graph of 12x+6y=432 & 9x+3y=270
The line \(12x + 6y = 432\) is represented by the red line, and the line equation \(9x + 3y = 270\)is represented by the blue line. The point where these two lines intersect is (36,0).
What is equation?In mathematics, an equation is an assertion that affirms the equivalence of two factors. An algebraic equation (=) separates two sides of an equation. For instance, the assertion \("2x + 3 = 9"\)states that the word "2x + 3" corresponds to the number "9". The goal of solution solving is to figure out which variable(s) must still be adjusted for the equations to be true. It is possible to have simple or intricate equations, recurring or complex equations, and equations with one or more components. For example, in the equations" \(x^2 + 2x - 3 = 0\)," the variable x is lifted to the powercell. Lines are utilised in many areas of mathematics, include algebra, arithmetic, and geometry.
To plot these lines on a graph, we first need to solve for y in terms of x for each equation.
can plot these lines
\(12x+6y 4326y=-12x+432y = -2x+729x+3y=2703y=9x+270y=-3x+90\)
\(|100|_ | . | . 90|_ . | . | .80|_ . | . | .70|_ . | . | .60 |___________________________________________ 0 30 60 90 120 150 180 210 240 270 300\)
The line\(12x + 6y = 432\)is represented by the red line, and the line 9x + 3y = 270 is represented by the blue line. The point where these two lines intersect is (36,0).
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Find the x-value for point C such that AC and BC from a 2:3 ratio.
Given:
Point C divides AB such that AC:BC=2:3.
To find:
The x-value for point C.
Solution:
Section formula: If a point divide a line segment in m:n, then
\(Point=\left(\dfrac{mx_2+nx_1}{m+n},\dfrac{my_2+ny_1}{m+n}\right)\)
Form the given graph it is clear that the endpoints of the line segment AB are A(-3,5) and B(3,0).
Point C divides AB such that AC:BC=2:3. Using section formula, the coordinates of point C are
\(C=\left(\dfrac{2(3)+3(-3)}{2+3},\dfrac{2(0)+3(5)}{2+3}\right)\)
\(C=\left(\dfrac{6-9}{5},\dfrac{0+15}{5}\right)\)
\(C=\left(\dfrac{-3}{5},\dfrac{15}{5}\right)\)
\(C=\left(-0.6,3\right)\)
The x-value of C is -0.6.
Therefore, the correct option is B.
heyy, please help! Thank you
Answer:
9
Step-by-step explanation:
3-(-6)=9
Hi there! :)
Answer:
\(\huge\boxed{q -r = 9}\)
q = 3
r = -6
q - r = 3 - (-6) = 9
Please help school is ending soon!Two days later, Kelly surveyed the same 13 classmates and found that none of them had been given math homework since she last surveyed them. By how much does the mean of Kelly’s second data set change in comparison with the mean of the data set in her original survey? Explain how to determine the change in the means without calculating the mean of either data set.
Since none of the 13 classmates had been given math homework between the original survey and Kelly's second survey, the sum of the values in the second data set is the same as the sum of the values in the original data set. Therefore, the change in the means can be determined without calculating the mean of either data set by considering the number of data points in each set.
Since both data sets have the same number of data points, the change in the means will be zero. This is because the mean is calculated by dividing the sum of the values by the number of data points, and since the sum of the values is the same in both data sets, the means will also be the same.
In other words, the change in the mean is calculated as follows:
Change in mean = Mean of second data set - Mean of first data set
Since none of the values in the second data set have changed, the mean of the second data set is the same as the mean of the first data set. Therefore, the change in the mean is:
Change in mean = Mean of second data set - Mean of first data set
= Mean of first data set - Mean of first data set
= 0
Thus, the change in the means between Kelly's original survey and her second survey is zero.
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what is the area under the standard normal curve between + 1 standard deviations and +2.5 standard deviation
The approximate probability of getting a z-score between +1 standard deviation and +2.5 standard deviations in a standard normal distribution is 0.1525.
What is the process to find the area under the standard normal curve between +1 standard deviation and +2.5 standard deviations?To find the area under the standard normal curve between +1 standard deviation and +2.5 standard deviations, we can use a standard normal distribution table or calculator. Here are the steps:
Find the area to the right of +1 standard deviation using the standard normal distribution table or calculator.Therefore, the area under the standard normal curve between +1 standard deviation and +2.5 standard deviations is approximately 0.1525.
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Factor the following expressions completely. Show and check all work on your own paper.
x^4 - 16
thx so much I will give brainiest
Answer:
(x² + 4)(x + 2)(x - 2)------------------------------
Factor the given expression, using the difference of squares identity:
a² - b² = (a + b)(a - b)Factoring in below steps:
x⁴ - 16 = (x²)² - 4² = (x² + 4)(x² - 4) = (x² + 4)(x² - 2²) = (x² + 4)(x + 2)(x - 2)A community recreational center has 500 ft of fencing with which to enclose a rectangular parking lot in the back of the property. The building itself will be used as one of the sides of the enclosed area.
What is the maximum area that can be enclosed by the fencing?
If the building itself will be used as one of the sides of the enclosed area. The maximum area that can be enclosed by the fencing is: 31,250ft².
How to find the maximum area?Let the area be x ft long
Let the width be (500 -x )/2
Hence,
x × (500 - x)/2 = -1/2x² + 250x
When,
x = 250
So,
Maximum area =-1/2 × 250² +250 ×250
Maximum area = -31,250ft + 62,500ft
Maximum area = 31,250ft²
Therefore 31,250ft² is the maximum area.
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Find the angle measures for each angle.
Based on angle relationship, the measures for each angle are:
m∠1 = 103°; m∠4 = 103°; m∠7 = 103°; m∠5 = 77°; m∠6 = 77°; m∠3 = 77°; m∠2 = 77°.
How to Find Angle Measures?The relationship between angles that are formed by two paralleled lines and a transversal can be used to determine the measures of each of the angles.
Using angles relationship, we have:
Angle 1 = 103° [corresponding angles are equal]
Angle 4 = 103° [alternate interior angles are equal]
Angle 7 = 103° [vertical angles are equal]
Angle 5 = 180 - 103 = 77° [supplementary angles]
Angle 6 = angle 5 = 77° [vertical angles are equal]
Angle 3 = angle 5 = 77° [alternate interior angles are equal]
Angle 2 = angle 5 = 77° [corresponding angles are equal]
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The formula d = rt gives the distance, d, traveled in time, t, at rate, r. A motorcycle traveled 67.2 mi in 1.2 h. What was its average speed (rate)? 30 mph 56 mph 66 mph 80 mph
Answer:
56mph
Step-by-step explanation:
If d=rt,
then s=d/t,
so if d=67.2 and t=1.2,
then 67.2/1.2=56
Scale Factor: 1/2; Center: point N
The new coordinates of points M and O is determined as;
M = (0.5, - 1)
O = (2.5, -2).
What is the new coordinate of points of M and O?The new coordinate of points M and O after applying the scale factor is calculated as follows;
The given scale factor = 1/2
The current coordinates of point M and O is;
M = (1, - 2)
O = (5, - 4)
A scale factor can be used to either enlarge a figure or decrease a figure.
When the scale factor is less than 1, it means the new figure will be smaller than the original figure.
However, if the scale factor is greater than 1, the new figure will be greater than the original figure.
The new coordinates of points M and O is determined as follows;
M = (1 x 1/2, -2 x 1/2) = (0.5, - 1)
O = (5 x 1/2, -4 x 1/2) = (2.5, -2)
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what is a better deal 12 cans for $0.88 each or 16 cans for $ 0.85 each
16 cans for .85 cents is a better deal because it is less cents per can than there is in the other deal. May I please be the brainiest? I have never been that and I would love it
PLEASEEE HELP !!
Matching equations with diagrams & finding unknown ancies
is on line WY. Find the value of b.
Which equation(s) and angemeurerents go with the
diagram. Choose ALL that apply
(Select all that apply.)
Answer: b+95+34=180, b+129=180, 51
Step-by-step explanation:
b+95+34=180 works because the angles add to form a straight angle.
From this, we can obtain b+129=180 by adding the two constants.
Subtracting 129 from both sides, we get b=51.
Type a simplified fraction as an answer. PLEASE ANSWER I AM BEGGING!!!!!!
Answer:
0.06944444444 as a fraction equals 6944444444/100000000000
Find the unit rates (pages per day) for Deon and Emily. Who read faster?
Deon: 36 pages in 3 days
Emily: 45 pages in 5 days
36 pages
3 days
?
pages per day
45 pages
5 days
?
pages per day
Deon read
pages per day than Emily.
Answer:
Deon: 12 pages/day
Emily: 9 pages/day
Deon's read faster.
Step-by-step explanation:
Deon: 36 pages in 3 days
(36 pages)/(3 days) = 12 pages/day
Emily: 45 pages in 5 days
(45 pages)/(5 days) = 9 pages/day
Deon's read faster.
Answer:
Deon read _3 more __ pages per day than Emily.
Step-by-step explanation:
3) In recent years, a growing array of entertainment options competes for consumer time. By 2004 , cable television and radio surpassed broadcast television, recorded music, and the daily newspaper to become the two entertainment media with the greatest usage (The Wall Street Journal, January 26, 2004). Researchers used a sample of 10 individuals and collected data on the hours per week spent watching cable television and hours per week spent listening to the radio. Use a .05 level of significance and test for a difference between the population mean usage for cable television and radio.
A study conducted in 2004 examined the usage of cable television and radio among 10 individuals to determine if there was a significant difference in the average hours spent on each medium. Using a significance level of 0.05, statistical analysis was performed to test for a disparity between the population mean usage of cable television and radio.
The researchers collected data on the number of hours per week spent watching cable television and listening to the radio from a sample of 10 individuals. The objective was to determine if there was a significant difference in the average usage between cable television and radio, considering the increasing competition among various entertainment options.
To test for a difference between the population mean usage for cable television and radio, a statistical hypothesis test was conducted. The significance level (α) of 0.05 was chosen, which means that the results would be considered statistically significant if the probability of obtaining such extreme results by chance alone was less than 5%.
The test compared the means of the two samples, namely the average hours spent watching cable television and listening to the radio. By analyzing the data using appropriate statistical techniques, such as a two-sample t-test, the researchers determined whether the observed difference in means was statistically significant or could be attributed to random variation.
After conducting the hypothesis test, if the p-value associated with the test statistic was less than 0.05, it would indicate that there was a significant difference between the population mean usage of cable television and radio. Conversely, if the p-value was greater than 0.05, there would be insufficient evidence to conclude a significant disparity.
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Find the slope of the line that passes through the points A(-3, 1) and B(2, -5).
Answer:
\(m = \frac{ - 5 - 1}{2 - ( - 3)} = - \frac{6}{5} \)
The length of each edge of a cube is x centimeters. If x is an integer, why can't the volume of the cube equal 15cm. Show work please
Let's try some integer values of x to see what volumes we get
If x = 0, then x^3 = 0^3 = 0*0*0 = 0If x = 1, then x^3 = 1^3 = 1*1*1 = 1If x = 2, then x^3 = 2^3 = 2*2*2 = 8If x = 3, then x^3 = 3^3 = 3*3*3 = 27We do not get 15 as a result in that list above. So there are no integer solutions to x^3 = 15
In other words, the value \(\sqrt[3]{15}\) is not an integer.
There are 15 chairs arranged evenly around t tables. Choose the expression that shows how many chairs are at each table.
Answer:
15/t
Step-by-step explanation:
15 chairs per table
(/) is used instead of the word 'per'
Use completing the square to solve this quadratic equation x^2+8x+16=2
Answer:
x = -4 ± √2
Step-by-step explanation:
x^2+8x+16=2
(x + 4)^2 = 2
x + 4 = ±√2
x = -4 ± √2
Which is the better buy?
Frozen Peas
Cost (dollars)
Weight (ounces)
O Brand A
A B
2
16
3
28
O Brand B
O The unit cost is the same.
The better buy is given by the following brand:
Brand A.
How to obtain the better buy?The better buy is obtained applying the proportions in the context of the problem.
A proportion is applied as the cost per ounce is given dividing the total cost by the number of ounces.
Then the better buy is given by the option with the lowest cost per ounce.
The cost per ounce for each brand is given as follows:
Brand A: 16/2 = $8 per ounce.Brand B: 28/3 = $9.3 per ounce.$8 per ounce is a lesser cost than $9.3 per ounce, hence the better buy is given by Brand A.
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suppose that $1,000 is deposited into an account that yields 0.85% interest, compounded annually? how much money will be in that account at the end of 4 years?
The money in the account at the end of the 4 years is $1034
What is compound interest?
Compound interest, also known as interest on principal and interest, is the practice of adding interest to the principal amount of a loan or deposit.
Now we are given that the initial amount deposited in the account is $1000
This account is giving 0.85% And we have to figure out how much amount will be there
We use compound interest formula to find the amount
\(A= P(1+r/n)^{nt}\\\\A= 1000(1+0.0085)^{4}\\A = 1000(1.034)\\A= 1034\)
Hence the amount will be after 4 years is $1034.
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What is the rate of change of the linear relationship modeled in the table? x y 1 2 3 5 5 8 7 11 (4 points) Group of answer choices negative three over two two over three three over two 1
Option C : The slope is constant for all three pairs of points, we can conclude that the rate of change of the linear relationship is 3/2.
To find the rate of change of a linear relationship, you need to calculate the slope of the line that represents the relationship. The slope of a line can be calculated as the change in y divided by the change in x between any two points on the line.
The rate of change of a linear relationship is equal to its slope.
Using the points (1, 2) and (3, 5) to calculate the slope:
slope = (change in y) / (change in x) = (5 - 2) / (3 - 1) = 3/2
Using the points (3, 5) and (5, 8) to calculate the slope:
slope = (change in y) / (change in x) = (8 - 5) / (5 - 3) = 3/2
Using the points (5, 8) and (7, 11) to calculate the slope:
slope = (change in y) / (change in x) = (11 - 8) / (7 - 5) = 3/2
This means that for every increase of 1 in x, the y value increases by 3/2. So the rate of change of the linear relationship is 3/2 or "three over two". Therefore, the rate of change of the linear relationship is 3/2.
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What is the rate of change of the linear relationship modeled in the table?
x y
1 2
3 5
5 8
7 11
Group of answer choices
A. negative three over two
B. two over three
C. three over two
D. 1
Round 81.469 to 1 decimal place.
81.469 correct to one Decimal place is 81.5
Hope This Helps You ❤️You will need 120 feet of fencing to put all the way around a rectangular garden. The
length of the garden is 40 feet. What is the width?
Answer:
Width=3
Step-by-step explanation:
Rectangle is width times height.
Therefore, height is perimeter divided by width.
120/40 = 3, so 3 is our width
Using the picture below, which angle is alternate exterior to angle 2?
Suppose James has a credit card with a balance of $4289. Each month, the credit card company charges 5% interest. James pays off all new purchases that he makes each month without paying off the old balance or its interest. He wants to know what the balance on his credit card will be one year from now. Is this situation an example of exponential growth or exponential decay?
The balance on his credit card will be the amount of $4076.56 one year from now.
What is the simple interest?Simple interest is defined as interest paid on the original principal and calculated with the following formula:
S.I. = P × R × T, where P = Principal, R = Rate of Interest in % per annum, and T = Time, usually calculated as the number of years. The rate of interest is in percentage r% and is to be written as r/100
First, we must compute James' monthly charges on his balance of 4289.
Principal = 4289
Rate = 5%
Time = 1 month = 1/12 year
Simple interest = 4289×5×1/12×100 = 17.87
The monthly charge is 17.87,
So the yearly charge would be: 12 × 17.87 = $214.44
His credit card balance one year from now = Principal - Interest
⇒ 4289 - 214.44
⇒ 4076.56
In one year, his credit card amount will be 4076.56.
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WILL GIVE BRAINLIEST (PLEASE SHOW WORK)
Evaluate sec (11pi/6) without using technology
what is the value of b
Answer:
Step-by-step explanation:
b is an inscribed angle. The rule for this is that the measure of an inscribed angle is half the measure of the arc it intercepts. The arc it intercepts is 56 degrees, so the measure of angle b is half of that at 28
ILL GIVE BRAINLIEST TO WHOEVER ANSWERS AND EXPLAINS!! HELP QUICK!
Answer:
4 or 8
Step-by-step explanation:
Find the equation for the
following parabola.
- Vertex (2,-1)
- Focus (2, 3)
A. (x-2)² = (y + 1)
B. (x-2)² = 16 (y + 1)²
C. (x-2)² = 4(y + 1)
D. (x-2)² = 16 (y + 1)
Answer:
\(\tt{D. (x-2)² = 16 (y + 1)}\)
Step-by-step explanation:
In order to find the equation of a parabola given its vertex and focus, we can use the standard form equation for a parabola:
\(\boxed{\bold{\tt{(x - h)^2 = 4p(y - k)}}}\)
where (h, k) represents the vertex and p is the distance between the vertex and the focus.
In this case, the vertex is (2, -1) and the focus is (2, 3).
The x-coordinate of the vertex and focus are the same, which tells us that the parabola opens vertically. Therefore, the equation will have the form:
\(\tt{(x - 2)^2 = 4p(y - (-1))}\)
Simplifying further:
\(\tt{(x - 2)^2 = 4p(y + 1)}\)
Now we need to find the value of p, which is the distance between the vertex and the focus.
The distance formula between two points (x₁, y₁) and (x₂, y₂) is given by:
\(\boxed{\bold{\tt{Distance = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}}}}\)
Using this formula, we can calculate the distance between the vertex (2, -1) and the focus (2, 3):
\(\boxed{\bold{\tt{Distance = \sqrt{(2- 2)^2 + (3 -(+1))^2}}}}\)
\(\boxed{\bold{\tt{Distance = \sqrt{4^2}}}}\)
Distance 4
Therefore, p = 4. Substituting this value back into the equation, we get:
\(\tt{(x - 2)^2 = 4(4)(y + 1)}\)
\(\tt{(x - 2)^2 = 16(y + 1)}\)
So, the equation of the parabola is\(\tt{ (x - 2)^2 = 16(y + 1)}\)