Answer:
523.33 cubic inches
Step-by-step explanation:
1. Solve the system by substitution- 2x+y=-11, 3x-4y=11.
Answers are:
C
B
B
C
A
Thank you so much T-T
Roy realized that some other conditions or constraints apply. Write an inequality for each constraint described below.
which would not be a step in solving 5x + 15 + 2x = 24 + 4x?
A. Isolate the variable.
B. Collect variable terms on one side.
C. Collect like terms.
D. Use the distributive property.
The step that would not be necessary in solving 5x + 15 + 2x = 24 + 4x is D. Use the distributive property.
What is an equation?An equation is a pair of algebraic equations with the equal sign (=) in the middle and the same value.
To solve the equation 5x + 15 + 2x = 24 + 4x, we need to simplify and manipulate the equation to isolate the variable on one side.
First, we can combine like terms:
5x + 2x - 4x = 24 - 15
3x = 9
Then, we can isolate x by dividing both sides by 3:
x = 3
Therefore, the correct steps to solve this equation are:
B. Collect variable terms on one side.
C. Collect like terms.
A. Isolate the variable.
We do not need to use the distributive property in this problem.
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The total area or NC is 53,800 square miles. Land accounts for 48800 square miles. What percent of North Carolina is covered in water?
9.3% of North Carolina is covered in water.
What is Area?The area is the entire amount of space occupied by a flat (2-D) surface or an object's form. On a sheet of paper, draw a square using a pencil. It has two dimensions. The area of a form on paper is the area that it occupies.
To find the percent of North Carolina covered in water, we need to subtract the land area from the total area, and then express the result as a percentage.
The water area is:
53,800 - 48,800 = 5,000 square miles
To express this as a percentage, we need to divide the water area by the total area and then multiply by 100:
(5,000 / 53,800) x 100 = 9.3%
Therefore, 9.3% of North Carolina is covered in water.
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Four consecutive integers that total -86
things you cant assume from a diagram
Each small square on the grid is 1 ft².
Which estimate best describes the area of this figure?
25 ft²
35 ft²
50 ft²
65 ft²
see the attached figure to better understand the problem
we know that
the area of the figure is the area of the square minus the areas marked with x
area of the square is equal to
[tex]A1=8*8=64\ ft^{2}[/tex]
the areas marked with x is equal to
[tex]A2=15\ ft^{2}[/tex]
so
the area of the figure is
[tex]A=A1-A2 \\ A=64-15=49\ ft^{2}[/tex]
therefore
the answer is
[tex]50\ ft^{2}[/tex]
Answer: here is the k12 test answer
Step-by-step explanation:
"The perimeter of a swimming pool is 126 feet. The difference between the length (x) and width (y) of the pool is 39 feet. What are the dimensions of the pool?"
I'm supposed to figure this out using substitution but I'm not sure how, and any help at all is appreciated!
The dimensions of the swimming pool are 51 feet (length) and 12 feet (width), determined by setting up equations based on the given information (perimeter and difference between the sides) and solving these equations using substitution.
Explanation:The problem at hand is a classic algebraic word problem. It involves determining the length (x) and width (y) of a swimming pool given the perimeter and the difference between the length and width. The formulas we'll use are for the perimeter of a rectangle (2x + 2y = perimeter) and a given equation based on the description (x - y = difference).
Step-by-step Solution
From the question, we know the perimeter of the swimming pool is 126 feet. We express this using the perimeter formula: 2x + 2y = 126. Likewise, we know the difference between the length and the width is 39 feet. This can be expressed as: x - y = 39. We want to use substitution to solve these equations. This means, we need to isolate one of the variables in the second equation. Let's isolate x by rewriting the second equation as: x = y + 39. Now, we can substitute (y + 39) for x in our perimeter equation: 2(y + 39) + 2y = 126. This simplifies to: 4y + 78 = 126. Solving for y, we get: y = 12 feet. Substitute y = 12 into our isolated equation from step 3, we get x = 12 + 39 = 51 feet.
So the dimensions of the swimming pool are 51 feet (length) and 12 feet (width).
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point P coordinates (-6,6) and P' is it's reflection across the x axis
Kyle has 125 marbles. Fifty of these marbles are red and the rest are other colors. What is the ratio of the number of red marbles to the total number of marbles expressed in simplest terms?
Answer:
2/5
Step-by-step explanation:
its asking in "simplest terms" so you would divide the number of marbles Kyle has by the 50 red marbles. 125 divide by 50 is 2.5 which equals to 2/5.
So 2/5 will be your answer. Hope this helps <3
Math problem...
375
x 6
------
The mathematics question asks to multiply the numbers 375 and 6. By following the multiplication process, we find the answer to be 2250, which is a basic arithmetic operation in middle school mathematics.
The student has presented a multiplication problem, which is a basic arithmetic operation in mathematics. The problem can be solved by multiplying the two numbers given, 375 and 6. The calculation goes as follows:
Multiply the digit in the one's place of the bottom number (6) by each digit of the top number (375), starting from the one's place of the top number.
Write down the result of each multiplication and carry over any tens if necessary.
After you complete the multiplication process, add any carried-over numbers to the resultant product.
The completed multiplication should give you the final answer to the problem.
Example Calculation:
375
x 6
------
2250
Here, the answer to the multiplication problem is 2250.
Suppose we build a sequence of numbers using the method of adding the previous two numbers to build the next one. this time, however, suppose our first two numbers are 2 and 1. generate the first 15 terms. this sequence is called the lucas sequence and is written as l1, l2, l3 , …. compute the quotients of consecutive terms of the lucas sequence as we did with the fibonacci numbers. what number do these quotients approach? what role do the initial values play in determining what number the quotients approach? try two other first terms and generate a sequence. what do the quotients approach?
The sequence is given below:
What is sequence?A sequence is an enumerated collection of objects in which repetitions are allowed and order matters.
Given:
The table showing the sequence of the first 15 terms is:
Sequence Term Quotient
1 2 2
2 1 2 (2 / 1)
3 3 (2 + 1) 0.333 (1 / 3)
4 4 (1 + 3) 0.750 (3 / 4)
5 7 (3 + 4) 0.571 (4 / 7)
6 11 (4 + 7) 0.633 (7 / 11)
7 18 (7 + 11) 0.611 (11 / 18)
8 29 (11 + 18) 0.621 (18 / 29)
9 47 (18 + 29) 0.617 (29 / 47)
10 76 (29 + 47) 0.618 (47 / 76)
11 123 (47 + 76) 0.618 (76 / 123)
12 199 (76 + 123) 0.618 (123 / 199)
13 322 (123 + 199) 0.618 (199 / 322)
14 521 (199 + 322) 0.618 (322 / 521)
15 843 (322 + 521) 0.618 (521 / 843)
The quotient converges around the value of 0.618, as shown in the above table.
The preceding sequence is a Lucas adaptation of the so-called Fibonacci sequence, where the initial two numbers serve as seeds and result in the quotient known as the "Golden Ratio," which is created by adding the previous two consecutive terms in each term.
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Ollie is catering a dinner party for more than 26 guests. Each guest has a choice between a vegetarian dinner or a steak dinner. The vegetarian dinner is $20 per plate and the steak dinner is $30 per plate. Ollie can spend no more than $690 on the entire party. If Ollie wants to purchase the most amount of food and still stay within budget, which combination of vegetarian and steak dinners is optimal?
Gustavo and Aiden are walking due west through the forest when they happen upon an angry grizzly bear. Gustavo runs away 2 3 23 ∘ 23, degree north of east for 3 0 0 300m300, space, m, and Aiden runs away 3 3 33 ∘ 33, degree south of east for 2 5 0 250m250, space, m. How far are Gustavo and Aiden away from each other?
We can actually solve this problem using the cosine law. We know that Gustavo ran 23° above the horizontal, while Aiden ran 33° below, hence the total angle between them is 56°. Therefore the distance between them is:
c^2 = a^2 + b^2 – 2 a b cos θ
c^2 = (300)^2 + (250)^2 – 2 (300) (250) cos 56
c^2 = 68,621.06
c = 262 m
They are 262 meters apart.
Gustavo ran 23° above the east horizontal, while Aiden ran 33° below the east horizontal. So, they are 262 meters apart.
What is a cosine law?Cosine law is a formula relating the length of the sides of a triangle to the cosine of one angle of the triangle.
Gustavo ran 23° above the east horizontal, while Aiden ran 33° below the east horizontal.
The total angle between them = 23 + 33 = 56°.
Let the distance between them be c. by using cosine law we have,
c² = a² + b² – 2ab cos θ
Where a and b are distances traveled by Gustavo and Aiden. θ is the angle between them.
Therefore,
[tex]c^2 = a^2 + b^2 - 2 a b cos \theta[/tex]
[tex]c^2 = (300)^2 + (250)^2 -2 (300) (250) cos 56[/tex]
[tex]c^2 = 68,621.06[/tex]
c = 262 m
Thus, the distance between them is 262 meters.
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How do you find the answer for 7x-(3x+8)
What is the mathematical sentence for 7 is subtracted from a number y. then the result is multiplied by 3. the final answer is less than or equal to 12?
Use geometry to evaluate the integral from 0 to 6 of the function f of x, dx for f of x equals 3 for x less than or equal to 3 and equals the quantity 6 minus x for x greater than 3.
27
13.5
12
10.5
Final answer:
To evaluate the given integral, split the function at x = 3 and integrate separately. The integral evaluates to 18, which makes the correct answer 18.
Explanation:
The function we're integrating is 1, which makes this the same integral as the one in example 3 on p. 178. To evaluate this integral, we need to split it at x = 3 and integrate the corresponding functions separately.
For x ≤ 3, the function is f(x) = 3. So, the integral from 0 to 3 of 3 dx equals 9.
For x > 3, the function is f(x) = 6 - x. Integrate this from 3 to 6: ∫(6 - x) dx = 6x - 0.5x^2. Evaluating this from 3 to 6 gives 9.
In right triangle ABC, B = 51° and AB = 14.
BC = _____
8.8
10.8
11.3
Given: the triangle is a right triangle, find a.
(The side opposite angle A.)
Answer:
a = 8.8104 ≈ 8.8
Step-by-step explanation:
∠A = ?, ∠B = 51°, ∠C = 90°
∠A = 180° - ( ∠B + ∠C )
∠A = 180° - ( 51° + 90° ) = 180° - 39°
∠A = 39°
[tex]\frac{a}{sin A}=\frac{b}{sin B} =\frac{c}{sin C}\\\\\frac{a}{sin39degrees}=\frac{14}{sin90degrees}\\\\\frac{14}{sin90degrees}*sin39degrees\\\\= 14 * 0.629\\= 8.8104[/tex]
So side a or BC = 8.8
The sophomore class sold a total of 700 adult and student tickets to the school play. adult tickets sold for $4.50 each, and student tickets cost $2.00 each. if they took in a total of $1,200, which system of equations can be used to find x, the number of student tickets sold, and y, the number of adult tickets sold
Answer:
Step-by-step explanation:
Given that the sophomore class sold a total of 700 adult and student tickets to the school play. adult tickets sold for $4.50 each, and student tickets cost $2.00 each.
Total = 1200
x, the number of student tickets sold, and y, the number of adult tickets sold
Then we have
[tex]x+y =700\\4.5x+2y = 1200[/tex]
These are the system to solve for x
The longer base of isosceles trapezoid is 12 cm. the side is 5 cm. the acute angle is 37º. find the shorter base.
The shorter base of the isosceles trapezoid is approximately 6 cm.
Explanation:To find the shorter base of the isosceles trapezoid, we need to use the properties of the trapezoid. Firstly, let's draw the isosceles trapezoid and label the given information.
The longer base is 12 cm, the side is 5 cm, and the acute angle is 37º. We can see that the trapezoid has two congruent triangles, and we can find the height of the triangle using trigonometry.
Step 1: Find the height of the triangle using the sine of the acute angle.
sine(37º) = opposite / hypotenuse
sin(37º) = h / 5
h = 5 * sin(37º) ≈ 3 cm
Step 2: Use the height to find the shorter base of the trapezoid.
The shorter base can be found by subtracting twice the height from the longer base.
shorter base = longer base - 2 * height
shorter base = 12 cm - 2 * 3 cm
shorter base = 12 cm - 6 cm
shorter base ≈ 6 cm
Therefore, the shorter base of the isosceles trapezoid is approximately 6 cm.
Which of the following best represents the average speed of a fast runner? (1 point) 10 meters per second 10 miles per minute 10 centimeters per hour 10 kilometers per second
Answer:
10 meters per second
Step-by-step explanation:
Great question, it is always good to ask away and get rid of any doubts that you may be having.
The best representation would be 10 meters per second. Usain Bolt, The fastest person person alive runs at approximately 12.5 meters per second.
10 miles per minute would be insanely fast. That is equivalent to 600 miles per hour, no human can run at that speed. Cars do not even reach that speed. Same goes for 10 kilometers per second.
10 centimeters per hour is incredibly slow. Although 470 times faster than a snail it is incredibly slow for a human.
I hope this answered your question. If you have any more questions feel free to ask away at Brainly.
Number 16. Solve the problem. Correct answer will get brainliest
What is the runner’s average rate of change between the hours: 0.5 and 2? mph 1.5 and 2.5? mph Average Rate of Change
Answer:
4mph
5mph
slower
Step-by-step explanation:
i did it
To calculate the average rate of change, divide the total change in distance by the total change in time. Without the specific distance covered in the given durations, it's impossible to provide absolute answers, but an example calculation has been given using an average speed of 9.5 mph.
Explanation:In your question, the average rate of change refers to the change in distance with respect to time, also known as velocity or speed. Since there are no concrete values mentioned in your question for the distances covered by a runner between time 0.5 and 2 hours, and 1.5 to 2.5 hours, it would be impossible to provide an accurate answer without such data.
However, allow me to explain how you could calculate these values. If you assume that a runner has the marathon runner's average speed of 9.5 miles per hour, then the average rate of change, or average speed, over a certain time period is just the total change in distance divided by the total change in time. For instance, if the runner covered 9.5 miles between 0.5 and 2 hours, then the average rate of change would be 9.5 miles per 1.5 hours, or approximately 6.33 mph. This same method would apply to calculations between 1.5 and 2.5 hours.
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HELP WITH SOLVING SYSTEMS WITH THREE VARIABLES, WILL MEDAL
-2x + 2y +3z = 0
-2x - y + z = -3
2x + 3y + 3z = 5
I'm not sure how to work it out, I have to do it by elimination
Which of the following equations is an example of a direct variation?
x + 2y = 6
x = 4
y = 3
y = 3.14 x
Answer:
Step-by-step explanation:
y=3.14x
Which equation shows how to find the product of 100,000 and 1,000,000 using scientific notation?
Answer:
[tex]10^5 * 10^6 = 10^{5+6} = 10^{11}[/tex]
Step-by-step explanation:
find the product of 100,000 and 1,000,000 using scientific notation
All whole numbers have a decimal point at the end
convert each number into scientific notation. To get scientific notation move the decimal point after 1
100000. -----> 1.00000 ----> 1* 10^5 ----> 10^5
1000000. -----> 1.000000 ----> 1* 10^6 ----> 10^6
a^m * a^n = a^m+n
[tex]10^5 * 10^6 = 10^{5+6} = 10^{11}[/tex]
Given f(x) and g(x) = f(x) + k, look at the graph below and determine the value of k.
k = ______
Can you explain how to figure this out?
Ohhhhh! I have a math Brainliest
Ken and roberta each sold fifty tickets for the school play. the cost of a student ticket was three fourths the cost of an adult ticket. roberta sold ten more student tickets that adult tickets and collected a total of $212.50.
a. how many tickets did roberta sell?
b. what was the cost of a student ticket?
c. if ken collected $200 in all, how many student tickets did he sell?
Roberta sold 30 tickets in total, with 10 adult tickets and 20 student tickets. The cost of a student ticket was $3. Ken collected $200 in total and sold 20 student tickets.
Explanation:To solve this problem, we can set up two equations based on the given information. Let's use variables to represent the unknown quantities.
Let's say the cost of an adult ticket is A dollars. Then the cost of a student ticket would be 3/4 of A dollars, or (3/4)A dollars.
Based on the information given, we can set up the following equations:
Robera sold 10 more student tickets than adult tickets, so let's say she sold X adult tickets and X + 10 student tickets.
The total collected by Roberta was $212.50, so we have the equation:
(A * X) + ((3/4)A * (X + 10)) = $212.50
Ken sold 50 tickets in total, so he sold 50 - (X + 10) student tickets. The total collected by Ken was $200, so we have the equation:
((3/4)A * (50 - (X + 10))) + (A * X) = $200
Now we can solve these equations to find the values of X and A.
Plugging in A = 4, we get X = 10. Therefore, Roberta sold 10 adult tickets and 20 student tickets. The cost of a student ticket was (3/4) * 4 = $3.
In conclusion, Roberta sold 30 tickets in total, with 10 adult tickets and 20 student tickets. The cost of a student ticket was $3. Ken collected $200 in total and sold 20 student tickets.
Which expression is equal to (x+2)(−3x2+3x+1)?
−3x2−3x+2
−3x2+5x+3
−3x3−3x2+7x+2
−3x3+9x2−5x+2
Option C is correct. The required product of the functions is -3x³ - 3x² + 7x + 2
Given the functions (x+2) and (-3x² + 3x + 1)
Taking the product of the functions:
= (x+2)(-3x² + 3x + 1)
Expand the bracket
= x(-3x²) + x(3x) + x(1) + 2(-3x²) + 2(3x) + 2(1)
= -3x³ + 3x² + x - 6x² + 6x + 2
Collect the like terms;
= -3x³ + 3x² - 6x²+ x + 6x + 2
= -3x³ - 3x² + 7x + 2
Hence the required product of the functions is -3x³ - 3x² + 7x + 2
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