1.A system of two linear equations is graphed on a coordinate plane. If the system of equations has infinitely many solutions, which statement must be true?
A.On the graph, there is exactly one point (x,y) that satisfies both equations.
B.On the graph, any point (x,y) that satisfies one of the equations cannot satisfy the other equation.
C.On the graph, there are no points (x,y) that satisfy both equations.
D.On the graph, any point (x,y) that satisfies one of the equations must also satisfy the other equation.
2.Mark drank a total of 10 glasses of water and iced tea yesterday.
Each glass of water contained 8 ounces. Each glass of iced tea contained 12 ounces.
All together, he drank 96 ounces. The system of equations below models this situation.
x + y = 10
8 x + 12 y = 96
How many glasses of water did Mark drink yesterday?
A.3 glasses
B.4 glasses
C.5 glasses
D.6 glasses
Mark drank 6 classes of water. :) im probably late on answering this, sorry
What does −2/3(12c−9)+14c simplify to?
Answer:
The simplified form of the provided expression is [tex]6c+6[/tex] or [tex]6(c+1)[/tex]
Step-by-step explanation:
Consider the provided expression.
[tex]\frac{-2}{3}(12c-9)+14c[/tex]
Use the distributive property:
[tex]a(b+c)=ab+ac[/tex]
By using the above property we can simplify it as shown:
[tex]\frac{-2}{3}\times 12c-\frac{-2}{3}\times 9+14c[/tex]
[tex]-2\times 4c+2\times 3+14c[/tex]
[tex]-8c+6+14c[/tex]
Add or subtract the like terms.
[tex]6c+6[/tex] or [tex]6(c+1)[/tex]
Thus, the simplified form of the provided expression is [tex]6c+6[/tex] or [tex]6(c+1)[/tex]
The simplest form of expression by applying distributive property would be, 6 (c + 1)
Given that,
The expression is,
[tex]\dfrac{- 2}{3} (12c - 9) + 14c[/tex]
Now, used the concept of distributive property to simplify the expression,
[tex]\dfrac{- 2}{3} (12c - 9) + 14c[/tex]
Apply distributive property,
[tex][\dfrac{- 2}{3} \times 12c - (\dfrac{- 2}{3} )\times 9] + 14c[/tex]
[tex][- 2 \times 4c + 2 \times 3] + 14c[/tex]
[tex][- 8c + 6] + 14c[/tex]
Combine like terms,
[tex]- 8c + 14c + 6[/tex]
[tex]6c + 6[/tex]
Take 6 as a common term,
[tex]6 (c + 1)[/tex]
So, the solution of expression 6 (c + 1).
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1/4 + -2/3 (SIMPLIFY)
Answer:
[tex]\large\boxed{\dfrac{1}{4}+-\dfrac{2}{3}=-\dfrac{5}{12}}[/tex]
Step-by-step explanation:
[tex]\dfrac{1}{4}+\left(-\dfrac{2}{3}\right)=\dfrac{1}{4}-\dfrac{2}{3}\\\\\text{You must find the common denominator.}\\\\\text{List of multiples of 3:}\ 0,\ 3,\ 6,\ 9,\ \boxed{12},\ 15,\ ...\\\text{List of multiples of 4:}\ 0,\ 4,\ 8,\ \boxed{12},\ 16,\ ...\\\\\text{The common denominator is}\ \boxeed{12}.\\\\3\cdot4=12\\\\\dfrac{1}{4}=\dfrac{1\cdot3}{4\cdot3}=\dfrac{3}{12}\\\\\dfrac{2}{3}=\dfrac{2\cdot4}{3\cdot4}=\dfrac{8}{12}\\\\\\\dfrac{1}{4}-\dfrac{2}{3}=\dfrac{3}{12}-\dfrac{8}{12}=\dfrac{3-8}{12}=-\dfrac{5}{12}[/tex]
A disc jockey must allow time for 24 minutes of commercials every hour, along with 4 minutes for news, 3 minutes for weather, and 2 minutes for public-service announcements. If each record lasts and average of 3 minutes, how many records per hour can the DJ play?
what is 4 1/2 divided by 3
Subtract 9 from z. 9-Z, Or Z-9
Which equation can be used to find the number of wolves in the state on January 1? A zoologist is recording the loss of wolves in her state. She notes the number of wolves, w, in the state on January 1. One year later, there were 84 wolves in the state, which is 23 fewer wolves than were in the state a year earlier. What is the number of wolves in the state on January 1? w−84=−23 w−23=84 23−w=84 w + 23 = 84
Answer: w - 23 = 84
Step-by-step explanation:
What is the average rate of change of f(x) = −2x + 1 from x = −5 to x = 1?
Answer:-2
Step-by-step explanation:
the quotient of a number and three is equal to negative eight
A package of breadcrumbs to feed the ducks at the duck pond costs $0.25. How many packages of bread crumbs could be bought with $23.50
You are standing above the point (5,4)(5,4) on the surface z=15−(2x2+3y2)z=15−(2x2+3y2). (a) in which direction should you walk to descend fastest? (give your answer as a unit 2-vector.)
To descend fastest from the point (5,4) on the surface z=15-(2x^2+3y^2), you should walk in the direction of the negative gradient vector, normalized to be a unit vector, which is approximately <0.640, 0.768>.
Explanation:To determine the direction in which you should walk to descend fastest from the point (5,4) on the surface z=15-(2x^2+3y^2), we can find the gradient of the surface at that point. The gradient vector will point in the direction of the steepest ascent, so the direction of the steepest descent is the opposite direction of the gradient vector.
First, calculate the partial derivatives of z with respect to x and y:
∂z/∂x = -4x
∂z/∂y = -6y
Next, evaluate these derivatives at the point (5,4):
∂z/∂x(5,4) = -4(5) = -20
∂z/∂y(5,4) = -6(4) = -24
The gradient vector at (5,4) is <-20, -24>. To get the direction of steepest descent, we take the negative of the gradient vector, which is <20, 24>.
Finally, normalize this vector to make it a unit vector (so it has a length of 1):
Length of gradient vector = √(20^2 + 24^2) = √(400 + 576) = √976 ≈ 31.24
The unit vector in the direction of steepest descent is <20/31.24, 24/31.24> ≈ <0.640, 0.768>.
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A 7 pound bag of grass seed covers 2,000 square feet. How many pounds would be needed to cover 35,000 square feet? Round your answer to the nearest pound.
35000 / 2000 = 17.5
17.5 * 7 = 122.5 pounds round to 123 pounds are needed
A Pitcher of fruit punch holds 2 gallons , If 9 people share the entire pitcher equally how much punch does ecah person get
the senior is having a car wash to raise money. They can wash about 35 cars in 5 hours. if they are washing the same number of cars each hour, how many cars do they wash in 1 hour
Hello!
your answer is 75 • $6 - $35
next time add the answers too for these questions that's why the other guy didn't give you the right answer
Help me asap!!! :) please
Mark you a brainly!
30 /10 = 3
so multiply 9 by 3
9*3 = 27
9/10 = 27/30
a = 27
For integer values of a and b, b^a = 8. The ratio of a to b is equivalent to the ratio of c to d, where c and d are integers. What is the value of c when d = 10?
To find the value of c when d = 10, we first need to determine the values of a and b. Given that b^a = 8, we know that 8 is the result of raising b to the power of a.
Since the question states that a and b are integers, there are a limited number of possibilities to consider. Let's examine the possible combinations of a and b that satisfy this equation: [tex]1^3 = 1 2^3 = 8 3^2 = 9[/tex](which is not 8) [tex]4^2 = 16[/tex] (which is not 8) [tex]5^1 = 5 6^1 = 6 7^1 = 7 8^1 = 8[/tex]From these calculations, we find that the only combination that satisfies the equation is a = 3 and b = 2. Now, let's consider the ratio of a to b and the ratio of c to d.
The ratio of a to b is a/b = 3/2. The question states that the ratio of a to b is equivalent to the ratio of c to d, which means: a/b = c/d Given that d = 10, we can substitute the value into the equation: [tex]3/2 = c/10[/tex] Next, we can cross-multiply to solve for c: [tex]3 * 10 = 2 * c 30 = 2[/tex] c Dividing both sides by 2, we get: c = 15 Therefore, when d = 10, the value of c is 15. In conclusion, when d = 10, the value of c is 15 based on the given equation and calculations.
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A water tank holds 24000 gallons. How many hours will it take for 2/3 of the water to be used if the water is used at an average rate of 650 gallons a day?
The complex number z = –1 + 3i can be expressed in trigonometric form as:
A hollow ball is made of rubber that is 1 centimeter thick. The ball has a radius of 5 centimeters at the outside surface.
What is the approximate volume of rubber used to make the ball?
Answer: I got the same answer. It's 255.4 cm3
Step-by-step explanation:
Name all sets of numbers to which each real number belongs
A real number can belong to several sets of numbers, including the integers, rationals, irrationals, and reals. Integers are the set of whole numbers and their negatives, rationals can be expressed as a fraction of two integers, irrationals cannot be expressed as a fraction, and reals represent all possible numbers on the number line.
Explanation:A real number can belong to several sets of numbers, including the integers, rationals, irrationals, and reals.
Integers are the set of whole numbers and their negatives, including zero. They don't include fractions or decimals.
Rationals are the set of numbers that can be expressed as a fraction of two integers, like 3/4 or -5/2.
Irrationals are the set of numbers that cannot be expressed as a fraction, like √2 or π.
Reals represent all possible numbers on the number line, including integers, rationals, and irrationals.
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there is a 20% markup on a tv if the tv is $450 before the markup what is the cost after the markup
The number of Adult tickets is the same as the number of Child (age 5-12) tickets. A total of 38 tickets was purchased. What is the total cost of the tickets? Explain.
Data: Adult Tickets $23
Child Tickets $17
Under 5 $8
f (x) = x5 − 8x4 + 21x3 − 12x2 − 22x + 20 Three roots of this polynomial function are −1, 1, and 3 + i. Which of the following describes the number and nature of all the roots of this function?
f (x) has two real roots and one imaginary root.
f (x) has three real roots.
f (x) has five real roots.
f (x) has three real roots and two imaginary roots.
Answer:
It's D on edge.
The f(x) has three real roots and two imaginary roots option (D) is correct.
What is polynomial?Polynomial is the combination of variables and constants systematically with "n" number of power in ascending or descending order.
[tex]\rm a_1x+a_2x^2+a_3x^3+a_4x^4..........a_nx^n[/tex]
We have a polynomial:
f(x) = x⁵ − 8x⁴ + 21x³ − 12x² − 22x + 20
The three roots of this polynomial function are −1, 1, and 3 + i.
We can write the function in a factored form:
f(x) = (x - 1)(x⁴ - 7x³ + 14x² +2x - 20)
Again factoring the above polynomial:
f(x) = (x - 1)(x + 1)(x - 2)(x² -6x + 10)
The roots of the polynomial are
x - 1 = 0
x = 1
x + 1 = 0
x = -1
x - 2 = 0
x = 2
x² - 6x + 10 = 0
The above quadratic equation has two complex roots.
x = 3 + i
x = 3 - i
Thus, the f(x) has three real roots and two imaginary roots option (D) is correct.
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What are the answers for both drop downs the first one is asking for 3.113 and the second is asking for 1.2795
What is the measure of the smallest angle?
52°
61°
67°
69°
Answer:
52° is ur answer
Step-by-step explanation:
I just did the quiz so i know
Is m=0.75d-2 proportional?
Answer:
No, the equation m=0.75d-2 does not represent proportional relationship.
Step-by-step explanation:
The given equation is
[tex]m=0.75d-2[/tex]
We need to check whether the given equation represents proportional relationship or not.
If variable y is proportional to variable x, then
[tex]y\propto x[/tex]
[tex]y=kx[/tex]
where, k is the constant of proportionality.
At x=0 the value of y is 0. It means, if a linear equation represents proportional relationship then it must be passes though the origin.
Substitute d=0 in the given equation.
[tex]m=0.75(0)-2[/tex]
[tex]m=-2[/tex]
The line passes through the point (0,-2).
Since the line does not pass through the origin, therefore it does not represent proportional relationship.
whats the awnser is it 600
3600/300 = 12
4800/400 = 12
the common ratio is 12 so divide pounds of milk by 12 to get pounds pf ice cream
6000 / 12 = 500
Answer is B
Mr.Chaves spent $199.99 for a new smart phone $39.99 on a carrying case, and $59.99 on accesiories. The expression l-199.99l+l39.99l+l59.99l represents the total amount that Mr.Chaves spent. How much did he spend all together.
First answer will get brainiliest
It is estimated that there are 10^20 grains of sand on a beach in Florida in April. The beach is heavily eroded by tourists over the peak summer holiday season. Approximately one hundredth of the beach is removed as a result of this erosion. How many grains of sand are removed from the beach?
Answer:
c
Step-by-step explanation:
____ provides a greater degree of security by implementing port-based authentication. ieee 802.3ad ieee 802.11n ieee 802.1x ieee 802.1z