Answer:B 1/3
Step-by-step explanation:
3/9=1/3
The probability that the selected marble is Green for the considered case is given by: Option B: 1/3
How to calculate the probability of an event?Suppose that there are finite elementary events in the sample space of the considered experiment, and all are equally likely.
Then, suppose we want to find the probability of an event E.
Then, its probability is given as
[tex]P(E) = \dfrac{\text{Number of favorable cases}}{\text{Number of total cases}} = \dfrac{n(E)}{n(S)}[/tex]
where favorable cases are those elementary events who belong to E, and total cases are the size of the sample space.
Given that:
Bag has 3 green, 3 red, and 3 blue marbles.A marble is selected at random.To find: P(selected marble is green)
Take:
E = event that a marble selected at random is green.
Numbre of cases in which E can be done is 3 (as there are 3 green marbles).
Number of total cases = 3+3+3 = 9 (total 9 marbles, each can come as an outcome).
Thus, we get:
[tex]P(E) = \dfrac{\text{Number of favorable cases}}{\text{Number of total cases}} = \dfrac{n(E)}{n(S)} = \dfrac{3}{9} = 1/3[/tex]
Thus, the probability that the selected marble is Green for the considered case is given by: Option B: 1/3
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A plane flies 2,342 miles on Monday. On Tuesday, it flies 586 more miles than on monday. What is the total number of miles the plane flies on Monday and Tuesday?
Answer:
I think it's 2,928 but i don't know if i'm right
if i'm right can you make in the brainliest
Answer:
2,928 miles
Step-by-step explanation:
To find the total add the two numbers (2342 + 586) to arrive at the answer
Which of the following numbers is 90 divisible by? 2,3,4,5,6,9,10
Answer:
2,3,5,6,9,10
Step-by-step explanation:
To do this, we can look at how each value divides into 90. If it produces a whole number, they will be consider to be divisible
[tex]90/2=45\\\\90/3=30\\\\90/4=22.5\\\\90/5=18\\\\90/6=15\\\\90/9=10\\\\90/10=9[/tex]
This means 4 is the only value that is not divisible into 90
Answer:
2, 3, 5, 6, 9, 10
Step-by-step explanation:
We are to determine which numbers is 90 divisible by:
[tex]2,3,4,5,6,9,10[/tex]
For this, we can use the divisibility rule which helps us find out whether a number is exactly divisible by other numbers (i.e. there is no remainder left).
Divisible by 2:
90 is divisible by 2 since it ends with a 0.
Divisible by 3:
90 is divisible by 3 because 90 is a multiple pf 3.
Divisible by 4:
90 is not divisible by 4 because the last two digits are not a multiple of 4
or the last two digits are not 00.
Divisible by 5:
90 is divisible by 5 since it ends with a 0.
Divisible by 6:
90 is divisible by 6 because it is divisible by 3.
Divisible by 9:
90 is divisible by 9 because it is a multiple of 9.
Divisible by 10:
90 is divisible by 10 since the last digit is 0.
The parent function, f(x) = 5x, has been vertically compressed by a factor of one-fourth, shifted to the right three units and up two units. Choose the correct function to represent the transformation
The correct function to represent the transformation of the parent function f(x) = 5x, after being vertically compressed by a factor of one-fourth, shifted to the right three units, and up two units, is g(x) = 1.25(x - 3) + 2.
To find the transformed function of the parent function f(x) = 5x after a series of transformations, we must apply the following transformations step by step:
Vertically compress by a factor of one-fourth, which means we multiply the output by 1/4 or 0.25. Therefore, f(x) becomes f(x) = (1/4) * 5x = 1.25x.
Shift to the right three units, which means we replace x with (x - 3). Therefore, our function becomes f(x - 3) = 1.25(x - 3).
Shift up two units, which means we add 2 to the function's output. Our function now becomes f(x - 3) + 2 = 1.25(x - 3) + 2.
Putting it all together, the function that represents the transformation is g(x) = 1.25(x - 3) + 2.
Winston pays $8 for a burger, an order of fries, and a soft drink. Tia buys 2 burgers and a soft drink for $10.50. George buys 2 orders of fries, a burger, and 2 soft drinks for $12. Let x, y, and z represent the cost of a burger, an order of fries, and a soft drink, respectively. If A is the coefficient matrix of the system of equations modeling this situation, identify the inverse matrix, A-1, and the solution matrix, X, of the system of equations.
Answer:
[tex]A^{-1}=\left[\begin{array}{ccc}2&0&-1\\3&-1&-1\\-4&1&2\end{array}\right][/tex]
X = 4
Step-by-step explanation:
* At first lets revise how to find the inverse of 3 × 3 matrix
- To find the inverse of a 3 x 3 matrix,
# first calculate the determinant of the matrix.
- If the determinant is 0, the matrix has no inverse.
# Second, transpose the matrix by rewriting the first row as the first
column, the middle row as the middle column, and the third row
as the third column.
# Third, Find the determinant of each of the 2 x 2 minor matrices,
- To find the right minor matrix for each term, first highlight the row
and column of the term you begin with. This should include five
terms of the matrix. The remaining four terms make up the
minor matrix.
- Find the determinant of each minor matrix by cross-multiplying
the diagonals and subtracting
# Fourth, create the matrix of cofactors.
- Place the results of the previous step into a new matrix of
co-factors by aligning each minor matrix determinant with the
corresponding position in the original matrix
- When assigning signs, the first element of the first row keeps its
original sign. The second element is reversed. The third element
keeps its original sign. Continue on with the rest of the matrix
- The final result of this step is called the Adj matrix of the original
# The inverse matrix = 1/determinant × Adj matrix
* Now lets find the matrix A from the story problem
∵ x, y, and z represent the cost of a burger, an order of fries, and
a soft drink
- Order of Winston: x + y + z = 8
- Order of Tia: 2x + z = 10.50
- Order of George: x + 2y + 2z = 12
* Lets make the matrix A
# [tex]A=\left[\begin{array}{ccc}1&1&1\\2&0&1\\1&2&2\end{array}\right][/tex]
# Determinant of A = 1(0×2 - 1×2) - 1(2×2 - 1×1) + 1(2×2 - 0×1)
∴ Determinant of A = 1(-2) - 1(3) + 1(4) = -2 - 3 + 4 = -1
* Lets transposed A
# [tex]A^{T}=\left[\begin{array}{ccc}1&2&1\\1&0&2\\1&1&2\end{array}\right][/tex]
* Lets find the minor matrix for each term
- The 1st row
# (0×2 - 2×1) = -2 , (1×2 - 2×1) = 0 , (1×1 - 0×1) = 1
- The 2nd row
# (2×2 - 1×1) = 3 , (1×2 - 1×1) = 1 , (1×1 - 2×1) = -1
- The 3rd row
# (2×2 - 1×0) = 4 , (1×2 - 1×1) = 1 , (1×0 - 2×1) = -2
* Lets Make Adj A
# [tex]AdjA=\left[\begin{array}{ccc}-2&0&1\\3&1&-1\\4&1&-2\end{array}\right] *\left[\begin{array}{ccc}+&-&+\\-&+&-\\+&-&+\end{array}\right]=\left[\begin{array}{ccc}-2&0&1\\-3&1&1\\4&-1&-2\end{array}\right][/tex]
* Lets write inverse of A
# [tex]A^{-1}=\frac{1}{-1}\left[\begin{array}{ccc}-2&0&1\\-3&1&1\\4&-1&-2\end{array}\right]=\left[\begin{array}{ccc}2&0&-1\\3&-1&-1\\-4&1&2\end{array}\right][/tex]
* Now lets find the solution matrix for X
# [tex]A_{x}=\left[\begin{array}{ccc}8&1&1\\10.5&0&1\\12&2&2\end{array}\right][/tex]
∴ Ax = 8(0×2 - 1×2) - 1(10.5×2 - 1×12) + 1(10.5×2 - 0×12)
∴ Ax = -16 - 9 + 21 = -4
* Lets find the value of X
∵ X = Ax/A
∴ X = -4/-1 = 4
The costs: burger ($3), fries ($1.50), and soft drink ($3.50). We used the inverse matrix A⁻¹ to solve the system Aˣ=b.
Let's define the system of equations based on the given information:
Burger + Fries + Soft Drink = $82 Burgers + Soft Drink = $10.502 Fries + Burger + 2 Soft Drinks = $12This can be written as:
x + y + z = 82x + 0y + z = 10.50x + 2y + 2z = 12In matrix form, this is:
A * X = BWhere:
[tex]A = \left[\begin{array}{ccc}1&1&1\\2&0&1\\1&2&2\end{array}\right][/tex]
[tex]X = \left[\begin{array}{c}x\\y\\z\end{array}\right][/tex]
[tex]B = \left[\begin{array}{c}8\\10.5\\12\end{array}\right][/tex]
The inverse matrix A-1 is found using matrix inversion methods. Let's denote A⁻¹:
[tex]A^{-1} = \left[\begin{array}{ccc}[2&-2.5&0.5\\-1&1.5&-0.5\\0&0&1\end{array}\right][/tex]
The solution matrix X is:
X = A⁻¹ * BAfter performing matrix multiplication:
[tex]X = \left[\begin{array}{ccc}[2&-2.5&0.5\\-1&1.5&-0.5\\0&0&1\end{array}\right] * \left[\begin{array}{c}8\\10.5\\12\end{array}\right] = \left[\begin{array}{c}3\\1.5\\3.5\end{array}\right][/tex]
Therefore, the cost of a burger is $3, an order of fries is $1.50, and a soft drink is $3.50.
3^c=1/27
Please help!!!
c = - 3
Hope this helps!
What is 120 divided by 1/6?
Answer:
120 divided by 1/6= 720
Step-by-step explanation:
120 divided by 1/6
When we divide by a fraction , we change the division to multiplication .
To divide 120 by a fraction 1/6.
We take reciprocal of 1/6 and multiply with 120
Reciprocal of 1/6 is 6/1
[tex]\frac{120}{\frac{1}{6} } = 120 * \frac{6}{1} = 720[/tex]
120 divided by 1/6 equals 720, which is found by multiplying 120 by the reciprocal of 1/6.
To find what 120 divided by 1/6 is, you use the principle of division of fractions.
In this case, you multiply 120 by the reciprocal of 1/6. The reciprocal of 1/6 is 6/1, or simply 6.
Therefore, the calculation you need to perform is:
120 × 6 = 720
This means that 120 divided by 1/6 equals 720.
The answer pls pls pls place
Answer:
A
Step-by-step explanation:
The equation of a parabola is y = ax² + bx + c : a ≠ 0
Given
y = 2 (x + 4)² - 7 ← expand the squared factor
y = 2(x² + 8x + 16) - 7 ← distribute the parenthesis by 2
y = 2x² + 16x + 32 - 7 ← collect constant terms
y = 2x² + 16x + 25 → A
What does 6÷3/4 equal
Answer:
8
Step-by-step explanation:
When you divide by a fraction, you can also say that you are multiplying by the reciprocal.
So [tex]6/\frac{3}{4}=6*\frac{4}{3}[/tex]
[tex]6=\frac{6}{1}[/tex]
[tex]\frac{6}{1}*\frac{4}{3}=\frac{24}{3}=8[/tex]
Estimate a line of best fit using two points on the line
A.y=-1/2x+9
B.y=2x+9
C.y=-2x+9
D.y=1/2x+9
Your answer is A.
y = -1/2x + 9
Answer:
Option A is correct.
Step-by-step explanation:
Given Two points on line are ( 2 , 8 ) & ( 8 , 5 )
We have to find A line of best fit for the graph using these two points.
We find the equation of line using two point form,
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]
So,
[tex]y-8=\frac{5-8}{8-2}(x-2)[/tex]
[tex]y-8=\frac{-3}{6}(x-2)[/tex]
[tex]y-8=\frac{-1}{2}(x-2)[/tex]
[tex]y-8=\frac{-1}{2}x-\frac{-1}{2}\times2[/tex]
[tex]y-8=\frac{-1}{2}x+1[/tex]
[tex]y=\frac{-1}{2}x+1+8[/tex]
[tex]y=\frac{-1}{2}x+9[/tex]
Therefore, Option A is correct.
Attachment Below 25 Points Thanks.
The side of a square is the square root of the area.
Side = √196
Side = 14 inches.
Which table of values does NOT represent a function?
the second one. the same value of x cannot go to two different y’s. if you plotted them on a graph they would not pass the vertical line test :)
Answer:
The second one.
Step-by-step explanation:
The values in the x variable are both 2's but have different y values. Therefore it's not an actual function.
A leaky faucet had already dripped 3 cups of water before it was discovered to be leaky. It leaked at a rate of 3/4 cup per hour. How long did it leak before it was discovered?
3/1 divided by 3/4 = 3/1 times 4/3. Multiply across to get 12/3 which = 4. It dripped for 4 hours.
A rectangular greenhouse has an area of 6,480 square meters. Its length is 120 meters.
The width of the greenhouse is
meters. If each flower bed needs an area of 240 square meters, the whole greenhouse can hold
flower beds
Answer:
the greenhouse can hold 27 flower beds.
Step-by-step explanation:
[tex]6480 \div 240 = 27[/tex]
if you need the width of the greenhouse, its
[tex]6480 \div 120 = 54[/tex]
For 5 and 6 plsssssssss
Answer:
is 5.?=5 and for 6.?=18
Step-by-step explanation:
Please solve this it is needed ASAP. Thanks.
So I don't remember how to do IQR or MAD but I can help you with the rest for the garter snake (hopefully I'll explain it well enough so that you can do the water snake on your own.
Mean: Add all the numbers together then divide the sum by the number of integers given
26 +30+22+15+21+24+28+32+24+25+18+35 = 300
If you count there are a total of 12 numbers so you have to divide 300 by 12
300 / 12 = 25
Median: Put the numbers in order from lest to greatest then find the number in the middle
^^^What I do for this is start on the out side and take away one on both sides each "round" until I reach the middle (Does that make sense?)
15 18 21 22 24 24 25 26 28 30 32 35
18 21 22 24 24 25 26 28 30 32
21 22 24 24 25 26 28 30
22 24 24 25 26 28
24 24 25 26
24 25
^^^Now this is tricky because there are two number remaining instead of one, so you have to find which number is in between the two left. This one is easy (the middle of 24 and 25 is 24.5) since they are only one number apart, but if it is more difficult what you do is take the mean of those two remaining numbers
24 +25 = 49
49 / 2 = 24.5
Mode: Which number appears the most often in the set of data?
15 18 21 22 24 24 25 26 28 30 32 35
24 appears two times in the data where the rest of the numbers appear only once therefore 24 is the mode of this set of data
Range: Subtract the largest number by the smallest number
Largest number: 35
Smallest number: 15
35 - 15 = 20
Hope this helpd!
Scott makes a scale drawing of a rectangular park. He uses the scale 5 centimeters: 3 meters. The length of his drawing is 20 centimeters and the width is 15 centimeters. What is the area of the park
Answer:
The area of the park is [tex]108\ m^{2}[/tex]
Step-by-step explanation:
we know that
The scale drawing is [tex]\frac{5}{3}\frac{cm}{m}[/tex]
step 1
Find the actual length of the rectangular park
Divide the length in the drawing by the scale drawing
[tex]20/(5/3)=12\ m[/tex]
step 2
Find the actual width of the rectangular park
Divide the width in the drawing by the scale drawing
[tex]15/(5/3)=9\ m[/tex]
step 3
Find the area of the park
[tex]A=(12)(9)=108\ m^{2}[/tex]
Determine the equation for the given line in slope intercept form.
Answer:
y = - [tex]\frac{3}{5}[/tex] x - 1
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Calculate m using the slope formula
m = (y₂ - y₁ ) / (x₂ - x₁ )
with (x₁, y₁ ) = (5, - 4) and (x₂, y₂ ) = (0, - 1) ← 2 points on the line
m = [tex]\frac{-1+4}{0-5}[/tex] = [tex]\frac{3}{-5}[/tex] = - [tex]\frac{3}{5}[/tex]
Note the line crosses the y- axis at (0, - 1) ⇒ c = - 1
y = - [tex]\frac{3}{5}[/tex] x - 1 ← equation in slope- intercept form
In mathematics, the slope-intercept form is a linear equation format represented as y = mx + b. In this equation, 'y' is the dependent variable, 'x' is the independent variable, 'm' is the slope or rate of change, and 'b' is the y-intercept, the point where the line intersects the y-axis. The equation of the line in slope-intercept form is y = -x + 2.
The equation of the line in slope-intercept form is y = -x + 2.
To determine the equation of the line, we can use the following steps:
Find the slope of the line.
Find the y-intercept of the line.
Substitute the slope and y-intercept into the slope-intercept form equation.
Step 1: Find the slope of the line
The slope of the line is the change in y divided by the change in x. We can find the slope of the line by choosing two points on the line and calculating the change in y divided by the change in x between those two points.
For example, we can choose the points (2, 2) and (6, -2).
slope = (y2 - y1) / (x2 - x1)
slope = (-2 - 2) / (6 - 2)
slope = -4 / 4
slope = -1
Step 2: Find the y-intercept of the line
The y-intercept of the line is the point where the line crosses the y-axis. We can find the y-intercept of the line by looking at the graph and finding the y-value of the point where the line crosses the y-axis.
In this case, the line crosses the y-axis at the point (0, 2). Therefore, the y-intercept of the line is 2.
Step 3: Substitute the slope and y-intercept into the slope-intercept form equation
The slope-intercept form equation is y = mx + b. In this case, the slope (m) is -1 and the y-intercept (b) is 2.
Therefore, the equation of the line in slope-intercept form is y = -x + 2.
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Find the image of NPQ under the translation of (x,y) -> (x + 8, y + 1).
Which triangle shows the image of NPQ after the translation?
Answer:
The image triangle NPQ is triangle KLM
Step-by-step explanation:
The vertices of triangle NPQ are at:
N(-7,-6), P(-4,-3) an Q(-4,-6).
The rule for the translation is:
[tex](x,y)\to(x+8,y+1)[/tex]
This implies that:
[tex]N(-7,-6)\to (-7+8,-6+1)=N'(1,-5)[/tex]
[tex]P(-4,-3)\to (-4+8,-3+1)=P'(4,-2)[/tex]
[tex]Q(-4,-6)\to (-4+8,-6+1)=Q'(4,-5)[/tex]
Therefore triangle N'P'Q' has vertices at N'(1,-5),P'(4,-2), and Q'(4,-5)
This coincides with K(1,-5),L(4,-2), and M(4,-5)
Hence the image triangle NPQ is triangle KLM
what is 1 pluse 1 i donk know tghis because i am only 6 yeasrs old oay
Answer:
2
Step-by-step explanation:
Because 1 ball + 1 Ball = 2 Ball
plz help thank you very much!
Answer:
(1, - 4 )
Step-by-step explanation:
To find the y- coordinate, substitute x = 1 into the equation
y = (3 × 1) - 7 = 3 - 7 = - 4
The missing value is -4.
Since you already know that x = 1, substitute that into the equation and simplify. y = 3(1) - 7
Anything times 1 equals itself. y = 3 - 7
Subtract. y = -4
the solution to the inequality 3(2x-1)>4x-2 can be written as x>n what is the value of n
Answer:
[tex]\large\boxed{x>\dfrac{1}{2}}[/tex]
Step-by-step explanation:
[tex]3(2x-1)>4x-2\qquad\text{use the distributive property}\ a(b+c)=ab+ac\\\\(3)(2x)+(3)(-1)>4x-2\\\\6x-3>4x-2\qquad\text{subtract 4x from both sides}\\\\2x-3>-2\qquad\text{add 3 to both sides}\\\\2x>1\qquad\text{divide both sides by 2}\\\\x>\dfrac{1}{2}[/tex]
To write the polynomial −x^3 + x^4 + x − x^2 in standard form, which term should go first?
A. the linear term
B. the cubic term
C. the constant term
D. the quartic term
Answer: OPTION D
Step-by-step explanation:
To express a polynomial in Standard form, you need to see the exponent of each term of the polynomial and then order the polynomial from highest exponent to lowest exponent.
Therefore, for the polynomial [tex]-x^3 + x^4 + x - x^2[/tex], you can see that the term that thas the highest exponent is x⁴ (The quartic term).
Then, this polynomial written in Standard form is:
[tex]x^4 - x^3 - x^2+x[/tex]
Therefore, the term that should go first is: the quartic term.
potential rational roots of f(x) = x4 – 2x3 + 5x2 – 7x + 9
Answer:
To quickly solve this problem, we can use a graphing tool or a calculator to plot the equation.
Please see the attached images below, to find more information about the graph
The equation is:
f(x) = x^4 – 2x^3 + 5x^2 – 7x + 9
The equation has only complex roots.
Answer:
+1,+3,+9
Step-by-step explanation:
Factors of the constant term
Dwayne answered 80% of the questions on a quiz correctly.If he answered 40 questions correctly what was the total number of questions on Dwayne's quiz
Answer:
hold up i know it
Step-by-step explanation:
50, because 4÷5=.80 or 80%.
So 40÷50=.80 or 80%
Y-4 = 4/3(x-2) which graph matches the function below
Answer:
Step-by-step explanation:
We need to find the graph of the following function:
Y - 4 = 4/3(x-2)
Solving for Y we have:
Y = 4/3(x-2) + 4
The graph is similar to the graph of f(x) = 1/x. But, with the following differences:
1. The graph is translated vertically upwards by 4 units.
2. The graph is translated horizontally to the right 2 units.
3. The graph is enlarged by a factor of 4/3.
Then, considering all these facts. The graph of f(x) = 1/x and the new graph according to all the characteristics stated before are attached.
A building contractor has a piece of crown molding that is 48 ½ inches long. He cuts off one piece measuring 10 ¼ inches and another piece 2 feet ⅛ inch.How much crown molding does he have left?
Answer:
14 1/8 inches of molding
Step-by-step explanation:
In order to find the solution, we'll have to do 2 fractions subtractions.
To be able to subtract fractions, we have to make sure they are placed in the same denominator. So, the first thing we'll do is to convert all the numbers in 8th, because that's the greatest denominator.
[tex]48 \frac{1}{2} = 48 \frac{4}{8} = \frac{(48 * 8) + 4}{8} = \frac{388}{8}[/tex]
[tex]10 \frac{1}{4} = 10 \frac{2}{8} = \frac{(10 * 8) + 2}{8} = \frac{82}{8}[/tex]
For the last one, we'll first convert the 2 feet into 24 inches.
[tex]24 \frac{1}{8} = \frac{(24 * 8) + 1}{8} = \frac{193}{8}[/tex]
Now, we'll subtract each of the two pieces cut from the original molding's length, first the 10 1/4 inches piece
[tex]\frac{388}{8} - \frac{82}{8} = \frac{388 - 82}{8} = \frac{306}{8}[/tex]
then the 2 feet 1/8 piece
[tex]\frac{306}{8} - \frac{193}{8} = \frac{306 - 193}{8} = \frac{113}{8} = 14 \frac{1}{8}[/tex]
So, the contractor is left with 14 1/8 inches of molding.
6.2 seconds The height, h, in feet of an object above the ground is given by h = −16t2 + 64t + 160, where t is the time in seconds. How long does it take the object to hit the ground? (to the nearest tenth of a second)
A)
5.1 seconds
B)
5.3 seconds
C)
5.7 seconds
D)
6.2 seconds
ANSWER
C) 5.7 seconds
EXPLANATION
The height of the object is given by:
[tex]h(t) = - 16 {t}^{2} + 64t + 160[/tex]
If the object hit the ground, then the height is zero.
[tex]- 16 {t}^{2} + 64t + 160 = 0[/tex]
Divide through by -16
[tex] {t}^{2} - 4t - 10 = 0[/tex]
Where a=1, b=-4 and c=-10
We substitute into the quadratic formula to obtain,
[tex]t= \frac{ - b \pm \sqrt{ {b}^{2} - 4ac} }{2a} [/tex]
[tex]t= \frac{ - - 4\pm \sqrt{ {( - 4)}^{2} - 4( 1)( - 10)} }{2(1)} [/tex]
[tex]t= \frac{ 4\pm \sqrt{56} }{2} [/tex]
[tex]t= \frac{ 4\pm 2\sqrt{14} }{2} [/tex]
t=2-√14 or t=2+√14
Time cannot be negative.
Hence, t=5.7 seconds to the nearest tenth.
What is 2000+3.5%+4 equals
Answer:
2004.035
Step-by-step explanation:
2000+4=2004, 3.5%= .035, and 2004+0.035=2004.035
what do N and M equal?
[tex]\bf ((5^{-2})(9^5))^{-6}\implies ((5^{-2\cdot -6})(9^{5\cdot -6}))\implies 5^{\stackrel{\stackrel{n}{\downarrow }}{12}}\times 9^{\stackrel{\stackrel{m}{\downarrow }}{-30}}[/tex]
the perimeter of a rectangular picture frame is 32 inches.the length of the frame is 2 inches longer than the width. what are the dimensions of the frame? STEP BY STEPPP
Answer:
The width is 7 inches and the length is 9 inches
Step-by-step explanation:
So we can divide 32 by 2 because we know perimeter is 2(l*w)
So it becomes 16, and it is now (l*w)
We know that the length is 2 inches longer so we subtract 2 from 16.
It then becomes 14 inches so therefore we can then divide it by 2.
14 divided by 2 is 7 and therefore we add 2 because we subtracted the two from earlier temporarily.
Therefore the width is 7 and the length is 9.
Final answer:
To find the dimensions of the picture frame with a perimeter of 32 inches and length 2 inches more than its width, equations based on the rectangle's perimeter formula are used. The width is found to be 7 inches, leading to a length of 9 inches.
Explanation:
To determine the dimensions of a rectangular picture frame where the perimeter is 32 inches and the length is 2 inches longer than the width, we can set up two equations based on the properties of a rectangle's perimeter. The perimeter (P) of a rectangle is given by the formula P = 2l + 2w, where l is the length and w is the width. Let's denote the width of the frame as w inches; thus, the length will be w + 2 inches since the length is 2 inches longer than the width.
Now, since the perimeter is 32 inches, we plug in our expressions for length and width into the perimeter formula: 2(w + 2) + 2w = 32. Simplifying this, we get 2w + 4 + 2w = 32. Combining like terms, we have 4w + 4 = 32. Subtracting 4 from both sides, we get 4w = 28. Dividing both sides by 4, we find w = 7 inches.
Therefore, the width of the frame is 7 inches, and the length, being 2 inches longer, is 7 + 2 = 9 inches. So the dimensions of the frame are 7 inches by 9 inches.