Consider the equation 5x-2y=3. If possible, find a second linear equation to create a system of equations that has: Exactly one solution Exactly two solutions No solutions Infinitely many solutions
Answers
b) Two solutions: not possible
c) No solutions: 5x -2y = 0 . . . . (any different line with the same slope)
d) Infinitely many solutions: 10x -4y = 6 . . . . (any other equation for the same line)
Answer with explanation:
1.⇒ The given equation is
5x-2y=3
For one solution ,you should write linear equation in such a way
ax+by=c, such that
[tex]\frac{5}{a}\neq \frac{-2}{b}\neq \frac{3}{c}[/tex]
So, the linear equation will be
→3x+4y=8
You can write many more by yourself.
2.⇒Exactly two solutions
The two lines intersect at only one point.So,there are no such lines which has two point of Intersection.
3.⇒No solutions
It means the two lines will never intersect.
For no solution ,you should write equation of line in such a way
ax+by=c, such that
[tex]\frac{5}{a}=\frac{-2}{b}\neq \frac{3}{c}[/tex]
So, the linear equation will be
→10x -4y=15
You can write many more by yourself.
4.⇒Infinitely many solutions
For Infinite number of solution ,you should write linear equation in such a way
ax+by=c, such that
[tex]\frac{5}{a}=\frac{-2}{b}=\frac{3}{c}[/tex]
→10x-4y=6
Related Questions
Jack purchased a box of 1,000 candy guitar lollipops to sell in the bakery for $20.00. How much did he pay for each lollipop?
Answers
NEED HELP ASAP!! WILL GIVE BRAINLIEST
5. Marco wrote the equation below.
cos(-pi/2)=cos(3pi/2)
which statement best describes marcos equation?
a. it is true because the cosine function is odd
b. it is false because the cosine function is even
c. it is true because the cosine function has a period of 2pi
d. it is false because the cosine function has a period of pi.
Answers
The given equation is represented below:
cos(-pi/2)=cos(3pi/2)
The value of cos(-pi/2) is 0 and the value of cos(3pi/2) is also 0
Further a function is defined as an even function if f(x) = f(-x)
Cosine function is an even function.
Therefore it is true and the correct option is c
It is true because the cosine function has a period of 2pi
Hope it helps ..!!
Answer:
Option C - It is true because the cosine function has a period of [tex]2\pi[/tex].
Step-by-step explanation:
Given : Marco wrote the equation below.
[tex]\cos (-\frac{\pi}{2})=\cos (\frac{3\pi}{2})[/tex]
To find : Which statement best describes Macro equation?
Solution :
Since, the period of the given cos function is 360°
So, it holds the property of trigonometric :
[tex]\cos \theta=\cos (2\pi+\theta)[/tex] then the function is an even function.
Taking [tex]\theta =-\frac{\pi}{2}[/tex]
Then , [tex]2\pi+\theta = 2\pi-\frac{\pi}{2}[/tex]
[tex]2\pi+\theta = \frac{4\pi-\pi}{2}[/tex]
[tex]2\pi+\theta = \frac{3\pi}{2}[/tex]
So, the given function is a even function in a period of [tex]2\pi[/tex].
Therefore, Option C is correct.
It is true because the cosine function has a period of [tex]2\pi[/tex].
8pints compared to 15 cups
Answers
First we need both in the same unit of measurement.
1 pint= 2 cups
Convert 15 cups to pints:
=15 cups ÷ 2 cups per pint
=7.5 pints
STEP 2:
Find percentage:
=8 pints ÷ 7.5 pints
=1.0666 decimal percent of 8 pints
STEP 3:
Convert to %:
=1.06666 x 100
=106.66% percent 8 is of 7.5 pints
*TIP: if you know you're changing to a percentage from a decimal, you will always move the decimal two places to the right.
ANSWER:
8 pints is 106.66% of 7.5 pints.
Hope this helps! :)
find the difference of the least common multiple and the greatest common factor of 12 and 32 show your work please
Answers
6*2. 8*4
3*2*2. 4*2 2*2
2*2*2*2*2
Do the rest of the math yourself lol
Jeannie's restaurant served 58 customers on Monday. After the first day the amount of customers served decreases at a rate of 2.5% each day.
What is the explicit rule for this situation and approximately how many customers will be served on the 6th day?
Round to the nearest customer.
Drag and drop the answers into the boxes to match the situation.
Explicit rule
Number of customers on the 6th day.
A n = 58 x (0.975) n - 1, A n = 58 x (0.025) n - 1, A n = 58 (1.025) n - 1, 51, 49, 48, 46,
Answers
Answer:
51 customers
Step-by-step explanation:
Jeannie's restaurant served 58 customers on Monday.
Rate of decrement r =2.5 % = 0.025
Formula : [tex]y=a(1-r)^{n-1}[/tex]
A is the initial amount
r is the rate
n is the no. of days
So, Substitute the values
[tex]y=58(1-0.025)^{n-1}[/tex]
[tex]y=58(0.975)^{n-1}[/tex]
So, explicit rule : [tex]A_n=58(0.975)^{n-1][/tex]
Now to find the no. of customers will be served on the 6th day
Substitute n = 6
[tex]A_6=58(0.975)^{6-1}[/tex]
[tex]A_6=51.1035[/tex]
So, 51 customers will be served on the 6th day
Kens turtle competed in a 0.50- meter race. His turtle had traveled 49/100 meter when the winning turtle crossed the finish line. What is 49/100 written as a decimal
Answers
There are a couple ways we can convert a fraction to a decimal, but I'll use a simple way.
To convert 49/100 to a decimal, we must divide the numerator (top of the fraction, 49) by the denominator (bottom of the fraction, 100).
49 ÷ 100 = 0.49
So, 49/100 is written as 0.49 as a decimal.
Well, to make it simple it's 0.49. Hope it helps!
The value of the digit in the hundreds place in the number 653,841 is 1/10 the value of the digit in the thousands place in which number?
Answers
we have that
the value of the digit in the hundreds place in the number 653,841 is------> 800
case A) 748,917
the value of the digit in the thousands place------> 8000
1/10 the value of the digit is-------> (1/10)*8000=800
800=800---------------> is ok
case B) 749,817
the value of the digit in the thousands place------> 9000
1/10 the value of the digit is-------> (1/10)*9000=900
900 is not 800
case C) 784,817
the value of the digit in the thousands place------> 4000
1/10 the value of the digit is-------> (1/10)*4000=400
400 is not 800
case D) 797,481
the value of the digit in the thousands place------> 7000
1/10 the value of the digit is-------> (1/10)*7000=700
700 is not 800
the answer is the option A) 748,917
The answer is 0.5.
To find the answer, understand the place value system in numbers.
The value of the digit in the hundreds place in the number 653,841 is 1/10 the value of the digit in the thousands place in which number.
To find the answer, we need to understand the place value system. In the number 653,841, the digit in the hundreds place is 8, and the digit in the thousands place is 5. Therefore, 1/10 of the digit in the thousands place is 0.5.
So, the answer is 0.5.
Cheryl paid $3.00 for a pair of socks and eight times as much for a pair of shoes. Her brother Kevin also bought socks and shoes but paid twice as much as Cheryl did for each. How much money did they spend together ?
Answers
Kevin: 2(3) + 2(24) = 6 + 48 = 54
27 + 54 = 81
They spent $81.00 all together.
Which of the following would NOT be a deduction from a paycheck?
Select the best answer from the choices provided.
taxes
FICA
hourly wages
health insurance
Answers
In a line of students ,Jenna is number 8.The teacher says the rule for a number pattern is add4.The first term 7.What number should Jenna say?
Answers
2. Let's call "n" to the number in the line where each student is. Then, you can express this as below:
4n+7
3. So, you have:
Student N°1=4(1)+7=11
Student N°2=4(2)+7=15
Student N°3=4(3)+7=19
Student N°4=4(4)+7=23
Student N°5=4(5)+7=27
Student N°6=4(6)+7=31
Student N°7=4(7)+7=35
Student N°8=4(8)+7=39
What number should Jenna say?
The answer is: 39
John always wears a shirt, pants, socks, and shoes. He owns 12 pairs of socks, 3 pairs of shoes, 5 pairs of pants, and 5 shirts. How many different outfits can John make?
Answers
Answer:
900
Step-by-step explanation:
Khan academy
Given a circle with a diameter of 4, which equation expresses π as the ratio of the circumference of a circle to its diameter?
Answers
is the formula (d*pi=C)
C /4 = π
Took the test myself, this is the answer.
Noah makes ceramic pots for the market. On the weekends he makes 11 more pots than he does during the week. Noah represented the number of pots he makes on weekends using the expression p + 11. Which expression represents the total mumber of pots Noah made one weekend if he made 14 more than his usual number?
Answers
number of pots = p + 25
Explanation:
On weekends, Noah makes 11 pots more than the normal weekdays.
We are given that the equation representing the number of pots is:
number of pots = p + 11
Now, Noah made 14 pots more that his usual numbers, this means that we will add 14 to the usual number of pots that he makes.
Therefore, the equation will become:
number of pots = p + 14 + 11
number of pots = p + 25
Hope this helps :)
The range of F(x) = 6 * 3x is all positive real numbers.
Answers
Janet makes homemade dolls. Currently, she produces 23 dolls per month. If she increased her production by 18%, how many dolls would Janet produce each month?
Answers
Brooke earns $7 an hour at her job now. She can represent the total she makes in a week using the expression 7r. Brooke has asked for a $1 an hour raise. Which expressing would represent the amount Brooke would make in a week after the raise?
Answers
(7 + 1) = 8 $ / h
Therefore we must now rewrite the weekly expression of your earnings.
Rewriting we have:
(7 + 1) r =
8r
Answer:
the amount Brooke would make in a week after the raise is:
8r
8R
y = -16x2 + 32x - 10 This parabola has x-intercepts, representing the times when the dolphin's height above water is feet.
Answers
Answer:
2
0
two real solutions
Step-by-step explanation:
from edge!!
To find the x-intercepts of the quadratic equation representing the height of a dolphin's jump, we can use the quadratic formula by plugging in the coefficients from the equation y = -16x^2 + 32x - 10. The intercepts indicate the times when the dolphin's height above water is zero feet.
Explanation:The question involves finding the x-intercepts of a quadratic equation, which represent the points where a parabola crosses the x-axis. In this context, the x-intercepts correspond to the times when the dolphin's height above water is 0 feet. To find the x-intercepts, we can use the quadratic formula:
x = −b ± √(b² − 4ac) / (2a)
For the equation y = −16x² + 32x − 10, the coefficients are a = −16, b = 32, and c = −10. By substituting these values into the quadratic formula, we can calculate the times when the dolphin is at the water level (y=0). Since this is a mathematical problem involving a real-world scenario, it is essential to check that the resulting times make sense within the context. Negative values for time, for example, would not be physically meaningful.
Learn more about Quadratic Equation here:https://brainly.com/question/30098550
#SPJ3
What is 30 divided by half plus 10
Answers
15 + 10
25 is your answer. Hope its helps! :)
Brent was looking at his cell phone bill and saw that the total number of texts he has sent is tracked, as shown below:
Month
Texts
1
120
2
237
3
354
4
471
The function representing Brent's texting per month is f(m) = 117m + 3. What does the 117 represent?
Answers
It should be the additional texts per month or D
Answer:
The number of texts he sends per month
Step-by-step explanation:
The function f(m) = 117m + 3 is a linear function, which is in the form f(x) = mx+b. In this form, m (the number beside our variable) is the slope, or rate of change, and b (the number added or subtracted) is the y-intercept.
In our function, 117 is the number beside the variable, which makes it the slope. This is the rate of change of this function; it describes how the dependent variable (number of texts) changes for every change in the independent variable (months).
In other words, it tells how many texts he sends per month.
Lines l and m are parallel and intersected by transversals t and s as shown in the figure below.
What is m
A) 180 degrees
B) 360 degrees
C) 540 degrees
D) 720 degrees
Answers
so W= 90 Y=90 X+Z= 180 . so 90+180+90 =360 degrees. B.
Two rectangular prisms have the same volume. The area of the base of the blue prism is 216 square units. The area of the base of the red prism is one third that of the blue prism. Which statement is true?
a) The height of the red prism is one-third the height of the blue prism.
b) The height of the red prism is the same as the height of the blue prism.
c) The height of the red prism is six times the height of the blue prism.
d) The height of the red prism is three times the height of the blue prism.
Answers
Let hb represent the height of the blue prism; let hr represent the height of the red prism.
216*hb = V = (1/3)*(216)*hr
3*hb = hr . . . . . . . . . . . . . . . divide by the coefficient of hr
The 4th selection is appropriate.
Answer:
D
Step-by-step explanation:
find the domain of
[tex]f(x) = \frac{ \sqrt{x + 2} }{ {x}^{2} - 25 } [/tex]
Answers
if c is the incenter of AMD, AMC=3x+6 AND dmc = 8X-49, FIND EACH MEASURE
Answers
-6. -6
__________
3x=8x-55
-8x. -8x
________
-5x=-55
x=11,
3(11)+6=39
8(11)-49=39
Answer:
[tex]m\angle AMC = 39\°[/tex] and [tex]m\angle DMC = 39\°[/tex].
Step-by-step explanation:
As you can observe in the image attached, angles AMC and DMC are congruent, because if point C is the incenter of AMD, that means each line the forms such point is a bisector.
Remember that a bisector is a line that equally divides an angle.
So,
[tex]\angle AMC = \angle DMC\\3x+6=8x-49[/tex]
Solving for [tex]x[/tex], we have
[tex]6+49=8x-3x\\5x=55\\x=11[/tex]
Then, we substitute this value in each expression to find the angles.
[tex]\angle AMC = 3x+6 = 3(11)+6=33+6=39[/tex]
[tex]\angle DMC = 8(11)-49=88-49=39[/tex]
Therefore, the measures of those angles are [tex]m\angle AMC = 39\°[/tex] and [tex]m\angle DMC = 39\°[/tex].
Use the expression below to complete the following tasks. (3a2 - 5ab + b2) - (-3a2 + 2b2 + 8ab) What is the additive inverse of the polynomial being subtracted?
Answers
We have then, that according with the coment below:
(3a2 - 5ab + b2) - (-3a2 + 2b2 + 8ab)
the additive inverse is:
(3a2 - 2b2 - 8ab) Note that is the same expression that
(-3a2 + 2b2 + 8ab)
but with different signs.
Answer:
the additive inverse of the polynomial being subtracted is
(3a2 - 2b2 - 8ab)
Answer:
Option 3
Step-by-step explanation:
edge 2020
Box i contains 4 red and 8 blue marbles while box ii contains 5 red and 3 blue marbles. an unfair coin is tossed –whose probability of turning up heads is 40%. if the coin comes up heads box i is chosen and a random marble is chosen, otherwise if it is tails the marble is chosen from box ii.(a)find the probability a red marble is chosen.(b)if a red marble is chosen, what is the probability it came from box i? (c)if a blue marble is chosen, what is the probability it came from box i?
Answers
a. If a red marble is drawn, either it's drawn from box 1 or box 2. The events [tex]B_1[/tex] and [tex]B_2[/tex] are mutually exclusive, so we have
[tex]\mathbb P(R)=\mathbb P((R\cap B_1)\cup(R\cap B_2))=\mathbb P(R\cap B_1)+\mathbb P(R\cap B_2)[/tex]
Now invoke the definition of conditional probability:
[tex]\mathbb P(R)=\mathbb P(B_1)\mathbb P(R\mid B_1)+\mathbb P(B_2)\mathbb P(R\mid B_2)[/tex]
We're explicitly given the probability of drawing from either box. We also know the probabilities of drawing a red marble from box 1 or 2 are, respectively,
[tex]\mathbb P(R\mid B_1)=\dfrac{\dbinom41\dbinom80}{\dbinom{12}1}=\dfrac4{12}=\dfrac13[/tex]
and
[tex]\mathbb P(R\mid B_2)=\dfrac{\dbinom51\dbinom30}{\dbinom81}=\dfrac58[/tex]
So
[tex]\mathbb P(R)=\dfrac25\times\dfrac13+\dfrac35\times\dfrac58=\dfrac{61}{120}\approx0.508[/tex]
b. Given that we draw a red marble, we're looking for the probability that it was drawn from box 1, i.e. [tex]\mathbb P(B_1\mid R)[/tex]. We use Bayes' theorem:
[tex]\mathbb P(B_1\mid R)=\dfrac{\mathbb P(B_1\cap R)}{\mathbb P(R)}=\dfrac{\mathbb P(B_1)\mathbb P(R\mid B_1)}{\mathbb P(R)}[/tex]
which is really just a matter of using the definition of conditional probability to rewrite the numerator on the the right side, as
[tex]\mathbb P(R\cap B_1)=\mathbb P(R)\mathbb P(B_1\mid R)=\mathbb P(B_1)\mathbb P(R\mid B_1)[/tex]
We know [tex]\mathbb P(R)[/tex] from part (a), so we compute
[tex]\mathbb P(B_1\mid R)=\dfrac{\dfrac25\times\dfrac13}{\dfrac{61}{120}}=\dfrac{16}{61}\approx0.262[/tex]
c. Now we look for [tex]\mathbb P(B_1\mid R^C)[/tex], which can be computed similarly.
[tex]\mathbb P(B_1\mid R^C)=\dfrac{\mathbb P(B_1\cap R^C)}{\mathbb P(R^C)}=\dfrac{\mathbb P(B_1)\mathbb P(R^C\mid B_1)}{1-\mathbb P(R)}[/tex]
[tex]\mathbb P(B_1\mid R^C)=\dfrac{\dfrac25\times\dfrac23}{1-\dfrac{61}{120}}=\dfrac{32}{59}\approx0.542[/tex]
Lexi's bulletin board is 40 centimeters wide. each of her ribbons is 4 centimeters wide, and her photos are 12 centimeters wide. what combination of ribbons and photos will fit side by side with no overlap on Lexi's bulletin
Answers
4 x 12 x 4 x 4 x 12 x 4= 40 cm.
Hope this helps!!
A guy-wire is attached from the ground to the top of a pole for support. If the angle of elevation to the pole is 67° and the wire is attached to the ground at a point 137 feet from the base of the pole, what is the height of the pole (round to 2 decimal places)?
Answers
Answer:
The height of the pole is 322.75 feet.
Step-by-step explanation:
Let the triangle Δ ABC with AC be the length of wire and AB be the Height of the pole
Length between the point of attachment of wire from base of the pole = BC = 137 feet
Angle of elevation to the pole = θ = 67°
We have to find the length of the pole that is AB Let the height of pole be h feet.
According to trigonometry :
[tex]\tan C=\frac{\text{perpendicular}}{\text{base}}[/tex]
Here, C = 67° , perpendicular = AB = h , base = BC = 137
Substitute the values,
[tex]\tan 67^{\circ}=\frac{AB}{BC}[/tex]
[tex]\tan 67^{\circ}=\frac{h}{137}[/tex]
[tex]h=\tan 67^{\circ} \times 137[/tex]
[tex]h=322.75[/tex]
Thus, the height of the pole is 322.75 feet.
Answer:60.1
Step-by-step explanation:
cos
Where is the vertex of the quadratic y = (x -7)2 + 9
Answers
rule: common equation for a parabola is y=ax²+bx+c. If to re-write this equation in the form y=(x+m)²+n, then point (-m;n) is vertex of this parabola.
According to the described rule vertex is (7;9).
The graph of this function is in the attachment.
Final answer:
The vertex of the quadratic function y = (x -7)² + 9 is at the point (7, 9).
Explanation:
Vertex of a quadratic function is the highest or lowest point on the graph of the function. In this case, the quadratic function is in the form y = (x -7)² + 9.
To find the vertex, we notice that the function is in the form y = (x - h)² + k, where (h, k) represents the vertex. Therefore, the vertex of the given quadratic function is at (7, 9).
Describe the test grades using the measures of center
Answers
4x. (2x^3 — x^2–18x+15) Standard Form
Answers
8x^4 - 4x^3 - 72x^2 + 60x
For this case, the first thing to do is multiply the value of 4x for each of the terms within the parenthesis.
You must take into account the following power properties:
Same exponents are added.
We have then:
(8x ^ 4 - 4x ^ 3-72x ^ 2 + 60x)
Answer:
The standard form is:
(8x ^ 4 - 4x ^ 3-72x ^ 2 + 60x)