Answers
Let x be the cost of each juice and y be the cost of each BBQ.
4x + 2y = 16
4x + 3y = 21
Subtract the second equation from the first
y = 5
Substitute y = 5 into 4x + 2y = 16
4x + 2(5) = 16
4x + 10 = 16
4x = 16 - 10
4x = 6
x=1.5
Therefore, a juice cost $1.5 and a BBQ cost $5
So, if the Emdin family pu rchased 3 juice and 3 BBQ, then
cost of juice = 3 x $1.5 = $4.5
cost of BBQ = 3 x $5 = $15
Total money spent by Emdin family = $4.5 + $15 = $19.5
Let x be the cost of each juice and y be the cost of each BBQ.
4x + 2y = 16
4x + 3y = 21
Subtract the second equation from the first
y = 5
Substitute y = 5 into 4x + 2y = 16
4x + 2(5) = 16
4x + 10 = 16
4x = 16 - 10
4x = 6
x=1.5
Therefore, a juice cost $1.5 and a BBQ cost $5
So, if the Emdin family pu rchased 3 juice and 3 BBQ, then
cost of juice = 3 x $1.5 = $4.5
cost of BBQ = 3 x $5 = $15
Total money spent by Emdin family = $4.5 + $15 = $19.5
Related Questions
What is the value of w?14w +12 = 180
Answers
Logan wants to know how many skateboards have defective parts. He inspects 20000 skateboards and keeps track of the number of defects per board. Use his probability distribution table to find the expected value for defects on a skateboard.(Rest of the problem needs to be sent as an image)a. 1/25b. 4/25c. 3/25d. 2/25
Answers
ANSWER:
2nd option: 4/25
STEP-BY-STEP EXPLANATION:
To find the expected value of the distribution, we multiply each outcome by its probability and the sum of this would be the expected value, like so:
[tex]\begin{gathered} E(x)=0\cdot\frac{9}{10}+1\cdot\frac{1}{20}+2\cdot\frac{1}{25}+3\cdot\frac{1}{100} \\ \\ E(x)=0+\frac{1}{20}+\frac{2}{25}+\frac{3}{100} \\ \\ E(x)=\frac{5}{100}+\frac{8}{100}+\frac{3}{100}=\frac{16}{100}=\frac{4}{25} \end{gathered}[/tex]Therefore, the correct answer is the 2nd option: 4/25
Find the area of a triangle with base 13 ft. and height 6 ft.
Answers
SOLUTION
The area of a triangle is given by the formula
[tex]Area=\frac{1}{2}\times base\times height[/tex]From the question we have been given the base as 13 and the height as 6.
So we will substitute base for 13 and height for 6 into the formula, we have
[tex]\begin{gathered} Area=\frac{1}{2}\times13\times6 \\ 6\text{ divides 2, we have 3, this becomes } \\ Area=1\times13\times3 \\ Area=39ft^2 \end{gathered}[/tex]Hence the answer is 39 square-feet
Which is the better buy: $40.00 for 30 gallons of gas or $8.50 for 8 gallons ofgas?
Answers
Ok, we need to calculate the value of each gallon and see which is the cheapest:
First Option: 40/30=1.33
Second Option: 8.5/8=1.0625
This mean that the better buy is $8.50 for 8 gallons of gas.
Find the missing parts of the triangle. Round to the nearest tenth when necessary or to the nearest minute as appropriate.C=111.1°a=7.1mb=9.6mOption 1: No triangle satisfies the given conditions.Option 2: c=19.6m, A=26.8°, B=42.1°Option 3: c=16.7m, A=30.8°, B=38.1°Option 4: c=13.8m, A=28.8°, B=40.1°
Answers
Answer: Option 4: c=13.8m, A=28.8°, B=40.1°
Explanation:
From the information given,
the known sides are a = 7.1 and b = 9.6
the known angle is C = 111.1
We would find side c by applying the cosine rule which is expressed as
c^2 = a^2 + b^2 - 2abCosC
By substituting the given values into the formula,
c^2 = 7.1^2 + 9.6^2 - 2 x 7.1 x 9.6Cos111.1
c^2 = 50.41 + 92.16 - 136.32Cos111.1
c^2 = 142.57 - 136.32Cos111.1 = 191.6448
c = √191.6448 = 13.8436
c = 13.8
To find angle A, we would apply the sine rule which is expressed as
a/SinA = c/SinC
Thus,
7.1/SinA = 13.8436/Sin 111.1
By cross multiplying, we have
13.8436SinA = 7.1Sin111.1
SinA = 7.1Sin111.1/13.8436 = 0.4785
Taking the sine inverse of 0.4785,
A = 28.8
Recall, the sum of the angles in a triangle is 180. Thus,
A + B + C = 180
28.8 + B + 111.1 = 180
139.9 + B = 180
B = 180 - 139.9
B = 40.1
Option 4: c=13.8m, A=28.8°, B=40.1°
I need help with a math question. I linked it below
Answers
1) We can fill in the gaps, this way since we can write the following when we translate into mathematical language:
[tex]\begin{gathered} \frac{b}{55}+8>6 \\ \frac{b}{55}>-8+6 \\ \frac{b}{55}>-2 \\ 55\cdot\frac{b}{55}>-2\cdot55 \\ b>-110 \end{gathered}[/tex]Note that we could do it in two steps. Subtracting and then multiplying and dividing
Write a linear function f with f (- 1/2) = 1 and f (0) = -4
Answers
The linear function f with f (- 1/2) = 1 and f (0) = -4 would be ; y = -5x -4.
What is linear equation?Linear equation is equation in which each term has at max one degree. Linear equation in variable x and y can be written in the form y = mx + c
Linear equation with two variables, when graphed on cartesian plane with axes of those variables, give a straight line.
We are asked to write the linear function f with f (- 1/2) = 1 and f (0) = -4
Let the equation in variable x and y can be written in the form y = mx + c
So f (- 1/2) = 1
this gives, 1 = -1/2m+c -----------eq 1
Also f (0) = -4
This gives -4 = c. --------------eq2
Now Putting value of c in equation in eq1 we get m=0.
So 1 = -1/2m+c
1 = -1/2m - 4
m = -5
Then we get;
y = -5x -4.
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1) f(x) = 60.73(0.95)x2) f(x) = 0.93(60.73)x3) f(x) = 60.04 – 8.25 ln x4) f(x) = 8.25 – 60.04 ln x
Answers
A logarithmic function is expressed as
y = a + blnx
We would substitute corresponding values of x and y into the function. This will give us two equations. We would solve the equations for a and b. We have
From the table, when x = 1, y = 60
Thus,
60 = a + b * ln1
60 = a + b * 0
60 = a
when x = 2, y = 54
Thus,
54 = a + bln2
54 = a + 0.693b
Substituting a = 60 into 54 = a + 0.693b, we have
54 = 60 + 0.693b
0.693b = 54 - 60 = - 6
b = - 6/0.693
b = - 8.65
The function would be
f(x) = 60 - 8.65lnx
9.State the slope and y-value of the y-intercept of the equation, y = 6x + 9Slopey-intercept
Answers
The slope is 6 and the y-intercept is 9
Explanation:The given equation is:
y = 6x + 9
The general form of the equation of a line is
y = mx + c
where m is the slope and c is the y-intercept.
Comparing these equations, we see that
m = 6 and c = 9
Therefore, the slope is 6 and the y-intercept is 9
If the discriminant is 22, then the roots of the quadratic equation are ________________.irrationalrationalreal and equalcomplex
Answers
Given:
The discriminant is 22.
Required:
To choose the correct option for the roots.
Explanation:
The desciminant is 22 means
[tex]b^2-4ac=22[/tex]We know that if
[tex]b^2-4ac>0[/tex]the equation has two distinct real number roots.
Therefore the roots are irrational or rational.
Final Answer:
The roots are irrational or rational.
Hello! Need help with this, please explain in an easy way I am in year 9
Answers
Let's factor the trinomial step by step:
1. Multiply and divide the whole trinomial by the leading coefficient. For the middle term, leave it expressed:
[tex]3x^2-20x+12\rightarrow\frac{9x^2-20(3x)+36}{3}[/tex]2. We'll factor just like a regular x^2+bx+c trinomial:
• Open two sets of parenthesis and put the square root of the first term on each one
[tex]\frac{(3x)(3x)}{3}[/tex]• Put the sign of the second term of the trinomial in the first set of parenthesis, and the result of multiplying the sign of the second term by the sign of the third term on the second set:
[tex]\frac{(3x)(3x)}{3}\rightarrow\frac{(3x-)(3x-)}{3}[/tex]• Find two numbers whose product is 36 and whose sum is 20
[tex]\begin{gathered} 18\cdot2=36 \\ 18+2=20 \\ \\ \rightarrow18,2 \end{gathered}[/tex]• Fill both sets with such numbers, in ascending order:
[tex]\frac{(3x-)(3x-)}{3}\rightarrow\frac{(3x-18)(3x-2)}{3}[/tex]3. Simplify one of the terms with the denominator:
[tex]\frac{(3x-18)(3x-2)}{3}\rightarrow\frac{3(x-6)(3x-2)}{3}\rightarrow(x-6)(3x-2)[/tex]Therefore, the factorization of our trinomial is:
[tex](x-6)(3x-2)[/tex]Find the coordinates of point p that partition AB in the ratio 1: 4,
Answers
Given:
[tex]A(1,-1)\text{ ; B(}4,4)\text{ m:n =1:4}[/tex][tex](x,y)=(\frac{mx_2+nx_1}{m+n},\frac{my_2+ny_1}{m+n})[/tex][tex](x,y)=(\frac{4+4}{1+4},\frac{4-4}{1+4})[/tex][tex](x,y)=(\frac{8}{5},0)[/tex]Therefore the point P be ( 1.6 ,0)
How many different amounts of money can be made
with six pennies, two nickels, and one quarter?
Answers
Based on the number of pennies, nickels, and quarters, the number of different amounts of money that can be made are 42.
How to find the different amounts that can be made?First, find out the number of ways to select the different amounts.
There are six pennies so there are 7 ways to collect them including:
(0 times, 1 time, 2, 3, 4, 5, 6)
There are 3 ways to collect nickels and there are two ways to collect quarters.
The number of different amounts of money that can be made are:
= 7 x 3 x 2
= 42 different amounts of money
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would this be (0, -1) since if b is greater than 1 but it is also -2
Answers
The y-intercept is the point where the graph cuts the y-axis. The y-axis is the line x = 0, therefore, to find the y-coordinate of this point we just need to evaluate x = 0 in our function.
[tex]\begin{gathered} y(x)=b^x-2 \\ y(0)=b^0-2 \end{gathered}[/tex]Any nonzero real number raised to the power of zero is one, therefore
[tex]y(0)=b^0-2=1-2=-1[/tex]The y-intercept is (0, -1).
Use the drawing tool(s) to form the correct answer on the provided graph, The function fx) is shown on the provided graph. Graph the result of the following transformation on f(X). f(x) + 6
Answers
We have that the line passes by the points (0, -2) & (1, 2). Using this we determine the slope (m) and then the function. After that we transformate the function. We proceed as follows:
[tex]m=\frac{2-(-2)}{1-0}\Rightarrow m=4[/tex]Now, using one of the points [In our case we will use (0, -2), but we can use any point of the line] and the slope, we replace in:
[tex]y-y_1=m(x-x_1)[/tex]Then:
[tex]y-(-2)=4(x-0)[/tex]Now, we solve for y:
[tex]\Rightarrow y+2=4x\Rightarrow y=4x-2[/tex]And we apply the transformation to our line, that is f(x) -> f(x) + 6:
[tex]y=4x-2+6\Rightarrow y=4x+4[/tex]Therefore our final line (After the transformation) is y = 4x + 4, and graphed that is:
Write an equation that expresses the following relationship.u varies jointly with p and d and inversely with wIn your equation, use k as the constant of proportionality.
Answers
Answer:
[tex]u=k\cdot\frac{p\cdot d}{w}[/tex]Explanation:
If a varies jointly with b, we write the equation
a = kb
If a varies inversely with b, we write the equation
a = k/b
So, if u varies jointly with p and d and inversely with w, the equation is
[tex]u=k\cdot\frac{p\cdot d}{w}[/tex]Find the slope of the line passing through the points(-2,6) and (-6, 3).
Answers
Answer:
3/4
Step-by-step explanation:
To find the slope (gradient) of the line = change in y / change in x
[tex]slope=\frac{y_{2}-y_{1} }{x_{2} -x_{1} }\\(x_{1} ,y_{1} ) = (-2,6)\\(x_{2} ,y_{2} ) = (-6,3)[/tex]
insert those coordinates in the equation:
[tex]slope=\frac{3-6}{-6-(-2)} =\frac{-3}{-4} =\frac{3}{4}[/tex]
if f(x)=3x-2/x+4 and g(x)=4x+2/3-x,prove that f and g are inverses of each other
Answers
You deposit $6000 in an account earning 6% interest compounded continuously. How much will you have in the account in 10 years?
Answers
Solution
Step 1:
Write the compounded interest continuously formula.
[tex]\text{A = Pe}^{rt}[/tex]Step 2:
Given data
P = $6000
r = 6% = 0.06
t = 10 years
Step 3:
Substitute in the formula
[tex]\begin{gathered} A\text{ = Pe}^{rt} \\ A\text{ = 6000 }\times\text{ 2.7183}^{10\times0.06} \\ A\text{ = 6000 }\times\text{ 2.7183}^{0.6} \\ A\text{ = 6000 }\times\text{ 1.822126} \\ A\text{ = \$10932.76} \end{gathered}[/tex]Final answer
A = $10933 ( nearest whole number)
1. Write a linear equation of the form y1 = mx + b for your first set of data.2. Write a linear equation of the form y2 = mx + b for the other equation in your system. 3. Graph and explain the solution.
Answers
Given:
Company A: transport 56 people in one hour for $40 per person in 30 minutes
Company B:
Calculate Sy for the arithmetic sequence in which ag = 17 and the common difference is d =-21.O A -46O B.-29.2O C. 32.7O D. 71.3
Answers
Given: An arithmetic sequaence has the following parameters
[tex]\begin{gathered} a_9=17 \\ d=-2.1 \end{gathered}[/tex]To Determine: The sum of the first 31st term.
Please note that the sum of the first 31st term is represented as
[tex]S_{31}=\text{ sum of the first 31st term}[/tex]The formula for the finding the n-term of an arithmetic sequence (AP) is
[tex]\begin{gathered} a_n=a+(n-1)d \\ \text{Where} \\ a_n=n-\text{term} \\ a=\text{first term} \\ d=\text{common difference} \end{gathered}[/tex]Since, we are given the 9th term as 17, we can calculate the first term a, as shown below:
[tex]\begin{gathered} a_9=17 \\ \text{Substituting into the formula} \\ a_9=a+(9-1)d \\ a_9=a+8d \\ \text{Therefore:} \\ a+8d=17 \\ d=-2.1 \\ a+8(-2.1)=17 \\ a-16.8=17 \\ a=17+16.8 \\ a=33.8 \end{gathered}[/tex]Calculate the sum of the first 31st term.
The formula for finding the first n-terms of an arithmetic series is given as
[tex]S_n=\frac{n}{2}(2a+(n-1)d)[/tex]We are given the following:
[tex]a=33.8,n=31,d=-2.1[/tex]Substitute the given into the formula:
[tex]\begin{gathered} S_{31}=\frac{31}{2}(2(33.8)+(31-1)-2.1) \\ S_{31}=15.5(67.6)+(30)-2.1) \\ S_{31}=15.5(67.6-63) \end{gathered}[/tex][tex]\begin{gathered} S_{31}=15.5(4.6) \\ S_{31}=71.3 \end{gathered}[/tex]Hence, the sum of the first 31st term of the A.P is 71.3, OPTION D
Are there no more tutors for mathematics, I can’t seem to find the option anymore for a tutor.
Answers
A quadratic equation is represented graphically as:
[tex]y=a(x-h)^2+k[/tex]Here the graph represents the parabola where (h,k) is the vertex of the parabola.
Put any value of h, k and a to get the graph as follows:
The graph of a quadratic equation is parabolic in nature.
Suppose that you have a quadratic equation given by:
[tex]y=x^2-5x+6[/tex]Convert the equation into perfect square by completing the square method
[tex]\begin{gathered} y=(x^2-5x+\frac{25}{4})+6-\frac{25}{4} \\ y=(x-\frac{5}{2})^2-\frac{1}{4} \end{gathered}[/tex]This is the method of conversion of quadratic to plot the graph.
A restaurant has 5 desserts, 3 side dishes and 4 main dishes. A student chooses one side dish, one main dish, and one dessert. How many different meals could he make?
Answers
30
Explanation
if the first event occurs in x ways, and the second event occurs in y ways, then two events occur in as sequence of xy ways.
so
event A ; choose (1) dessert , 5 ways
event B , chosen (1) side dish, 3 ways
event C, choose (1) main dish, 2 ways
so
a meal( 1 dessert+1 side dish+main dish) is the product of the 3 ways
[tex]\begin{gathered} \text{ways a meal could be made= (5}\cdot3\cdot2)\text{ ways} \\ \text{ways a meal could be made=}30\text{ ways} \end{gathered}[/tex]therefore, the answer is
30
I hope this helps you
use the figure at the right . if JK=5x+23 and NO=29, what is the value of x?
Answers
From the triangle midpoint theroem,
[tex]\begin{gathered} NO=\frac{1}{2}JK \\ 29=\frac{1}{2}(5x+23) \\ 58=5x+23 \\ 58-23=5x \\ 35=5x \\ x=7 \end{gathered}[/tex]3/4 = m + 1/4
What is m? m = ?
Answers
Answer 3/4 = m + 1/4 is 2/4
Explanation.3/4 = m + 1/4
m = 3/4 - 1/4
m = (3 - 1)/4
m = [tex]\frac{2}{4}[/tex]
__________________
Class: Elementary School
Lesson: Fractions
[tex]\boxed{ \colorbox{lightblue}{ \sf{ \color{blue}{ Answer By\:Cyberpresents}}}}[/tex]
The graph below shows the length of Jutta's hair over 6 months period. Each month point represents a measurement at the beginning of a month. How many inches did her hair grow between the beginning of February and the beginning of July?
Answers
Given:
Length of hair at the beginning of february is 4.1''
Length of hair at the beginning of July is 7.7''
[tex]\begin{gathered} \text{Hair grown between beginning of February an beginning of July=7.7''-4.1''} \\ =3.6^{\doubleprime} \end{gathered}[/tex]What is the solution to14h + 6 = 2(5 + 7h) - 4 ?
Answers
14h + 6 = 2(5 + 7h) - 4
First , apply distributive porperty to solve the parentheses:
14h+6 =2(5)+2(7h)-4
14h+6 = 10+14h-4
Move the "h " terms to the left:
14h-14h = 10-4-6
0 = 0
h has infinite solutions.
Find the median:1,4,2,7,3,9,5,12,4,8
Answers
Take into account that the median of a data set is given by the element of the set that is at the center of the ordered list of elements. If there is no possible to determine a central element in the list, then, you take two elements of the center and calculate the average value in between such elements.
Then, first order the elements, as follow:
1 , 2 , 3 , 4 , 4 , 5 , 7 , 8 , 9 , 12
THe number of elements is 10, then, you conisder the two elements at the center of the list, that is, the 5th and 6th elements:
1 , 2 , 3 , 4 , 4 , 5 , 7 , 8 , 9 , 12
and calculate the average in between these numbers:
median = (4 + 5)2 = 9/2 = 4.5
Hence, the median of the given data set id 4.5
Match each expression to the equivalents value. 4. i^121 A. 15. i^240 B. -16. i^90 C. -i7. i^43 D. i
Answers
Let's find the value of each expression.
[tex]undefined[/tex]Which of the sketches presented in the list of options is a reasonable graph of y = |x − 1|?
Answers
ANSWER
EXPLANATION
The parent function is y = |x|. The vertex of this function is at the origin.
When we add/subtract a constant from the variable, x, we have a horizontal translation, so the answer must be one of the first two options.
Since the constant is being subtracted from the variable, the translation is to the right. Hence, the graph of the function is the one with the vertex at (1, 0).