Identify whether each system of equations has infinitely many solutions or no solution.
Answers
The first system of equations has no solution and the second set of equations has a unique solution.
If we are having two equations as
[tex]a_{1} x^{2} +b_{1} x+ c_{1} =0[/tex]
and [tex]a_{2} x^{2} +b_{2} x+ c_{2} =0[/tex]
The condition at which these equations will have infinitely many solutions is
[tex]\frac{a_{1} }{a_{2} } =\frac{b_{1} }{b_{2} } =\frac{c_{1} }{c_{2} }[/tex]
The condition at which these equations will have infinitely many solutions is
[tex]\frac{a_{1} }{a_{2} } =\frac{b_{1} }{b_{2} } \neq \frac{c_{1} }{c_{2} }[/tex]
For, the 26th question, we have
4x +8y = -8
4x +8y +8 = 0
x +2y +2 =0 equation(1)
x =-2y +1
x +2y -1 = 0 equation(2)
On comparing these equations with the general form, we have
[tex]a_{1} = 1, a_{2} =1\\b_{1} = 2, b_{2} = 2\\c_{1} = 2, c_{2} = -1[/tex]
So, [tex]\frac{a_{1} }{a_{2} } =\frac{b_{1} }{b_{2} } \neq \frac{c_{1} }{c_{2} }[/tex]
Thus, this system of equations has no solution.
Now, For the 27th question, we have
2x - 3y = 6
2x -3y -6 = 0 equation(3)
[tex]y = \frac{2}{3}x -2 \\\\3y = 2x -6\\\\3y -2x +6 = 0[/tex] equation (4)
On comparing these equations with the general form, we have
[tex]a_{1} = 2, a_{2} =3\\b_{1} = -3, b_{2} = 2\\c_{1} = -6, c_{2} = 6[/tex]
So, [tex]\frac{a_{1} }{a_{2} } \neq \frac{b_{1} }{b_{2} }[/tex]
Thus, this system of equations has a unique solution.
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Related Questions
A pirate ship found a treasure chest that contained 127 gold coins and 253 silver coins. If there are 38 pirates on the ship and they split the coins evenly, how many coins did they collect?
A. 10
B. 11
C. 380
D. 418
Answers
The number of coins that the pirates collect is A. 10.
How to calculate the value?From the information, the pirate ship found a treasure chest that contained 127 gold coins and 253 silver coins and there are 38 pirates on the ship.
The number of coins that way person will get will be:
=>Total coins / Number of pirates
= (253 + 127) / 38
= 380 / 38
= 10
Each person gets 10 coins.
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find the annual salary of a person who is paid $835.50 per week
Answers
Answer:
43446
Step-by-step explanation:
52 weeks in an year
835.5 × 52 = 43446
Find the perimeter of triangle ABC. Round your answer to two decimal places.
Answers
Check the picture below.
[tex]~\hfill \stackrel{\textit{\large distance between 2 points}}{d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2}}~\hfill~ \\\\[-0.35em] ~\dotfill\\\\ A(\stackrel{x_1}{-7}~,~\stackrel{y_1}{2})\qquad B(\stackrel{x_2}{3}~,~\stackrel{y_2}{-8}) ~\hfill AB=\sqrt{(~~ 3- (-7)~~)^2 + (~~ -8- 2~~)^2} \\\\\\ ~\hfill AB=\sqrt{( 10)^2 + ( -10)^2} \implies \boxed{AB=\sqrt{ 200 }}[/tex]
[tex]B(\stackrel{x_1}{3}~,~\stackrel{y_1}{-8})\qquad C(\stackrel{x_2}{-4}~,~\stackrel{y_2}{-9}) ~\hfill BC=\sqrt{(~~ -4- 3~~)^2 + (~~ -9- (-8)~~)^2} \\\\\\ ~\hfill BC=\sqrt{( -7)^2 + ( -1)^2} \implies \boxed{BC=\sqrt{ 50 }} \\\\\\ C(\stackrel{x_1}{-4}~,~\stackrel{y_1}{-9})\qquad A(\stackrel{x_2}{-7}~,~\stackrel{y_2}{2}) ~\hfill CA=\sqrt{(~~ -7- (-4)~~)^2 + (~~ 2- (-9)~~)^2} \\\\\\ ~\hfill CA=\sqrt{( -3)^2 + (11)^2} \implies \boxed{CA=\sqrt{ 130 }} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\stackrel{\textit{\LARGE perimeter}}{\sqrt{200}~~ + ~~\sqrt{50}~~ + ~~\sqrt{130}} ~~ \approx ~~ \text{\LARGE 32.61}[/tex]
Daniela bakes 36 cookies and gives 2 cookies to her friends
Answers
anwser: she has 34 cookies left
In this problem we determine the first time after 10 o'clock at which the minute hand and the hour hand of a clock point in the exact same direction ( meaning when they are " on top of" each other). See if you can find the time on your own before reading the following steps. ( Assume that both hands move continously. For example, from 10 o'clock to 11 o'clock, the hour hand smoothly and gradually moves from pointing at the 10 to pointing at the 11.)
a) Let m be the number of mintues after 10 o'clock at which the minuet hand and hour hand are pointing in the same direction. In terms of m, trhough what fraction of hte entire face of the clock has the minute hand traveled during the m minutes after 10 o'clock?
b) In terms of m, what fraction of hte distance from 10 to 11 has the hour hand traveled during the m minutes after 10 o'clock?
c) Trough what farction of the entire clock's face doe sthe hour hand travel during the m minutes after 10 o'clock?
d) At what exact time do the minute hand and hour hand point in the same direction?
( GIVE BRAINLIST IF CORRECT AND ANSWER!! )
Answers
Answer:
a) 1:25 b) 2:06 c) 5:00 d) 4:10
Step-by-step explanation:
help please and thankyou
Answers
The value of x will be 24.
What is mean by Triangle?
A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.
Given that;
For a given right triangle, the expression is,
⇒ sin (3x - 7) = cos (x + 1)
Now,
Solve for x as;
The expression is,
⇒ sin (3x - 7) = cos (x + 1)
Since, sin x= cos (90 - x)
So, We get;
⇒ sin (3x - 7) = cos (x + 1)
⇒ cos (90 - (3x - 7)) = cos (x + 1)
⇒ 90 - (3x - 7) = (x + 1)
⇒ 90 - 3x + 7 = x + 1
⇒ 97 - 3x = x + 1
⇒ 97 - 1 = x + 3x
⇒ 96 = 4x
⇒ 4x = 96
⇒ x = 96/4
⇒ x = 24
Thus, The value of x will be 24.
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Does y vary directly with x? If it does, what is an equation for the direct variation?
Answers
The variable y varies directly with x and the variation equation is (b) y = -1/2x
How to determine the equation of the variation?The graph represents the given parameter
On the graph, we can see that:
The values of x are divided by -2 to get y
This means that the graph represents a direct variation
Recall that we stated that:
The values of x are divided by -2 to get y
This means that the constant of variation is -1/2
The direct variation equation is represented as:
y = kx
Where k represents the constant of variation i.e. k = -1/2
Substitute the known values in the above equation So, we have the following equation
y = -1/2x
Hence, the equation of variation is y = -1/2x
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1. Find the y-intercept of the line paing through the point A (3, -2) and B (-1, 3). (5 pt)
Answers
Find the equation of the line passing through the given point and parallel to the given line.
( 1, 9 ), y = 4x + 2
( 5 , 2 ), y = -2x + 7
Answers
The line equation passing through the given points and parallel to the given lines are:
Line 1: y=-4x+13...(i)
Line 2: y=2x-12...(ii)
Line 1
The first line is passing through point (1,9) and parallel to the y=4x+2 line.
Since line 1 would be parallel to line y=4x+2, hence both lines would have the same value of slope (m).
Using the standard formula of line equation, we could identify that line y=4x+2 has:
ay = bx + c, m= -b/a
y=4x+2, m=-4
We could use the line equation formula, where:
y-y1 = m (x-x1)
we use the given point (1,9) and the slope value (m=-4) to get the line equation passing through the point:
y-9 = -4(x-1)
y-9=-4x+4
y=-4x+13...(i)
Line 2
The first line is passing through point (5,2) and parallel to the y=-2x+7 line.
Since line 2 would be parallel to line y=-2x+7, hence both lines would have the same value of slope (m).
Using the standard formula of line equation, we could identify that line y=-2x+7 has:
ay = bx + c, m= -b/a
y=-2x+7, m=-2
We could use the line equation formula, where:
y-y2 = m (x-x2)
we use the given point (5,2) and the slope value (m=2) to get the line equation passing through the point:
y-2 = 2(x-5)
y-2 = 2x-10
y=2x-12...(ii)
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Given the points A(-5,-5) and B(7, 1), find the coordinates of the point P on directed line segment AB that partitions AB in the ratio of 1:5, but not necessary In that order, give two possible coordinates of point P. Graph segment AB and P in the coordinate plane.
Answers
The two coordinates on the segment AB due to internal division are (5,0) and (-3,-4).
What is internal division?
When a point P divides the line joining the two points and the potint P lies in between the two coordinates then the division is internal division. If the point lies outside of the given coordinates then the division is known as external division.
The division is internally because point P lies on the line as given in the question.
The formula for the internal division is as follows:
[tex]X=\frac{mx_1+nx_2}{m+n}\\Y=\frac{my_1+ny_2}{m+n}[/tex]
Since points are A(-5,-5) and B(7,1) hence, [tex]x_1=-5,x_2=7,y_1=-5,y_2=1[/tex] and ratio is 1:5 then [tex]m=1,n=5[/tex].
Substute all value to obtain the coordinates.
[tex]X_1=\frac{1(-5)+5(7)}{1+5}\\X_1=5\\Y_1=\frac{1(-5)+5(1)}{1+5}\\Y_1=0[/tex]
Hence, the first cordinate is (5,0).
As given in the question that the ratio in not necessarily in the order of 1:5 so, consider the ratio is 5:1.
Now, m=5 and n=1.
Again substitute all values in to find the new coordinate.
[tex]X_2=\frac{5(-5)+1(7)}{5+1}\\X_2=-3\\Y_2=\frac{5(-5)+1(1)}{5+1}\\Y_2=-4[/tex]
Hence, another coordinate is (-3,-4).
Hence, the two coordinates on the segment AB due to internal division are (5,0) and (-3,-4).
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HELP ASAP GIVING BRAINLIEST
Answers
Answer: C
Step-by-step explanation:
If a-b=-5 and ab=0 then find a³-b³
What’s the answer?
Answers
If a - b = -5 and ab = 0 then the value of the expression a³-b³ is -125.
In the question ,
it is given that ,
the value of a - b = -5 and ab = 0
we need to find the value of the expression (a³-b³) ,
we know the identity that a³-b³ = (a - b)(a² + b² + ab)
we first need the value of a² + b² .
given that a - b = -5
squaring both the sides , we get
(a - b)² = 25
a² + b² - 2ab = 25
given ab = 0, so a² + b² = 25
Substituting a² + b² = 25 in the identity a³-b³ = (a - b)(a² + b² + ab) ,
we get ,
a³-b³ = (-5)(25 + 0)
a³-b³ = -5 × 25
a³-b³ = -125
the answer is -125 .
Therefore , If a - b = -5 and ab=0 then the value of the expression a³-b³ is -125.
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What translation is made from f(x) → f(x) + 6? sliding it up reflection across the y-axis rotation around the origin reflection across the x-axis
Answers
The translation made from f(x) → f(x) + 6 is sliding it up
what is translation in geometry?A translation is a geometric change in Euclidean geometry that involves moving each point in a figure, shape, or space by the same amount in one direction.
A translation can also be thought of as moving the origin of the coordinate system or as adding a constant vector to each point.
Any translation in a Euclidean space is an isometry.
the translation made from f(x) → f(x) + 6 involves moving the graph up 6 units
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Q2.
I am thinking of two numbers.
The first number is x
The second number is 7.5 more than x.
Write down an expression, in terms of x for the second number.
For the two numbers,
the product is double the sum.
Work out the numbers I could be thinking of.
Give both possible pairs of answers.
Answers
Answer:
second number = (x + 7.5)
Since the product of the two numbers is double of their sum,
x(x + 7.5) = 2(x + x + 7.5)
x² + 7.5x = 2(2x + 7.5)
x² + 7.5x = 4x + 15
x² + 7.5x - 4x - 15 = 0
x² + 3.5x - 15 = 0
∴ x = -6 or 2.5
∴ second number
= -6 + 7.5 or 2.5 + 7.5
= 1.5 or 10
∴ The two numbers that I am thinking of are either -6 and 1.5 or 2.5 and 10.
HELP ME PLEASE, I NEED TO FINISH THIS MATH PROBLEM!
Anna is working two summer jobs, making $9 per hour washing cars and $12 per hour landscaping. Last week Anna worked a total of 7 hours and earned a total of $78. Determine the number of hours Anna worked washing cars last week and the number of hours she worked landscaping last week.
ANSWER: ANNA WORKED _____ HOURS WASHING CARS AND ______ HOURS LANDSCAPING.
Answers
Answer: anna worked 4.33repeating hours washing cars and 3.25 hours landscaping
Step-by-step explanation:
i personally used a guess and check method.
i multiplied 9(hourly wage for washing cars) and 4.33repeating(number of hours) = 39
i multiplied 12(hourly wage landscaping) and 3.25(number of hours) = 39
39 + 39 = $78
What is 125 in simplest form?
Answers
Answer:
125 in simplest form is 1/8.
Step-by-step explanation:
If that was a typo and you meant to say 12/5, the answer is 2 2/5.
5 fits inside of 12 two times, with 2 left over.
We can check this by multiplying 5 by 2 (denominator by remainder), and adding 2 (the numerator). With this, we get 12/5, and we know our math is correct.
1/25 is already is simplest form.
A bookstore had 150 copies of a magazine. Yesterday the bookstore sold 2/5 of these copies. How many copies were sold yesterday
Answers
Answer:
Hi
Step-by-step explanation:
so the question is asking what is 2/5 of 150
if 150 is able to evenly be split up into 5 even parts we can the add two of those parts to get our answer.
does 150 split up into 5 even parts??
hmmm you probably are thinking, 15 does divide by 5 evenly into 3 parts, so we now know that 150 also splits up into 5 even parts of 30 :)
2 time 30 = 60
so there is how to figure out the answer and , the answer 60 :)
Riley found a receipt for a pair of jeans for $142.95, tax included. If the sales tax rate was 6%, what was the list price of the jeans? Round your answer to the nearest cent.
Answers
Answer:
$134.86
Step-by-step explanation:
Let the original price before tax be x.
A whole amount is 100% of the amount, so x is 100% of the original price without tax.
The tax rate is 6%, so the tax on x is 6% of x. Add 6% of x to 100% of x, and you have 106% of x. The item plus tax cost 106% of x.
106% of x = $142.95
106/100 × x = 142.95
1.06x = 142.95
x = 142.95/1.06
x = $134.86
Answer: $134.86
mario tiene una cinta de 6 m y su amiga beatriz tiene una cinta de 8 m ¿cuantas veces es la longitud de la cinta de mario comparada con la longitud de la cinta de beatriz?
Answers
La cinta de Mario tiene una longitud que es 0.75 veces la longitud de la cinta de Beatriz.
¿Como se comparan las longitudes?
Sabemos que la longitud de la cinta de Mario tiene una longitud de 6 metros, mientras que su amiga Beatriz tiene una cinta de longitud de 8 metros.
Para saber cuantas veces es la longitud de la cinta de mario comparada con la longitud de la cinta de beatriz, tenemos que tomar el cociente entre ambas longitudes, obtendremos:
6m/8m = 0.75
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Find the equation of the parabola with the given x-intercepts and point on the graph. Use y = a(x-p)(x-q).
1. x-int: (-2,0) , (5,0)
P (3,6)
Answers
Answer:
Below
Step-by-step explanation:
a(x-p)(x-q) p = -2 q = 5
a ( x- - 2)(x - 5) sub in the values of the point given (3,6) to calculate 'a'
6 = a (3+2)(3-5)
a = -6 /10 = - 3/5
y = -3/5 (x+2)(x-5)
Answer:
[tex]\textsf{Intercept form}: \quad y=-\dfrac{3}{5}(x+2)(x-5)[/tex]
[tex]\textsf{Standard form}: \quad y=-\dfrac{3}{5}x^2+\dfrac{9}{5}x+6[/tex]
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{6 cm}\underline{Intercept form of a quadratic equation}\\\\$y=a(x-p)(x-q)$\\\\where:\\ \phantom{ww}$\bullet$ $p$ and $q$ are the $x$-intercepts. \\ \phantom{ww}$\bullet$ $a$ is some constant.\\\end{minipage}}[/tex]
If the x-intercepts are (-2, 0) and (5, 0) then:
p = -2q = 5Substitute the values of p and q into the formula:
[tex]\implies y=a(x-(-2))(x-5)[/tex]
[tex]\implies y=a(x+2)(x-5)[/tex]
To find a, substitute the given point on the curve P (3, 6) into the equation:
[tex]\implies 6=a(3+2)(3-5)[/tex]
[tex]\implies 6=a(5)(-2)[/tex]
[tex]\implies 6=-10a[/tex]
[tex]\implies a=\dfrac{6}{-10}[/tex]
[tex]\implies a=-\dfrac{3}{5}[/tex]
Substitute the found value of a into the equation:
[tex]\implies y=-\dfrac{3}{5}(x+2)(x-5)[/tex]
Expand to write the equation in standard form:
[tex]\implies y=-\dfrac{3}{5}(x^2-3x-10)[/tex]
[tex]\implies y=-\dfrac{3}{5}x^2+\dfrac{9}{5}x+6[/tex]
A bank employee notices an abandoned checking account. The bank charges a monthly fee for the account modeled by the function
A(m)=184-8m, where M is in months and A(m) is in dollars.
What is the domain of the function within the context? Use inequality Notation.
Answers
The domain of the function A(m) = 184 - 8m representing the bank charges on monthly fees is m ≤ 23
How to find the domain of the functionThe equation is linear equation in the slope intercept form as
y = mx + c
where
m = slope = -8
c = intercept = 184
x = input variables = m
y = output variables = A(m)
The domain refers to all possible values of m, generally the equation has no restriction for m however for the problem being discussed y should not be negative. hence we solve for m when y = 0
0 = 184 - 8m
8m = 184
m = 23
The maximum value of m is 23 hence the domain is m ≤ 23
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This is part B to my last question
Answers
The y-intercept of the graph of the function g(n) represents the height of the flower.
We are given:
A researcher is following the growth of a particular type of flower. She writes the given equation to show the height of the flower g(n), in inches, after n days.
g(n) = 10(1.02)^n
which is an exponential function.
We need to find what the y-intercept of the graph of the function g(n) represents.
We have the exponential function;
g(n) = 10(1.02)^n
where,
x-coordinate of the graph represents the number of days.
y-coordinate of the graph represents the height of the flower.
Thus, the y-intercept of the graph of the function g(n) represents the height of the flower.
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Jon needs to buy a backpack and several folders for school. If she shops at smart supply, the backpack will cost $45 and folders cost $0.45 each. If she shops at supply Guys, the backpack will cost $50.40 and folders cost 0.15 each. Write and solve an inequality to find the number of folders Jan would need to buy for the Supply Guys to be the cheaper option
Answers
Considering the definition of an inequality, the number of folders Jan would need to buy for the Supply Guys to be the cheaper option is more than 18.
Definition of inequalityAn inequality is the existing inequality between two algebraic expressions, connected through the signs:
greater than >.less than <.less than or equal to ≤.greater than or equal to ≥.An inequality contains one or more unknown values in addition to certain known data.
Solving an inequality consists of finding all the values of the unknown for which the inequality is true.
Inequality in this caseIn this case, you know that:
If she shops at smart supply, the backpack will cost $45 and folders cost $0.45 each. If she shops at supply Guys, the backpack will cost $50.40 and folders cost 0.15 each.The Supply Guys is the cheaper option.Being "x" the number of folders, the inequality that expresses the previous relationship is
45 + 0.45x > 50.40 + 0.15x
Solving:
0.45x - 0.15x > 50.40 -45
0.30x> 5.4
x> 5.4÷ 0.3
x> 18
Finally, the number of folders Jan would need to buy is more than 18.
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help please!!! asap!
Answers
Answer:
The registration fee is $28
Step-by-step explanation:
5,600/100=56 which is 1% of 5,600.
56/2=28 which is 0.5% of 5,600.
;)
Answer: $28
Step-by-step explanation:
you calculate what 0.5 percent is of 5,600 :)
The tens digit of a two-digit number is twice the ones digit. Its reversed number is 36 less than the original number.
Answers
From the calculation, the original number is obtained as 84.
What is the original number?We know that we are told in the question that in the question, we are required to obtain the number and that is what we are going to do below.
Let the tens digit be T and let the units digit be U
We can then write
10U+T = 10T+U-36
Since the reversed number is 36 less than the original number.
Then;
9U = 9T -36
Dividing both sides of the equation by 9
U = T -4
U=2U-4
U=4
T = 8
It then follows that the original number is 84.
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how many distinct 5-letter strings can be created using the letters a, b, c, d, e if repetition is allowed, but the letters a appears at most twice?
Answers
2944 distinct 5-letter strings can be created using the letters a, b, c, d, and e if repetition is allowed but the letter a appears at most twice
Given that
form 5-letter distinct strings can be created using the letters a,b,c,d, and e, and repetitions are allowed but the letter a appears at most twice
let's consider that letter a is not there in the string
each letter is repetitive then it is [tex]4^{5}[/tex]
now letter a is considered once
5c1 ×[tex]4^{4}[/tex]
now letter a is repetitive twice
5c2 × [tex]4^{3}[/tex]
[tex]4^{5}[/tex] + 5c1 × [tex]4^{4}[/tex] + 5c2 × [tex]4^{3}[/tex]
1024+ 1280 + 640 = 2944
2944 distinct 5-letter strings can be created using the letters a, b, c, d, and e if repetition is allowed but the letter a appears at most twice
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The graph below shows distance over time.
A student is walking to class. The student increases their speed for 20 seconds for 3 meters. The student then walks a constant speed for 5 seconds and then increases their speed the last 3 meters to class.
Which of these situations could be represented by this graph?
Answers
A situation which could be represented by this graph is: A student walks 1.5 km to a friend’s house in 20 minutes. The two students then walk another 1.5 km to school in 40 minutes.
What is a graph?In Mathematics, a graph can be defined as a type of chart that is typically used to graphically represent data points or ordered pairs on both the horizontal and vertical lines of a cartesian coordinate, which are the x-coordinate and y-coordinate respectively such as time (min) and distance (km).
In this scenario, the time (in minutes) was plotted on the x-axis of the graph while the distance covered (in kilometers) was plotted on the y-axis of the graph.
By critically observing the graph (see attachment), we can reasonably and logically deduce that the first student walked a distance of 1.5 kilometer to his or her friend’s house in 20 minutes, then, they both walked at a constant speed for 5 seconds before increasing their speed, covering another distance of 1.5 kilometer to their school within 40 minutes (60 - 20 minutes).
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Complete Question:
The graph below shows distance over time. Which of these situations could be represented by this graph?
answer choices
A student walks 1.5 km to a friend’s house in 40 minutes. The two students then walk another 1.5 km to school in 20 minutes.
A student walks 1.5 km to a friend’s house in 20 minutes. The two students then walk another 1.5 km to school in 40 minutes.
A student walks 1.5 km to a friend’s house in 30 minutes. The two students then walk another 1.5 km to school in 30 minutes.
A student walks 1.5 km to a friend’s house in 20 minutes. The two students then walk another 1.5 km to school in 60 minutes.
3.6 x 10^7 + 2.1 x 10.7=
a) 14
b) 5.7
c) 3.6
d) none of these
Answers
The value of the exponent 3.6 x 10^7 + 2.1 x 10.^7 is D. None of the above.
What is an exponent?The exponent is the number of times that a number is multiplied by itself. It should be noted that the power is an expression which shows the multiplication for the same number. For example, in 6⁴ , 4 is the exponent and 6⁴ is called 6 raise to the power of 4.
In this case, the value of 3.6 x 10^7 + 2.1 x 10^7 will be:
= 3.6 x 10^7 + 2.1 x 10.^7
= 5.7 × 10^7
Therefore, the correct option is D.
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Kenya went to the convenience store to buy some snacks. She spent a total of $12. 00 on soda and candy. The soda cost $3. 00 and each candy bar cost $1. 50. If kenya bought one soda, how many candy bars did kenya buy?.
Answers
The number of candy bar that she bought is 6
The total amount that she spend for soda and candy= $12
The cost of one soda = $3
The cost of one candy bar = $1.50
Number of soda that she bought = 1
Consider the number of candy bar that she bought as x
Then the equation will be
3×1 + 1.50 × x = 12
Multiply the terms
3 + 1.50x = 12
Move 3 to right hand side of the equation
1.50x = 12 - 3
1.50x = 9
Move 1.50 to the right hand side of the equation
x = 9 / 1.50
x = 6
Hence, the number of candy bar that she bought is 6
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< GRADES / 2022 RATIOS AND PROPORTIONS UNIT TEST Q21
21
What percent represents the shaded part of the hundredths grid shown?
Answers
Answer: A) 0.05%
Step-by-step explanation: Converting the shaded area of the hundredths grid to a fraction would be 5/100 (or 1/20 simplified). Then convert 5/100 to a percentage by calculating 5 ÷ 100, which is 0.005%, therefor the answer is A.