Answer:
54mph
Step-by-step explanation:
To find the speed in "miles per hour" or miles/hour, divide the number of miles by number of hours.
1080 miles/20 hours
= 54miles/hour
His speed is 54 miles per hour.
A shopper bought a 12-pound bag of oranges for 18.75. What is the unit price per ounce?
Answer:
About $0.10 per ounce
Step-by-step explanation:
12 pound costs $18.75. Lets find the cost per pound first:
Cost Per Pound = [tex]\frac{18.75}{12}=1.5625[/tex]
We know, there are 16 ounces in 1 pound.
We know 1 pound costs 1.5625
To find cost per ounce, we have to divide this by 16.
So,
Cost Per Ounce = [tex]\frac{1.5625}{16}=0.097[/tex]
Rounded to nearest cent, that would be 10 cents per ounce
Factor completely. x^2-4
Answer:
(x - 2)(x + 2).
Step-by-step explanation:
This is the difference of 2 squares:
a^2 - b^2 = (a - b)(a + b)
So
x^2 - 4 = (x - 2)(x + 2).
An account earned interest of 3% per year. The beginning balance was $150. The equation t=log1.03 (E/150) represents the situation, where t is the time in years and E is the ending balance. If the account was open for 8 years, what was the ending balance?
Answer:
190.02
Step-by-step explanation:
Trust
The ending balance of the account after 8 years is approximately $184.16.
Explanation:To find the ending balance of the account after 8 years, we can use the equation t=log1.03(E/150), where t is the time in years and E is the ending balance. Since the account was open for 8 years, we can substitute t=8 into the equation.
8=log1.03(E/150)
To solve for E, we can isolate it by first multiplying both sides of the equation by 150 and then raising both sides to the power of 1.03.
E/150=1.03⁸
E=150*1.03⁸
Using a calculator, we can find that E is approximately $184.16.
HELP PLS IM IN CLASS RN!!!
Answer:
48 inches
Step-by-step explanation:
Dagne can jump 13.2 inches that is 27.5% of her height. Let x inches be Dagne's height.
Then
x inches - 100%
13.2 inches - 27.5%
Write a proportion:
[tex]\dfrac{x}{13.2}=\dfrac{100}{27.5}[/tex]
Cross multiply:
[tex]27.5x=13.2\cdot 100\\ \\27.5x=1,320\\ \\x=\dfrac{1,320}{27.5}\\ \\x=48\ inches[/tex]
The clock face in a famous clock tower has a radius of 4 meters. What is the area of the clock face to the nearest square meter
Final answer:
To find the area of the clock face with a 4-meter radius, use the area formula for a circle, which gives approximately 50.265482 m². Rounded to the nearest square meter, the clock face area is about 50 m².
Explanation:
The clock face in a famous clock tower has a radius of 4 meters, and we want to find the area of the clock face to the nearest square meter. To do this, we use the formula for the area of a circle, which is A = πr², where A is the area and r is the radius of the circle.
Plugging in the radius of the clock face:
A = π(4 m)² = π(16 m²) ≈ 50.265482 m²
However, since we want the answer to the nearest square meter, we round this to:
A ≈ 50 m²
Final answer:
The area of the clock face with a radius of 4 meters is approximately 50 square meters when rounded to the nearest square meter.
Explanation:
The area of a clock face in a famous clock tower, given its radius is 4 meters, can be calculated using the formula for the area of a circle, which is [tex]A = πr^2[/tex] where A is the area and r is the radius of the circle. In this case, substituting the radius of 4 meters into the formula gives us[tex]A = π(4m)^2 = π16πm^2.[/tex] To give an answer to the nearest square meter, we use the value π = 3.14, resulting in [tex]A = 16(3.14)m^2 = 50.24m^2[/tex], which rounds to 50 m².
How do you find the sum of cube ?
Answer:
[tex](2x+5)(4x^{2} -10x+25)=0[/tex]
Step-by-step explanation:
Given:
The given equation is.
[tex]8x^{3} +125=0[/tex]
Find the some of cube.
Solution:
[tex]8x^{3} +125=0[/tex]
[tex]2^{3}x^{3} +5^{3}=0[/tex]
[tex](2x)^{3} +5^{3}=0[/tex]----------(1)
The sum of the cube formula is given below.
[tex](a^{3} +b^{3})=(a+b)(a^{2} -ab+b^{2} )[/tex]-----------(2)
By comparing equation 1 and equation 2
[tex]a=2x, b=5[/tex]
substitute a and b value in equation 2
[tex]((2x)^{3} +5^{3})=(2x+5)((2x)^{2} -(2x)(5)+5^{2})[/tex]
[tex]((2x)^{3} +5^{3})=(2x+5)(4x^{2} -(10x)+25)[/tex]
[tex]((2x)^{3} +5^{3})=(2x+5)(4x^{2} -10x+25)[/tex]
Therefore the sum of the cube [tex](2x+5)(4x^{2} -10x+25)=0[/tex]
problem solving involving rational equation
1. The reciprocal of 5 plus the reciprocal of 7 is the reciprocal of what number?
2. The reciprocal of the product of two consecutive intergers is 1/72
1. The reciprocal of 5 plus the reciprocal of 7 is the reciprocal of what number?
Answer:The reciprocal of 5 plus the reciprocal of 7 is the reciprocal of [tex]\frac{12}{35}[/tex]
Solution:1. The reciprocal of 5 plus the reciprocal of 7 is the reciprocal of what number?
From given question,
[tex]\text{ reciprocal of 5} = \frac{1}{5}[/tex]
[tex]\text{ reciprocal of 7} = \frac{1}{7}[/tex]
Given that,
reciprocal of 5 + reciprocal of 7 = ?
[tex]\frac{1}{5} + \frac{1}{7} = x[/tex]
On cross-multiplying we get,
[tex]\frac{1}{5} + \frac{1}{7} = \frac{7+5}{5 \times 7} = \frac{12}{35}[/tex]
Thus reciprocal is [tex]\frac{35}{12}[/tex]
So the reciprocal of 5 plus the reciprocal of 7 is the reciprocal of [tex]\frac{12}{35}[/tex]
Question 22. The reciprocal of the product of two consecutive integers is 1/72
Answer:The value of two consecutive numbers are 8 and 9
Solution:Let the two consecutive integers be x and x + 1
Given that reciprocal of product of two consecutive integers is [tex]\frac{1}{72}[/tex]
product of two consecutive integers = x(x + 1) = [tex]x^2 + x[/tex]
reciprocal of the product of two consecutive integers = [tex]\frac{1}{72}[/tex]
[tex]\frac{1}{x^2 + x} = \frac{1}{72}\\\\x^2 + x = 72\\\\x^2 + x - 72 = 0[/tex]
Solve the above quadratic equation by grouping method
[tex]x^2 + x - 72 = 0\\\\x^2 -8x + 9x - 72 = 0\\\\x^2 + 9x + (-8x - 72) = 0\\\\x(x + 9) -8(x + 9) = 0\\\\(x + 9)(x - 8) = 0[/tex]
Thus x = -9 or 8
Ignoring negative value,
x = 8
Thus two consecutive integers are x = 8 and x + 1 = 8 + 1 = 9
8 and 9 are two consecutive integers
tanA / 1-tan^2 = √3 /2
Answer:
A = π/6 + kπ, or A = 2π/3 + kπ
Step-by-step explanation:
tan A / (1 − tan² A) = √3 / 2
Cross multiply and simplify:
√3 (1 − tan² A) = 2 tan A
√3 − √3 tan² A = 2 tan A
3 − 3 tan² A = 2√3 tan A
0 = 3 tan² A + 2√3 tan A − 3
Solve with quadratic formula:
tan A = [ -2√3 ± √((2√3)² − 4(3)(-3)) ] / 2(3)
tan A = [ -2√3 ± √(12 + 36) ] / 6
tan A = (-2√3 ± √48) / 6
tan A = (-2√3 ± 4√3) / 6
tan A = -√3 or √3/3
Solve for A:
A = 2π/3 + kπ, or A = π/6 + kπ
In this equation 5Z=-3 (z+7) in which order would you solve the problem? Put the steps below in the correct order
A. Use distribute property to simplify the right side (multiply the Z in the seven by -3)
B. Add 3z to both sides
C. Divided by -8 on both sides
Answer:
Use distributive property, add 3z to both sides, divide by -8 on both sides
Step-by-step explanation:
You have to do parenthesis first, then equal both sides, then divide
PLEASE HELP I WILL GIVE BRAINLIEST
Answer:
[tex]AB=\dfrac{38}{3}\ units[/tex]
Step-by-step explanation:
ABCD is a rhombus, then
[tex]AB=BC=CD=DA[/tex]
Since
[tex]BC=2x+8\\ \\CD=5x+1,[/tex]
then
[tex]BC=CD\Rightarrow 2x+8=5x+1[/tex]
Solve this equation:
[tex]2x-5x=1-8\\ \\-3x=-7\\ \\3x=7\\ \\x=\dfrac{7}{3}[/tex]
Then
[tex]BC=2\cdot \dfrac{7}{3}+8=\dfrac{14}{3}+8=\dfrac{14+8\cdot 3}{3}=\dfrac{14+24}{3}=\dfrac{38}{3}\ units[/tex]
Therefore,
[tex]AB=\dfrac{38}{3}\ units[/tex]
-6x+3y=-7−6x+3y=−7minus, 6, x, plus, 3, y, equals, minus, 7
x
Answer: none
Step-by-step explanation: since -6x+3y can't equal to -7−6x+3y
Square root of 60 divided by square root of 5
Answer: 2√3
Step-by-step explanation: To divide √60 by √5, we simply divide the numbers that are inside the radicals.
Since the quotient of 60 divided by 5 is 12,
the square root of 60 divided by the square root of 5 is √12.
However, we can simplify the square root of 12.
The √12 breaks down into 4 · 3 and 4 breaks down into 2 · 2.
The 2's match up, so a 2 comes outside of the radical.
Since the 3 doesn't pair up, it stays inside.
So our answer is 2√3.
Final answer:
The simplification of [tex]\sqrt{60}/\sqrt{5[/tex] results in [tex]2\sqrt{3,[/tex] by combining the square roots into one and then simplifying the inner value.
Explanation:
The question asks for the simplification of the expression which is the square root of 60 divided by the square root of 5. To simplify this expression, one can utilize the property of square roots that allows the division within a single square root function. Here’s a step-by-step explanation:
Write the expression as [tex]\sqrt{60}/\sqrt{5[/tex]
Combine the square roots using the property[tex]\sqrt{(a)}/\sqrt{(b)} = \sqrt{(a/b),[/tex] giving[tex]\sqrt{60}/\sqrt{5[/tex]
Simplify 60/5 to get 12.
Now take the square root of 12, which is not a perfect square. However, we can express 12 as the product of 4 (which is a perfect square) and 3 (4 * 3 = 12).
Finally, we write the expression [tex]\sqrt{4} * \sqrt{3,[/tex] which simplifies to [tex]2\sqrt{3,[/tex]
Thus, the simplified form of [tex]\sqrt{60}/\sqrt{5[/tex] is [tex]2\sqrt{3,[/tex], which cannot be simplified any further as [tex]\sqrt{3[/tex] is an irrational number and does not have a precise decimal representation.
It is always important to remember that when rounding is necessary, you should round the result up if the digit following the last significant digit is 5 or greater, and round it down if it is less than 5.
What is 4 and square root of 72
Answer:
square root of 72 is approximately 8.49
i hope that right!
Step-by-step explanation:
Based on the information given say whether or not △ABC∼△FED. Explain your reasoning.
m∠A=m∠B, m∠C=m∠A+30°, m∠E=m∠F=x, m∠D=2x−20°.
Answer:
Yes, △ABC ∼ △FED by AA postulate.
Step-by-step explanation:
Given:
Two triangles ABC and FED.
m∠A = m∠B
m∠C = m∠A + 30°
m∠E = m∠F = [tex]x[/tex]
m∠D = [tex]2x-20[/tex]°.
Now, let m∠A = m∠B = [tex]y[/tex]
So, m∠C = m∠A + 30° = [tex]y+30[/tex]
Now, sum of all interior angles of a triangle is 180°. Therefore,
m∠A + m∠B + m∠C = 180
[tex]y+y+y+30=180\\3y=180-30\\3y=150\\y=\frac{150}{3}=50[/tex]
Therefore, m∠A = 50°, m∠B = 50° and m∠C = m∠A + 30° = 50 + 30 = 80°.
Now, consider triangle FED,
m∠D+ m∠E + m∠F = 180
[tex]2x-20+x+x=180\\4x=180+20\\4x=200\\x=\frac{200}{4}=50[/tex]
Therefore, m∠F = 50°
m∠E = 50° and
m∠D = [tex]2x-20=2(50)-20=100-20=80\°[/tex]
So, both the triangles have congruent corresponding angle measures.
m∠A = m∠F = 50°
m∠B = m∠E = 50°
m∠C = m∠D = 80°
Therefore, the two triangles are similar by AA postulate.
7. The cost of renting the party room for 10 people is $117.50. The cost of renting the room is $151.25 for 15 people. Write an equation that represents the cost of renting the party room in terms of the number of people attending the party .
Answer:
C = 6.75n + 50
Step-by-step explanation:
The equation for the cost of renting the party room can be written in the form;
C= mn+k ......i
Where C = cost
n = number of people
Substituting the 2 cases into the equation we have,
Case 1
117.5 = 10m + k ......1
Case 2
151.25 = 15m + k .....2
Subtracting eqn 1 from 2 we have
151.25 - 117.50 = 15m - 10m
5m = 33.75
m = 33.75/5 = 6.75
Substituting m = 6.75 into eqn 1, we have
117.50 = 10(6.75) + k
k = 117.5 - 67.50
k = 50
Therefore, rewriting the eqn i, we have
C = 6.75n + 50
What is the slope of y=4-6x
Answer:
the slope, m, is -6
Step-by-step explanation:
One of the most commonly used equations for a straight line is y = mx + b, where m is the slope and b is the y-intercept.
Comparing y=4-6x to y = b + mx, we see that the slope, m, is -6 and the y-intercept, b, is 4.
The slope of the line y = 4 - 6x is -6, which shows that for every increase of 1 in the x-coordinate, the y-coordinate decreases by 6.
The equation is given as follows:
y = 4 - 6x
As we know that the equation is in slope-intercept form, y=mx+b.
Here, m is the slope and b is the y-intercept.
As per the question, the y-intercept is 4, which means the line crosses the y-axis at (0,4).
The slope, -6, tells us that for every increase of 1 in the x-coordinate, the y-coordinate decreases by 6.
Thus, the slope of the line y = 4 - 6x is -6.
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The solution to the equation x? = 45 is between
Answer:
9
Step-by-step explanation:
9 times 5 =45
Answer:
9
Step-by-step explanation:
When you do the math, 9 multiplied by 5 will get you 45
let f = {(-2,4), (-1,2), (0,0), (1,-2), (2,-5)}
let g= {(-3,3), (-1,1), (0,-3), (1,-4), (3,-6)}
what is g(f(2))?
Answer:9
Step-by-step explanation:4
Louisiana biologists tagged 250 fish in the oxbow lake False River on October 5. On a later date, they found 7 tagged fish in a sample of 350 fish. Estimate the total number of fish in False River to the nearest hundred.
At a school, the school population is 2/5 boys. There are 450 boys in the school. How many total students are in the school?
A bag contains quarter and dimes in a ratio of 3:5. If there is $6 in quarters in the bag, how many dimes are there?
1. Set up a ratio:
7 tagged / 350 fish = 250 tagged / x fish
Solve for x:
x = (350 * 250) / 7
x = 12,500 fish
2. Divide number of boys by the population ratio:
450 / 2/5 = (450 *5) /2 = 2250 / 2 = 1125 total students.
3. 4 quarters = $1, so they have 24 quarters total.
The ratio 3:5 means for every 3 quarters there are 5 dimes.
24 quarters / 3 = 8
8 x 5 = 40 dimes.
(1) The population of fish in the False river is 12500.
(2) There are 1125 total number of students in the school .
(3) There are 40 dimes in the bag.
(1) Number of fish tagged by Louisiana biologists = 250
On the next day a sample was collected from the False river
The number of fish in the sample = 350
Number of tagged fish in the sample = 7
Let the population of fish in the False river = P
Takin the ratio we can
[tex]\rm \dfrac{7}{350}= \dfrac{250}{P} \\\\P = (250)(350)/(7)\\P = 12500[/tex]
So the population of fish in the False river = 12500
(2) The number of boys in the school = 450
Let the total number of students in the school be B
According to the given condition
[tex]\rm \dfrac{2}{5}\times B = 450\\\\B = (450\times 5) /2 \\B = 2250/2 =1125[/tex]
So the total number of students in the school = 1125
(3) Let the number of dimes in the bag be x
According to the given condition we can write
[tex]\rm \dfrac{Number\; of\; quarters }{Number\; of\; dimes } = \dfrac{3}{5} ........(1)[/tex]
Also it is given that there are $6 in quarters in the bag.
$1 = 4 quarters
So $6 has [tex]\rm 4\times 6 = 24 \; quarters[/tex]
So we can put this value in equation (1)
[tex]\dfrac{24}{x} =\dfrac{3}{5} \\\\x = 40 dimes[/tex]
So we can conclude that there are 40 dimes in the bag.
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What is the x-coordinate of the point that divides the
directed line segment from Kto J into a ratio of 1:3?
K(9,2)
1 2 3 4 5 6 7 8 9 10 11 12 x
top Tuppo
OOOO
J (1.-10)
The x-coordinate of the point that divides the directed line segment from K to J into a ratio of 1:3 is 7
Step-by-step explanation:
The formula for x-cooridnate of a point that divides a line in ratio m:n is given by:
[tex]x = \frac{nx_1+mx_2}{m+n}[/tex]
Given
K(9,2) = (x1,y1)
J(1,-10) = (x2,y2)
m = 1
n = 3
Putting the values in the formula
[tex]x = \frac{(3)(9)+(1)(1)}{1+3}\\x = \frac{27+1}{4}\\x = \frac{28}{4}\\x = 7[/tex]
Hence,
The x-coordinate of the point that divides the directed line segment from K to J into a ratio of 1:3 is 7
Keywords: Ratio, fraction
Learn more about ratios at:
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help me???????????????????
Answer:
To answer X and Y, all you need is a little common sense and a little bit of algebraic thinking. -x can equal: -x = 0? -6?, etc. Y could equal: 3?, 6?, 12?, etc. But the answer will always no matter what number will be 6.
Simplify the expression.
7x + 7 +5(x + 3) + 3
Answer:
12x+25
Step-by-step explanation:
7x+7+5x+15+3
12x+25
Please help me! I'm having trouble solving this! In the △PQR, PQ = 39 in, PR = 17 in, and the height PN = 15 in. Find QR. Consider all possible cases.
Answer: 44
Step-by-step explanation:
we will find RN and NQ, then add together to give us RQ.
To find RN;
RP= 17 PN = 15 and RN =?
using pythagoras theorem,
adj^2 = hyp^2 - opp^2
RN^2 = RP^2 - PN^2
?^2 = 17^2 - 15^2
?^2 = 17^2 - 15^2
?^2 = 289 - 225
?^2 = 64
? = √64
? = 8
RN=8
To find NQ,
PN = 15 PQ=39 and NQ=?
using pythagoras theorem
NQ^2 = PQ^2 - PN^2
?^2 = 39^2 - 15^2
?^2 = 1521 - 225
?^2 = 1296
? = √1296
? = 36
NQ= 36
RQ = RN + NQ
RQ= 8 + 36
RQ=44
There are 452 pictures of dogs in 4 equal groups. How many pictures are in each group? Explain how you can use place value to place the first digit in the quotient. Please show with working
By dividing 452 pictures of dogs by 4, we find that each of the 4 equal groups has 113 pictures. The division process involves using place value and the standard algorithm for long division.
Explanation:To find out how many pictures of dogs are in each group, we need to divide the total number of pictures by the number of groups. The question states there are 452 pictures of dogs and these are divided into 4 equal groups. We can use long division to solve this.
Step-by-Step Solution:
Write down the division: 452 ÷ 4.
Start by looking at the hundreds place in 452. There are 4 hundreds in 452. Since 4 divided by 4 is 1, we put 1 in the hundreds place of the quotient.
Multiply the divisor (4) by the quotient (100) to get 400.
Subtract 400 from 452 to get 52.
Now, look at the tens place in 52. There are 5 tens in 52, and since 5 divided by 4 is 1 with a remainder, we put 1 in the tens place of the quotient and have a remainder of 12 after subtracting 40 (1 x 4 tens) from 52.
Next, look at the ones place in 12. There are 12 ones, and since 12 divided by 4 is 3, we put 3 in the ones place of the quotient.
After placing 3 in the ones place, we have no remainder, which means the division is complete and the quotient is 113.
Therefore, each group has 113 pictures of dogs.
Solving a Real-World Problem
Brigid is picking strawberries at the Pick-Your-Own Farm. Her goal is to pick 5 bushels of strawberries. She has
already pick
ushels, and she picks at a rat
hel per hour. The scenario is represented as
ah+15 = 5, where h is the number of hours she picks. How many more hours will it take Brigid to fill 5 bushels o
strawberries?
hours
16
hours
10
hours
unu
hours
) Intro
Done
Answer: The answer is 5 and 3/5 hours
Step-by-step explanation:
Answer:
5 and 3/5 hours
Step-by-step explanation:
What is the value of the expression shown below?
2 over 3 to the power of 2 + 5 × 2 − 4
6 and 8 over 9
6 and 4 over 9
6 and 2 over 3
6 and 1 over 3
(2/3)²+5×2-4
(4/9)+5×2-4
(4/9)+10-4
10 4/9 - 4
6 4/9
answer: second choice
refer to the graphic novel frame below. write and solve an equation to find how many movies they have time to show.
Answer:
Number of movies that can be shown = 2
Step-by-step explanation:
Given:
Movie night duration = 4 hours
Duration of each movie = 1.75 hours
Time given for eating popcorn = 0.5 hours
Time alloted for movies (excluding popcorn time) = 4 - 0.5 = 3.5 hours.
Number of movies that can be shown = [tex]\frac{Total\ time\ alloted\ for\ movie}{Time\ for\ 1\ movie}=\frac{3.5}{1.75}= 2[/tex]
To determine the number of movies that can be watched, an equation M*X <= T can be formulated where M is the length of the movie, X is the number of movies, and T is the total time available. To find X, divide T by M. This works when the time for each movie is the same.
Explanation:Without the actual graphic novel frame, it's hard to provide a specific equation. However, I can give you an example on how to approach this situation. Let's assume each movie is of length 'M' minutes and you have a total of 'T' minutes available for watching movies.
,
Let 'X' be the number of movies you can watch. You would write this as a mathematical equation like this: M*X <= T. This equation states that the total time spent watching movies should be less than or equal to the total time available.
,
To solve the equation, you would divide both sides of the equation by 'M'. The result will be X <= T/M. If you know the values of 'M' and 'T', you can plug them in here to get the maximum number of movies you can watch.
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What is the area of an equilateral triangle that has a perimeter of 36 centimeters? Round to the nearest square centimeter.
Find base and height of the triangle to find area.
Base=Perimeter/3
Base=36/3=12 cm
Height²=12²-6²
Height²=108
Height=(6√3) cm
area=base×height
area=1/2×12×6√3=62 cm² approx.
answer: 3rd choice
Answer:
Find base and height of the triangle to find area.
Base=Perimeter/3
Base=36/3=12 cm
Height²=12²-6²
Height²=108
Height=(6√3) cm
area=base×height
area=1/2×12×6√3=62 cm² approx.
answer: 3rd choice
Step-by-step explanation:
What is the equation of the line that passes through the point (7,-6)and has a slope of -2
Answer:
The equation of the required line is: 2x + y = 8
Step-by-step explanation:
When a point on the line and the slope of the line are given, we use the slope - one - point form to determine the equation of the line.
Say, [tex]$ (x_1, y_1) $[/tex] is the point passing through the line and the slope of the line is say, [tex]m[/tex]. Then the equation would be:
[tex]$ (y - y_1) = m(x - x_1) $[/tex]
Here [tex]$ (x_1, y_1) = (7, -6) $[/tex] and slope, [tex]$ m = - 2 $[/tex].
Therefore, the equation of the line becomes:
[tex]$ y - (-6) = -2(x - 7) $[/tex]
[tex]$ \implies y + 6 = -2x + 14 $[/tex]
Rearranging we get:
[tex]$ 2x + y - 8 = 0 $[/tex] which is the required equation of the line.
Mike and Menna were instructed to graph the function y = 12 x + 1. Their graphs are shown.
The figure shows two graphs in the xy-plane. The graph on the left is labeled as Mike's Graph. The values on the x-axis range from negative 8 to 8 in increments of 2 and the values on the y-axis range from negative 8 to 8 in increments of 2. A line is shown which intersects the x-axis at negative 0.5 and y-axis at 1. The graph on the right is labeled as Menna's Graph. The values on the x-axis range from negative 8 to 8 in increments of 2 and the values on the y-axis range from negative 8 to 8 in increments of 2. A line is shown which intersects the x-axis at 2 and y-axis at 1.
Which student graphed the function correctly?
What mistake did the other student make?
Answer:
The function is y = 2x + 1.
And mike graphed the function correctly.
Menna took the point where the function touches x-axis incorrectly.
Instead of (-1/2,0), Menna took it as (-2,0)
Step-by-step explanation:
The equation y = mx +c indicates a straight line whose slope is m
And y-intercept is c.
y-intercept is nothing but the distance between origin and point where the graph crosses the y-axis (0,c).
Now, this graph crosses x-axis when y = 0.
⇒ mx + c = 0; ⇒ x = [tex]\frac{-c}{m}[/tex].
Now, by comparing y = 2x + 1 with y = mx + c.
m=2 and c=1
⇒ the graph should crosses y-axis at (0,c) = (0,1)
And touch x-axis at ([tex]\frac{-c}{m}[/tex] , 0) = ([tex]\frac{-1}{2}[/tex],0)
⇒ mike graphed the function correctly.
Menna took the point where the function touches x-axis incorrectly.
Instead of (-1/2,0), Menna took it as (-2,0)
Answer:
Step-by-step explanation:
y = 2x + 1.