ou are making identical door prizes for a charity event. You want to use all of the following items.
54 packages of peanuts
81 fruit bars
18 CDs
You can make at most
door prizes. Each door prize would have
packages of peanuts
fruit bars, and CDs
Answers
Putting the important informations, we want to use all items and divide them into equal groups in a way that we get the most prizes.
We we want a factor that is common to the three quantities, 54, 81 and 18, and is the greatest of them.
This is a question of Greatest Common Factor or Greatest Common Divisor (different names, same thing).
To calculate it, we have to find all the common factors of theses numbers.
One way to do that is to look for numbers that can divide all of them.
The numbers are 54, 81 and 18. As we can see the three numbers are divisable by 3:
[tex]\begin{gathered} \frac{54}{3}=18 \\ \frac{81}{3}=27 \\ \frac{18}{3}=6 \end{gathered}[/tex]So, we now that 3 is a common factor. Let's note it to use later on.
Now have got 18, 27 and 6. We can see that, again, all of them are divisable by 3:
[tex]\begin{gathered} \frac{18}{3}=6 \\ \frac{27}{3}=9 \\ \frac{6}{3}=2 \end{gathered}[/tex]And let's note the "3" again to use later on.
The numbers now are 6, 9 and 2. 2 is only divisable by 2, but 9 isn't, so we don't have any more common factors.
In the end, we have the factor 3 and 3, which makes 3*3 = 9. Thus, 9 is the Greates Common Factor of 54, 81 and 18 and it divides them into 6, 9 and 2.
These are the answers we are looking for, because now we know that the most groups we can divide the items into is 9 and each group will have 6, 9 and 2 of those items.
So the phrase of the answer is:
"You can make at most 9 door prizes. Each door prize would have 6 packages of peanuts, 9 fruit bars, and 2 CDs."
Related Questions
according to a census, there were 66 people per square mile (population density) in a certain country in 1980. By 2000, the # of people per square mile had grown to 76. This information was used to develop a linear equation in slope intercept form, given below, where x is the time in years and y is the population density. Think of 1980 as year zero. what is the population density expected to be in 2018? y = 1/2x + 66
Answers
Determine the value of x for taking 1980 as 0.
[tex]\begin{gathered} x=2018-1980 \\ =38 \end{gathered}[/tex]The equation is y = 1/2x + 66.
Substitute the value of x in the equation to determine the population density in 2018.
[tex]\begin{gathered} y=\frac{1}{2}\cdot38+66 \\ =19+66 \\ =85 \end{gathered}[/tex]So population density in year 2018 is 85.
Answer: 85
A freight train is carrying goods across the country. The distance it has traveled directly with the number of gallons of fuel it has used. See the graph below
Answers
1) To find how many miles per gallon that freight train makes is to find a rate. We can find it in two ways, either by setting a proportion or by finding the slope.
2) Note that this direct variation depicted by the graph is proportional. Therefore, let's find the slope by picking two points:
[tex]\begin{gathered} (200,50),(400,100) \\ \\ m=\frac{y_2-y_1}{x_2-x_1}=\frac{100-50}{400-200}=\frac{50}{200}=\frac{1}{4} \end{gathered}[/tex]3) Thus, the answers are:
Find the X-Intercept and the y-intercept of 4x- 5y = 15X-Intercept:???Y-intercept: ???help
Answers
The y-intercept is (0,-3) while the x-intercept is (18.75,0)
Here, we want to find the x and y-intercepts of the given line
Firstly, we have to rewrite the equation of the line in the standard form
We have this as;
[tex]\text{y = mx + b}[/tex]m is the slope and b is the y-intercept
Rewriting the given equation, we have this as;
[tex]\begin{gathered} 5y\text{ = 4x-15} \\ y\text{ =}\frac{4}{5}x-\frac{15}{5} \\ \\ y\text{ = }\frac{4}{5}x\text{ - 3} \end{gathered}[/tex]We have the y-intercept as -3
In the coordinate form, this is (0,-3)
To get the x-intercept, we set the y value to zero
We have this as;
[tex]\begin{gathered} 0\text{ = }\frac{4}{5}x-15 \\ 15\text{ = }\frac{4x}{5} \\ \\ 4x\text{ = (15}\times5) \\ 4x\text{ = 75} \\ x\text{ = }\frac{75}{4} \\ x\text{ = 18.75} \end{gathered}[/tex]The x-intercept is 18.75 which in the coordinate form is (18.75,0)
the first drop down answers are 18,10,7,14the second drop down box options are 16.5,30.5,44.5the third options are 2.5, 1.5, 1,3 the fourth options are 14n, 18n, 7n, 10nthe fifth options are each movie tickets cost the same amount, there is a service fee for buying tickets online, the cost increase as tge number of tickets increase, the leaste amount of tickets you cab buy is 1
Answers
Answer:
Recursive formula:
a_n = a_n-1 + 14,
a_1 = 16.5
Explicit formula: a_n = 14(n - 1) + 16.5
Each movie costs the same amount.
Explanation:
Looking at the numbers we see that each next term a_n is 14 added to the previous term, a_n-1 and the first term a_1 is 16.5; therefore, we can say
[tex]\begin{gathered} a_n=a_{n-1}+14, \\ a_1=16.5 \end{gathered}[/tex]
3.What are the coordinates of the center and the length of the radius of the circle whose equation is(x + 1)^2 + (-5)^2 = 16?
Answers
The general equation of circle with centre (h.k) and radius r is,
[tex](x-h)^2+(y-k)^2=r^2[/tex]Simplify the equation to obtain the centre and radius of circle.
[tex]\begin{gathered} (x+1)^2+(y-5)^2=16 \\ (x-(-1))^2+(y-5)^2=(4)^2 \end{gathered}[/tex]So center of circle is (-1,5) and radius 4.
How to solve this problem step by step in depth. I have no idea how to solve this
Answers
Answer
[tex]f^{-1}(x)=\frac{-1}{5}x-\frac{4}{5}[/tex]Explanation
The given function is
[tex]f(x)=-5x-4[/tex]Let y = f(x), this implies
[tex]y=-5x-4[/tex]Now, make x the subject of the formula
[tex]\begin{gathered} y=-5x-4 \\ 5x=-y-4 \\ \text{To get x, we divide both sides by 5} \\ \frac{5x}{5}=\frac{-y-4}{5} \\ \\ x=\frac{-y-4}{5} \end{gathered}[/tex]Since f(x) = y, then x = f⁻¹(y)
[tex]\begin{gathered} f^{-}^{1}\mleft(y\mright)=\frac{-y-4}{5} \\ \therefore f^{-1}(x)=\frac{-x-4}{5} \end{gathered}[/tex]The above inverse function can be rewritten as follows
[tex]\begin{gathered} f^{-1}(x)=\frac{-x}{5}-\frac{4}{5} \\ f^{-1}(x)=\frac{-1}{5}x-\frac{4}{5} \end{gathered}[/tex]Hello, I need help writing a recursive formula for these I’m struggling bad
Answers
1) Notice that:
[tex]\begin{gathered} 3=\frac{30}{10}, \\ \frac{3}{10}=\frac{3}{10}, \\ \frac{3}{100}=\frac{\frac{3}{10}}{10}. \end{gathered}[/tex]Therefore the recursive formula for the first sequence is:
[tex]\begin{gathered} a_1=30, \\ a_n=\frac{a_{n-1}}{10}\text{ for }n\geq2. \end{gathered}[/tex]2) Notice that:
[tex]\begin{gathered} 11=14-3, \\ 8=11-3, \\ 5=11-3. \end{gathered}[/tex]Therefore the recursive formula for the second sequence is:
[tex]\begin{gathered} a_1=14, \\ a_n=a_{n-1}-3\text{ for }n\geq2. \end{gathered}[/tex]Answer:
Left sequence:
[tex]\begin{gathered} a_1=30, \\ a_n=\frac{a_{n-1}}{10}\text{ for }n\geq2. \end{gathered}[/tex]Right sequence:
[tex]\begin{gathered} a_1=14, \\ a_n=a_{n-1}-3\text{ for }n\geq2. \end{gathered}[/tex]
Sketch vector v. Be sure to number your axes. Then find the magnitude of vector v. Show all work.
Answers
Step 1
Sketch the vector V.
[tex]v=-2i\text{ +5j}[/tex]Step 2
Find the magnitude of the vector. The magnitude of a vector is given as;
[tex]\begin{gathered} |v|=\sqrt{(i)^2+(j)^2} \\ i=-2 \\ j=5 \\ \left|a+bi\right|\:=\sqrt{\left(a+bi\right)\left(a-bi\right)}=\sqrt{a^2+b^2} \end{gathered}[/tex][tex]\begin{gathered} |v|=\sqrt{(-2)^2+(5)^2} \\ |v|=\sqrt{4+25} \\ |v|=\sqrt{29} \end{gathered}[/tex]Therefore, the magnitude is given as;
[tex]|v|=\sqrt{29}[/tex]Caleb is renting a kayak for 14.50 per half hour. how much would it cost Caleb to rent the kayak for 5 minutes
Answers
Answer:
It would cost Caleb approximately $2.4 to rent kayak for 5 minutes
Explanation:
Given that Caleb is renting a kayak for $14.40 per half hour.
This means he rents it for 30 minutes, as 30 minutes is half an hour.
In an equation form, we can write as:
$14.40 = 30 minutes
So that:
1 minute = $(14.50/30)
= $0.48
This mean he rents at $0.48 per minute
For 5 minutes, it would cost him:
$0.48 * 5 = $2.4 approximately.
5. Determine the value of each variable for parallelogram INDY that has diagonals that intersect at P.IP = 3x, DP = 6x-2, NP = 3y, and YP = 7x - 2.
Answers
Given the INDY
The diagonals has intersected at the point P
IP = 3x, DP = 6x - 2
NP = 3y , YP = 7x - 2
So, IP = DP
[tex]6x-2=3x[/tex]Solve for x :
[tex]\begin{gathered} 6x-2=3x \\ 6x-3x=2 \\ 3x=2 \\ \\ x=\frac{2}{3} \end{gathered}[/tex]And : NP = YP
[tex]3y=7x-2[/tex]substitute with the value of x :
[tex]\begin{gathered} 3y=7\cdot\frac{2}{3}-2=\frac{23}{3}-2=\frac{17}{3} \\ \\ y=\frac{17}{9} \end{gathered}[/tex]So, the answer is :
[tex]\begin{gathered} x=\frac{2}{3} \\ \\ y=\frac{17}{9} \end{gathered}[/tex]1/ (gg^2 e^5)^2 Write your answer with only positive exponents
Answers
ANSWER
[tex]\frac{1}{g^6e^{10}}[/tex]EXPLANATION
In the denominator, we have the product of g and g². The product of two powers with the same base is the base raised to the sum of the exponents,
[tex]\frac{1}{(gg^2e^5)^2}=\frac{1}{(g^{2+1}e^5)^2}=\frac{1}{(g^3e^5)^2}[/tex]Now, we also have the power of a product. The exponents can be distributed into the multiplication,
[tex]\frac{1}{(g^3e^5)^2}=\frac{1}{(g^3)^2(e^5)^2}[/tex]And finally, for both g and e, we have the power of a power. The result is the base raised to the product of the exponents,
[tex]\frac{1}{(g^3)^2(e^5)^2}=\frac{1}{g^{3\cdot2}e^{5\cdot2}^{}}=\frac{1}{g^6e^{10}}[/tex]Hence, the simplified expression is,
[tex]\frac{1}{g^6e^{10}}[/tex]differentiatey = 3x√x⁴-5
Answers
Given:
[tex]y=3x\sqrt{x^4-5}[/tex]Required:
We need to differentiate the given expression.
Explanation:
Consider the given expression.
[tex]y=3x\sqrt{x^4-5}[/tex][tex]y=3x(x^4-5)^{\frac{1}{2}}[/tex]Differentiate the given expression with respect to x.
[tex]Use\text{ }(uv)^{\prime}=uv^{\prime}+vu^{\prime}.\text{ Here u=3x and v=}(x^4-5)^{\frac{1}{2}}.[/tex][tex]y^{\prime}=3x(\frac{1}{2})(x^4-5)^{\frac{1}{2}-1}(4x^3)+(x^4-5)^{\frac{1}{2}}(3)[/tex][tex]y^{\prime}=\frac{3x(4x^3)}{2\left(x^4-5\right)^{\frac{1}{2}}}+3(x^4-5)^{\frac{1}{2}}[/tex][tex]y^{\prime}=\frac{6x^4}{\left(x^4-5\right)^{\frac{1}{2}}}+3(x^4-5)^{\frac{1}{2}}[/tex][tex]y^{\prime}=\frac{6x^4}{\left(x^4-5\right)^{\frac{1}{2}}}+\frac{3(x^4-5)^{\frac{1}{2}}(x^4-5)^{\frac{1}{2}}}{(x^4-5)^{\frac{1}{2}}}[/tex][tex]y^{\prime}=\frac{6x^4}{\left(x^4-5\right)^{\frac{1}{2}}}+\frac{3(x^4-5)}{(x^4-5)^{\frac{1}{2}}}[/tex][tex]y^{\prime}=\frac{6x^4}{\left(x^4-5\right)^{\frac{1}{2}}}+\frac{3x^4-15}{(x^4-5)^{\frac{1}{2}}}[/tex][tex]y^{\prime}=\frac{6x^4+3x^4-15}{\left(x^4-5\right)^{\frac{1}{2}}}[/tex][tex]y^{\prime}=\frac{9x^4-15}{\left(x^4-5\right)^{\frac{1}{2}}}[/tex][tex]y^{\prime}=\frac{3(3x^4-5)}{\left(x^4-5\right)^{\frac{1}{2}}}[/tex][tex]y^{\prime}=\frac{3(3x^4-5)}{\sqrt{x^4-5}}[/tex][tex]y^{\prime}=\frac{3(3x^4-5)}{\sqrt{x^4-5}}\times\frac{\sqrt{x^4-5}}{\sqrt{x^4-5}}[/tex][tex]y^{\prime}=\frac{3(3x^4-5)\sqrt{x^4-5}}{x^4-5}[/tex]Final answer:
[tex]y^{\prime}=\frac{3(3x^4-5)\sqrt{x^4-5}}{x^4-5}[/tex]find the shaded area to the nearest tenth, use 3.14 for pi. help pls due tmrw
Answers
The area of the shaded region inside the circle is 49.04cm².
What is a circle?All points in a plane that are at a specific distance from a specific point, the center, form a circle.
In other words, it is the curve that a moving point in a plane draws to keep its distance from a specific point constant.
So, the shaded area is:
We can easily tell that the diameter of the circle here is 12cm.
So, the radius will be 6cm.
Now, calculate the area of a circle as follows:
A = πr²
A = 3.14(6)²
A = 3.14(36)
A = 113.04cm²
Now, the area of the smaller square:
A = s²
A = 2²
A = 64²
Area of the shaded region:
113.04 - 64
49.04 cm²
Therefore, the area of the shaded region inside the circle is 49.04cm².
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3. If the mZLKI - 174º and KR bisects LLKI, then find the mLLKR.
R
E
K
87°
1740
0740
90°
Answers
SOLUTION
Given the question in the image, the following are the solution steps to answer the question.
STEP 1:
[tex]undefined[/tex]Answer:
87°
Step-by-step explanation:
Angle bisector:Angle bisector is a ray that divides an angle into two congruent angles.
∠LKR = ∠LKJ ÷ 2
= 174° ÷ 2
= 87°
If Rosa is at most 27 years old. What symbol does at most refer to less than greater than less than or equal to greater than or equal to
Answers
The correct answer is less than or equal to because at most 27 years means that Rosa's highest age is 27.
. Find the value of the variables in the rhombus below. B A 0
Answers
As the triangles are congruent and isosceles we get that
[tex]\begin{gathered} B=37=A=D \\ C=180-2\cdot37=106 \\ 24=4x-4 \\ 4x=28\rightarrow x=\frac{28}{4}=6 \end{gathered}[/tex]A committee must be made up of two students from grades 9, 10, or 11, and another two students from grade 12. How many different committees can be made? Explain and show all of your work.
Answers
to make the committee
Use the value of x to find the measure of Angle 1.x=25 5x-5 2x+10
Answers
Given:
• x = 25
,• ∠1 = 5x - 5
,• ∠2 = 2x + 10
Let's find the measure of angle 1.
To find the measure of angle 1, substitute 25 for x in (5x - 5) and evaluate.
We have:
m∠1 = 5x - 5
m∠1 = 5(25) - 5
m∠1 = 125 - 5
m∠1 = 120
Therefore, the measure of angle 1 is 120 degrees.
ANSWER:
∠1 = 120°
which portion must be true?
Answers
The two figures are similar
Using the similarity theorem
The only true proportion is
[tex]\frac{8}{2}\text{ = }\frac{x}{y}[/tex]_________ ____________ allows us to derive new facts quickly from those we know. (spelling counts)
Answers
Derived Facts allows us to derive new facts quickly from those we know.
What is a derived fact?
Derived facts are math facts that are derived from known facts. For example, if we know the doubles fact, 3+3=6, then we can derive the answer to 3+4 by using the 3+3 fact and adding 1 to it. So a derived fact strategy is the mental process of deriving a new fact from a known fact.
What is a related fact example?
We say: Two plus One equals Three. We can also use these same three numbers in our math fact: 2, 1, and 3 to make a related fact. This time our math fact will read: 1 + 2 = 3 because we added 1 and then 2 to get a total of 3.
What are the 3 phases of multiplication fact mastery?
Phase 1: Modeling or counting to find the answer.
Phase 2: Deriving answers using reasoning strategies based on known facts.
Phase 3: Efficient production of answers (Mastery).
Hence the answer is Derived Facts allows us to derive new facts quickly from those we know.
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write an equation of the line that satisfies the given conditions. give the equation (a) in slope intercept form and (b) in standard form. m=-7/12 ,(-6,12)
Answers
Given the slope of the line:
[tex]m=-\frac{7}{12}[/tex]And this point on the line:
[tex](-6,12)[/tex](a) By definition, the Slope-Intercept Form of the equation of a line is:
[tex]y=mx+b[/tex]Where "m" is the slope and "b" is the y-intercept.
In this case, you can substitute the slope and the coordinates of the known point into that equation, and then solve for "b", in order to find the y-intercept:
[tex]12=(-\frac{7}{12})(-6)+b[/tex][tex]12=\frac{42}{12}+b[/tex][tex]\begin{gathered} 12=\frac{42}{12}+b \\ \\ 12=\frac{7}{2}+b \end{gathered}[/tex][tex]\begin{gathered} 12-\frac{7}{2}=b \\ \\ b=\frac{17}{2} \end{gathered}[/tex]Therefore, the equation of this line in Slope-Intercept Form is:
[tex]y=-\frac{7}{12}x+\frac{17}{2}[/tex](b) The Standard Form of the equation of a line is:
[tex]Ax+By=C[/tex]Where A, B, and C are integers, and A is positive.
In this case, you need to add this term to both sides of the equation found in Part (a), in order to rewrite it in Standard Form:
[tex]\frac{7}{12}x[/tex]Then, you get:
[tex]\frac{7}{12}x+y=\frac{17}{2}[/tex]Hence, the answers are:
(a) Slope-Intercept Form:
[tex]y=-\frac{7}{12}x+\frac{17}{2}[/tex](b) Standard Form:
[tex]\frac{7}{12}x+y=\frac{17}{2}[/tex]evaluate the expression 0.03^3
Answers
The given expression is,
[tex]0.03^3[/tex]So, expanding we have,
[tex]0.03^3=0.03\times0.03\times0.03=\text{0}.000027[/tex]what is 8q= 96 what is it?
Answers
To find the value of q, divide both sides of the equation by 8:
[tex]\begin{gathered} 8q=96 \\ \Rightarrow\frac{8q}{8}=\frac{96}{8} \end{gathered}[/tex]Simplify both members of the equation:
[tex]\begin{gathered} \Rightarrow q=\frac{96}{8} \\ \Rightarrow q=12 \end{gathered}[/tex]Therefore:
[tex]q=12[/tex]Write 3 equivalent ratios for 5:8
Answers
Given data:
The given ratio is a=5:8.
Multiply 2 on numerator and denominator both.
[tex]\begin{gathered} a=\frac{2(5)}{2(8)} \\ =\frac{10}{16} \end{gathered}[/tex]Multiply 3 on numerator and denominator both.
[tex]\begin{gathered} a=\frac{3(5)}{3(8)} \\ =\frac{15}{24} \end{gathered}[/tex][tex]\begin{gathered} a=\frac{4(5)}{4(8)} \\ =\frac{20}{32} \\ \end{gathered}[/tex]2. Identify the vertex from the quadratic function y=-5(x-6)^2+8 *2 points(-5, 6)(-6,8)(6,8)(8,6
Answers
Answer
2) Option C is correct.
The vertex of the quadratic function is at
x = 6, y = 8.
In coordinate form, the vertex = (6, 8)
4) Option A is correct.
-3 stretches the graph and reflects it about the x-axis.
Explanation
2) We are told to find the vertex of the quadratic function. The vertex of a quadratic function is the point at the base of the curve/graph of the function. It is the point where the value of the quadratic function changes sign.
The x-coordinate of this vertex is given as
x = (-b/2a)
The y-coordinate is then obtained from the value of the x-coordinate.
The quadratic function for the question is
y = -5 (x - 6)² + 8
We first need to put the quadratic function in the general form of
y = ax² + bx + c
So, we first simplify the expression
y = -5 (x - 6)² + 8
= -5 (x² - 12x + 36) + 8
= -5x² + 60x - 180 + 8
y = -5x² + 60x - 172
So,
a = -5
b = 60
c = -172
For the vertex
x = (-b/2a)
= [-60/(2×-5)]
= [-60/-10]
= 6
So, if x = 6.
y = -5x² + 60x - 172
y = -5(6²) + 60(6) - 172
y = -5(36) + 360 - 172
y = -180 + 360 - 172
y = 8
So, the vertex of the quadratic function is at
x = 6, y = 8.
In coordinate form, the vertex = (6, 8)
Option C is correct.
4) y = -3(x²)
The graph of x² is a parabola, but multiplying the function x² by -3 transforms the graph.
The 3, because it is greater than 1, stretches or enlarges the graph.
And the minus sign in front of the 3, ,that is, -3 reflects the graph about the x-axis.
So, altogether, -3 stretches the graph and reflects it about the x-axis.
Option A is correct.
Hope this Helps!!!
. Compare: what is greater 5/3 or 9/16
Answers
hello
between 5/3 and 9/16, 5/3 is greater than 9/16
[tex]\frac{5}{3}>\frac{9}{16}[/tex]solve equation 10 - 25x = 5 what is the value of x
Answers
ANSWER
x = 1/5
EXPLANATION
We are given the equation:
10 - 25x = 5
To find the value of x, first we subtract 10 from both sides of the equation:
10 - 25x - 10 = 5 - 10
10 - 10 - 25x = 5 - 10
-25x = -5
Now, divide both sides by 5:
=> x = -5 / -25
x = 1/5
That is the value of x.
Some roads in the Rocky Mountains have a rise of 7 feet for every 100 horizontal feet.What is the slope of such roads?
Answers
Let's begin by listing out the information given to us:
The road rises by 7 feet every 100 horizontal feet
The equation becomes:
Slope (m) = Δy/Δx = 7/100 = 0.07
Slope (m) = 0.07
5. In a 45-45-90 right triangle if the hypotenuse have length "x V 2", the leg 2 pointshas length IOхO 2xO x 2XV3
Answers
Given data:
In a right angle triangle hypotenues is given that is
[tex]H=x\sqrt[]{2}[/tex]Now, by the Pythagorean theorem we have
[tex]\text{Hypotenues}^2=Perpendicular^2+Base^2[/tex]So, by the hit and trial method
Let , perpendicular = base = x we get
[tex]\begin{gathered} H^{}=\sqrt[]{x^2+x^2} \\ H=\sqrt[]{2x^2} \\ H=x\sqrt[]{2} \end{gathered}[/tex]Thus, the correct option is (1) that is x
As we learn more about lines, we will occasionally have to consider perfectly vertical lines as a special case and treat them differently. Think about applying what you have learned in the last couple of activities to the case of vertical lines. What is the same? What is different?
Answers
If the line of the graph is vertical then the slope of the graph is zero. The coordinate of the y-value will never change on vertical lines.
What are vertical lines?The vertical line is a line that is parallel to the y-axis. A vertical line can be defined as a line on the coordinate plane where all the points on the line have the same x-coordinate. A form of test employed in relation is the vertical line test. Any kind of vertical line equation lacks a y-intercept. The vertical line test is used to determine whether or not the given relation is a function. The vertical line is another name for the vertical bar. A mathematical sign is an upright slash. Depending on the context, it may be used to represent a certain kind of logic or an operation. The vertical line is the line that runs along the y-axis.
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