One small box of orange costs $6
Explanation:Let x represent the cost of one small box of oranges, and y represent one large box of oranges.
For Krystal, we have:
2x + 13y = 246 .......................................................................(1)
For Alberto, we have:
10x + y = 78 ............................................................................(2)
From (2), we have:
y = 78 - 10x .............................................................................(3)
Using the expression for y given in (3) in (1)
2x + 13(78 - 10x) = 246
2x + 1014 - 130x = 246
2x - 130x = 246 - 1014
-128x = -768
x = 768/128
= 6
Substitute x = 6 in (3)
y = 78 - 10(3)
= 78 - 30
= 48
Therefore, x = $6, and y = $48
One small box costs $6
The ones with the X’s are the only ones i cannot get the answer for. please help
Order the winning scores from least to greatest, and do so with the losing scores.
[tex]\begin{gathered} winning \\ 14,16,16,16,17, \\ 20,20,20,21,21,23,23,24,24,24,26,27,27,27,27,27,29 \\ 30,31,31,31,31,32,32,33,34,34,35,35,35,37,38,38,39 \\ 42,46,48,49, \\ 52,55 \end{gathered}[/tex]As for the losing scores,
[tex]\begin{gathered} losing\text{ } \\ 3,6,7,7,7,7,7,9 \\ 10,10,10,10,10,10,10,13,13,14,14,14,16,16,16,16,17,17,17,17,17,17,17,19,19 \\ 20,21,21,21,21,23,24,24,25,26,29 \\ 31 \end{gathered}[/tex]Therefore, the correct diagram for the losing scores is
As for the winning scores,
find three rational numbers between 3/4 and 0.750.75 is a repeating decimal
3/4 can be written in decimal form as,
[tex]\frac{3}{4}=0.75[/tex]0.75 is a repeating decimal. So, 0.75 with repeating decimal can be written as 0.757575.
We have to find three rational numbers between 0.75 (3/4) and 0.757575.
So, three rational numbers between 0.75 (3/4) and 0.757575 should have values in between 0.75 (3/4) and 0.757575 itself.
So, three rational numbers between 3/4 and 0.75 are 0.753, 0.754 and 0.756.
I need help solving this math problem by using substitution method
To solve by substitution method:
1. Substitute the x in the first equation by the value of x given in the second equation:
[tex]-3(-5y)-6y=45[/tex]2. Solve y:
[tex]\begin{gathered} 15y-6y=45 \\ 9y=45 \\ \\ \frac{9}{9}y=\frac{45}{9} \\ \\ y=5 \end{gathered}[/tex]3. Use the value of y to find x:
[tex]\begin{gathered} x=-5y \\ x=-5(5) \\ x=-25 \end{gathered}[/tex]Then, the solution for the given system of equations is: x= -25 and y=5 (-25,5)Base on definition of the inverse, f(g(x))=x and vice versa. Given f(x)=1/2x+3 and g(x)=2x-6, write a composition (s) should be used to prove that f(x) and g(x) are inverses of each other.
To verifiy if these are inverses we need to calculate the expression "f(g(x))" which uses the expression for "g(x)" in place of x on the expression of "f(x)". We have:
[tex]\begin{gathered} f(g(x))=\frac{1}{2}(2x-6)+3 \\ f(g(x))=\frac{2x}{2}-\frac{6}{2}+3 \\ f(g(x))=x-3+3 \\ f(g(x))=x \end{gathered}[/tex]Since the result is f(g(x)) = x, they are inverses of each other.
Find an nth-degree polynomial function with real coefficients satisfying the given conditions. If you are using a graphing utility, use it to graph the function and verify the real zeros and the given function value.n=3-3 and 5 + 5i are zeros f(-1)= 122
Given:
a.) n = 3
b.) -3 and 5 + 5i are zeros
c.) f(-1) = 122
Step 1: Let's determine the factors based on the zeros.
-3 and 5 + 5i are zeros
Therefore, the factors will be:
x + 3
5 + 5i = 5(1 + i)
x + 5(1 + i)
x - 5(1 + i)
0
Write an equation describing the relationship of the given variables Y varies directly as the square root of x and when x=81, y=45
Solution
Step 1:
[tex]\begin{gathered} If\text{ y varies directly as square root of x.} \\ We\text{ have,} \\ y\text{ }\propto\sqrt[]{x} \end{gathered}[/tex]Step 2:
Plug in constant k to change the proportionality sign into an equal sign.
[tex]\begin{gathered} y\text{ }\propto\sqrt[]{x} \\ y=k\sqrt[]{x} \end{gathered}[/tex]Step 3:
Substitute the values of x = 81 and y = 45 to find the value of constant k.
[tex]\begin{gathered} \text{y = k}\sqrt[]{x} \\ 45\text{ = k}\sqrt[]{81} \\ 45\text{ = 9k} \\ \text{Divide both sides by 9 to find the value of k.} \\ k\text{ = }\frac{45}{9} \\ k\text{ = 5} \end{gathered}[/tex]Step 4:
Write an equation describing the relationship of the given variables.
[tex]\begin{gathered} \text{y = k}\sqrt[]{x} \\ y\text{ = 5}\sqrt[]{x} \end{gathered}[/tex]Final answer
[tex]\text{y = 5}\sqrt[]{x}[/tex]How many 5-letter arrangements of the letters T, E, X, A, S can be created if eachletter is used only once?What is the answer?
ANSWER
120
EXPLANATION
We have to find the number of permutations of 5 letters in 5 spots:
[tex]_5P_5=\frac{5!}{(5-5)!}=5!=5\cdot4\cdot3\cdot2\cdot1=120[/tex]please help methe cube of one more than two times a number as an algebraic expression
[tex](1+2x)^3[/tex]
Explanation
Step 1
Let
x, a number
2x, two times a number,
cube=exponent 3
Step 2
replace
one more than two times a number =1+2x
the cube of one more than two times a number=
[tex](1+2x)^3[/tex]what is the product of 2x^2-3xy+y^2 and 2x-4y?
4x³ -14x²y +14xy²-4y³
1) Let's calculate it
(2x²-3xy+y²) (2x-4y) Applying the Distributive Property
4x³-8x²y-6x²y+12xy²+2xy²-4y³ Combining like terms
4x³ -14x²y +14xy²-4y³
Answer:
(2x²-3xy+y²) (2x-4y) Applying the Distributive Property
4x³-8x²y-6x²y+12xy²+2xy²-4y³ Combining like terms
4x³ -14x²y +14xy²-4y³
which of the following are like terms?3y^5 ,2x^53y^5, 2y^56y^2, 2z3y^4, 4x^3
1) Like terms have the same variable and the same exponent. Therefore we can add, subtract, and combine them when operating polynomials.
2) Examining the options, we can state that:
3y^5, 2y^5
We can add those, subtract them, and so on.
3) So the answer is 3y^5, 2y^5 for they have the same variable,
1/2x - 7 = 1/3(× - 12)what ia the value of x?
Distributing:
[tex]\begin{gathered} \frac{1}{2}x-7=\frac{1}{3}x-\frac{1}{3}\cdot12 \\ \frac{1}{2}x-7=\frac{1}{3}x-4 \end{gathered}[/tex]1/3x is adding on the right, then it will subtract on the left.
7 is subtracting on the left, then it will add on the right
[tex]\begin{gathered} \frac{1}{2}x-\frac{1}{3}x=-4+7 \\ \frac{1\cdot3-1\cdot2}{6}x=3 \\ \frac{1}{6}x=3 \end{gathered}[/tex]1/6 is multiplying on the left, then it will divide on the right
[tex]\begin{gathered} x=3\cdot6 \\ x=18 \end{gathered}[/tex]Lisa has collected data to find that the number of pages per book on a book shelf has a normal distribution. What is the probability that a randomly selected book has fewer than 169 pages if the mean is 194 pages and the standard deviation is 25 pages? Use the empirical rule. Enter your answer as a percent rounded to two decimal places if necessary.
15.85%
Explanations:According to the empirical rule for normal probability;
• 68% of given, data falls within 1σ of the mean
,• 95%, of the given data falls within 2σ of the mean
,• 99.7% of all data falls within 3σ of the mean
This rule shows an even distribution among the mean
From the data, we can say that 34% of the data is within μ±1σ
Given the following data
Mean = 194 pages
Standard deviation = 25
Hence 1 standard deviation of the mean will be 194 - 25 = 169 showing that 34% of data fall in that range
Since we need the probability that a randomly selected book has fewer than 169 pages, we use the normal distribution property which states:
50% of the data is left of the mean of which 34% fall within 1 standard deviation, hence the remaining would fall fewer than 169.
Pr(a randomly selected book has fewer than 169 pages) = 50% - 34% = 16%
To determine the final probability, we will subtract the half of 0.3(100-99.7) to have:
Pr(a randomly selected book has fewer than 169 pages) = 16 - 0.3/2
Pr(a randomly selected book has fewer than 169 pages) = 16 - 0.15
Pr(a randomly selected book has fewer than 169 pages) = 15.85%
Instead of the installment plan, suppose the Sanchez family went to the bankand borrowed $273 with 8% interest.
8. Amount of interest: $273*8% = $21.84
9. Total amount: $273 + $21.84 = $294.84
Describe howfactoring can help you find the x-interceptsof the graph of the quadratic functiony=x2 - 4x + 3.
hello
the quadratic equation given is
[tex]x^2-4x+3=0[/tex]now let's find two factors to the equation and proceed to solve the equation.
to do this, i'll write down the standard form of a quadratic equation out
[tex]ax^2+bx+c=0[/tex]to solve this by factorization, we need to find two numbers that when they're multiplied will give us the value of c but when added will give the value of b
in this case, our value of b = -4 and c = 3
two numbers that will give us the desired value are (-1, -3)
[tex]x^2-4x+3=(x-1)(x-3)[/tex]the factorized form of the equation would be (x - 1)(x - 3)
Find the simplest form, of C, starting with the further point where the graph of C crosses the y axis.
We are given the function f(x) = x^3 - 6x^2 + 10x - 3, where x is a real number. We are supposed to translate it by (-2, 3) which means that we are moving the entore graph 2 units to the right and 3 units up.
The first thing to do is write the cubic function in the form f(x) = a(x - h)^3 + k where h is the horizontal translation and k is the vertical translation.
So, f(x) = x^3 - 6x^2 + 10x - 3 moved 2 units to the right and 3 units up would be written as:
[tex]C=(x+2)^3-6(x+2)^2+10(x+2)-3+3[/tex]We can simplify this as:
[tex]\begin{gathered} C=(x+2)^{3}-6(x+2)^{2}+10(x+2)-3+3 \\ C=(x^3+6x^2+12x+8)-6(x^2+4x+4)+(10x+20) \\ C=x^3+6x^2+12x+8-6x^2-24x-24+10x+20 \\ C=x^3-2x+4 \end{gathered}[/tex]The graph crosses the y-axis when x = 0.
[tex]\begin{gathered} C=x^{3}-2x+4 \\ y=0^3-2(0)+4 \\ y=4 \end{gathered}[/tex]The point where the graph crosses the y-axis is (0, 4).
Hi yea thank you thank goodness for your help today please
Given:
[tex]h(t)=3300-54t-300e^{-0.18t}[/tex]Find-:
(1)
Velocity at the instant when t = 6 sec.
(2)
The time when velocity is -45 meter per sec
Explanation-:
Velocity is define as a:
[tex]\begin{gathered} v(t)=\frac{dh(t)}{dt} \\ \\ v(t)=h^{\prime}(t) \end{gathered}[/tex]The value of the h'(t) is:
[tex]\begin{gathered} h(t)=3300-54t-300e^{-0.18t} \\ \\ h^{\prime}(t)=-54-300(-0.18)e^{-0.18t} \end{gathered}[/tex]Value is:
[tex]\begin{gathered} h^{\prime}(t)=54e^{-0.18t}-54 \\ \\ v(t)=h^{\prime}(t) \\ \\ v(t)=54e^{-0.18t}-54 \end{gathered}[/tex]At t=6 velocity is:
[tex]\begin{gathered} v(t)=54e^{-0.18t}-54 \\ \\ v(6)=54e^{-0.18\times6}-54 \\ \\ v(6)=54e^{-1.08}-54 \\ \\ v(6)=54\times0.333-54 \\ \\ v(6)=18.333-54 \\ \\ v(6)=-35.66 \end{gathered}[/tex]At t=6 velocity is -35.66 meters per sec.
(b)
Velocity is -45 meter per second then time is:
[tex]\begin{gathered} v(t)=54e^{-0.18t}-54 \\ \\ v(t)=-45\text{ then time is:} \\ \\ -45=54e^{-0.18t}-54 \\ \\ 54-45=54e^{-0.18t} \\ \\ 9=54e^{-0.18t} \\ \\ \frac{9}{54}=e^{-0.18t} \\ \\ 0.166=e^{-0.18t} \end{gathered}[/tex]Taking log both side then,
[tex]\begin{gathered} \ln0.166=\ln e^{-0.18t} \\ \\ \ln0.166=-0.18t\ln e \\ \\ -1.79175=-0.18t \\ \\ t=\frac{-1.79175}{-0.18} \\ \\ t=9.95 \end{gathered}[/tex]So, the time is 9.95 second
I’m always getting the wring answer. Can you help. I know it’s a very long process.
To make the table of values we need to determine in which interval we need to use each of the expressions of the piecewise function. For any value less than zero we need to use the expression y=3. For any value greater or equal than zero we are going to use the expression x+1; with this in mind we have the following table:
Now that we have this table we plot the points given and graph the function:
Now, in here it is important to notice that the horizontal lines goes till x=0 BUT we draw a hollow point indicating that this line does not touch the zero, this measn that the function y=3 is defined for x<0 like the function stated.
Furthermore we have to draw a solid circle in the point (0,1) that indicates that the function takes that value when x=0.
Now from the graph we notice that the function is defines for all values of x then we have that the domain is:
[tex]\text{domf}=(-\infty,\infty)[/tex]Also from the graph we notice that the range is the interval:
[tex]\text{rangeF}=\lbrack1,\infty)[/tex]Two linear functions are represented below , f(x) by a table , and g(x) by a graph .which function has the greater rate of change
The rate of change of a function is equal to the derivative of that function.
So, we can proceed by finding the derivative of functions f and g. The one with the greatest derivative will then have the greatest rate of change.
Function f(x).
From the table, we can observe that
x=0-->f(x)=4 and x=5-->f(x)=7
Let's see if this function is a line. Remember that to define a line we only need two points, we can take (x,f(x))=(0,4),(5,7) so as to facilitate the solution.
[tex]\begin{gathered} (0,4),(5,7) \\ f(x)-f(x_1)_{}=\frac{(f(x_2)_{}-f(x_1)_{})}{(x_2-x_1)}(x-x_1) \\ \Rightarrow f(x)-4=\frac{(7-3)}{(5-0)}(x-0) \\ \Rightarrow f(x)-4=\frac{4}{5}x \end{gathered}[/tex]Now, let's verify that this equation models the information displayed in the table:
x=-10-->f(x)=-2
Evaluate the function [p - 25]+pf where p=10 and f=3
ANSWER
[tex]15[/tex]EXPLANATION
We want to evaluate the expression given:
[tex]\lbrack p-25\rbrack+pf[/tex]for:
[tex]p=10;f=3[/tex]To do this, we substitute the values of p and f into the expression and simplify it:
[tex]\begin{gathered} \lbrack10-25\rbrack+(10\cdot3) \\ -15+30 \\ \Rightarrow15 \end{gathered}[/tex]That is the answer.
Find the measure of each numbered angle and name the theorem or postulate that justify your work.
Answer:
m∠2 = 94
m∠3 = 94
Explanation:
Angle 2 and 3 are vertical angles. They are opposite and are formed when two lines cross. Since they are vertical angles, they have the same measure, so we can write the following equation:
[tex]\begin{gathered} m\angle2=m\angle3 \\ 4x-26=3x+4 \end{gathered}[/tex]So, solving for x, we get:
[tex]\begin{gathered} 4x-26+26=3x+4+26 \\ 4x=3x+30 \\ 4x-3x=3x+30-3x \\ x=30 \end{gathered}[/tex]Now, we can calculate the measure of angle 2 and 3 as:
[tex]\begin{gathered} m\angle2=4x-26=4\cdot30-26=120-26=94 \\ m\angle3=3x+4=3\cdot30+4=90+4=94 \end{gathered}[/tex]Therefore, the measures of angles 2 and 3 are 94
write a coordinate rule for the composition
The coordinate rule for the composition is (x, y) ⇒ 2(-x, -y)
How to determine the coordinate rule?From the graph, the coordinates of the triangles are
Triangle ABC: A = (-2, 1), B = (-4, 1) and C = (-2, 4)Triangle DEF: D = (4, -2), E = (8, -2) and F = (4, -2)The triangles are in opposite quadrants
This means that the triangles are rotated by 180 degrees
This is represented as
(x, y) ⇒ (-x, -y)
Next, we can see that the side lengths of triangle DEF is twice the side lengths of triangle ABC
This means that the triangle ABC is dilated by 2
So, we have
(x, y) ⇒ 2(-x, -y)
Note that we assume that the triangle is transformed from ABC
Read more about transformation at
https://brainly.com/question/27224272
#SPJ1
hello can you tell me what I need to do to get the answer please
We'll first sort the data in ascending order:
[tex]30,\text{ 88, 90, 96}[/tex]The median is the number in the "middle" of a sorted list of numbers. Since in ths case we have two "middle" numbers because we have four data point, we just need to average them. That is:
[tex]\frac{88+90}{2}=89[/tex]And so, 89% is the median of the quiz grades given.
Which pair of functions are inverses of each other?O A. f(x) = and g(x) = 6 x3B. f(x) = 1 + 6 and g(x) = 5x - 6C. f(x) = 7x- 2 and g(x) = x+2O D. f(x) = -2 and g(x) = 2+2SUBMIT
Explanation:
To find the inverse of a function, we need to replace f(x) by y, then solve the function for x, and finally interchange the variables x and y.
So, the inverse function for each option is:
Option A.
[tex]undefined[/tex]Is this set of values a function? Yes or No
No, the set doesn't represent a function because the number 1 has two diferent images which are 3 and 8.
Judy drew an isosceles triangle.One side of the triangle was 6 incheslong. The other side of the triangle was 9 inches long. What couldbe the length of the third side of the triangle Judy drew? Explainyour reasoning.
Isosceles triangles Have two sides that have the same measure, and one of them is different.
So, we can have two situations:
6 - 6 - 9
or
9 - 9 - 6
what is the difference of the rational expressions below? *photo
Answer: C.
[tex]\frac{-2x+1}{x^2}[/tex]Explanation
Given
[tex]\frac{3x+1}{x^2}-\frac{5}{x}[/tex]We have to find the minimum common denominator, which in our case is x². Then, we divide this denominator over the denominator of each term in the given equation, multiply it times the numerator, and place the result as follows:
[tex]\frac{3x+1}{x^{2}}-\frac{5}{x}=\frac{3x+1-5x}{x^2}[/tex]Simplifying by adding similar terms we get:
[tex]=\frac{1-2x}{x^2}[/tex]Three friends went to a school play. Each ticket was$5. They each spent different amounts of money on food and drink. Chris$5, Ben $3 and Danica$6 which is these expression can be used to find out the total amount of money all three friends spent on tickets, food, and drink(3+5*(5+6) (3*5)+(5+3+6)(3+5)+(5*5*6)
Answer:
(3*5) + (5 + 3 + 6)
Explanation:
To know the total amount of money that they spend, we need to sum the amount that they spend on tickets to the amount that they spend on food and drink.
So, if each ticket cost $5 and they are 3 friends, the total amount that they spend on tickets can be calculated as:
3*5
On the other hand, if Chris spent $5, Ben $3, and Danice $6, the total amount that they spent on food and drink is:
5 + 3 + 6
Therefore, the expression to calculate the total amount that they spent is:
(3*5) + (5 + 3 + 6)
find the missing angle measures of each polygon in 8
The sum of the interior angles of a pentagon is 540°
angle H +angle I + angle J + angle K +angle L=540°
we substitute the values
100+143+85+92 angle L= 540°
angle L= 540-100-143-85-92
angle L=120°
e Calculate the area of the regular hexagon. Round your answer to the nearest tenths. 3.4cm X. 20.4cm? .. 29.6cm? c.59.1cm? 4.9cm?
The side of hexagon is s = 3.4 cm.
The apothem is a = 2.9 cm.
The formula for the area of regular hexagon is,
[tex]A=\frac{1}{2}\cdot P\cdot a[/tex]Here, P is perimeter of hexagon.
Determine the perimeter of hexagon.
[tex]\begin{gathered} P=6s \\ =6\cdot3.4 \\ =20.4 \end{gathered}[/tex]Substitute the value in the area formula to obtain the area of regular hexagon.
[tex]\begin{gathered} A=\frac{1}{2}\cdot20.4\cdot2.9 \\ =29.58 \\ \approx29.6 \end{gathered}[/tex]So answer is 29.6 square centimeter.
Simply The Expression 12+3(7y-8)
First we use the distributive property to eliminate the parenthesis:
[tex]\begin{gathered} 12+3(7y-8)=12+3(7y)+3(-8) \\ =12+21y-24 \end{gathered}[/tex]Now we add similar terms and we get the following:
[tex]12+21y-24=21y-12[/tex]Notice that 21 and 12 are divisible by 3, therefore, we have::
[tex]21y-12=3(7y-4)[/tex]Finally, the simplifed expression of 12+3(7y-8) is 3(7y-4)