MAPS On a map, Wilmington Street, Beech Drive, and Ash Grove Lane appear to all be parallel. The on
ilmington to Ash Grove along Kendall is 820 feet and along Magnolia, 660 feet. If the distance between Beech and
ove along Magnolia is 280 feet, what is the distance between the two streets along Kendall?
Answers
The distance between the two streets along Kendall is 347.9 feet.
Solution:
The image of the problem is attached below.
Distance between Wilmington to Ash Grove along Kendall = 820 feet
Distance between Wilmington to Ash Grove along Magnolia = 660 feet
Distance between Beech and Ash Grove along Magnolia = 280 feet
Distance between Wilmington to Beech along Magnolia
= 660 feet – 280 feet
= 380 feet
Let us x be the distance between Wilmington to Beech along Kendall and
820 – x be the distance between Beech and Ash Grove along Kendall.
The given streets are parallel.
By proportionality theorem, parallel lines cut by a transversal are in proportion.
[tex]$\Rightarrow\frac{380}{280} =\frac{x}{820-x}[/tex]
Do cross multiplication.
[tex]$\Rightarrow{380}({820-x}) =280x[/tex]
[tex]$\Rightarrow 311600-380x =280x[/tex]
[tex]$\Rightarrow 311600 =280x+380x[/tex]
[tex]$\Rightarrow 311600 =660x[/tex]
[tex]$\Rightarrow x=472.1[/tex]
Distance between Beech and Ash Grove along Kendall
= 820 – x
= 820 – 472.1
= 347.9
Hence the distance between the two streets along Kendall is 347.9 feet.
Final answer:
By analyzing the given distances along two parallel paths and using proportional reasoning, it is determined that the distance between Beech Drive and Ash Grove Lane along Kendall is approximately 547.33 feet.
Explanation:
Since Wilmington Street, Beech Drive, and Ash Grove Lane are parallel, and given the distances along Kendall and Magnolia, we can deduce the relationships between these distances to find the desired measurement. Utilizing the ratio of distances along Magnolia, we can apply the same ratio to the distances along Kendall.
We know that the total distance along Magnolia (660 feet) minus the distance between Beech and Ash Grove (280 feet) gives the distance between Wilmington and Beech along Magnolia, which is 380 feet. Assuming the distance distribution is proportional along Kendall, the distance between Beech and Ash Grove along Kendall would be given by:
(280 feet / 660 feet) * 820 feet = (2/3) * 820 feet = 547.33 feet.
Therefore, the distance between Beech Drive and Ash Grove Lane along Kendall is approximately 547.33 feet.
Related Questions
Does -2 4/5 + 6 1/3= 2/5
Answers
Answer:
yes.
Step-by-step explanation:
To qualify for a store discount, Clay’s soccer team must spend at least $560 for new jerseys
Answers
Answer:
Step-by-step explanation: they must spend a minimum of $28 per jersey
The area of a square in square feet is represented by a^2 + 16a + 64
a- Find an expression for a side length of the square
b- Find the perimeter of the square when a=9
Answers
Answer:
a. a side length is (a+8)
b. a=9. (9+8)= 17
17×4= 68 is the perimeter
A female executive selecting her wardrobe purchased five blazers, three blouses, and five skirts in coordinating colors. How many ensembles consisting of a blazer, a blouse, and a skirt can she create from this collection?
Answers
(9-7i)–(4i +15)
What’s the answer
Answers
Answer:
-6 - 11i.
Step-by-step explanation:
(9-7i)–(4i +15)
= 9 - 7i - 4i - 15 Add like terms:
= -6 - 11i.
counting back from 5 what number follow 4
Answers
Answer:
5 4 3 2 1
Step-by-step explanation:
is this what ur asking
The answer is 3. Counting backwards (In this case) would be 5, 4, 3, 2, 1. After 4, when counting backwards, comes the Number 3. So, your answer is 3.
Plz answer!! ASAP!!
Answers
(1) ∠ABC = 65°, ∠DBE = 65°, ∠CBE = 115°, ∠ABD = 115°
(2) ∠ABC = 62°, ∠DBE = 62°, ∠CBE = 118°, ∠ABD = 118°
Solution:
(1) In the given image ABC and DBE are vertical angles.
Vertical angle theorem:
If two angles are vertical then they are congruent.
⇒ ∠ABC = ∠DBE
⇒ 3x° + 38° = 5x° + 20°
Arrange like terms one side.
⇒ 38° – 20° = 5x° – 3x°
⇒ 18° = 2x°
⇒ x° = 9°
∠ABC = 3(9°) + 38° = 65°
∠DBE = 5(9°) + 20° = 65°
Adjacent angles in a straight line = 180°
⇒ ∠ABC + ∠CBE = 180°
⇒ 65° + ∠CBE = 180°
⇒ ∠CBE = 115°
∠ABD and ∠CBE are vertical angles.
∠ABD = 115°
(2) In the given image ABC and DBE are vertical angles.
⇒ ∠ABC = ∠DBE
⇒ 4x° + 2° = 5x° – 13°
Arrange like terms one side.
⇒ 13° + 2° = 5x° – 4x°
⇒ 15° = x°
∠ABC = (4(15°) + 2°) = 62°
∠DBE = 5(15°) – 13° = 62°
Adjacent angles in a straight line = 180°
⇒ ∠ABC + ∠CBE = 180°
⇒ 62° + ∠CBE = 180°
⇒ ∠CBE = 118°
∠ABD and ∠CBE are vertical angles.
∠ABD = 118°
3. What value of y makes this true?
25 - y<15
A. 8
B. 9
C. 10
D. 11
Answers
To figure out which value of y makes this true, plug in each option:
y = 8
25 - y < 15 Plug in 8 for y
25 - 8 < 15
17 < 15 This is false because 17 is not less than 15
y = 9
25 - y < 15 Plug in 9 for y
25 - 9 < 15
16 < 15 This is false because 16 is not less than 15
y = 10
25 - y < 15 Plug in 10 for y
25 - 10 < 15
15 < 15 This is false because 15 can't be less than itself (15)
y = 11
25 - y < 15 Plug in 11 for y
25 - 11 < 15
14 < 15 This is true because 14 is less than 15
Your answer is D
Terrence and Lee were selling magazines for a charity. In the first week, Terrance sold 30% more than Lee. In the second week, Terrance sold 12 magazines, but Lee did not sell any. If Terrance sold 50% more than Lee by the end of the second week, how many magazines did Lee sell?
Choose any model to solve the problem. Show your work to justify your answer.
Answers
Lee sold 60 magazine
Step-by-step explanation:
Terrence and Lee were selling magazines for a charity
In the first week, Terrance sold 30% more than LeeIn the second week, Terrance sold 12 magazines, but Lee did not sell anyTerrance sold 50% more than Lee by the end of the second weekWe need to find how many magazines Lee sold
Assume that Lee sold x magazines
∵ Terrance sold 30% more than Lee in the first week
∵ Lee sold x magazines in the first week
- Find 30% of x and add it to x to find how many magazines
Terrance sold
∵ Terrance sold = 30% × x + x
∴ Terrance sold = [tex]\frac{30}{100}[/tex] × x + x = 0.3 x + x
∴ Terrance sold = 1.3 x magazines in the first week
∵ Terrance sold 12 magazines in the second week
- Add 1.3 x to 12 to find the number of magazines that Terrence
sold in the two weeks
∴ Terrence sold 1.3 x + 12 magazines in the two weeks
∵ Lee did not sell any in the next week
∴ Lee sold x magazines in the two weeks
∵ Terrance sold 50% more than Lee by the end of the 2nd week
- Equate 1.3 x + 12 by the sum of x and 50% of x
∴ 1.3 x + 12 = 50% × x + x
∵ 50% × x = [tex]\frac{50}{100}[/tex] × x = 0.5 x
∴ 1.3 x + 12 = 0.5 x + x
- Add the like terms in the right hand side
∴ 1.3 x + 12 = 1.5 x
- Subtract 1.3 x from both sides
∴ 12 = 0.2 x
- Divide both sides by 0.2
∴ 60 = x
Lee sold 60 magazine
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What is the answer to this inequality -45x+12<112?
Answers
The solution to the given inequality is [tex]x<-\frac{20}{9}[/tex].
Step-by-step explanation:
Given inequality is;
-45x+12<112
For solving the inequality, we will subtraction 12 from both sides in step 1;
[tex]-45x+12-12<112-12\\-45x<100[/tex]
Now, we will divide both sides by -45
[tex]\frac{-45x}{-45}<\frac{100}{-45}\\\\x<-\frac{100}{45}\\\\x<-\frac{20}{5}[/tex]
The solution to the given inequality is [tex]x<-\frac{20}{9}[/tex].
Keywords: inequality, division
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The slope of (3,6) and (5,2)
Answers
[tex]\text{Hey there!}[/tex]
[tex]\mathsf{The\ slope\ formula\ is: \dfrac{y_2-y_1}{x_2-x_1}}[/tex]
[tex]\mathsf{y_2=2}\\\mathsf{y_1=6}[/tex]
[tex]\mathsf{x_2=5}\\\mathsf{x_1=3}[/tex]
[tex]\mathsf{Equation: \dfrac{2-6}{5-3}}\\\\\bullet\mathsf{2-6=-4\leftarrow your\ \bf{y}\mathsf{\ value}}\\\\\bullet{\mathsf{5-3=2\leftarrow your\ \bf{x}\ \mathsf{value}}}\\\\\mathsf{New\ equation/answer:\ \dfrac{-4}{2}}\\\\\boxed{\bf{Answer:\mathsf{-2\ or\ \dfrac{-4}{2}}}}[/tex]
[tex]\text{Good luck on your assignment enjoy your day!}[/tex]
~[tex]\frak{LoveYourselfFirst:)}[/tex]
Which expression is equivalent to 1/3y
Answers
Answer:
1/6y + 1/6(y + 12) - 2
Answer:
C
Step-by-step explanation:
Edge 2020
A game designer must decide how to color five buildings that are in a row. Using only the colors yellow, green, red, and blue, each building must be painted with exactly one color. Any two neighboring buildings must be different colors, and the first, third, and fifth buildings must be different colors. How many ways are there to paint the five buildings?
Answers
Answer:
20
Step-by-step explanation:
Yellow, Green, Red, Green, Blue
Yellow, Red, Green, Red, Blue
Yellow, Blue, Red, Blue, Green
Yellow, Blue, Green, Blue, Red
5x4 = 20 because those are all the possible ways with yellow as the first building color, so there are 4 possible ways with yellow being in front, meaning all five of the colors have 4 possible ways of being in front. so 5x4=20
Answer:
84
Step-by-step explanation:
84 cause there will be 108 ways - 24 ways
If the function m not-equals 0 has an inverse function, which statement must be true?
Answers
Note: Your question is missing some details. After a little research, I am able to find the complete question which is as follows:
If the function f(x) = mx + b has an inverse function, which statement must be true?
a) m=/0
b) m = 0
c) b=/0
d ) b = 0
Answer:
The value of [tex]m[/tex] cannot be equal to 0. In other words,
[tex]m\:\ne \:0[/tex]
Step-by-step explanation:
Considering the function
[tex]f(x) = mx + b[/tex]
Lets find the inverse of this function.
Suppose
[tex]y=f\left(x\right)[/tex][tex]y=mx+b[/tex]Lets exchange the variables [tex]x[/tex] and [tex]y[/tex] such as
[tex]x=my+b[/tex]
Lets isolate the variable [tex]y[/tex]
[tex]my=x-b[/tex]
[tex]y=\frac{x-b}{m}[/tex]
Suppose
[tex]f\left(x\right)^{-1}=y[/tex]
As
[tex]y=\frac{x-b}{m}[/tex]
So, inverse function is
[tex]f\left(x\right)^{-1}=\frac{x-b}{m}[/tex]
As the denominator [tex]m[/tex] cannot be zero in the inverse function.
Thus, the value of [tex]m[/tex] cannot be equal to 0. In other words,
[tex]m\:\ne \:0[/tex]
Keywords: function, inverse function
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Answer:
a
Step-by-step explanation:
4/6 is less than or greater than 4/2
Answers
Answer:
No.
Step-by-step explanation:
4/6 as a decimal is 0.667 whereas 4/2 as a decimal is 2.
;D
The admission fee at a small fare is $1.50 for children and four dollars for adults. One certain day $5050 is collected. If 1000 adults attended the fair right and solve the Larry Quetion to find the number of children that attended
Answers
700 children attended the fair
Solution:
Let "a" be the number of children attended
Let "b" be the number of adults attended
Cost for each children = $ 1.50
Cost for each adult = $ 4
1000 adults attended the fair
b = 1000
One certain day $5050 is collected. Therefore, we frame a equation as:
number of children attended x Cost for each children + number of adults attended x Cost for each adult = 5050
[tex]a \times 1.50 + 1000 \times 4 = 5050\\\\1.5a + 4000 = 5050\\\\1.5a = 5050 - 4000\\\\1.5a = 1050\\\\Divide\ both\ sides\ by\ 1.5\\\\a = 700[/tex]
Thus 700 children attended the fair
1) In the diagram, l || m. If the measure of angle 3 is 120 find the measure of the following angles
a) angle 4
b) angle 6
c) angle 8
2)Describe the sequence of transformations from quadrilateral WXYZ to W” X” Y” Z”.
Answers
Answer:
i) angle 3 is 120°
ii) angle 3 + angle 4 = 180° as both angles make up a staright line
∴ angle 4 = 180° - angle 3 = 180° - 120° = 60°
iii) angle 6 = angle 3 = 120° as they are opposite interior angles
iv) angle 6 + angle 8 = 180° as both angles make up a straight line
∴ angle 8 = 180° - angle 6 = 180° - 120° = 60°
Step-by-step explanation:
i) angle 3 is 120°
ii) angle 3 + angle 4 = 180° as both angles make up a staright line
∴ angle 4 = 180° - angle 3 = 180° - 120° = 60°
iii) angle 6 = angle 3 = 120° as they are opposite interior angles
iv) angle 6 + angle 8 = 180° as both angles make up a straight line
∴ angle 8 = 180° - angle 6 = 180° - 120° = 60°
I can't get the answer!!!! >:(
Answers
Answer:
The scale factor of the smaller rectangle to the larger rectangle is 3/2
Step-by-step explanation:
we know that
If two figures are similar, then the ratio of its corresponding sides is proportional and this ratio is called the scale factor
In this problem
To find out the scale factor of the smaller rectangle to the larger rectangle. set up a proportion
[tex]\frac{9}{6}=\frac{3}{2}[/tex] ----> ratio of corresponding heights
or
[tex]\frac{12}{8}=\frac{3}{2}[/tex] ----> ratio of corresponding bases
therefore
The scale factor of the smaller rectangle to the larger rectangle is 3/2
Which matrix represents A-B.
Answers
Answer Option C
Step-by-step explanation:please see attachment for explanation
Answer:
C
Step-by-step explanation:
Each element in B is subtracted from the corresponding element in A, that is
A - B
= [tex]\left[\begin{array}{ccc}3-4&-7-(-1)\\6-0&1-8\\-8-(-5)&5-3\end{array}\right][/tex]
= [tex]\left[\begin{array}{ccc}-1&-6\\6&-7\\-3&2\end{array}\right][/tex] → C
What is the slope Intercept form of 8x-2y=-72
Answers
Answer:
y = 4x + 36
Step-by-step explanation:
To find the equation in slope-intercept form, rearrange to isolate "y".
Slope-intercept form is y = mx + b. The variables mean:
"x" and "y" - points that are on the line, or solutions.
"m" - the slope, how steep the line is
"b" - the y-intercept, when the line touches the y-axis
Isolate "y".
8x - 2y = -72
8x - 8x - 2y = -72 - 8x Subtract 8x from both sides.
-2y = -72 - 8x Left side : 8x - 8x = 0
[tex]\frac{-2}{-2}y = \frac{-72}{-2} - \frac{8}{-2}x[/tex] Divide both sides by -2
y = 36 - (-4)x Simplify the fractions
y = 36 + 4x Remember two negatives make a positive, add 4x.
y = 4x + 36 Put "4x" in front of 36. It looks like y = mx + b now.
"m" would be 4.
"b" would be 36.
Lydia decides to provide cheddar cheese for the competition. She buys 4.2 kilograms for 39.90. She estimates the cost of 1 kilogram of cheese to be $1. Is her estimate reasonable?
Answers
The rate of cheese is $9.5 per kilogram which does not match Lydia's estimation.
What is the rate?The rate is the ratio of the amount of something to the unit. For example - If the speed of the car is 20 km/h it means the car travels 20 km in one hour.
Lydia decides to provide cheddar cheese for the competition. She buys 4.2 kilograms for 39.90.
She estimates the cost of 1 kilogram of cheese to be $1.
Let's check the rate of cheese. Then we have
Rate = $39.90 / 4.2
Rate = $9.5 per kilogram
The rate of cheese is $9.5 per kilogram which does not match Lydia's estimation.
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15 times 18 + 12 divided by 3 +9
Answers
Answer:
23.5
Step-by-step explanation:
[tex]\text{Hey there!}[/tex]
[tex]\text{In order for you to solve for you solve for the equation, you have to do}\\\text{PEMDAS}[/tex]
[tex]\text{PEMDAS means}\downarrow\\\text{Parentheses}\\\text{Exponents}\\\text{Multiplication}\\\text{Division}\\\text{Addition}\\\text{Subtraction}[/tex]
[tex]\text{In this equation we have}\downarrow\\\bullet\text{Multiplication}\\\bullet\text{Division}\\\bullet\text{Addition}[/tex]
[tex]\bf{15\times18+\dfrac{12}{3} +9}\\\\\\\bf{15\times18=270}\\\\\\\bf{\dfrac{12}{3} = 4}\\\\\\\bf{270+4+9}\\\\\\\bf{270+4=270}\\\\\\\bf{274+9=answer}\\\\\\\boxed{\bf{Answer}:283}\checkmark[/tex]
[tex]\text{Good luck on your assignment and enjoy your day!}[/tex]
~[tex]\frak{LoveYourselfFirst:)}[/tex]
Factor the expression:
30 + 100c
Answers
This expression has a common factor of 10
Use angle relationships and the diagram at right to write and solve an equation for 4x-5 2x+9
Answers
The value of x in the diagram given is : 7
What are Alternate Angles ?
These angles are located on the inner side of the parallel lines and on opposite sides of the transversal. Alternate angles are equal.
To solve, equate both values;
4x - 5 = 2x + 9
4x - 2x = 9 + 5
2x = 14
x = 14 / 2
x = 7
The value of x is 7
3)
Which numerical expression equals − 1?
A) − 1(1− 1)
B) − (− 1)(− 1)
C) (− 1) + 1 − 1 (− 1)
D) − (− 1) − (− 1)(− 1)
Answers
Answer:
the correct answer is B
Answer: b
i just wrote it down on paper and used a calculator to reassure.
A particular bacterial colony doubles its population every 15 hours. A scientist running an experiment is starting with 100
bacteria cells. She expects the number of cells to be given by the formula, where t is the number of hours since the
experiment started.
C = 100 (2 ^t/15)
After how many hours would the scientist expect to have 300 bacteria cells?
Give your answer to the nearest hour.
A) 2 hours
B) 24 hours
C) 1,048,557 hours
D) 104,857,699 hours
Answers
Answer:
24 hours
24 hours is the solution to 300=10(2)^t/15
After 24 hours the scientist expect to have 300 bacteria cells.
Given :
the number of cells to be given by the formula, where t is the number of hours since the experiment started.
[tex]C=100(2)^{\frac{t}{15} }[/tex]
't' represents the time taken for the cells to grow.
we need to find out the time taken to have 300 bacteria cells.
So, we replace C with 300 and solve for t
[tex]C=100(2)^{\frac{t}{15} }\\300=100(2)^{\frac{t}{15} }\\\frac{100\cdot \:2^{\frac{t}{15}}}{100}=\frac{300}{100}\\2^{\frac{t}{15}}=3\\\frac{t}{15}\ln \left(2\right)=\ln \left(3\right)\\t=\frac{15\ln \left(3\right)}{\ln \left(2\right)}\\t=23.77443[/tex]
So, it takes 24 hours to have 300 bacteria cells.
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Danica is in the observation area of the sears tower in chicago overlooking lake michigan. She sights two sailboats going due east from the tower. The angles of depression to the two boats are 42 degrees and 29 degrees. If the observation deck is 1,353 feet high, how far apart are the boats?
Answers
The distance between the two sailboats is approximately 2,197 feet.
1. Find Distances to Boats:
- Use the tangent function for each angle of depression to find the distances from the observation deck to each sailboat. For boat 1 (42 degrees), use [tex]\(\tan(42^\circ) = \frac{\text{height}}{\text{distance}}\)[/tex], and for boat 2 (29 degrees), use [tex]\(\tan(29^\circ) = \frac{\text{height}}{\text{distance}}\)[/tex].
2. **Calculate Individual Distances:**
- For Boat 1: [tex]\( \text{Distance}_{\text{Boat 1}} = \frac{\text{height}}{\tan(42^\circ)} \)[/tex]
- For Boat 2: [tex]\( \text{Distance}_{\text{Boat 2}} = \frac{\text{height}}{\tan(29^\circ)} \)[/tex]
3. Determine Distance Between Boats:
- The distance between the two boats is [tex]\( \text{Distance}_{\text{Boat 1}} - \text{Distance}_{\text{Boat 2}} \)[/tex].
4. Final Answer:
- The final answer is the distance between the two sailboats, which is approximately 2,197 feet.
y=2x-5
write in y=mx+b form
Answers
The base of an isosceles triangle is 7 units.
What could the length of the other sides be?
Answers
In an isosceles triangle with a base of 7 units, the two other sides have to be greater than 3.5 units but less than 7 units due to the triangle inequality theorem, which means each side must always be shorter than the sum of the other two sides.
Explanation:An isosceles triangle is a triangle with two sides of equal length. If the base of the triangle is 7 units, the lengths of the other sides could be any value greater than 3.5 units but less than 7 units. This principle is rooted in the triangle inequality theorem which states that any side of a triangle always needs to be shorter than the sum of the other two sides.
So in this case, since the base is 7 units, the other two equal sides (let's call them 'a' and 'b') could be, for example, 5 units each, but don't forget they must fulfill two conditions: firstly, 'a' + 'b' > 7 (which is true if both 'a' and 'b' are more than 3.5 units), and secondly, 'a' + 7 > 'b' as well as 'b' + 7 > 'a' (which are true as long as 'a' and 'b' are less than 7 units). Consequently, both 'a' and 'b' could be a range of lengths, but they must be greater than 3.5 units and less than 7 units in order to ensure that the triangle inequality theorem is respected.
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36 cups equal how many ounces
Answers
Multiply 36X8.
36X8=288
288 is your answer.
Answer:
288
Step-by-step explanation:
You multiply the number of cups by 8 to get how many ounces the cup(s) are.
36 times 8= 288