The area of a rectangle with a length of 12x and a width of (x + 3) is 12x² + 36x, which is option D in the provided list of answers.
To find the area of a rectangle, you multiply the length by the width. In this case, the length is given as 12x and the width is (x + 3). Multiplying these two expressions together, you get:
Area = Length × Width
Area = 12x × (x + 3)
Now, distribute the 12x across the terms inside the parentheses:
Area = 12x × x + 12x × 3
Area = 12x² + 36x
Therefore, the area of the rectangle is 12x² + 36x, which corresponds to option D in your list of possible answers.
The correct option is D.
The area of the rectangle is 12x² + 36x.
To find the area of a rectangle, multiply its length by its width. In this case, the length is given as 12x and the width is given as (x + 3).
So, Area = Length × Width = (12x) × (x + 3).
Expanding this expression, we get:
Area = 12x² + 36x.
Therefore, the area of the rectangle is 12x² + 36x.
So, the correct answer is option D) 12x² + 36x.
Here's why:
1. Substitute the given values for length and width into the formula for the area of a rectangle.
2. Multiply the length by the width, distributing the 12x over the (x + 3).
3. Combine like terms to simplify the expression.
4. The final expression for the area is 12x² + 36x.
Solve the inequality-2(6+s)_>-15-2s
Answer:
s can take any real value.
Step-by-step explanation:
Given that
-2(6+s)_>-15-2s
Distribute -2 over 6+s
-12-2s >= -15-2s
Simplify both the sides
Add 2s to both the sides.
We get 2s cancel out and -12>=-15 which is true.
Hence the given inequality is valid for all values of s.
This is a special case of inequality which has infinite number of solutions.
s can take any real number and this inequality is valid.
Answer:
Solution of inequality: -12 ≥ -15 Which is true.
Step-by-step explanation:
Given data:
Equation:-2(6+s)_>-15-2s
-2(6+s)_>-15-2s
=-12 - 2s ≥ - 15 -2s
By dividing -2s on both sides:
= -12 - 2s/-2s ≥ - 15 -2s/-2s
= -12 ≥ -15
-2(6+s)_>-15-2s = -12 ≥ -15
a total of 360 people came to the play. there were 100 more adults than children. how many adults and how many children came to the play?
For each scenario, identify the independent and dependent variable.
1.Spending time petting an animal for an hour decreases stress levels by 10%.
2.The population of field mice doubles each hour.
3.The height of an elevator increases 10 feet for each floor it ascends.
how should anyone know this
Answer:
The independent variable is the time spent petting an animal, and the dependent variable is the stress level.
The independent variable is time, and the dependent variable is the population of field mice.
The independent variable is the number of floors ascended, and the dependent variable is the height of the elevator.
john ran 6 2/3 miles last week he ran 1 1/3 miles each day how many days did he run
[tex]6\frac{2}{3} = \frac{3(6) + 2}{3} = \frac{20}{3} miles[/tex]
[tex]1\frac{1}{3} = \frac{3(1) + 1}{3} = \frac{4}{3} miles/day[/tex]
[tex]\frac{20}{3} miles[/tex] ÷ [tex]\frac{4}{3} miles/day[/tex]
= [tex]\frac{20(miles)}{3}[/tex] * [tex]\frac{3(days)}{4 (miles)}[/tex]
= [tex]\frac{20(3) days}{3(4)} = \frac{20 days}{4} = 5 days[/tex]
Answer: 5 days
how can one logically explain the distance formula?
Final answer:
The distance formula calculates the straight-line distance between two points on a coordinate plane using the Pythagorean theorem, which is applied to the differences in the x and y coordinates of the points to form a right triangle.
Explanation:
Explaining the Distance Formula
The distance formula is a way to calculate the straight-line distance between two points in a coordinate plane. This formula is derived from the Pythagorean theorem which states that in a right-angled triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b). In other words, a² + b² = c².
To understand the distance formula, consider two points (x1, y1) and (x2, y2) on a coordinate plane. The difference in the x values (x2 - x1) and the y values (y2 - y1) represent the lengths of the legs of a right triangle, where the straight-line distance we are trying to find is the hypotenuse. Thus, by the Pythagorean theorem, the distance (d) can be found by taking the square root of the sum of the squares of these differences. The resulting distance formula is d = √((x2 - x1)² + (y2 - y1)²).
The distance formula logically extends the Pythagorean theorem to two-dimensional space, where distances on the plane are calculated irrespective of the orientation or position of the line connecting the two points.
How to do 15x28 distributive property
15 * 28 = 420. Should be your answer.
Find an equation of the line through (4,5) and parallel to y=3x+5.
GIVEN: y = 3x + 5
--> slope of given line = 3
--> This means that your equation must have the same slope, or "m"
FORMULA OF A LINE: y = mx + b
--> Use point-slope form to find "b"
POINT SLOPE FORM: y - y₁ = m ( x - x₁ )
--> Plug in your given point AND the slope of the given line
y - 5 = 3 ( x - 4 )
y - 5 = 3x - 12
y = 3x - 7
Write into an algebraic expression. Double the sum of 2 and x increased by one-half x squared.
Final answer:
The algebraic expression for 'Double the sum of 2 and x increased by one-half x squared' is 2(2 + x) + (1/2)x².
Explanation:
To translate the phrase 'Double the sum of 2 and x increased by one-half x squared' into an algebraic expression, we break it down into parts:
The sum of 2 and x is given by the expression (2 + x).
Double this sum can be written as 2(2 + x).
One-half x squared is written as (1/2)x².
Increasing the doubled sum by one-half x squared means adding (1/2)x² to it.
Therefore, the complete algebraic expression is 2(2 + x) + (1/2)x².
Regarding the concept of squaring of exponentials, remember that when you square a term like x², you are effectively raising x to the power of 4 because the exponents are multiplied.
Find the midpoint. Please and thanks.
The formula of a midpoint:
[tex]M_{AB}\left(\dfrac{x_A+x_B}{2},\ \dfrac{y_A+y_B}{2}\right)[/tex]
We have:
[tex]M(-6,\ 8)\to x_M=-6,\ y_M=8\\A(-2,\ 10)\to x_A=-2,\ y_A=10[/tex]
Substitute:
[tex]\dfrac{-2+x_B}{2}=-6\qquad|\cdot2\\\\-2+x_B=-12\qquad|+2\\\\x_B=-10\\\\\dfrac{10+y_B}{2}=8\qquad|\cdot2\\\\10+y_B=16\qquad|-10\\\\y_B=6[/tex]
Answer: B. (-10, 6)Jonathan went to the movies with$48 he earned at his after school job. The ticket cost $8.75. He spent $7.45 for refreshments. How much money did he have left
Which of these values could be the slope of the line? Check all that apply.
–2
-8/5
0
7/4
3
undefined
Answer:
7/4 or 3
Step-by-step explanation:
To determine the slope of the line , we look at the position of the line
From the given graph , the line goes up
When line goes up , the slope is positive
when a line goes down , the slope is negative
If we have a vertical line then slope is undefined
For horizontal line the slope is 0
Here the line goes up, so slope is positive
We pick the slope from the given option that is positive
7/4 or 3
A swimming pool is 50 meters long. How many times would a swimmer have to swim the length of the pool in order to swim 1 kilometer?
one lap is .05 km so it will take 20 laps
Olivia purchased x child tickets and y adult tickets at the movies. She spent a total of $46. The equation below describes the relationship between the number of child tickets and the number of adult tickets purchased. The ordered pair (4, 2) is the solution to the equation. What does the solution (4, 2) represent?
Let
x---------> the number of child tickets
y--------> the number of adult tickets
we know that
the equation that describes the relationship between the number of child tickets and the number of adult tickets is a linear equation
If the point[tex](4,2)[/tex] is the solution
then
the number of child tickets is [tex]4[/tex]
the number of adult tickets is [tex]2[/tex]
therefore
the answer is
the solution [tex](4,2)[/tex] represent that
the number of child tickets is [tex]4[/tex]
the number of adult tickets is [tex]2[/tex]
The solution (4, 2) means Olivia purchased 4 child tickets and 2 adult tickets at the movies for a total of $46.
The student's question involves interpreting the solution to a linear equation in the context of purchasing movie tickets. The specific solution given is the ordered pair (4, 2). In the context of the problem described, the number '4' represents the quantity 'x', which is the number of child tickets purchased, and the number '2' represents the quantity 'y', which is the number of adult tickets purchased. Therefore, the solution (4, 2) means that Olivia purchased 4 child tickets and 2 adult tickets at the movies for a total expenditure of $46.
Tommy has a piece of toast that has butter on one side, and he dropped it twice. Both times, it landed with the butter side up. If he drops it 2 more times, what is the probability that it will have landed butter side up a total of 3 times?
Answer: 1/2.
Explanation:
First, note that since the previous drops have already happened, their result do not modify the occurrence of future results when the toast is dropped again.
In oder to have a total of three time landing butter side up, exactly, there are two possibilities:
Since there are two ways of totaling side up 3 times, you have to sum both chances.
1) Next drop butter side up and second drop butter side down:
1/2 × 1/2 = 1/4
2) Next drop butter side down and second one butter side up:
1/2 × 1/2 = 1/4
3) Add both probabilities: 1/4 + 1/4 = 1/2
And that is the answer: 1/2
Determine the equation of the line given by the graph.
A) y = 5/7 x − 2/3
B) y = 5/7 x − 3/2
C) y = 7/5 x − 2/3
D) y = 7/5 x − 3/2
BRAINLIEST ANSWER TO FIRST ANSWERER
Which of the following are exterior angles? Check all that apply.
A. 5
B. 6
C. 2
D. 4
E. 1
F. 3
C. <2 is the correct answer
How can I do this ???? Plz help
An industrial machikne is able to make 9 pens in 3 seconds. What is the rate made per second?
This problem can be solved using proprtions. Once you set up the proportion, the calculations are easy.
Let x = number of pens made in 1 second.
[tex]\frac{9pen}{3sec} = \frac{xpen}{1 second}[/tex]
Now, you just cross multiply and solve.
9 = 3x
x = 3
The rate is 3 pens per second.
Toya can run one lap of the track on 1 minute 3 seconds, which is 90% of her younger sister niki’s time. What is niki’s time for one lap of the track?
63 seconds is 90% of Niki's time for one lap. So, Niki's time for one lap is 63/0.9, which equals 70 seconds or 1 min. 10 seconds.
Galera preciso resolver essa questão é não sei como resolvê-la me ajudem por favor
Calculate f(3) by replacing X with 3:
f(x) = x^2 -1
f(3) = 3^2 -1
F(3) = 9-1
f(3) = 8
Now calculate f(-4) by replacing x with -4:
f(x) = x^2 -1
f(-4) = (-4)^2 - 1
f(-4) = 16 -1
f(-4) = 15
Now add f(3) to f(-4)
8 + 15 = 23
The answer is a) 23
what is the answer to n-2 = 10n+4/2
n = -4/9 hope this helps
n-2=10n+4/2
We move all terms to the left:
n-2-(10n+4/2)=0
We add all the numbers together, and all the variables
n-(10n+2)-2=0
We get rid of parentheses
n-10n-2-2=0
We add all the numbers together, and all the variables
-9n-4=0
We move all terms containing n to the left, all other terms to the right
-9n=4
n=4/-9
n=-4/9
what is a fraction equation that equals 4
Any fraction that, when dividing the numerator and denominator, it'll give you 4.
For example:
8/2, which, when divided: 8/2 = 4
16/4, which, when divided: 16/4 = 4
hope this helps
~Rise Above the Ordinary
If the area of a park is exactly halfway between 2.4 and 2.5 acres, what is the area of the park
The area of the park is 2.45 acres.
The area of a park is determined to be exactly halfway between 2.4 acres and 2.5 acres. To find this midpoint or average, we add the two values together and then divide by 2.
First, we add 2.4 acres and 2.5 acres:
2.4 acres + 2.5 acres = 4.9 acres
Now, we divide this sum by 2 to find the midpoint:
Midpoint = 4.9 acres / 2 = 2.45 acres
Therefore, the area of the park is 2.45 acres. This means that it is precisely halfway between the two given values.
Understanding the midpoint or average is essential in various contexts, such as real estate, land measurement, and statistical analysis. In this case, it signifies that the park occupies an area that is equidistant from 2.4 acres and 2.5 acres. It can be seen as a balanced point between these two values, serving as a useful concept for situations where precision or fairness is required, such as in property assessments or distributing resources evenly.
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By selling old CDs, Sarah has a store credit for $153. A new CD coat $18. What are the possible numbers of new CDs Sarah can buy? (Inequalities)
We can find the maximum number of CDs she can buy by dividing 153 by 18. The answer ends up being 8.5. Since she can't buy 0.5 of a CD, she can buy a maximum of 8 CDs. Written as an inequality, I think it should be x is less than or equal to 8. I hope this helps!
help please, I'm having so much trouble! It's quite easy!
May you please help me with this question
The angle of cba is 3.408* if you wanna know
cba is 3.408 and just ask if you want to know how
*Simple math question* The eighth grade class at grade school has 15 girls and 14 boys. How many different boy-girl dates can be arranged?
The eighth grade class at grade school has 15 girls and 14 boys. The different boy-girl dates that can be arranged is 210 boy-girl.
What is the unitary method?The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.
The eighth grade class at grade school has 15 girls and 14 boys.
The different boy-girl dates can be arranged
15 x 14 = 210
210 boy-girl
Hence, The different boy-girl dates that can be arranged is 210 boy-girl.
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To determine how many different boy-girl dates can be arranged from 15 girls and 14 boys, multiply the number of boys by the number of girls, leading to 210 different boy-girl dates.
The question asks how many different boy-girl dates can be arranged if an eighth-grade class has 15 girls and 14 boys. To solve this, we can use the concept of multiplication principle in combinations. Each boy in the class has the option to date any of the 15 girls. This means each of the 14 boys has 15 choices for who to date. Therefore, to calculate the total number of distinct boy-girl date arrangements, we multiply the number of boys by the number of girls they can potentially date.
Calculating: 14 boys × 15 girls = 210 different boy-girl dates can be arranged.
This simple calculation shows how combinations are used to determine possibilities in everyday scenarios, reinforcing the importance of basic arithmetic skills in problem-solving.
Kendra is making a large salad for a party. She buys lettuce for 2.25 per pound and tomatoes for 2.65 per pound. She spends at least $8. Let x represent the number of Linda of lettuce that Kendra buys. Let y represent the number of pounds of tomatoes that Kendra buys. Which inequality represents this situation ?
Answer:
Step-by-step explanation:
Kendra buys x pounds lettuce.
If lettuce costs $2.25 per pound.
Then for x pounds of lettuce,
cost=2.25x
Kendra buys y pounds tomatoes.
If tomatoes costs $2.65 per pound.
Then for y pounds of tomatoes,
cost=2.65y
So, total cost=2.25x+2.65y
Now, this total cost will be at least $8
So, the inequality is-
[tex]2.25x+2.65y\geq8[/tex]
The problem can be represented by the inequality [tex]2.25x + 2.65y \geq 8[/tex] where x is the number of pounds of lettuce Kendra buys and y is the number of pounds of tomatoes she buys. The total cost of the vegetables equals or exceeds $8.
Explanation:In this situation of buying lettuce and tomatoes, the cost of lettuce per pound is $2.25 and the cost of tomatoes per pound is $2.65. Kendra spends at least $8 on lettuce and tomatoes. Let x represent the number of pounds of lettuce that Kendra buys and let y represent the number of pounds of tomatoes that she buys. Understanding the problem, the inequality that represents this situation is
[tex]2.25x + 2.65y \geq 8[/tex]. This is because each pound of lettuce ('x') is multiplied by its cost, and each pound of tomatoes ('y') is multiplied by its cost. If Kendra spends at least $8, then the total cost equals or exceeds $8.
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the equation y+6=1/3(x-9) is written in point-slope form. What is the equation written in slope-intercept form?
A. y= 1/3x-3
B. y=1/3x+9
C.y=1/3x-9
D. y=1/3x+3
y+6=1/3(x-9)
Moved all terms from left to right that doesn't contain y
Y=-6 +1/3x-3
Simplify
Y=1/3x-9
Your answer is c.
Answer: [tex]y=\dfrac{1}{3}x-9[/tex]
Step-by-step explanation:
The equation of a line in slope -intercept form is written as :-
[tex]y=mx+c[/tex]
The given equation : [tex]y+6=\dfrac{1}{3}(x-9)[/tex]
To write the given equation in slope - intercept form , we need to first solve the right -hand sides in the equation.
[tex]y+6=\dfrac{1}{3}(x-9)\\\\\Rightarrow\ [tex]y+6=\dfrac{1}{3}x-3\\\\\Rightarrow\ y=\dfrac{1}{3}x-3-6\\\\\Rightarrow\ y=\dfrac{1}{3}x-9[/tex]
Hence, the equation written in slope-intercept form : [tex]y=\dfrac{1}{3}x-9[/tex]
A candle is 12 inches tall and burns at a rate of 1 inch per hour. Write an equation that you could use to determine how long it would take for the candle to be 2 inches tall.