The width of the border around the stained glass window is approximately 1.15 feet, calculated by subtracting the stained glass area from the total area including the border.
To find the width of the border, we need to subtract the area of the stained glass window from the total area including the border.
Given:
- Length of stained glass window = 4 feet
- Width of stained glass window = 2 feet
- Area of stained glass window = [tex]\(4 \times 2 = 8\)[/tex] square feet
- Total area including the border = Area of stained glass window + Area of border = 8 + 7 = 15 square feet
Let's denote the width of the border as x feet.
The total length including the border is 4 + 2x feet, and the total width including the border is 2 + 2x feet.
The area of the total window with the border is the product of its length and width:
(4 + 2x)(2 + 2x) = 15
Expanding this equation:
8 + 4x + 4x + 4x^2 = 15
8 + 8x + 4x^2 = 15
4x^2 + 8x - 7 = 0
Now, let's solve this quadratic equation using the quadratic formula:
[tex]\[x = \frac{{-b \pm \sqrt{{b^2 - 4ac}}}}{{2a}}\][/tex]
Where a = 4, b = 8, and c = -7.
[tex]\[x = \frac{{-8 \pm \sqrt{{8^2 - 4 \times 4 \times (-7)}}}}{{2 \times 4}}\][/tex]
[tex]\[x = \frac{{-8 \pm \sqrt{{64 + 112}}}}{8}\][/tex]
[tex]\[x = \frac{{-8 \pm \sqrt{{176}}}}{8}\][/tex]
[tex]\[x = \frac{{-8 \pm 4\sqrt{{11}}}}{8}\][/tex]
[tex]\[x = \frac{{-2 \pm \sqrt{{11}}}}{2}\][/tex]
Since the width cannot be negative, we take the positive root:
[tex]\[x = \frac{{-2 + \sqrt{{11}}}}{2} \approx 1.15 \text{ feet}\][/tex]
Therefore, the width of the border is approximately 1.15 feet.
NEED HELP FAST!!!!!!!!!!
Answer:
A. [tex]h=\dfrac{2A}{b}[/tex]
Step-by-step explanation:
You are given formula
[tex]A=\dfrac{1}{2}bh[/tex]
Multiply this equation by 2 to get rid of fraction:
[tex]2A=bh[/tex]
Divide this equation by b to find h in terms of A and b:
[tex]h=\dfrac{2A}{b}[/tex]
What proportion results in the equation 9m=10n
It might have come from
9/n = 10/m
Answer: Hi, in the equation 9*m = 10*n the proportion is 9 to 10, which means that 9 times the number m is equal to 10 times the number n.
So n is proportional to m in the way that n= (9/10)*m
and m is proportional to n in the way that m= (10/9)*n
This means that the proportion can be written as 9 to 10, or 9:10.
What is the degree of x4 – 3x + 2?
Answer: 4
Step-by-step explanation:
The degree is the highest exponent , in which in this problem it is 4. The 3x counts as an exponent of 1 because the variable x is 1, and the 2 counts as an exponent of zero. Which means the degree is 4.
Solve for a!
264=π×a×(20-a)
Thank you!
Answer:
a ≈ 14 or 6
Step-by-step explanation:
264 = π × a × (20 - a)
a(20 - a) = [tex]\frac{264}{Pi}[/tex] ≈ 84 (rounded off to nearest whole number)
Opening the brackets we get;
a² - 20a + 84 = 0
Applying the quadratic formula we get:
a ≈ 14 or 6
Given: - 1/2x > 6.
Choose the solution set.
{x | x R, x > -12}
{x | x R, x < -12}
{x | x R, x > -3}
{x | x R, x < -3}
Answer:
It's option 2.
Step-by-step explanation:
- 1/2x > 6
Divide both sides by -1/2:
x < -12 (Note the inequality sign flips when we divide by a negative value).
Answer: {x |x ∈ R, x < -12}
Step-by-step explanation:
Given the following inequality:
[tex]-\frac{1}{2}x>6[/tex]
You can find the solution set by solving for the variable "x".
Then, to solve for the variable "x" you need to multiply both sides of the inequality:
[tex](-\frac{1}{2}x)(2)>(6)(2)[/tex]
[tex]-x>12[/tex]
And finally, you must multiply both sides of the inequality by (-1). Notice that the direction of the symbol of the inequality will change:
[tex](-x)(-1)>(12)(-1)[/tex]
[tex]x<-12[/tex]
Therefore, the solution set is: {x |x ∈ R, x < -12}
what is the y-intercept ofa line that has a slope of -3 and passes through (0,-7)
Answer:
y = - 7
Step-by-step explanation:
The y- intercept is the point on the y- axis that the line passes through.
The line passes through the y- axis at (0, - 7), hence
the y- intercept is - 7
Slope-intercept form: y = mx + b [m is the slope, b is the y-intercept or the y value when x = 0 ---> (0 , y)]
Since you know m = -3, you can plug that into the equation
y = mx + b
y = -3x + b To find b, plug in the point they gave you into x and y, but since x = 0, your y-intercept is -7
What is the cosine ratio for angle F?
Check the picture below.
Ieda bakes 73 cupcakes and accidentally drops 5 of them. She divides them equally into 13 containers for a bake sale for the school band. How many cupcakes does Ieda have left
Answer:
3 left
Step-by-step explanation:
If she starts out with 73 and drops 5 she is left with 68, an you cannot evenly divide 68 and 13 so you divide it as much as you can evenly which is five containers leaving 3 extra cupcakes.
For this case we have that initially there are 73 cupcakes, if Leda dropped 5 then we are left with:
[tex]73-5 = 68[/tex]
Now, you must equally divide the 68 cupcakes into 13 containers:
putting 5 cupcakes in each of the 13 containers we have;
[tex]13 * 5 = 65[/tex]
[tex]68-65=3[/tex]
So, we have 3 cupcakes left.
Answer:
3 cupcakes
what are two division expressions that have the same value as 61.12 divided by 3.2
Answer:
Other division expression that have the same value as 61.12 divided by 3.2 are
122.24 divided by 6.4 AND
183.36 divided by 9.6
Step-by-step explanation:
61.12/3.2 = 19.1
Other division expression that have the same value as this:
122.24/6.4 = 19.1
183.36/9.6 = 19.1
Which of the following would best be solved using factoring by grouping?
1) x^2+3x- 10=0
2)3x^2+12x=8
3)x^2=25
4)x^3+ 5x^2- 9x- 45=0
Answer:
The fourth
Step-by-step explanation:
It has 4 terms
ANSWER
4)x^3+ 5x^2- 9x- 45=0
EXPLANATION
Factoring by grouping is used to factor expressions that have four terms.
Among the given options, the fourth option is
[tex]x^3+ 5x^2- 9x- 45=0[/tex]
There are already four terms in this expression.
So we group the first two and the last two and factor.
We can see that x² is common to the first two terms and -5 is common to the last 2 terms.
The fourth choice is correct.
What is the volume of the cylinder?
A.
600π ft3
B.
720π ft3
C.
300π ft3
D.
60π ft3
Answer:
300π ft^3
Step-by-step explanation:
let's use the volume of a cylinder formula:
π*r^2*h
π=3.14
r=5
h=12
since we need to solve in terms of pi, do not plug the value of pi into the formula
π*5^2*12= 300π
300π
Please help me with this circle area problem for geometry
Answer:
circle area = PI * radius^2
circle area = 11^2 * PI
circle area = 121 * PI
That would be the area for the ENTIRE area but the circle but we are only dealing with 135 degrees of a circle so the area equals
121 * (135 / 360) * PI
= 45.375 PI
Answer is C
Step-by-step explanation:
how many solutions do these equations have
Answer:
[tex]\large\boxed{\bold{one\ solution}\ (1,\ -4)\to x=1,\ y=-4}[/tex]
Step-by-step explanation:
[tex]\left\{\begin{array}{ccc}y=2x-6\\y=-x-3\end{array}\right\\\\\text{These are linear functions. We only need two points to draw a graph.}\\\\\text{Choice two values of x, substitute to the equation,}\\\text{and calculate the values of y.}\\\\y=2x-6\\for\ x=0\to y=2(0)-6=0-6=-6\to(0,\ -6)\\for\ x=3\to y=2(3)-6=6-6=0\to(3,\ 0)\\\\y=-x-3\\for\ x=0\to y=-0-3=0-3=-3\to(0,\ -3)\\for\ x=-3\to y=-(-3)-3=3-3=0\to(-3,\ 0)\\\\\text{Look at the picture}[/tex]
[tex]\text{The intersection of the line is the solution of the system of equations:}\\\\(1,\ -4)\to x=1,\ y=-4[/tex]
Roger needs to buy supplies for his model airplane. He needs glue and paint, but he
wants to spend less than $3. Glue costs $0.75 a tube, and paint costs $0.95 a bottle. If x
is the cost of the glue and y is the cost of the paint, which inequality should Roger solve?
Answer:
TELL HIM TO STOP BEING SO CHEAP!!!!!!!!! <3
and i oop-
Step-by-step explanation:
What is the area of the regular hexagon? This is due tomorrow please help! :)
Check the picture below.
so then, the perimeter of that hexagon will just be the sum of all its 6 sides, or namely 3⅖ + 3⅖ + 3⅖ + 3⅖ + 3⅖ + 3⅖, or just 6( 3⅖ ).
[tex]\bf \textit{area of a regular polygon}\\\\ A=\cfrac{1}{2}ap~~ \begin{cases} a=apothem\\ p=perimeter\\[-0.5em] \hrulefill\\ a=3\\ p=6\left(3\frac{2}{5} \right) \end{cases}\implies A=\cfrac{1}{2}(3)\left[ 6\left(3\frac{2}{5} \right) \right]\implies A=\cfrac{1}{2}(3)\left[ 6\left(\cfrac{17}{5} \right) \right] \\\\\\ A=\cfrac{1}{2}(3)\left(\cfrac{102}{5} \right)\implies A=\cfrac{1}{2}\left( \cfrac{306}{5} \right)\implies A=\cfrac{153}{5}\implies A=30\frac{3}{5}[/tex]
if the dimensions of a rectangle are decreased by 50%, then the area of the rectangle is decreased by what percent?
The area of the rectangle is decreased by 75%, when the dimensions of a rectangle are decreased by 50%.
What is Area of rectangle?The area of the rectangle is the multiplication of length and width.
Area = l × b
It is given that: length and breadth is by 50%
New Length = l × (1-50/100)
= l × (1-1/2)
= l/2
New Width = b × (1-50/100)
= b × (1-1/2)
= b/2
New area = new length × new width
= (l/2) x (b/2)
= lb/4
Change percent =[tex]\frac{Final Area\;-\; Initial Area}{Initial Area} * 100[/tex]
= [tex]\frac{(lb/4)\;-\; lb}{lb} * 100[/tex]
= (- 3lb)/4× 100
= (-3)/4 × 100
= -75%
Hence, the area decreased by 75 %.
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Final answer:
Decreasing the dimensions of a rectangle by 50% results in a new area that is 25% of the original, equating to a decrease of 75% in the area.
Explanation:
When the dimensions of a rectangle are decreased by 50%, each dimension (length and width) becomes 50% of the original. To determine the effect on the area, you can use the formula for the area of a rectangle, which is Area = length tmes width.
Let's consider the original length to be L and the original width to be W. The original area is L times W. When both dimensions are decreased by 50%, the new length is 0.5L and the new width is 0.5W. Therefore, the new area is (0.5L) times (0.5W), which is 0.25 times (L times W). This means the new area is 25% of the original area, representing a 75% decrease.
Examine the following table of points, which are all on a certain line.
x y
−2 4
0 2
1 1
3 −1
What is the slope of this line? Enter your answer as a number, like this: 42, or, if the slope is undefined, enter the lowercase letter "u".
[tex]\bf \begin{array}{|cc|ll} \cline{1-2} x&y\\ \cline{1-2} {-2}~~\ast&{4}~~\ast\\ 0&2\\ 1&1\\ {3}~~\ast&{-1}~~\ast\\ \cline{1-2} \end{array}~\hspace{10em} (\stackrel{x_1}{-2}~,~\stackrel{y_1}{4})\qquad (\stackrel{x_2}{3}~,~\stackrel{y_2}{-1}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{-1-4}{3-(-2)}\implies \cfrac{-5}{3+2}\implies \cfrac{-5}{5}\implies -1[/tex]
The slope of this line is -1.
The slope formula is useful:
m = (y2 -y1)/(x2 -x1)
where:
m is the slope of the line
y1 and y2 are the y-coordinates of two points on the line
x1 and x2 are the x-coordinates of the two points on the line
m = (2 -4)/(0 -(-2)) = -2/2 = -1
The slope of this line is -1.
The points on the line drop 1 unit for each 1 unit to the right.
m = rise/run = -1/1 = -1
Question: A manufacturer keeps track of his monthly costs by using a “cost function” that assigns a total cost for a given number of manufactured items, x. The function is C(x) = 7,500 + 2.4x a) What is the reasonable domain of the function? b) What is the cost of 3,500 items? c) If costs must be kept below $20,000 this month, what is the greatest number of items she can manufacture? You must show your work
Answer:
a) Domain: -∞ < x < ∞
b) Cost required to manufacture 3500 items is $15,900.
c) Number of items she can manufacture is 5208 if cost is kept at $20,000
Step-by-step explanation:
a) What is the reasonable domain of the function?
The function is C(x) = 7,500 + 2.4x
The domain of the function is the set of values for which the function is defined and valid.
In the given function there is no constraint or undefined points so domain is:
-∞ < x < ∞
b) What is the cost of 3,500 items?
We are given x = 3500 and we need to find the cost.
Putting values in the function given:
C(x) = 7,500 + 2.4x
C(x) = 7,500 + 2.4 (3500)
C(x) = 7500 + 8400
C(x) = 15,900
Cost required to manufacture 3500 items is $15,900.
c) If costs must be kept below $20,000 this month, what is the greatest number of items she can manufacture?
We are given cost, and we need to find x
C(x) = 7,500 + 2.4x
20,000 = 7500 +2.4x
20,000 - 7500 = 2.4x
12500 = 2.4 x
=> x = 12500/2.4
x= 5208.3 ≅ 5208
So, Number of items she can manufacture is 5208 if cost is kept at $20,000
Which line is the best model for the data in the scatter plot? I need this question answer really fast and who ever gets it gets a brain list plz I need it ASAP
I think it is bottom right because it goes through the most points.
PLEASE HELP RIGHT AWAY
Answer:
203 minutes
Step-by-step explanation:
This can be expressed as an arithmetic sequence, that is
20, 23, 26, 29,...
With first term a = 20 and common difference d = 3
The sum to n terms of an arithmetic sequence is
[tex]S_{n}[/tex] = [tex]\frac{n}{2}[/tex] [ 2a + (n - 1)d ], hence
[tex]S_{7}[/tex] = [tex]\frac{7}{2}[/tex] [ (2 × 20) + (6 × 3) ]
= 3.5 ( 40 + 18) = 3.5 × 58 = 203
the area of the rectangular park is 4 1/2 square miles. if the length is 1/2 mile, how wide is the park?
Answer: 9
Step-by-step explanation: 4.5=.5xZ. 4.5/.5=9=z
this year,15 of the 40 computers in the math lab are not new. which representation is equivalent to the fraction of computers that are new.
Answer:
5/8
Step-by-step explanation:
Subtract the total computers from the old computers.
40-15=25
Then put the number of new computers over the total computers
25/40
Then, simplify
5/8
What is the midpoint of the segment shown below
Answer:
D
Step-by-step explanation:
Using the midpoint formula
midpoint of 2 points (x₁, y₁ ) and (x₂, y₂ ) is
[ [tex]\frac{1}{2}[/tex](x₁ + x₂), [tex]\frac{1}{2}[/tex](y₁ + y₂ ) ]
let (x₁, y₁ ) = (- 1, 5) and (x₂, y₂ ) = (5, 5), then midpoint is
[ [tex]\frac{1}{2}[/tex](- 1 + 5), [tex]\frac{1}{2}[/tex](5 + 5) ]
= (2, 5) → D
The midpoint of the segment is (2,5).
To find the midpoint of a line segment with endpoints [tex]\((-1, 5)\) and \((5, 5)\)[/tex], we can use the midpoint formula:
[tex]\[ \text{Midpoint} = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) \][/tex]
Given the endpoints:
[tex]\( x_1 = -1 \), \( y_1 = 5 \)[/tex] (coordinates of the first point)
[tex]\( x_2 = 5 \), \( y_2 = 5 \)[/tex] (coordinates of the second point)
Now, let's plug these values into the midpoint formula:
[tex]\[ \text{Midpoint} = \left( \frac{-1 + 5}{2}, \frac{5 + 5}{2} \right) \][/tex]
[tex]\[ = \left( \frac{4}{2}, \frac{10}{2} \right) \][/tex]
[tex]\[ = \left( 2, 5 \right) \][/tex]
Therefore, the midpoint of the segment is (2, 5)
Among the given options, the correct one is option D: (2, 5).
Find the value of 21 + 4(3^2 - 5). 25 37 100
Answer:
21 + 4(3^2 - 5 = 37
Step-by-step explanation:
Please answer right awat
Answer:
The correct answer option is 0.2.
Step-by-step explanation:
We are given that there are 3 red marbles and 3 green marbles in an opaque bag.
If two marbles are chosen one after one without replacement, we are to find the probability of getting both green marbles.
P (1st green marble) = [tex] \frac { 3 } { 6 } [/tex]
P (2nd green marble) = [tex] \frac { 2 } { 5 } [/tex]
P (both green marbles) = [tex] \frac { 3 } { 6 } \times \frac { 2 } { 5 } [/tex] = 0.2
Answer:
i think its forty
Step-by-step explanation:
im sorry if its wrong
kieran is flying a kite. he gets tired, so he stakes the kite into the ground. the kite is on a string that is 18 feet long and makes a 30 degree angle with the ground. how high is the kite
see if u understand, note that the degree is 90
The height of the kite is 9 feet.
Trigonometric ratio is used to show the relationship between the sides of a triangle and its angles.
Let h represent the height of the kite. Hence, using trigonometric ratios:
sin(30) = h / 18
h = 9 feet
Therefore the height of the kite is 9 feet.
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what is 48 35 26 31 27 52 55 63 18 74 35 61 28 42 76 35 38 64 71 26 53 65 47 41 102 38 35 84 41 26 73 62 35 39 62 49 104 62 54 19 28 64 36 39 53 89 26 53 43 75 35 39 29 26 45 39 31 30 70 42 37 54 85 42 36 91 25 28 53 65 78 42 68 44 41 50 46 48 75 29 53 72 17 28 38 30 48 43 27 46 36 48 62 31 42 48 61 22 124 27 53 86 60 47 41 37 27 36 45 80 45 70 53 25 29 16 30 36 38 42 48 51 38 39 43 61 75 38 42 55 72 39 28 51 43 49 67 25 37 39 46 41 50 93 53 82 47 36 38 51 42 40 24 68 38 36 34 49 65 68 62 53 67 23 51 40 43 49 57 61 26 54 35 32 38 39 24 added all together
The numbers added together resulted in 8419.
What is addition?In addition, items are combined and counted as a single large group. The process of adding two or more numbers together is known as an addition in mathematics. The terms "addends" and "sum" refer to the numbers that are added and the result of the operation, respectively.
To find the addition of all 177 numbers.
First, we arrange in ascending terms, we get,
16, 17, 18, 19, 22, 23, 24, 24, 25, 25, 25, 26, 26, 26, 26, 26, 26, 27, 27, 27, 27, 28, 28, 28, 28, 28, 29, 29, 29, 30, 30, 30, 31, 31, 31, 32, 34, 35, 35, 35, 35, 35, 35, 35, 36, 36, 36, 36, 36, 36, 36, 37, 37, 37, 38, 38, 38, 38, 38, 38, 38, 38, 38, 39, 39, 39, 39, 39, 39, 39, 39, 40, 40, 41, 41, 41, 41, 41, 42, 42, 42, 42, 42, 42, 42, 42, 43, 43, 43, 43, 43, 44, 45, 45, 45, 46, 46, 46, 47, 47, 47, 48, 48, 48, 48, 48, 48, 49, 49, 49, 49, 50, 50, 51, 51, 51, 51, 52, 53, 53, 53, 53, 53, 53, 53, 53, 53, 54, 54, 54, 55, 55, 57, 60, 61, 61, 61, 61, 62, 62, 62, 62, 62, 63, 64, 64, 65, 65, 65, 67, 67, 68, 68, 68, 70, 70, 71, 72, 72, 73, 74, 75, 75, 75, 76, 78, 80, 82, 84, 85, 86, 89, 91, 93, 102, 104, 124.
Therefore, the sum is 8419.
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The question 'what is 48 35 26 31 27 52 55 63... added all together?' is asking for the sum of all the provided numbers. This can be calculated with a calculator or by manual addition. Be aware it may take time due to the large number of values.
Explanation:To answer the question, 'what is 48 35 26 31 27 52 55 63 18 74 35 61 28 42 76 35 38 64 71 26 53 65 47 41 102 38 35 84 41 26 73 62 35 39 62 49 104 62 54 19 28 64 36 39 53 89 26 53 43 75 35 39 29 26 45 39 31 30 70 42 37 54 85 42 36 91 25 28 53 65 78 42 68 44 41 50 46 48 75 29 53 72 17 28 38 30 48 43 27 46 36 48 62 31 42 48 61 22 124 27 53 86 60 47 41 37 27 36 45 80 45 70 53 25 29 16 30 36 38 42 48 51 38 39 43 61 75 38 42 55 72 39 28 51 43 49 67 25 37 39 46 41 50 93 53 82 47 36 38 51 42 40 24 68 38 36 34 49 65 68 62 53 67 23 51 40 43 49 57 61 26 54 35 32 38 39 24 added all together?', you would have to add up all the numbers provided. Calculating this would involve simply adding the given values together. To get the answer, you can use a calculator or manually add each number, but it may take a bit of time due to the large number of values given.
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A sales representative from a local radio station is trying to convince the owner of a small fitness club to advertise on her station. The representative says that if the owner begins advertising on the station today, the club's total number of members will grow exponentially each month. She uses the given expression to model the number of club members, in hundreds, after advertising for t months. 1.8(1.02)^12t What does the value 1.8 represent?
Answer:
The value 1.8 represent the club's total number of members today or the present number of members
Step-by-step explanation:
Given an exponential function;
[tex]y=ab^{x}[/tex]
b is the base or the growth factor
a is the initial value, that is the value of y when x = 0
We have been given the exponential function;
[tex]y=1.8(1.02)^{12t}[/tex]
The value 1.8 simply represents the initial value of y. Plug in t = 0 in the equation;
[tex]y=1.8(1.02)^{12(0)}=1.8[/tex]
Therefore, the value 1.8 represent the club's total number of members today or the present number of members.
Part A
a national achievement test is administered annelida to third graders. The test has a mean score of 100 and a standard deviation of 15. if Jane z-score is 120, what was her score on the test?
Part B
the grades on a history midterm at Gardiner high School are normally distributed with a mean of 73 and standard deviation of 4.0. The z score for Ben is 0.50. find the Ben's score
Answer:
Step-by-step explanation:
z score= x - mean/standard deviation
1.20= x -100/15
18= x -100
118=x
z score= x - mean/standard deviation
0.5=x-73/4
2=x-73
75= x
The zero of F -1(x) in F(x) = x + 3 is
Answer:
-3
Step-by-step explanation:
We have
y = F(x) = x + 3
so
x = y - 3
so
F⁻¹(y) = y - 3
which we can write
F⁻¹(x) = x - 3
We solve
0 = F⁻¹(x) = x - 3
x = 3
Answer: 3