We are given the following system of equations
[tex]\begin{gathered} x-2y=1 \\ ax+by=5 \end{gathered}[/tex]Let us find the conditions on a and b such that the following system has no solution, one
solution and infinitely many solutions.
No solution:
A system of equations has no solution when the two equations are parallel.
Recall that two parallel equations have equal slopes.
If the value of a = 1 and the value of b = -2 then the two equations will be parallel and hence they will have no solution.
[tex]\begin{gathered} x-2y=1 \\ x-2y=5 \end{gathered}[/tex]The graph of the above system of equations is shown below
Related Questions
Which measure is the best estimate of the area of the banner in square meters?
Answers
Answer:
6 square meters.
Explanation:
The banner is made up of two congruent triangles and two congruent trapezoids.
The banner forms a triangle with base:
[tex]\begin{gathered} 1\frac{3}{4}+1+1+1\frac{3}{4} \\ =5.5\text{meters} \end{gathered}[/tex]The height of the triangle = 2 meters.
Therefore, the area of the banner:
[tex]\begin{gathered} A=\frac{1}{2}bh \\ =\frac{1}{2}\times5.5\times2 \\ =5.5m^2 \end{gathered}[/tex]The measure that is the best estimate of the area of the banner is 6 square meters.
The value of a stock decreases by an average of 17 dollars each week. Which of the following represents the total average decrease in the stock after 6 weeks?
6|−17| = 102 dollars
|−17| − |6| = 11 dollars
|−17| − 6 = 11 dollars
−6|17| = 102 dollars
Answers
The total average decrease in the stock after 6 weeks is represented by 6|−17| = 102 dollars.
It is given that the value of a stock decreases by an average of 17 dollars each week.We need to find the total average decrease in the stock after 6 weeks.Let the starting price of the stock be "p".Let the number of weeks passed be represented by "x".We know that each week, the value of the stock decreases by 17 dollars.So, in "x" number of weeks, the decrease in the price of the stock is the product of the decrease per week and the number of weeks.The decrease in the price of the stock is |-17|*x.We need to find the decrease after 6 weeks.This means that the value of "x" is 6.The decrease in the price of the stock is |-17|*6.The decrease in the price of the stock is 102.Thus, the equation that represents the above situation is 6|−17| = 102 dollars.To learn more about equations, visit :
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I need this for today , thank you
Answers
The completed two-column format used to prove the congruency of the segments [tex]\overline{ST}[/tex] and [tex]\overline{NR}[/tex] is presented as follows;
Statements [tex]{}[/tex] Reasons
1. [tex]\overline{SU}[/tex] ≅ [tex]\overline{LR}[/tex], [tex]\overline{TU}[/tex] ≅ [tex]\overline{LN}[/tex] [tex]{}[/tex] 1. Given
2. [tex]\overline{SU}[/tex] = [tex]\overline{LR}[/tex], [tex]\overline{TU}[/tex] = [tex]\overline{LN}[/tex] [tex]{}[/tex] 2. Definition of congruent segments
3. SU = ST + TU [tex]{}[/tex] 3. Segment addition postulate
LR = LN + NR [tex]{}[/tex]
4. ST + TU = LN + NR [tex]{}[/tex] 4. Substitution property of equality
5. ST + LN = LN + NR [tex]{}[/tex] 5. Substitution property of equality
6. ST + LN - LN = LN + NR - LN [tex]{}[/tex] 6. Subtraction property of equality
7. ST = NR [tex]{}[/tex] 7. Substitution property of equality
8. [tex]\overline{ST}[/tex] ≅ [tex]\overline{NR}[/tex] [tex]{}[/tex] 8. Definition of congruency
What are the postulates, properties and definition used to prove the congruency of the segments?The segment addition postulate states that a third point B can only be located on a line that has two points A and C when the distances between the points satisfy the equation, AC = AB + BCThe substitution property of equality states that if a variable, a = b then the variable a can be substituted with b in any equation.The subtraction property of equality states that the expressions on both sides of an equation remains equivalent following the subtraction of the same amount from the left and right hand side of the equation.Two segments, angles, or figures, are said to be congruent if their size and shape are the same.Learn more about the two column method used to prove statements in geometry here:
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Divide:5.52 x 1031.2 x 105Write your answer in scientific notation. For example, you'd enter 2.3*10^4 for 2.3 x 104
Answers
The question can be solved as follows:
[tex]\frac{5.52\times10^3}{1.2\times10^5}=\frac{5.52}{1.2}\times10^{-2}=4.6\times10^{-2}[/tex]Hence the value of the given expression in scientific notation is expressed as:
[tex]\frac{5.52\times10^3}{1.2\times10^5}=4.6\times10^{-2}[/tex]what algebra property is this equation: (4y+1)x0=0
Answers
Answer:
It would be called the algebraic property of 0.
Step-by-step explanation:
question will be in picture
Answers
Solution
Step 1
Trace 30mm per bacteria to the corresponding hour on the graph
From the traced line 30 bacteria per mm corresponds to 6 hours
EASY MATH PLEASE ANSWER
Two trains leave the same station, each 40 minutes apart. Train X leaves first at 9:45 am and heads west at a speed of 144 km/h. Train Y leaves at noon and travels directly east at a speed of 165 km/h. How far apart are these trains at 1:30 pm? Show your work.
Answers
The two trains will be a distance of 1049 km apart after 1:30 pm.
Velocity, distance and time
Velocity v is given by the distance d divided by the time t, hence according to the following rule:
v = d/t.
In the context of this problem, both trains are moving in the opposite direction from the station, hence their distance will be the sum of the distances of each train from the station.
The velocity equation can be solved for the distance as follows:
d = vt.
For train X, the velocity and the time are given as follows:
Velocity of 144 km/h, as stated in the text.Time of 3.75 hours, as 1:30 pm is 3 hours 45 minutes after 9:45 am, which is the time the train left, and 45 minutes is 75% = 0.75 of 60 minutes, which is one hour.Hence the distance that the train X will be from the station at 1:30 pm is given by:
dX = 144 x 3.75 = 540 km.
For train Y, the velocity and the time are given as follows:
Velocity of 165 km/h, as stated in the text.Time of 3.0833 hours, as the train leaves 40 minutes after train X, hence 1:30 pm is 3 hours and 5 minutes after train X left, and 5 minutes is 5/60 = 0.0833 of an hour.Hence the distance that the train Y will be from the station at 1:30 pm is given by:
dY = 165 x 3.0833 = 509 km.
Then the distance between both trains is given by:
d = dX + dY = 540 km + 509 km = 1049 km.
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Find the 11th term in this sequence. *10 poin1) -2, 4. -8, 16, ...Find a11
Answers
Given the terms
-2, 4, -8, 16
The first term = -2
The second term is 4
The third term is -8
The fourth term is 16
We can observe that this is a geometric sequence
So to get the 11th term, we will first get the formula
Step 1: Get the common ratio (r)
[tex]\text{common ratio=}\frac{\sec ond\text{ term}}{first\text{ term}}=\frac{third\text{ term}}{\sec ond\text{ term}}[/tex][tex]r=\frac{4}{-2}=\frac{-8}{4}=-2[/tex]Step 2: Get the formula for the nth term
The formula is given by
[tex]T=r^n[/tex][tex]T=(-2)^n[/tex]where T is the nth term
n is the number of terms
Step 3: Find the 11th term
[tex]T_{11}=(-2)^{11}[/tex][tex]T_{11}=-2048[/tex]The 11th term is -2048
Hello, I was wondering what [tex]f(x) = 4 \times {5}^{x} [/tex]would look like if it were graphed
Answers
Answer:
Step-by-step explanation:
For the given function,
[tex]f(x)=4*5^x[/tex]Since it is an exponential function,
A rectangle has a height of 3x and a width of 2x-3Express the area or the entire triangle
Answers
Answer
6x² - 9x
Explanation
Given:
Height = 3x
Width = 2x - 3
The area of a rectangle = Length x Width
From the figure, length = height = 3x
Area = 3x(2x - 3)
In expanded form, we shall open the parenthesis
Area = (6x² - 9x) squared unit
is 4 / 3 is 4 divided by 3/2 the same as 4 divided 2/3 explain.
Answers
We will investigate the equivalence of fractions.
We have the first statement as follows:
" 4 divided by 3/2"We will go ahead and decrypt the above statement mathematically by the use of fractions as follows:
[tex]\frac{4}{\frac{3}{2}}[/tex]We will now use the conversion of division operator to a multiplication operator by reciprocating the denominator as follows:
[tex]4\cdot\text{ }\frac{2}{3}[/tex]Simplify the above fraction as follows:
[tex]\frac{8}{3}[/tex]The next statement is given as such:
" 4 divided by 2/3"We will go ahead and decrypt the above statement mathematically by the use of fractions as follows:
[tex]\frac{4}{\frac{2}{3}}[/tex]We will now use the conversion of division operator to a multiplication operator by reciprocating the denominator as follows:
[tex]4\cdot\frac{3}{2}[/tex]Simplify the above fraction as follows:
[tex]6[/tex]If we compare the results of two statement we can say that the statements are not equal.
[tex]\frac{8}{3}\text{ }\ne\text{ 6}[/tex]what number is part of the solution set to the inequality below?m-20> 12 _
Answers
What is the distance between the points (3,4) and (1,5)?
Answers
Answer:
distance between the points (3,4) and (1,5) = 2.236
Step-by-step explanation:
The distance between two points is the length of the path connecting them. The shortest path distance is a straight line. In a 2 dimensional plane, the distance between points (X1, Y1) and (X2, Y2) is given by the Pythagorean theorem:
[tex]d = \sqrt {(x_{2} - x_{1})^2 + (y_{2} - y_{1})^2}[/tex]'
For:
[tex](X1, Y1) = (3, 4)\\\\(X2, Y2) = (1, 5)[/tex]
[tex]d = \sqrt {(1 - 3)^2 + (5 - 4)^2}\\\\d = \sqrt {(-2)^2 + (1)^2}\\\\d = \sqrt {{4} + {1}}\\\\d = \sqrt {5}\\\\d = 2.236068[/tex]
Answer:
Exact distance is [tex]\sqrt{5}[/tex]
Approximate distance is 2.2361
Round the decimal value however your teacher instructs.
====================================================
Work Shown:
I used the distance formula to get the following.
[tex](x_1,y_1) = (3,4) \text{ and } (x_2, y_2) = (1,5)\\\\d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\\\\d = \sqrt{(3-1)^2 + (4-5)^2}\\\\d = \sqrt{(2)^2 + (-1)^2}\\\\d = \sqrt{4 + 1}\\\\d = \sqrt{5}\\\\d \approx 2.2361\\\\[/tex]
----------------
A slight alternative is to plot the points A(3,4) and B(1,5) and C(3,5).
Points A and B are the original points we were given. Point C helps form a right triangle. The hypotenuse is AB and the legs are AC and BC.
Leg AC = 1 unit and leg BC = 2 units
Use the pythagorean theorem [tex]a^2+b^2 = c^2[/tex] to plug in a = 1 and b = 2 to find that the hypotenuse is exactly [tex]c = \sqrt{5}[/tex] units long, which is the distance from A to B.
The equation of a line is x + 5y = 12. What is the y-intercept of the line? D-12 0¹2 12 please answer quickly
Answers
Answer:
12/5
Step-by-step explanation:
Find the y-intercept form of the line by isolating y:
x + 5y = 12
5y = -x + 12
5 5
y = (-1/5)x + 12/5
y = mx + b
In this form, 12/5 is b, which is the line's y-intercept.
Please help it’s due tonight I will give a brainlist
Answers
The seller's marked up price is 0% of 279.30 cost is 279.30
For the seller,
The cost price of the T.V. is $210.00
The selling price of the T.V. is $279.30
If the seller's mark up the price 33% of 210 cost.
The marked up price = 210 + 33% of 210
= 210 + (33/100) x 210
210 + 0.33 x 210
210 + 69.3
Therefore, the seller's marked up price was 33% of 210 cost is 279.30
Percent markup on the selling price of 279.30 is
279.30 + x% of 279.30 = 279.30
(x/100) 279.30 = 0
x = 0
Therefore the seller's marked up price is 0% of 279.30 cost is 279.30
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The vertex form of a function is g(x) = (x-3)² +9. How does the graph of g(x) compare to the graph of the function f(x) = x²?
• g(x) is shifted 3 units left and 9 units up.
• g(x) is shifted 3 units right and 9 units up.
• g(x) is shifted 9 units left and 3 units down.
• g(x) is shifted 9 units right and 3 units down.
Answers
The correct option is g(x) is shifted 3 units left and 9 units up, for the given graph of function f(x) = x².
Whats is referred as the translation?In geometry, translation refers to a function which also shifts an object a specified distance. The component is not otherwise altered. It hasn't been rotated, mirrored, or resized.Every spot of the item should be moved in same direction for much the same distance during a translation.When conducting a translation, this same initial object is referred to as the pre-image, as well as the object after translation is referred to as the image.For the given question,
The graph of the parent function is f(x) = x².
To from the vertex form of a function is g(x) = (x-3)² +9, the process is-
First, shift three units to the left, such that g(x) becomes (x-3)².Now, shift the function 9 units up to form (x-3)² + 9.Thus, the vertex of the function is g(x) = (x-3)² +9 is formed by translation of g(x) is shifted 3 units left and 9 units up.
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help meeee pleasee!!!
thank youu
Answers
Answer:
(-7, 3)
Step-by-step explanation:
Since the endpoints of the interval are not included, use parentheses.
Write an expression that could represent an estimated cost for the party. Use at least one letter. State what each part of the expression represents
Answers
The expression that can be used to represent the estimated cost for the party is T =si
How to illustrate the information?It should be noted that expression show the relationship between variables. We can get an estimated cost for the party by using the following expression:
T = s×i
where:
T = total cost of the ice cream party
s = number of ninth students
i = unit cost of ice cream
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As a reward for achieving their goals, all students in the ninth grade are invited to an ice cream party.
1) Write an expression that could represent an estimated cost for the party. Use at least one letter. State what each part of the expression represents.
the ratio of baseballs to basketballs is 3 to 7 if there are 21 basketballs how many baseballs are there? how many baseballs and basketballs in total?
Answers
Answer:
30 baseballs and basketballs
Hope I helped
Step-by-step explanation:
21 divided 7 = 3 times 3 = 9 plus 21 = 30 baseballs and basketballs in total.
Answer:9:21
Step-by-step explanation: 3*3=9 and 7*3=21
A rectangle has a width of centimeters and a perimeter of centimeters. What is the rectangle's length?
Answers
Answer: We have to find the length and the width of the rectangle provided that the perimeter is 44m:
[tex]\begin{gathered} P=2L+2W=44\rightarrow(1) \\ \\ \end{gathered}[/tex]Therefore using the information provided and plugging in the equation (1) we get the following answer:
[tex]\begin{gathered} P=2L+2W=44 \\ \\ L=2W+4 \\ \\ P=2(2W+4)+2W=44 \\ 6W=36\rightarrow W=\frac{36}{6}=6 \\ \\ W=6m \\ \\ L=\frac{44-2W}{2}=\frac{44-12}{2}=16 \\ \\ L=16m \end{gathered}[/tex]
Find the variance of the given data
147, 141, 120, 124, 128
The answers that I already tried are
11.510864 and rounded
10.29563 and rounded
Answers
Answer:
......................................
Step-by-step explanation:
If 49600 dollars is invested at an interest rate of 8 percent per year, find the value of the investment at the end of 5 years for the following compounding methods. a) annual: b) semiannual: c) monthly: d) daily:
Answers
a) Value of invest when compounded annually= $72878.67
b) Value of invest when compounded semi-annually is $73420.12
c) Value of invest when compounded monthly is $73896.35
EXPLANATION
a)Annually
Given:
Principal(p)= 49600
rate (r) = 8% = 0.08
time(t) =5
Since it is compounded anually, n=1
Using the formula;
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]Substitute the value and evaluate.
[tex]A=49600(1+\frac{0.08}{1})^5[/tex][tex]=49600(1.08)^5[/tex][tex]=72878.67[/tex]Therefore, the value of the investment when compounded annually is $72878.67
b) Semi-annually
In this case, the we are going to substitute all our initial values except for n.
In the case of semi annually, n= 2
That is;
Principal(p)= 49600
rate (r) = 8% = 0.08
time(t) =5
n=2
Substitute into the formula and evaluate.
[tex]A=49600(1+\frac{0.08}{2})^{2\times5}[/tex][tex]=49600(1+0.04)^{10}[/tex][tex]=49600(1.04)^{10}[/tex][tex]=73420.12[/tex]Therefore, the value of the investment when compounded semi-annually is $73420.12
c)monthly
In this case n= 12 and all other values remains the same.
That is;
Principal(p)= 49600
rate (r) = 8% = 0.08
time(t) =5
n=12
Substitute the values into the formula and evaluate.
[tex]A=49600(1+\frac{0.08}{12})^{12\times5}[/tex][tex]=49600(1+0.667)^{60}[/tex][tex]=49600(1.0667)^{60}[/tex][tex]=73896.35[/tex]Therefore, the value of the investment when compounded monthly is $73896.35
1
5. What is the value of 4x² + x + x
11
2)
9
1|2
1/2
3) 10호
4) 17를
-1*
when x = 16?
Rational Exponent Defin
Answers
Answer:
[tex] 17\frac{1}{2} [/tex]
Step-by-step explanation:
Explanation in the photo.
Use the normal distribution to the right to answer the questions. (a) What percent of the scores are less than 19? (b) Out of 1500 randomly selected scores, about how many would be expected to be greater than 21?
Answers
Percent of the scores are less than 19 is 45.4%.
591 many would be expected to be greater than 21.
A data set with a normal distribution has the majority of its values clustered in the middle of the range, while the remainder taper off symmetrically toward either extreme.
(a) μ = 19.6, σ = 5.2
First, find the z-score.
z = (x − μ) / σ
z = (19 − 19.6) / 5.2
z = -0.115
To calculate the probability, use a chart or calculator.
P(Z < -0.115) = 0.454
45.4 % of the scores are under 19.
(b) First, find the z-score.
z = (x − μ) / σ
z = (21 − 19.6) / 5.2
z = 0.269
To calculate the probability, use a chart or calculator.
P(Z > 0.269) = 1 − P(Z < 0.269)
P(Z > 0.269) = 1 − 0.606
P(Z > 0.269) = 0.394
Among the scores, 39.4% are higher than 21.
There are 1500 scores, therefore 591 represent 39.4% of those.
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Which of the following are solutions to the system graphed below?
Answers
The solution to the system of inequalities is the shaded area shown in the graph. This also includes the bounding lines of the shaded area since they are all solid lines.
To find the answer, we will check the coordinates provided in the options to see which falls within the shaded portion.
On observation, we can see that the following coordinates fall within the shaded area:
[tex]\begin{gathered} (-5,5) \\ (-4,1) \end{gathered}[/tex]The correct options are OPTION 3 and OPTION 4.
#4 ALGEBRA: Find the value of x and then determine the measure of the obtuse angle.
Answers
Answer:
See below
Step-by-step explanation:
The three angles sum to 180 degrees
4x + 3x + 8x = 180
15x = 180
x = 12
So the obtuse angle would be 8x
8 * 15 = 120°
Owen is deciding between two parking garages. Garage A charges an initial fee of $10 to park plus $1.50 per hour. Garage B charges an initial fee of $4 to park plus $3 per hour. Let A represent the amount Garage A would charge if Owen parks for tt hours, and let BB represent the amount Garage B would charge if Owen parks for tt hours. Graph each function and determine the number of hours parked, t that would make the cost of each garage the same. I NEED THIS ON A GRAPH
Answers
Answer:
At 4 hours both options will be $16.00
Step-by-step explanation:
The function y=f(x) is graphed below. Plot a line segment connecting the points on ff where x=-4 and x=1. Use the line segment to determine the average rate of change of the function f(x) on the interval −4≤x≤1.
Answers
The line connecting the points on the graph is shown below:
From it we notice that to get to the first point of the lineto the second we need to:
• Move down 6 squares; since each square has a length of 2 units this means that we move 12 units down.
,• Move 5 units to the right.
Therefore, we have that:
[tex]\begin{gathered} \Delta y=-12 \\ \Delta x=5 \end{gathered}[/tex]and that:
[tex]\text{ average rate of change=-}\frac{12}{5}[/tex]Which logical symbol would you use to change the sentence, "He can get his driver's license," into, "He cannot get his driver's license"?
Answers
Answer: The logical symbol for that sentence isV
Find the area of the shaded region. Round your answer to one decimal place, if necessary. Note: The figure is not drawn to scale.
Answers
Area is the quantity that expresses the extent of a region on the plane or on a curved surface. the area of shaded region is 15.728 inches square.
What is Area?Area is the quantity that expresses the extent of a region on the plane or on a curved surface
The diameter of circle is 5, d=5
and the length of side of the equilateral triangle is 3.
to find the area of shaded region we need to find the area of circle and then we have to remove the area of triangle.
π(d/2)²-1/2×a²×sin60⁰
3.14(5/2)²-1/2×3²×√3/2
3.14×2.5²-1/2×9×√3/2
3.14×6.25 -1/2×9×0.866
3.14×6.25-7.794/2
3.14×6.25-3.897
19.625-3.897
15.728
Hence area of shaded region is 15.728 inches square.
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