The equation 16x + 11y = -88 when rearranged in slope-intercept form is y = (-16/11)x - 8, with a slope of -16/11 and a y-intercept of -8.
Explanation:To write the equation 16x + 11y = -88 in slope-intercept form, we need to solve for y in terms of x. The slope-intercept form of a straight line is y = mx + b, where m is the slope and b is the y-intercept. Following the algebra of straight lines, we rearrange the equation as follows:
Subtract 16x from both sides: 11y = -16x - 88.Divide each term by 11 to solve for y: y = (-16/11)x - 8.This gives us the slope-intercept form, where the slope (m) is -16/11 and the y-intercept (b) is -8. The slope means that for every increase of 11 units in the x-direction, y decreases by 16 units. The y-intercept is the point where the line crosses the y-axis, which is at y = -8 when x = 0.
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PLEASE HELP!!!!!!!!!! Nobody will help me!! :(
Triangle ABC has the following vertices.
A( -6, 1) B(6, 1) C(6, 6)
List the sides of the triangle in order from largest length to smallest length.
CA, AB, and BC are the options that need to be placed in order.
the equation y equals 0.25 x describes a proportional relationship between X and Y what is the constant of proportionality
Quincy found 120 shells during four days at the beach. if quincy found the same number of shells each day, how many shells did he find each day?
What is the y-intercept of the line y=3x-7?
How do you construct a 112.5 degree angle? (step by step) Please help =)
Which values are solutions to the inequality below?
Check all that apply.
Sam earned $450 during winter vacation. He needs to save $180 for a camping trip over spring break. He can spend the remainder of the money on music. Write an inequality to show how much he can spend on music.
ms. galan spent 55% of her savings on a television that cost $550. how much money did she have in her savings before she bought the television
Answer:$1000
Step-by-step explanation:my frend found this
Henry has 2/3 of a bag of popcorn he eats half of the popcorn during the movie what fraction of a bag of popcorn does henry eat during the movie
Find the percent of increase from 320 to 380. Round to the nearest tenth of a percent if necessary.
Answer:
18.8% (gradpoint)
Step-by-step explanation:
The percent of increase from 320 to 380 is approximately 18.8%. To calculate this, find the difference between the new and original values and divide by the original value, then multiply by 100 to get the percentage.
To find the percent of increase from 320 to 380, use the formula:
Percentage increase =
[(new value - original value) / original value]
× 100%
Firstly, calculate the change in value: 380 - 320 = 60.
Then, plug this change into the formula:
Percentage increase = (60 / 320) × 100%
Now, compute the result:
Percentage increase = (0.1875) × 100%
Convert this to a percentage:
Percentage increase = 18.75%
Finally, round to the nearest tenth of a percent if necessary:
Percentage increase
= approximately 18.8%
Aimi is making Valentine’s Day cards for everyone in her class. She plans to use a whole sheet of paper for each of her 6 closest friends. She will use 1/8 of a sheet of paper for everyone else in the class. She has 34 sheets of paper. How many of the smaller cards can she make?
Aimi can make 224 of the smaller Valentine's Day cards after allocating a whole sheet of paper to each of her 6 closest friends, using the 34 sheets of paper she has available.
Explanation:The subject of the question is mathematics, specifically working with fractions and multiplication to solve a real-world application problem. Aimi is making Valentine's Day cards for her class and needs to calculate how many smaller cards she can make from the paper she has available. She is allocating a whole sheet of paper for each of her 6 closest friends and then needs to determine how many 1/8 sheet cards can be made with the remaining paper.
To solve this, we first calculate the amount of paper used for her close friends: 6 sheets (one for each friend). Then, we subtract this number from the total amount of paper she has, 34 sheets, leaving us with 34 - 6 = 28 sheets for the rest of the class.
The smaller cards use 1/8 of a sheet each, so we divide the remaining sheets by 1/8 to determine how many such cards she can make: 28 ÷ (1/8) = 28 × 8 = 224. Therefore, Aimi can make 224 of the smaller Valentine's Day cards.
Final answer:
After accounting for the 6 full sheets of paper used for her closest friends, Aimi can make 224 of the smaller Valentine's Day cards using the remaining 28 sheets.
Explanation:
Aimi is interested in creating Valentine's Day cards for her class and needs to determine how many of the smaller cards she can make after allocating a whole sheet of paper for each of her 6 closest friends. First, we need to calculate the total amount of paper Aimi will use for her 6 closest friends, which is 6 sheets since she is using one whole sheet per friend. Next, we'll subtract those 6 sheets from the total 34 sheets she has available, leaving us with 28 sheets for the rest of the class.
Since each of the smaller cards uses 1/8 of a sheet of paper, we'll divide the remaining sheets by 1/8 to find out how many of those cards she can make. We perform the following calculation: 28 sheets ÷ 1/8 which equals 224 cards. Therefore, Aimi can make 224 of the smaller Valentine's Day cards.
Select the term that best describes the statement.
All lines are straight or a triangle has four sides.
solve the inequality. graph the solution.
8a-15>73
How many 2.00-L bottles could be filled from a 24-can case of cola if in the United States a typical can holds 355 mL?
The number of bottles which could be filled are:
Approx 4 bottles ( since we got 4.260 )
Step-by-step explanation:One can case of cola holds- 355 mL
This means that:
24 can case of cola will hold= 24×355 mL
= 8520 mL
Also, 1 L=1000 mL
This means that:
1 mL= 0.001 L
Hence,
8520 mL= 8.520 L
Total amount of cola is: 8.520 L
Now, the number of bottles of 2 L which could be filled from this liquid is:
8.520/2=4.260 bottles.
some investments in the stock market have earned 10% annually. At this rate, earning can be found using the formula A=p(1.10)n, where A is the total value of the investment, P is the initial value of the investment, and n is the number of years the money is invested. If $1,5oo is invested in the stock market at this annual rate of return, what is the expected total value after 18 years?
A.) $29,700.00 B.) $28,050.00 C.) $8,339.88 D.) $7,581.71 I need some help on this one, I cant figure it out. I would say what I think it is, but I don't even have a good guess.
Frogs have been breeding like flies at the Enormous State University (ESU) campus! Each year, the pledge class of the Epsilon Delta fraternity is instructed to tag all the frogs residing on the ESU campus. Two years ago (t = 0) they managed to tag all 42,000 of them (with little Epsilon Delta Fraternity tags). This year's pledge class discovered that all the tags had all fallen off, and they wound up tagging a total of 54,600 frogs.
Function: 42000 (1.3^t/2)
Assuming exponential population growth, and that all this year's tags have fallen off, how many tags should Epsilon Delta order for next year?
Final answer:
Using the provided exponential growth function for frog population, 42000 (1.3^t/2), with t=3 for next year, the fraternity should order approximately 59621 tags.
Explanation:
To calculate the number of tags the Epsilon Delta fraternity should order for next year, we need to use the exponential population growth function provided: 42000 (1.3^{t/2}), where t is the number of years since the initial tagging. Since two years ago was t = 0, this year is t = 2. Next year will be t = 3.
Plugging t = 3 into the function, we get:
Tags needed = 42000 (1.3^{3/2})
This is an arithmetic problem involving an exponential function representing the population growth of frogs.
To solve the equation, first calculate 1.3^{3/2}, which is approximately 1.41907. Then multiply this by 42000 to get the number of tags needed for next year.
Tags needed ≈ 42000 * 1.41907
Tags needed ≈ 59621
So the fraternity should order approximately 59621 tags for next year.
Gilbert is graduating from college in twelve months, but he will need a loan in the amount of $5,125 for his last two semesters. He may either receive an unsubsidized Stafford Loan with an interest rate of 6.8%, compounded monthly, or his parents may get a PLUS Loan with an interest rate of 7.8%, compounded monthly. The Stafford Loan has a grace period of six months from the time of graduation. Which loan will have a higher balance at the time of repayment and by how much? (3 points)
The Stafford Loan has a higher balance by $134.35. The Stafford Loan has a higher balance by $274.36. The PLUS Loan has a higher balance by $54.79. The PLUS Loan has a higher balance by $85.22.
To determine which loan will have a higher balance at the time of repayment, we need to calculate the future value of both loans. The Stafford Loan will have a higher balance by approximately $234.36.
Explanation:To determine which loan will have a higher balance at the time of repayment, we need to calculate the future value of both loans. Let's start with the Stafford Loan:
Principal: $5,125
Interest Rate: 6.8%
Compounding Period: Monthly
Time: 12 months
Using the formula for future value of an ordinary annuity, we can calculate the balance of the Stafford Loan at the time of repayment:
FV = P * ((1 + r)^n - 1) / r
FV = 5125 * ((1 + 0.068/12)^(12*1) - 1) / (0.068/12)
Calculating this gives us an approximate loan balance of $5,259.35.
Now let's calculate the future value of the PLUS Loan:
Principal: $5,125
Interest Rate: 7.8%
Compounding Period: Monthly
Time: 12 months
Using the same formula, we can calculate the balance of the PLUS Loan at the time of repayment:
FV = P * ((1 + r)^n - 1) / r
FV = 5125 * ((1 + 0.078/12)^(12*1) - 1) / (0.078/12)
Calculating this gives us an approximate loan balance of $5,024.99.
Therefore, the Stafford Loan will have a higher balance at the time of repayment by approximately $234.36. The correct answer is: The Stafford Loan has a higher balance by $234.36.
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For the function f(x) = (x − 2)2 + 4, identify the vertex, domain, and range.
a. The vertex is (–2, 4), the domain is all real numbers, and the range is y ≥ 4.
b. The vertex is (–2, 4), the domain is all real numbers, and the range is y ≤ 4.
c. The vertex is (2, 4), the domain is all real numbers, and the range is y ≤ 4.
d.The vertex is (2, 4), the domain is all real numbers, and the range is y ≥ 4.
Answer:
The vertex is (2, 4), the domain is all real numbers, and the range is y ≥ 4.
Step-by-step explanation:
The equation of the parabola is [tex]f(x)=(x-2)^2+4[/tex]
The vertex form of the parabola is given by
[tex]f(x)=a(x-h)^2+k[/tex], here (h,k) is the vertex.
Comparing given equation with the vertex form of the parabola, we get
h = 2, k = 4
Hence, the vertex of the parabola is (h,k) = (2,4)
Now, domain is the set of x values for which the function is defined. The given function is defined for all real values of x.
Hence, domain is all real numbers.
Range is the set of y values for which the function is defined.
Since, here a = 1>0 hence it is a upward parabola and the vertex is the minimum point of this parabola.
Since, vertex is (2,4) hence, y values never less than 4.
Hence, range is y ≥ 4.
D is the correct options.
solve for d when 2x-2yd=y+xd ...?
true or false. sin(a-b) = -sin(b-a).
explain. ...?
A horseshoe weigs 8.2 ounces. The nails make up 0.2 of that weight. What is the weight of the horseshoe without the nails?
what fraction is equivalent to the expression 4/8 + 2/8
Choose the correct simplification of the expression (3x2y3z4)(2x5y2z3).
6x7y5z7
6x10y6z12
5 x7y5z7
5x10y6z12 ...?
yep, your answer is A.
Graph the function y = 2x3 – x2 – 4x + 5. To the nearest tenth, over which interval is the function decreasing?
(1, ∞)
(–∞, –0.7)
(–0.7, 1)
(–1, 0.7)
Answer:
On (-2/3, 1) the given function is decreasing
Step-by-step explanation:
Do you know calculus? If so:
Differentiate y = 2x^3 – x^2 – 4x + 5 and set the derivative = to 0:
dy/dx = 6x^2 - 2x - 4 = 0, or 3x^2 - x - 2 = 0.
This factors as follows: (x - 1)(3x + 2) = 0.
The roots of this equation are {1, -2/3}.
Plot these two roots on a number line and then set up intervals as follows:
(-infinity, -2/3), (-2/3, 1), (1, infinity)
Choose a test number from each interval: { -1, 0, 2 }
By evaluating the derivative 6x^2 - 2x - 4 at each of these three test numbers, we get:
dy/dx = 6x^2 - 2x - 4 is positive on (-infinity, -2/3), and so we conclude that the given function is increasing on that interval.
dy/dx = 6x^2 - 2x - 4 is negative on (-2/3, 1), and so we conclude that the given function is decreasing on that interval. To the nearest tenth:
(-0.7, 1)
To find where the function y = 2x^3 - x^2 - 4x + 5 is decreasing, calculate the derivative, set it less than zero, solve for x, and use a sign chart to determine the intervals where the function is decreasing. The correct interval is (1, ∞).
Explanation:To determine where the function y = 2x3 − x2 − 4x + 5 is decreasing, we need to analyze its derivative. The first derivative of the function represents the slope of the tangent line to the curve at any given point, and when this slope is negative, the function is decreasing. Let's find the first derivative, f'(x) which is 6x2 − 2x − 4. To find where f'(x) is negative, we look for the x-values that make the derivative less than zero. This inequality can be solved by looking for the critical points where the derivative equals zero or is undefined, and then testing intervals around these points to see when the derivative is negative.
By factoring or using the quadratic formula, we find the critical points of f'(x) and then use a sign chart or test values to determine where the derivative is negative. For example, if we find that the derivative switches from positive to negative at x = 1, we can conclude that the function is decreasing for x values greater than 1. Therefore, the correct answer would be that the function is decreasing over the interval (1, ∞).
According to charles law, the pressure P in pascals of a fixed volume of gas is linearly related to the temperature T in degrees celcius. In an experiment, it was found that when T =40, P=90 and when T=80, P=100.
a. What is the slope of the line containing these 2 points?
b. explain the meaning of slope in this context.
Represent the ratio 6 : 18 in two other ways ...?
What is the decimal equivalent of 11/8 ??
The solution is : 1.375 is the decimal equivalent of 11/8.
Here, we have,
given that,
equivalent of 11/8
Given the following mathematical expression;
11 / 8
We would apply the law of division for fractions.
11 / 8
= 11 ÷ 8
= 1.375
the decimal form.
Hence, The solution is : 1.375 is the decimal equivalent of 11/8.
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Please help! After five years of earning interest at an annual rate of 4%, an investment has earned $1,200 in interest. Determine the amount of the initial investment. Show all work for full credit.
What is an equation that shows that two ratios are equivalent?
An equation that shows two ratios are equivalent is a proportion. Proportions can be applied in various fields like economics to show equivalent satisfaction based on price paid for goods, or in unit conversion to represent equivalent quantities in different units.
Explanation:An equation showing that two ratios are equivalent is a proportion. A proportion is a mathematical statement that two ratios are equal. For example, 2/4 = 1/2 is a proportion because the two ratios are equivalent. Other forms of this equation could be obtained by rearranging terms, showing the direct and indirect proportions.
In a more practical context, ratios are used to compare the relationship between different quantities. For example, we could state the ratio of the prices of two goods should be equal to the ratio of the marginal utilities. When we divide the price of good 1 by the price of good 2, this should equal the marginal utility of good 1 divided by the marginal utility of good 2. This indicates that the utility or satisfaction obtained is equivalent based on the price paid.
Also, proportions can be used as a unit conversion factor where the ratio of two equivalent quantities expressed with different measurement units can lead to a conversion factor. For example, the lengths of 2.54 cm and 1 in. are equivalent, thus providing a ratio that could be used for conversion.
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PLEASE HELP Indicate the method you would use to prove the two 's . If no method applies, enter "none". SSS
SAS
ASA
None
Answer: 1) ASA
2) none
3) ASA
Step-by-step explanation:
In the first picture we have two angles and one included side of one triangle is congruent to corresponding two angles and one included side of another triangle, therefore by ASA postulate of congruence both triangles are congruent.
In the second picture , the two have two equal angles, the third angle of both triangles by using angle sum property =[tex]180^{\circ}-70^{\circ}-30^{\circ}=80^{\circ}[/tex],
Now, two corresponding angles and one included side (10 units) of both triangles are congruent therefore by ASA postulate of congruence both triangles are congruent.
In the third picture, we have two triangle with one same vertex, then their vertical angles must be congruent.
Thus, in third picture, two angles and one included side of one triangle is congruent to corresponding two angles and one included side of another triangle, therefore by ASA postulate of congruence both triangles are congruent.