The rectangle's length is 12 cm, and the width is 9 cm, calculated by setting up a system of equations using the given perimeter and the relationship between length and width.
Explanation:To find the length and width of the rectangle when given its perimeter and a relationship between its length and width, we can set up a system of equations. First, let's denote the length of the rectangle as L and the width as W. According to the question, the width is 3 centimeters more than half the length, so we have W = ½L + 3.
Since the perimeter (P) of a rectangle is given by P = 2L + 2W, and we know the perimeter is 42 centimeters, we can set up an equation: 42 = 2L + 2(½L + 3). Simplifying this, we get 42 = 2L + L + 6 or 42 = 3L + 6. Subtracting 6 from both sides gives us 36 = 3L or L = 12 centimeters for the length.
Now we can find the width using the previous relationship W = ½L + 3. Substituting the value of L, we get W = ½(12) + 3 = 6 + 3 = 9 centimeters for the width.
Therefore, the length is 12 centimeters and the width is 9 centimeters.
Solve the inequalities by graphing. Select the correct graph. y > x y < -x
The solution to the system of inequalities y > x and y < -x is a V-shaped region in the second and fourth quadrants of the coordinate plane.
Graph attached.
To solve the system of inequalities graphically, you need to shade the regions on the coordinate plane that satisfy both inequalities.
The first inequality is y > x. This means that all points above the line y = x satisfy this inequality.
The second inequality is y < -x. This means that all points below the line y = -x satisfy this inequality.
Now, let's graph both lines and shade the regions that satisfy both inequalities:
Graph the line y = x. This is a straight line with a slope of 1 that passes through the origin (0,0) and goes up and to the right.
Graph the line y = -x. This is also a straight line with a slope of -1 that passes through the origin (0,0) and goes down and to the right.
Graph attached.
The shaded region that satisfies both inequalities is the area between these two lines, below y = -x, and above y = x.
It forms a V-shaped region in the second and fourth quadrants of the coordinate plane.
Therefore, the correct graph should show the shaded V-shaped region that represents the solution to the system of inequalities.
Graph attached.
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Econometrics answers using the ols estimates shown in the table below, compare the estimated effects of a 13 % increase in average district income on test scores in california and massachusetts.
If triangle XYZ is reflected across the line y = 1 to create triangle X'Y'Z', what is the ordered pair of X'? (2 points)
Answer:(4,-3)
Step-by-step explanation:
The accountant at patton company has determined that income before income taxes amounted to $11,000 using the fifo costing assumption. if the income tax rate is 30% and the amount of income taxes paid would be $600 greater if the lifo assumption were used, what would be the amount of income before taxes under the lifo assumption? $11,600 $13,000 $9,000 $10,400
what is 9/10 take away 6 tenths
the answer is 3/10 because since they are both tenths its like doing 9 - 6
When full, a 5/8in binder is 8 in. Wide, 11 inches tall, and 5/8 inches thick. What is the volume of the binder?
pete's pools installs rectangular pools that are all 10 feet wide. the length can vary from 10 feet to 30 feet. the company installed a pool with a perimeter of 76 feet. what was the length of the pool ?
The length of pool is 28 feet.
What is perimeter?The complete length of a shape's boundary is referred to as the perimeter in geometry. A shape's perimeter is calculated by adding the lengths of all of its sides and edges. Its dimensions are expressed in linear units like centimetres, metres, inches, and feet.
Given rectangular pool
width of pool is 10 feet,
and length is between 10 to 30 feet
perimeter of pool = 76 feet
perimeter = p = 2(l + b)
where l = length and b = breadth/width
76 = 2(l + 10)
l + 10 = 38
l = 38 - 10
l = 28 feet
Hence length of pool is 28 feet.
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Find the distance from the point to the given plane. (1, −7, 8), 3x + 2y + 6z = 5
To find the distance from the point (1, -7, 8) to the plane 3x + 2y + 6z = 5, we use the formula for the distance of a point from a plane, resulting in a distance of 32/7 units.
Explanation:The question deals with finding the distance from a point to a given plane. Specifically, it asks for the distance from the point (1, −7, 8) to the plane defined by the equation 3x + 2y + 6z = 5. To solve this, we use the formula for the distance of a point (x1, y1, z1) from a plane ax + by + cz = d:
D = |ax1 + by1 + cz1 − d| / √(a2 + b2 + c2)
Substituting the given values, we get:
D = |3(1) + 2(−7) + 6(8) − 5| / √(32 + 22 + 62)
This simplifies to:
D = |3 − 14 + 48 − 5| / √(9 + 4 + 36)
D = |32| / √49
D = 32 / 7
Therefore, the perpendicular distance from the point to the plane is 32/7 units.
why is the number 2 a prime or composite?
2 is prime because it is a positive integer only divisible by itself and 1.
Step-by-step explanation:2 is the smallest prime.
A composite number is one that has more than one prime factor. 4 = 2·2 is composite, for example.
The number 1 is neither prime nor composite.
Answer:
prime
Step-by-step explanation:
A hypothesis test has a significance level of 10%. Explain what this significance level represents.
Answer:
A significance level of 10% i.e.0.10 represents the chance of rejecting the null hypothesis
Step-by-step explanation:
Given :A hypothesis test has a significance level of 10%.
To Find :Explain what this significance level represents.
Solution :
Definition : The significance level is the probability of rejecting the null hypothesis when it is true.
So, significance level = 10%.
This means there is a 0.10 chance of rejecting the null hypothesis
Hence a significance level of 10% i.e.0.10 represents the chance of rejecting the null hypothesis
How do you write 5.82 × 10^3 in standard form?
A landscaper has 3/4 ton of mulch. She puts 1 1/6 ton of mulch on each flower bed. How many flower beds does she put mulch on?
Plzzzzz i will give brainliest!!
Answer:
B = 24Step-by-step explanation:
[tex](6p+2)^2\qquad\text{use}\ (a+b)^2=a^2+2ab+b^2\\\\=(6p)^2+2(6p)(2)+2^2=36p^2+24p+4\\\\\\36p^2+24p+4=36p^2+Bp+4\\\\\therefore B=24[/tex]
Eric and his work crew have 50 trees to plant. In 8 hours today, they planted 40 trees. If they work at the same rate tomorrow, how long will it take to finish planting the trees? 2 hours
Answer:
a.) 2 hours to finish planting trees
Which inequalities have no solution? Check all of the boxes that apply.
A. x > x
B. –3x mr001-1.jpg –3x
C. –4 + x > –2 + x
D. x – 2 < x + 3
Answer: The answer is (A) and (C).
Step-by-step explanation: We are given four options and we are to check which of these inequalities have no solution.
(A) We have
[tex]x>x\\\\\Rightarrow x-x>0\\\\\Rightarrow 0>1,[/tex]
which cannot be possible, so this inequality will have no solution.
(B) We have
[tex]-3x=-3x\\\\\Rightarrow -3x+3x=0\\\\\Rightarrow 0=0,[/tex]
which is always true, so this equation will have infinitely many solutions.
(C) We have
[tex]-4+x>-2+x\\\\\Rightarrow -4+x+2-x>0\\\\\Rightarrow -2>0,[/tex]
which is never true, so this inequality will have no solution.
(D) We have
[tex]x-2<x+3\\\\\Rightarrow x-2-x-3<0\\\\\Rightarrow -5<0,[/tex]
which is always true, so this inequality will have infinitely many solutions.
Thus, the correct options are (A) and (C).
Answer:
A. x > x
C. –4 + x > –2 + x
Step-by-step explanation:
in a sentence,describe the relevant angle relationship in the diagram. that is,descr
Determine whether each decimal is equal to 77%.
Decimal
Yes
-
Yes
No
-
No
0.077
0.770
0.77
7.7
Helen makes $66 a day . How much will she make if she works 5 1/2 days ?
What is the least common denominator of the equation 2/9x+2/3x=7
select the correct product (x2+3)(x3-5)
The question involves multiplying two polynomials, (x^2+3) and (x^3-5), using the distributive property to find the product x^5 - 5x^2 + 3x^3 - 15.
The question asks for the product of the polynomials (x2+3) and (x3-5). To find the product, each term in the first polynomial is multiplied by each term in the second polynomial. This is known as the distributive property or the FOIL method when dealing with binomials. Therefore, the product is:
x^5 - 5x^2 + 3x^3 - 15.
To summarize the multiplication process:
Multiply x2 by x3 to get x5
Multiply x2 by -5 to get -5x2
Multiply 3 by x3 to get 3x3
Multiply 3 by -5 to get -15
Hence, This is the standard process for multiplying polynomials.
What is the area of a sector with a central angle of 2π9 radians and a diameter of 20.6 mm? Use 3.14 for π and round your answer to the nearest hundredth.
Answer:
37.01
Step-by-step explanation:
a magazine contains fourteen pages. You open to a random page, the page number is three or seven..... where do i start i need to show work
At a store, 3 chairs and 4 desks together cost $367.95. The total costof 4 chairs and 6 beds is $$720.72. If the price of the desk is 2 times as much as the price of the chair, what is the total cost of 5 desks and 4 beds?
After creating equations based on the given costs and solving for the price of chairs, desks, and beds, we find that the total cost for 5 desks and 4 beds is $725.78.
Explanation:To solve this problem, we will start by setting up two equations based on the information given about the prices of chairs, desks, and beds. Let's denote the cost of one chair as C, the cost of one desk as D, and the cost of one bed as B. According to the problem, the desk costs 2 times as much as the chair, so we have D = 2C.
Now, we can create equations based on the total costs provided:
3 chairs and 4 desks cost $367.95 -> 3C + 4D = 367.954 chairs and 6 beds cost $720.72 -> 4C + 6B = 720.72Substitute the value of D from D = 2C into the first equation:
3C + 4(2C) = 367.95 -> 11C = 367.95 -> C = 33.45
With the cost of a chair found, we can find the cost of a desk:
D = 2C = 2(33.45) = 66.90
Now, to find the cost of a bed, we use the second equation and substitute values for C:
4C + 6B = 720.72 -> 4(33.45) + 6B = 720.72 -> 133.80 + 6B = 720.72 -> 6B = 586.92 -> B = 97.82
Finally, we calculate the total cost of 5 desks and 4 beds:
5D + 4B = 5(66.90) + 4(97.82) = 334.50 + 391.28 = 725.78
The total cost of 5 desks and 4 beds is $725.78.
Martha has 8 cookies split upon 6 friends. How many cookies will her friends and her get
Graph each quadrilateral ABCD. Then determine the most precise name for it.
A(3, -2). B(5,4). C(3,6). D(1,4).
Suppose you are climbing a hill whose shape is given by the equation z = 1400 − 0.005x2 − 0.01y2, where x, y, and z are measured in meters, and you are standing at a point with coordinates (100, 120, 1206). the positive x-axis points east and the positive y-axis points north. (a) if you walk due south, will you start to ascend or descend?
If walking due south from the point (100, 120, 1206) will cause you to descend, as the slope of the hill in the southward direction is negative.
To determine whether you will ascend or descend when walking due south from the point (100, 120, 1206), we need to consider the slope of the hill in the southward direction, which corresponds to the negative y-direction.
Given the equation of the hill's shape: [tex]\[ z = 1400 - 0.005x^2 - 0.01y^2 \][/tex]
We can find the slope in the y-direction (southward) by taking the partial derivative of z with respect to y:
[tex]\[ \frac{\partial z}{\partial y} = -2 \cdot 0.01 \cdot y \][/tex]
Evaluating this derivative at the point (100, 120, 1206) gives us the slope in the y-direction at that point:
[tex]\[ \frac{\partial z}{\partial y}\Bigg|_{(100, 120, 1206)} = -2 \cdot 0.01 \cdot 120 = -2.4 \][/tex]
Since the slope is negative, this means that as you move in the positive y-direction (northward), the height z decreases. Conversely, moving in the negative y-direction (southward) will also result in a decrease in height z, because the slope is linear and does not change direction.
Therefore, walking due south from the point (100, 120, 1206) will cause you to descend, as the slope of the hill in the southward direction is negative.
Explain how to write an equivalent expression using the distributive property. 2(11 + y)
Final answer:
To write an equivalent expression using the distributive property for the expression 2(11 + y), distribute 2 to both terms inside the parentheses and simplify.
Explanation:
To write an equivalent expression using the distributive property for the expression 2(11 + y), we can distribute the 2 to both terms inside the parentheses.
This gives us:
2 * 11 + 2 * y = 22 + 2y
So, the equivalent expression using the distributive property is 22 + 2y.
A sample is selected from a population with a mean of u=100 and a standard deviation of o-20 what is the expected value of m and the standard error for a sample of n=4
Find the equations of the tangent line to the curve at the given point. y = 9cos x. (π/3,4.5)
The equation of the tangent line to the curve is
y = -9 ( √3 / 2 )x + [ ( 3π√3 + 9 ) / 2 ]
What is an Equation of a line?
The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept
And y - y₁ = m ( x - x₁ )
y = y-coordinate of second point
y₁ = y-coordinate of point one
m = slope
x = x-coordinate of second point
x₁ = x-coordinate of point one
The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Given data ,
Let the curve be y = 9 cos ( x )
To find the equation of the tangent line to the curve y , take the derivative of y , we get
dy / dx = 9 ( - sin ( x ) )
dy / dx = -9 sin ( x )
So , y' = -9 sin ( x )
when x = π/3
Now plug in your value for x into y'
-9 sin ( π/3 ) = -9 ( √3 / 2 )
This is the slope of the tangent line at x = π/3
And , To find the equation of the tangent line, we need a value for y. Simply plug your x value into the original equation for y
So ,
y = 9 cos x
y = 9 cos ( π / 3 )
y = 9 ( 1/2 )
y = 9/2
Now use point slope form to find the equation of the tangent line
y - y₁ = m ( x - x₁ )
Substituting the values in the equations , we get
y - 9/2 = -9 ( √3 / 2 ) ( x - π/3 )
On simplifying the equation , we get
y - 9/2 = -9 ( √3 / 2 )x + 9 ( √3 / 2 ) ( π/3 )
Adding 9/2 on both sides of the equation , we get
y = -9 ( √3 / 2 )x + [ ( 3π√3 + 9 ) / 2 ]
Hence , the equation is y = -9 ( √3 / 2 )x + [ ( 3π√3 + 9 ) / 2 ]
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How long will it take for 2 g of a sample of iodine-131, which has a half-life of about 8 days, to decay to 0.04 g?