The students in Mr. Raith's art class created various quantities of bluish green paint using pints of yellow and blue paint. The table shows the different mixtures of paint, in pints, that the students made. 1. How many different shades of paint did the students make? How do you know?
Answers
To find how many many different shades of paint did the students make
We will find the ratio between the yellow paint and the blue paint
So,
Row number 1 , yellow : blue = 1 : 2
Row number 2 , yellow : blue = 2 : 3
Row number 3 , yellow : blue = 2 : 4 = 1 : 2
Row number 4 , yellow : blue = 4 : 8 = 1 : 2
Row number 5 , yellow : blue = 6 : 9 = 2 : 3
Row number 6 , yellow : blue = 8 : 12 = 2 : 3
So, the number of different ratios are 2 ratios, which are [ 1 : 2 ] and [ 2 : 3 ]
so, There are 2 different shades of paint the students made
We know using the ratio between yellow and blue
Related Questions
I'm looking answer for my question please answer for me number one work out find value of k
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if a polynomial P(x) is divided by a binomial (x-c) then the remainder is equal to P(c).
where c=-3
[tex]\begin{gathered} P(-3)=-19+9k=8 \\ \text{ }9k=8+19\text{ } \\ 9k=27 \\ k=\frac{27}{9} \\ k=3 \end{gathered}[/tex]the value of k=3
Solve the following problems related to sequences. Show all of your work and clearly indicate your final answer. a) Find the 7th term in the sequence: -19,-9, 1, ... b) Find the 8th term in the sequence: -3, -9,-27, ... c) Find the common difference and use it to fill in the missing terms in this arithmetic sequence. ..., -32, , -12,
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The sequence of numbers is an arithmetic sequence. The sequence,
[tex]-19,-9,1[/tex]has a common difference of 10.
This is derived by deducting each term from the next one. That is deduct the first term from the second term, deduct the second term from the third, and so on. So you would have,
[tex]\begin{gathered} d=-9-\lbrack-19\rbrack \\ d=-9+19 \\ d=10 \end{gathered}[/tex]To find the nth term, we shall apply the formula;
[tex]\begin{gathered} n_{th}=a+(n-1)d \\ a=-19,d=10 \\ To\text{ find the 7th term (n=7)} \\ 7_{th}=-19+(7-1)10 \\ 7_{th}=-19+(6)10 \\ 7_{th}=-19+60 \\ 7_{th}=41 \end{gathered}[/tex]The 7th term in the sequence is 41
For the sequence,
-3, -9, -27...
What we have is a geometric sequence and the common ratio is derived by dividing each term by the next one. So you would have
[tex]\begin{gathered} r=\frac{-9}{-3} \\ r=3 \\ \text{Also,} \\ r=\frac{-27}{-9} \\ r=3 \end{gathered}[/tex]To find the nth term of a geometric sequence;
[tex]\begin{gathered} N_{th}=ar^{n-1} \\ a=-3,r=3 \\ To\text{ find the 8th term (N=8)} \\ 8_{th}=-3\times(3^{8-1}) \\ 8_{th}=-3\times(3^7) \\ 8_{th}=-3\times2187 \\ 8_{th}=-6561 \end{gathered}[/tex]Can someone pls help me thxs .Y - 3 = -3*Y - 43
Answers
We have the following:
[tex]Y-3=-3\cdot Y-43[/tex]Solving for Y:
[tex]\begin{gathered} Y+3\cdot Y=-43\text{ + 3} \\ 4\cdot Y\text{ = -40} \\ Y\text{ = }\frac{-40}{4} \\ Y\text{ = }-\text{10} \end{gathered}[/tex]Therefore the question is -10
A person plans to invest a total of $6500 in one bank account at 2.8% annual interest and another bank account at 18% annual interest. how much should he invest in each account so that the total interest in one year will be $410
Answers
We will do a system of equations
x amount invested at 2.8%
y amount invested at 18%
the first equation will be the total invest
x+y=6500
then the second equation is about the simple interest
0.028x+0.18y=410
then we isolate the x of the first equation
x=6500-y
we substitute this equation on the second equation
0.028(6500-y)+0.18y=410
then we simplify the expression
[tex]182-0.028y+0.18y=410[/tex]then we sum like terms
[tex]0.152y=410-182[/tex][tex]0.152y=228[/tex]then we isolate the y
[tex]y=\frac{228}{0.152}[/tex][tex]y=1500[/tex]then we substitute the value of y in the equations with x isolate
[tex]x=6500-1500[/tex][tex]x=5000[/tex]5000 amount invested at 2.8%
1500 amount invested at 18%
Find the sum of the first 14 terms of the geometric series 1+4+16+64+….
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Solution
Given the question in the image, the following are the solution steps to answer the question.
STEP 1: Write the given geometric series
[tex]1+4+16+64+...[/tex]STEP 2: Write the formula to calculate the sum of nth terms of a geometric series
[tex]S_n=\frac{a(r^n-1)}{r-1}[/tex]where r is the common ration
a is the first term
Sn is the sum of the nth term
n is the number of terms
STEP 3: Write the required data values
[tex]n=14,a=1,r=\frac{T_2}{T_1}=\frac{4}{1}=4[/tex]STEP 4: substitute the values to find the sum of the first 14 terms
[tex]\begin{gathered} S_{14}=\frac{1(4^{14}-1)}{4-1} \\ =\frac{268435456-1}{3}=\frac{268435455}{3}=89478485 \end{gathered}[/tex]Hence, the sum of the first 14 terms of the given geometric series is 89478485
y= 2x^2 +6x+11In vertex form
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Given:
[tex]y=2x^2+6x+11[/tex][tex]y=2(x^2+3x+\frac{11}{2})[/tex][tex]y=2(x^2+3x+\frac{9}{4}-\frac{9}{4}+\frac{11}{2})[/tex][tex]y=2(x^2+3x+(\frac{3}{2})^2)-\frac{9}{2}+\frac{22}{2}[/tex][tex]y=2(x+\frac{3}{2}^{})^2+\frac{13}{2}[/tex]Above equation is the vertex form.
Find the area of the region enclosed by f(x) and the x-axis for the given function over the specified interval x2 + 2x +2 x
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In order to determine the area in the interval [-3, -3] of the function enclosed by:
[tex]f(x)=\begin{cases}x^2+2x+2 \\ 3x-4\end{cases}[/tex]When the first term is for x<2 and the second when x>=2.
We proceed as follows:
[tex]\int ^3_{-3}(x^2+2x+2)-(3x-4)\rbrack dx[/tex][tex]\Rightarrow\int ^3_{-3}(x^2-x+6)dx=\frac{x^3}{3}-\frac{x^2}{2}+6x|^3_{-3}=54[/tex]If a fair die is rolled 7 times, what is the probability, rounded to the nearestthousandth, of getting at least 4 threes?
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If a fair die is rolled 7 times, what is the probability, rounded to the nearest
thousandth, of getting at least 4 threes?
we have that
probability that get three is
P=1/6
and the probability that get other number is P=5/6
therefore'
the probability that get at least 4 threes is
P=C(7,4)*(1/6)^4*(5/6)^3
P=C(7,4)*(1/1,296)*(125/216)
Find out C(7,4)
C(7,4)=7!/(7-4)!*3!)=
Total Price (dollars)Tomatoes Purchased (pounds)o The number of pounds depends on the total price.The number of tomatoes depends on the number of pounds.The total price depends on the number of pounds.The total price depends on the number of tomatoes.Submit
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Generally, we use the y-axis to express the values of the pedendent variable, and the x-axis to express the values of the independent variable.
So, since the y-axis shows the total price, and the x-axis shows the tomatoes purshased in number of pounds, we can say that:
THe total price depends on the number of pounds.
Therefore, o
if $4.44 3 PEOple get a piece of the $4.44 how much does the people all get
Answers
since yolanda, xavier and zachary have the same amount of money, if x represents that amount, we have the following expression:
[tex]x+x+x=4.44[/tex]solving for x, we get:
[tex]\begin{gathered} x+x+x=4.44 \\ \Rightarrow3x=4.44 \\ \Rightarrow x=\frac{4.44}{3}=1.48 \\ x=1.48 \end{gathered}[/tex]thus, they each have $1.48
a floral shop has ALL single roses marked 40 percent OFF. What is the amount of the discount if a single rose is $2.35?
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The amount of the discount on a single rose is $0.94
OR
94 cents
purpose of bar graphs and data example
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To compare the different variables and to know which variable has more percent compare to the others.
In this bar graph, we compare different frutis and which fruit prefer the people
If the side opposite to the 72° angle is 42 units, what is the length of the hypotenuse
Answers
Answer:
44.21 units
Explanation:
For a right angle with an angle of 72 degrees:
[tex]\frac{\text{Opposite}}{\text{Hypotenuse}}=\frac{19}{20}[/tex]Given that the side opposite to the 72° angle = 42 units
[tex]\begin{gathered} \implies\frac{19}{20}=\frac{42}{\text{Hypotenuse}} \\ \text{Hypotenuse}\times19=20\times42 \\ \text{Hypotenuse}=\frac{20\times42}{19} \\ \text{Hypotenuse}=44.21 \end{gathered}[/tex]The length of the hypotenuse is 44.21 units.
New company games 95 customers each year each year they also lose 16 customers write a linear function that represents the number of customers the company has acquired over time
Answers
A company gains 95 customers each year. They lose 16 each year. write a linear function that represents the number of customers the company has acquired over time
Let
x -----> the number of years
y ----> the number of customers the company has acquired over time
we have that
y=(95-16)x
therefore
the linear equation is
y=79xsurface area of a sphere whos circle has a circumference of 14(pi symbol) cm
Answers
Given:
The circumference of a circle is
[tex]14\pi cm.[/tex]Required:
We need to find the surface area of a sphere whose circle has a circumference of
[tex]14\pi cm.[/tex]Explanation:
Consider the circumference of the circle formula.
[tex]C=2\pi r[/tex][tex]Substitute\text{ C=}14\pi cm\text{ in the formula.}[/tex][tex]14\pi=2\pi r[/tex][tex]Divide\text{ both sides by }2\pi.[/tex][tex]\frac{14\pi}{2\pi}=\frac{2\pi r}{2\pi}[/tex][tex]7=r[/tex]We get r =7cm.
Consider the surface area of the sphere.
[tex]SA=4\pi r^2[/tex]Substitute r = in the formula,
[tex]SA=4\pi(7)^2[/tex][tex]SA=4\pi(49)[/tex][tex]SA=196\pi cm^2[/tex]Final answer:
[tex]The\text{ s}urface\text{ area of the sphere}=196\pi cm^2[/tex][tex]The\text{ s}urface\text{ area of the sphere}=196\times3.14cm^2[/tex][tex]The\text{ s}urface\text{ area of the sphere}=615.44cm^2[/tex]QUESTION IS IN IMAGE! DONT NEED TO SHOE WORK JUST NEED THE ANSWER!
Answers
Solution:
From the given circle
[tex]\begin{gathered} reflex\text{ m}\angle FEH=128\degree+126\degree=254\degree \\ reflex\text{ m}\angle FEH=254\degree \end{gathered}[/tex]Then,
[tex]\begin{gathered} m\angle FEH=360-254\degree=106\degree \\ m\angle FEH=106\degree \end{gathered}[/tex]To find ∠FGH,
[tex]m\angle FGH=\frac{1}{2}m\angle FEH[/tex]Substitute for ∠FEH
[tex]\begin{gathered} m\angle FGH=\frac{1}{2}\times106\degree=53\degree \\ m\angle FGH=53\degree \end{gathered}[/tex]Hence, ∠FGH is 53°
-3(a + 5) = 30 distribution
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To solve this using the distributive property you multiply the term oit the parenthesis by the terms in the parenthesis:
[tex]\begin{gathered} -3(a+5)=30 \\ \\ -3\cdot a-3\cdot5=30 \\ \\ \\ -3a-15=30 \end{gathered}[/tex]Then, to solve a you:
add 15 in both sides of the equation:
[tex]\begin{gathered} -3a-15+15=30+15 \\ \\ -3a=45 \end{gathered}[/tex]Divide both sides of the equation into -3
[tex]\begin{gathered} \frac{-3}{-3}a=\frac{45}{-3} \\ \\ a=-15 \end{gathered}[/tex]Then, a is -15
Please see the picture below I NEED BOTH A AND B. (A&B) not just A
Answers
To solve this question, use the law of cosines shown below:
[tex]c^2=a^2+b^2-2*a*b*cosC[/tex]In this question,
a = 6
b = 8
C = 10°
First, let's find c:
[tex]\begin{gathered} c^2=6^2+8^2-2*6*8*cos10 \\ c^2=36+64-94.54 \\ c^2=5.46 \\ \sqrt{c^2}=\sqrt{5.456} \\ c=2.34 \end{gathered}[/tex]Second, let's find A.
Now, a, b, and c are known, and Cos A is not known:
[tex]\begin{gathered} a^2=b^2+c^2-2bc*cosA \\ 6^2=8^2+2.34^2-2*8*2.34*cosA \\ 36=64+5.48-37.44*cosA \\ 36=69.48-37.44*cosA \\ \text{ Subtracting 69.46 from both sides:} \\ 36-69.48=69.46-37.44*cosA-69.46 \\ -33.48=-37.44*cosA \\ \text{ Dividing both sides by -37.44:} \\ \frac{-33.48}{-37.44}=\frac{-37.44}{-37.44}cosA \\ 0.8942=cosA \\ Then, \\ A=cos^{-1}(0.8942) \\ A=26.6 \end{gathered}[/tex]Answer:
c = 2.34 units
A = 26.6°
which ordered pair is in the solution set of x>8
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First of all, we need to make a draw:
The solution of x>8 will be all numbers biggers that 8... that is the answer.
Show the equations in slope intercept form and determine how many solutions does the system of equations have? Explain.2x - 9y = -5 4x - y = 2
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first solve each equation for y
[tex]\begin{gathered} 2x-9y=-5 \\ -9y=-5-2x \\ y=\frac{5}{9}+\frac{2}{9}x \end{gathered}[/tex][tex]\begin{gathered} 4x-y=2 \\ -y=2-4x \\ y=-2+4x \end{gathered}[/tex]the equations are
[tex]\begin{gathered} y=\frac{5}{9}+\frac{2}{9}x \\ \\ y=-2+4x \end{gathered}[/tex]we can substract the equations to remove y
[tex]\begin{gathered} y=\frac{5}{9}+\frac{2}{9}x \\ \\ y=-2+4x \\ \\ ---------------- \\ 0=\frac{23}{9}-\frac{34}{9}x \end{gathered}[/tex]now solve x
[tex]\begin{gathered} \frac{23}{9}-\frac{34}{9}x=0 \\ \\ 23-34x=0 \\ 34x=23 \\ \\ x=\frac{23}{34} \end{gathered}[/tex]the value of x is 23/34, now replace on any equation to find Y, I will replace on the second
[tex]\begin{gathered} y=-2+4(\frac{23}{34}) \\ \\ y=-2+\frac{46}{17} \\ \\ y=\frac{12}{17} \end{gathered}[/tex]the value of y is 12/17
the solution point is ( 23/34 , 12/17)
A rectangle has length=4x-3 and the width=-5x+7What is the perimeter?
Answers
You have a rectangle with length l = 4x - 3 and width w = -5x + 7
In order to know the perimeter of the rectangle you use the following formula:
P = 2w + 2l
where w and l are the width an length of the rectangle respectively.
By replacing the algebraic expressions for w and l into the previous equation for the perimeter you obtain:
P = 2(4x -3) + 2(-5x + 7) apply distribution property
P = 8x - 6 - 10x + 14
P = -2x + 8
P = 8 - 2x
Hence, the perimeter of the rectangle is 8 - 2x
4. A plumber charges $50 to make a house call. He also charges $25.00 per hour for labor. A. Write an equation that you could use to the amount a plumber charges for a house call based on the number of hours of labor.How much would it cost for a house call that requires 2.5 hours of labor? C. If the bill from the plumber is $162.50, how many hours did the plumber work at your house?
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We are given a problem that can be solved using a line equation. We are told that a plumber charges initialy $50 and from then he charges $25 per hour. Therefore, the amount charged must be equal to the initial amount
Solve the following system of equations using any method you want. (1 pt)y = 2x + 33x + 2y = 34O No solution(3,9)(6,8)(4, 11)
Answers
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data
eq1. y = 2x + 3
eq2. 3x + 2y = 34
Step 02:
eq1. in eq2.
3x + 2 (2x + 3) = 34
3x + 4x + 6 = 34
7x = 34 - 6
x = 28 / 7
x = 4
eq1.
y = 2 (4) + 3
y = 8 + 3
y = 11
The answer is:
(4 , 11 )
12. Lyla has $150 to purchase shrubs for her front yard. Small shrubs cost $20
per shrub and large shrubs cost $35 per shrub.
Part A: Write an equation that can be used to determine the number of small
shrubs, x, and the number of large shrubs, y that Lyla can purchase.
Answers
20x+35y=150
A) Since Lyla has $150 to buy shrubs, and the small ones cost $20, and the large ones $35, we can write out the following equation
[tex]\begin{gathered} \\ 20x+35y=150 \end{gathered}[/tex]Note that, we need to find the number of shrubs altogether in order to set another equation and solve this linear system.
In addition to this, this equation relates the cost of each shrub and the total expenditure.
Thus, the equation for Part A is 20x+35y=150
What is the value of s in the equation 4(2s − 1) = 7s + 12? 12163234
Answers
Explanation:
The equation is given below as
[tex]4(2s-1)=7s+12[/tex]Step1:
Expand the parenthesis
[tex]\begin{gathered} 4(2s-1)=7s+12 \\ 8s-4=7s+12 \end{gathered}[/tex]Step 2:
Collect the similar terms, we will have
[tex]\begin{gathered} 8s-4=7s+12 \\ using\text{ the cross over technique} \\ 7s\text{ moves to the left hand side and takes the negative sigh\lparen-7s\rparen} \\ -4\text{ moves to the right hand side and becomes +4} \\ 8s-7x=12+4 \\ s=16 \end{gathered}[/tex]Hence,
The value of s will be
[tex]\Rightarrow s=16[/tex]Identify each congruence transformation that maps triangle ABC to triangle DEF
Answers
The first step is to write the coordinate of corresponding vertices in triangles ABC and DEF. Let us consider vertex C in triangle ABC and the corresponding vertex F in triangle DEF. The coordinates are
C = (3, 2)
F = (- 1, - 2)
We want to transform (3, 2) to (- 1, - 2)
Recall, if we reflect a vertex, (x, y) over the x axis, the x coordinate remains the same while the sign of the y coordinate is reversed. Thus, by reflecting (3, 2) over the x axis, the new coordinate is (3, - 2)
Also, if we reflect a vertex, (x, y) over the y axis, the y coordinate remains the same while the sign of the x coordinate is reversed. Thus, by reflecting (3, - 2) over the x axis, the new coordinate is (- 3, - 2)
Recall, if a vertex, (x, y) is translated d units to the right, the new vertex would be (x + d, y). If we translate (- 3, - 2) 2 units to the right, the new vertex would be (-3 + 2, - 2) = (- 1, - 2). This corresponds to vertex F
Thus, the correct option is
A reflection in the x axis, followed by a reflection in the y axis and then a translation, 2 units to the right
Also, if we rotate a point, (x,y) 180 degrees about the origin, the new point would be (- x, - y). By rotating (3, 2) by 180 degrees about the origin, the new vertex would be (- 3, - 2). If we translate (- 3, - 2) 2 units to the right, the new point is (-3 + 2, - 2) = (- 1, - 2). This corresponds to vertex F
Thus, another correct option is
A rotation 180 degrees about the origin followed by a translation 2 units to the right
how do I know which triangle is Similar to ABC?
Answers
I just need an explanation 1.alternative exterior 2.correspnding 3.alternative exterior 4.aternative interior 5.consecutive exterior 6.consecutive interior 7. corresponding 8.corresponding 9.correspondingI already answered it but I need help with explanation for each one the one which is correct in my Understanding will be brainliest
Answers
The transversal is the line that crosses the parallel lines.
1) They are alternate exterior angles because they are on the alternating sides of the transversal and outside the parallel linesthe transversal
I need help with his geometry question can someone please help
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Notice that
[tex]\angle BOM\cong\angle DON[/tex]Because they are vertical angles, and
[tex]\angle AOM\cong\angle DON[/tex]is a given congruence.
Therefore, we can conclude that
[tex]\angle AOM\cong\angle BOM[/tex]Because they are congruent to the same angle: Angle DON.
Therefore, the correct answer is Option D.
Find the equation of a line that is parallel to Y = 2x +5 and contains the points (2,-4)
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GIVEN:
We are given the equation of a line as follows;
[tex]y=2x+5[/tex]Required;
To find the equation of a line that is parallel to this line and that contains the coordinates;
[tex](2,-4)[/tex]Step-by-step solution;
First thing to note is that, the equation of the line is given in the slope-intercept form. The slope-intercept form of a linear equation is generally written as;
[tex]\begin{gathered} y=mx+b \\ \\ m=slope,\text{ }b=y-intercept \end{gathered}[/tex]For a line that is parallel to another, the slopes are equal in value. This simply means the slope of the other line (the line parallel to the one given) is 2.
Note that the slope of the line given is;
[tex]\begin{gathered} y=mx+b \\ \\ y=2x+5 \\ \\ Therefore; \\ \\ m=2 \end{gathered}[/tex]For a line that contains the point (2, -4) and the slope is 2, we can now write the following;
[tex]\begin{gathered} y=mx+b \\ \\ Where,\text{ }x=2,y=-4,m=2 \\ \\ Then; \\ \\ -4=2(2)+b \\ \\ -4=4+b \end{gathered}[/tex]Now we subtract 4 from both sides of the equation;
[tex]\begin{gathered} -4-4=4-4+b \\ \\ -8=b \end{gathered}[/tex]Now we have the slope and the y-intercept as;
[tex]\begin{gathered} m=2 \\ \\ b=-8 \end{gathered}[/tex]We can now write the equation of the line as follows;
[tex]\begin{gathered} y=mx+b \\ \\ Hence; \\ \\ y=2x+(-8) \\ \\ y=2x-8 \end{gathered}[/tex]Therefore.
ANSWER:
[tex][/tex]