Answer:
Step-by-step explanation:
To find the parallel slope of a given slope, we need to remember that parallel lines have the same slope.
The given slope is -2/4.
To simplify the slope, we can reduce -2/4 by dividing the numerator and denominator by their greatest common divisor, which is 2:
-2/4 = (-12)/(22) = -1/2
Therefore, the parallel slope to -2/4 is -1/2.
Write two expressions to show the total area of advertisement space on one page.
The area covered by the advertisement on the page is [tex]ab \ unit^2[/tex].
What is the definition of area of a rectangle?The area of a rectangle covers is the space it takes up inside the boundaries of its four sides. The dimensions of a rectangle determine its area. In general, the area of a rectangle is equal to the product of its length and breadth of the rectangle.
The formula of area of rectangle is [tex]length \times breadth[/tex] [tex]unit^2[/tex]
let the given page represents a rectangle.
We take the length of the advertisement is [tex]a[/tex] unit and breadth of the advertisement is [tex]b[/tex] unit.
The area of the advertisement [tex]=a \times b \ unit^2[/tex]
[tex]=ab \ unit^2[/tex]
Therefore, the area covered by the advertisement on the page is [tex]ab \ unit^2[/tex]
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place 3 numbers between 12 and 60 to make a sequence of 5 numbers with a common difference
The 3 numbers which should be placed between 12 and 60 are; 24, 36 and 48.
What three numbers should be placed between 12 and 60?It follows from the task content that the first and last numbers are; 12 and 60 respectively.
Hence, since the difference between 12 and 60 is 48 and there are 4 transitions between the two numbers to have 5 total numbers,
It follows that the common difference is; 48/4 = 12 and the three numbers required are; 24,36 and 48.
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If B is the midpoint of AC, and AC = &r - 20 find BC.
The measure of BC from the figure shown is 26
What is a line?A line is the distance between two points. From the given line AC;
AC = AB + BC
Given the following parameters
AC = 8x - 20
AB = 3x - 1
Required
Length BC
Substitute
8x-20 = 3x-1 + BC
BC = 8x-20 -(3x - 1)
BC = 8x - 20 - 3x + 1
BC = 5x - 19
Since B is the midpoint of AC, then;
AB = BC
3x - 1 = 5x - 19
-2x = -18
x = 9
Determine the length of BC
BC = 5(9) - 19
BC = 45 - 19
BC = 26
Hence the measure of BC from the figure shown is 26
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A construction company is repaving a damaged road. So far, they have repaved a total of 55,721 centimeters of the road. Today, they repaved 34,066 centimeters of the road. How many centimeters of the road had they repaved before today?
Answer:
21655
Step-by-step explanation:
minus the values
Given that a function, h, has a domain of -3 ≤ x ≤ 11 and a range of 1 ≤ h(x) ≤ 25 and that h(8) = 19 and h(-2) = 2, select the statement that could be true for h.
The true statement for h regarding the function is that C. h(2) = 16.
How to illustrate the function?From the information given, the function, h, has a domain of -3 ≤ x ≤ 11 and a range of 1 ≤ h(x) ≤ 25.
This illustrates that the range or h has to be less than or equal to 25.
The option that correctly fits this is C.
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is perpendicular to and passes through point C(5, 12).
If the coordinates of A and B are (-10, -3) and (7, 14), respectively, the x-intercept of is
(12, 0)
. The point
lies on .
If CD is perpendicular on AB then the x intercept of CD is (17,0).
Given that CD is perpendicular on AB and passes through C(5,12) and the coordinates of A and B are (-10,-3), (7,14).
When two lines are perpendicular on other line then the product of their slopes is equal to -1.
It is given that CD is perpendicular on AB. So we need to first calculate the slope of AB.
Slope=[tex](y_{2} -y_{1} /x_{2} -x_{1} )[/tex]
Slope of AB=(14+3/7+10)
=(17/17)
=1
According to rule product of slopes of AB and CD should be -1.
So the slope of CD will be -1.
Now we have to form equation of CD from slope -1 and point (5,12).
y-12=-1(x-5)
y-12=-x+5
x+y-17=0
We have to find out x intercept.
We know that x intercept is a point where the line touches x axis. So here the value of y =0.
x+y-17=0
put the value of y=0.
x+0-17=0
x=17
Point will be (17,0)
Hence the x intercept of CD will be (17,0).
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Question is incomplete as it should include in its beginning that CD is perpendicular on AB.
On a coordinate plane, shapes show the size of swings, a slide, a merry-go-round, and a sandbox. The sandbox has points (0, 6), (8, 12), (12, 6), and (8, 0).
A sandbox is shaped like a kite. Each unit on the coordinate plane represents one foot. A planner would like to replace the wooden border around the sandbox. How many feet of wood does he need? Round up to the nearest whole number.
feet
The number of feet of wood that is needed is given as 35 feet of wood.
How to solve for the woodWe have to do this through the use of pythagoras theorem
a² = b² + c²
8² + 6²
a = √100
= 10
4² + 6²
= 52
a = √52
Then we would have
10 + 10 + √52 + √52
= 34.42
This is approximately 35 feet
The feet of wood that is needed is given as 35 feet
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Answer:
The number of feet of wood that is needed is given as 35 feet of wood
Step-by-step explanation:
I just did it on E2020 and got it right
10 points please help me I've been struggling with these
Answer:
57pi
Step-by-step explanation:
First, let's get the area of the entire circle, including the shaded region:
pi*(8+3)^2 = 121pi
Next, let's get the area of the unshaded circle
pi*8^2 = 64pi
If we subtract the inner circle from the full circle, we get the shaded region:
121pi-64pi =
57pi
Answer: 57π
Step-by-step explanation:
You have to calculate the area of the whole circle created by the sum of the inner circle and the ring, so 8+2=11=r, now use the formua for getting area of a circle, π*r², which is "121π"
After that, subtract the area of the inner circle (its area is π*8²)
So 121π-64π = 57π
11y^2-xy dxUse the method for solving homogeneous equations to solve the following differential equation.
The solution to the homogenous differential equation, (11y² - xy)dx + x²dy = 0, is [tex]y = \frac{x}{11 ln (x) + C}[/tex].
A homogeneous differential equation has a homogeneous function as one of its components, if f(λx, λy) = λⁿf(x, y), for any non-zero constant λ, the function is said to be homogenous. The homogeneous differential equation's generic form is of the type f(x, y).dy + g(x, y).dx = 0. The degree of the homogeneous differential equation is the same for the equation's variables x and y.
In the question, we are asked to solve the homogeneous differential equation, (11y² - xy)dx + x²dy = 0.
The given equation can be solved as follows:
Grouping by differentials, gives us: x²dy = (xy - 11y²)dx.We now substitute, u = yx, making y = ux, or, dy = u.dx + x.du.Making the substitutions, we get: x²(u.dx + x.du) = (u - 11u²)x²dx.Expanding the parentheses, we get: ux².dx + x³.du = ux².dx - 11u²x².dx.Reducing ux².dx, we get: x³.du = -11u²x².dx.Dividing by x³ and u², we get du/u² = -11/x.Now, we integrate both sides of the equation: [tex]\int \frac{1}{u^2}du = \int -\frac{11}{x}dx[/tex]Calculating the resulting integrals, we get: -1/u = C - 11 ln(x).Undoing the substitution, u = y/x, we get: -x/y = C - 11 ln(x)The final solution is: [tex]y = \frac{x}{11 ln (x) + C}[/tex]Thus, the solution to the homogenous differential equation, (11y² - xy)dx + x²dy = 0, is [tex]y = \frac{x}{11 ln (x) + C}[/tex].
The provided question is incomplete. The complete question is:
"Use the method for solving homogenous equations to solve the following differential equation.
(11y² - xy)dx + x²dy = 0".
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Which of the following is a geometric sequence?
Answer:
A
Step-by-step explanation:
Geometric sequence is when, during each successive number, a constant is being multiplied. In answer choice A, each number is getting multiplied by 3, so it is a geometric sequence.
Is the point (−2, 10) on the circle with radius 5 and center (2, 13)?
Answer:
yes
Step-by-step explanation:
The point can be demonstrated to lie on the circle by plotting both on a graph. It can also be shown to lie on the circle by showing the distance from center is equal to the radius.
GraphThe attachment shows a graph of the circle. Its equation is ...
(x -h)² +(y -k)² = r² . . . . . . for center (h, k) and radius r
We have (h, k) = (2, 13) and r = 5, so the equation is ...
(x -2)² +(y -13)² = 25 . . . . graphed equation
The point in question is also graphed, and is shown to lie on the circle.
DistanceIf the given point satisfies the circle's equation, it lies on the circle.
For (x, y) = (-2, 10), we find ...
(-2 -2)² +(10 -13)² = (-4)² +(-3)² = 16 +9 = 25 . . . . . the equation is satisfied
3. The scores on a test are normally distributed, with a mean of 82 and standard deviation of 8. What percent of scores are less than 90? Explain your answer.
Answer:
8 ×10=80
Step-by-step explanation:
because 1 time
8
10 times
add so
90
less
so that's it
80
Which of these tables represents a function
W
a system can only be a function if there are no more than one value of y for each value of x. if a value of x is repeated twice or more in a table, it means it is not a function.
The formula d=1/2n+26 relates the nozzles pressure n (in pounds per square inch) of a free hose and the maximum horizontal distance the water reaches d (in feet). How much pressure is needed to reach a fire 50 feet away?
The pounds of pressure needed to reach a fire 50 feet away is 48 pounds
Formulad = 1/2n + 26
where
n = nozzle pressure in pounds per square feetd = distance the water reachesIf d = 50 feet
d = 1/2n + 26
50 = 1/2n + 26
50 - 26 = 1/2n
24 = 1/2n
n = 24 ÷ 1/2
n = 48 pounds
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Complete the recursive formula of the geometric sequence -0.25\,,-2\,,-16\,,-128,...−0.25,−2,−16,−128,...minus, 0, point, 25, comma, minus, 2, comma, minus, 16, comma, minus, 128, comma, point, point, point.
b(1)=b(1)=b, left parenthesis, 1, right parenthesis, equals
b(n)=b(n-1)\cdotb(n)=b(n−1)⋅b, left parenthesis, n, right parenthesis, equals, b, left parenthesis, n, minus, 1, right parenthesis, dot
The recursive formula of the geometric sequence is [tex]b(1) = -0.25[/tex], [tex]b(n) = b(n-1)\cdot 8[/tex]
How to determine the recursive formula?The sequence is given as:
[tex]-0.25\,,-2\,,-16\,,-128,..[/tex]
The first term of the above sequence is
[tex]b(1) = -0.25[/tex]
Calculate the common ratio using
r = b(2)/b(1)
So, we have:
r = -2/-0.25
Evaluate
r = 8
So, we have:
[tex]b(n) = b(n-1)\cdot 8[/tex]
Hence, the recursive formula of the geometric sequence is [tex]b(1) = -0.25[/tex], [tex]b(n) = b(n-1)\cdot 8[/tex]
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Complete question
Complete the recursive formula of the geometric sequence
[tex]-0.25\,,-2\,,-16\,,-128,..[/tex]
[tex]b(1) =[/tex]
[tex]b(n) = b(n-1)\cdot[/tex]
Ms. drake invests $1000 at a simple interest rate of 8.5% for 2 years. how much interest will she earn in this time?
Ms. Drake will earn [tex]\$ 170[/tex] in this time from the investment of [tex]\$ 1000[/tex] at a simple interest with rate of interest [tex]8.5\%[/tex]
What is the definition of simple interest?Simple interest is a way to figure out how much interest will be charged on a sum of money at a specific rate and for a specific duration of time. Conversely, for compound interest, where we add the interest of one year's principal to the next year's principal to compute interest, the principal amount under simple interest remains constant.
Formula for finding simple interest is [tex]\frac{principal \times rate \ of \ interest \times time}{100}[/tex]
Given principal of Ms. Drake is [tex]\$1000[/tex]
Rate of interest is [tex]8.5 \%[/tex]
Time is [tex]2[/tex] years.
Interest [tex]=\frac{1000 \times 8.5 \times 2}{100}[/tex]
[tex]=\frac{17000}{100}\\=170[/tex]
Therefore, Ms. Drake will earn [tex]\$ 170[/tex] in this time.
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This system of equations has been placed in a matrix:
y = 700x + 200
y = 5,000 − 75x
Complete the matrix by filling in the missing numbers.
Answer:
Hello,
Step-by-step explanation:
here is the answer in a picture.
What is the distance between the points (4,3) and (1,-1) on the coordinate
plane?
A. 10 units
B. 50 units
C. 5 units
D. 25 units
Answer:
The distance between the points (4,3) and (1,-1) is C. 5 units.
Step-by-step explanation:
Find the area of the shaded regions.
The area of the shaded circle is given as follows: 84.82 cm².
What is the area of a circle?The area of a circle of radius r is given by pi multiplied by the radius squared, as given by the formula presented next:
[tex]A = \pi r^2[/tex]
In this problem, we have that the important data is given in the bullet-points as follows:
The radius is of r = 6 cm.The shaded area is 75% of the circle.Hence the shaded area in cm² can be found a applying the formula given at the beginning of this problem, as is presented below:
[tex]A = 0.75\pi \times 6^2 = 84.82[/tex]
The multiplication by 0.75 happened because as stated in the bullet point, the shaded area corresponds to only 75% of the entire circle.
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What is 125x + 64y¹2 written as a sum of cubes?
O (25x3)3 + (44)3
O (5x³)3 + (164)³
O (25x³)3 + (8y4)3
(5x3)3 + (4y4)3
quick answer: (5x3)3 + (4y4)3
please hit the like button if it is correct :D
0 divided by 0 is? 45 points for who answer its correct not for a homework
Answer:
Undefined
Step-by-step explanation:
No multiplicative inverse exists for 0
Answer:
undefined
Step-by-step explanation:
a single value can't be assigned to a fraction where the denominator is 0 so the value remains undefined.
A boat traveled north for 28 miles, then turned x° southwest and traveled for 25 miles before stopping. When it stopped, the boat was 18 miles from its starting point.
A triangle shows the course of a boat. Starting at the dock, it travels 18 miles to the left, then 25 miles up and to the right, and then 28 miles down and back to the dock. The angle between 25 miles and 28 miles is x degrees.
Law of cosines:
By how many degrees did the direction of the boat change when it made its first turn? Round to the nearest degree.
30 degrees
39 degrees
46 degrees
The number of degrees that the direction of the boat change when it made its first turn is 39°.
How to calculate the value?From the information given, we would use the cosine function to solve the information.
This will be:
18² = 28² + 25² - 2(28)(25)(cos x)
324 = 784 + 625 - 1400cosx
x = 39.19
Therefore, the value is 39°.
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Determine the intercepts of the line. Do not round your answers. 7x-5=4y-6
x intercept: (_),(_)
y intercept: (_),(_)
Please help!
The intercepts are x intercept: (-1/7,0) and y intercept: (0,1/4)
How to determine the intercepts?The function is given as:
7x-5=4y-6
Set y = 0 to determine the x-intercept
7x - 5 = -6
Add 5 to both sides
7x = -1
Divide by 7
x = -1/7
Set x = 0 to determine the y-intercept
- 5 = 4y - 6
Add 6 to both sides
4y = 1
Divide by 4
y = 1/4
Hence, the intercepts are x intercept: (-1/7,0) and y intercept: (0,1/4)
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What is the approximate side length of the square? 3.0 units 3.5 units 4.2 units 4.9 units
Answer:
(っ◔◡◔)っ ♥ the answer is C ♥
Step-by-step explanation:
Can anyone solve this?
Answer:
BT = 18, DA = 6
Step-by-step explanation:
- EBT and SDA are similar triangles
- EBT has a perimeter of 63
- SDA has a perimeter of 21
- BT = 6x
- DA = x+3
We know that EBT has side lengths that are three times bigger than the side lengths of SDA since 63 = 21 x 3.
so
6x is equal to 3(x+3).
6x = 3x + 9
3x = 9
x = 3
Now we know that:
BT = 18
and
DA = 6
The duration of shoppers' time in BrowseWorld's new retail outlets is normally distributed with a mean of 41.8 minutes and a standard deviation of 17.3 minutes. How long must a visit be to put a shopper in the longest 20 percent
A visit must be of at least 56.33 minutes to put a shopper in the longest 20 percent.
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula. In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z=\frac{X-\mu}{\sigma}[/tex]
How long must a visit be to put a shopper in the longest 20 percent?
Here [tex]\mu=41.8 , \sigma=17.3[/tex]
The 100-20=80th percentile, which is X when Z has p-value of 0.8, so Z=0.84
[tex]Z=\frac{X-\mu}{\sigma}[/tex]
[tex]0.84=\frac{X-41.8}{17.3}[/tex]
14.532=X-41.8
X=14.532+41.8
X=56.33
A visit must be of at least 56.33 minutes to put a shopper in the longest 20 percent.
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WILL MARK BRAINLIEST 35 POINTS Write a paragraph proof for this please
The proofing of the triangle is illustrated below.
How to illustrate the proof?AB = c
BC = a
AC = b
h² = b² - x²
h² = a² - y²
a² - y² = b² - x²
a² = b² - x² + y²
Note that x = c - (c - x) = c
a² = b² - (-x)² + y²
a² = b² + c² + y²
Cos A = x/b
cos = adjacent/hypothenuse
x = bcosA
a² = b² + c² - 2bx
a² = b2 + c² - 2bccosA
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If I start with the number 7 and count by 4s, the following sequence is obtained: 7, 11, 15, 19, 23, and so forth. A new sequence is formed when I start with a different number and count by a different number. Suppose the 2nd number of the new sequence is 8 and the 5th number is 17. What is the 10th number of the new sequence
Answer:
a₁₀ = 32
Step-by-step explanation:
the sequence is arithmetic since there is a count on , a common difference
the nth term of an arithmetic sequence is
[tex]a_{n}[/tex] = a₁ + (n - 1)d
where a₁ is the first term and d the common difference
given a₂ = 8 and a₅ = 17 , then
a₁ + d = 8 → (1)
a₁ + 4d = 17 → (2)
subtract (1) from (2) term by term to eliminate a₁
3d = 9 ( divide both sides by 3 )
d = 3
substitute d = 3 into (1)
a₁ + 3 = 8 ( subtract 3 from both sides )
a₁ = 5
Then
a₁₀ = 5 + (9 × 3) = 5 + 27 = 32
Can 1775 dollars buy 2 large balloons and 16 small balloons 1 large balloon = 300 cubic feet 1 small balloon - 40 cubic feet helium costs $1.60 per cubic foot
No, 1775 dollars cannot buy 2 large balloons and 16 small balloons if helium costs $1.60 per cubic foot.
Calculating the Costs of Balloons
It is given that,
Helium costs $1.60 per cubic foot.
Volume of one large balloon = 300 cubic feet
Thus, the price of one large balloon = $1.60 × 300
= $480
Volume of one small balloon = 40 cubic feet
Thus, the price of one small balloon = $1.60 × 40
= $64
How much buying 2 large and 16 small balloons costs?
So, as calculated above,
One large balloon costs $480, and one small balloon costs $64
Therefore, the cost of two large balloons = $480 × 2
= $960
Cost of 16 small balloons = $64 × 16
= $1024
Total cost of balloons = $960 + $ 1024
= $1984
Since, $1984>$1775,
Therefore, $1775 cannot buy all those balloons if helium costs $1.60 per cubic foot.
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Suppose that you are interested in determining the average height of a person in a large city. You begin by collecting the heights of a random sample of 256 people from the city. The average height of your sample is 64 inches, while the standard deviation of the heights in your sample is 4 inches.The standard error of your estimate of the average height in the city is .
The standard error of the estimate of average height in the city is 0.25.
Given average height 64 inches, sample mean and sample standard deviation of 4 inches.
We have to determine the standard error of the estimate of the average height in the city.
Standard error is the error which is predicted before research to happen in research. It is calculated by dividing the standard deviation of the sample by the square root of the sample size.
n=256
μ=mean
s = sample standard deviation
Standard error=s/[tex]\sqrt{n}[/tex]
=4/[tex]\sqrt{256}[/tex]
=4/16
=0.25
Hence the standard error of the estimate of the average height is 0.25.
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