Let
x-------> the number of dinner
y-------> the number of lunch
we know that
[tex]8x+5y \leq 42[/tex] -------> equation A
[tex]x=y[/tex] ------> equation B
Substitute equation B in equation A
[tex]8[y]+5y \leq 42[/tex]
[tex]13y \leq 42[/tex]
[tex]y \leq 42/13[/tex]
[tex]y \leq 3.23[/tex]
so
the greatest number of lunch is [tex]y=3[/tex]
[tex]x=y[/tex]
Hence
the greatest number of dinner is [tex]x=3[/tex]
therefore
the greatest number of meals is
[tex]x+y=3+3=6[/tex]
the answer is
[tex]6[/tex]
Zach is 4 years older than twice his sister Maya’s age.
Let m represent Maya’s age.
Which expression represents Zach’s age?
m + 4
2m + 4
4m + 2
2m
For tax reasons, I need to create a rectangular vegetable patch with an area of exactly 50 sq. ft. The fencing for the east and west sides costs $4 per foot, and the fencing for the north and south sides costs only $2 per foot. What are the dimensions of the vegetable patch with the least expensive fence? ...?
help me with algebra 2
Final answer:
Algebra 2 involves solving simultaneous equations through a multi-step process, simplifying where possible and carefully verifying solutions to ensure reasonableness.
Explanation:
Algebra 2, typically taught in high school, involves solving simultaneous equations for unknown values. The process includes several algebraic steps, where students are advised to eliminate terms where possible to simplify the algebra and carefully check their work at each step. After finding the potential solutions, it's crucial to check the answers to ensure they are reasonable within the context of the problem. This systematic approach to solving algebraic problems, such as equations in one variable, is a methodical and critical part of Algebra 2's curriculum.
Can a cubic equation have 3 complex roots? 3 real roots? ...?
Final answer:
A cubic equation can have either three real or three complex roots (including a real root and a pair of complex conjugate roots), determined by its discriminant. Complex roots arise in pairs due to the conjugate root theorem, ensuring that the coefficients of the equation remain real.
Explanation:
A cubic equation, which is an equation of the form ax^3 + bx^2 + cx + d = 0, can indeed have 3 complex roots or 3 real roots, depending on the discriminant and the nature of the coefficients. According to the Fundamental Theorem of Algebra, every cubic equation has three roots in the complex number system, which includes real numbers as a subset.
If the discriminant is positive, the cubic equation has three distinct real roots. If the discriminant is zero, the equation has a multiple root and all its roots are real.
Equilibrium problems in mathematics may require using cube roots when finding the solution, and utilizing the correct functions on a calculator is vital for these calculations. This could be in applied sciences like chemistry or physics, where cubic equations may arise.
if the point (x, –1) is on the unit circle, what is the value of x?
Answer:
0^2 (–1)2 = 1.
Step-by-step explanation:
Raisins sell for $3.50 per pound, and granola sells for $5.90 per pound. Terri bought some raisins and some granola. The total weight was 2.1 pounds and cost $8.79.
How many pounds of raisins and how many pounds of granola did Terri buy?
A.
0.6 pounds of raisins; 1.5 pounds of granola
B.
1.1 pounds of raisins; 1 pound of granola
C.
1 pound of raisins; 1.1 pounds of granola
D.
1.5 pounds of raisins; 0.6 pounds of granola
Simplify the expression.
(8 + 7a) + 4
Answer:
its 12+7a
Step-by-step explanation:
i used the answer that was below and it was backwards! please dont use it if you want it to be correct! the correct answer is 12+7a
The GCF of the numbers in the expression (32 + 16) is . The numbers left inside the parentheses after factoring out the GCF are and .
Answer:
The answer is :
2 and 1
Step-by-step explanation:
The GCF means greatest common factor between given numbers.
The GCF of the numbers in the expression (32 + 16) is 16.
Factor each with a common factor of 16:
[tex](16\times2+16\times1)[/tex]
After factoring out 16, we have:
[tex]16(2+1)[/tex]
So the answer is :
2 and 1
Which relation is a function?
I. {(2, 4), (–1, 7), (3, 0), (5, 4)}
II. {(–3, 6), (–3, 6), (8, 6), (8, 10)}
III. {(4, 1), (–2, 5), (–8, 3), (4, 6)}
A. II only
B. I only
C. I and II
D. II and III
Mai's penny bank is 7/10 full. After she removes 200 pennies, it is 1/2 full. How many pennies can Mai's bank hold?
7x-5y=4; what does x and y equal
Clovis wants to make a surprise visit to his uncle who lives out of town. He purchases an airline ticket for $69. There is a 15% sales tax on the price of the airline ticket. In addition he must pay a baggage fee of $20. When he arrives at the airport, Clovis takes a taxi to his uncle's house which is 8 miles from the airport. The taxi fee is $2.50 per mile. If Clovis has spent a total of $123.35 for the airline ticket and taxi, at what percent of his fare did Clovis tip the taxi driver?
a.
10%
b.
15%
c.
20%
d.
25%
Answer:
20%
Step-by-step explanation:
edge 2021
In the diagram below, BC is an altitude of ABD. To the nearest whole unit, what is the length of CD?
Answer:
Actually the answer is 56, so D.
Step-by-step explanation:
To the nearest whole unit, the length of CD is approximately 4 units.
Given Information:
In triangle ABD, BC is an altitude (perpendicular) from point B to side AD.
We need to find the length of CD.
Approach:
Since BC is an altitude, triangle BCD is a right triangle with BC as one of its legs and BD as its hypotenuse.
We can use the Pythagorean theorem to relate the lengths of BC, CD, and BD.
Pythagorean Theorem: The Pythagorean theorem states that in a right triangle:[tex][ \text{Hypotenuse}^2 = \text{Leg}_1^2 + \text{Leg}_2^2 ][/tex]
Application to Triangle BCD:
Let’s denote the length of CD as (x).
BC is given as 30 units.
BD can be expressed as (BD = AB + AD), where AB is the length of the other leg.
Using Triangle ABC:
Triangle ABC is also a right triangle.
We have AC = 16 units (given).
Using the Pythagorean theorem for triangle ABC: [tex][ AB^2 + BC^2 = AC^2 \ AB^2 + 30^2 = 16^2 \ AB^2 + 900 = 256 \ AB^2 = 256 - 900 \ AB^2 = -644 ][/tex]
Since we cannot have a negative side length, we discard this solution.
Using Similar Triangles:
Notice that triangle BCD is mathematically similar to triangle ACE.
The coefficient of similarity is evident from the side CE.
We can set up the following proportion: [tex][ \frac{BC}{CD} = \frac{AC}{CE} \ \frac{30}{x} = \frac{16}{CE} \ CE = \frac{16x}{30} ][/tex]
Finding BD:
We know that (BD = AB + AD).
Since we couldn’t find AB directly, we express it in terms of CE:[tex][ AB = AC - CE = 16 - \frac{16x}{30} = \frac{480 - 16x}{30} ][/tex]
Now, we can find BD: [tex][ BD = AB + AD = \frac{480 - 16x}{30} + 16 = \frac{480 + 480 - 16x}{30} = \frac{960 - 16x}{30} ][/tex]
Applying the Pythagorean Theorem to Triangle BCD: [tex][ BD^2 = BC^2 + CD^2 \ \left(\frac{960 - 16x}{30}\right)^2 = 30^2 + x^2 \ 960^2 - 32x \cdot 960 + 256x^2 = 900x^2 + 900 \cdot 30^2 \ 960^2 - 32x \cdot 960 = 900x^2 - 900 \cdot 30^2 \ 960^2 + 900 \cdot 30^2 = 932x^2 \ x^2 = \frac{960^2 + 900 \cdot 30^2}{932} \ x \approx 3.75 ][/tex]
To the nearest whole unit, the length of CD is approximately 4 units.
If f(x) = 3a|2x – 4| – ax, where a is some constant, find f ′(2).
Answer:
so would the answer be DNE?
Step-by-step explanation:
Patty has a fish pond in her backyard. Even though the air temperature outside has change 35 degrees from sunrise to sunset, the water temperature in the fish pond has only changed 2 degrees. The reason for this lack of temperature change in the water is that it has a high
_____________.
Answer:
The reason for this lack of temperature change in the water is that it has a high specfic heat .
Step-by-step explanation:
Definition of specfic heat .
The amount of heat required per unit mass to raise the temperature by one degree Celsius .
Reason = The reason for this lack of temperature change in the water is due to hydrogen bonding present in water molecules .These hydrogen bonds takes large amount of heat gain for just 1 degree Celsius change in temperature. therefore water temperature increases slowly.
The x-intercept of the line x = 3.5 is ____? and the y-intercept of the line y = -6.5 is ____? Enter your answer as an ordered pair.
What is the measure of angle KML?
What are the real-number solutions of the equation 2x5 = 12x3 - 16x ?
Which expression represents the composition f(g(h(x))) for the functions below?
f(x) = 2x + 1
g(x) = 4x^2
h(x) = x^2
4x^4
8x^4 + 1
8x^2 + 1
(8x^2 + 1)^2
In one week, 103 students were absent,17 fewer students were absent than the week before. howe many students were absent in those two weeks?
In the first week, 120 students were absent, and in the second week, 103 students were absent. Total absentees in the two weeks are 223 students.
To determine how many students were absent in two weeks, we first need to find the number of students absent in the first week. We know that 103 students were absent in the second week and that this number is 17 fewer students than the number absent the week before.
Let the number of students absent in the first week be denoted as x.
According to the information given:
x - 17 = 103.To find x, we solve the equation:
x - 17 + 17 = 103 + 17 x = 120 students.Hence, 120 students were absent in the first week. Adding the absences from both weeks:
Total absentees in two weeks = 120 (first week) + 103 (second week) = 223 students
If the price of an item is $34 and the sales tax on it is $1.36, what is the sales-tax rate? You can use the calculator tool.
Answer:
$0.04 per $1
Step-by-step explanation:
If you pay $1.36 for $34, then the tax rate is 1.36/34=0.04
That's for each dollar value of an item, you pay $0.04
solve for x... 4(-2x+3)=-5x
Simplify equation -2b^3 +2^3
Determine which two values the following number is between.
3√176
A. 5.59 and 5.6
B. 5.6 and 5.61
C. 5.62 and 5.63
When Emma was born, she weighed 3.2 kilograms. In 2 months, she weighed
5.15 kilograms.
How much did Emma gain in her first 2 months?
**^^**
While doing a math problem in class, Jared's answer was different from his teacher's. So she had him come up and work the problem on the board. Here's Jared's work.
36.47
x 12
----------
7294
+ 3647
-----------
109.41
What was his mistake?
A>He multiplied incorrectly.
B>He left out the place holder under the 4.
C>There are not enough numbers after the decimal.
D>The sum of 7,294 and 3,647 is incorrect.
Answer:
The other answer is wrong, actually
Step-by-step explanation:
The real answer is B, He left out the place holder under the 4.
Jared did not multiply incorrectly.
square root of 85 is between what two consecutive number
Identify the like terms in the expression -4x2-2x+8+6x-9
Brandon can paint a fence in 12 hours and Elaine can paint the same fence in 11 hours. How long will they take to paint the fence if they work together?
A) 5 13/24 hr
B) 5 ¾ hr
C) 11 ½ hr
D) 5 17/23 hr
Answer:5 17/23
Step-by-step explanation:
Camille Keegan sells lamps for $105.55 that cost her $75.00. Camille's percent of markup based on the selling price is:
Markup = $105.55 - $75 = $30.55. Percentage markup based on selling price = $30.55 / $105.55 * 100% = 28.94%
Camille's percent of markup based on the selling price is calculated by finding the difference between the selling price and the cost price, dividing by the selling price, and then multiplying by 100. The calculation reveals that the markup percentage is approximately 28.94%.
Explanation:The question asks us to calculate Camille Keegan's percentage of markup based on the selling price of the lamps. The markup is the difference between the selling price and the cost price. To find the percentage of markup based on the selling price, we use the formula: (Markup / Selling Price) × 100. First, we find the markup by subtracting the cost price from the selling price, which is $105.55 - $75.00 = $30.55. Then we divide the markup by the selling price: $30.55 / $105.55. Finally, we multiply the result by 100 to get the percentage of markup based on the selling price.
Step-by-step calculation:
Therefore, Camille's percent of markup based on the selling price of the lamps is approximately 28.94%.